SINGLE-MOLECULE BIOPHYSICS OF

KINESIN FAMILY MOTOR

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF PHYSICS

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Johan Oscar Lennart Andreasson

August 2013

© 2013 by Johan Oscar Lennart Andreasson. All Rights Reserved. Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/fy688zk4161

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Steven Block, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Sebastian Doniach

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Alexander Dunn

Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost for Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii

iv Abstract

Kinesin family proteins are nanoscale motors involved in many essential biological processes, such as intracellular transport and . The biological function of most kinesin motors is to use the energy from ATP hydrolysis to move cargo through a crowded cellular environment, quickly taking 8-nm steps along cytoskeletal . By maintaining its two motor domains (heads) out of phase, kinesin can complete hundreds of steps per encounter with the , and can do so against pN-scale loads. The physiological role of kinesin is directly related to its movement and in this dissertation I present several single-molecule studies where the force- dependent of individual kinesin motors was studied using optical trapping techniques. In , the kinesin superfamily includes over forty genes encoding different kinesin proteins, classified into 15 families, and motors from several families were studied in this work.

Optical traps use lasers to detect the position of biological molecules, at nm- scale resolution, and to directly manipulate them by applying pN-scale forces. In this dissertation, I present two novel optical traps. The first uses highly linear electro-optic deflection of the laser light to create an instrument with fast feedback that is optimized for work with kinesin motors. The second instrument, an “Optical Torque Wrench”, is a trap that can apply both forces and torques on birefringent particles. By controlling the light polarization in the sample plane, the rotation of nanofabricated quartz cylinders can be controlled in real time while the applied torque is measured directly. The functionalized particles can be used to twist DNA or other biological molecules.

The kinesin motor domains are coordinated during stepping and the inter-head communication is believed to be conferred by the neck linker, a 14-amino acid structural element connecting the head to the common coiled-coil stalk. By extending this segment, we could examine its role in gating the mechanochemical cycle. A six- amino acid insert in the neck linker of a cysteine-light kinesin construct led to unexpected ATP-dependent backstepping under load. These observations could be explained by a branched pathway where both ATP unbinding and hydrolysis were

v gated by the direction of the neck linker. Lengthening the neck linker also led to futile hydrolysis. Further experiments on the effects of neck linker length were done with a series of Kinesin-1 mutants, with one to six extra residues in the neck linker. The rate of force-dependent rear head release and the internal strain developed during stepping was determined from force-dependent velocities and we also found that the mechanism of detachment from the microtubule depends on the direction of load.

The heterotrimeric Kinesin-2 motors are unique in that they are the only kinesin family motors that consist of two different catalytic domains. Here, the mammalian Kinesin-2, KIF3A/B, was studied in detail by performing optical trapping experiments with both the wild-type dimer and with homodimers (KIF3A/A and KIF3B/B). A pathway that incorporates the individual catalytic cycles for KIF3A and KIF3B could explain all force- and ATP-dependent kinetics and surprisingly we found that the run lengths for KIF3A/B were significantly shorter than for Kinesin-1. Furthermore, motors with the weakly force-dependent KIF3A head “slipped” and exhibited short run lengths that were rescued under no load, indicating that KIF3A/B combines a Kinesin-1-like motor domain (KIF3B) with a unique and “weak” one (KIF3A).

Finally, I present motility experiments where force-dependent kinetics were explored for several other kinesin family motors. KIF17 (Kinesin-2) and CENP-E (Kinesin-7) are robust, processive motors whereas KIF4A, a Kinesin-4 motor, is fast but unable to sustain significant loads. These results, together with those for Kinesin- 1, KIF3A/B (Kinesin-2), and other motors, show that forces are needed fully reveal the motor characteristics and differences between various kinesin proteins. They also illustrate the remarkable diversity within the kinesin superfamily.

vi Acknowledgements

There are many people I would like to thank for making my graduate career a very rewarding experience. First of all, I would like to thank Steve, my advisor, who has been an inspiring mentor throughout my years in the lab. I knew very little about kinesin or optical traps when I first attended a seminar by Steve, but his impressive work and excitement for science inspired me to pursue a career in biophysics. Steve is not only extremely bright but also has a great sense of humor. And I attribute the Block lab’s positive atmosphere to his straightforward and witty personality, as well as his aspiration to give people the freedom to pursue their own ideas. He instills in his students a rigorous approach to science and not to mention a very careful attention to presentation skills. By attracting many talented scientists. he has built an exceptional lab that allows people to grow in a friendly and collaborative environment.

I have been fortunate to work daily with several of these scientists who have also become good friends over the years. It was the original Team Kinesin who helped me get started in the lab. I worked on my first project with Megan who taught me a lot about kinesin and set me on the path for my future work in this area. Together with her, Nick, Adrian and Braulio, I also had my first hands-on experience in building traps, and the knowledge they passed on to me was put to good use as Braulio and I continued the building. Braulio was not only a master of optics, but also of electronics, cheap effective solutions, and enjoying life. As the original team Kinesin moved on to new challenges, Bason took over as the senior kinesin team leader, who I was fortunate to not only have the opportunity to work with but also to become close friends with. And in the most recent years, I have enjoyed continuing on the kinesin legacy in the Block lab together with Kevin.

I would like to give a special acknowledgement to the the undergraduates and high school students whom I’ve had the privilege of mentoring. Bojan, who worked with me since his first year of college, has never failed to impress me. Over the years, he’s become a good friend, and I look forward to working with him further as we both continue our careers at Stanford. Benamy was a very bright undergraduate who I

vii enjoyed working with for two summers given his positive attitude and great sense of humor. Alice was the first high school student to volunteer for me in the lab, and her dedicated work set the path for bringing in addititional students. Taddy volunteered twice and even brought in his friend Ronak for the second summer, and both brought with them a lot of excitement and energy to the lab. Finally, I’d like to extend my thanks to all the rotation students who came through the lab at least partly under my guidance: Sonny, Andrew, Koning, Joel, Jacob and Quintin.

In the Block lab, you not only interact with your direct collaborators but also with all of the other lab members as well who have really made the lab an enjoyable place to come to work everyday. After rotating in a position where I worked alone in a concrete office, the welcoming atmosphere of the Block lab was such a stark contrast that I immediately felt at home. Kristina and Will were the senior RNAP team members at the time who provided a lot of inspiration. I also have enjoyed the company of Matt G., Matt L., Peter, and Cuauh, whether in the city, at the gym, or on bikes in the mountains. I’ve shared my longest time in lab with Kirsten, Jing, and Christian, who joined around the time as I did, and with Christian I also enjoyed all the travails and good memories of the physics program. After my fellow European, Volker, left the lab, the remaining Block lab now consists of the following team: Dan, Furqan, Van, Arthur, Andrew, Irena and Anirban. I have great expectations for the future work that will come out of the basement of the Herrin Lab building and will look back fondly on the Block lab, including all the good times, hard work, group meetings, conferences, parties, procrastination, and humorous discussions.

Several other colleagues at Stanford and at other institutions have also helped me greatly during my graduate career. My thesis committee, Prof. Dunn, Prof. Doniach, Prof. Stearns, and Prof. Bryant have all been very helpful in providing good suggestions for my research. I also enjoyed collaborating with Prof. William Hancock at Penn State and his student Shankar on Kinesin-1 and -2, as well as Prof. Steven Rosenfeld, now at the Cleveland Clinic, and Will Parks on Kinesin-1 and other motors. In addition, it was a pleasure working with Prof. Arthur La Porta to complete the Torque Wrench project he started.

viii I would also like to thank my family and all the great friends I have made while studying at Stanford. My mother and father have always been very supportive, and I could not wish for more encouraging, devoted, and loving parents. I am also very thankful to my two sisters for all the joy and support they’ve shared and provided throughout the years. I’d also like to express my gratitude to my entire extended family in Sweden who are always inquiring about what I’ve been up to in the US and whom I always look forward to visiting whenever I go home. In Julie’s family, I have found a second embracing family, and I look forward to knowing them even better. Finally, my love and appreciation goes to Julie, my great love and wonderful girlfriend since many years. I am blessed to have met her at Stanford, and for her unwavering support and love I am always grateful.

ix Table of Contents

Abstract ...... v Acknowledgements ...... vii Table of Contents ...... x List of Tables ...... xiv List of Illustrations ...... xiv Chapter 1: Introduction to kinesin family proteins and optical trapping ...... 1 1.1 Kinesin family proteins ...... 1 1.1.1 Transport ...... 1 1.1.2 Mitotic and other kinesins ...... 4 1.2 Kinesin structure ...... 6 1.3 Kinesin motility ...... 9 1.4 Optical trapping ...... 11 1.5 Chapter overview ...... 15 Chapter 2: Precision steering of an optical trap by electro-optic deflection ...... 18 2.1 Abstract ...... 18 2.2 Results and discussion ...... 18 Chapter 3: An optical apparatus for rotation and trapping ...... 25 3.1 Abstract ...... 25 3.2 Introduction ...... 25 3.3 Optical trapping and rotation of micro-particles ...... 27 3.3.1 The principles of optical manipulation ...... 27 3.3.2 Sources of particle anisotropy ...... 30 3.4 The instrument ...... 34 3.4.1 Overview ...... 34 3.4.2 The microscope ...... 35 3.4.3 Signal detection and processing ...... 39 3.5 Fabrication of anisotropic particles ...... 40 3.5.1 Particles with shape asymmetry ...... 40 3.5.2 Particles with optical asymmetry ...... 42

x 3.6 Instrument calibration ...... 46 3.6.1 Standard optical tweezers calibration methods ...... 46 3.6.2 Force calibration ...... 48 3.6.3 Torque calibration ...... 50 3.6.4 Implementation of an optical torque clamp ...... 51 3.7 Simultaneous application of force and torque using optical tweezers ...... 54 3.7.1 Twisting single DNA molecules under tension ...... 54 3.8 Conclusions ...... 56 Chapter 4: A universal pathway for kinesin stepping ...... 57 4.1 Abstract ...... 57 4.2 Introduction ...... 57 4.3 Results ...... 59 4.3.1 Kin6AA moves backwards processively ...... 59 4.3.2 The KIN6AA stall force is ATP-dependent ...... 61 4.3.1 The randomness constrains possible models ...... 61 4.3.1 Mechanochemistry: The forward stepping pathway ...... 61 4.3.2 Mechanochemistry: The backward stepping pathway...... 63 4.3.1 Inclusion of futile hydrolysis ...... 64 4.3.2 Ensemble experiments ...... 68 4.3.3 Two-heads-bound state studied using TMR ...... 70 4.3.4 Binding of a fluorescent ATP analog suggests Kin6AA is gated ...... 74 4.3.5 Additional tests of the model ...... 74 4.4 Discussion ...... 75 4.4.1 Neck-linker orientation also gates kinesin ...... 75 4.4.2 Kinesin is gated by strain and by steric effects ...... 80 4.5 Methods ...... 81 4.5.1 Single-molecule experiments ...... 81 4.5.2 Ensemble fluorescence experiments ...... 85 Chapter 5: Effects of neck linker length on Kinesin-1 force generation and motility . 90 5.1 Introduction ...... 90

xi 5.2 Results ...... 94 5.2.1 Assisting loads can rescue reduced velocities for constructs with extended neck linkers ...... 94 5.2.1 A three-state model explains force dependencies ...... 95 5.2.2 Extending the neck linker stabilizes the two-heads-bound state ...... 99 5.2.3 Run lengths exhibit asymmetry with respect to the direction of load .. 100 5.2.4 Differences between cysteine-light and wild-type Kinesin-1 ...... 102 5.2.5 Cysteine substitutions reduces Kinesin-1 run lengths ...... 104 5.3 Discussion ...... 104 5.3.1 A high internal strain contributes to Kinesin-1 velocity ...... 105 5.3.2 Implications for dominant gating mechanisms ...... 106 5.3.3 Rear head rebinding is effectively gated in Kinesin-1 ...... 107 5.3.4 The Kinesin-1 neck linker is optimized for long runs under load ...... 108 5.3.5 Conclusions ...... 111 5.4 Methods ...... 111 Chapter 6: Mechanochemical properties of the heterotrimeric mammalian Kinesin-2 motor, KIF3A/B, studied by optical trapping ...... 114 6.1 Abstract ...... 114 6.2 Introduction ...... 114 6.2.1 Kinesin-2 in bidirectional transport ...... 116 6.3 Results ...... 120 6.3.1 Load-dependent KIF3A/B stepping studied using optical trapping ..... 120 6.3.2 Model for processive stepping of KIF3A/B under load ...... 123 6.3.3 Backstepping ...... 125 6.3.4 Kinesin-2 processivity is strongly force-dependent ...... 126 6.3.5 Force-dependent unbinding dynamics ...... 129 6.3.6 Testing the role of the neck linker domain in load-dependent processivity ...... 133 6.4 Discussion ...... 135 6.5 Experimental procedures ...... 139

xii 6.5.1 Kinesin constructs ...... 139 6.5.2 Optical trapping assay ...... 140 6.5.3 Instrumentation ...... 140 6.5.4 Data analysis ...... 141 6.5.5 Expressions for fitting ...... 145 Chapter 7: Exploratory motility experiments with unconventional kinesin family motors ...... 149 7.1 Introduction ...... 149 7.2 Methods ...... 150 7.2.1 Optical trapping assay ...... 150 7.2.2 Instrumentation and analysis ...... 151 7.2.3 Preparation of kinesin constructs ...... 152 7.3 Results ...... 154 7.3.1 KIF17 is a fast and strong kinesin motor ...... 154 7.3.2 KIF4A does not move substantially against load ...... 156 7.3.3 CENP-E is a motor similar to Kinesin-1 ...... 159 7.4 Discussion ...... 162 Bibliography ...... 165

xiii List of Tables

Table 4.1 Kinetic parameters for Kin6AA, measured and fit...... 69 Table 5.1 Kinetic parameters from global fit to data from neck linker mutants...... 98 Table 6.1 Kinetic parameters for kinesin-1 and kinesin-2 mutants...... 126 Table 6.2 Run length parameters for kinesin-2 mutants...... 134

List of Illustrations

Figure 1.1 Transport kinesins ...... 2 Figure 1.2 The structure and phylogeny of major mouse kinesins...... 3 Figure 1.3 The structure of dimeric Kinesin-1...... 7 Figure 1.4 The kinesin catalytic cycle...... 11 Figure 1.5 The kinesin motility assay...... 14 Figure 2.1 Schematic layout for the EOD-based optical trap...... 20 Figure 2.2 Transmittance as a function of trap position for orthogonal deflectors. .... 22 Figure 2.3 Linearity of EOD and AOD response ...... 23 Figure 2.4 Experimental kinesin trace...... 24 Figure 3.1 Principles of optical manipulation and signal detection...... 29 Figure 3.2 Particle anisotropy for optical trapping and rotation...... 33 Figure 3.3 Optical schematic of the optical torque wrench...... 36 Figure 3.4 Photograph of the OTW instrument, with components as indicated...... 38 Figure 3.5 Optically anisotropic particles based on form birefringence...... 41 Figure 3.6 Fabrication of birefringent quartz cylinders...... 46 Figure 3.7 Calibration of the optical torque wrench using a quartz cylinder...... 49 Figure 3.8 Realization of a continuous torque clamp...... 53 Figure 3.9 Supercoiling of a single dsDNA molecule...... 55 Figure 4.1 Single-molecule records and backstepping velocity for Kin6AA...... 60 Figure 4.2 ATP- and load-dependent bi-directionality of Kin6AA...... 62 Figure 4.3 Model for stepping by kinesin dimers...... 65 Figure 4.4 Lack of memory for successive steps...... 66

xiv Figure 4.5 The ATPase rate per dimer for KinWT and Kin6AA...... 67 Figure 4.6 2′dmD release from KinWT and Kin6AA in the presence of MTs...... 70 Figure 4.7 Fluorescence data for Kin6AA and KinWT...... 71 Figure 4.8 Binding of 2′dmT to Kin6AA...... 73 Figure 4.9 An independent test of the five-state model...... 75 Figure 4.10 Average backward velocities under load...... 79 Figure 4.11 Processivities of KinWT, Kin6AA, and Kin6P...... 80 Figure 5.1 Overview of gating in kinesin motility...... 91 Figure 5.2 Crystal structure of dimeric D. melanogaster Kinesin-1...... 92 Figure 5.3 Velocities as a function of force...... 95 Figure 5.4 Three state model for kinesin force dependence ...... 96 Figure 5.5 ADP exchange rate as a function of neck linker insert length...... 100 Figure 5.6 Run lengths under force for Kinesin-1 constructs...... 101 Figure 5.7 Force-velocity curves for human and Drosophila Kinesin-1 constructs.. 103 Figure 5.8 Run lengths under force for wild-type and cysteine-light Kinesin-1...... 104 Figure 6.1 Processive motion of KIF3A/B...... 120 Figure 6.2 KIF3A/B, KIF3A/A and KIF3B/B velocities and randomness...... 122 Figure 6.3 KIF3A/A data under low ATP concentrations or high force...... 123 Figure 6.4 Model for KIF3A/B stepping...... 124 Figure 6.5 Kinesin run lengths...... 128 Figure 6.6 Examples of 3A-KHC and 3B-KHC stepping...... 129 Figure 6.7 Unbinding force measurements...... 131 Figure 6.8 Rate of dissociation during processive stepping...... 132 Figure 6.9 Run lengths and velocities for chimeric kinesin-2 mutants...... 134

Figure 6.10 Velocities and run lengths for Kinesin-1DAL ...... 135 Figure 7.1 KIF17 velocity as a function of force...... 156 Figure 7.2 KIF4A velocity as a function of ATP concentration...... 159 Figure 7.3 CENP-E velocity and run length as a function of force...... 162 Figure 7.4 Velocity as a function of force for kinesin family motors...... 164

xv

xvi Chapter 1: Introduction to kinesin family proteins and optical trapping

1.1 Kinesin family proteins

Proteins in the kinesin superfamily are essential to eukaryotic life and are involved in many cellular processes, including intracellular transport and the organization of the during cell division. The human genome encodes at least 44 kinesin proteins [1] and other organisms have an even higher number, such as with at least 60 genes [2]. Kinesins from all organisms are classified into 15 families that constitute the kinesin superfamily [3]. Common to all kinesin proteins is a catalytic domain (head) that binds microtubules (MTs) and ATP. In the cell, kinesin proteins are generally dimers with two heads joined through a coiled-coil stalk (the tail) that can bind cargo or accessory factors at the other end, as illustrated in Figure 1.1 below [4]. Most kinesins are motors that use energy from ATP hydrolysis to move along MTs, by alternating the relative positions of the heads in a hand-over-hand fashion, but some kinesins also function as MT depolymerizers, crosslinkers, or signaling factors.

The large kinesin family tree contains proteins with remarkable diversity in kinesin structure and function. Figure 1.2, reprinted from a review by Hirokawa et al. [3], shows both the phylogeny and the global structure of the mouse kinesin family members. Although some of these kinesin proteins have been well-studied, much remains to be known about the roles and functions of many others. Below is a short overview of the kinesin subfamilies and their members, illustrating the various roles they assume in the cell. The subsequent sections discuss the structure of the proteins and the motility of kinesin motors.

1.1.1 Transport kinesins The first three kinesin families (Kinesin-1 to -3) are mainly implicated in intracellular transport, moving cargo such as vesicles, mitochondria and mRNA from the center of the cell to its periphery [3]. Kinesin-1 (conventional kinesin) is the founding kinesin superfamily member and the most abundant. It was discovered in Squid 1985 [5] and

1 humans have three isoforms, Kinesin Family Member (KIF) 5A, 5B and 5C. These proteins are efficient transport motors, taking hundreds of steps along the MT with a velocity of about a micron per second. Kinesin-1 is enriched in neuronal tissue and has been linked to several neuronal diseases, including Alzheimer’s [6], Huntington’s [7], and hereditary spastic paraplegia [6], some of which have a genetic origin. The kinesin transport can also be hijacked by external pathogens, such as viruses [8] and Salmonella [9].

Figure 1.1 Transport kinesins Artistic renditions of motors from the three cargo transporter kinesin subfamilies (adapted from ref. [4]). The purple motor domains are joined to the grey stalk through the neck linkers. Purple globular domains and green light chains at the end of the tail mediate cargo binding.

Reprinted from Cell, 112:4, Vale, R.D., The Toolbox for Intracellular Transport, p. 470, Copyright (2003), with permission from Elsevier. http://www.sciencedirect.com/science/journal/00928674.

2

Figure 1.2 The structure and phylogeny of major mouse kinesins. a) A phylogenetic tree of all 45 kinesin superfamily genes in the mouse genome. b) The domain structure of kinesin proteins. PH, pleckstrin homolog; CAP-Gly, a 42-residue Gly-rich domain; PH, Phox homology.

Reprinted by permission from Macmillan Publishers Ltd: Nature Reviews. Molecular Cell Biology, 10, (Hirokawa, N., Noda, Y., Tanaka, Y. & Niwa, S., Kinesin superfamily motor proteins and intracellular transport), copyright (2009) [3].

The Kinesin-2 family members are the canonical motors for intraflagellar transport (IFT) [10]. In humans the product from the gene KIF3A binds to that from either KIF3B or KIF3C, as well as the light chain kinesin-associated 3 (KAP3), to form the heterotrimeric motors KIF3A/B and KIF3A/C. Whereas the heterotrimeric

3 Kinesin-2 motors are confined to the flagella in many lower , KIF3A/B is also present in the [3]. Its functions include neuronal transport and cell division [11, 12]. The last Kinesin-2 member in human is KIF17. This motor is a homodimeric motor, like Kinesin-1. The Kinesin-2 members have been linked to several diseases. As they are crucial for ciliogenesis, mutations in these proteins lead to ciliopathies which in turn lead to developmental changes in left-right asymmetry or polycystic kidney disease [11, 13]. Both KIF3A and KIF3B have also been implicated in cancer [14, 15].

Kinesin-3 is the third kinesin family of intracellular transport kinesin motors, comprising eight members in human. KIF1A, 1B and 1C are involved in . The motors are predominantly monomeric and can undergo reversible dimerization in what is believed to be a regulatory mechanism for enabling long-range transport [4]. KIF13A and 13B are also axonal transport motors and the last kinesin-3 members, KIF16A and 16B, are conventional transport motors, but these have all been much less studied.

1.1.2 Mitotic and other kinesins Several families of kinesin motors are involved in cell division, contributing to all major steps in from spindle formation to congression, chromosome segregation and cytokinesis. Many of the mitotic kinesin have been implicated in cancer and several inhibitors against these motors have entered clinical trials. Several oncology drugs that act on microtubules, such as Taxol, are commonly used in the clinic suggesting that mitosis is an attractive target process. Although kinesin inhibitors have yet to show great efficacy in human patients, the significant research in the area will hopefully lead to future treatments [16, 17].

The kinesin-4 motors are referred to as chromokinesins as they attach to in addition to microtubules [18]. They are essential proteins during cell division [19] where they function in chromosome condensation and segregation [20]. The motors are dimeric with long tails [21] and the members include KIF4A, 4B, 17, 21A, 21B and 27.

4 Kinesin-5, also known as KIF11 or Eg5, has a unique tetrameric structure [22] and plays a crucial role in mitotic spindle pole separation and spindle polarity [23]. Pairs of motor domains at each end of a central stalk bind MTs during mitosis, thereby stabilizing the mitotic spindle, and the processive motor activity contributes to pushing the two spindle poles in opposite directions [23].

The three proteins in the Kinesin-6 subfamily, KIF20A, 20B and 23, are involved in central spindle assembly [24] and the relocation of factors to the spindle [25, 26]. Theyalso play important roles during cytokinesis [27-31]. KIF23 and 20A are known as mitotic kinesin-like protein 1 and 2 (MKLP1 and MKLP2),

Centromere-associated protein E (CENP-E) [32] is the sole Kinesin-7 member. Also called KIF10 in , it associates with during chromosome congression [33] as it moves along MTs, and it is essential for metaphase chromosome alignment [34, 35].

The Kinesin-8 proteins include KIF18A, 18B, 19A and 19B. The motors do not produce a large force but are the furthest moving kinesins, slowly reaching the end of MTs during mitosis where they act as depolymerizers [36]. The number of kinesins landing on the MT is dependent on MT length and hence the motors act as regulators of spindle size [37, 38].

Kinesin-10 (KID or KIF22 in human) is a plus-end directed motor [39] that binds both MTs and DNA and contributes to chromosome movement and alignment at the metaphase plate [40, 41]. It has been suggested that KIF22-mediated chromosome compaction prevents formation of multinucleated cells [42].

Like Kinesin-5, KIF15 in the Kinesin-12 subfamily is involved in stabilization and maintenance of spindle polarity [43-45]. It also functions in regulation of MT patterns in neurons [46]. The other Kinesin-12 member, KIF12, is highly expressed in the kidney and has been linked to cystic kidney diseases, but its function is poorly understood [47]

Not only are kinesin motors involved in transport or cell division. A little studied sub-family, is Kinesin-9 which is limited to flagellated species [48]. The

5 Kinesin-9 motors have a role in cilia distinct from intraflagellar transport [49] and KIF9 is expressed in neurons.[50]. The Kinesin-11 motors KIF26A and 26B also stand out from other kinesin proteins. KIF26A lacks full ATPase activity and instead function as non-motile regulators that bind to MTs [51].

All kinesins described above have N-terminal motor domains, but the remaining families, Kinesin-13 and 14, do not share this structure. Most Kinesin-13 members, KIF2A, 2B and 2C, have the catalytic domain in the middle of their amino acid sequence and are therefore called M-type kinesins [1]. These proteins are non- processive, unlike most N-terminal kinesins, and use diffusion to reach the end of the MT where they function as MT depolymerizers [52], thereby regulating spindle microtubule length during cell division [53]. KIF2C is also known as MCAK (mitotic centromere-associated kinesin) [54]. Another member of the Kinesin-13 family is KIF24, which is a centriolar kinesin [55].

The last kinesin subfamilies are Kinesin-14a and Kinesin-14b. Also known as C-type kinesins, KIFC1, C2, C3 and KIF25 have a C-terminal motor domain [1, 56]. Unlike other kinesins they produce motion toward the MT minus end and are involved both in transport and spindle organization [3, 57]. These motors are non-processive and produce directed motion through single directionally biased conformational changes upon each encounter with the MT [58]. NCD is a common name for Kinesin- 14 in Drosophila [2].

1.2 Kinesin structure

The catalytic motor domain (head) of conventional kinesin (Kinesin-1) consists of 326 amino acids (in rat), arranged into a central eight-stranded beta sheet surrounded by three alpha helices on either side. Opposite of the MT binding surface is the nucleotide active site which share homologies with G proteins and , including the P-loop, switch I, and switch II nucleotide binding motifs [59]. Nucleotide binding and hydrolysis leads to conformational changes in the switch regions that are conferred to other domains, thereby modulating the MT affinity. The crystal structure has been solved for many kinesin motor domains in the absence of MTs [60], as shown in

6 Figure 1.3, and cryo-EM reconstructions have provided insights into the conformational states during MT binding and ATP hydrolysis [61]. Models have been proposed where the catalytic head rotates in a see-saw mechanism around the MT binding domain upon ATP binding [62]. This in turn allows a ~14-amino acid segment termed the neck linker to dock as a beta sheet against the motor domain, providing the displacement and directional bias needed for the other head to reach the next binding site.

Figure 1.3 The structure of dimeric Kinesin-1. The crystal structure for rat kinesin-1 is shown in two different views with blue β-strands, red α-helices. Highlighted features are ADP (orange), nucleotide-binding regions (purple) and the microtubule- binding region (green).

Reprinted from Cell, 91:7, Kozielski, F. et al., The crystal structure of dimeric kinesin and implications for microtubule-dependent motility, 985-994., Copyright (1997), with permission from Elsevier. [60]

7 The neck linker is a key structural element that is studied in detail in subsequent chapters. It joins one kinesin head to the neck region, where it dimerizes with its partner head. The neck linker sequence is highly conserved between kinesin families and organisms [63]. Changing the sequence can lead to diminished velocities and run lengths and the length seems finely tuned, as shortening the segment abolishes processive motion in Kinesin-1 [64]. The immobilized conformation of the neck linker upon MT and ATP binding was originally described in what is commonly referred to as the neck linker docking model, introduced by Rice et al. 1999 [65]. The model stipulates that the directionality of kinesin motion along MTs is governed by the neck linker. When it is docked in the head bound to the MT but not in the free partner head, the latter can access the next binding site along the MT.

The neck region is a helix segment that forms a coiled-coil in the kinesin dimer. This relatively short segment (34 amino acids in the rat crystal structure) is sufficient for dimerization of a minimal processive motor. The kinesin neck not only links the two heads but can also interact with the MT, specifically the C- termini (E-hooks) [66, 67].

The neck domain is followed by the rest of the stalk that consists of several coiled-coil regions joined by flexible segments, termed hinges. The stalk spans most of the remaining protein which in the case of Kinesin-1 measures about 70 nm from the globular heads to the end of the tail [68]. In contrast to the motor domains, the structure and length of the stalk varies significantly between different kinesin sub- families [3, 68]. For heterotrimeric Kinesin-2, the stalk regions are responsible for combining two different polypeptides and unlike Kinesin-1, the entire stalk is necessary for dimerization. In Kinesin-3 motors, the stalk is not even dimerized at all times [4].

The kinesin polypeptide chains are often terminated by a globular tail domain that may bind cargo or accessory factors. In addition, cargo binding can be mediated by kinesin light chains (KLCs), accessory factors that bind to kinesin near the C- terminal domain of the tail. In Kinesin-1, a pair of light chains bind to the coiled-coil

8 stalk whereas in heterotrimeric Kinesin-2 the KAP3 polypeptide binds to the globular end domain [4].

In addition to cargo binding to the end of the tail, the kinesin activity is also regulated through auto-inhibitory mechanisms whereby the kinesin fold over at a hinge region [69, 70]. In Kinesin-1, a segment of the tail binds the catalytic domains to prevent MT binding, as demonstrated in crystallographic detail [71], and similar mechanisms are present in Kinesin-2 [72, 73].

1.3 Kinesin motility

Most kinesin proteins transport cargo or function as motors during cell division. The function of these motors in the cell is intrinsically linked to their movement along MTs. The kinesin dimers move along the MT in a hand-over-hand fashion, whereby the trailing head becomes the leading head after completing a 16.4-nm displacement while the other head is attached to the MT. The center-of-mass position of the kinesin motor increases by 8.2 nm, the kinesin step size. Microtubules are tubular cytoskeleton polymers usually containing 13 protofilaments that consist of alternating α- and β- tubulin subunits. Conventional kinesin moves unidirectionally along a single of these protofilaments [74] and the step size equals the length of an α/β pair of tubulin subunits. Other kinesin family members, as well as mutants of Kinesin-1, display a larger variety in stepping patterns, including sidestepping, backstepping and slipping [75]. Some kinesins, notably single-headed Kinesin-3 and M-type kinesins, also exhibit diffusional sliding modes where a weak contact is maintained between the kinesin and the microtubule.

Kinesin motility is driven by ATP hydrolysis. Conventional kinesin hydrolyses one ATP molecule for each step and the hydrolysis cycle is tightly coordinated to provide a highly efficient motor. The energy of an 8-nm step taken near the maximum force generated by kinesin, about 6 pN, is 6 pN x 8 nm = 48 pN nm, or 12 kT. This amounts to over half of the energy in an ATP molecule (~20 kT) and the kinesin efficiency is markedly higher than that of a combustion engine.

9 The binding and hydrolysis of ATP in the kinesin head controls the binding affinity for microtubule. A kinesin head with ADP bound has low affinity for the MT, whereas the motor domain binds tightly to the MT in the presence of ATP or in the absence of nucleotides. The motor can execute many turnovers per encounter with the MT by ensuring that the catalytic cycles of the two motor domains are maintained out of phase, such that at least one head is firmly attached to the MT at all times. In practice this means that the free head, with ADP bound, completes its step while the other is bound to the MT with ATP or no nucleotide in its binding pocket. The binding to the next MT binding site by the free head is completed before ATP hydrolysis and subsequent release of the bound head, which in turn becomes the free head as a new cycle resumes. The canonical cycle for processive kinesin motion that includes the major steps in the ATP hydrolysis cycle and the main mechanical transitions is shown in Figure 1.4. Kinesin does not execute this general cycle perfectly and the probability of out-of-sync hydrolysis and other off-pathway events determines the likelihood of detachment from the MT and the resulting run length, i.e., the average distance a kinesin molecule travels before falling off.

Several checkpoints, or gating mechanisms, are employed by kinesin where rates in the reaction cycle in one motor domain are either decreased or increased in response to where the other head is in its own reaction cycle. For example, binding and/or hydrolysis of ATP in the bound leading head is slowed down or prevented until the rear trailing head has completed its ATP hydrolysis and released from the microtubule, being ready to step to the next MT binding site. Several other gating mechanisms exist and these are central to understanding both the details of kinesin mechanochemistry and how various aspects of the hydrolysis cycle has been modified in different kinesin subfamilies.

10

Figure 1.4 The kinesin catalytic cycle. The MT bound kinesin head binds ATP (1→2) followed by the docking of the neck linker and the completion of the 8-nm step (2→3). ADP is released upon binding of the free head to the MT whereby the kinesin enters the “two-heads-bound state” (3→4). After ATP is hydrolyzed (4→5), phosphate is released (5→6) and the detachment of the rear head returns the molecule to the “ATP waiting state” (6→1). Mechanical transitions involving movements, such as 2→3 and 6→1, are dependent on internal or external forces (F)

The cell is a crowded environment and conventional kinesin is capable of transporting large cargos through a dense cytoskeleton by employing biologically large forces up to 6 pN. The response to force by kinesin motors is an important parameter for understanding both how transport takes place in the cellular environment and how force-balances occur in the mitotic spindle. It also crucial for understanding how several kinesins together can accomplish very long range neuronal transport and how teams of several kinesin motors work against opposing motors, such as , in bidirectional transport.

1.4 Optical trapping

Single-molecule techniques have been instrumental in characterizing kinesin family motors, for teasing out details in their mechanochemical cycles and how these relate to

11 the function of the motors in the cell. From the early days of kinesin research, optical trapping has been a method of choice as it allows for the simultaneous detection of kinesin position to nm accuracy and the application of controlled pN-scale forces.

An optical trap is, in its most rudimentary form, a strong laser tightly focused by an objective. Dielectric particles get attracted to the focus as the sharp gradient in light intensity near the diffraction limited spot interacts with the induced polarization of the particle. Small objects, such as micron-scale glass or plastic beads, can thereby be stably held in a fixed position with restoring forces that can be likened by a three dimensional spring of light.

Particles in an optical trap are subject to Brownian motion and to stably trap them the trapping force must overcome both this thermal motion and any destabilizing optical forces produced by the scattering of light by the particle. For small and moderate displacements the restoring force increases as the particle is displaced from the center of the trap. The trap stiffness is linear (Hookean) and depends on many variables, such as the light intensity, the numerical aperture (NA) of the objective, the quality of the diffraction limited spot, and the size, shape and material of the trapped particle. Optical trapping forces between one and a few tens of picoNewtons are common in biophysics, but even higher forces can be applied [76].

For biological experiments, beads linked to the biological molecule of interest are introduced, in a suitable buffer, into a flow cell. The flow cell, which consists of a microscope glass slide on top and a cover slip on bottom, is then mounted on a microscope-based setup. Many optical traps are based on commercial microscopes, which allow for integration with standard components and visualization using various imaging techniques, such as differential interference contrast (DIC) or fluorescence.

As the focused laser beam imparts a force on a particle, the particle also slightly displaces the beam. These deflections can be detected, making the optical trap both a pN-scale manipulator and a sub-nm detection device. The laser is collected after the microscope condenser and focused onto a quadrant photodiode (QPD) or a position-sensitive detector (PSD) which converts the change in position to a voltage

12 that is read by a computer, providing the important position information used to interpret the biological experiment.

In practice an additional beam of a different wavelength is often used for detection and many instruments use several traps at once to remove the coupling to the flow cell surface and to minimize experimental noise and drift. Modern optical traps also have advanced optics which enable movements of the laser focus in the microscope sample plane, using acousto-optic deflectors (AODs), piezo controlled mirrors or electro-optic deflectors. Together these techniques allow for accurate, low noise detection on the nanometer scale at kilohertz bandwidths coupled with forces, updated using active feedback control, that can resolve minute movements by protein motors and characterize biological molecules, such as DNA or RNA.

For experiments with kinesin family motors, a single-beam trap with a separate detection laser is typically employed, see Figure 1.5. The movement of kinesin is observed under force-clamp conditions where the force is kept constant by maintaining a fixed distance, Δx, between the center of a polystyrene bead and the trap, which has a stiffness k. The force, F = k Δx, is updated hundreds of times each second as the kinesin, linked to the bead, moves across the active detection region. The kinesin can either move the bead behind it, resulting in a hindering load, or be actively pulled by the trap in an assisting load configuration. A two-dimensional feedback system can also be employed for sideways loads.

The kinesin motors are generally recombinant constructs expressed in E. coli or Sf9 cells. A specific tag (often six histidine residues) is added to the tail and is used both for purification and for specific attachment to the polystyrene beads in the motility assay. The tail is often truncated for better expression yields.

13

Figure 1.5 The kinesin motility assay. A trap with stiffness k applies a constant force (F) to a bead by maintaining a fixed distance (Δx) between the trap and bead centers.

The microtubules (MTs) are firmly attached to the flow cell surface during the experiment, providing a rigid track for the kinesin. Several methods exist for attaching MTs to glass surface, ranging from electrostatic interactions from poly-L-lysine- coated coverslips to antibodies or biotinylated tubulin. We use a direct covalent linkage between glutaraldehyde-treated silanized glass and the MTs that has proved superior for eliminating non-specific sticking between the surface and the kinesin molecules.

The data collected from single-molecule trapping experiments are later analyzed on a computer and provide a basis, together with unloaded video tracking and bulk biochemistry experiments, for modeling that elucidates the different steps in the mechanochemical cycle of the kinesin motors.

14 1.5 Chapter overview

During my graduate career I have been fortunate to have both developed new instrumentation and applied it to interesting new biological systems. This thesis documents work done in both areas.

In Chapter 2, I present a new type of optical trap that was subsequently used for all kinesin studies. This novel instrument uses electro-optic deflection to steer the trapping beam, giving unprecedented precision and linearity in trap movement and hence more accurate recordings of kinesin movement. This published work [77] was a collaborative effort with Megan T. Valentine, Nicholas R. Guydosh, Braulio Gutiérrez-Medina and Adrian N. Fehr.

Light can be used to manipulate the angle of a particle, in addition to its position, if the particle is birefringent and the polarization of the optical trap is controlled. Chapter 3 documents a new instrument, an “optical torque wrench,” that I completed together with Braulio Gutiérrez-Medina. The work was done in collaboration with Arthur La Porta and William J. Greenleaf and published in Methods in enzymology [78]. The optical torque wrench allows the user to detect and apply precisely controlled forces and torques on nanofabricated birefringent quartz cylinders. Torque detection and manipulation open up a wide range of possibilities for the study of biological molecules. Examples include feedback measurements of rotary motors and studies of DNA and DNA binding proteins.

Kinesin-1 is a good model system for studying gating mechanisms. In this thesis, a primary focus has been the kinesin neck linker and its role in gating. Chapter 4 describes experiments with kinesin mutants that contained lengthened neck linkers which revealed new behavior, such as back-stepping under load. By combining force- clamp data with stopped-flow fluorescence experiments, an improved model for kinesin motion could be constructed that included both ATP dependent back-stepping and futile hydrolysis. I participated in designing experiments, collecting and analyzing data, and in writing the manuscript. This published work [79] was spearheaded by

15 Bason E. Clancy and the biochemistry was done in collaboration with William M. Behnke-Parks and Steven S. Rosenfeld.

Further studies of the Kinesin-1 neck linker are explained in Chapter 5 where the neck linker length-dependence of several gating mechanisms was explored. We also studied important differences between Drosophila and human constructs and the effects of commonly used cysteine-light mutations. Small increases in neck linker length had moderate effects on overall velocity and prevention of rebinding of the free head to the rear MT binding site was maintained. The run length fell dramatically, however, indicating that the neck linker length is optimized for long runs. Elongated neck linkers in combination with assisting loads also provided a means of estimating the internal strain in the two-heads-bound state and the effect of this force in stimulating the rate of rear head release from the MT. The project was performed together with Bojan Milic, in collaboration with William O. Hancock. The experiments were the basis for Bojan’s Honors Thesis [80] from which some sections and most figures were adapted.

Although Kinesin-1 has been studied for two decades with optical traps, very little has been known about many other kinesin family members. To better understand their physiological role and the generality of the canonical model for kinesin, a theme in this thesis has been to characterize the mechanochemistry of previously unstudied kinesin family proteins. KIF3A/B, the major heterotrimeric Kinesin-2 motor in mammals, is the topic of Chapter 6. This enzyme is particularly interesting since is contains two different catalytic domains. Measurements of both the wild-type motor and homodimeric mutants were used to establish a global model that shows how the characteristics of the full heterodimer can be explained by those of the individual heads. Furthermore, by studying chimeric mutants containing the stalk from Kinesin-1 and heads and neck linkers from either Kinesin-1 or Kinesin-2 we could identified the features that can be explained by the motor domains, such a new weakly bound state for KIF3A that permits slipping, and the features that be attributed to the different neck linkers and neck domains. This work was performed in collaboration with

16 William O. Hancock and Shankar Shastry at The Pennsylvania State University. Data collection was also performed by Alice Shen and Thaddeus Jordan.

In the final part of this thesis, Chapter 7, results are provided from experiments where the techniques from previous work have been applied to a range of other kinesin motors from different families. These experiments were done in collaboration with Bojan Milic, Kevin R. Wheeler, William M. Behnke-Parks and Steven S. Rosenfeld. KIF17 (Kinesin-2) and CENP-E (Kinesin-7) are robust, processive motors with velocities higher and lower than those of Kinesin-1, respectively. KIF4A, a Kinesin-4 motor, is also fast but is much more sensitive to force than the other motors. Together our data and previous studies indicate that although the overall structure of processive kinesin motors is similar, velocities, run lengths and the responses to force can vary significantly. This shows that there is yet much more to learn in the exciting field of kinesin.

17 Chapter 2: Precision steering of an optical trap by electro-optic deflection

2.1 Abstract

We designed, constructed, and tested a single-beam optical trapping instrument employing twin electro-optic deflectors (EODs) to steer the trap in the specimen plane. Compared to traditional instruments based on acousto-optic deflectors (AODs), EOD- based traps offer a significant improvement in light throughput and a reduction in deflection-angle (pointing) errors. These attributes impart improved force and position resolution, making EOD-based traps a promising alternative for high precision nanomechanical measurements of biomaterials.

2.2 Results and discussion

Optical traps are formed by focusing an intense laser to a diffraction-limited spot using a microscope objective of high numerical aperture (NA), and allow the precise manipulation of micron-scale polarizable objects, such as polystyrene or silica beads [81]. The force response of an optical trap is Hookean for small displacements and scales linearly with laser power. Once trap stiffness is appropriately calibrated, a constant force can be exerted on a moving particle by implementing a force clamp, which typically uses feedback to maintain a fixed separation between the particle and trap center [82-86]. By applying forces to biomolecules, the energy landscapes for mechanochemical reactions can be tilted in controlled ways, revealing mechanistic details of biological processes involving motion [86-88].

When a trapping instrument is operated in force-clamp mode, the position of the beam must be rapidly updated with high precision. This task is commonly performed using an acousto-optic deflector (AOD), a crystal subjected to ultrasound that generates an optical diffraction grating with a period set by the acoustic wavelength and a diffraction efficiency that scales with amplitude [82, 84, 86]. Using an AOD, it is possible to control trap position and stiffness by modulating the acoustic drive frequency and amplitude, respectively. The first-order diffracted light is deflected through an angle, θ, that depends on frequency, f, through θ = λf v , where λ

18 is the optical wavelength and v is the acoustic wave velocity. Maximum deflections around ±1° are possible at λ = 1064 nm. AODs suffer from disadvantages that limit their usefulness in high-resolution applications. Transmittance varies over the working range of drive frequencies, which can cause trap stiffness to change as it is moved. More importantly, AODs exhibit ‘wiggles’: systematic angular deviations from a linear response to the acoustic drive frequency. These small nonlinearities lead to tracking errors in position, resulting in uncertainties for the applied force and measured position.

To improve transmission and pointing characteristics of the beam-steering optics, we constructed an instrument that incorporates twin electro-optic deflectors (EODs; Conoptics 4CryLTA, 302RM; 200 kHz bandwidth) to deflect the beam along orthogonal axes. An EOD is based on a gradient in refractive index across a crystal subjected to an external electrostatic field. Light is deflected through θ = c LV w2 , where L and w are the crystal length and diameter, V is the applied voltage, and the proportionality constant, c, depends on material properties. For a device with L = 11 cm, w = 2 mm, and V = 375 V, maximal deflections around ±0.1° are possible. In contrast to AODs, which deflect a fraction of the incoming light, EODs, deflect the entire beam, leading to increased throughput and higher trap stiffness.

In our design, we formed a single-beam trap using a continuous wave, near- infrared laser (5 W; 1064 nm) (Figure 2.1). Because it is not possible to modulate EOD transmittance, beam intensity was adjusted using halfwave plate (HWP) and polarizing beam-splitting cube (PBS) pairs. One such pair included a motorized rotary HWP (MHWP), allowing computer control of trap stiffness. A single HWP was placed immediately before EOD1 to align polarization to the input axis of the crystal.

For angular deviations from the optimal polarization, a “shadow” beam was observed exiting the EODs, with polarization different from that of the primary beam and deflected to a lesser extent. With optimal alignment however, the power in this parasitic beam could be reduced to ~1-2% of that of the fully-deflected beam. To minimize the contribution of the shadow beam, we placed all HWP-PBS pairs in front

19 of both EODs. We verified that the shadow beam did not significantly perturb the trapping potential by measuring trap stiffness over the range of deflections. Trap stiffnesses measured by three standard methods (the mean-squared displacement for a trapped bead, the corner frequency of its power spectrum, and the drag force at constant fluid velocity) agreed to within 20% at a fixed trap position [81]. Measurements at different trap deflection positions by any single method agreed within 10%; for all positions, power spectra were Lorentzian and distributions of displacements were Gaussian.

Figure 2.1 Schematic layout for the EOD-based optical trap. Dichroic mirror (DM) DM1 combines trapping (dark red) and detection (light orange) beams. DM2 directs both beams through a Wollaston prism (W) into a high-NA (1.40) microscope objective (O); an optical trap is formed in the specimen plane (SP). A series of lens pairs placed in both laser paths image the objective back focal plane onto the steering lenses and EODs (conjugate planes are indicated by blue hatching). An NA-matched condenser lens (C) collects forward-scattered laser light. DM3 reflects the trapping and detection beams while passing brightfield illumination light from an arc lamp (solid green). A short-pass filter (F) blocks the trapping laser, and a duolateral position-sensitive detector (PSD) collects the detection light. S = shutter, BB = beam block, PBS = polarizing beam splitter, ISO = optical isolator, HWP = halfwave plate, MHWP = motorized halfwave plate.

20 EODs were situated such that their axes of deflection were positioned in planes optically conjugate to the back focal plane (BFP) of the objective [81], which produces pure rotations of the beam at the objective entrance pupil. Rotations in this plane, in turn, generate pure translations of the focal spot in the specimen plane. Despite the length of the EOD, a narrowly-defined deflection plane could be identified empirically by measuring deflections over a range of voltages and tracing the beams back to a single vertex within the crystal body.

To characterize our instrument, we measured the transmission and tracking error of the two EODs placed in series. We then compared the performance of this device to one where trap steering was performed by two AODs in series and aligned for maximal throughput.

The transmittance of both EODs (measured by a meter placed after EOD2) was 81% and varied by <0.5% over the deflection range, which corresponded to a trap displacement of ±0.76 μm in the specimen plane (Figure 2.2). For two AODs (IntraAction DTD-274HA6, ATD-274HA1-6, CVE), the transmittance in the first- order diffracted beam was 55% at maximal amplitude. Transmission varied by ~5% for displacements of ±0.75 μm; for larger displacements of ±2.5 μm, >20% variation in transmittance was observed (Figure 2.2).

We compared the accuracy of AOD- and EOD-based deflection by moving a particle along a programmed, linear trajectory. To test deflections at different angles, a 0.44 μm diameter bead was moved in an eight-armed ‘star’ pattern as position was determined by monitoring the scattering of a detection laser (830 nm wavelength), as described previously [83, 85]. For EOD-based deflection, measured displacements corresponded quite well with the target trajectories (Figure 2.3, left). For deflections along the positive y-axis, the std. dev. in position on the x-axis was 0.5 nm. For AOD- based deflection, significant and reproducible deviations from target trajectories were observed (Figure 2.3, right). These quasi-periodic wiggles arise from unwanted back- reflections from absorbers glued to the crystal inside the AOD, resulting in interference between forward and counter-propagating acoustic traveling waves. The positions and amplitudes of wiggles can change with the amplitude and frequency of

21 the drive signal, as well as with the age of the device, making it difficult to remove these by any simple calibration process; systematic pointing errors have been observed for all AOD crystals used in our laboratory. For deflections along the positive y-axis, the std. dev. in position on the x-axis was 2.0 nm.

Figure 2.2 Transmittance as a function of trap position for orthogonal deflectors. The EOD-based optical trap (left) displayed ~81% transmittance with <0.5% variation for displacements of ±0.76 μm in the specimen plane (corresponding to the full working range), whereas the AOD-based optical trap (right) displayed ~55% transmittance with >20% variation for displacements of ±2.5 μm (±2.5 MHz around center frequencies of 21.8 MHz in the x-dimension; 30 MHz in the y-dimension).

To demonstrate the resolution attained by the EOD-based optical trap, we performed single-molecule motility assays using recombinant kinesin protein, as previously described [89]. Individual molecular steps taken by bead-bound kinesin motors, measuring 8.2 nm, could be clearly resolved (Figure 2.4, black trace), as a constant (hindering) load of –4.9 pN was maintained using EOD-based feedback to control trap position (red line).

22

Figure 2.3 Linearity of EOD and AOD response A. A particle trapped ~500 nm above the coverslip surface was moved in an eight-armed star pattern by EOD- (left) or AOD-driven (right) deflections of the trapping beam. Data were sampled at 50 kHz and Bessel filtered at 25 kHz; 1000 samples were averaged at each of 200 positions per arm. The x and y trap stiffnesses (κ) were determined by averaging values estimated by two methods: (1) the mean- squared displacement and (2) the corner frequency of the Lorentzian power spectrum [81]. For the -1 -1 EOD-based device, κx = 0.16 pN nm and κy = 0.20 pN nm ; for the AOD-based device, κx = -1 -1 0.27 pN nm and κy = 0.16 pN nm .

B. EOD-driven beads accurately followed the targeted trajectory, as seen in an expanded view (left). AOD-driven particles (right) displayed characteristic wiggles (see text). C. Histograms of the displacement data in panel B.

In summary, there are clear advantages to the use of EODs for steering optical traps. EODs offer comparatively greater throughput (~50% more), reduced variation in transmittance with deflection (ten-fold less), and increased linearity in deflection (a four-fold improvement). These features facilitate more precise control over trap stiffness and position. Furthermore, in conjunction with nanoscale distance standards,

23 the improved deflection accuracy may simplify the process of instrument calibration [90]. Excepting applications requiring large-scale deflections, future high- resolution biomechanical measurements stand to benefit from this technology.

Figure 2.4 Experimental kinesin trace. Experimental record showing the displacement of a single kinesin molecule bound to a bead (black) and the corresponding trap position (red) vs. time under force-clamped conditions [86], showing steps of 8.2 nm (dashed grey). A recombinant derivative of D. melanogaster kinesin (DmK612) was used in this assay [89], with [ATP] =100 μM, trap stiffness = 0.07 pN nm-1, and hindering force = -4.9 pN. Inset: cartoon showing the experimental geometry (not to scale), where a single kinesin motor, bound to a bead held in the optical trap, steps along a microtubule attached to the coverslip.

24 Chapter 3: An optical apparatus for rotation and trapping

3.1 Abstract

We present details of the design, construction and testing of a single-beam optical tweezers apparatus capable of measuring and exerting torque, as well as force, on microfabricated, optically anisotropic particles (an ‘optical torque wrench’). The control of angular orientation is achieved by rotating the linear polarization of a trapping laser with an electro-optic modulator (EOM), which affords improved performance over previous designs. The torque imparted to the trapped particle is assessed by measuring the difference between left- and right-circular components of the transmitted light, and constant torque is maintained by feeding this difference signal back into a custom-designed electronic servo loop. The limited angular range of the EOM (±180°) is extended by rapidly reversing the polarization once a threshold angle is reached, enabling the torque clamp to function over unlimited, continuous rotations at high bandwidth. In addition, we developed particles suitable for rotation in this apparatus using microfabrication techniques. Altogether, the system allows for the simultaneous application of forces (~0.1–100 pN) and torques (~1–10,000 pN nm) in the study of biomolecules. As a proof of principle, we demonstrate how our instrument can be used to study the supercoiling of single DNA molecules.

3.2 Introduction

Optical tweezers have proved to be an extremely powerful tool in the investigation of biophysical processes, particularly the activity of motor proteins and other processive enzymes, whose biological activity involves converting chemical energy into mechanical work. The ability to measure displacements with subnanometer resolution and to apply piconewton-level forces in a controlled manner makes optical trapping ideal for studying the motion of biological macromolecules [81, 91, 92]. Through the use of active servo loops or passive optical configurations that can clamp the force, position, loading rate, or other physical quantities, precisely defined perturbations can be applied to identify the kinetic processes that underlie enzyme mechanisms.

25 Force and displacement, however, represent just one aspect of the physical picture. A host of important biomolecular complexes, including the F1-ATPase [93] and the bacterial flagellar motor [94], generate torque and rotation—rather than force and displacement—as the mechanical output. Moreover, owing to the helical structure of DNA, many processive nucleic-acid based enzymes undergo rotation and generate torsional strain as a consequence of their translocation. Torsional strain in DNA and is regulated, directly and indirectly, by a variety of proteins such as topoisomerases, , gyrases, histones and chromatin remodeling factors [95], and it is well established that such strain is a major factor in [96]. Finally, mechanoenzymes that translocate along linear polymers, such as or kinesin, may also generate (or respond to) torque [97]. Practical benefit can therefore be gained by generalizing single-molecule methods to include the precise detection of rotation and the application of torque. Currently, the well-established technique of magnetic tweezers permits controlled rotation of magnetic micro-particles by adjusting the orientation of an external magnetic field, enabling a variety of single-molecule manipulations. Magnetic tweezers are comparatively simple in their design and operation, and take advantage of the biologically non-invasive character of the magnetic field, typically producing constant forces over distances of several microns. However, conventional magnetic tweezers have certain practical limitations. There is no direct way to measure the torque imparted to the trapped particle, nor to conveniently record its angular displacement with respect to the applied field. Also, most magnetic tweezers determine displacement using frame-by-frame video processing of particle images, and are therefore limited by video acquisition rates, whereas laser-based optical trapping systems tend to use dedicated photosensors (quadrant photodiodes or position-sensitive detectors) with bandwidths exceeding several kilohertz. Finally, the magnitudes and directions of the fields produced by permanent or electro-magnets cannot be changed very quickly, making it harder to adjust external control variables, such as the torque and force, as rapidly as one might like.

26 In the following sections, we describe the latest generation of an optical torque wrench, based on an improved design. Like conventional optical tweezers, the instrument has the ability to manipulate micron-sized particles, and to monitor both force and displacement. Additionally, it has the capacity to produce rotation, and to measure angle and applied torque with excellent precision (~1 pN nm of torque) at high bandwidth (~10-100 kHz).

3.3 Optical trapping and rotation of micro-particles

3.3.1 The principles of optical manipulation A single beam, gradient-force optical trap is based on the interaction of a micron-sized dielectric particle with a beam of light that is brought to a diffraction-limited focal spot. Under the influence of the electric field (E), the particle develops an electric polarization P whose magnitude depends on material properties of the particle (Figure 3.1A). For isotropic materials, P = χE, where χ is the polarizability of the material. The interaction of the induced polarization vector with the applied electric field leads to a net force proportional to χ∇E2, where ∇E2 is the gradient of the electric field intensity [98, 99]. In the presence of a highly focused laser beam, a particle is therefore drawn towards the focal point, which constitutes the lowest energy state.

An electric dipole interacting with an external electric field can also generate a torque, in addition to force, whose magnitude is given by τ = E× p = E psinθ , where

θ is the angle between E and p. To produce non-zero torques, it follows that the net induced dipole moment must have a component perpendicular to the average external field. This condition can be satisfied using anisotropic particles, where either form or material birefringence (or both) lead to different polarizabilities along perpendicular axes. Form birefringence is a purely geometrical property, arising from the way that the shape of a small particle scatters light (e.g., an oblate ellipsoid), whereas material birefringence is an intrinsic optical property of the material from which the particle is produced (e.g., crystalline quartz). When an object is birefringent, the expression relating the induced dipole to the external field is replaced by the matrix equation

27 p = χE , which reduces to the scalar relations pi = χiEi whenever the coordinate system coincides with the principal axes of a birefringent crystal, or with the symmetry axes of an anisotropic shape. Figure 3.1B illustrates an example where the external field makes an angle of 45 degrees with respect to two principal axes. The induced dipole tends towards the easy optical axis, and the resulting torque acts to bring the most polarizable axis into alignment with the external field.

From Newton’s Laws, the amount of force and torque generated by an optical trap can be computed by considering linear and angular momentum, respectively, transferred from the laser beam to the trapped particle. A single photon carries energy ε = hc/λ, linear momentum p = h/λ, and the angular momentum associated with its spin is L = ±h/2π (for right- and left-circularly polarized light), where h is Planck’s constant, c is the speed of light and λ is the wavelength. The rate of change of linear momentum (equal to the force) is therefore given by F = dp dt = (1 c)dε dt , or F =℘ c , where ℘= dε dt is the optical power. Similarly, the torque, τ, is equal to the rate of change of angular momentum, which leads to τ = (λ 2πc)℘. Assuming a laser with λ = 1064 nm and conversion efficiencies in the range of 1-10% (typical of optical traps, in practice), it follows that an optical trap might generate 0.03–0.3 pN of force and 6–60 pN nm of torque per milliwatt of incident optical power. When these values are compared with the forces needed to extend a coil of double stranded DNA (5 pN) [100, 101] or to melt double-stranded DNA (~100 pN) [102], or with the torque necessary to unwind double-stranded DNA (~10-100 pN nm) [103], it becomes clear that the linear and angular momentum carried by a laser beam is adequate to produce biologically relevant forces and torques at modest power.

28

Figure 3.1 Principles of optical manipulation and signal detection. (A). The electric field (E, blue arrow) associated with a tightly focused laser beam induces a collinear polarization dipole (P, red arrow) on an isotropic dielectric particle. As the particle moves away from the center of the laser focal volume, the induced dipole-electric field interaction produces a net restoring force (F, black arrows) towards the center, confining the particle in 3D.

(B). For an optically anisotropic particle, different axes exhibit different polarizabilities. The induced polarization vector, therefore, is not collinear with the external electric field, and inclines towards the most polarizable (easy) axis. This effect gives rise to a net torque on the particle that tends to align the easy axis with the electric field.

(C). Force can be detected by measuring trapping beam deflections (corresponding to changes in linear momentum) induced by an off-center, trapped particle, using a position sensitive detector.

(D). Analogously, the torque exerted by a linearly-polarized beam on an anisotropic particle can be detected, based on the imbalance in the right- and left-circular polarization components in the beam after scattering by the particle, which can be measured independently.

29 Torque may also be applied to optically trapped particles by taking advantage of the ‘orbital’ angular momentum of the light, which is associated with the geometry of the laser beam, rather than with the individual photon spin. Practical implementations of this strategy include optical vortices and higher order Gaussian- Laguerre modes [104, 105], where the flow of energy (the Poynting vector) in the optical mode carries angular momentum about the beam axis. Orbital angular momentum can also be developed from a pair of ordinary laser beams that propagate along non-intersecting, non-parallel paths, or by using a spatially anisotropic trapping beam in conjunction with an asymmetrically-shaped particle. In addition, torque is developed whenever microscopic chiral particles scatter light in such a way as to induce orbital angular momentum [106]. Although the changes in torque from an asymmetric trapping beam might, in principle, be measured [107], doing so would likely involve detecting subtle changes in the phase profile of the outgoing beam, requiring interferometric imaging of the outgoing trap beam and sophisticated real- time image analysis.

By contrast, the optical torque wrench (OTW) represents a conceptually simpler arrangement, based on the ‘spin’ angular momentum of light, which is associated with its polarization. The OTW scheme provides a straightforward way to apply and detect torque [108] by monitoring the net change in the polarization of an optical trapping beam as it interacts with a transparent, anisotropic (birefringent) particle. The OTW controls rotation of the specimen by turning the polarization of the incoming beam, and determines the torque by separating the right- and left-circular components of the outgoing beam and measuring their intensities using standard polarization components. It then becomes possible to use a single trapping laser beam for both linear and angular manipulation, and the detection of force (Figure 3.1C) and torque (Figure 3.1D). The OTW has the additional advantage that the angular and linear trapping effects are relatively independent, with little crosstalk between them.

3.3.2 Sources of particle anisotropy Two types of birefringence are suitable for producing the optical anisotropy necessary for use with an OTW: form birefringence and material birefringence. In form

30 birefringence, a tiny particle with differing dimensions along perpendicular axes is easier to polarize along the more extended direction, provided that the dimensions are comparable to, or smaller than, the wavelength of the scattered light. Such a small particle will exhibit birefringence even when the material comprising the particle itself is isotropic, resulting in indirect coupling between the particle shape and the polarization of the trap beam. For optical rotation purposes, oblate particle symmetry is desirable, so that the two extended axes lead to stable orientation within the trapping beam and simultaneous alignment of the net polarization vector with the trapping electric field (see Figure 3.2A). This configuration allows the particle to rotate, as necessary, to present the attachment point of a biological molecule downward in response to upward tension (assuming an inverted microscope arrangement, with the laser beam introduced from below the objective) [109].

An optimum aspect ratio for form birefringence that maximizes the torque for oblate particles can be derived ( ρ = rmax rmin ), assuming that the particle is small compared to the wavelength of the trapping radiation. The torque exerted on an oblate ellipsoid in a uniform electric field is given by:

(ε −1)2 (1− 3ε)E 2V sin 2α τ = , (1) 8π(πε +1− n)([1− n]ε +1+ n) where V is the volume of the particle, n is the depolarizing factor along the symmetry axis, ε is the dielectric constant, α is the angle between the electric field direction and the polar axis of the particle, and E is the electric field [110]. Assuming that volume is conserved, the torque asymptotically approaches a constant value as ρ goes to infinity, a limit that is not physically relevant, because the expression for torque is only valid when the major axis remains small compared to the size of the trapping beam. Instead, a meaningful optimization is obtained by varying the aspect ratio under the constraint that the major axis remains constant and on the order of the trap size, in which case the volume of the particle is proportional to ρ−1. The torque, normalized to the incident electric field, E, is plotted in Figure 3.2C: a maximum value is obtained with an aspect

31 ratio of ρ ≈ 3. The torque computed from Eq. (1) with this aspect ratio for an oblate ellipsoid made of silica is approximately 60% of the corresponding torque for a sphere of equivalent volume made from quartz, which is intrinsically birefringent.

The alternative to form birefringence is material birefringence. Birefringent materials have distinct principal axes exhibiting different polarizabilities. Some substances, such as quartz and calcite, have two (ordinary) axes that are equivalent, and one (extraordinary) axis that is different from the other two. For quartz, the extraordinary axis is the most easily polarized, and so the overall polarizability can be represented by a prolate ellipsoid. In the presence of an external electric field, quartz experiences a torque that tends to align the extraordinary axis with the electric field vector (Figure 3.2D). For calcite, however, the extraordinary axis is the least polarizable, so the overall polarizability is represented by an oblate ellipsoid. In this case, the extraordinary axis is repelled from, and the two ordinary axes are drawn towards, the electric field vector (Figure 3.2E-F). While it may be possible to exert torque on calcite particles using the configuration shown in Figure 3.2E, quartz offers more optimized conditions for combined optical trapping (translation) and rotation. Inside an optical trap, quartz particles with prolate shapes can be stably trapped in a vertical orientation dictated by their shape, then rotated about the optical axis due to the prolate polarizability ellipsoid.

32

Figure 3.2 Particle anisotropy for optical trapping and rotation. (A) A small, oblate particle made of an optically isotropic material tends to align its long radii with the trapping beam axis (vertical) and the polarization direction (red arrow). (B) A birefringent cylinder tends to align its long axis with the trapping beam axis, allowing the extraordinary optical axis of the crystal to track the trap polarization direction. Possible materials for birefringent particles include quartz and calcite. (C) Theoretical estimate of the torque exerted on a sub-wavelength, oblate particle subjected to a uniform electric field, shown as a function of its aspect ratio (maximum to minimum radius). Bigger torques correspond to larger negative values; the greatest torque (curve minimum) occurs near an aspect ratio of 3. (D)-(F) The polarization ellipsoids for quartz (D), and calcite (E), (F) are shown, where red (grey) zones represent regions of maximum (minimum) electric susceptibility. Axes corresponding to red regions tend to align with the direction of the electric field vector E (green axis). For optical trapping and rotation, an ideal configuration is obtained when rotation is possible around the direction of the beam propagation vector, k, (blue axis). This is the case for quartz (D). For calcite, the configuration shown in (E) can be used to exert torque (although alignment of the polarization ellipsoid with respect to the direction of E is not unique), whereas in the arrangement shown in (F) the particle exhibits no net birefringence on the plane perpendicular to k and no torque can be generated about the beam axial direction.

33 Ideally, particles used in an OTW need to be strongly and stably trapped in all three dimensions, readily rotated, and functionally consistent with any planned biological experiments (e.g., functional attachment of the particles to macromolecules must be possible). One particularly important experimental geometry for single- molecule experiments is the surface-based assay, where the molecule of interest—for example, DNA—is tethered to the coverglass surface by one end and to the trapped particle by the other. In the OTW, force can then be applied upwards to stretch the tether while controlled rotation takes place around the vertical axis. For this purpose, the use of cylindrical quartz particles is particularly convenient (Figure 3.2B). Cylinders whose length exceeds their diameter will naturally tend to align their long axis with the optical axis of the trap, and the extraordinary optical axis of the material can be chosen to lie parallel to the base and top of the cylinder, facilitating rotation in the horizontal plane [111]. Micrometer-scale cylinders are also comparatively easy to fabricate, and their flat end-surfaces can be chemically derivatized to facilitate connections to biomolecules. In Section 4, we present detailed protocols to produce both oblate polystyrene ellipsoids and quartz cylinders.

3.4 The instrument

3.4.1 Overview The optical layout for the OTW is shown in Figure 3.3, highlighting several differences compared with previous implementations [108, 109, 112]. A single laser beam is used both for optical trapping and rotation of micro-particles, and for the simultaneous detection of force and torque. Rotation of the polarization in the sample plane is achieved by means of an electro-optic modulator (EOM), which replaces the pair of acousto-optic modulators (AOMs) used in a previous apparatus in an interferometer arrangement that shifted the relative phases of the vertical and horizontal polarization components of the input beam [108].

Upon passage through the EOM, an incoming polarized light beam with electric field components (Ex, Ey) along the optical axes of the EOM crystal will experience a relative phase retardation (α) between Ex and Ey that is proportional to

34 the applied voltage. The EOM thus behaves as a variable waveplate: it transforms an incoming linear polarization into elliptical polarization, where the degree of ellipticity is controlled by the voltage signal. After the EOM, the laser beam passes through an input λ/4-waveplate whose main optical axes are aligned at 45° with respect to those of the EOM, thereby restoring linear polarization, but now rotated by an angle θ = 2α with respect to its initial orientation. One constraint of the EOM is that its dynamic range is limited, typically corresponding to α = ±90° (max). However, this limitation can be circumvented by implementing additional control electronics (see Section 5.4). The use of an EOM offers several distinct advantages over a dual-AOM interferometer: (1) a symmetric beam profile is preserved throughout, which improves optical trap performance and calibration, (2) the polarization is no longer subject to significant long-term drift, as observed in the AOM-based system, and (3) the beam polarization angle is directly proportional to the EOM drive voltage, so there is no longer a need for additional input-angle detection optics. The new design is also considerably simpler to construct and align, involving fewer optical components.

3.4.2 The microscope We now describe the instrument in further detail. The trapping beam is produced by a stable, diode-pumped solid state Nd:YVO4 laser (BL-106C, λ = 1064 nm, CW, Spectra Physics), operated near its peak power of 5 W to produce a beam with a clean

TEM00 mode, with typical intensity fluctuations of < 0.2%. The optical power used for trapping is computer-controlled by means of a λ/2-waveplate mounted on a motorized rotary stage (PRM1-Z7E, Thorlabs) followed by a polarizing beam splitter (PBS). An alternative for controlling the power is an AOM; however, we found that the profile of the diffracted beam produced by an AOM was somewhat distorted, leading to an angular asymmetry in the trap that degraded the performance of the instrument. While a motorized stage is comparatively slow, rapid control of the intensity is nonessential, because trapping experiments are typically performed at constant power in the sample plane. After the PBS, the resulting beam has linear polarization of high purity (> 99.5%) and a Gaussian profile, providing excellent starting conditions for subsequent manipulation of the polarization.

35

Figure 3.3 Optical schematic of the optical torque wrench. The trapping beam (thick red line) is produced by a near-infrared laser, and the output power is adjusted by a λ/2-waveplate and polarizing beam splitter (PBS). Rotation of linear polarization in the sample plane is achieved using an EOM and a λ/4-waveplate placed before the microscope objective. The optical axes for components relevant to torque generation and detection are shown (grey axes), along with the polarization state of the trapping beam as it travels along the optical path. To detect torque, a λ/4-waveplate is placed after the condenser to convert the polarization components from circular to linear; these are then separated by a PBS and measured using position sensitive detectors (PSDl, PSDr). Each PSD produces X, Y and Sum (Z) voltages, which are combined to yield x, y, z, and torque (τ) signals. D1, D2: dichroic mirrors; PD: photodiode; LED: blue light-emitting diode illuminator; CCD: charge-coupled device video camera.

36 The next element in the optical pathway is the EOM (360-80, Conoptics), mounted on a V-shaped aluminum block attached to a five-axis alignment mount (9082, New Focus). This scheme allows for manual rotation of the EOM along its longitudinal axis (roll), as well as for fine adjustment of position, pitch and yaw. Precise control of the orientation is necessary to align the EOM crystal, given its narrow aperture (~2 mm) and long length (~10 cm). The optical axes of the EOM can be aligned with respect to the incoming polarization by placing a temporary PBS after the EOM, and then oscillating the drive voltage from minimum to maximum range (corresponding to α = ±90°). As the transmitted intensity is recorded with a photodiode, the EOM housing is rotated until the maximum contrast is observed, signaling polarization changes from linear (vertical) to circular and back to linear (horizontal). While it is possible to rotate the incoming laser polarization instead of rotating the EOM, considerable care must be taken with subsequent polarization alignments.

After the EOM, the beam is expanded to a final waist size of w ~ 3 mm and sent to a periscope that elevates the beam height to ~20 cm above the optical table. To minimize depolarization effects arising from non-orthogonal reflections, we use silver mirrors in the periscope, rather than dielectric mirrors. Before the beam enters the microscope, two lenses of equal focal length (f = 75 mm) are placed in the optical path, forming a 1:1 telescope, with one of the lenses mounted on a x-y-z translation stage and placed in a plane optically conjugate to the back focal plane of the objective. This telescope provides a means of steering the trap in the sample plane without beam clipping at the back of the objective [81, 83]. Finally, the beam is coupled into the microscope by reflection from a dichroic mirror, passes through the input λ/4- waveplate, and reaches the entrance pupil of the objective. We confirmed the EOM- controlled rotation of the laser polarization by removing the microscope objective and monitoring the transmitted intensity after an auxiliary polarization analyzer (a PBS).

37

Figure 3.4 Photograph of the OTW instrument, with components as indicated. A commercial Nikon microscope was modified to improve mechanical and optical stability (see main text). The trapping laser, EOM, and associated optics are enclosed in plexiglass boxes (right side) to minimize beam instabilities due to air currents. The sample is held on a 3D piezoelectric stage with a 2D piezomotor substage.

The uniformity of the beam polarization is the figure of merit in an OTW, and a few precautions were taken to maintain its quality. First, all mirrors transporting the beam after the EOM into the microscope were aligned at 45º angles with respect to the incoming beam direction to avoid depolarization effects. Second, the fast and slow axes of the EOM were matched to the S- and P-axes of any subsequent mirror reflections. In this fashion, any phase retardation between the S and P components is equivalent to an additive constant to the phase retardation generated by the EOM, which can easily be nulled out. Finally, positioning the input λ/4-waveplate directly below the condenser minimizes depolarization effects induced by torque exerted on the mirrors themselves, which would otherwise introduce a spurious torque signature into the output detector.

The apparatus was based on a commercial inverted microscope (Eclipse TE2000-S, Nikon), modified to accommodate the optics needed to couple the trapping beam into the objective and to produce and detect the beam polarization. The vertical

38 arm carrying the microscope condenser was removed and replaced by a structure designed to improve mechanical stability (Figure 3.4). This structure was formed by two large vertical construction rails (XT95, Thorlabs), cross-linked at the top by a third rail, and further supported by additional beams joining the vertical rails to the optical table. An optical breadboard was suspended vertically from the structure and used to hold the condenser plus all detection optics. We used an oil-immersion, high NA objective (100X/1.4NA/ PlanApo, part 93110IR, Nikon), which has improved throughput in the near IR region and maximizes trapping efficiency while minimizing depolarization effects. The condenser lens (1.4NA, Nikon) was mounted on an x-y-z translation stage, which greatly facilitates alignment. The microscope was set up for bright-field illumination of the sample using a blue LED illumination source (LEDC3, Thorlabs) attached on top of the rail structure. Trapped beads are imaged through the microscope video port using a CCD camera. The original Nikon specimen stage was also removed and replaced by a custom-fabricated aluminum mount that supports several items, including the dichroic mirror coupling the laser light into the objective, a precision rotary stage holding the input λ/4-waveplate below the objective, and piezomotor and piezoelectric stages (M-686.1PM and P-517.3CD, Physik Instrumente). The x-y piezomotor substage is used for coarse positioning of the sample, and features 100-nm step resolution over a 25 mm travel range with enhanced mechanical stability compared to conventional crossed-roller-bearing mechanical stages [113]. The x-y-z piezoelectric main stage is used for all fine positioning and has nm-level step resolution over 100×100×20 µm.

3.4.3 Signal detection and processing Torque detection from the forward-scattered light exiting the sample chamber is based on an output λ/4-waveplate placed immediately after the condenser, which maps the right- and left-circular components of the beam polarization into vertical and horizontal linear polarizations, respectively. These polarization components are separated by an analyzer and their intensities measured by separate detectors (Figure 3.3). In our setup, due to space constrains, an intermediate dichroic mirror placed after the output λ/4-waveplate directs the beam towards the analyzer. We use two

39 independent duolateral position sensitive detectors (PSDs) with built-in pre-amplifiers (Pacific Silicon Sensors), aligned for back-focal plane detection [81] to measure bead displacements and the magnitude of polarization components independently. Each detector produces x, y, and sum (z) voltages for its corresponding circular polarization component, either left or right, to generate Vlx, Vly, Vlz, Vrx, Vry, Vrz. The net x, y, z, and torque (τ) signals are obtained by combining these voltages using a simple linear analog electronic circuit, with x = Vlx + Vrx, y = Vly + Vry, z = Vlz + Vrz, and τ = Vlz −

Vrz. To generate the z signal, the output beam passes through an aperture that allows the intensity of the central portion of the beam (only) to be measured [114]. The position and torque voltages go through lowpass multipole filters to remove noise (3988, Krohn-Hite) and are fed directly into a computer-acquisition board (PCI- 6052E, National Instruments), where the signals are further processed by custom software written in LabView (Version 7.1, National Instruments).

3.5 Fabrication of anisotropic particles

3.5.1 Particles with shape asymmetry One simple way to obtain oblate particles is to mechanically deform polystyrene microspheres by compression [109]. In our procedure, spherical particles (1.1 μm diameter, Bangs Labs) were suspended in water (~1-3% by volume) and flattened between a pair of glass microscope slides mounted in a simple vise consisting of two machined aluminum blocks. The vise was padded with 3-mm rubber gaskets to seal the sample and maintain uniform pressure, and compression was obtained by gradually tightening the four ¼-20 bolts holding the vise together, producing an estimated pressure of at least 107 Pa. After compression at room temperature for ~2 min, the vice was disassembled and the microspheres were washed off the slide surface. A fraction of these pressure-treated beads (~1-10%) exhibited an aspect ratio of ~3 when examined by electron microscopy from different angles (Figure 3.5A shows a top view), and were easily distinguished in the light microscope, where they could be trapped and rotated Figure 3.5B). Coating of the surface with chemical or antibody labels is possible either before or after compression. Alternative strategies for

40 deforming uniform polystyrene spheres include compression in conjunction with heat treatment to near the glass point of polystyrene (~90°C), or flattening between vise faces in the presence of a mixture of smaller, incompressible silica spheres, which act as spacers to limit the compression distance.

Figure 3.5 Optically anisotropic particles based on form birefringence. (A) Scanning electron microscope picture of an oblate particle (white arrow) created by compressing polystyrene spheres (see main text). The smaller adjacent particle is a 600-nm silica bead. Field of view is 5×5 µm2. (B) Kymograph showing a sequence of bright-field images corresponding to a trapped, oblate particle being rotated by the OTW. Time between frames, 0.12 s. Field of view is 2×2 µm2.

We compressed polystyrene spheres initially coated with either biotin or avidin labels. Using either of these approaches, compressed beads were attached to one end of a single DNA molecule via a biotin-avidin linkage and tethered to a coverslip surface by the opposite end, and torque was exerted on the DNA. While it is possible to perform single-molecule experiments using compressed beads, the uniform labeling of the entire bead surface can make calibration difficult. If the DNA molecule happens to attach to the bead in a non-equatorial position—which, statistically, is the most likely occurrence—the tethered particle will tend to adopt an off-axis orientation, leading to signal crosstalk and thereby to the introduction of uncontrolled forces and torques. This difficulty may be circumvented by carefully selecting for those compressed beads that happen to be tethered by an equatorial point, but these are comparatively rare and may be difficult to identify. However, despite the random variation present in points of attachment, we found compressed beads to be extremely useful during alignment and initial testing phases of the OTW calibration. Because their shape asymmetry is readily seen in the light microscope, it becomes possible to

41 monitor bead rotation using an independent method that does not rely on PSD signals, such as video tracking. This permits measurement of the rotation angle even when the laser trap is off, a helpful trait that we used to confirm the formation of rotationally- constrained DNA tethers (see Section 6), by twisting DNA molecules attached to compressed beads and observing unwinding after the trapping beam is blocked.

3.5.2 Particles with optical asymmetry Conventional microlithographic techniques can be employed to manufacture birefringent particles of specific shapes in a controlled and reproducible fashion [111]. Although chemically-produced particles of birefringent materials, such as vaterite, have been used to apply torque in previous applications [115, 116], lithography offers several advantages. First, the particles can be chemically derivatized for biological labeling on specific surfaces, facilitating their vertical orientation when tethered in surface-based assays, thereby minimizing undesired forces and torques. Second, micro- or nanofabrication methods can yield large numbers of uniform particles, whose sizes can easily be controlled by changing mask features or adjusting etching parameters. Finally, among the many possible birefringent materials that might be used, in principle, quartz is chemically stable, readily available in wafer form at relatively low cost, and suitable for use with a variety of established etching chemistries, making it a natural choice for OTW applications.

Here, we present a protocol to produce cylinder-shaped particles by a single lithographic exposure of a quartz wafer. The particles are designed to have their extraordinary optical axis perpendicular to the axis of cylindrical symmetry, and are chemically functionalized at only one of the bases (Figure 3.6). Our protocol was developed from a previous implementation [111], but modified to comply with restrictions imposed by the Stanford Nanofabrication Facility, which precluded placing anti-reflective coatings on the back sides of wafers.

3.5.2.1 Mask design and wafers

Reticle design typically depends on the stepper system used. To produce arrays of upright cylinders 400-700 nm in diameter, we divide the mask into 4×4 mm2 areas, at

42 wafer level, each with about 107 evenly spaced octagons of a particular size. Lithographic imaging of tiny octagon (or square) shapes in the mask produces nearly circular patterns on wafers after UV exposure, due to light diffraction effects. The exposure to create uniform patterns of small, high aspect ratio cylinders can reach the practical limit of i-line steppers, especially with a transparent substrate. If multiple patterned regions are placed on a single mask, it is therefore advisable to select just one or two patterns and place them in the center of the reticle, thereby reducing possible astigmatism from the outermost part of the stepper lens. We use 4″ X-cut, single-crystal quartz wafers with double-side polish (University Wafer).

3.5.2.2 Protocol

1. Clean the wafer in hot piranha solution (9:1 mixture of H2SO4 and H2O2, 120°C) for 20 min. Rinse in water followed by a spin rinse dryer cycle.

2. Functionalize surface for biological labeling with 3- aminopropyltriethoxysilane (APTES) or any other desired organosilane coupling reagent:

i. Add 0.6 ml of APTES (99%, Sigma-Aldrich) to 30 ml ethanol solution (95% (v/v) ethanol, 5% (v/v) water, pH 5.0 using acetic acid).

ii. Place wafer in solution and sonicate for 5 min.

iii. Rinse by sonicating wafer for 30 s in 50 ml methanol, 3 times.

iv. Cure in oven for 20 min at 115°C.

3. Spin coat 1.0 µm photoresist (Megaposit SPR 955-CM, Rohm and Haas Company) onto wafer. We use a Suss MicroTec ACS200 spin coater for these steps:

i. 1700 rpm, 20 s, followed by edge bead removal (Microposit EC solvent 13) and a final spin at 1200 rpm, 8 s.

ii. Bake for 90 s on a 90°C hotplate.

43 4. Apply dicing tape (Z18551-7.50, Semiconductor Equipment Corporation) to the back side of the wafer and cut along the wafer edge. The use of tape prevents reflections from the stepper exposure chuck and avoids using extra anti-reflective coatings that may interact with the chuck surface.

5. Expose the pattern. We use an ASML PAS 5500/60 i-line Stepper with 5X magnification and a 110 mJ cm−2 dose. Adjustments of focus and tilt offsets are necessary for optimal uniformity.

6. Remove tape and bake wafer for 90 s on a 110°C hot plate.

7. Manually develop the wafer by placing it in the developer (Megaposit MF- 26A, Rohm and Haas Company) for 30 s and then gently agitate in solution for an additional 30 s. Rinse in a water beaker and air-blow dry. The manual developing procedure reduces the risk of breaking the high-aspect-ratio resist posts.

8. UV cure for 15 min followed by 1 h bake in 110°C oven.

9. (Optional) Instead of the previous step, the resist can be cured using a Fusion UV Cure System, which combines high-intensity UV light with a fast temperature ramp (100°C to 200°C over 45 s). This can improve resist selectivity during the etching process, leading to more vertical cylinder side walls.

10. Etch the wafer. We use an Applied Materials Precision 5000 Etcher at the following settings: power 50 W, pressure 10 mTorr, gas flow 36 sccm CHF3 and 36 sccm CF4, magnetic field 30 G and helium cooling 5 Torr. The resulting etch rate is ~150 Å min−1.

11. (Optional) To reduce the APTES-coated area at the top cylinder, an additional dry-etching step can be performed using O2 plasma for 3 min in a Matrix Plasma Asher (3.75 Torr, 450 W, 100°C, pins down). As the remaining resist cap is etched, the outer rim of the top quartz surface is exposed to the plasma (Figure 3.6F), removing the APTES in this region. The linking of biological

44 molecules can thereby be concentrated towards the center of the cylinder, reducing any potential wobbling of the particle during rotation in the optical trap. Another way to reduce the top area is to perform Step 10 until the top cylinder diameter shrinks as a result of a diminished resist layer (Figure 3.6G).

12. The remaining resist is stripped by rinsing and sonicating in acetone for 20 min.

13. Quartz cylinders are recovered by manually scraping the wafer surface with a microtome blade and collecting the material in a test tube. This can be done in the presence of liquid, such as buffer or cross linking reagents, to maximize yield.

14. The cylinders are functionalized with coupling proteins of interest, such as avidin, by cross-linking to the primary amines in the APTES using a conventional glutaraldehyde kit (Cat. #: 19540, Polysciences).

In the light microscope, nanofabricated quartz cylinders appear as thick, short rods that can be optically trapped with ease. As expected, trapped cylinders align themselves with their long axis along the direction of beam propagation, with the functionalized surface facing towards (or away from) the coverglass surface—an ideal geometry for producing tethers in a surface-based, single-molecule assay.

45

Figure 3.6 Fabrication of birefringent quartz cylinders. (A) Schematic showing the major steps of the fabrication protocol. SEM images of the cylinders during fabrication are shown on the wafer after etching (B) and after cutting (C). (D) and (E), examples of particles made with different final sizes. The functionalized area at the top of cylinders may be minimized by shrinking resist (F) or the cylinder itself (G).

3.6 Instrument calibration

3.6.1 Standard optical tweezers calibration methods A number of well-established methods have been developed to calibrate the stiffness of an optical trap (κ) acting on spherical beads. The most common methods are based on analysis of measurements of particle variance, power spectrum, or Stokes’ drag, and have been described in greater detail previously [81, 83, 91]. Briefly, under low Reynolds number conditions, the thermal of a trapped bead in solution depend on the bead’s viscous drag coefficient and the trap stiffness. The simplest of all calibration methods is variance-based, and uses the positional variance of a bead 〈x2〉 in combination with the Equipartition Theorem to compute the stiffness from κx =

46 2 〈x 〉/kBT, where kBT is the thermal energy. In the power spectrum method, the frequency-dependent amplitude of positional fluctuations is computed, and data are fitted with the behavior of a thermal particle bound in a harmonic potential, which is a

Lorentzian function. The spectral roll-off frequency of the fit, fc = 1 (2πt0 ), where t0 is the relaxation time of the bead, can be used to obtain the trap stiffness through the relation κx = β/t0, assuming that the drag coefficient of the spherical particle, β = 6πηa, is known, where η is the viscosity and a is the radius. Finally, in the Stokes’ drag method, the trapped sphere is subjected to a constant fluid velocity, vx, and its displacement from the equilibrium position is measured. Flow is typically created by moving the piezoelectric stage holding the sample at constant velocity (for example, using a triangle wave). The dependence of the bead displacement, x, on vx has slope t0 = β/κx, from which κx can be obtained.

All three methods require a prior calibration of the PSD voltage, Vx,, as a function of x, the true displacement from the equilibrium position. In a configuration where the same laser beam is used both for trapping and position detection, the calibration of V(x) is typically achieved by scanning a bead immobilized on the coverglass surface across the laser beam, taking care to perform the scanning directly through the trap center. In 1D, the PSD response is well fit by the derivative of a Gaussian function [117], and from the linear, central, part of the profile the conversion factor from nanometers to volts, ξ, can be obtained. Alternatively, in 2D, the immobilized bead can be raster-scanned throughout the trapping area, and the resulting voltage profile can be fit with a 2D polynomial [85].

Although fairly straightforward to implement, these calibration methods generally require knowledge of the particle drag coefficient, which is influenced by its shape and the proximity of any nearby surfaces [91]. Alternatively, the power spectrum and Stokes’ drag calibration methods can be combined to yield experimental estimates for ξ, κ, and β for trapped particles of any shape. To do so, first the power spectrum of the Vx signal is computed, from which the roll-off frequency

~ 2 2 fc = 1 (2πt0 ) = κ x (2πβ) and the amplitude at zero frequency, Px = kBT /(κ x π fcξ ) ,

47 are obtained. Next, the Stokes’ drag method is used to find Vx vs. fluid velocity, v, yielding a linear relationship with slope s = β κξ. The last three equations are

2 ~ 2 ~ combined to yield κ x = 4kBT fc s Px , β = 2kBT s πP x , and ξ = 1 (2πsfc ), as

-1 -1 ~ functions of the experimentally measured parameters s (V nm s), fc (s ), and Px (V2 Hz-1).

3.6.2 Force calibration The calibration method just discussed may be applied immediately to the case of trapped, nonspherical particles in the OTW along directions transverse to the beam propagation direction (x, y). Because nonspherical particles do not bind to a surface in a unique orientation, the traditional method of scanning the beam diametrically across a stuck bead to obtain the volts-to-nanometers conversion factor poses problems with oblate ellipsoids or quartz cylinders. Instead, we performed x- and y-calibrations using the combined power spectrum Stokes’ drag method of the previous section: sample results for quartz cylinders are shown in Figure 3.7. The Stokes’ drag results display the expected linear relationships between Vx,y and vx,y, and the power spectra calculated from the x- and y-signals are well fit by Lorentzian functions with the parameters shown in the caption of Figure 3.7.

Careful calibration of the optical trap in the axial direction is, operationally speaking, the most important of all, because the OTW apparatus is mainly intended for the simultaneous application of torque and vertical loads. Calibration in the z- direction, however, involves different considerations compared to x-y [81]. First, the finite axial trapping depth restricts the range over which the Stokes’ drag calibration method can be performed. Second, when the sample chamber is moved vertically, an intensity modulation at the detector arises from interference between the forward scattered light and light reflected from the coverslip/solution interface, an effect that must be taken into account. Finally, motions of the sample chamber relative to the microscope objective will induce a focal shift that displaces the trap axial position [118]. Recent efforts aimed at addressing some of these limitations include the unzipping of a known DNA template to obtain a calibrated reference [112] or

48 performing back-scattered light detection (optionally, with spatial filtering) to reduce systematic errors [119, 120].

Figure 3.7 Calibration of the optical torque wrench using a quartz cylinder. (top) Calibrations of the linear dimensions. First, the power spectra for x, y and z signals were computed

and fit to Lorentzian functions, giving roll-off frequencies f c, x = 639 ± 1 Hz, f c, y = 631 ± 1 Hz f c, z =

~ -6 2 -1 ~ 147.2 ± 0.2 Hz, and zero-frequency amplitudes Px = (1.158 ± 0.003)×10 V Hz , Py = (1.148 ±

-6 2 -1 ~ -6 2 -1 0.003)×10 V Hz , and Pz = (2.382 ± 0.005)×10 V Hz . Next, linefits to Stokes’ drag

-6 -1 measurements in x and y (a, right inset) provided the slopes sx = (2.255 ± 0.008)×10 V s nm and

-6 -1 sx = (2.158 ± 0.008)×10 V s nm , which were combined with the power spectral results to yield

-1 -1 ξ x = 1 (2π s x f c, x )= 110 nm V and ξ y = 117 nm V . For the z signal, vertical scanning of a fixed cylinder (a, left inset) produced a record well fit by the derivative of a Gaussian (amplitude A = (1.395 ±

49 3 2 -1 0.006)×10 V nm, std. dev. σ = 708 ± 2 nm), from which we obtain ξ z = σ A = 359 nm V . These

−2 -1 measurements were combined to obtain the trap stiffnesses κ x = 4.5⋅10 pN nm ,

−2 -1 −3 -1 κ y = 4.1⋅10 pN nm , and κ z = 9.1⋅10 pN nm . (bottom) Calibration of torque. A procedure analogous to the linear x, y cases was carried out. From the experimentally measured values, fc,τ =

~ -4 2 -1 -2 -1 24.29 ± 0.05 Hz, Pτ = (5.04 ± 0.01)×10 V Hz , and sτ = (1.84 ± 0.03) 10 V s rad , the rotational

-1 drag coefficient ξτ = 1 (2π sτ f c,τ )= 0.37 rad V and the angular trap stiffness

2 ~ -1 κτ = 4 k BT f c,τ sτ Pτ = 264 pN nm rad were obtained. All power spectrum records represent averages from 50 measurements sampled at 66 kHz. For these measurements, the trapping laser power was ~20 mW (measured before entry into the objective rear pupil).

In our instrument, we performed z-calibrations of force and displacement using quartz cylinders by taking advantage of the stable orientation of these nanofabricated ~ particles within the trap. First, we obtained fc and Pz from the power spectrum of the z signal (Figure 3.7). Next, we impaled a trapped, vertically-oriented cylinder on the coverglass by adjusting the piezoelectric stage position until its base bound non- specifically to the surface. Vertical scanning of the piezoelectric stage while recording -1 Vz yielded the required voltage-displacement calibration factor, ξz (nm V ). Scanning a surface-bound cylinder axially is effective because the trap stabilizes the vertical orientation, contrary to the x-y case, where transverse scanning tends to tilt the

~ 2 2 particle. The axial stiffness is calculated as before, from κ z = k BT /(Pzξ π f c ) . Using spherical test beads, we have compared calibrations obtained by ‘parking’ the particle on the surface with previous methods, and obtained good agreement (data not shown).

3.6.3 Torque calibration Torque calibration may be carried out using methods that are entirely analogous to those used for spatial displacement [108]. In the OTW apparatus described here, the input polarization angle is automatically known (relative to some arbitrary reference), and is proportional to the EOM input voltage. A rotational Stokes’ drag method can therefore be implemented by periodically adjusting the EOM voltage such that the input polarization changes with a fixed angular velocity (ωθ). The power spectrum of

50 the torque signal voltage (Vτ) can also be readily computed. We therefore have used a combination of power spectrum and rotational Stokes’ drag techniques to obtain the torque signal volts-to-radians conversion factor, ξθ, the trap angular stiffness, κθ, and the rotational drag coefficient of the trapped particle, βθ. The experimental quantities measured were the slope of the Vτ vs. ωθ line, along with the roll-off frequency and zero-frequency amplitude of the angular power spectrum.

Figure 3.7 shows results from torque and force calibrations for a quartz cylinder. Fits of the various calibration signals to the expected functional forms are excellent, and the experimental parameters derived from such fits have uncertainties of less than 1%. For small displacements (<150 nm) and small angles (<20 degrees), the detector signals are linear. As anticipated, modest laser power (10-50 mW) is sufficient to provide tight confinement of particles translationally as well as rotationally, making it possible to exert transverse and axial forces in excess of 20 pN and 5 pN, respectively, and torques of at least 300 pN nm.

3.6.4 Implementation of an optical torque clamp An anisotropic particle trapped in a laser beam with fixed linear polarization will undergo rotational thermal motion whose amplitude depends on the angular trapping stiffness. In this ‘passive’ mode, the mean torque exerted by the trap on the particle is zero, and non-zero torques will develop only if the particle is forced to change its angular orientation, for example, when twisted by a molecular motor. While it is possible to study rotary biomolecular processes in the passive mode, data taken under more precisely defined conditions, such as under constant applied torque, can provide more specific information. A torque clamp is the rotary analog of a force clamp, which provides high-resolution data on molecular displacements [83]. We implemented a torque clamp mode by creating a servo loop that feeds the torque signal back into an external electronic circuit driving the EOM (Figure 3.8A). Although it may be possible to implement feedback control in computer software, we decided instead to employ a dedicated proportional-integral (PI) circuit that circumvents delays associated with computer interrupts. The analog PI controller is based on a single

51 operational amplifier (OP27, Analog Devices) that compares the input torque signal with a reference voltage and sends an output voltage proportional to this difference, stabilized by an integral filter that smoothes the response [121].

The torque clamp works for particles with either form or material birefringence. In the example shown in Figure 3.8B, an oblate particle is first trapped in the passive mode and then feedback mode is established, keeping the particle at constant (here, zero) torque. As the active mode is enabled, the r.m.s. value of the torque signal (τrms) decreases by 7-fold compared to the r.m.s. amplitude of thermal fluctuations in the passive mode, yielding τrms= 14 pN nm. The torque clamp has high bandwidth (~10 kHz) and is limited chiefly by the angular relaxation time of the particle under low Reynolds number conditions.

The restricted dynamic range of an EOM (±180°) constrains any simple servo loop in keeping the torque constant over multiple revolutions. To overcome this limitation, we included an additional circuit that monitors the EOM drive signal using a microcontroller (Arduino deicimila, Arduino, Italy). Once an angular threshold is reached, the microcontroller triggers an analog switch (AD7512, Analog Devices) that momentarily disables the feedback, flips the polarization by ±180°, and re-enables the servo loop (Figure 3.8A). The performance of this circuit is illustrated in Figure 3.8C, where rapid EOM voltage jumps are evident, but during which the torque signal reflects persistent clamp conditions. Because polarization reversals are completed within 10 µs, the bandwidth of the servo loop is unaffected.

52

Figure 3.8 Realization of a continuous torque clamp. (A) Schematic showing the signals and feedback loops used in the OTW. Constant torque is maintained by a servo loop that feeds the torque signal into a proportional-integral circuit controlling the EOM. An additional ‘feedback control’ circuit extends the dynamic range of the EOM to maintain constant torque over continuous rotations (see main text). (B) Demonstration of the torque clamp. In passive mode, the torque servo loop is disabled, and the signal reflects the rotational Brownian motion of an oblate trapped particle. At time t = 0 s, the servo loop is closed, clamping the torque at τ = 0 pN nm. (C) To clamp torque at non-zero values, the EOM drive signal (gray curve) flips by an amount value corresponding to ±180° once an angular threshold is reached. These rapid reversals (black arrows) are automatically executed by the feedback control circuit. A non-zero torque signal (green curve) remains constant over unlimited rotations.

53 3.7 Simultaneous application of force and torque using optical tweezers

3.7.1 Twisting single DNA molecules under tension The nanomechanical properties of DNA have been extensively studied at the single- molecule level using magnetic tweezers [122], but only recently using optical traps [123]. To demonstrate the capabilities of our calibrated instrument, we studied the supercoiling of single DNA molecules under tension. Nanofabricated quartz cylinders were tethered to a coverglass surface by a 2.1 kb segment of double stranded DNA (dsDNA) using standard protocols (Lang et al., 2004). Briefly, a dsDNA template was constructed with an array of six digoxigenin labels (spaced at 10 bp intervals) located at the 5′ end of one strand, and six biotin labels (similarly spaced) at the 5′ end of the complementary strand. Neutravidin-labeled quartz cylinders and template DNA molecules were incubated together at ~100 fM in phosphate buffer for several hours at 4°C. Next, the DNA-cylinder complexes were diluted in PEM80 buffer (80 mM Pipes, pH 6.9, 1 mM EGTA, 4 mM MgCl2) with 20 mg/ml BSA, introduced into a sample chamber where antibodies against digoxigenin had previously been adsorbed on the coverglass surface, and allowed to bind for 20 min at room temperature. A final wash with PEM80 removed unbound cylinders, and the sample chamber was then sealed and moved to the instrument for measurements. The use of multiple ligands at each end of the DNA molecule hinders free swiveling about the attachment points, creating a rotationally constrained tether, as illustrated in Figure 3.9. After a tethered bead was identified in the microscope, judging by the restricted Brownian fluctuations, it was captured using the trap and centered with the piezoelectric stage, such that its point of surface attachment was located directly below the trapped cylinder.

54

Figure 3.9 Supercoiling of a single dsDNA molecule. A 2.1 kbp dsDNA molecule was tethered to the coverglass surface and a quartz cylinder using multiple dig-antidig and biotin-neutravidin linkages, respectively, to prevent free swiveling at the ends. The DNA molecule was stretched with 3 pN force in the vertical direction, while being twisted at a rate of 0.5 turns/s (inset drawing). The vertical load was kept constant by a software-based PID feedback loop that controlled the piezoelectric stage position with a 20 Hz update rate. The records clearly display the plectonemic transition at σ = 0.05, and a direct measurement of the imposed torque. Data were collected at 5 kHz (extension, light red trace) and boxcar-averaged to 10 Hz (extension, red trace) and 0.5 Hz (torque, green trace).

The dsDNA tether was then subjected to vertical tension by lowering the piezoelectric stage until the quartz cylinder was displaced below the trap center by a specified distance, Δz, corresponding to a force Fz = –κz⋅ Δz, where κz is the axial trap stiffness. Then, the bead was rotated by ±180° and the corresponding torque signal was recorded. Negligible torque is expected to develop from the DNA during these initial half-turns at the forces used (2-10 pN). Therefore, any residual signal variations (arising, for example, from imperfections in the polarization optics) were taken as an average ‘background’ signal that was subtracted from subsequent data (modulo 2π). After acquisition of this background signal, the dsDNA molecule was twisted, typically at rates of 0.5 turn/s, while Fz was clamped by monitoring the PSDs sum voltage and adjusting the piezoelectric stage position as necessary. (Although this vertical force clamp does not take into account variations in the sum signal arising from interference as the coverglass is displaced, we estimate that these effects

55 introduce errors of less than 10% in Fz.) The effect of twisting dsDNA is shown in Figure 3.9, where the molecular extension and the torque developed are displayed as functions of the degree of supercoiling, σ = n/Lk0, where n is the number of turns and

Lk0 is the number of pitch periods spanned by the dsDNA molecule. Initially, the extension remains nearly constant until a torque τ ∝ n develops. After a characteristic number of turns, nb (corresponding to a torque for bending, τb), the energy required for further twisting of the DNA exceeds that for bending, and the molecule begins to buckle, exhibiting a sharp change in length as nb is reached. As further twisting proceeds, plectonemes are formed in the DNA, and the torque remains roughly constant as the extension of the molecule decreases linearly with n [124]. Because supercoiling involves close coupling between torque and force exerted on the DNA, the OTW setup is ideal to monitor and control both of these experimental parameters.

3.8 Conclusions

We have constructed an optical torque wrench capable of exerting simultaneous torque and force on micron-sized particles exhibiting either form or material birefringence. Compared to previous implementations, the instrument described here features improved mechanical and optical stability along with a simplified design. We presented procedures for the construction and calibration of the new instrument, along with detailed protocols for fabrication of appropriate birefringent particles. We anticipate that the methods presented here will find applications not only in biophysical studies, but in other fields, including colloid- and nano-engineering.

56 Chapter 4: A universal pathway for kinesin stepping

4.1 Abstract

Kinesin-1 is an ATP-driven, processive motor that transports cargo along microtubules in a tightly regulated stepping cycle. Efficient gating mechanisms ensure that the sequence of kinetic events proceeds in proper order, generating a large number of successive reaction cycles. To study gating, we created two mutant constructs with extended neck-linkers and measured their properties using single-molecule optical trapping and ensemble fluorescence techniques. Due to a reduction in the inter-head tension, the constructs access an otherwise rarely populated conformational state where both motor heads remain bound to the microtubule. ATP-dependent, processive backstepping and futile hydrolysis were observed under moderate hindering loads. Based on measurements, we formulated a comprehensive model for kinesin motion that incorporates reaction pathways for both forward and backward stepping. In addition to inter-head tension, we find that neck-linker orientation is also responsible for ensuring gating in kinesin.

4.2 Introduction

Kinesin-1 is a motor protein that proceeds unidirectionally towards the plus end of the microtubule in discrete, 8.2-nm steps [125] by alternately advancing each of its two heads, walking in an asymmetric, hand-over-hand fashion [89, 126, 127]. Kinesin motion is remarkably processive, with single motors typically taking ~100 steps before detaching from the microtubule [128]. The processivity and thermodynamic efficiency of kinesin-1 arise from a coordinated mechanochemical cycle in which a single ATP molecule is hydrolyzed per mechanical step [129-131]. Deviations from that cycle, such as those resulting in backsteps towards the microtubule minus end, occur only rarely, or in response to external loads that approach or exceed the stall force [132]. Therefore, the kinesin molecule must employ gating mechanisms to coordinate its catalytic heads and move efficiently [133].

57 Mechanical strain developed within the kinesin molecule is thought to underlie the mechanism by which kinesin gates the enzymatic activity of its heads [134-136]. Within the crystal structure of the kinesin dimer [60], the microtubule-binding domains of the twin heads are separated by ~5 nm. When both heads bind strongly to the microtubule, they become separated by a distance corresponding to the tubulin- dimer lattice spacing of 8.15 nm. Substantial inter-head tension is consequently thought to be developed between the heads via the neck-linker regions: molecular dynamics simulations suggest that 15–35 pN of tension may be produced [63, 137]. There are two competing models explaining the roles that tension and conformational changes domains play in gating. Generally speaking, front head-gated models propose that tension reduces the binding affinity of the front head for ATP until the rear head has detached from the microtubule [135, 138, 139]. Rear head-gated models propose that tension from the front head accelerates the detachment of the rear head [136, 140, 141]. These models are not mutually exclusive, and kinesin may utilize both mechanisms to maintain coordination during processive stepping. Loss of coordination between the heads can lead to conformational states that promote detachment from the microtubule, backward steps, and/or futile hydrolysis cycles. Investigations into the prevalence of backward steps near the stall force [142] and beyond [143] have demonstrated that ATP binding, but not necessarily hydrolysis, is required to backstep. Various kinetic models have been advanced to explain this process [143-145], but the rate equations implied by such models have not yet been shown to describe quantitatively the detailed data available from single-molecule studies, such as velocities under load, ratios of forward to backward steps, and randomness parameters.

The neck-linker consists of a short, largely unstructured ∼14 amino acid sequence that connects each of the kinesin heads to the common stalk, and it has been implicated in the thought to drive motility [65]. To better understand gating mechanisms and kinetics in the kinesin enzymatic cycle, we lengthened the neck-linker, introducing six additional amino acids with a net neutral charge (AEQKLT) into the C-terminal portion of the linker region in a truncated

58 construct based on the human kinesin heavy chain, expressed in bacteria. When hindering loads were applied to this construct (Kin6AA) in a single-molecule optical- trapping assay, the motion was found to consist of an admixture of forward and backward steps, in a proportion that was strongly force dependent. Essentially identical results were obtained with a construct carrying a 9-residue insert with 6 adjacent prolines in its linker (Kin6P). In contrast to wild-type (WT) kinesin, the stall force of the mutant constructs varied greatly with the ATP concentration, and the average velocity smoothly reversed and became negative as the hindering load was increased beyond stall. Comparisons of data from the mutant and WT kinesin molecules led to the development of a unified, five-state minimal kinetic model that accounts quantitatively for both forward and backward stepping by kinesin.

4.3 Results

4.3.1 Kin6AA moves backwards processively The stepping dynamics of Kin6AA were studied using an optical force clamp, which employs feedback to servo the optical trap to a fixed distance from the bead center, maintaining constant force, of either sign, during subsequent motion [77, 84]. Representative displacement records for Kin6AA under different loads are presented in Figure 4.1A. The traces display a striking difference from those obtained with WT kinesin with respect to the frequency of backstepping. Whereas WT kinesin backsteps only rarely, with 2–4% probability when subjected to ~3 pN hindering load [131, 142, 143, 146], Kin6AA backsteps ~20% of the time under comparable forces. The prevalence of backsteps in the mutant gives experimental access to kinetic states that are too rare or too transient in the WT for practical study.

The differences between Kin6AA and WT kinesin became more dramatic as load was increased. At forces approaching stall with WT kinesin, processivity is lost and motors typically display small numbers of forward and backward steps before detaching from the microtubule [142]. By contrast, Kin6AA motors approaching stall remained bound to the microtubule while undertaking numerous forward and backward steps with equal probability, leading to a large mean-squared displacement

59 but no net progress (Figure 4.1A, red trace). As the force was increased beyond stall, Kin6AA began to step rearwards processively, with a slow velocity that was strongly dependent upon the ATP concentration, but comparatively insensitive to load (Figure 4.1B and Figure 4.2A). The velocities for processive backstepping were broadly consistent with rates previously measured for WT kinesin subjected to super-stall loads [143], supporting the notion that backsteps in Kin6AA and WT kinesin arise from a common molecular mechanism. The backward step size for Kin6AA averaged 8.12 nm, indicating that the motor accesses the same microtubule binding sites as during forward stepping (Figure 4.1B, inset). In contrast to one study that employed much longer inserts in the neck-linker [136], steps that were integral multiples of the 8 nm spacing were not prevalent for Kin6AA. Although the velocity data (Figure 4.1B) displayed ATP dependence suggestive of Michaelis-Menten kinetics, these and other single-molecule data (Figure 4.1 and Figure 4.2) were globally fit to a more detailed five-state model.

Figure 4.1 Single-molecule records and backstepping velocity for Kin6AA. (A) Representative traces obtained under constant force at loads of −3 pN (gray), −4 pN (red), and −7 pN (blue), at 2 mM ATP. Light traces are unfiltered, darker traces are median-filtered. The records show clear 8-nm forward and backward steps.

(B) Double-log plot of backstepping velocity vs. ATP concentration under −7-pN load (black dots; mean ± s.e.m.; N = 21−62). The solid line (red) shows the global fit to all single-molecule data for the model described in the text. Inset, histogram of the backward step size at a −7-pN load for all ATP concentrations (8.12 ± 1.72 nm, mean ± s.d., N = 1,906) and Gaussian fit (red line), centered at 7.97 nm.

60 4.3.2 The KIN6AA stall force is ATP-dependent The neck-linker insert exerted a substantial effect on the stall force. In contrast to WT kinesin, the stall force for Kin6AA depended sharply upon the ATP concentration, as evidenced by plots of the velocity and forward/backward step ratio (Figure 4.2A-B). Here, a stall was operationally defined as either the force where the mean velocity, v, dropped to zero or the force where the ratio of forward to backward steps (the step ratio, SR) became unity. These metrics were mutually consistent (Figure 4.2A-B), with v = 0 and SR = 1 occurring at the identical force for each ATP concentration.

4.3.1 The randomness constrains possible models In addition to v and SR, we computed the randomness parameter, r, which is a statistical measure of the regularity of steps [131, 147-149]. For a clock-like process with identical stepping times, r = 0. A Poisson process with exponentially distributed times (and no backsteps) produces a value of r = 1. The reciprocal randomness, r-1, has been used to distinguish between competing kinetic pathways for kinesin [131, 150]. In the case of an unbranched kinetic cycle, the maximal value of r–1 supplies the minimum number of rate-limiting transitions. In practice, distributions of dwell times can vary enormously for different kinetic models with otherwise identical cycle times, requiring a metric such as randomness to differentiate among them [151]. A plot of r–1 versus load for two different ATP concentrations is shown in Figure 4.2C. Because r–1 is proportional to the mean velocity, the randomness value changes sign and crosses the abscissa at stall.

4.3.1 Mechanochemistry: The forward stepping pathway Five states proved necessary to account for the range of single-molecule data acquired in these experiments. The data (Figure 4.1 and Figure 4.2) were globally fit by a model that incorporates explicit reaction pathways for both forward and backward steps. A block diagram of the kinetic scheme, together with the molecular configurations presumed to correspond to these states, is shown in Figure 4.3. The pathway begins at an arbitrary starting point, labeled State {1}, which represents the so-called ‘ATP waiting state’ [152-154]. At low ATP concentrations, WT kinesin

61

Figure 4.2 ATP- and load-dependent bi-directionality of Kin6AA. Solid lines (red) show the global fits to all single-molecule data for the model described in the text.

(A) Velocity, v (mean ± s.e.m.) vs. force for 2 mM ATP (blue circles; N = 25−164) and 10 µM ATP (green squares; N = 18−74). Stall occurs where the fit data cross the horizontal dashed line (grey) at v = 0.

(B) Step ratio, SR (mean ± s.e.m.; ratio of number of forward to backward steps) vs. force at 2 mM ATP (blue circles; N = 264−3,331), 10 µM ATP (green squares; N = 235−1,412), and 2 µM ATP (purple diamonds; N = 90−368). Stall occurs where the fit data cross the horizontal dashed line (grey) at SR = 1.

(C) Reciprocal randomness, r-1, (mean ± s.e.m.), color-coded as in (A). Note that the fit data cross r-1 = 0 at the stall forces for the data in (A).

62 is found predominantly in this state, where the leading head is without nucleotide and strongly bound to the microtubule, while the trailing head, carrying ADP, remains detached from the microtubule [152], or is perhaps transiently (weakly) associated [154, 155]. Because Kin6AA carries an extended linker designed to relieve inter-head tension, it is possible, in principle, for its trailing head to bind and unbind the microtubule transiently from this state, provided that this conformation is not excessively prone to releasing its bound ADP. This characteristic permits State {1} to serve a common starting point for both forward and backward step cycles. The choice of a common starting point is consistent with a Markov property of stepping, which was confirmed experimentally: the probability of a step in any direction is uncorrelated with the direction of the preceding step (Figure 4.4). In the forward- stepping pathway (Figure 4.3B, yellow), ATP binding to the leading head advances the motor from State {1} to State {2}. Next, a largely irreversible, load-dependent forward step occurs between States {2} and {3} as [156] the leading and trailing heads swap positions and ADP is released. The motor returns to State {1} and completes its cycle after subsequent ATP hydrolysis followed by Pi release. Both here and elsewhere, multiple biochemical transitions occurring in rapid succession have been lumped into single states to form a minimal model. Similar, unbranched reaction pathways for forward steps have been proposed [157] based on the available mechanochemical, biochemical, and structural data, and an analogous 3-state cycle was used to model single-molecule data [150]. However, these pathways do not account for backstepping and futile hydrolysis.

4.3.2 Mechanochemistry: The backward stepping pathway. Unlike forward steps, backward steps may be completed following alternative, branched kinetic paths (Figure 4.3B, orange). Beginning from State {1}, two general properties must be satisfied to generate a successful backstep. First, the trailing head must be able to bind the microtubule to generate a two-heads-bound state, leading to release of ADP from the rear head. Second, the backward cycle must incorporate an ATP binding event to account for the ATP dependence of processive backstepping (Figure 4.1B). In the model, reversible ATP binding can occur in two ways: either

63 prior to the rear head binding the microtubule, following the sequence {1}→{2}→{5}→{1}, or afterwards, following the sequence {1}→{4}→{5}→{1}. The existence of alternative backstepping pathways results in a forward/backward step ratio exhibiting ATP dependence (Figure 4.2B). Unbranched cycles, which lack this property, have been proposed to explain the much weaker ATP dependence of the step ratio for WT kinesin [143, 144], which, in the context of this model, predominantly follows the sequence {1}→{2}→{5}→{1}. From State {5}, which is a state unique to the backstepping pathway, we propose that ATP hydrolysis by the front head leads to a weakly-bound ADP state and head detachment, and thereby promotes backstepping, leading to a return to State {1}.

4.3.1 Inclusion of futile hydrolysis The model also incorporates a pathway for futile hydrolysis, where ATP binds the trailing head, following the sequence {4}→{3}→{1} (Figure 4.3B). Absent such a pathway, the only route of departure from State {4} is via an obligatory backstep, which has a maximal rate of ∼3 s–1 under saturating ATP conditions (Figure 4.1B). Without futile hydrolysis, the slow backstepping rate would result in extended dwell times, yielding small values of r–1 at low forces, which were not observed (Figure 4.2C). The inclusion of a futile hydrolysis cycle leads to an accurate fit of the randomness data. Direct evidence for futile hydrolysis by Kin6AA is provided by the ensemble ATPase data, where the measured rate of ATP hydrolysis was 143 s-1 molecule–1 (Figure 4.5). Because the unloaded velocity of Kin6AA is 40 steps s–1 under saturating ATP conditions, an average of 3.5 ATP molecules are hydrolyzed per forward step. Futile hydrolysis is suppressed in the WT, leading to greater efficiency and ~1 ATP per forward step [129-131].

64

Figure 4.3 Model for stepping by kinesin dimers. Model showing forward stepping, backward stepping, and futile hydrolysis pathways. See text. (a) Left, the numbers assigned to each of the five states. The molecular configurations of the kinesin dimer on the microtubule thought to correspond to each of the states are illustrated, along with any nucleotides bound. No particular docking state of the neck-linker is implied in this diagram. Kinesin heads are color-coded (red, blue). Starting from State {1} (middle row), forward steps are accomplished by ascending the diagram; backward steps by descending. (b) Reaction diagram for the model, displaying the transition rates among states. Load- and ATP-dependent transitions are indicated. Three main pathways are shaded: forward stepping (yellow), backward stepping (orange), and futile hydrolysis (light green). Largely irreversible transitions between states that produce ±8-nm displacements are shown (green arrows). In this minimal model, fast transitions occurring in rapid succession were combined to generate composite states in several instances. Note: The transition from State {4} to State {3} in the futile hydrolysis pathway involves ATP binding to the rear head, but, unlike the stepping pathways, heads do not swap positions and no step is taken.

65

Figure 4.4 Lack of memory for successive steps.

The estimated probabilities for taking a forward step or a backward step are given by P+ = n+/(n+ + n−) and P− = n−/(n+ + n−), where n+ and n− are the numbers of positive and negative steps scored at any given force and ATP concentration, respectively. The probability of observing two backward steps in succession will be given by P− − = n− −/(n+ + + n− − + n+ − + n− +), where the nij represent the numbers of pairs of successive forward steps (++), pairs of successive backward steps (− −) , or pairs consisting of a step in each direction (+ −, − +). From these expressions, it follows that P+ − = n+ −/(n+ + + n− − + n+ − + n− +)

2 (A) The ratio of (P−) to P− − as a function of load. When successive steps are uncorrelated (zero memory), this ratio will tend to unity, since P− − will simply equal the probability of taking a single backward step, P−, times the probability of taking another, statistically independent backward step, P−. The experimentally determined ratio is statistically consistent with unity for all forces and ATP concentrations, demonstrating that steps have no memory of the preceding step direction (Markov property).

(B) Analogous reasoning applies to the forward steps. The ratio of (P+ ⋅ P−) to P+ − as a function of load. As in (A), the ratio is unity for uncorrelated steps.

66

Figure 4.5 The ATPase rate per dimer for KinWT and Kin6AA. The plot shows the MT-stimulated ATPase rates for KinWT (red filled circles; mean ± s.e.m.; N = 3) and Kin6AA (purple filled circles; mean ± s.e.m.; N = 3) as a function of the MT concentration. The solid lines represent fits to the standard Michaelis-Menten expression. KinWT has an ATPase rate of -1 102 ± 4 s per dimer and a K0.5, MT of 82 ± 14 nM. This is in contrast to Kin6AA, which has an ATPase -1 rate of 143 ± 6 s per dimer and a K0.5, MT of 38 ± 8 nM, roughly half that of KinWT. Under unloaded conditions, the average velocity of KinWT is 762 ± 7 nm s-1; Kin6AA is slower, averaging 323 ± 4 nm s-1. Assuming an 8 nm step size, these velocities imply head-stepping rates of 95 s-1 and 40 s-1 for KinWT and Kin6AA, respectively. The very similar values for ATP-hydrolysis and mechanical- stepping rates for KinWT (102 s-1, 95 s-1) imply that ATP hydrolysis is coupled 1:1 to motion. However, for Kin6AA (143 s-1, 40 s-1) the rate of ATP hydrolysis is significantly greater than the head- stepping rate, suggesting that, on average, multiple ATP molecules are hydrolyzed per 8-nm advance by this motor. This inefficiency is likely to be a consequence of futile hydrolysis, although some backstepping may contribute.

Analytical expressions for the velocity, randomness, and step ratio were developed from the cycle of Figure 4.3B following the approach of Chemla et al.

[149]. Equations for v, r, and SR in terms of transition rates between the states, kij, and the ATP concentration are found in the methods section. A global fit to the data (Figure 4.1 and Figure 4.2) was carried out to determine all transition rates. The three

transition rates that involve taking a forward step (k23) or rebinding the rear head to the

microtubule during a backstep (k14, k25) were found to carry load dependence and were

modeled by Boltzmann expressions, = exp , where δij is a 0 푘푖푗 푘푖푗 �퐹δ푖푗⁄푘퐵푇�

67 characteristic distance. This distance was a free parameter in the fits. Values for the rates and distances are found in Table 4.1. We note that a state where both heads bind ATP and remain bound to the microtubule was not included in the model. The existence of such a state would introduce one additional pathway for futile hydrolysis as well as one for backstepping, increasing the model complexity but without adding any new observable features. Additional states or transitions can always be added, in principle, but the sequence of Figure 4.3 is a minimal scheme that effectively captures the experimental data for processive stepping. We have not, however, modeled any branching reaction paths that lead to loss of processivity through head release and microtubule dissociation.

4.3.2 Ensemble experiments Results from fits to the model in Figure 4.3 supply predictions about molecular configurations and transitions between states. To test such predictions independently, we performed ensemble kinetic experiments using a stopped-flow fluorimeter. One of the key features distinguishing the present model from earlier representations of the kinesin cycle is State {4}, where both heads bind the microtubule in rigor. It has long been known [158] that kinesin dimers labeled with a fluorescent ADP analog will release just one ADP molecule upon binding the microtubule, while release of the second ADP requires the further addition of ATP [158, 159]. However, when Kin6AA with 2′−deoxy 3′−mant ADP (2′dmD) bound was rapidly mixed with microtubules, both bound nucleotides were released together (Figure 4.6). This finding supports a two-heads-bound state. The simultaneous release of both nucleotides, with consequent support for a two-heads-bound state, was previously reported by Hackney and coworkers for a different mutant construct that also carried an extended neck-linker [160].

68

Table 4.1 Kinetic parameters for Kin6AA, measured and fit. Para- Description Global fit value Ensemble Comment meter for model measurement

–1 –1 –1 –1 k12, ATP binding rates to 3.7 ± 0.5 µM s 2.6 ±0.3 µM s ATP binding rate, a k45 front head average of both heads

–1 –1 k43 ATP binding rate to rear 4.0 ± 0.8 µM s ND Transition leading to head futile hydrolysis

–1 –1 k21, ATP dissociation rates 68 ± 10 s 55−135 s ATP dissociation rate,

k54 from front head average of both heads a,b –1 k34 ATP dissociation rate 12 ± 7 s ND ATP unbinding rate from rear head from read head

–1 k23(F) Forward step and ADP 570 ± 90 s ND Load-dependent step release transition; value for F = 0

δ23 Characteristic distance 4.3 ± 0.2 nm ND Transition distance for k23(F) leading to a forward step –1 –1 c k31 ATP hydrolysis, Pi 57 ± 5 s 79 ± 4 s Head dissociation rate release, and dissociation of the rear head –1 k51 ATP hydrolysis, Pi 6.5 ± 0.4 s ND ATP hydrolysis and release, front head backstep –1 –1 k14(F), Rates for rear head 14 ± 3 s 11 ± 4 s Load-dependent head c k25(F) rebinding to microtubule rebinding rates value for F = 0

δ14, Characteristic distances –1.0 ± 0.2 nm ND Transition distance δ25 for k14(F), k25(F) leading to a backward step or futile hydrolysis Ensemble values were derived from afit to 2′dmT data, initial exponential increase (Figure 4.8B) and cfit to the concentration dependence of initial TMR decay (Figure 4.8C). Rates that describe comparable b processes (k12 and k45, k21 and k54, k14 and k25) were set to be equal during global fitting. The range of values for the ATP dissociation rate constant based on ensemble measurements was calculated as described in the methods section. ND, Not Determined.

69

Figure 4.6 2′dmD release from KinWT and Kin6AA in the presence of MTs. (A) The rate of 2′dmD release was measured by rapidly mixing KinWT (pre-incubated with equimolar amounts of 2′dmD) with MTs and 2 mM ATP, or MTs without ATP. When KinWT is mixed with MT without added nucleotide, the fluorescence amplitude is 66% of the amplitude in the presence of MTs and 2 mM ATP. (B) When the same experiment is performed with Kin6AA, mixing the motor with MTs without added nucleotide results in a fluorescence amplitude change that is 99% of the amplitude change experienced with the addition of 2 mM ATP.

4.3.3 Two-heads-bound state studied using TMR Further structural and kinetic evidence for State {4} came from steady-state and kinetic ensemble experiments employing tetramethylrhodamine (TMR) labels (Figure 4.7). TMR dyes were covalently linked to a cysteine residue introduced at amino-acid position 333, in the middle of the neck-linker, in both Kin6AA and KinWT constructs (cys-light versions of human kinesin-1). TMR dyes positioned in sufficiently close proximity [161] (~1 nm) interact in an orientation that quenches fluorescence. We had previously shown that separation of these dyes occurs when WT kinesin takes a forward step, and results in a large fluorescence enhancement [135]. Previous experiments with kinesin have shown that both motor domains bind tightly to the microtubule in the presence of the non-hydrolyzable analog, AMP−PNP [162]. TMR- labeled KinWT produced a large fluorescence signal when incubated with AMP−PNP and microtubules (Figure 4.7A), indicating that its neck-linkers separate when the motor binds the microtubule. An intermediate-level signal was measured for KinWT in the absence of nucleotide, however, indicating a closer average neck-linker

70

Figure 4.7 Fluorescence data for Kin6AA and KinWT. Data for constructs with TMR probes attached to both neck-linkers. (A, B) Steady-state TMR fluorescence emission spectra for KinWT (A) and Kin6AA (B)), which monitors neck-linker separation under the following conditions: microtubules plus 2 mM AMP−PNP (red), microtubules plus apyrase to remove nucleotides (black, dashed), and 2 mM ADP without microtubules (blue). The large signal increase in the absence of nucleotide (apyrase present) for Kin6AA is consistent with neck-linker separation. In the inset cartoons, approximate locations of the TMR probes (at position 333) are indicated (yellow circles), as well as the neck-linker inserts (blue lines). (C, D) Pre-steady-state TMR kinetic records for KinWT and Kin6AA. TMR-labeled motors complexed to a five-fold excess of microtubules and treated with apyrase were mixed with 2 mM ATP. The initial increase in fluorescence seen for KinWT is absent for Kin6AA, indicating that prior to mixing with ATP, both heads of Kin6AA are bound to the microtubule, and consequently, the neck-linkers of this mutant are separated.

71 separation. This finding is consistent with a single head being strongly bound to the microtubule while its partner remains tethered, or alternatively, with an admixture of singly- and doubly-bound head states [162, 163]. By contrast, Kin6AA not only permits neck-linker separation on microtubules in the presence of AMP−PNP, but also in the absence of nucleotide (Figure 4.7B).

Transient-state kinetic studies of KinWT and Kin6AA (Figure 4.7C-D) also support the existence of a two-heads-bound state. TMR-labeled KinWT or Kin6A were complexed with an excess of microtubules and rapidly mixed with ATP. When this procedure was performed using KinWT, a rapid initial rise in fluorescence was observed, followed by a slower exponential fall (Figure 4.7C). The initial increase reflects the separation of the neck-linkers, and its kinetics are consistent with ATP- induced forward stepping [135, 155]. The subsequent decay occurs in two phases. The faster phase constitutes 80−85% of the total amplitude of the decay phase, and it has kinetics consistent with the dissociation of the new trailing head from the microtubule to regenerate a singly-attached species. That species consists of a strongly-bound leading head and a trailing head that is unbound and mobile, or possibly in an admixture of unbound and weakly-attached states that interconvert. The slower phase has kinetics consistent with the subsequent dissociation of the motor from the microtubule, because this phase is absent when the experiment is repeated in low ionic-strength buffer [135]. The data also suggest that the TMR dyes are in rapid equilibrium between quenched and unquenched states prior to the addition of ATP, as anticipated for a motor in a one-head, strongly-bound state. Notably, the trace for Kin6AA (Figure 4.7D) lacked any initial rising phase, indicating that prior to ATP binding, its neck-linkers were fully separated. Combined with the finding that both heads are nucleotide-free in this state (Figure 4.6), this result suggests that both heads are bound to the microtubule in rigor. After a delay of ∼2 ms, fluorescence was quenched at an initial rate that depended upon ATP concentration. Fitting the concentration dependence of this decay to a hyperbola generates a curve with a y- intercept of 11 ± 4 s–1 (Figure 4.8), which we interpret as the rate at which the trailing head rebinds the microtubule.

72

Figure 4.8 Binding of 2′dmT to Kin6AA. (A) A complex of Kin6AA and microtubules was pre-formed and mixed in a stopped-flow apparatus with 2′dmT. The resulting fluorescence signal (red) consisted of three sequential phases: a first phase of increasing fluorescence, a lag phase, and a second phase of increasing fluorescence. Fitting this signal required three exponential terms (black curve). Two terms, corresponding to the phases of increasing fluorescence, were associated with rate constants of 81.5 ± 21.0 s−1 and 3.0 ± 0.1 s−1. The third term was associated with a low-amplitude, decreasing phase, consistent with a lag, and a rate constant of 55.6 ± 24.8 s−1. The same experiment in the absence of microtubules (grey) produced a fluorescence increase

with a single exponential phase with a rate constant of 45.0 ± 1.0 s−1. Inset: Fractional amplitude of the first phase vs. [2′dmT]. (B) Rate constant for the first phase of fluorescence increase vs. [2′dmT]. Data (black dots; mean ± s.e.m.) were fit to a hyperbola (red curve) that extrapolates to 61 ± 12 s−1 at zero

[2′dmT] and is associated with a second-order rate constant of 2.6 ± 0.3 µM−1 s−1. Inset: Rate constant for the second phase of fluorescence vs. [2′dmT], which averages 3.0 ± 0.4 s−1 (red line) (C) Rate of initial decay of TMR fluorescence as a function of [ATP], compared to the rate of the lag phase in (A). Data (mean ± s.e.m.; N = 18−35; red dots) were fit to a rectangular hyperbola (black curve); the asymptotic rate at saturating ATP was 90 ± 4 s−1. The y-intercept of the fit at 11 ± 5 s−1 is interpreted as the rate at which a head rebinds to the microtubule. Rate constant for the lag phase vs. [2′dmT] (mean ± s.e.m.; N = 10−20; blue squares).

73 4.3.4 Binding of a fluorescent ATP analog suggests Kin6AA is gated We monitored the binding of 2′−deoxy 3′−mant ATP (2′dmT) to investigate the binding and release of ATP to the heads. FRET between intrinsic tryptophan residues (in the motor domain and microtubule) and the mant fluorophore in 2′dmT produces fluorescence when binding occurs. Figure 4.8A displays the signal produced when Kin6AA was complexed with an excess of microtubules and rapidly mixed with 2′dmT in the stopped-flow spectrophotometer. The fluorescence changes progress in three phases. A rapid initial increase could be fit to a single exponential process, with a rate constant that displayed a hyperbolic dependence on 2′dmT concentration (Figure 4.8B). Next came a brief lag phase, followed in turn by a second, slower exponential increase with a rate constant of ∼3 s–1 that displayed little 2′dmT concentration- dependence (Figure 4.8B, inset). Both phases of increasing fluorescence were of similar magnitude for all 2′dmT concentrations (Figure 4.8A, inset). These results suggest that nucleotide binding occurs sequentially to the two heads when these are bound to the microtubule. This interpretation is bolstered by the observation that mixing Kin6AA with 2′dmT in the absence of microtubules produces a rapid increase in fluorescence consisting of a solitary phase, with amplitude similar to that in the presence of microtubules (Figure 4.8A, grey). Furthermore, the rate constant associated with the lag phase (Figure 4.8C, blue) closely matches the corresponding rate constant for dissociation of the trailing head, as measured by the TMR transient (Figure 4.8C, red). Because both TMR- and 2′dmD-release experiments indicate that Kin6AA starts from a two-heads-bound state prior to addition of nucleotide (State {4}), the results from this experiment imply that the Kin6AA heads continue to be gated, despite any possible reduction in inter-head tension due to the neck-linker extension.

4.3.5 Additional tests of the model All rates and load dependencies for the five-state model were determined by a global fit to the single-molecule data for the backward velocity, step ratio, and randomness as functions of load and ATP concentration for Kin6AA (Figure 4.1, Figure 4.2 and Table 4.1). In all, ten parameters were fit. Direct, independent measurements of four

74 of these rates were obtained from the ensemble kinetic measurements of Kin6AA, and these were in close agreement with the globally fit values (Table 4.1). In addition, the single-molecule dataset for the unloaded forward velocity of Kin6AA as a function of ATP was not used to fit the parameters of the model. The model should therefore predict this function independently, with no adjustable parameters: the agreement between the data and prediction was excellent (Figure 4.9).

Figure 4.9 An independent test of the five-state model. The graph shows the unloaded velocity of forward stepping for Kin6AA as a function of ATP concentration. The experimental data (blue filled circles; mean ± s.e.m.; N = 8−179) are displayed together with the prediction of the five-state model (red solid line) using the rate constants of Table 4.1. The forward velocity values represent an independent dataset, because these were not used as a part of the global data for the model fit that generated the rate constants of Table 4.1. There are therefore no adjustable parameters involved in modeling the data shown here.

4.4 Discussion

4.4.1 Neck-linker orientation also gates kinesin Although an extended neck-linker is thought to mitigate the effectiveness of strain- based gating mechanisms [136, 160], our results clearly indicate that Kin6AA is still well gated, and therefore support the notion that there is more to gating than the tension exerted between heads [136, 152]. The 2′dmT binding data reveal that even

75 when both heads bind the microtubule, nucleotide binding is sequential. The rates fit to the five-state model also show that heads maintain excellent coordination. From the data in Table 4.1, the average rate of ATP hydrolysis by the trailing head is nearly 9- fold faster than the corresponding rate for the leading head. Similarly, the model predicts that the average rate of ATP unbinding is almost 6-fold faster in the front than the rear. The picture that emerges is that when the neck-linker is in its forward (docked) orientation, ATP hydrolysis is fast and ATP unbinding is slow. Conversely, when the neck-linker is in a rearward orientation, ATP hydrolysis is slow and ATP unbinding is fast. In effect, some conformational change associated with neck-linker docking (or simply orientation) ‘locks’ ATP in place in the rear head and efficiently hydrolyses it before ATP tightly binds to the front head. We emphasize that this gating mechanism does not require substantial inter-head tension to function, and is most easily understood in a two-heads-bound state, where the neck-linker of the trailing head is free to dock, but the neck-linker of the leading head is restricted from so doing, because it is oriented backwards (i.e., unfavorably) by the trailing head.

Such a mechanism is fully consistent with a model conjectured previously to explain gating in WT kinesin at low ATP concentrations, where only one head is generally bound [152]. It is also consistent with the kinetics of 2′dmT binding to Kin6AA (Figure 4.8), as compared to KinWT [135]. The binding of 2′dmT to Kin6AA occurs in two steps, with similar amplitudes that are separated by a lag (Figure 4.8A). The kinetics of the lag (Figure 4.8C, blue) strongly suggests that it corresponds to the dissociation of one of the two heads, as monitored by TMR fluorescence (Figure 4.8C, red). This result implies that binding of 2′dmT to the second head can only occur after dissociation of the first head, and the concomitant reduction of any inter-head tension imposed by microtubule binding. In Kin6AA, the reorientation of the head with a lengthened neck-linker (in the absence of any external load) is a comparatively slow process, (~3 s-1, Figure 4.8B inset) and it is this process, and not the relief of inter- head tension, per se, that gates ATP binding. We had previously noted that in KinWT, by contrast, the change in neck-linker orientation associated with head repositioning is at least two orders of magnitude faster [155]. We therefore propose that it is the

76 orientation of the neck-linker, and not inter-head tension, that forms the basis for gating in kinesin. This proposal is supported by recent single-molecule and ensemble- fluorescence measurements [155] indicating that the gating of ATP binding to the leading head requires neck-linker separation, but does not require strong binding of both heads to the microtubule. It is also supported by results showing that in the ATP- waiting state, the trailing head carrying ADP is mobile and free of the microtubule [152], and therefore unable to exert substantial tension on the leading head. A neck- linker orientation-based gating mechanism can explain the large processivity of native kinesin, even under force [164], since it reduces the probability of ATP hydrolysis until a mechanical step has been completed.

When kinesin binds a non-hydrolyzable ATP analog, such as AMP−PNP or

ADP−BeFx, its motion becomes arrested, and an obligatory backstep becomes necessary to unbind the analog before allowing any forward motion to continue in the presence of ATP [138]. It was concluded that the analog could only be released from the leading head, and not the trailing one, necessitating a backstep to interchange head positions whenever the (former) trailing head bound analog. Because such analogs are preferentially released from the leading head, these results were interpreted as evidence for front-head gating. Our results are fully consistent with that interpretation, since the predicted rate of nucleotide unbinding is almost six-fold faster in the leading than the trailing head. Therefore, a backstep should efficiently release the bound nucleotide. Although inter-head tension was invoked to explain why the front head had a reduced nucleotide affinity, we note that these findings are equally consistent with a mechanism involving gating through neck-linker orientation.

A previous study of kinesin mutants with a series of neck-linker extensions was carried out by Yildiz et al. [136]. In that work, 2−26 additional prolines were inserted into the neck-linkers of kinesin, including one mutant with an extra six prolines, and the behavior was characterized by single-molecule, optical trapping assays. It was discovered that the neck-linker mutants moved uniformly slower along microtubules than wild-type kinesin, but that their velocities could be increased substantially via the application of assisting load. Based on this property, it was

77 conjectured that additional inter-head tension, due to ATP-induced neck-linker docking, increased the rate of rear-head detachment and was largely responsible for coordination between the heads. To compare directly with our results, we prepared an analogous construct with six additional prolines (nine extra amino acids), identical in linker sequence to one of the mutants studied by Yildiz and coworkers. We confirmed that this construct stepped backwards processively in the presence of ATP, at a velocity comparable to Kin6AA, for loads beyond stall (Figure 4.10). Kin6AA and the six-proline construct displayed similar unloaded run lengths (Figure 4.11). High processivities are predicted by the model, since the mutants spend a greater portion of the reaction cycle with both heads attached to the microtubule, which reduces the chance of detachment from a one-head-bound state. Based on our results, we would interpret the decrease in velocity for the neck-linker mutants to be a consequence of their increased propensity to enter a doubly-bound state on the microtubule, rather than to a large modulation in the rear-head detachment rate, especially under hindering loads. The only escape from a doubly-bound state (Figure 4.3B) is via futile hydrolysis or a backstep, both of which act to decrease the velocity and efficiency. The application of an assisting load decreases the probability that the trailing head will bind tightly to the microtubule, due to the force dependence of the rebinding rates (k14, k25), which effectively increases the average velocity: this supplies an alternate explanation for the earlier results, but without invoking inter-head tension as a gating mechanism.

The minimal (five-state) reaction cycle for kinesin stepping presented here can account successfully for a variety of single-molecule and ensemble kinetic measurements. It incorporates explicit pathways for both forward and backward stepping, as well as for futile hydrolysis. It fits well to the experimentally determined force-velocity data, as well as to the randomness and the stepping ratios as functions of load, while capturing the apparent Michaelis-Menten behavior of velocity as a function of ATP concentration. Although some biochemical states known to be distinct were modeled as composites (e.g., ADP and Pi release), the rate constants associated with such a minimal model represent the ones most directly responsible for

78 the mechanochemistry. Presumably, the dynamics of any kinesin dimer that steps discretely along a microtubule may be modeled in similar fashion, albeit with different rates. The values for the reaction rates obtained here suggest how exquisitely tuned head coordination is in kinesin, and shed additional light on the mechanisms responsible for gating.

Figure 4.10 Average backward velocities under load. Average backward velocities under load for the Kin6AA and Kin6P constructs carrying neck-linker inserts. The KinWT linker insert sequence is AEQKLT; the Kin6P (6-proline) insert is KKPPPPPPG. Data were acquired under −7 pN hindering load and 2 mM ATP. (A) Histogram of velocities for Kin6AA, with associated errors. The mean velocity for the distribution is 25.6 ± 1.8 nm/s (mean ± s.e.m.) Velocities were computed from the slopes of linefits to single-molecule records of position vs. time. (B) Histogram of velocities for Kin6P. The mean velocity for the distribution is 28.4 ± 1.8 nm/s (mean ± s.e.m.) The Kin6AA and Kin6P velocities are statistically indistinguishable, within error.

79

Figure 4.11 Processivities of KinWT, Kin6AA, and Kin6P. Run-length distributions were acquired under unloaded (F = 0) and saturating ATP (2 mM) conditions.

Histograms are displayed with std. statistical errors and fits to an exponential, A exp(−x/x0) (red lines); bins with <6 counts were not included in fits. (A) Distribution of run lengths for KinWT. The characteristic run length estimate, based on fit parameter x0, is 728 ± 73 nm. (B) Distribution of run lengths for Kin6AA. The characteristic run length estimate is 1,327 ± 155 nm. (C) Distribution of run lengths for Kin6P. The characteristic run length estimate is 1,743 ± 340 nm. All three constructs were found to be fully processive; the processivities of Kin6AA and Kin6P were comparable and somewhat longer than for KinWT.

4.4.2 Kinesin is gated by strain and by steric effects The kinetics implied by the mechanochemical model and associated single-molecule data (Figure 4.3), the TMR data, and the 2′dmT binding experiments all suggest that kinesin employs multiple gating strategies to maintain coordination between its heads during a processive run. The TMR data provide direct evidence that extending the neck-linkers allows both Kin6AA heads to attach stably to the microtubule in rigor (State {4}). This conformational state is partially suppressed in WT kinesin, which tends to adopt a configuration where just one head is strongly attached to the microtubule [158, 159], while the partner head, carrying ADP, is more-or-less free of

80 the microtubule [152-154], particularly at low ATP concentrations. The inhibition of the rear head from binding leads to efficient, unidirectional forward motion by reducing backstepping, futile hydrolysis, and access to states where both heads are released, leading to loss of processivity [152]. The experiments with Kin6AA demonstrate that moderately lengthening the neck-linker allows the trailing head to bind strongly to the microtubule and release ADP, yet retain substantial aspects of gating. Indeed, the processivity of Kin6AA exceeds that of the KinWT construct, supporting long runs that average over 150 steps (Figure 4.11). However, a price is clearly paid, through increased backstepping under load and marked reductions in both speed and stall force, along with energy efficiency. Our results do, however, support a mechanism whereby attachment of the trailing head is strain-based, with the accessibility of this state being promoted by a reduction in inter-head tension.

4.5 Methods

4.5.1 Single-molecule experiments

4.5.1.1 Assays

Experimental flowcells (volume, ∼10 µl) were constructed by attaching APTES (Sigma)-coated coverslips to glass microscope slides using pieces of double-sided tape (3M). Microtubules were chemically attached to the coverslip surface by crosslinking with glutaraldehyde before the surface was passivated using bovine serum albumin (BSA, Sigma). Polystyrene beads (0.44 µm diameter, Spherotech) were functionalized with penta-His antibody (Qiagen) and incubated with the appropriate kinesin construct at 4°C for a minimum of 3 hr. The motor protein-bead ratio was adjusted so that fewer than 25% of kinesin-coated beads captured by the optical trap and tested on microtubules showed motility. The buffer used for motility assays consisted of 80 mM

PIPES (pH 6.9), 1 mM EGTA, 4 mM MgCl2, 50 mM potassium acetate, 2 mM dithiothreitol, 10 µM Taxol (), 2 mg ml-1 BSA, and the desired concentration of ATP. Immediately prior to performing measurements, an oxygen-scavenging system was added to the buffer, consisting of 50 µg ml-1 glucose oxidase (Calbiochem), 12 µg ml-1 catalase (Sigma), and 1 mg ml-1 glucose.

81 4.5.1.2 Instrumentation and analysis

Loads were applied to kinesin-coated beads by an optical trapping apparatus previously described [77]. Data were filtered at 1 kHz, acquired at 20 kHz, decimated, and then recorded at 2 kHz. The velocities, v, were calculated from the slopes of straight line fits to single-molecule traces. Average velocities, 〈v〉, were computed as the statistical mean of all individual velocities and associated standard errors. To determine randomness, the individual variance was calculated for each run, σ2(∆t) = (x(t+∆t) − (x(t)+〈v〉∆t))2, as a function of ∆t. The individual variances were used to create an average variance, 〈σ2(∆t)〉, to which a straight line was fit over the first 20 nm 〈v〉-1, neglecting the first 3.5 ms of each record, which is dominated by the viscous relaxation time of the bead. The randomness, r, was calculated from the slope of the linefit to the average variance, divided by d〈v〉. Randomness error was propagated from the error in determining the average velocity. The step ratio, SR, was calculated by counting the number of forward steps, n+, and backward steps, n−, at a given force and ATP concentration, and determining the ratio (n+/n−). The estimated errors in the numbers of steps were taken to be the statistical errors (square root of the numbers of events). All data for forces exceeding −3 pN were obtained under force clamped conditions using a feedback-based optical trapping system. However, for small forces below −3 pN, data were collected without force feedback, leading to a minor change in force during the course of each step. In such cases, step ratio was determined by collecting n+ and n− in force bins of width 0.25 pN, a bin size chosen to correspond approximately to the change in force experienced by a motor as it undertakes an 8-nm step in a trap with average stiffness 0.03 pN nm-1.

4.5.1.3 Global Curve Fitting

The single-molecule data in Figure 4.1 and Figure 4.2 were fit using the mechano- chemical model presented in Figure 4.3. Global fits of the M = 10 model parameters (and associated parameter errors) of Table 4.1 to the N = 73 data points displayed in Figure 4.1 and Figure 4.2, corresponding to N−M = 63 degrees of freedom, were carried out using software written in Igor (Wavemetrics, Inc.) that implements the

82 Levenberg-Marquardt algorithm for minimization. Reaction diagrams composed of states connected by rate constants, of the type displayed in Figure 4.3, are generally modeled by systems of coupled, first-order differential equations. Such systems can represented by a single Master Equation, with vectors that correspond to the arrays of input and output states connected by a matrix comprised of the transition rates. The eigenvalues of the transition matrix, for example, supply the time constants for relaxation of the system. However, unless the transition matrix happens to be sparse, it is not generally possible to solve analytically for the eigenvalues and eigenvectors of any matrices larger than 4 x 4. However, as Chemla et al. [149] have shown using Fourier-Laplace transform techniques, expressions for the velocity and randomness of any reaction system can be obtained analytically, in closed form, directly from the three lowest order terms of the characteristic equation of the transition matrix, without any need to solve for its eigenvalues or eigenvectors. Analytical expressions for the velocity (v), step ratio (SR) and randomness (r) were obtained by applying their published formalism to the reaction system in Figure 4.3 with the aid of Mathematica (Wolfram Research, Inc.). These expressions are:

= = ( ) ′ ′ 푣step 푣ratio+ − , 푣SR− = 훾+ − 훾 − ⁄훽 ′ ′ = ( + 2 훾+⁄훾− 2 ) ′′ ′ ′ ′ 2 −1 where푟 훾 d ⁄is훾 the step훽 ⁄size훽 − and훼 훾 ⁄훽 ∙ 푑

= [ATP] ( + + ) ′ 2 훾+ = 푑 ∙ [ATP] ∙[푘23 ∙ 푘31 ∙ 푘12 ∙(푘51 +∙ 푘45 ) 푘(51 ∙ 푘+43 푘+54 ∙ 푘)43+ [ATP] ′ ( )] 훾− 푑 ∙ +∙ 푘14 ∙ 푘51 ∙+푘45 ∙ 푘31 푘 34 ∙ 푘23 푘25 푘21 ∙ 푘25 ∙ 푘51 ∙ 푘12=∙ 푘31 ∙ 푘45 푘31 ∙ 푘43 푘45 ∙ 푘34 ′ ′ ′ 훾 = 훾 + −( 훾− + ) ′′ ′ ′ 훾 = 푑 ∙ ( 훾+ +훾− ) ( + ) ( + + ) + [ATP] ( + )

(훽 푘+14 ∙ )푘51( 푘+54 ∙ 푘+31 푘) 34+ ∙ 푘23( 푘+25 )푘21( + )∙ �푘(45 ∙ +푘14 +푘51 ∙ 푘31 푘34 ∙ 푘23 푘25 푘21 푘43 ∙ 푘14 푘31 ∙ 푘51 푘54 ∙ 푘23 푘25

83 ) + ( + ) + ( + ) + [ATP] 2 [푘21 ( 푘12 +∙ �푘25)∙ 푘(54 ∙ +푘31 )푘+34 푘23 ∙ 푘(34 ∙ +푘51 )푘+54 �� ( + ∙ 푘)12 ∙ ( ) ( )] 푘45 ∙+푘25 +푘51 ∙ 푘31 푘34+ 푘45 ∙ 푘23 ∙ 푘51 푘34 푘43 ∙ 푘23 푘31 ∙ 푘51= 푘[54ATP]푘43[ ∙ 푘25 ∙ 푘31 푘(54 + ) ( + ) ′ ( 23 31 12 54 )]51 [25 51] 12 ( 31 34) 14 훽 푑 ∙ ∙+푘 ∙+푘 ∙ 푘+ ∙ 푘+ 푘 + − 푘 ATP∙ 푘 ∙ 푘 ∙ 푘 + 푘 − 푘 ∙ ( ) 2 푘51 ∙ 푘45 ∙ 푘23 푘25 푘21 푘31 푘34 푑 ∙ ∙ 푘12 ∙ 푘45 푘43 ∙ 푘=23 (∙ 푘31+− 푘25 +∙ 푘51 + ) ( + ) ( + ) + ( + + + ) ( ) [ ] [ ( ) ( 훼 푘23 +푘25 +푘21 푘+14ATP∙ 푘54 푘51 ∙ 푘34 +푘31 +푘14 ∙ 푘51 푘54 +푘31 ) ( ) ( ) ( ) 푘34 ∙+ 푘23 푘25 + 푘21 + ∙ 푘12+ ∙ 푘23 +∙ 푘51 푘34 + 푘12+∙ 푘54 ∙+ 푘23 ( ) ( ) ( ) ( 푘25 + 푘12 ∙+푘51 +푘54 푘25 ∙+푘34 푘31 + 푘45 ∙ +푘51 푘14 +푘31 +푘34 ∙+ 23) ( 25 21 45) 51 ( 14 31) ( 34 43)] [51 ] 54 31 푘 푘 + 푘 + 푘 +∙ 푘 푘 +∙ 푘 푘 + 푘 ∙+푘ATP 푘 푘 [ ( ) ( 2 )] 푘14 ∙ 푘23 + 푘25 + 푘21 + 푘43+∙ 푘31 + 푘14 ∙ 푘51+ 푘54+ + +∙ 푘12 ∙ 45 23 25 51 31 34 43 23 25 31 51 54 푘 ∙ 푘[ATP]푘 is the 푘ATP concentration푘 푘 and푘 the∙ 푘 kij are푘 the rates푘 between푘 states.푘 The minus sign was swapped between the second and third terms in the expression for r, above, to account for any change of sign in the velocity (i.e., forward or backstepping). Load dependence was introduced by multiplying k23, k25, and k14 by the appropriate Boltzmann factor, exp(F δij/ kBT), where F is the force, δij is a characteristic distance, and kBT is the thermal energy. The resulting equations for v,

SR, and r are explicit functions of the parameters, kij and δij, and the ATP concentration. We note that they are not functions of the ADP or Pi concentrations, which are taken to be negligible in the domain of applicability of this model.

All transitions involving the binding of ATP to the kinesin head were taken to proceed at rates proportional to the ATP concentration, and therefore modeled by

(pseudo) second-order binding constants (k12, k43, k45). This approximation is valid over the range of loads and concentrations studied here. In actuality, such rates will saturate at the highest ATP levels in a Michaelis-Menten-type fashion, because the formation of a weak collision complex between ATP and the motor domain is followed by a transition to a tighter binding state that takes finite time. If KD represents the dissociation constant for the ATP-head collision complex, then

84 [ATP] = [ATP] + 푘max 푘 describes the saturation of these binding rates (derived퐾퐷 below). Based on the data for

−1 Figure 4.8B, we obtain KD = 632 ± 270 µM and kmax = 1,517 ± 443 s for the binding of the analog 2′dmT, which likely represents a lower bound for ATP itself. At 2 mM ATP, these values imply a binding rate in excess of 1,153 ± 337 s−1. That rate is to be compared with the next-fastest rate returned by our fitting, which is the load- 0 dependent stepping transition, 23 = 23 exp[ ]. From the data in Table 4.1, the value for the step transition푘 at 푘−1 pN 퐹loadδ⁄푘 퐵(i.e.,푇 the worst-case scenario) is (570 s−1)exp(−4.3/4.05) = 197 s−1, which is already nearly six-fold slower than the

ATP binding rate. For all other loads studied (−2 pN on up), the stepping transition slows to 68 s−1 or below, which becomes comparable to other reaction rates (e.g., to the ATP dissociation rate from the front head), all of which are more than an order of magnitude slower than the saturated ATP binding rate. ATP binding is therefore well approximated by a second-order binding constant, with a rate proportional to the ATP concentration.

4.5.2 Ensemble fluorescence experiments

4.5.2.1 Engineered Constructs

The template for a ‘wild-type’ kinesin, KinWT, was based on a 560-residue (truncated), cysteine-light version of the human ubiquitous kinesin-1 gene, an extended version of a 413-residue construct described previously [165]. To generate Kin6AA, an insert consisting of six amino acids residues with net neutral charge (AEQKLT) was introduced in the C-terminal end of the neck linker region (after T336), N-terminal to the start of the dimerization domain of the stalk. Previous work involving constructs with insertions in the neck linker region [136] focused instead on the addition of prolines to ensure that no protein secondary structure would form. For comparison purposes (see main text), we therefore generated and tested one additional construct, based on KinWT, carrying a 9-residue insert in its neck-linker region with

85 six adjacent prolines, designated as the Kin6P construct. The Kin6P construct carries its insert after L335, with the sequence KKPPPPPPG. The basic rationale for this particular sequence was furnished by Yildiz et al. [136] In brief, prolines have restricted dihedral angles that present an entropic barrier to conformational changes. To ameliorate this concern, a glycine ‘swivel’ residue was introduced C-terminal to the prolines, adjacent to the dimerization domain of the stalk. In addition, wild-type kinesin is believed to form an electrostatic interaction between positively-charged lysines found in its proximal dimerization domain and C-terminus of tubulin, which carries a complimentary negative charge. To allow for such a possibility, two adjacent lysine residues were incorporated adjacent to the 6-proline insert (above), designed to mimic the charged residues found in the dimerization domain. The KinWT, Kin6AA, and Kin6P constructs all formed fully functional, processive motors when expressed in bacteria and subsequently purified.

4.5.2.2 Protein expression and purification

The kinesin constructs were expressed and purified as described [166]. Briefly, the DNA encoding the constructs was transformed into BL21 cells (Stratagene), which were grown in LB medium (2% (w/v) tryptone, 1% (w/v) extract, 0.5% (w/v) -1 NaCl, 0.2% (w/v) glycerol, 50 mM Na2HPO4, 50 mM K2HPO4, 50 mg L ampicillin, 50 mg L-1 chloramphenicol) to O.D. 1.0 at wavelength 595 nm, then induced using IPTG (isopropyl-beta-D-thiogalactopyranoside). The proteins were expressed for 48 hours at 18°C before harvesting and lysing. A batch method was used to purify proteins over Ni-Sepharose high-performance beads (GE Healthcare). The elutant was then dialyzed overnight at 4°C in low ionic strength buffer (25 mM HEPES (pH 7.5),

10 mM KCl, 2 mM MgCl2, 1 M DTT, 1 mM ATP) and centrifuged at 25,000 RCF to remove any aggregated proteins.

4.5.2.3 Experiments with 2′dmT and 2′dmD

Fluorescently labeled 2′−deoxy 3′−mant ATP (2′dmT) and 2′−deoxy 3′−mant ADP (2′dmD) were synthesized by reacting the corresponding 2′−deoxyadenosine precursors (Sigma-Aldrich) with N-methylisatoic anhydride (Invitrogen). The 2′dmD

86 and 2′dmT reaction products were purified by chromatography over a Sephadex LH20 column to >98% purity, determined from the relative absorbances at 255 and 356 nm, as described [167].

Measurements of the kinetics of 2′dmD release were carried out by incubating the kinesin constructs overnight with a slight excess of 2′dmD. The sample (1.0 µM) was then mixed in a stopped-flow fluorimeter with microtubules (10.0 µM polymerized tubulin), and the 2′dmD or 2′dmT fluorescence was monitored through FRET from protein tryptophans excited at 290 nm. The sensitized emission was observed at 90° from the excitation by using a broad bandpass filter centered at 450 nm.

For 2′dmT-binding experiments, Kin6AA and KinWT were incubated with a 5− to 10−fold excess of microtubules and treated with 0.2 U ml-1 apyrase for 20 min. The complex was then mixed with 2′dmT in the stopped-flow spectrometer, and the sensitized fluorescence emission was observed as in the 2′dmD-release measurements. All kinetic experiments were performed at 20°C in 100 mM KCl, 25 mM HEPES,

2 mM MgCl2, pH 7.50. For the experiments shown in Figure 4.8, the complex of 2.0 µM Kin6AA and 10 µM polymerized tubulin was made nucleotide-free by first incubating with apyrase (0.2 U ml-1) and then mixing in the stopped-flow spectrometer with 40 µM 2′dmT.

4.5.2.4 Derivation of dissociation rate constant for ATP release from ensemble kinetic measurements

As previously demonstrated [168], we can depict the reaction of 2′dmT with a microtubule-kinesin complex as follows:

/ / + 퐾퐷 푘1 푘−1 푘2 푘−2 푘3 ∗ ∗ ∗ 푖 where 푀M ∙is퐾 the 푇microtubule,�� 푀 ∙ 퐾 ∙ 푇 K� is⎯⎯ ⎯kinesin,� 푀 ∙ 퐾 T∙ 푇is 2′dmT,�⎯⎯⎯� 푀D ∙is퐾 2′dmD,∙ 퐷 ∙ 푃 and→ 푀Pi ∙is퐾 inorganic∙ 퐷 phosphate. The binding of 2′dmT first occurs via the formation of a collision complex

(characterized by the dissociation constant KD) followed by a first-order transition that produces enhancement of the 2′dmT fluorescence (designated by an asterisk, with

87 associated rate constants k1 and k-1). The hydrolysis of ATP (k2/k-2) is followed by phosphate release (k3), which under the conditions of the experiment is essentially irreversible. The solution of the rate equations for each state has been described previously [169-171]. At low [2′dmT], the observed rate constant is c/b, where:

= + + + +

1 −1 2 −2 3 = ( +푏 푘�+ 푘) + 푘( 푘+ )푘+ , and

푐 푘�1 푘2 푘−2 푘3 푘−1 [푘−]2 푘3 푘2푘3 = [ ]+ 푘1 ∙ 푇 푘1 The y-intercept of the plot of the observed rate푇 constant퐾퐷 versus 2′dmT concentration

−1 (Figure 4.8B, 61 ± 12 s ) defines an apparent dissociation rate constant, kd, which can be derived by setting [T] to 0 in the ratio c/b:

( + ( + )) = ( + + + ) 푘2푘3 푘−1 푘−2 푘3 푘d Previous studies of the kinetics of ATP푘−1 interaction푘2 푘− 2with푘 3kinesin provide estimates for

−1 −1 the values of k2 (100-120 s [168, 172]) and k3 (80-100 s [173]). Although the hydrolysis step (k2/k−2) is reversible in the presence of microtubules under certain conditions [174], k−2 << k2 or k3 and can therefore be ignored in the denominator.

Using these values, we can derive a range of values of k−1, the rate constant for ATP dissociation, from 55–135 s−1 (Table 4.1).

4.5.2.5 ATPase activity

The MT-activated ATPase activities of KinWT and Kin6AA were measured in 25 mM

HEPES (pH 7.5), 2 mM MgCl2, 1 mM EGTA, 2 mM DTT, 20 mM KCl at 20°C with microtubules in a >50-fold molar excess over kinesin active site. The reaction was initiated by adding ATP to 2 mM, and was monitored using an EnzCheck Phosphate Assay Kit (Invitrogen).

88 4.5.2.6 Mutant construction

DNA for the 6 proline insert [136] kinesin mutant was generated by PCR from the KinWT construct in two fragments, and ligated into pET21 vector in a three-way ligation. For the mutant with insert ‘AEQKLT’ the DNA was made by Genscript in a pET21a vector using NdeI and XhoI digestion sites. DNA for all constructs made was confirmed by sequencing.

89 Chapter 5: Effects of neck linker length on Kinesin-1 force generation and motility

5.1 Introduction

Kinesin-1 is a highly processive biological motor that completes over a hundred steps on average per encounter with a microtubule (MT), thereby transporting its cargo about 1 µm. This would not occur if the two catalytic motor domains progressed through their individual hydrolysis cycles independently, indicating that there is tight coordination between the heads. Several gating mechanisms maintain the reaction cycles out of phase by promoting some mechanochemical steps in one head and preventing others, depending on the state of the partner head [128, 131, 175, 176]. In a simplified processive kinesin cycle there are, in principle, at least three points where gating could occur, designated A, B, and C in Figure 5.1 below. These states are associated with the three different relative positions of the two heads. In the two- heads-bound state (A), the first gate (Gate A) may prevent the front head from unbinding while simultaneously promote the detachment of the rear head in order to ensure unidirectional motion towards the MT plus end. Following the rear head detachment (B) the next gate (Gate B) would act to inhibit the reattachment to the rear binding site. It would also prevent premature unbinding of the bound head which would result in the kinesin falling off the MT, effectively ending the run. A similar mechanism may be active once a force generating step has been completed (C). This final gate (Gate C) may also promote the binding of the free head to the next MT binding site. The gating mechanisms are not mutually exclusive and several of them may contribute to maintaining processivity.

90 Gate B Front head prevents unbinding Rear head prevents rebinding

kD1 B

k3

k−3

A k−1 k1

Gate A k−2

Front head k2 prevents unbinding kD2 Rear head C promotes unbinding

Gate C Front head Dissociated states promotes binding Rear head prevents unbinding

Figure 5.1 Overview of gating in kinesin motility. The three main gates in the simplified cycle contribute to the kinesin processivity. In this work they are arbitrarily designated Gate A, B, and C. The cycle progresses clockwise as indicated by the arrows and associated rate constants (k).

Many features of the Kinesin-1 catalytic cycle have been characterized over the last couple of decades but the mechanistic understanding is still incomplete [177]. The role of the kinesin neck linker (NL) is of particular interest since it is the element that connects the two catalytic motor domains and allows for head-to-head communication through mechanical means [65, 79, 177, 178]. In the crystal structure of Kinesin-1 the heads are separated by about 5 nm, indicating that the 14-amino acid (AA) neck linker is highly stretched when kinesin enters the two-heads-bound state (A) [89, 179]. The high internal strain that is developed is believed to contribute to gating.

91 The length of the neck linker is highly conserved between organisms and would be expected to influence all three gates discussed above. In Gate A, longer neck linkers would decrease the internal strain and its effects of stimulating unbinding. In Gates B and C the length of the neck linkers alters the accessible space for the free head. To better understand the kinesin gating mechanisms and the role of the neck linker we therefore generated a series of constructs where the neck linker was incrementally lengthened by up to 6 amino acids. The constructs (DmK1-1AA to DmK1-6AA) were based on truncated wild-type Kinesin-1 with 560 amino acids. The crystal structure of a minimal dimer with a shorter stalk is shown in Figure 5.2 [71]. Single AA increments in NL length were chosen to capture details not seen in previous studies with lengthened neck linkers [79, 136, 160, 179] where the kinetic cycle was either disrupted or not studied in the detail afforded by optical trapping.

Insert 1–6 AA

Figure 5.2 Crystal structure of dimeric D. melanogaster Kinesin-1. A recent x-ray crystal structure of truncated wild-type Kinesin-1 (PDB ID: 2Y65) [71]. The catalytic domains (black) are connected to the coiled-coil stalk (blue) via the neck linkers (red). Also shown are ADP (desert brown) and a magnesium ion (orange). For extended NL constructs, amino acids were inserted at the end of the neck linker, as indicated by the red arrow.

The work presented here used several experimental techniques aimed at elucidating the role of the neck linker in kinesin gating. To study the internal strain developed in the two-heads-bound state and the magnitude of accelerated rear head release (Gate A), the velocities of the kinesin constructs were measured over an unprecedented range of forces, both hindering and assisting. The detachment of the

92 rear head is a mechanical transition involving motion is therefore expected to be influenced by internal strain or an external force. Longer neck linkers lead to less strain, slowing down the rear head release rate and consequently the overall kinesin velocity. An external force, transmitted from the stalk to the head via the neck linker, should partially compensate for losses in internal strain and we model this rescue in velocity, generated by the optical trap, to obtain the internal strain in the wild-type molecule, the unloaded rear head release rate and its force dependence.

Gate B, which prevents rebinding of the free head to the rear MT binding site, was shown to be disrupted in our previous work (Chapter 4). A 6-AA extension in a human cysteine-light kinesin (Kin6AA above, here HsK1-CL-6AA) allowed the rear head to bind, generating a two-heads-bound state where both heads were missing nucleotides in their binding pockets. The newly accessible state led to the possibility of processive backstepping under load and futile hydrolysis. Here we use our series of neck linker mutants to investigate at which neck linker length this state becomes populated. Two bulk fluorescence techniques were used. The first is the classical half- site ADP release experiment [79, 158, 160, 180] where the kinesin is preincubated with mantADP, a fluorescent ADP analog, followed by mixing with MTs. The resulting drop in fluorescence is a measure of the proportion of heads that bind upon contact with the MTs. In a second fluorescence assay, kinesin was preincubated with MTs and limited amounts of ADP and the rise in fluorescence upon addition of mantADP was monitored. The signal is a measure of the ability of the one-head-bound kinesin to transiently bind with the second free head and exchange ADP. A longer neck linker is expected to facilitate this exchange.

The third gate (Gate C), which acts after the force producing mechanical step has taken place, is studied using run lengths collected from single-molecule traces. The number of steps kinesin takes is the inverse of the probability of dissociation during each cycle and to a first approximation this probability is governed by the competing rates of front head binding and premature rear head release. By comparing run lengths under various forces for all neck linker mutants the role of the neck linker in this part of the cycle can be probed.

93 The primary aim of the work described in this chapter was to characterize and better understand the role gating mechanisms play in kinesin motility. We specifically studied the force dependent steps of binding and unbinding of the tethered head using neck linker extensions in combination with optical trapping or bulk fluorescence.

5.2 Results

5.2.1 Assisting loads can rescue reduced velocities for constructs with extended neck linkers Velocities were measured for wild-type kinesin (DmK1-WT) and the constructs with extended neck linkers (DmK1-1AA to DmK1-6AA). The force-velocity data were collected under force-clamp conditions over an unprecedented range of forces and are plotted in Figure 5.3 below. Wild-type kinesin velocities decreased under hindering load but did not change significantly for assisting loads, in line with previous observations [86, 177]. The addition of a single amino acid in the neck linker resulted in reduced velocities at all forces, compared with wild-type, with the unloaded velocity being about 150 nm/s lower. Unlike the wild type, the velocity of the neck linker mutants increased under assisting loads, approaching that of the wild-type beyond 20 pN. This indicates that an external force can rescue the loss in velocity caused by the lengthening of the neck linker. Interestingly, while a single AA insert clearly altered the motility, no appreciably changes were observed by lengthening the neck linker further.

94

Figure 5.3 Velocities as a function of force. Velocity measurements for Drosophila Kinesin-1 constructs with extended neck linkers (mean ± standard error; N = 49–1,022). Data were collected with an optical trap under force clamp conditions at saturating ATP concentrations (2 mM). The lines represent a global fit to a three-state model for processive motion that included two force-dependent steps.

5.2.1 A three-state model explains force dependencies The data described above (Figure 5.3) can be explained quantitatively by a simple three-state model of the processive kinesin cycle that incorporates the effects of internal strain and is summarized in Figure 5.4 below. This model adequately reflects the canonical kinesin cycle, as represented in Figure 1.4 or Figure 5.1, but focuses on the variables that are observed and controlled in the experiments above.

95 1

k3 (F)

3 k1 (F)

k2 2

Figure 5.4 Three state model for kinesin force dependence The model arbitrarily starts in the ATP-waiting state (1) and the first step in the cycle is the mechanical, force-producing step that advances kinesin along the microtubule. The rate (k1) is affected by force, with an exponential dependence on the force applied, such that

trap 1 = 퐹 B 훿 (1) 0 � 푘 푇 � 1 1 where is the unloaded rate푘 constant,푘 푒 B is the Boltzmann constant, is 0 temperature,푘1 trap is the applied force, and푘 represents the characteristic푇 distance parameter. Loads퐹 against the direction of kinesin훿1 motion are negative and the force- dependence manifests itself in the sharp slowdown of the motors under hindering load, approaching zero near the stall force of −6 pN. The force-dependence is defined by the characteristic distance parameter, . The internal strain does not contribute to the transition between state (1) and (2)훿 1since the kinesin is not in the two-heads-bound state.

The subsequent step in the model encompasses most biochemical events in the hydrolysis cycle, including binding to the next binding site, ADP release of the front head and ATP hydrolysis and phosphate release in the rear head. No significant motion of the heads is expected in these steps and the combined rate constant, k2, is not force-dependent. The rate is approximately the unloaded turnover rate for wild-

96 type kinesin, assuming that the other two rates are very fast under unloaded conditions. Here, the kinesin is mainly in a two-heads-bound state (3) where the neck linkers are stretched and confer internal strain.

The stepping cycle is completed as the kinesin transitions from the two-heads- bound state (3) back to the one-head-bound ATP-waiting state (1). The detachment of the rear is akin to overcoming an energy barrier where the reaction coordinate is physical displacement. Consequently a force-dependence can be assigned to the rear

head detachment (k3) where the force is applied by both the external trap (Ftrap) and the

internal strain (Fi):

= �퐹푡푟푎푝+퐹푖�훿3 (2) � � 0 푘퐵푇 The force-dependence is푘 3exponential푘3푒 with an unloaded rate, , and a characteristic 0 distance parameter, . It reflects the increase in velocity under푘3 assisting loads, especially for the neck훿3 linker insert mutants where the effect is not masked by a high internal strain.

Analytical expressions for the velocity from the kinetic scheme in Figure 5.4 were globally fit to the complete force-velocity dataset plotted in Figure 5.3. The internal strain in the wild-type was determined from the curve-fitting whereas the mutant constructs (DmK1-1AA to DmK1-6AA) were all assigned a negligible internal strain (0 pN). Only the difference in internal strain is detectable as any residual internal strain is degenerate and can be incorporated into . Six extra amino acids are 0 expected to increase the neck linker length by over 40%, so푘3 the assumption of a low internal strain is reasonable. All other variables in equations (1) to (3), except for the

constant kBT, were also determined by curve fitting and the results are shown in Table 5.1.

.

97 Table 5.1 Kinetic parameters from global fit to data from neck linker mutants. The parameters were obtained from a quantitative analysis of the three-state model applied to wild-type kinesin and mutants with extended neck linkers. The values are fit parameters with associated errors from the global fit.

Parameter Parameter Description Value

( ) ATP binding, NL docking, and stepping 4900 ± 300 s-1 ퟎ 풌ퟏ 푭 ATP hydrolysis 95 ± 1 s-1

ퟐ 풌 , Distance parameter (WT construct) 4.6 ± 0.1 nm

ퟏ 퐖퐓 휹 , Distance parameter (mutant constructs) 4.0 ± 0.1 nm

ퟏ 퐦퐮퐭퐚퐧퐭 휹 , Internal strain (mutant constructs) 0 pN (fixed)

풊 퐦퐮퐭퐚퐧퐭 푭 , Internal strain (WT constructs) 26 ± 3 pN

푭풊 퐖퐓 Distance parameter (release) 0.35 ± 0.02 nm

휹ퟑ( ) Rear head release 260 ± 10 s-1 ퟎ 풌ퟑ 푭

The parameters in Table 5.1 associated with steps (1→2) and (2→3) are in good agreement with previous optical trapping studies of Kinesin-1 [86]. The variables for step (3→1) have not been previously reported and give new insight into the contribution of internal strain to gating, within the framework of our simplified three-state model. The rate of rear head release under no load is = 260 ± 10 s-1. 0 This is significantly faster than the hydrolysis rate = 95 ± 1 s푘-13. The force- dependence is quite weak, = 0.35 ± 0.02 nm, but푘 consistent2 with a bond-breaking mechanism. The internal strain휹ퟑ for the wild-type motor is = 26 ± 3 pN. This value falls within the range of 15–35 pN that has been predicted퐹 in푖 published molecular dynamics simulations [174]. By multiplying the internal strain with the distance parameter we obtain an energy of 9 pN nm, or a little more than 2 . From

Equation 2 we find that the internal퐹 푖strain훿3 ≈ accelerates the rear head release by푘퐵 푇an order of magnitude, as exp( ) 9.

퐹푖 훿3⁄푘퐵푇 ≈

98 5.2.2 Extending the neck linker stabilizes the two-heads-bound state Wild-type Kinesin-1 in the presence of ADP releases a single ADP molecule per kinesin dimer when mixed with MTs, indicating that only one of the two heads can bind tightly to the MT in a no nucleotide state. Performing half-site release experiments with a Drosophila 6-AA insert construct (DmK1-6AA) pre-incubated with fluorescent mantADP resulted in a loss of fluorescence upon mixing corresponding to almost complete binding of all motor domains, consistent with previous studies with 6 AA inserts [79, 160, 180]. On the other hand, the same experiment repeated with a 5-AA insert (DmK1-5AA) retained the loss in fluorescence of approximately 50% seen in with the wild-type motor.

The half-site release experiments suggest that 6 AAs is the critical length needed to fully allow both heads to bind to the microtubule in the absence of ATP- induced processive stepping, thereby disrupting Gate B’s prevention of rear-head rebinding to the microtubule. To validate this finding we measured the ADP exchange rate for several Drosophila Kinesin-1 constructs (DmK1-WT, DmK1-3AA, DmK1- 5AA, and DmK1-6AA), as shown in Figure 5.5 below. Upon mixing with MTs in the presence of equimolar amounts of ADP, Kinesin-1 is predominantly in a one-heads- bound state but the tethered head can interact transiently with the MT, stimulating the release of ADP. With an excess of mantADP in solution, the lost ADP is replaced by its fluorescent analog, leading to an increase in bulk fluorescence over time. Fitting the time traces of fluorescence yields the ADP exchange rate. As seen in Figure 5.5, the ADP exchange rate for the kinesin constructs increases significantly with longer neck linkers. The rates for short insert constructs are negligible, but the DmK1-5AA rate, at about 1 s−1, is significant and the DmK1-6AA rate is almost five times higher than that. The results confirm that entering the two-heads-bound state is facilitated for the construct with the 6-AA insert.

99

Figure 5.5 ADP exchange rate as a function of neck linker insert length. The rate of ADP exchange (mean ± standard error) by the rear head of Drosophila Kinesin-1 constructs preincubated with MTs and ADP and later mixed with mantADP. The data points represent fits to the increase in fluorescence over time.

5.2.3 Run lengths exhibit asymmetry with respect to the direction of load The kinesin run length serves as a proxy for the ratio of the rates of front head binding and premature release of the bound head. Gate C may act on both these rates to improve the processivity. To gain understanding of the effect of the neck linker on Gate C we measured run lengths under both hindering and assisting loads for wild- type Kinesin-1 and the mutants with extended neck linkers, as shown in Figure 5.6 below.

In agreement with previous publications we measured an unloaded run length for wild-type kinesin of about 1 µm. The run length decreased continuously as a hindering load was imposed, up to the stall force of −6 pN. Interestingly, the run lengths under assisting loads were significantly shorter for all forces. Already at 2 pN, which was the smallest force used in the measurements, the run length under assisting load was about seven times lower than the corresponding one under hindering load. The dependence of run length on force was fit by an exponential function

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= 퐹 훿퐿 (3) �− 푘B푇 � 퐿 퐿0푒

100 where is the extrapolated unloaded run length, is the external force from the optical퐿 trap,0 and is a distance parameter that characterizes퐹 the force dependence. For wild-type Kinesin훿퐿 -1 (DmK1-WT) the fit parameters for hindering loads, = 1,220 ± 60 nm and = 2.3 ± 0.1 nm, were an order of magnitude larger than퐿0 −those for assisting loads, 훿퐿− = 92 ± 7 nm and = 0.28 ± 0.03 nm. 퐿0+ 훿퐿+

Figure 5.6 Run lengths under force for Kinesin-1 constructs. Run lengths for each force (fit value ± error from fit) were obtained by fitting experimentally collected distributions of run lengths (N = 49–1,022) to exponential functions. Data were collected at saturating ATP (2 mM). Run lengths under hindering and assisting loads were fit separately (lines) to exponential functions that depend on force.

Lengthening the neck linker by a single amino acid (DmK1-1AA) drastically reduced the run length by more than a factor of three under no load or hindering loads, with fit parameters = 351 ± 33 nm and = 1.6 ± 0.1 nm. Longer extensions reduced the run lengths퐿0− further but to a smaller훿퐿− extent. The run length under assisting

101 load were all relatively short and not appreciably affected by extensions of the neck linker, highlighting another asymmetry with respect to the direction of load.

5.2.4 Differences between cysteine-light and wild-type Kinesin-1 The data for Drosophila Kinesin-1 in the sections above, notably that for DmK1-6AA, presented discrepancies compared with previous studies based on a human cysteine- light (CL) construct (HsK1-CL) [65, 79]. In contrast to the data presented here, the 6- AA insert construct used in the previous chapter (here termed HsK1-CL-6AA) slowed down substantially and exhibited ATP-dependent processive backstepping under hindering load, prompting the question of whether the disagreements are caused by differences between Drosophila and human Kinesin-1 motors, between cysteine-light and wild-type motors, or a combination of both. This question is of great importance since cysteine-light constructs are widely used in the scientific community.

To answer this question, force clamp data were collected and analyzed for both wild-type and cysteine-light constructs based on Kinesin-1 from both Drosophila and human. Unlike the human motor, the cysteine-light Drosophila construct only had two mutations (C45S and C338S) due to sequence differences. A partially cysteine-light construct (DmK1-C338S), with only the cysteine in the neck linker mutated, was also studied and a human kinesin with a 6-AA insert but no cysteine mutations (HsK-6AA) was generated as well. The experimental data for the constructs were compared with those for DmK1-6AA and HsK1-CL-6AA described above. The force-velocity curves are shown in Figure 5.7 below and illustrate several important differences between the motors. The wild-type motors from Drosophila (DmK1-WT, blue trace) and human (HsK1-WT, orange trace) are remarkably similar over the entire force range, with robust velocities of about 200 nm/s at high hindering loads of −5 pN and no significant increase in velocity for assisting loads. The cysteine-light motors (DmK1-CL, purple trace, and HsK-CL, black trace), on the other hand, show a more dramatic dependence on force, slowing down considerably for moderate opposing forces. The DmK1- C338S (green trace) exhibits velocities intermediate of those for DmK1-WT and DmK1-CL, indicating that the cysteine in the neck linker is crucial for full

102 functionality but does not, by itself, explain all of the increased sensitivity to force. Interestingly, the human CL motor velocity increases under assisting loads, surpassing that of the wild-type by almost 200 nm/s at +4 pN. It is also more sensitive to force than the Drosophila CL protein, suggesting that the six substitutions of cysteine residues in the commonly used human CL construct modifies the motility to a much higher degree than the two in the cysteine-light Drosophila version. Further differences are highlighted by comparing the data for kinesins with neck linker extensions. The extended Drosophila wild-type construct (DmK1-6AA, red trace) exhibits normal unidirectional motility, without obvious backstepping, and only speeds up moderately under assisting loads. In contrast, the human constructs with long neck linkers have lower velocities which can increase significantly under moderate loads. The cysteine-light construct can move a speeds beyond those of the wild-type motor by applying assisting forces of +10 pN. Interestingly, while both the human motors were slow, only the cysteine-light version exhibited long processive runs in the backward direction under high loads.

Figure 5.7 Force-velocity curves for human and Drosophila Kinesin-1 constructs. Velocity (mean ± standard error; N = 42–1,022) data taken under force clamp condition and saturating ATP concentrations (2 mM) for wild-type Drosophila and human Kinesin-1 as well as cysteine-light (CL) and neck linker extension mutants. The lines are either fits to the three-state model presented in previous sections, or, in the case of HsK-6-AA and HsK1-CL-6AA, an interpolation using splines.

103 5.2.5 Cysteine substitutions reduces Kinesin-1 run lengths Cysteine-light mutations also modify the run lengths of Kinesin-1 motors. As shown in Figure 5.8 below, the run lengths for DmK1-CL (purple trace) are five-fold shorter than those for the wild-type (DmK1-WT, blue trace). As was the case for the force- dependent velocities, the run lengths for DmK1-C338S were intermediate of those for the wild-type and the full cysteine-light constructs, confirming that the substitution for the cysteine at position 338, in the neck linker, can only partially explain the reduced processivity. The run lengths for the human cysteine-light motor were also shorter than the wild-type run lengths, especially under force, showing that cysteine mutations have significant effect for the force-generating capacity of Kinesin-1 motors.

Figure 5.8 Run lengths under force for wild-type and cysteine-light Kinesin-1. Run length data (N = 63–729) for wild-type (WT) and cysteine-light (CL) versions of human (HsK1) and Drosophila (DmK1) Kinesin-1. The conditions and analysis were identical to those in Figure 5.6.

5.3 Discussion

This study aimed at better understanding the role of the neck linker in Kinesin-1 gating mechanisms, in particular the force-dependent steps in the processive mechanochemical cycle. Three gating mechanisms (Gate A, B and C in Figure 5.1) were studied by investigating the effects of neck linker lengths and external forces on

104 kinesin velocity, run length, and bulk biochemistry kinetics. Briefly, the effects of Gate A, which stimulates rear-head-release in the two-heads-bound state, were quantified by fitting a kinetic model to force-velocity data. Gate B, which prevents the tethered head from rebinding the rear MT binding site, was characterized by observing the probability of entering a stable two-heads-bound state, as measured by ADP release upon MT binding, and the ability of the free tethered head to transiently interact with the MT in the one-head-bound state, as measured by the rate of ADP exchange. Finally, the third gate, Gate C, promotes the binding to the next MT binding site while preventing premature dissociation. This gate was studied by means of kinesin run lengths under force.

5.3.1 A high internal strain contributes to Kinesin-1 velocity By collecting a dataset with an unprecedented range and quality we were able to calculate the internal strain developed during processive stepping, at about 26 pN. Although model-dependent, this value is the first experimentally obtained estimate of the strain, which is a central concept in many models of kinesin gating [135]. The value is within the range of molecular dynamics simulations [174] and in our model the strain acts to increase the rear head release rate by almost an order of magnitude (9x). The characteristic distance parameter is a third of a nanometer, which is consistent with the distance to the transition state for a simple bond-breaking mechanism, modeled as an energy barrier with distance as the reaction coordinate. The internal strain effectively lowers the barrier over this distance, accelerating the unloaded detachment from about 260 s−1 to a very high rate. The time of this kinetic step then becomes almost negligible compared to other rate limiting steps in the kinetic cycle. Phosphate release has been observed at rates similar to rear head release in biochemical experiments, suggesting that the detachment is concomitant with phosphate release [135]. The rate presented here is faster than the previously reported rates and is consistent with a force-dependent physical detachment immediately following the phosphate release.

105 Extending the neck linker by as little as one amino acid essentially relieves the internal strain, as longer neck linkers do not meaningfully decrease the velocity further. We conclude that the neck linker, at 14 AA, is optimized in Kinesin-1 to maximize the velocity. The mutants used in our experiments included inserts with varying amino acid sequences (L, HV, DAL, LAST, LASQT LQASQT) where the final tyrosine for long inserts overlapped the native sequence, indicating that the reduction in velocity was not due to specific sequence-dependent effects. The kinesin neck linkers have been modeled as short worm like chains (WLC) or freely jointed chains [181] but a preliminary analysis using these models did not adequately explain our data. This suggests that such simple polymer-based frameworks may be insufficient, possibly due to the short length scales involved and extensive interactions of the neck linkers with the surfaces of the microtubule and the catalytic domains.

5.3.2 Implications for dominant gating mechanisms The internal strain accelerated the rate of read head release, but our data strongly indicate that kinesin is still primarily front head gated, where the two-heads-bound state inhibits ATP binding or hydrolysis in the front head, rather than rear head gated, where the binding of ATP to the front head induces the transition to the one-head- bound state [135]. The rate of rear head release was high (260 s−1) even after the tension between the heads was relieved by extending the neck linkers by 6 amino acids. This rate is not rate limiting and the small effects of added load suggest that the rear head is not pulled off by a force-generating step in the front head. The kinesin stall force (6 pN) is four-fold lower than the internal strain and with a characteristic distance of 0.35 nm such a force would only increase the rate by a factor of 1.7, according to Equation (2). The fast dissociation in combination with the limited ability for the free head to rebind the MT, as seen in the bulk fluorescence experiments, indicate that the rear head is mostly free in the ATP waiting state, corroborating earlier studies [152, 153].

Interestingly, the studies suggesting a two-heads-bound ATP waiting state were largely based on cysteine-light human constructs, since these are amenable for

106 single-molecule fluorescence experiment where fluorophores are attached to site- specific cysteine residues inserted in the neck-linker or the motor domain [135, 136, 154]. Here we found that a cysteine-light construct was much more sensitive to hindering force, and could be sped up beyond its unloaded velocity using assisting forces. The run lengths were also significantly reduced, so cysteine-light mutations render a much less robust motor. A 6-AA neck linker extension also introduced processive back-stepping not observed in analogous, non-cysteine-light Drosophila or human constructs with an equally long neck linkers. During backstepping the kinesin has to be in a two-heads-bound state when the front head releases. This suggests that human cysteine-light proteins with extended neck linkers are mostly in a two-heads- bound ATP waiting state, whereas the non-cysteine-light motors have a free tethered head. The neck linker lengths of the motors are identical so the affinity for the MT of the cysteine-light heads in the weak ADP state must be higher. The strongly bound state may conversely be weaker, as an external force can increase the motor speed, presumably by accelerating the rear head release. The generality of conclusions drawn from experiments with cysteine-light mutants should therefore be regarded with caution, especially those that propose a rear head gating mechanism together with a two-heads-bound ATP waiting state as a dominant gating mechanism [136]. We instead favor the view that the front head is gated during the two-heads-bound state and that although the rear head detaches quickly for wild-type motors, even in the absence of high internal strain, a weak interaction with the microtubule is possible for mutant constructs without positively contributing to kinesin gating.

5.3.3 Rear head rebinding is effectively gated in Kinesin-1 The prevention of rebinding of the tethered head to the rear MT binding site is necessary for the unidirectionality of Kinesin-1 motion towards the MT plus end. The bulk fluorescence experiments in this study showed that a 6-AA extension of the neck linker is needed to effectively disrupt this gate (Gate B). The ADP exchange rates indicated that five additional amino acids in the neck linker compromises the gating, as the exchange rate was an order of magnitude higher than those for one or three amino acids. It did not stabilize the two-heads-bound state, however, as seen in the

107 half-site ADP release experiment that returned an intact one-head-bound state, measured as a reduction in fluorescence of about one half. The corresponding experiment with the 6-AA NL insert, on the other hand, indicated a fully stabilized two-heads-bound state and the ADP exchange rate was also five-fold higher than for the 5-AA insert. We conclude that Gate B, the prevention of rear head rebinding, is relatively insensitive to the neck linker length. Several amino acids can be inserted without disrupting the mechanism so the ability of the tethered head to bind the MT is low. We also note that even a 6-AA insert did not lead to long processive backward runs for motors without cysteine-light mutations, suggesting that even for neck linker mutants the rate of rebinding, in the context of processive motion, is still relatively low. It is lower than or comparable with the rate of Kinesin-1 unbinding completely from the MT.

5.3.4 The Kinesin-1 neck linker is optimized for long runs under load The run length data for wild-type Kinesin-1 and the mutant constructs reveal several important details about the dynamics during the transition from the one-head-bound state to the stable two-heads-bound state, when Kinesin-1 completes the 8-nm movement to the next MT binding site. For this transition there is an apparent competition between the completion of the step and the off-pathway dissociation that sets the limit for processivity. The first finding from the experiments is that run lengths exhibit a strong, previously unrecognized dependence on the direction load. By probing run lengths over a large range of assisting loads we found that both the extrapolated unloaded run lengths and the force dependencies differ by an order of magnitude, depending on the direction of load. This observation was not expected. During processive stepping the tethered head has to reach the next MT binding site and this step should normally not be facilitated by hindering loads, as the optical trap in this case actively biases the motor away from the binding site. However, hindering loads of 5 pN, more than 80% of the stall force, resulted in runs that were as long as those for the smallest assisting loads attempted. The kinetic cycle is not visibly altered under assisting force since the velocity is constant, even up to 20 pN of load. Also, the duration of the last step before falling off was not clearly shorter than the other steps

108 and it increased consistently as the ATP concentration was lowered. This points to a model of unbinding where the detachment occurs during a specific point in the cycle, when the kinesin is in the one-heads-bound state after release of the rear head, and where this state is particularly vulnerable to assisting loads following ATP binding. The weak force-dependence under assisting loads ( = 0.28 ± 0.03 nm) is very similar to that measured for the rear head release during훿퐿+ processive stepping and it is consistent with bond breaking. Under hindering loads, on the other hand, the force- dependence is much stronger ( = 2.3 ± 0.1 nm) and it is conceivable that it is instead dominated by rebinding훿 퐿to− the next MT binding site, against the applied load, which is a mechanical process involving large motions rather than simple detachments. A characteristic distance of several nanometers is analogous to the force- dependence of the velocity under opposing forces ( 4 nm). The picture that emerges is that after rear head unbinding the one-head훿퐿−-bound≈ kinesin is prone to dissociate under assisting loads but resists detachment under hindering loads. Assisting forces are directly transmitted to the bound head via the stalk and the neck linker, which points forward, so the rebinding of the free head is largely unaffected by assisting loads, resulting in a weak force-dependence. Under hindering forces the neck linker of the bound head is instead stretched backwards, making it harder for the free head to bind the next site. The backward bias also prevents the bound head from unbinding, however, until the tethered head has productively reattached to the MT. This is the essence of a gating mechanism, where important transitions in one head are biased by the state of the other. It is possible that the gating that prevents detachment under hindering load is based on the same mechanism that gates the front head during the two-heads-bound state, where the internal neck linker tension plays the same role as the tension from the trap in the one-heads bound state. The vertical component of the external force is the same under hindering and assisting loads, and is not considered to play a large role here. Just as in the Chapter 4 our data points to a gating mechanism that is primarily controlled by the direction of the neck linker, rather than the absolute forces transmitted by it. The experiments here do not fully distinguish between the direction of load modulating the detachment rate directly or indirectly by

109 means of increasing the rate of ATP hydrolysis in the bound head, but we note that both effects have been reported in the literature [79, 182] and may play important roles in gating.

By studying the run lengths for kinesin constructs with extended neck linkers we learned how the neck linker length affects the gating. We found that a single extra amino acid in the neck linker was enough to reduce the unloaded run length by a factor of more than three. Similar large effects were observed under hindering loads whereas the assisting load data were remarkably similar to those for the wild-type motor. Further reductions in run length, albeit of smaller magnitudes, were observed as the neck linkers became even longer. The results are consistent with our model of unbinding. Under hindering loads, a longer neck linker means that the tethered head will be further biased away from the next binding site, on average. This increases the time of rebinding and the resulting decrease in the ratio of rebinding to detachment rate is translated into a higher probability of falling off, and a shorter run length. For assisting loads, the neck linker of the bound head is already biased forward and the optical trap does not readily affect the free tethered head that can easily bind the next binding site, once the necessary biochemical steps have taken place in the bound head. Increasing the neck linker length does not significantly reduce the binding rate so the short run lengths are still dominated by the fast unbinding of the bound head with its neck linker pointing forward.

The asymmetry in run length with respect to the direction of load has direct implications for understanding multi-motor transport, where teams of several kinesin motors work together to transport cargos, either alone [183] or against opposing dynein motors [184]. For a team of identical motors attached to the same cargo, strain will develop in the system as soon as any motor fall behind the leading motor by a distance larger than the difference of the attachment points plus the stalk lengths. Since motors under moderate assisting loads detach almost an order of magnitude more readily than motors under comparable hindering loads, any such straggling motors will quickly fall off the MT rather than slowing down the team as a whole. The resistance to falling off under hindering loads, on the other hand, suggests that kinesin

110 is optimized to withstand opposing forces and is not prone to dynamic switching where stochastic binding and unbinding would lead to frequent reversal in overall cargo transport direction [184].

5.3.5 Conclusions In this study we examined the effects of neck linker length on kinesin motility to better understand several gating mechanisms in the kinesin mechanochemical cycle (Figure 5.1). From velocity measurements, we found that a high internal strain is developed in the wild-type motor and that this strain accelerates the rear head release by an order of magnitude. However, the unloaded rate of rear head detachment is fast and not rate limiting and we conclude that this gating mechanism is not dominant in the kinesin cycle. The prevention of rebinding of the tethered head to the rear MT binding site is effective for kinesin with neck linkers extended by up to five amino acids, but breaks down for six-amino acid inserts, indicating that this gating mechanism is relatively insensitive to the length of the neck linker. Finally, we observed a dramatic asymmetry in run length with respect to the direction of load and attribute this primarily to a directional bias of detachment of the bound head. The force dependence under hindering loads also suggests that the rate of attachment to the next MT binding site is affected by the load applied by the optical trap. The reduction in run length from extended neck linkers is the consequence that will have the largest effect on the physiological function of kinesin, since the velocity is only moderately reduced. A conclusion is therefore that the neck linker length in Kinesin-1 is primarily optimized for long runs, in particular under hindering loads.

5.4 Methods

Optical trapping assays were prepared, performed and analyzed similarly to those described in section 6.5 below. Several improvements to the optical trap described in Chapter 2 were implemented. The detection scheme was expanded to include both the trap laser and a separate detection laser, detected separately by two PSDs. This setup afforded an expanded active range for detection such that force clamp experiments could be initiated near-instantaneously without the need for compensating stage

111 movements. In combination with new, more efficient, force clamp software which lowered the feedback response time, data yield could be increased in order to capture significant numbers of short runs under high assisting loads.

Truncated Kinesin-1 constructs were expressed in E. coli and purified in-house or by collaborators as previously described [64, 80, 166, 179]. All constructs contained a poly-histidine tag at the C-terminal end and site-directed mutagenesis (QuikChange, Agilent Technologies) was used in most cases to produce NL extensions. Preparations were stored in buffer with 10% sucrose at −80°C, in small aliquots.

Drosophila kinesin-1 (DmK1) neck linker mutant constructs were based on the first 560 residues of the wild-type (WT) motor fused to a green fluorescent protein (GFP). The NL was extended after residue L335 by 1 (DmK1-1AA; L), 2 (DmK1- 2AA; HV), 3 (DmK1-3AA; DAL), 4 (DmK1-4AA; LAST), 5 (DmK1-5AA; LASQT), and 6 AA residues (DmK1-6AA; LQASQT), respectively. The cysteine-light version of DmK1 (DmK1-CL) included the first 401 residues with the cysteines at position 45 and 338 mutated to serine (C45S and C338S). A mutant with only one of these two point mutations, DmK1-C338S, was also created.

The ‘wild-type’ human construct of kinesin-1, HsK1-WT, included the first 595 residues of the wild-type sequence whereas the human cysteine-light mutant (HsK1-CL) was based on the first 560 amino acids. In the latter, a total of 6 cysteine residues were substituted with alanine or serine (C65A, C168A, C174S, C294A, C330S, and C421A) [65, 79]. NL-extension constructs (HsK-6AA and HsK1-CL- 6AA; AEQKLT) were based on the WT and cysteine-light constructs, respectively [79].

ADP release experiments were performed as previously described [79, 158, 160, 180]. Kinesin was preincubated with fluorescent mantADP and the drop in fluorescence was measured upon addition with MTs. For ADP exchange rates, the kinesin was incubated in the presence of ADP and the rate of change in fluorescence

112 was recorded after addition of mantADP. These experiments were carried out by William O. Hancock, Pennsylvania State University.

113 Chapter 6: Mechanochemical properties of the heterotrimeric mammalian Kinesin-2 motor, KIF3A/B, studied by optical trapping

6.1 Abstract

The mammalian kinesin-2, KIF3A/B, is a heterotrimeric protein involved in many cellular processes, notably intraflagellar transport. In a number of cellular processes, bidirectional transport results from the opposing activities of KIF3A/B and dynein bound to the same cargo, but the load-dependent characteristics of kinesin-2 are not known. Here, we used a feedback-controlled optical trap to probe the nanomechanical properties, such as velocity, run length and unbinding kinetics, of mouse KIF3A/B under various load regimes and nucleotide conditions. In addition, each motor domain was characterized by studying homodimeric mutants with modified neck-linker and dimerization domains. A comprehensive pathway is introduced for the processive cycle of KIF3A/B, quantifying the principal force-dependent kinetic transitions from global fits. We also find that KIF3A/B run lengths under load are strongly force- dependent, particularly when compared to conventional kinesin, which has important implications for understanding multi-motor transport in cells.

6.2 Introduction

KIF3A/B, a kinesin-2 motor, is an essential protein in mice and is involved in transport and mitosis [12]. The two different motor domains, KIF3A and KIF3B, and a light chain, KAP3, form a heterotrimeric protein complex that is expressed ubiquitously in mammals. It is one of the most abundant kinesin family motors [185], and is particularly enriched in neuronal tissue where is plays a role in fast axonal transport and axonogenesis [11]. Heterotrimeric kinesin-2 motors are present in many diverse organisms, including algae and protozoa, and their functions are often linked to ciliogenesis and intraflagellar transport (IFT) [10]. Ciliopathies resulting from disruption of IFT are linked to developmental disruptions and polycystic kidney disease [11, 13].

114 Conventional kinesin-1 moves along microtubules, toward the plus-end, taking 8-nm steps in an asymmetric, hand-over-hand fashion before dissociating [125, 127]. Its mechanochemistry has been studied extensively, providing details of force- dependent kinetic transitions [86] and the gating mechanisms by which the ATP hydrolysis cycles of the two motor domains are maintained out of phase to ensure efficient stepping and high processivity [138, 152]. KIF3A/B and other kinesin-2 motors are also processive, ATP-dependent transport motors [186], but the details of their force-dependent mechanochemistry are lacking.

Most kinesin family members share a similar structure, with two N-terminal motor domains joined to a common coiled-coil stalk and a C-terminal domain that binds cargo and/or other protein subunits. Kinesin-2 is unique in that it has two non- identical motor domains with full ATPase activity. KIF3A can associate both with KIF3B and KIF3C, another closely related gene product [187], but the biological basis for having different motor domains and a combinatorial association is still unknown. In this study we aimed to carefully characterize the enzymatic cycles of KIF3A and KIF3B to fully understand the contribution from each subunit to the function of the wild-type holoenzyme, especially under force.

While the structures of kinesin motors from various families are similar, the observed characteristics, such as velocity and run lengths, can vary by orders of magnitude [37, 150]. For conventional kinesin-1 many structural elements have been studied but the generality of the structure-function relationships across kinesin families is not well known. The neck-linker, a 14–18 amino acid segment joining the motor domains to the neck coiled-coil, has been shown to dock to the motor domain upon ATP-binding [65] and this docking, coupled with the tension between the kinesin heads mediated by the neck-linker, is thought to underlie much of the gating of the ATPase cycles. Varying the neck-linker length can modulate run lengths and the kinetic cycle [64, 79, 136].

Because the cellular roles of kinesin-2 motors are distinct from kinesin-1, the mechanochemical properties of the motors are expected to differ. Consistent with this, we showed previously that the unloaded velocity and processivity of kinesin-2 motors

115 are less than those of kinesin-1. Furthermore, kinesin-2 motors differ structurally from kinesin-1 in having longer neck linker domains and having two different motor domains, in contrast to the homodimeric structure of Kinesin-1. Hence we set out to answer the following questions: 1) How do kinesin-2 motors behave under load. 2) Are the two heads of kinesin-2 functionally equivalent? 3) What influence does the dimerization domain and extended neck linkers of kinesin-2 have on the load- dependent properties of the motor. Answering these questions is important both for understanding the fundamental mechanism by which N-terminal kinesins generate force and for understanding how different kinesins are tuned for their cellular functions.

6.2.1 Kinesin-2 in bidirectional transport During intracellular transport cargos are often attached to several motors, including kinesin family motors, and even myosins [156]. This leads to saltatory motion, where the organelle frequently changes direction along its track and also frequently pauses before restarting [188]. The bidirectional transport along microtubules is very common and is displayed by many cargos, including mitochondria, endosomes, phagosomes, secretory vesicles, viruses and intermediate filaments [189]. The main biological utility from moving such back and forth is not clear, but several advantages have been proposed [188, 189]. One advantage may be economy, where motors from a small number of protein families can be used for many different tasks by modifying the overall temporal and spatial characteristics of the transport. The saltatory motion could also facilitate establishing polarized distributions of organelles and may help the motors circumvent obstacles on the crowded microtubule tracks. The bidirectional transport may also allow the cargos to explore the cellular space more efficiently to promote their target binding through a search and capture mechanism. Jolly and Gelfand [188] extend this idea to the promotion of interaction between cargos, guided by the partition of the motor-bound cargos by means of posttranslational modifications of the microtubules. Finally, bidirectional transport may act as a proofreading mechanism where errors in motor attachment and track selection can be corrected. By continuously evaluating and

116 changing the motion in response to local conditions, the accuracy of the transport may be increased.

The mechanisms governing the change in direction during bidirectional transport have not been unequivocally determined and are the subject of ongoing research. Several studies have shown that the physiological cargos have both kinesin and dynein attached at the same time [156, 190-192], as reviewed by Bryantseva and Zhapparova [193]. In U. maydis early endosomes, the minus end motion was favored by the presence of dynein, but in most other cases both dynein and kinesin motors are present during both minus- and plus-end directed motion. Consequently, two general models have been proposed for explaining the change in direction during bidirectional transport: mechanistic tug-of-war and coordinating regulation of motors [193]. The latter could be accomplished either through an external coordinating complex or through direct stochastic regulation of the motors by binding partners or post- translational modifications [188]. Results have been reported supporting both models and they need not be mutually exclusive.

The coordination model was motivated by experiments showing that inactivation of one motor abrogated transport by the opposite-polarity motor, as reviewed by Jolly and Gelfand [188]. This was seen by directly affecting the motors [194-197] and also by disrupting the cofactor [198-202]. Regulators of bidirectional transport include Halo [203], Klar [204], LSD2 [205] and Huntingtin [7], but a master coordination complex has not been found and may not exist [188], as Ally et al. showed that the existence of active opposite polarity motors is sufficient for activating bidirectional transport of peroxisomes in Drosophila [206].

The tug-of-war model posits that the change in directionality is not due to regulatory events but is a direct consequence of the properties of the individual motors, acting as teams moving the cargo in opposite directions. Load-dependent dissociation of opposite-acting proteins can lead to instabilities as an initial unbinding event increases the load the on the remaining proteins [207]. A model where this positive feedback is applied to bidirectional transport was proposed by Müller et al. [184, 208]. It is based on six parameters for each type of motor and the model is

117 attractive partly due to its simple assumptions. The number of motors that are bound to the microtubule substrate over time is governed by a binding rate, π0, an unloaded detachment rate, ε0, forward and back velocities, vF and vB, and stall and detachment forces, Fs and Fd, that characterize the force-induced deceleration and detachment rates, respectively. The total force in each direction is assumed to be shared equally between motors in each team and force balance is achieved by matching the overall velocity of the cargo with the force-velocity relationships for each motor. Müller et al. assumes an exponential dependence in detachment rate, such that ( ) =

exp ( ), where Fd is determined from an exponential decrease휖 퐹in run length under휖0 force.퐹⁄퐹푑 In reality, the unbinding rate of a motor is equal to the velocity divided by the run length and this expression should be used instead for future simulations. For the kinesin mechanochemical cycle, this force dependence is more complex and there is no a priori reason for it to even be monotonic. Dynein’s velocity has been shown to have a higher force sensitivity and the motor displays a catch-bond attachment under load, whereby the resident time on the microtubule increases with load [209, 210]. This suggests that the model may instead predict behaviors opposite from fast dynamic switching. Nevertheless, both Müller et al. and other groups claim reasonable agreement between the simplified model and experiments [156].

Other studies show experimental evidence of tug-of-war mechanisms in the transport of endosomes [191], filament switching [211], and myosin transport and several theoretical extensions of the model have been proposed [212-216]. Some of these extend beyond simple load-sharing scenarios, which may be applicable since experiments indicate that the behavior of several motors may be more complicated [217-219].

Despite the relative success of the tug-of-war approach, several authors report incompatibilities with such models and experiments. Kunwar et al. [220] obtained good agreement using a stochastic tug-of-war model for one condition, but the results did not scale properly with motor numbers. Leidel et al. [210] trapped lipid droplets and found that, after detaching, the droplets had a high propensity to resume motion in the same direction. Such a memory effect points toward regulation rather than a

118 stochastic model. Finally, measurements with programmable DNA scaffolds that allow for precise control of motor number did not show fast switching in the presence of dynein and kinesin-1 [221], pointing toward a regulatory mechanism in vivo.

In summary, bidirectional transport in the cell is far from fully understood and both regulation and tug-of-war mechanisms may be responsible for aspects of this process. To distinguish between models, more refined experimental data are needed. Mechanistic models can be further refined, but they all critically depend on several experimentally determined variables, notably the force-dependent velocities and unbinding rates, as well as the rate at which the motors associate with the microtubule. Combining both tug-of-war interactions and biases from regulation of the individual motors may necessitate studying individual motors also in the presence of cofactors. Autoinhibitory mechanisms within the motors have to be characterized as well, since they may modulate the attachment rate significantly. To assess different models, understanding the force-dependent behavior of the individual motors is crucial. Kinesin-1 is relatively well studied, but few force-dependent characteristics have been reported for other motors, such as Kinesin-2, which is even more abundant on many cargos [156]. The Kinesin-2 unloaded velocity and run length have been reported but there has been no detailed description of its force-dependent parameters. In a tug-of- war situation, these are key determinants for the switching probabilities and since the phase-space of the models can be large, accurate outcomes depend on input parameters from high-quality optical trapping experiments [222]. In the present work we characterize the force-dependent properties of Kinesin-2 and find that a number of key mechanochemical parameters differ significantly from previously assumed values. The run lengths display a bimodal behavior, the motors ‘slip’ and reattach quickly, the motors detach rather than stall, and the activity in the optical trap is suggestive of a weak autoinhibitory mechanism.

119 6.3 Results

6.3.1 Load-dependent KIF3A/B stepping studied using optical trapping To understand the influence of external load on the stepping kinetics of kinesin-2, we used a bead assay and an optical trap to study heterodimeric mouse KIF3 and homodimeric mutants, comparing their stepping behavior to the well characterized Drosophila kinesin-1 [135, 186]. Hereafter we refer to the motor domains and neck- linkers from the KIF3A and KIF3B gene products as “A heads” and “B heads”, respectively. Our KIF3A/B was a full-length, his-tagged dimeric wild-type motor with both A and B heads. The KIF3A/A and KIF3B/B constructs had the B head substituted by an A head and vice versa, generating motors with two identical heads while retaining the wild-type heterodimeric coiled-coil stalk, as described previously [186].

All three constructs showed robust, processive movement for ATP concentrations as low as 100 nM, see Figure 6.1. We verified single-motor regimes using Poisson statistics [128]. Steps of 8 nm, the microtubule lattice spacing, were observed under a variety of forces and ATP concentrations indicating that kinesin-2 moves in a hand-over-hand fashion along the microtubules, similar to kinesin-1, as seen in Figure 6.1A. No asymmetries in step size were observed.

Figure 6.1 Processive motion of KIF3A/B. A,B. Traces of KIF3A/B motion under hindering load in an optical trap, indicating forward steps (blue), backsteps (yellow) and slips (red). Conditions were 5 µM ATP, 4 pN in panel A and 2 mM ATP, 2 pN in panel B. Traces for 3A-KHC and 3B-KHC are shown in Figure 6.6.

120 Kinesin-2 runs were infrequent but consistent from run to run for all constructs. This intermittent activity was not observed in chimeras where KIF3 motor domains were fused to kinesin-1 coiled-coil domains (see below). Both kinesin-1 and KIF17, a homodimeric kinesin-2 motor, are known to be autoinhibited by their stalks [71, 72] and our observations are consistent with a mechanism by which the native KIF3A/B stalk or tail, but not the stalk of kinesin-1, weakly inhibits the KIF3A/B motor domains in a similar way.

Using force-clamp conditions, the motion of all three KIF3 constructs and kinesin-1 was recorded across a wide range of forces and ATP concentrations. A striking observation was that the velocity of wild-type kinesin-2, KIF3A/B, was affected much less by hindering load than that of kinesin-1 (Figure 6.2A). This contrast indicates that there are differences in force-dependent rate constants between motor families with implications for bidirectional cargo transport. To uncover differences in the mechanochemical properties of the two heads of KIF3A/B, the force-velocity relationships of all motors were characterized (Figure 6.2B). KIF3B/B was faster than KIF3A/A at low loads but the KIF3B/B velocity was slowed to a greater extent by a hindering load. The ATP dependence of velocity at different loads was also assessed for the KIF3 motors (Figure 6.2C-D). Interestingly, for all conditions, the KIF3A/B velocity is close to the average of the KIF3A/A and KIF3B/B velocities (Figure 6.2), meaning that the wild-type heterodimeric KIF3A/B motor is kinetically largely the sum of its parts, the A and B heads. This result is further supported by the KIF3A/B randomness parameters (Figure 6.2E-F), which are intermediate of those for KIF3A/A and KIF3B/B. Data were also collected for the load-dependence of KIF3A/A under low ATP (5 µM), as shown in Figure 6.3.

121

Figure 6.2 KIF3A/B, KIF3A/A and KIF3B/B velocities and randomness. A–F Motor velocities and randomness a function of applied hindering load (A,B,E) or ATP concentration (C,D,F). The data in panels A, B and E were collected under saturating ATP conditions (2 mM) and the data in panel F were collected at 4 pN of hindering load. Data points and error bars (s.e.m.) indicate experimental velocities or randomness values. The curves represent the result from a global fit. For KIF3A in 5 µM ATP, see also Figure 6.3A-B.

122

Figure 6.3 KIF3A/A data under low ATP concentrations or high force. Panel A, B. KIF3A/A velocity and randomness a function of applied hindering load under a low ATP concentration (5 µM). Solid line indicates the same global fit to the experimental data as in Figure 6.2.

Panel C, D. KIF3A/A run lengths as a function of load under a low ATP concentration (5 µM) or as a function of ATP concentration under high hindering load (−6 pN). The curves represent fits to an exponential function (force-dependence) or a flat line (ATP-dependence).

6.3.2 Model for processive stepping of KIF3A/B under load To understand kinetic and mechanical differences between the A and B heads in greater detail, we constructed a combined minimal kinetic pathway for KIF3A/B and used the model to fit all of the velocity and randomness results from the force-clamp experiments shown in Figure 6.2 and Figure 6.3. Figure 6.4 shows the mechanochemical cycle for KIF3A/B, which encompasses two 8-nm steps. The corresponding cycle for the KIF3A/A motor was obtained by replacing the states involving the B head cycle ([1B]–[4B]) with those for the A head ([1A]–[3A]), and vice versa for KIF3B/B. All 13 kinetic parameters were globally fit to the 17 velocity and randomness curves using analytical expressions. Final parameter values are given

123 in Figure 6.4 and fits of the model to the data are shown as solid lines in Figure 6.2 and Figure 6.3A-B.

Figure 6.4 Model for KIF3A/B stepping.

Left. Processive stepping pathway for the kinesin-2 constructs. Transitions k5A and k5B (red arrows) are associated with backsteps, i.e., steps toward the microtubule minus-end.

Right. Diagram of kinesin-2 constructs and a table of fit parameters from the global fit of kinetic model to the experimental data shown in Figure 6.2. Tentative assignments to the mechanochemical transitions, as shown to the left, are indicated. Corresponding values for kinesin-1 and kinesin-2 mutants can be found in Table 6.1.

As an arbitrary starting point for the processive cycle, we use the A head in the microtubule-attached no-nucleotide state [1A]. At a given force the ATP-dependence for each construct exhibits Michaelis-Menten-type kinetics. To account for changes in the apparent Michaelis-Menten constant, KM, with force, we introduce reversible ATP binding, [1A]↔[2A], directly followed by a force-dependent transition [2A]→[3A], ref. [164]. The forward stepping of the motor occurs during this transition and its rate slows exponentially as the hindering load is increased, i.e., k2A(F)=k2A,0 exp(−F·δ/kBT), where k2A,0 is the unloaded rate and δ is a characteristic distance parameter. The next step in the pathway, [3A]→[4A], includes ATP hydrolysis and attachment of the tethered head, generating a two-head-bound state. The final step [4A]→[1B] consists of trailing head detachment and phosphate release to complete one step. While a three state model (combining states 3 and 4) was sufficient to model most of the data, fitting the model to the randomness data required

124 four states for head B. The data for head A were not sufficient to constrain parameter k4A, so in the actual fit, states 3A and 4A were lumped, equivalent to an infinitely fast [3A]→[4A] transition. For more information about the fitting, the parameters and their confidence intervals, see section 6.5.4.

6.3.3 Backstepping Backstepping, in which a kinesin motor moves 8 nm towards the microtubule minus- end, occurs occasionally for conventional kinesin-1 but the frequency can increase significantly if gating is reduced, for example by lengthening the neck-linker [79]. While backstepping generally has only a small effect on velocity, except near the stall force, it can have a large effect on second-order parameters such as the randomness. We observed 3% backstepping for kinesin-1 in line with previous observations, but the probabilities were higher for the kinesin-2 constructs: 8% for KIF3A/A (N=1206), 6% for KIF3A/B (N=1504) and 3% for KIF3B/B (N=1107) under 4 pN of hindering load and 5 µM ATP in the buffer.

Because the high randomness values observed for kinesin-2 (Figure 6.2E-F) could not be reproduced using simpler kinetic schemes, we introduced backstepping into the model as a kinetic step connecting the ATP-bound states with the initial states for the other respective head, i.e., [2A]→[1B] and [2B]→[1A], see Figure 6.4. These kinetic steps, with rates k5A and k5B, are associated with physical 8.2 nm backsteps towards the microtubule minus (−) end. For simplicity all necessary events included in the backstepping pathways, such as rebinding of the rear-head and possible premature ATP hydrolysis have been combined. The KIF3A/B backstepping fraction from the kinetic model fit alone varies with force and ATP and at 9% for the same conditions as above it is comparable to the experimentally observed value, suggesting that our model represents a reasonable minimal pathway.

125 Table 6.1 Kinetic parameters for kinesin-1 and kinesin-2 mutants. A. Kinetic parameters, kinesin-1 Rate Transition Value −1 k2 Neck-linker docking (s ) 3188 ± 197 −1 k3 ATP hydrolysis (s ) 97.9 ± 0.5 δ Distance parameter (nm) 3.68 ± 0.05

B. Kinetic parameters, kinesin-2 mutants

Rate Transition 3A-KHC 3A-KHCP>A 3A-KHCP>A, ΔDAL 3B-KHC −1 k2 Neck-linker docking (s ) 2800 ± 400 1300 ± 300 800 ± 100 3200 ± 1000 −1 k3 ATP hydrolysis (s ) 46.1 ± 0.3 47.6 ± 0.8 48.7 ± 0.7 50 ± 1 δ Distance parameter (nm) 3.0 ± 0.1 2.1 ± 0.2 2.1 ± 0.1 3.5 ± 0.5 Kinetic parameters for the processive stepping of kinesin-1 (panel A) and kinesin-2 mutants (panel B). The experimental force-velocity curves in Figure 6.2 and Figure 6.9, obtained under 2 mM ATP, were fit to the following kinetic scheme:

[ATP]/ [1] [2] 퐹훿 [3] [1] 푘2 exp�− � 푘1 푘−1 푘푇 푘3

The scheme is similar to that in Figure�⎯⎯⎯⎯ 6.4⎯⎯⎯.⎯ The� rates�⎯ k⎯3⎯ and⎯⎯⎯ k⎯4� in Figure→ 6.4 have been combined into k3 here, and the back-stepping pathway was not included. As ATP binding was fast at these saturating −1 −1 conditions the assumed second order ATP binding rate, k1 = 3 µM s and ATP unbinding rate, k−1 = 50 s−1 could be fixed.

6.3.4 Kinesin-2 processivity is strongly force-dependent The force-dependence of kinesin processivity is a critical measure for determining how kinesin-driven intracellular transport is affected by opposing motors or obstacles in the cell. Maintaining long-range processive motion against these opposing forces requires a high degree of inter-head coordination and a strong motor-microtubule interaction. To determine whether kinesin-2 processivity is maintained under load, we analyzed the dependence of motor run lengths on hindering load in force-clamp experiments. Unexpectedly, we found that the apparent processivity of kinesin-2 drops markedly when force is applied such that runs consist of only a handful of steps under moderate pN-level loads, see Figure 6.5 and Figure 6.3C-D. Unlike kinesin-1, where

126 run lengths depend only moderately on load, there were two regimes of processivity for kinesin-2. Under no load the runs were long, approaching those of kinesin-1, but in the second regime, where any external load is applied, this motion is disrupted and the motor becomes poorly processive.

We also observed short detachments under hindering load, hereafter referred to as slips, for motors containing the KIF3A motor domain (Figure 6.1). We score the end of a run at slips larger than two steps (16 nm), which are easily identified under force. The slips were present also for constructs containing KIF3A heads and a kinesin-1 neck and stalk (described below) so the effects can be attributed to properties of the motor domain. Similarly, the sharp drop in run length under force is even more apparent for these chimeric constructs but absent for kinesin-1.

The mean run lengths, L, for all constructs were determined by curve fitting to exponential distributions. For hindering loads these run lengths exhibit an exponential dependence on force (F), L=L0 exp (−F·δ/kBT). The data and results from fits are displayed in Figure 6.5 and we found that the force dependencies, measured by the distance parameter, δ, are similar between kinesin-1 and kinesin-2 but that extrapolated unloaded run lengths, L0, differ by an order of magnitude. L0, representing the second run length regime, is also significantly lower than the observed run lengths in the unloaded regime, Lobs, for constructs with a KIF3A head. There was no clear ATP dependence, as run lengths for a given force (0, 4 or 6 pN) were unchanged when the ATP concentration was decreased from 2000 to 0.5 µM, see Figure 6.5C-D and Figure 6.3D. Run lengths were asymmetric with respect to the direction of applied load, with assisting loads leading to even shorter run lengths that were not readily measured.

The run lengths for KIF3A/B fell between those of KIF3A/A and KIF3B/B for nearly all ATP and force conditions, indicating that also the detachment pathway for the wild-type motor is an ad-mixture of those for each motor domain.

127

Figure 6.5 Kinesin run lengths. Kinesin run lengths as functions of force (A, B) or ATP concentration (C, D). Panel A shows kinesin-1 and kinesin-2 data across all forces and panel B includes only kinesin-2 data under load to show differences between motor constructs. Curves represent fits to exponential functions (force dependence) or flat lines (ATP dependence), with fit parameters indicated in the table in panel E. Lobs is the unloaded run lengths observed using video tracking, averaged for all ATP concentrations, whereas L0 is the extrapolated zero-force run length from force-clamp experiments. For KIF3A/A in 5 µM ATP and at 6 pN see also Figure 6.3C-D.

In the canonical mechanochemical cycle, kinesin detaches from the microtubule in its one-head-bound state, following ATP binding. Thus, processivity is determined by the competition between the on-pathway rebinding of the tethered head to the next tubulin binding site, on one hand, and detachment or entry into a weakly bound off-pathway state, on the other. We hypothesized that the greater load dependence of processivity of kinesin-2 is due to either faster dissociation from the

128 one-head bound state or slower binding of the tethered head under load. To test these hypotheses, we first measured the unbinding kinetics of kinesin-1 and kinesin-2 motors subjected to rapid increases in load, as described in the next section. Second, we tested whether modifying the neck linker domains, which is predicted to alter tethered head binding kinetics, changes the load dependence of processivity.

6.3.5 Force-dependent unbinding dynamics By measuring unbinding forces, i.e., the forces at which kinesin motors detach from microtubules in response to ramp increases in load, it is possible to probe the load dependence of dissociation of KIF3A, KIF3B and kinesin-1 motor domains in different nucleotide states [182]. To avoid potential artifacts from dimerization domains and to collect sufficient data for meaningful curve fitting, the experiments were carried out using homodimeric chimeras: 3A-KHC and 3B-KHC. These motors consist of KIF3 motor domains and neck linkers fused to a truncated kinesin-1 dimerization domain and stalk. They have been fully characterized in single-molecule assays [64], and step along microtubules, as seen in Figure 6.6. The binding frequency was considerably greater than for the full-length KIF3 constructs, and the identical stalk removed uncertainties in elasticity between the motor types.

Figure 6.6 Examples of 3A-KHC and 3B-KHC stepping. The motors were attached to a bead in an optical trap under force clamp conditions ([ATP] = 2 mM, 5 pN hindering load)

The force-dependent unbinding rate, koff(F), is characterized by an unloaded off-rate, k0, and a distance parameter, δ, such that koff(F)=k0 exp (F·δ/kBT) [223]. In

129 our experiments the load increased linearly with time, i.e., F = αt, where α is the loading rate in pN s−1. The corresponding unbinding force distribution is

N(F) = C·exp((Fδ/kBT) + (1 − exp(Fδ/kBT))·kBT/(δ·α·τ)) (1), where τ = 1/k0 and C is a constant (adapted from [182]). The free parameters, k0 and δ, are obtained by fitting to the experimental histograms, all shown in Figure 6.7.

Unbinding forces were measured in different nucleotide states and for different directions of pulling. 0.5 mM AMP-PNP was used to mimic the ATP state and 10 U/ml apyrase with no added nucleotide was used to assess the no nucleotide (apo) state. Both of these state were studied using the loading rate α=10 pN s−1, but the faster unbinding rates in 1 mM ADP required a higher loading rate, α=100 pN s−1.

A few general conclusions can be made from the unbinding data. First, all kinesin constructs bound tightly to the microtubule in AMP-PNP or no nucleotide. The unbinding rates from these states were much lower than the detachment rates under similar load during processive runs (see Figure 6.8), so detachment from either of these states is unlikely. Second, in ADP the unbinding rates are faster for KIF3A and KIF3B than for kinesin-1, consistent with shorter run lengths seen for kinesin-2 motors. Third, in ADP the detachment rates in the forward (plus-end) direction were faster than corresponding rates in the backward (minus-end) direction. Finally, the load dependence of all the detachment rates was generally small (max δ of 1.1 nm). As the run lengths are more dependent on force, the unbinding itself is likely not the main force-dependent parameter. Stated a different way, the unbinding rates are correlated with the run lengths under load, but cannot explain the precipitous drop in run length between unloaded and loaded runs.

130

Figure 6.7 Unbinding force measurements. Top. Unbinding force measurements for 3A-KHC, 3B-KHC and kinesin-1 (rows) for different nucleotide conditions (columns). Experimental histograms are plotted with the fits for each pulling direction. Negative unbinding forces correspond to pulling the kinesin toward the microtubule minus- end (hindering load), and positive forces toward the plus-end (assisting load). The loading rate was 100 pN s−1 in the presence of ADP and 10 pN s−1 for AMP-PNP and no nucleotide (apyrase). Data at low forces were excluded in the fits due to possibility of missed events.

Bottom. Fit parameters, with associated errors from the fits, are shown for each construct and experimental condition, using the parameters indicated in equation (1). k0 is the unloaded off-rate and δ is the characteristic distance parameter. For microtubule dissociation rates during processive stepping see also Figure 6.8

131 In ADP the observed unbinding rates for kinesin-1 were considerably higher than those previously reported for kinesin-1 using a 20-fold slower loading rate [182]. From fits to the backward pulling data (Figure 6.7 bottom), it can be seen that for

KIF3A and KIF3B, k0 is 2–3 fold faster than kinesin-1. Asymmetry between forward and backward pulling has been reported previously for kinesin-1 [182] and it is a feature of kinesin-2 as well. Using separate unloaded unbinding rates for each loading direction resulted in significantly better fits for the measured distributions (e.g., reduced χ2=1.0 for kinesin-1 in ADP) compared with the case of one common variable (reduced χ2=3.3).

In AMP-PNP under assisting loads the unloaded unbinding rates, k0=0.1– 0.2 s−1, were similar between constructs but reverse loads gave rise to lower unbinding forces for kinesin-2 than for kinesin-1. The distributions for AMP-PNP were unimodal and mostly had clear maxima, indicating relatively strong force-dependences, with characteristic distance parameters, δ, of about 1 nm.

In the absence of nucleotides the average unbinding force was between 9 and 16 pN for all constructs. Unlike the AMP-PNP or ADP cases, where motors repeatedly attached to the microtubule, only a single measurement per molecule was possible under no-nucleotide conditions. The force-dependence for unbinding was undetermined, but the rates were low (k<1 s−1) for all constructs.

Figure 6.8 Rate of dissociation during processive stepping. Force dependence of the rate of dissociation from the microtubule during processive stepping for kinesin-1 and KIF3A/B. The rates were calculated by dividing the velocities and the run lengths shown in Figure 6.2 and Figure 6.5.

132 6.3.6 Testing the role of the neck linker domain in load-dependent processivity Besides differing in their core catalytic domains, kinesin-1 and kinesin-2 also differ in their neck linker domains – while the kinesin-1 neck linker has a 14 residues, the two heads of kinesin-2 both have 17 residue neck linkers [179]. We showed previously that differences in unloaded processivity between kinesin-1 and kinesin-2 result not from differences in the core motor domain but in the length of the neck linker domains [64, 179]. Here, we tested whether the contrasting load-dependent properties of kinesin-1 and kinesin-2 resulted from differences in the properties of the head domains or from the different lengths of their neck linker domains.

We focused on the 3A-KHC construct [64] and compared the load-dependence of velocity and run length to 3A-KHCP>A, which effectively has a longer neck linker due to swapping out a kinked proline residue [179], and 3A-KHCP>A,ΔDAL, which has a 14-residue neck linker like kinesin-1. At zero load, run lengths depended strongly on the length of their neck linkers, with 3A-KHCP>A being less and 3A-KHCP>A,ΔDAL being considerably more processive than 3A-KHC (Figure 6.9A). These effects were even larger than previous observations [179], possibly due to using beads in the present experiments. Remarkably, the influence of neck linker length vanished when force was applied, with all motors having similar run lengths (Figure 6.9A). This suggests that even a small external force can disrupt any enhanced gating that results from shortening the neck-linker.

Similarly, changing the neck linker length had no major effect on velocities of the different 3A-KHC constructs at either low or high loads (Figure 6.9B). The force- velocity relationship for 3B-KHC was similar to 3A-KHC, and the dependence of velocity on load was slightly less than for the corresponding 3A and 3B homodimers that included the normal kinesin-2 coiled coil, see Table 6.1 and Figure 6.4. The run lengths of 3B-KHC were very short, only a few steps on average, for all forces.

133

Figure 6.9 Run lengths and velocities for chimeric kinesin-2 mutants. Run lengths (panel A) and velocities (panel B) for chimeric mutants of kinesin-2 heads fused to a kinesin-1 stalk. The run lengths under force, shown more clearly in the inset to panel A, were much shorter than the unloaded run lengths. The experiments were performed under saturating ATP conditions (2 mM). The force dependences for the velocities were fit using a simple 3-state model with one force-dependent transition and run lengths were fit to exponential functions (see Tables S1 and S2).

Corresponding data for kinesin-1DAL are shown in Figure 6.10.

Table 6.2 Run length parameters for kinesin-2 mutants. Run length parameters, kinesin-2 mutants

Rate Transition 3A-KHC 3A-KHCP>A 3A-KHCP>A, ΔDAL

Lobs Unloaded run length (nm) 1344 ± 151 893 ± 95 2855 ± 299

L0 Extrapolated run length (nm) 139 ± 10 119 ± 8 115 ± 12

δ Distance parameter (nm) 1.3 ± 0.1 1.6 ± 0.1 1.4 ± 0.1

Lobs is the observed unloaded run length, whereas L0 is the no-load run length extrapolated from run length data under force.

We also compared the behavior of kinesin-1 to kinesin-1DAL, which includes the last three residues of the kinesin-2 neck linker. As seen in Figure 6.10, extending the kinesin-1 neck linker significantly reduced the unloaded run length and moderately reduced the unloaded velocity, as seen previously [179], but the force dependences were not influenced in a major way. Hence, the contrasting behavior of kinesin-1 and kinesin-2 under load could not be explained by differences in the length of their neck linker domains.

134

Figure 6.10 Velocities and run lengths for Kinesin-1DAL

Panel A. Kinesin-1DAL velocity as a function of force under saturating ATP concentrations (2 mM). Experimental data were fit to a 3-state model.

Panel B. Kinesin-1DAL run length as a function of force at saturating ATP concentrations (2 mM). The data were fit to an exponential force-dependence.

As a final test, we asked whether the sequence of the neck-linker domain and its interactions with the motor domain is crucial for the force-dependent properties. To assess this, we swapped the neck linker domains between kinesin-1 and kinesin-2. 3A- KHC with a kinesin-1 neck linker behaved similarly to 3A-KHC (data not shown) whereas kinesin-1 with a KIF3A neck-linker was not-functional. Why the kinesin-2 motor remained functional, unlike the kinesin-1 motor, is not clear, but it is possible that a strong, specific, docking of the neck-linker is necessary for kinesin-1 but not for kinesin-2.

6.4 Discussion

The goal of this study was to understand the performance of kinesin-2 motors under load and to uncover relative contributions made by the two motor domains and the neck linker and coiled-coil domains to kinesin-2 motility. By performing force-clamp optical trapping measurements with kinesin-2, we found unexpected and unique features that set this family apart from previously studied kinesin family motors. The run lengths for KIF3A/B, the mouse kinesin-2 ortholog, are very short under load, in sharp contrast to the unloaded run lengths or those of kinesin-1. In contrast to this greater force-dependence of processivity, KIF3A/B velocity is less affected by load

135 than kinesin-1, suggesting there are structural or kinetic differences between the two motor families. By analyzing homodimeric mutants, we were able to derive a two- head stepping model that fit all of the force-clamp data. The force-velocity and force- run length curves for KIF3A/B were almost perfectly intermediate between KIF3A/A and KIF3B/B, demonstrating that the heterodimer characteristics are an admixture of the two motor domains. Furthermore, when fused to the kinesin-1 coiled-coil, both KIF3A and KIF3B homodimers were functional, suggesting that the heterodimeric coiled-coil domain does not play a dominant role in motor function.

Our data and modeling for KIF3A/B show that the canonical model for kinesin-1 stepping is applicable to kinesin-2. Kinesin-2 binds strongly in the no- nucleotide ATP-waiting state and the unbinding from the microtubule takes place from another, distinct, point in the kinetic cycle, as illustrated by the run lengths, which are unchanged from very low to saturating ATP concentrations. When moving against a hindering load, the velocity of KIF3B/B was slowed to a greater extent than KIF3A/A, and the run length of KIF3B/B was reduced to a lesser extent than KIF3A/A. In a simple sense, the behavior of KIF3B/B was more similar to kinesin-1 than was KIF3A/A. In the two-headed cycle shown in Figure 6.4, the data were best fit by a model in which the load dependence of neck linker docking (δ for step k2) for KIF3B is twice that for KIF3A. The structural basis for this difference is not clear, since the neck linkers only differ by two residues, not implicated in key docking interactions with the core catalytic domain and neck cover [224].

A kinesin step involves both a concerted conformational change (neck linker docking) and a diffusive component whereby the tethered head finds its next binding site. The distance parameters associated with the conformational change were correlated with the run lengths and one possibility is that in kinesin-2 this conformational change, which is affected by external load, accounts for a smaller fraction of the 8-nm step, leading to diminished gating and drastically reduced run lengths. The diffusive component can be affected by the total length of the neck-linker but we found that the effects on the velocity or run lengths, under force, were minor when modifying the neck-linker length.

136 From the load-dependence of KIF3A/B velocity and run length, relevant metrics for motor function in vivo, no obvious emerging properties resulted from combining two different motor domains. The properties of the mouse KIF3A/B subunits differ substantially from those of the C. elegans kinesin-2 ortholog KLP11/20 where the engineered homodimer KLP11/11 (equivalent to KIF3B/B) was two-fold slower but fully functional in gliding assays, but was nonprocessive in single-molecule bead assays [73]. From that work, it was concluded that the heterodimeric structure is necessary for proper regulation of the motor domains by the stalk/tail domain. Subsequent work showed that the C. elegans, X. laevis, and S. purpuratus kinesin-2 orthologs spiral around microtubules in multi-motor bead assays, while mouse kinesin-2 follows a straight path similar to kinesin-1. However, the experiments indicated that the spiraling is not determined by the motor domains per se, but by sequences in the neck-coil domain, leading to a model where coiled-coil instabilities determine the spiraling [225]. Interestingly, we found that KIF3A motor domains, when fused to the kinesin-1 coiled-coil, performed very similarly to KIF3A/A, the homodimer containing the native heterodimeric coiled-coil, while fusing KIF3B to the kinesin-1 coiled-coil resulted in a functional but minimally processive motor even at zero load. Also, the frequency of events for motors containing the native KIF3A/B coiled-coil domain was very low compared to the-kinesin-1-stalk homodimers, consistent with an auto-inhibitory mechanism whereby the native KIF3A/B stalk/tail inhibits the initial binding of the motor domains to the microtubule, without altering their subsequent processive movement.

To determine whether microtubule affinities are a determining factor for the poor kinesin-2 processivity under load, we performed unbinding force experiments in different nucleotide states. In line with the processivity at low ATP concentrations, we found that the kinesin-2 motor domains are strongly bound in the no-nucleotide state. This is also the case in the presence of AMP-PNP, where they assume an ATP-bound- like state. While off-rates resulting from pulling backwards in these high-affinity states are higher for kinesin-2 than kinesin-1, they are significantly lower than the detachment rate when motors are stepping against hindering loads at saturating ATP

137 (Figure 6.7 and Figure 6.8). Unbinding in the ADP state was slower for kinesin-1 than KIF3A or KIF3B heads. While this broadly consistent with the contrasting run length behavior, the force dependencies do not differ significantly between motor families and are significantly weaker than those for the run lengths (e.g., 0.4 nm versus 1.8 nm for kinesin-1). If the determining factor for the run length were detachment from the ADP state we would expect similar force dependencies. This suggests that external loads modulate the processivity by accelerating entry into, or slowing exit from, an off-pathway low affinity ADP or ADP-Pi state.

The largest drop in kinesin-2 run length occurs from zero load to 1 pN, the smallest force clamp load, such that there are essentially two regimes for kinesin-2 processivity – unloaded and loaded. This was also seen for the 3A-KHC constructs. The run lengths, which were modulated by neck linker length under no load, were independent of the neck linkers and reduced by an order of magnitude under load (Figure 6.9). This contrasts with kinesin-1, where extending the neck linker reduced run lengths to a similar degree from zero load to near stall force (Figure 6.10).

Another distinguishing characteristic of kinesin-2 was its tendency to slip backwards during processive walking and rapidly reattach to the microtubule and continue stepping (Figure 6.1). This points to a mechanism by which the motors either spend a fraction of their hydrolysis cycle in a weakly-bound state that is readily dissociated by external load or, alternatively, they periodically detach and rapidly reattach during processive runs and external loads block the reattachment by dissociating the motor. This mechanism may share similarities to diffusive mechanisms proposed for processive KIF1A monomers [226]. Similar behavior is seen when kinesin-2 motor domains are fused to kinesin-1 coiled-coils, arguing against electrostatic tethering by the neck-coil domain being a primary determinant of this behavior [66].

The load-dependence of processivity has important implications for understanding bidirectional transport by kinesin-2 in cells. IFT particles, neuronal vesicles, melanosomes, and other cargo transported by kinesin-2 also contain bound dynein motors, and the direction of movement is thought to be determined by a

138 competition between plus- and minus-end directed motors [10, 156, 227]. Whereas kinesin-1 slows under a hindering load and eventually stalls, kinesin-2 motors tend to dissociate under hindering loads and rapidly rebind after slipping backward. Hence, kinesin-2 is a more dynamic motor than kinesin-1 and it partially compensates for poor mechanochemical gating by slipping and rapidly reattaching to the microtubule.

The run lengths suggest that one or more steps in the dissociation pathway is exponentially dependent on force. However, we note that the effective overall rate for dissociation from the microtubule during stepping is not governed by such a simple expression, as it incorrectly has been assumed in some proposed models [184]. The appropriate measure for the dissociation rate is the velocity divided by run length, see Figure 6.8. The kinesin-2 detachment rate increases steeply with load, making the motor somewhat amenable to dynamic switching during bidirectional transport, whereas the kinesin-1 residence time on the microtubule changes very little under the influence of opposing motors.

To conclude, we have characterized the mechanochemistry of kinesin-2, quantifying in great detail the force-dependent dynamics, and we found that the motor is distinct from other kinesin family members, such as kinesin-1, when force is applied. Many of these effects are not readily observed without the active application of force, but are determining factors for the motion of cargos within the cell, where often many motors are attached to the same cargo in a viscous environment. Our results therefore highlight the importance of studying such motors under force to properly analyze main pathways of movement and dissociation. Our results suggest that there is more diversity among members of various kinesin sub-families than generally expected.

6.5 Experimental procedures

6.5.1 Kinesin constructs Kinesin constructs were prepared as described previously [186]. The KIF3A/B, KIF3A/A and KIF3B/B constructs, having native stalks, were expressed in Sf9 cells. The kinesin-2 light chain, KAP3, was not included.

139 The other constructs were all expressed in E. coli. [64, 179]. The construct herein referred to as kinesin-1 is D. melanogaster kinesin heavy chain (KHC) with a stalk truncated at residue 560 and fused to a his-tagged GFP. The remaining constructs all had identical stalks (residues 345-560) to kinesin-1 above. The motor domains and neck-linkers for 3A-KHC and 3B-KHC were those from KIF3A and KIF3B respectively. 3A-KHCP>A and 3A-KHCP>A, ∆DAL are identical to 3A-KHC, with the exception of a proline-to-alanine substitution in the neck linker (AA 375) and, for the latter, a deletion of the three last amino acids (DAL) of the neck-linker.

6.5.2 Optical trapping assay Optical trapping was carried as previously described [79]. For all experiments a motility buffer was used, consisting of 80 mM PIPES, 1 mM EGTA, 4 mM MgCl2, 2 mg ml-1 BSA, 2 mM dithiothreitol, 10 µM Taxol (Paclitaxel) and nucleotides at desired concentration. An oxygen scavenging system (1 mg ml-1 glucose, 50 µg ml-1 glucose oxidase and 12 µg ml-1 catalase) was added immediately before use, with increased concentrations were for high-force unbinding experiments. The 6x-his- tagged kinesin was linked to 440-nm-diameter streptavidin-coated polystyrene beads (Spherotech) via a biotinylated Penta-his anti-body (Qiagen). Beads and protein were incubated on a rotator at 4°C for 2 h or more.

6.5.3 Instrumentation All data were collected with a previously described instrument [77]. For force-clamp experiments the position signal was filtered at 1 kHz. The data were recorded at 20 kHz and decimated to 2 kHz. The force-clamp was updated at 500 Hz to maintain a constant offset between trap and bead centers of about 80 nm. The laser power was adjusted for each force and each bead was calibrated as previously described.

For unbinding force experiments the trap was maintained at a fixed position and force was increased by moving the stage at a constant velocity. The trap stiffness was adjusted appropriately to assure that the bead stayed within the linear region of the trap (~120 nm). For all experiments the proportion of active beads was low (<30%) to ensure a single-molecule regime.

140 6.5.4 Data analysis The data were analyzed using IGOR Pro 6.0 (WaveMetrics) to obtain velocities, run lengths and randomness values for each condition. Velocity distributions were obtained from individual linear fits to kinesin runs (N=50 to 700) and the average and standard error of the mean was calculated, weighted by the run lengths. Each run length distribution (N=50 to 700) was fit to an exponential distribution, excluding the first bins, to account for missing events, and bins with fewer than six counts. In total, over 25000 events were used in the analysis.

The force-dependences for the run lengths were fit using exponentials for hindering loads. As no clear ATP-dependence was observed, a flat line was fit to the data as function of ATP concentration.

For unbinding force measurements, separate fits were performed for the distributions for forward and backward pulling directions (see the section 6.3.5 for the full expression). The characteristic distance, δ, was constrained to be positive.

To obtain expressions for the observables in our kinetic model we followed a method by Chemla et al. [149]. The formalism was used previously for Kinesin-1 (Chapter 4) and allowed us to quickly obtain analytical expressions for velocity and randomness, in closed form, without solving eigenvalues and eigenvectors for a large transition matrix. The following description is a short summary of the method, as outlined by Chemla et al. The progress through the mechanochemical cycle is described as a set of coupled first-order differential equations for the probability density Pi(xj,t) of being in a certain state, i, at a given position j along the microtubule. By applying a Fourier transform, the Master Equation can be represented in matrix form, ( , ) = ( ) ( , ). is the transition matrix where diagonal elements, 휕 Mi=j, correspond휕푡 퐏 푞 푡 to퐌 transitions푞 퐏 푞 푡 out퐌 of state i and other elements j on line i, represent transitions into state i from state j. Fourier weights, ± = , are introduced for ∓푖푞푑 forward (+) and backward steps (−), respectively. By휌 taking푒 the Laplace transform of the matrix equation above and inverting, we obtain ( , ) = ( , ) (0), where ( ) ( ) ( ) −1 0 is the vector of initial conditions and , =퐏� 푞 푠 퐑 .푞 As푠 explained퐏 by 퐏 퐑 푞 푠 푠퐈 − 퐌 푞 141 Chemla et al., the velocity and randomness can be solved by only considering the lowest order terms from the characteristic polynomial of , which is the same as the determinant of : 퐌 퐑 | ( , )| = + + ( ) + ( ) + ( ) 푛 2 The expression for the퐑 velocity푞 푠 is푠 ⋯ 훼 푞 푠 훽 푞 푠 훾 푞

(0) = (0) 훾̇ 푣 −푖 and the randomness becomes 훽

(0) (0) (0) (0) = 2 + 2 (0) (0) (0) 푖 훾̈ 훽̇ 훼 훾̇ 푟 − � − 2 � To obtain these expressions in푑 practice훾̇ , the훽 matrix was훽 entered manually in

Mathematica 8.0 (Wolfram Research), and the terms퐌 α, β, and γ were collected after solving the determinant | |. After taking derivatives of β and γ, q was set to 0 and the resulting expressions푠퐈 − for퐌 v and r were compiled. In the model described here, an 8-state model was used (Figure 6.4) and the resulting expressions were parsed for use in IGOR 6, as seen in section 6.5.5.

The experimental data were fit in IGOR Pro. The Global analysis tool uses the Levenberg-Marquardt algorithm for nonlinear regression, minimizing the Chi-square value, = ( ) , where y is the fitted value for a given point i, yi is the 2 2 measured휒 data∑ value푦 − 푦 for푖⁄휎 the푖 point, and σi is and estimate of the standard deviation for yi. For the velocities, yi is the average velocity and σi is the standard error of the mean. The randomness was calculated from the slope of the linefit to the average variance, divided by the step size, 8.2 nm, and the average velocity. The linefit returns a relative error much lower than that for the velocity, so the randomness error was propagated from the standard error of the mean for the velocity at each condition.

The data included in the fit were the force velocity relationships, the ATP dependences for both no load and for 4 pN hindering load, and the randomness as a function of ATP and force. The data sets for both KIF3A/A, KIF3A/B, and KIF3B/B

142 were used. Due to the weak force dependence for KIF3A/A, we also collected velocity and randomness data as a function of force at 5 µM ATP to fully constrain the model. These values were also included in the fit. In all, more than 25000 individual traces were analyzed into 108 average values with associated errors. These values, incorporated into 17 different types of datasets, were used to constrain 13 free parameters. During fitting the same model was used for both KIF3A/A, KIF3A/B and KIF3B/B, but the parameters were linked such that both twin variables (i.e., k1a and k1b) referred to a single rate for the homodimers.

Several models were evaluated and the expression in section 6.5.5 includes a full 8-state model, with reversible ATP binding, a reversible force-dependent step, two additional biochemical steps and a force-dependent backstepping rate. The reverse of the force-dependent step and the force-dependence of the backstepping could not be constrained with the available data, so they were excluded by setting their parameters (k5a, k5a, d5a, d5b, d6a, d6b) equal to zero. In addition, only one of the two biochemical rates (k3a and k4a) could be constrained for the A head. This does not preclude the existence of two steps but suggests that the randomness cannot be used to determine one of them. Consequently, rate k4a was fixed to a very high value (50000 s-1) during the global fitting and was not assigned a numerical value in the table in Figure 6.4. The fit converged properly and the errors in Figure 6.4 are the error for this nonlinear least-squares fit. The reduced Chi-square is rather high (~30) indicating that statistically the fit is not good. The origin of the high Chi-square is most likely the very small errors for each data point, which may be artificially small due to the large number of experimental data points used to calculate each average value and its associated standard error. No systematic errors were included in the present analysis and incorporating these would likely lower the Chi-square while still constraining the fit.

Although a branched 8-state model with 13 free parameters may seem very complicated and unreliable for fitting purposes, it is important to note that many largely orthogonal datasets were used, each constraining separate parts of the model. First, KIF3A/A and KIF3B/B are each used to constrain half of the model at a time.

143 Second, the force-velocity curve at saturating ATP set the distance parameter delta, since the nucleotide binding site is presumably always occupied by ATP. The ATP dependencies each give the ATP binding rates and by also collecting them under a relatively high hindering force of 4 pN the ATP unbinding rate, which competes with the force-dependent step in the forward direction, can be determined. The combined rate for the remaining biochemical steps, in the A and B half of the cycle, respectively, are directly seen in the unloaded velocity at saturating ATP. The other steps, including the second biochemical step (Pi release) for KIF3B/B and the backstepping rates, are less certain as they are derived from the randomness. This second order parameter shows more variability between different conditions, although the statistical error for each data point is relatively low, just like for the velocities. The second biochemical step (Pi release) is a direct consequence of the low randomness values for KIF3B/B under moderate loads. For these conditions, the force-dependent step is far from comparable with the hydrolysis rate and since the reciprocal randomness is a measure of the number of rate limiting steps in a linear cycle, another step has to be present. Backstepping would only increase the randomness and can therefore not explain the small values. The backstepping was instead introduced to account for the large randomness values at low ATP concentrations, especially below 5 µM where the value exceeds 1, as seen in Figure 6.2. For a strictly linear cycle, the randomness never exceeds this value. As backstepping was observed in the optical trapping data, this phenomenon was introduced as the best explanation for the high randomness values. In the cycle it was included at a position similar to that in the model in Chapter 4. There, backstepping competed with productive ATP binding and forward translocation and here we introduced it competing with ATP binding, since backstepping increased at lower ATP concentrations. The backstepping pathway combines all the steps involved in backstepping and is the least well defined part of the cycle.

Although the fitting procedure returns values with an error estimate, these errors may underrepresent the true error of the parameters. Analogous experiments have been performed, for example by Chuan et al. [228] who studied the force dependent cycle of myosin VI. They implemented both bootstrapping techniques and

144 confidence contour analyses as described by Johnson et al. [229]. Such analyses may return better estimates for the confidence intervals and also serve to identify any cases where two variables are highly covariant and where traditional error estimates fail to indicate that a fit may not be properly constrained. For example, in the present model the ATP unbinding rate and the forward force-dependent rate compete directly and could, in theory, scale together without influencing the total Chi-square by a large amount. Such cases should be investigated for this work and the analysis implemented as part of a future publication.

6.5.5 Expressions for fitting Velocity(F, T)=vel1/(vel2+vel3) and

Randomess(F, T) = ddgamma/dgamma-2*dbeta/beta+2*alpha*dgamma/(beta^2) where d=8.2, kT=4.056, d5a=0, d5b=0, d6a=0, d6b=0, k4a=50000, k5a=5, k5b=0 and vel1=(2*T*d*k1a*k1b*k3a*k3b*k4a*k4b*(exp(((d2a+d5a)*F)/kT)*k2b*k5a+exp(((d2a+d2b+d5a+d5 b)*F)/kT)*k5a*k5b+k2a*(k2b+exp(((d2b+d5b)*F)/kT)*k5b)- exp(((d2a+d2b+d6a+d6b)*F)/kT)*k6a*k6b)) vel21=exp((d2b*F)/kT)*k1a*k1mb*k2a+exp((d2a*F)/kT)*k1b*k1ma*k2b+(k1a+k1b)*k2a*k2b+exp(( (d2a+d2b+d5a)*F)/kT)*k1a*k1mb*k5a+exp(((d2a+d5a)*F)/kT)*(k1a+k1b)*k2b*k5a+exp(((d2a+d2b+ d5b)*F)/kT)*k1b*k1ma*k5b vel22=exp(((d2b+d5b)*F)/kT)*(k1a+k1b)*k2a*k5b+exp(((d2a+d2b+d5a+d5b)*F)/kT)*(k1a+k1b)*k5a *k5b+exp(((d2a+d2b+d6a)*F)/kT)*k1a*k1mb*k6a+exp(((d2a+d6a)*F)/kT)*(k1a+k1b)*k2b*k6a+exp( ((d2a+d2b+d5b+d6a)*F)/kT)*(k1a+k1b)*k5b*k6a vel23=exp(((d2a+d2b+d6b)*F)/kT)*k1b*k1ma*k6b+exp(((d2b+d6b)*F)/kT)*(k1a+k1b)*k2a*k6b+exp (((d2a+d2b+d5a+d6b)*F)/kT)*(k1a+k1b)*k5a*k6b+exp(((d2a+d2b+d6a+d6b)*F)/kT)*(k1a+k1b)*k6a *k6b vel2=k3a*k3b*k4a*k4b*(vel21+vel22+vel23) vel31=exp((d2a*F)/kT)*k2b*k3b*k4a*k4b+exp(((d2a+d2b+d5a)*F)/kT)*k3b*k4a*k4b*k5a+exp(((d2a +d5a)*F)/kT)*k2b*(k4a*k4b+k3b*(k4a+k4b))*k5a+exp(((d2a+d2b+d5b)*F)/kT)*k3b*k4a*k4b*k5b vel32=exp(((d2a+d2b+d5a+d5b)*F)/kT)*k3b*(k4a+k4b)*k5a*k5b+exp(((d2a+d2b+d6a)*F)/kT)*k3b* k4a*k4b*k6a+exp(((d2a+d6a)*F)/kT)*k2b*k4a*(k3b+k4b)*k6a vel325=exp(((d2a+d2b+d5b+d6a)*F)/kT)*k3b*k4a*k5b*k6a+exp(((d2a+d2b+d6b)*F)/kT)*k3b*k4a*k 4b*k6b+exp(((d2a+d2b+d5a+d6b)*F)/kT)*k3b*k4b*k5a*k6b

145 vel33=k2a*(k2b*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)+k3b*(exp((d2b*F)/kT)*k3a*k4a *k4b+exp(((d2b+d5b)*F)/kT)*(k3a*k4a+(k3a+k4a)*k4b)*k5b+exp(((d2b+d6b)*F)/kT)*(k3a+k4a)*k4 b*k6b) vel3=T*k1a*k1b*(k3a*(vel31+vel32+vel325)+vel33) beta11=exp((d2b*F)/kT)*k1a*k1mb*k2a+exp((d2a*F)/kT)*k1b*k1ma*k2b+(k1a+k1b)*k2a*k2b+exp( ((d2a+d2b+d5a)*F)/kT)*k1a*k1mb*k5a+exp(((d2a+d5a)*F)/kT)*(k1a+k1b)*k2b*k5a beta12=exp(((d2a+d2b+d5b)*F)/kT)*k1b*k1ma*k5b+exp(((d2b+d5b)*F)/kT)*(k1a+k1b)*k2a*k5b+ex p(((d2a+d2b+d5a+d5b)*F)/kT)*(k1a+k1b)*k5a*k5b+exp(((d2a+d2b+d6a)*F)/kT)*k1a*k1mb*k6a beta13=exp(((d2a+d6a)*F)/kT)*(k1a+k1b)*k2b*k6a+exp(((d2a+d2b+d5b+d6a)*F)/kT)*(k1a+k1b)*k5 b*k6a+exp(((d2a+d2b+d6b)*F)/kT)*k1b*k1ma*k6b beta14=exp(((d2b+d6b)*F)/kT)*(k1a+k1b)*k2a*k6b+exp(((d2a+d2b+d5a+d6b)*F)/kT)*(k1a+k1b)*k5 a*k6b+exp(((d2a+d2b+d6a+d6b)*F)/kT)*(k1a+k1b)*k6a*k6b beta1=k3a*k3b*k4a*k4b*(beta11+beta12+beta13+beta14) beta21=exp((d2a*F)/kT)*k2b*k3b*k4a*k4b+exp(((d2a+d2b+d5a)*F)/kT)*k3b*k4a*k4b*k5a+exp(((d2 a+d5a)*F)/kT)*k2b*(k4a*k4b+k3b*(k4a+k4b))*k5a+exp(((d2a+d2b+d5b)*F)/kT)*k3b*k4a*k4b*k5b beta22=exp(((d2a+d2b+d5a+d5b)*F)/kT)*k3b*(k4a+k4b)*k5a*k5b+exp(((d2a+d2b+d6a)*F)/kT)*k3b *k4a*k4b*k6a+exp(((d2a+d6a)*F)/kT)*k2b*k4a*(k3b+k4b)*k6a beta23=exp(((d2a+d2b+d5b+d6a)*F)/kT)*k3b*k4a*k5b*k6a+exp(((d2a+d2b+d6b)*F)/kT)*k3b*k4a*k 4b*k6b+exp(((d2a+d2b+d5a+d6b)*F)/kT)*k3b*k4b*k5a*k6b beta24=k2b*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)+k3b*(exp((d2b*F)/kT)*k3a*k4a*k4b +exp(((d2b+d5b)*F)/kT)*(k3a*k4a+(k3a+k4a)*k4b)*k5b+exp(((d2b+d6b)*F)/kT)*(k3a+k4a)*k4b*k6 b) beta2=T*k1a*k1b*(k3a*(beta21+beta22+beta23)+k2a*beta24) beta=T*exp(-(((d2a+d2b)*F)/kT))*(beta1+beta2) dgamma=-2*T^2*exp(- (((d2a+d2b)*F)/kT))*k1a*k1b*k3a*k3b*k4a*k4b*(exp(((d2a+d5a)*F)/kT)*k2b*k5a+exp(((d2a+d2b+ d5a+d5b)*F)/kT)*k5a*k5b+k2a*(k2b+exp(((d2b+d5b)*F)/kT)*k5b)- exp(((d2a+d2b+d6a+d6b)*F)/kT)*k6a*k6b) ddgamma=-4*T^2*exp(- (((d2a+d2b)*F)/kT))*k1a*k1b*k3a*k3b*k4a*k4b*(exp(((d2a+d5a)*F)/kT)*k2b*k5a+exp(((d2a+d2b+ d5a+d5b)*F)/kT)*k5a*k5b+k2a*(k2b+exp(((d2b+d5b)*F)/kT)*k5b)+exp(((d2a+d2b+d6a+d6b)*F)/kT) *k6a*k6b)

146 dbeta=-2*T^2*exp(- (((d2a+d2b)*F)/kT))*k1a*k1b*(k4a*k4b*(exp(((d2a+d5a)*F)/kT)*k2b*k3b*k5a+exp(((d2b+d5b)*F)/k T)*k2a*k3a*k5b+exp(((d2a+d2b+d5a+d5b)*F)/kT)*(k3a+k3b)*k5a*k5b)- exp(((d2a+d2b+d6a+d6b)*F)/kT)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)*k6a*k6b) alpha11=exp(((d2a+d2b)*F)/kT)*(k1b*k1ma+k1a*k1mb)*k3a*k3b*k4a*k4b+(k1a+k1b)*k2a*k2b*(k3 a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b) alpha12=exp((d2a*F)/kT)*k2b*(k1b*k1ma*k3a*k3b*k4a+k1a*k3a*k3b*k4a*k4b+k1b*(k1ma*k3a*k 3b+k3a*k3b*k4a+k1ma*(k3a+k3b)*k4a)*k4b) alpha13=exp((d2b*F)/kT)*k2a*(k1a*k1mb*k3a*k3b*k4a+k1b*k3a*k3b*k4a*k4b+k1a*(k1mb*k3a*k 3b+k3a*k3b*k4a+k1mb*(k3a+k3b)*k4a)*k4b) alpha14=exp(((d2a+d5a)*F)/kT)*(k1a+k1b)*k2b*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)* k5a alpha15=exp(((d2a+d2b+d5a)*F)/kT)*(k1a*k1mb*k3a*k3b*k4a+k1b*k3a*k3b*k4a*k4b+k1a*(k1mb* k3a*k3b+k3a*k3b*k4a+k1mb*(k3a+k3b)*k4a)*k4b)*k5a alpha16=exp(((d2b+d5b)*F)/kT)*(k1a+k1b)*k2a*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)* k5b alpha17=exp(((d2a+d2b+d5b)*F)/kT)*(k1b*k1ma*k3a*k3b*k4a+k1a*k3a*k3b*k4a*k4b+k1b*(k1ma* k3a*k3b+k3a*k3b*k4a+k1ma*(k3a+k3b)*k4a)*k4b)*k5b alpha18=exp(((d2a+d2b+d5a+d5b)*F)/kT)*(k1a+k1b)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)* k4b)*k5a*k5b+exp(((d2a+d6a)*F)/kT)*(k1a+k1b)*k2b*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a) *k4b)*k6a alpha19=exp(((d2a+d2b+d6a)*F)/kT)*(k1a*k1mb*k3a*k3b*k4a+k1b*k3a*k3b*k4a*k4b+k1a*(k1mb* k3a*k3b+k3a*k3b*k4a+k1mb*(k3a+k3b)*k4a)*k4b)*k6a alpha20=exp(((d2a+d2b+d5b+d6a)*F)/kT)*(k1a+k1b)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)* k4b)*k5b*k6a+exp(((d2b+d6b)*F)/kT)*(k1a+k1b)*k2a*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a) *k4b)*k6b alpha21=exp(((d2a+d2b+d6b)*F)/kT)*(k1b*k1ma*k3a*k3b*k4a+k1a*k3a*k3b*k4a*k4b+k1b*(k1ma* k3a*k3b+k3a*k3b*k4a+k1ma*(k3a+k3b)*k4a)*k4b)*k6b alpha22=exp(((d2a+d2b+d5a+d6b)*F)/kT)*(k1a+k1b)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)* k4b)*k5a*k6b+exp(((d2a+d2b+d6a+d6b)*F)/kT)*(k1a+k1b)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+ k4a)*k4b)*k6a*k6b

147 alpha23=k3a*k3b*k4a*k4b*(k2a+exp((d2a*F)/kT)*(k1ma+exp((d5a*F)/kT)*k5a+exp((d6a*F)/kT)*k6 a))*(k2b+exp((d2b*F)/kT)*(k1mb+exp((d5b*F)/kT)*k5b+exp((d6b*F)/kT)*k6b)) alpha30=exp(((d2a+d2b)*F)/kT)*k3a*k3b*k4a*k4b+exp((d2a*F)/kT)*k2b*(k3a*k3b*k4a+k3b*k4a*k 4b+k3a*(k3b+k4a)*k4b)+exp(((d2a+d2b+d5a)*F)/kT)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)* k4b)*k5a alpha31=exp(((d2a+d5a)*F)/kT)*k2b*(k4a*k4b+k3b*(k4a+k4b)+k3a*(k3b+k4a+k4b))*k5a+exp(((d2a +d2b+d5b)*F)/kT)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)*k5b alpha32=exp(((d2a+d2b+d5a+d5b)*F)/kT)*(k3b*(k4a+k4b)+k3a*(k3b+k4a+k4b))*k5a*k5b+exp(((d2a +d2b+d6a)*F)/kT)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)*k6a alpha33=exp(((d2a+d6a)*F)/kT)*k2b*(k4a*(k3b+k4b)+k3a*(k3b+k4a+k4b))*k6a+exp(((d2a+d2b+d5b +d6a)*F)/kT)*(k3b*k4a+k3a*(k3b+k4a))*k5b*k6a alpha34=exp(((d2a+d2b+d6b)*F)/kT)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)*k6b+exp((( d2a+d2b+d5a+d6b)*F)/kT)*(k3b*k4b+k3a*(k3b+k4b))*k5a*k6b alpha35=k2a*(exp((d2b*F)/kT)*(k3a*k3b*k4a+k3b*k4a*k4b+k3a*(k3b+k4a)*k4b)+k2b*(k3b*k4a+(k 3b+k4a)*k4b+k3a*(k3b+k4a+k4b))+exp(((d2b+d5b)*F)/kT)*(k3b*k4a+(k3b+k4a)*k4b+k3a*(k3b+k4 a+k4b))*k5b+exp(((d2b+d6b)*F)/kT)*(k3b*(k3a+k4a)+(k3a+k3b+k4a)*k4b)*k6b) alpha=exp(-(((d2a+d2b)*F)/kT))*(T*(alpha11+alpha12+alpha13+alpha14+alpha15+alpha16+alpha17+ alpha18+alpha19+alpha20+alpha21+alpha22)+alpha23+T^2*k1a*k1b*(alpha30+alpha31+alpha32+alp ha33+alpha34+alpha35))

148 Chapter 7: Exploratory motility experiments with unconventional kinesin family motors

7.1 Introduction

The kinesin superfamily of motors consists of a large and diverse group of proteins that are involved in cellular transport and cell division. An introduction of the different subfamilies and their primary functions was given in Chapter 1. Kinesin-1 has long been a model system for studying the force dependent kinetics of kinesin motors [132, 136, 143, 164, 230] and other kinesin families have also been studied with optical traps, such as Kinesin-5 [150, 231], Kinesin-7 [232] Kinesin-8 [75], Kinesin-10 [39], Kinesin-14 [233] and the Kinesin-2 motors OSM-3 [234] and KIF3A/B. Fluorescence and other video tracking techniques have also been used for other families, including Kinesin-3 [235] and diffusive Kinesin-13 depolymerizers [52]. The response to force can not be determined using fluorescence and many of the optical trapping studies did not analyze the kinetic cycle in detail, so much remains to be discovered about the proteins mentioned above. Furthermore, important characteristics, such as velocities and run lengths as a function of force, are completely unknown for a large number of other motors in the kinesin superfamily.

The kinetic cycle for Kinesin-1 motion along microtubules is well studied and a consensus reaction diagram is shown in Figure 1.4 (Chapter 1). For Kinesin-2 and Kinesin-5, which have been studied in detail using optical traps [150], the mechanical states and the ATP hydrolysis cycle can be mapped onto the same general sequence, yet the characteristics for these motors are substantially different from Kinesin-1 and from each other. This suggests that steps and rates in the catalytic cycle can differ in significant ways, leading to new global behavior, and that motors in other families may have equally unique properties. Understanding how individual steps contribute to velocities and processivity, and how these kinetic steps relate to the structure of the motors, is of great interest, both for informing us how applicable our generic model for kinesin is in the context of the entire kinesin superfamily and for understanding

149 how the cycles have been tweaked for the various roles the motors assume in a cellular context.

Detailed comparisons between motors from different kinesin families, and also within such families, have been limited both by the extent of the existing studies and the inconsistency between the conditions used in each study. For example, the ionic strength of the buffer was almost 20-fold higher in one study of Eg5 [150] compared with a Kinesin-1 study [136] and different surface passivation techniques have been implemented [186, 236]. Microtubules have been attached to microscope slides through charged or silanized surfaces [163, 237], by antibody linkages [238] or by biotinylating microtubules that bind streptavidin [150]. The tubulin can also be labeled with fluorophores [237]. The conditions are often tweaked to reach conditions where the motors move satisfactorily and can be detected using fluorescence or optical trapping without interference from nonspecific binding to the microscope slide glass surface or beads.

To explore the great diversity of motors in the kinesin superfamily, we studied several motors from different subfamilies. In order to facilitate comparisons between the constructs, experimental conditions were refined to work for all the examined constructs. Here, I present preliminary studies with the motors KIF17 (Kinesin-2), KIF4A (Kinesin-4), and CENP-E (Kinesin-7) and very limited data for MKLP1 (Kinesin-6). These can be compared directly to the experiments with Kinesin-1 and KIF3A/B (Kinesin-2) described previously in this thesis (Chapters 5 and 6). The studied motors showed a remarkable variety in both in their velocities and their ability to withstand load.

7.2 Methods

7.2.1 Optical trapping assay The optical trapping assays were similar to those outlined in Chapters 4 and 6. Microscope cover slips were plasma cleaned for 5 min (Herrick plasma cleaner, 1000- 2000 mTorr, high RF setting) and submersed for 1 h in a beaker with pure ethanol and 2% (3-Aminopropyl)triethoxysilane (APTES, Sigma). The coverslips were then rinsed

150 for at least 5 min in another beaker with pure ethanol and subsequently dried in an oven for 30 min at 115°C. Flow cells with a volume of 5–10 µL were assembled by attaching the APTES-treated cover slips to a microscope slide by double-sticky tape (3M). The dried cover slips or assembled flow cells can be stored for several days in an enclosed container.

The assay buffer (AB) consisted of PEM80 (80 mM PIPES, pH 6.9, 1 mM

EGTA, 4 mM MgCl2), 2 mM dithiothreitol (DTT), 10 µM Taxol (Paclitaxel), 2 mg ml-1 bovine serum albumin (BSA), and ATP. To prepare the flow cell, PEM80 with 10 µM Taxol (PemTax) was also prepared.

Kinesin-attached beads were prepared by diluting frozen aliquots of kinesin and mixing with equal volumes of diluted polystyrene beads of diameter 440 nm (Spherotech, Inc.). The beads were diluted by a factor of 1000 to 4000 from the stock solution concentration. The kinesin linkage consisted of a Penta·His biotin conjugate (Qiagen 34440) that was bound to the streptavidin-coated beads. Kinesin and beads were incubated on a rotator at 4°C for 2 hours or more to allow for binding. Prior to the introduction of each 20 µL sample into the experimental flow cell, an oxygen scavenging system was added to obtain final concentrations of 1 mg ml-1 glucose, 50 µg ml-1 glucose oxidase (Calbiochem) and 12 µg ml-1 catalase (Sigma).

Microtubules were bound through a covalent glutaraldehyde linkage to the free amine groups on the APTES-treated glass, which was later passivated using BSA. For motility experiments, the flow cells were treated in the following way: add 10 μL glutaraldehyde (8% in phosphate buffered saline), wait at least 30 min, flow 200 µL PemTax, flow 30 µL microtubules diluted in PemTax, wait at least 10 min, flow 100 µL PemTax, flow 50–100 µL AB, wait at least 5 min, flow at least 30 µL AB, flow 20 µL kinesin-bound beads in AB (including the oxygen scavenging system), and seal with vacuum grease.

7.2.2 Instrumentation and analysis All optical trapping data were collected using the instrument described in Chapter 2 (Valentine et al. [77]). LabView 7.1 (National Instruments) was used for data

151 collection. Data were acquired at 20 kHz, decimated to 2 kHz and filtered at 1 kHz. The active force clamp was updated at 500 Hz. Each bead was calibrated and the trap stiffness was determined using the average of estimates from the bead signal variance and from the Lorentzian corner frequency derived from a fit to the power spectrum.

The traces were analyzed using IGOR Pro 6 (Wavemetrics). The beginning and end of the individual kinesin runs were scored manually and the velocity for each trace calculated using a linear least squares fit. Individual run lengths were scored as the difference between the last and the first positions of each trace. The average velocity at each force was determined by averaging the velocity for each run, weighted by the run length, whereas the average run length was obtained by fitting the distribution of experimental run lengths to an exponential function, limiting the range to bins with more than six counts and discarding bins for short run lengths to account for missing events. The bin widths were adjusted manually to account for the number of total points and the run length for the construct at the given force. The dependence of velocities and run lengths on the force or ATP concentration was calculated using weighted non-linear least squares fitting in IGOR Pro. The reported errors are the errors from this fit.

7.2.3 Preparation of kinesin constructs

7.2.3.1 KIF17

A synthetic human KIF17 was ordered from Integrated DNA Technologies, Inc. The gene contained the first 738 amino acids from the full length motor and a 6x-His tag at the C-terminal end. It was ordered in a plasmid that also contained T7 promoter and terminator sequences, and a ribosome binding site originally found in a commercial bacterial expression plasmid (pET3a, Novagen). Expression in E. coli of both this construct and a shortened version with 473 amino acids gave low yields that were just enough to occasionally see moving beads in the optical trap, but insufficient for significant measurements to be made. Consequently, the 738-amino acid gene was transferred to a pBiEx plasmid (Novagen) and expressed using Sf9 cells. This expression was kindly done by the lab of Prof. Zev Bryant at Stanford University.

152 Both the growth of the cells and the preparation of the clarified lysate were performed as previously described by the Bryant group [239]. The clarified lysate was mixed 1:1 with binding buffer and added to a small amount (~100 µL) of Ni-NTA agarose (Invitrogen) previously washed in binding buffer. After incubation on a rotator for more than one hour, the Ni-NTA agarose was washed three times in wash buffer with a 10 minute mixing step in between each wash. Finally, the kinesin was eluted in several steps, using ~200 µL of elution buffer each time, before being flash frozen in liquid nitrogen and stored at −80°C. All buffers contained 20 mM Tris, 500 mM NaCl, 5 mM MgCl, imidazole (40 mM for binding and wash buffers, 500 mM for elution buffer) and 10% (w/w) sucrose. Before use, 1 mM DTT and 75 µM ATP was also added.

7.2.3.2 KIF4A

The gene for a human KIF4A construct consisting of the first 744 amino acids was synthesized by Integrated DNA Technologies, Inc. Just like for the KIF17 gene above, promoter and terminator sequences identical to those in the pET3a plasmid were also incorporated to allow for immediate expression in E. coli. The plasmid was transformed into One Shot® BL21(DE3) Chemically Competent E. coli (Invitrogen). The cells were grown in Terrific Broth with 100 µg/ml ampicillin until the optical density reached ~1. Expression was induced by 100 µM isopropyl-beta-D- thiogalactopyranoside (IPTG) and the temperature was dropped to 18°C. After ~60 h the cells were pelleted and frozen for later purification. After thawing, the cells were resuspended in lysis buffer and lysed using a French press followed by two steps of centrifugation, at 15 krpm for 30 min and 50 krpm for 1 h, respectively. After diluting the clarified lysate by adding two volumes of Buffer A, it was purified further by FPLC. The sample bound to a HisTrap HP column and was eluted using a four-step gradient with levels of 0%, 25%, 60% and 100% Buffer B. The lysis buffer consisted of 50 mM Tris, 300 mM NaCl, 5 mM MgCl, 40 mM imidazole and 10% (w/w) sucrose. Before use 0.25 mM ATP and 1 mM DTT was added together with 2 mM PMSF, 20 µg/ml soybean TI (Sigma T9003), 2 µg/ml pepstatin A (Sigma P4265),

153 20 µg/ml TPCK (Sigma T4376), 20 µg/ml TAME (Sigma T4626) and 2 µg/ml leupeptin (Sigma L9783). Buffer A and B were identical to the wash and elution buffers described for KIF17 above. For each step in the gradient, the resulting fractions were pooled and concentrated using Amicon Ultra-15 centrifuge filters (Millipore). The final solution was aliquoted into 10 µL volumes and flash frozen in liquid nitrogen before storage at −80°C.

7.2.3.3 Other

A truncated CENP-E construct fused to a GCN4 domain was expressed by the lab of Steven Rosenfeld at Columbia University, as previously described [240]. The MKLP1 gene was synthesized and the motor was expressed in E Coli, following a protocol similar to that used for the KIF4A construct. The Kinesin-1 and KIF3A/B motors were described in previous chapters. These were expressed in E. Coli and Sf9 cells, respectivel, and purified by William Hancock’s lab at the Pennsylvania State University.

7.3 Results

The kinesin motors were attached to beads and their motion was measured with an optical trap. In this chapter negative forces correspond to hindering loads and saturating ATP concentrations (2 mM) were used unless otherwise indicated.

7.3.1 KIF17 is a fast and strong kinesin motor KIF17 is the human homodimeric Kinesin-2 motor. It is involved in both intraflagellar and axonal transport and has been shown to be a processive motor [72]. The study by Hammond et al. [72] also showed that the full length motor is autoinhibited so here we use a truncated construct that included the first 738 amino acids with a 6x-his tag at the C-terminal end.

Under saturating ATP conditions (2 mM ATP) KIF17 has a high unloaded velocity of about 1200 nm/s and the full force-velocity curve is shown in Figure 7.1. The unloaded velocity is close to previous reported values for fluorescently tracked KIF17 [72] and for its C. elegans homologue, OSM-3 [241], and it makes KIF17 the

154 fastest motor discussed in this thesis. It is approximately 50% faster than Kinesin-1 under no load and just like Kinesin-1 is moves fast under substantial hindering loads. The force-velocity data can be described by a simple two-state model

e 퐹훿 [1] [2] � �[1] (1) 1 푘퐵푇 푘 2 푘 + → → where the first step represents푑 the catalysis rate (including all biochemical steps), k1, and the second step is a force-dependent transition with unloaded rate k2 and a characteristic distance parameter δ. F is the external load, with hindering loads having a negative sign, and d is the 8.2-nm step size. The resulting expression for the force- dependent velocity is

퐹훿 = �− � = 푘 푇 (2) 푑 푘1푘2e 퐵 푑 푘1푘2 퐹훿 퐹훿 �− � �− � 푣 푘 푇 푘 푇 푘1+푘2e 퐵 푘1e 퐵 +푘2 When fitting the two-state model we found that the catalysis rate is =

159 ± 6 s and that the force-dependent transition is characterized by the푘 unloaded1 −1 rate, = (3.2 ± 0.6) 10 s , and the distance parameter, = 3.9 ± 0.2 nm. The 3 −1 distance푘2 parameter is similar∙ in magnitude to the 4–4.6 nm reported훿 for various Kinesin-1 constructs in the previous chapters and much higher than those for other motor domains in the Kinesin-2 family, i.e., KIF3A and KIF3B.

The run lengths for KIF17 are very long as the free motors routinely moved several microns to the end of the microtubule in our experimental setup, and as trapped constructs often reached the end of our detection area. Long runs of 6–7 µm were previously reported for KIF17 constructs [72]. The force-dependence of the run length should be further studied, but it is clear that both the run lengths, velocities and force dependencies of this motor are very different from those of KIF3A/B. In fact, this motor resembles Kinesin-1 more than any other motor, indicating that the unique features found for KIF3A/B in the previous chapter are specific to this motor rather than the entire Kinesin-2 family. Those features include the short run length under load, slipping and the weak force dependence for the velocity.

155

Figure 7.1 KIF17 velocity as a function of force. The velocity of KIF17 under saturating ATP conditions ([ATP] = 2 mM) was fit to a simple 2-state model with one force-dependent step (green line, see main text).

7.3.2 KIF4A does not move substantially against load The Kinesin-4 family includes chromokinesins that associate with chromosomes during mitosis [18]. The human Kinesin-4 protein KIF4A contains 1232 amino acids [242] and its mouse homologue is a dimer with two motor domains and a long coiled- coil stalk of 116 nm [21]. KIF4A is an essential protein during cell division where it is localized to the midzone and midbody of dividing cells [19] and functions in chromosome condensation and segregation [20]. It has also been linked to DNA damage response [243] and chromatin maintenance [244] and the stalk associates to chromatin through a leucine Zip motif and cysteine-rich motif in the C-terminal region [245]. Kinesin-4 acts by being a negative regulator of microtubule plus-end dynamics [246] and suppresses microtubule growth [247] to establish a tight metaphase plate [40]. The mouse KIF4 moved microtubules at a slow velocity in microtubule gliding experiments [21]. The direction of motion of pointed to a plus-end directed motion but no detailed single-molecule motility experiments have been reported.

156 We used an optical trap to study a truncated human KIF4A construct that contained the first 744 amino acid and a 6x-His tag at the C-terminal end. This construct showed consistent movement along microtubules when the bead was free but, surprisingly, they were unable to produce long range processive motion against moderate hindering loads imposed by the optical trap. Even for small forces of 1 pN the motor quickly detached. Although the motor could be tracked with both very low hindering and assisting loads at 0.5 pN and 2 µM ATP, it was not possible to clearly discern individual steps since the low stiffness resulted in large Brownian noise from the bead. To investigate ATP binding and hydrolysis, the unloaded motion was measured by video tracking for several ATP concentrations and the data were fit to Michaelis-Menten kinetics

[ATP] [1] [2] [1] (3) 1 푘 +푘2 ↔ → where the reversible푘−1 ATP푑 binding is characterized by the second-order ATP-binding rate, k1, and the unbinding rate, k-1. The hydrolysis rate, k2, signifies other biochemical events, including hydrolysis and ADP release. It is coupled to the 8.2-nm step, d, leading to the following velocity relation

[ ] = [ ] (4) 푑 푘2 ATP 푣 ATP +퐾푀 where v is the velocity, [ATP] is the ATP concentration, and the Michaelis constant is

= (5) 푘2+푘−1 푀 퐾 푘1 -1 The fit, shown in Figure 7.2, returned k2 = 83 ± 6 s and KM = 34 ± 4 µM. The dissociation rate, k-1, was not determined here but from equation (5) we get a lower -1 -1 bound for the binding rate, k1, of about 2.7 µM s . This rate falls in the range 2– 4 uM-1 s-1 seen for KIF3A, KIF3B and the Kinesin-1 mutants in previous chapters of this thesis. The hydrolysis rate, 83 s-1 is also close to those for KIF3A/B and Kinesin-1 suggesting that the basic ATP hydrolysis activity of the KIF4A heads is similar to those of other motors.

157 The run lengths were very short under load, but were sufficiently long to measure in the absence of external forces. The average run length was 651 ± 151 nm at saturating ATP (2 mM) for a small sample (N = 17). Here, the direct average is reported rather than parameters from a fit to an exponential distribution. The KIF4A remained attached for longer times at low ATP concentrations, indicating that the no- nucleotide state is strongly bound to the microtubule, just like for Kinesin-1 and Kinesin-2, but the run length decreased as the ATP concentration was reduced. The unloaded run lengths were 110 ± 16 nm (5 µM ATP, N = 31), 143 ± 43 nm (2 µM ATP, N = 28), and 47 ± 6 nm (0.5 µM ATP, N = 30).

The inability of the motor to support moderate loads limits the possibilities to use optical trapping for probing the KIF4A mechanochemical cycle, but the preliminary data presented here already show that this protein is drastically different from most other processive kinesin motors. Several key rates in the ATP hydrolysis cycle are comparable with those for Kinesin-1 or Kinesin-2, suggesting that something in the coupling between the ATP hydrolysis and the mechanical steps sets KIF4A apart. The main role in the cell for KIF4A seems to be regulation of microtubule growth and the binding of chromatin, and it is possible that the enzyme is highly optimized for this process while sacrificing its ability to generate large forces over long distances. Complementary experimental techniques, such as single-molecule fluorescence, bulk biochemistry techniques, and structural studies may provide important insight into the mechanisms underlying the unique behavior of KIF4A and how it is coupled to microtubule regulation.

158

Figure 7.2 KIF4A velocity as a function of ATP concentration. The velocity data of KIF4A as a function of ATP concentration under no load were fit to Michaelis- Menten kinetics, as indicated by Equation (4) in the main text, with the line in the graph representing the fit.

7.3.3 CENP-E is a motor similar to Kinesin-1 Centromere-associated protein E (CENP-E) [32] is a kinesin-like protein that associates with kinetochores during chromosome congression and later relocates to the spindle midzone during anaphase [33] after its phosphorylation by mitotic kinase maturation promoting factor [248]. It is essential for metaphase chromosome alignment [34, 35] and in the absence of CENP-E the spindle poles fragment and the mitotic checkpoint signaling cascade is triggered [249, 250]. Inhibiting the critical role of CENP-E during mitosis has been observed to yield anti-tumor activity [251].

CENP-E is a processive kinesin [232] that moves towards the plus end tips of dynamic microtubules. The crystal structure [252] for free CENP-E has been solved and there is a cryo-EM reconstruction of the microtubule-CENP-E complex [253]. Interestingly, the protein combines the processive motor with a secondary microtubule binding site that act as an anchor that facilitates microtubule end-tracking [254]. Rates in the CENP-E kinetic cycle have been measured by bulk fluorescence techniques

159 [240, 255] and the motion of CENP-E and CENP-E/Kinesin-1 chimeras have been observed using single-molecule fluorescence techniques [64, 232, 254, 256] and microtubule gliding assays [257]. Measurements of the stall force have also been performed using a fixed optical trap [232], but the dependence on force for the velocity and run length has not been reported.

Here, we studied a previously described Xenopus CENP-E construct containing the first 392 amino acids fused to a GCN4 domain [240]. The velocity and run length was determined as a function of force under saturating ATP conditions ([ATP] = 2 mM), as shown in Figure 7.3. The velocity data were fit to the same two- state model used for KIF17 above (Equation (2)). Under no load CENP-E moves at just over half the velocity of kinesin one, at 408 ± 4 nm s-1. The minimal model captures a small increase in velocity under assisting loads so the catalysis rate, k1 = 58.4 ± 6 nm s-1, corresponds to a marginally higher maximum velocity of 478 nm s-1. -1 The unloaded rate for the force-dependent step, k2 = 444 ± 28 s , is substantially lower than for Kinesin-1 but the distance parameter, δ = 3.55 ± 0.08 nm, is close to both that for Kinesin-1 and for KIF17 above. This indicates that the overall force-dependences are similar for the three motors. In the framework of our minimal two-state model, the low unloaded rate for the force-dependent step, k2, manifests itself as a reduction in velocity even at low hindering loads and as a larger increase under assisting loads than for Kinesin-1, as seen in Figure 7.3. We note that the difference between the unloaded velocity here, 408 ± 4 nm s-1, and a previously reported velocity of 342 ± 10 nm s-1 [232] for the same construct may be explained by differences in the experimental buffers. Another study reported a 50-fold lower velocity (8 nm s-1) for a Xenopus CENP-E construct with 473 amino acids and the full-length motor had a velocity of 30 ± 7.6 nm s-1 under conditions similar to ours [256]. The shorter of the constructs also had a diffusive component to its motion, which we did not observe. Our construct includes a GCN4 domain, a very stable coiled-coil motif, and although the authors of the other study verified a dimeric state by measuring hydrodynamic parameters and photobleaching, it is possible that the dimerization was not fully stable in the other study.

160 The run lengths for several loads are shown in the right panel of Figure 7.3. At just under 600 nm the unloaded run length for CENP-E was somewhat lower than that for Kinesin-1. By fitting the run lengths under hindering loads to the following exponential expression

= 퐹 훿퐿 (5) �푘B푇� 0 we obtained퐿 퐿the푒 unloaded run length, L0 = 598 ± 52 nm, and the distance parameter, δ = 1.7 ± 0.1 nm. The magnitude of the distance parameter is identical to that for KIF3A/B and 0.6 nm smaller than that for Kinesin-1. The run lengths under assisting loads are short, just like for Kinesin-1. The run lengths reported here are shorter than previous reports of 2.6 ± 0.2 µm [232] and 1.5 ± 0.1 µm [256]. This is probably due to use of a lower ionic strength buffer the first study and to a different construct in the second.

Although some of the parameters differ significantly between CENP-E and Kinesin-1, notably the force-dependent rate and the maximum velocity, we find that the motors behave in a similar fashion overall. Both are relatively strong motors that can move long distances under moderate hindering loads, and both slow down continuously before reaching the stall force between 6 and 7 pN. Yardimci et al. [232] also concluded that Kinesin-1 and CENP-E share many features. Here we have been able to extend that conclusion to the force-dependent velocities and run lengths.

161

Figure 7.3 CENP-E velocity and run length as a function of force. Left. Velocity data from force clamp experiments were fit to a two-state model with one force- dependent step (red line, Equation (2)). Right. Run lengths under hindering negative loads were fit to a simple exponential ([ATP] = 2 mM).

7.4 Discussion

Motors from several kinesin families were measured under force clamp conditions to obtain force-dependent kinetic parameters. Figure 7.4 below shows a summary for the force dependent velocities described in this and other chapters. A single unloaded velocity is displayed for KIF4A, as force-dependent data were not obtained due to its fast detachment under load, and for a truncated MKLP1 (Kinesin-6) construct. Also shown is a published force-velocity curve for Eg5 from Valentine et al. [150], measured under conditions with a higher ionic strength. It is immediately clear that kinesin motors are remarkably diverse. The velocities vary by 15-fold at no load and the motors cover a range of values for any given force. The force dependencies are strong for Kinesin-1, KIF17, and CENP-E but are weak for KIF3A/B and Eg5. As a consequence, KIF3A/B is the fastest motor for hindering forces beyond −5 pN. Eg5 is as fast as CENP-E at −5 pN despite the former being about 5 times faster under no load. This illustrates how force-dependent measurements are needed to fully understand the motors over the entire regime in which they may function in the cell.

162 The run lengths show an even greater diversity. Under no load the KIF17 run length is several microns, at least 50-fold higher than the Eg5 run length (67 nm). Kinesin (~900 nm), KIF4A (~651 nm), CENP-E (~600 nm), and KIF3A/B (~400 nm) all have all intermediate run lengths. When moderate loads are applied KIF4A is not processive at all and the KIF3A/B run length drops to a handful of steps. Eg5, in contrast, is barely affected by forces up to −4 pN. This suggests that the either the microtubule affinity of the motor domains or the coordination between the heads changes significantly between the motors.

Kinesin-1 is routinely expressed using E. coli as are many other motors, such as truncated Eg5, CENP-E, and chimeras of other motors with Kinesin-1 stalks. In our exploratory work we successfully expressed KIF4A in E. Coli from a synthetic gene, but many other motors were not functional or did not give a sufficient yield using this bacterial expression system. MKLP1, for example, only showed robust motility occasionally, as indicated by the unloaded data in Figure 7.4. For the most parts, however, this motor was inconsistent or not functional, despite having tested a wide range of expression conditions. KIF17 expressed in E. Coli was fully functional, but both a long (738 amino acids) and a short (473 amino acids) construct gave insufficient numbers of motors at the highest possible concentrations, even for single- molecule experiments. Again, many conditions were attempted with E. coli. When expressed in Sf9 cells the KIF17 was purified at satisfactory concentrations. This suggests that eukaryotic expression is a preferable route for future work with new motors.

The conclusion from this exploratory study is that the variability within the kinesin superfamily is large and that some of this variability manifests itself only when external loads are applied. The load experienced by motors in the cell depends on their physiological function and force-dependent data may aid us in distinguishing between different models. For example, the fact that KIF4A was extremely weak in our hands reinforces the idea that this motor is not primarily applying forces to move chromosomes during chromosome congression, but that its function is indeed to regulate the growth of microtubules. The motors described here constitute a starting

163 point for further exploration and the protocols outlined in the methods section should allow for interesting future studies of these motor and many more interesting members in the kinesin superfamily.

Figure 7.4 Velocity as a function of force for kinesin family motors.

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