Measuring the Mechanical Properties of Primary Cilia with An

Home , Cilium

MEASURING THE MECHANICAL PROPERTIES OF PRIMARY CILIA WITH AN

OPTICAL TRAP

TARA DIBA

Bachelor of Science in Physics

Azad University, Central Tehran

December, 2011

Submitted in partial fulfillment of requirements for the degree

MASTER OF SCIENCE IN BIOMEDICAL ENGINEERING at the

CLEVELAND STATE UNIVERSITY

December, 2015

©COPYRIGHT BY TARA DIBA 2015

We hereby approve this thesis for

(Tara Diba)

Candidate for the Master of Science in Biomedical Engineering degree for the

Department of Chemical and Biomedical Engineering

and the CLEVELAND STATE UNIVERSITY

College of Graduate Studies

______Thesis Chairperson, (Dr. Andrew Resnick) Physics, Cleveland State University/Dec.4.2015 Department & Date

______Thesis Committee Member, (Dr. Chandra Kothapalli) Chemical and Biomedical Engineering, Cleveland State University/ Dec.4.2015 Department & Date

______Thesis Committee Member (Dr. Christopher L. Wirth) Chemical and Biomedical Engineering, Cleveland State University/ Dec.4.2015 Department & Date

______Thesis Committee Member (Dr. Moo Yeal Lee) Chemical and Biomedical Engineering, Cleveland State University/ Dec.4.2015 Department & Date

Student’s Date of Defense: (Dec.4.2015) iii

ACKNOWLEDGEMENTS

I would like to first and foremost express my appreciation and sincere gratitude to Dr.

Andrew Resnick for providing me this wonderful opportunity to conduct research under his astute guidance. His boundless energy, wonderful analytical skills, cool and calm composure, and motivational power has made this experience a truly memorable one. I am sure this will stand me in good stead in my future research and professional career as well. I sincerely thank him for introducing me to the research of biomedical optics.

Because of him, I was able to work on many intriguing projects and learn more than I ever dreamed possible. I must also acknowledge the seemingly infinite support and kind advice from Dr. Chandra Kothapalli and Dr. Moo Yeal Lee as well. I also would like to thank Dr. Joanne Belovich for playing a pivotal role in my thesis. I owe my deepest thanks to my parents who have always stood by me with patience and satisfaction, they guided me through life and I wouldn’t have been able to finish my degree without them.

Moreover, I offer my regards and blessing to all of the people, especially Rebecca Laird and Darlene Montgomery, who did not hesitate to help me in my entire life in the US.

MEASURING THE MECHANICAL PROPERTIES OF A PRIMARY CILIA WITH AN

OPTICAL TRAP

TARA DIBA

ABSTRACT

Nonmotile primary cilia are slender subcellular structures that extend from the mother centrosome, are typically several microns long, and are used by eukaryotic cells to sense fluid flow. Cilia perform various roles to maintain tissue homeostasis through multiple signaling pathways, and their sensing ability is not restricted to physical stimuli but also biochemical stimuli from the extracellular environment. Cilia play a mechanosensory role in numerous tissues including kidney, liver and bone; where mechanical deflection of cilia due to mechanical loading leads to a cellular response. However, the relationship between cilia mechanical responses and downstream regulatory processes that are ciliary- initiated is still unknown. Optical tweezers provide a unique method to mechanically stimulate a primary cilium because of the noncontact nature of the method. We present a method to measure the mechanical properties of a primary cilium by exciting a resonant oscillation of the cilium. This is done by by applying an optical force directly to the cilium. We will show that the resonant frequency of cilia can be used to extract mechanical properties of the cilium base.

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ...... IV

ABSTRACT ...... V

NOMENCLATURE ...... IX

LIST OF TABLES ...... XI

LIST OF FIGURES ...... XII

CHAPTER I ...... 1

INTRODUCTION AND OBJECTIVE OF THE THESIS ...... 1

1.1 INTRODUCTION ...... 1

1.2 MOTIVATION ...... 2

1.3 OBJECTIVE ...... 3

CHAPTER II ...... 4

HISTORY AND ADVANCEMENT OF OPTICAL TWEEZERS ...... 4

2.1 INITIAL DEVELOPMENT OF OPTICAL TWEEZERS ...... 4

2.2 BASIC OPTICS ...... 6

CHAPTER III ...... 11

THEORY AND APPLIED FORCE ...... 11

3.1 THEORY OF OPTICAL TWEEZERS ...... 11

3.2 OPTICAL FORCES ...... 14

3.2.1 RAYLEIGHT SCATTERING ...... 17

3.2.2 RAY OPTICS APPROXIMATION ...... 22

3.2.3 GENERALIZED LORENTZ MIE THEORY (r~λ) ...... 24

3.3 FORCE CALIBRATION ...... 25

3.4 QPD POSITION DETECTION ...... 27

CHAPTER IV ...... 29

MOTILE AND NONMOTILE CILIA ...... 29

4.1 CILIA ...... 29

4.2 PRIMARY CILIA ...... 32

4.3 CILIOPATHY ...... 35

CHAPTER V ...... 38

DEVELOPED MODEL OF THE PRIMARY CILIUM ...... 38

5.1 CILIARY MECHANICS AND MODELS ...... 38

CHAPTER VI ...... 41

METHODS AND MATERIALS ...... 41

6.1 METHODS ...... 41

6.2 CELL CULTURE ...... 42

6.3 IMMUNOCYTOCHEMISTRY ...... 43

6.4 OPTICAL TWEEZERS APPARATUS ...... 44

6.4.1 Major Components Description ...... 47

CHAPTER VII ...... 50

PRIMARY CILIUM TRAPPING ...... 50

vii

7.1 TRAPPING PROTOCOLE ...... 50

CHAPTER VIII ...... 52

RESULTS ...... 52

8.1 ANALYSIS AND RESULT ...... 52

8.2 TWEEZERS CALIBRATION ...... 64

CHAPTER IX ...... 69

CONCLUSION ...... 69

9.1 CONCLUSION AND FUTURE WORK ...... 69

REFERENCES ...... 70

APPENDIX A ...... 87

APPENDIX B ...... 94

viii

NOMENCLATURE

PCP: planar cell polarity

HH: Hedgehog

CICR: Calcium-induced Calcium release

Intraflagellar Transport: IFT

Bardet-Biedl Syndrome: BBS

Electromagnetic: EM

Continuous wave: CW

Infrared: IR

Pre-implantation Genetic Diagnosis: PGD

Holographic Optical Tweezers: HOT

Atomic Force Microscopy: AFM

Numerical Aperture: NA

Quadrant Photo Diode: QPD

Microtubules: MT

Polycystin-1 and Polycysin-2: PC1 and PC2

Sonic hedgehog: Shh

Platelet-Derived Growth Factor: PDGFR

Polycystic kidney disease: PKD

Autosomal Dominant Polycystic Kidney ADPKD Disease:

Autosomal Recessive PKD: ARPKD

Polycystic Kidney and Hepatic Disease1 and 2: Pkhd1 and 2

Nephronophthisis: NPHP

Madin-Darby canine Kidney: MDCK

Mouse Mortical Collecting Duct: mCCD

Epithelial Growth Factor: EGF

Fetal Bovine Serum: FBS

Bovine Serum Albumin: BSA

Virtual Instrument: VI

Standard Deviation: STD

The Mean Square Displacement: MSD

LIST OF TABLES

Table Page

TABLE 1 - DATA OF THE 5 RUNS FOR 2M BEADS AT TRAP FOLLOWING THE STD, AVERAGE AND FORCE ..68

TABLE 2- BOUNDARY CONDITIONS OF THE BEAM ...... 90

TABLE 3- RAW QPD ACQUIRED DATA ...... 101

LIST OF FIGURES

Figure Page

FIGURE 1- EVOLUTION OF OPTICAL TWEEZERS ...... 6

FIGURE 2- 2ΜM MICROSPHERE IN AN OPTICAL TRAP ...... 10

FIGURE 3- CHANGING IN THE MOMENTUM OF THE BEAM PARTICLE ...... 14

FIGURE 4- OPTICAL FORCES ON A DIELECTRIC SPHERE IN RAY REGIME...... 22

FIGURE 5- QS, QG AND QT MAGNITUDE ...... 24

FIGURE 6- QPD DIAGRAM THAT USED IN OUR EXPERIMENTS ...... 27

FIGURE 7- MOTILE CILIA SCHEMATIC ...... 32

FIGURE 8-CILIA SCHEMATIC ...... 34

FIGURE 9- HEALTHY KIDNEY VERSUS KIDNEY WITH PKD. LEFT IS THE SCHEMATIC OF THE ...... 36

FIGURE 10- EN FACE IMAGES OF THE STAINED MCD CELLS ...... 44

FIGURE 11- HARDWARE CONFIGURATION OF THE LASER TWEEZERCOMPUTER ...... 46

FIGURE 12- LEICA CTR 6000 FRONT SIDE POWER SUPPLY ...... 47

FIGURE 13- Z CONTROLLER ...... 48

FIGURE 14- PRIOR PRESCAN II AT THE RIGHT AND ERGONOMIC JOYSTICK IS AT THE LEFT SIDE ...... 48

FIGURE 15- CRYSTALASER LASER SHUTTER AND POWER SOURCE ...... 49

FIGURE 16- QPD POSITION AND SCHEMATIC...... 49

FIGURE 17- CILIUM AT THE TRAP ...... 51

FIGURE 18- NATIONAL INSTRUMENT LABVIEW DATA ACQUISITION SOFTWARE FRONT VIEW ...... 53

FIGURE 19- RESULTS VS. MSD PLOT...... 54

FIGURE 20- A SAMPLE OF RAW QPD OUTPUT A) X-DIRECTION DATA B) Y-DIRECTION DATA ...... 56

FIGURE 21- RAW ACQUIRED DATA FROM THE QPD ...... 56

xii

FIGURE 22- DECOMPOSED SIGNAL...... 58

FIGURE 23- X VERSUS Y DIRECTION THAT SHOWS THE PATH OF THE TRAPPED PARTICLE ...... 59

FIGURE 24- CILIA IN A TRAP ANIMATION ...... 59

FIGURE 25- HISTOGRAM OF THE DATA WITH A GAUSSIAN MODELED FIT ...... 61

FIGURE 26- FOURIER TRANSFORM OF THE DATA ...... 62

FIGURE 27- POWER SPECTRUM ...... 63

FIGURE 34- PRIMARY CILIUM MODELED AS A CLASSICAL CANTILEVERED ...... 92

FIGURE 35- PRIMARY CILIUM MODELED AS A CANTILEVERED BEAM WITH ROTATORY SPRING ...... 93

xiii

CHAPTER I

INTRODUCTION AND OBJECTIVE OF THE THESIS

1.1 INTRODUCTION

Cilia are antenna-like organelles that emanate from the surface of the either growth- arrested or differentiated eukaryotic cells [1]. Cilia originate from the mother centriole of the mother-daughter pair of centrioles in the centrosome of the cell [2], consist of 9 microtubule doublets arranged in a ring, and are encased in the cell membrane. Cilia are generally characterized as either motile or non-motile. Motile cilia are distinguished from non-motile cilia (primary cilia or sensory cilia) by the presence of an extra microtubule doublet in the center of the axoneme. Primary cilia are hypothesized to be a mechanotransduction structure. Primary cilia can bend as a result of applied fluid flow, and ciliary bending initiates a variety of signaling cascades [4] such as; non-canonical

Wnt/planar cell polarity (PCP) pathway, Hedgehog (HH) pathway, and Polycystin

pathway. Typically, initiation of a mechanotransduction pathway is accompanied by an increase of intracellular Calcium, through Calcium-induced Calcium release (CICR) [5].

Measuring the essential mechanical properties of the cilia can support the mechanosensation hypothesis, and provide improved understanding of its signaling role in the cell. In contrast to application of fluid flow, manipulating individual cilia via optical trapping allows us to better define the connection between mechanical stimulation and initiation of mechanosensation pathways. Optical trapping is a non-contact method that can cause cilia to bend. Cilium deflection occurs along the axoneme land rotating. around the hinge located at the basal body. Thus, quantitative stimulation of a single cilium, coupled with careful measurements of the mechanical response, can provide a significant amount of new information regarding the mechanical properties of the cells’ mechanical sensor. In this study, the force was applied to the tip of the cilia directly by the laser tweezers. In previous studies, microspheres were attached to the cilium, and the microspheres were trapped and used to dislocate the tip of the cilia.

1.2 MOTIVATION

The primary cilium exists in the majority of the human body cells. Because the cilium contains no ribosomes, all proteins present in cilia must be trafficked into and out of the cilia via intraflagellar transport (IFT) particles. The length of the primary cilium is controlled by an unknown regulatory mechanism. Since cilium originate from the centrioles, any mutation that changes either function or structure of the centrosome can potentially have an effect on the function of the cilia [6], which associated, with a broad spectrum of complex human diseases known as ciliopathies. Cilia have various roles in

sensory transduction of many eukaryotic cells. They can probe the extracellular environment with transmembrane proteins and ciliary associated proteins have been shown to participate in chemosensing, osmosing and mechanosensing processes. [7].

Mutations that cause a disruption in the structure of the cilia can be responsible for shortened or absent primary cilia, and this has been shown to lead to disease phenotypes, most notably in the ORPK mouse model. Conclusive evidence has shown that, cilia dysfunction in either motile or non-motile cilia can affect multiple organ systems, generally causing devastating, pathologies.

Many ciliopathies are associated with a common set of symptoms including polydactyly, hydrocephalus, cysts, and infertility. A few ciliopathies include: situs inverses (defects of left-right patterning), obesity, [6] Bardet-Biedl syndrome (BBS), blindness, deafness, chronic respiratory infections, diabetes, Retinal degeneration, rod-cone dystrophy and retinitis pigmentosa, cystic liver disease and skeletal abnormality. We generally focus on polycystic kidney disease, and specifically autosomal dominant polycystic disease.

1.3 OBJECTIVE

The structure and mechanical properties of the cilium and the way that these features contribute to the function of the cilia are still not completely known. In this study, the mechanical properties of the cilium present on kidney epithelial cells (Principal

Cortical Collecting Duct cells from the Immortomouse and Madin–Darby canine kidney) were measured. The purpose was to apply an well controlled and repeatable mechanicl stimulus to a single cilium.

CHAPTER II

HISTORY AND ADVANCEMENT OF OPTICAL TWEEZERS

2.1 INITIAL DEVELOPMENT OF OPTICAL TWEEZERS

At the early 17th century the German astronomer Johannes Kepler suggested that the reason a comet’s tail points away from the sun is because the sun’s radiation exerted a pressure. Later, in 1873, James Clerk Maxwell probed the consequences of electromagnetic (EM) radiation and deduced the radiation pressure of light [8]; he showed that light itself could exert force or pressure. This theory was not verified until the turn of the century. The primary experimental difficulty was because of the weakness of radiation pressure. Milliwatts of power impinging on an object produce piconewtons of force (l pN = 10-12 N) [9]. Pico-newton forces was measured in 1901 by Lebedev [10] and Nicolas and Hull [11]. That discovery was not useful in the real world applications until 1960’s after the discovery of the laser [12]. Laser light consists of highly coherent light that can focus down to a volume about the size of a single wavelength. The use of

lasers to create optical traps enables the stable, three-dimensional optical trapping of dielectric particles [14]. In 1987, Ashkin and his coworkers showed another use of optical tweezers. By choosing an appropriate wavelength it can be used to manipulate living cells, while minimizing any optical damage. In 1993, Ashkin and his colleague Dziedzic were awarded the 1993 Rank Prize in Optoelectronics for their groundbreaking work

[15]. The first commercial optical tweezers, known as “Laser Tweezers”, was brought to market by Cell Robotics, Inc., of Albuquerque, New Mexico in 1992 [16]. Ashkin successfully captured viruses, yeasts, bacteria and protozoa by utilizing the continuous wave (CW) near infrared (IR) laser (Nd: YAG) with the wavelength of 1064nm [17-18].

After the first observation of the accelerating and trapping particles by an optical trap in

1970 by Ashkin and Colleagues [19], optical trapping has developed from two- dimensions (2D) to three-dimensions (3D), and [13] from single to dual trap [20] or even multi optical trap [21-23]. In addition, the laser beam itself that forms the optical trap has been changed, while many traps are formed by TEM00 mode Gaussian laser beams, hollow beam [24], Laguerre-Gaussian beams [25], and vector beam [26], have all been sued to create stable optical traps. All of these advancements give optical traps some new design characteristics, such as; orbital angular momentum, variable trap stiffness, and trap depth. Optical tweezer instruments have also advanced from simple to sophisticated devices under the feedback control by the computer for the measurement and control of forces and displacement with resolutions approaching single nanometer and piconewton.

Figure 1- Evolution of optical tweezers

2.2 BASIC OPTICS

Once an optical beam is incident on an interface, the beam is deflected because of reflection and refraction. The beam carries momentum and this momentum changes due to deflection of the beam, and these changes in the momentum is the origin of optical forces applied to the trapped object. The optical forces can be along the same direction or opposite to the propagation direction of the incident photons. These optical forces are typically classified into either scattering and gradient [13] that will be expanded in later chapters. The scattering force results from reflection, scattering, and absorption of incident photons, and this scattering force is always along the direction of the optical beam propagation. The gradient force is along to the intensity gradient of the optical field and causes the object to move toward the position of the highest intensity. Basically, an optical trap is an optical field that can apply optical forces on the particles that located with in the field and hence, confine the position of the particles, as if the particles are

“trapped” by the optical field. 3D optical traps have an equilibrium position therefore,

any displacement from this position will cause a restoring force analogous to a spring but in all three dimensions. To create a stable 3D optical trap, the beam needs to be tightly focused in order to achieve a large optical field gradient, and the particle must have a refractive index higher than the solvent fluid. Additionally, the size of the trapped object should be small enough to mostly fit within the focal volume

2.4 OPTICAL TWEEZERS APPLICATION

The history and development of the optical tweezers gives it unique characteristic in a broad range of fields such as physics, biology, medicine, nanotechnology, micro- hydrodynamics and so forth. Since 1986, Dr. Arthur Ashkin is one of the foremost researchers in this field who has trapped a particles ranging from polystyrene beads to bacteria to different proteins [18]. It can be used to measure the elasticity, force, torsion, position, surface structure and particle interaction [27]. One of the reasons that it has such broad application is due to the unique, non-contact and non-invasive nature of the applied force. Optical tweezers are used widely in the area of biology and medicine, immunology and molecular genetics [28] too.

Some common applications of optical tweezers in life science are immune assay development, single molecule binding, trapping cells and bacteria, micelle and liposome analysis and in nanoparticles. Additionally, optical trapping has applications in material science, synthesis and analysis of the nanoparticles, nano-assembly of hybrid nanostructures, and the analysis of the optical interaction [29]. In 2005 by collaboratin of the by John Joannopolous's group at MIT and Federico Capasso's group at Harvard they conclude that it is possible to use gradient force on a chip. The theories from the Maxwell equations used ultimately for the conclusion that the sufficient gradient force can 7

generated in the piconewtons, more than enough to get a nanometer-scale oscillator thrumbing. Based on the calculation of the researchers on a device involving two parallel waveguides, which are light-conducting channels engineered to confine waves of a given frequency in a beam so that it can travel through the guide with very little loss. Even though the two waveguides kept their beams separate, the bonding of the optical fields between the beams was surprisingly strong. In the single-waveguide case, the optical field around the waveguide must be asymmetrical, in order to create the inequality which required to exert a total force.

Technologies such as optical tweezers and correlate with electrical, magnetic and acoustic systems, with a focus on obtaining synergies among different modalities and on novel bio-applications. Optical trapping also covers applications in emerging fields of optofluidics, lab-on-a-chip, nanophotonics, plasmonics, fiber-based manipulation, aerosol analysis and holographic techniques.

2.4.1 BIOPHYSICAL APPLICATION

Optical tweezers used as an effective micromanipulator in the field of biology, biophysics, and medicine for a two main reasons. First is the advantage of the capturing and trapping objects without any true mechanical contact, which can cause even contaminations or damage to the sample. Second, is the ability of the optical tweezers in the exertion of the forces in the range of pN and can be related to the microscopic organisms. Consequently, this technology has all sorts of use in biophysics, begging from the study of the exerted forces by the molecules that can cause particles move around in

the cells. Ashkin and his co-workers first used optical tweezers on the large enough particles and materials to manipulate directly by using optical tweezers. They used it to capture bacteria and a small number of tobacco mosaic viruses [1] and after this the single cell manipulation and cell organelles had been done. Eventually, the force of cell organelle in the living cell measured [2]. The first calibrated measurement of the compliance of bacterial flagella by tweezers to grab and rotate the bacteria by force done at 1989, by Block et al. [3]. In most of the biological study of the tweezers instead of the direct manipulation, a latex (polystyrene) microsphere applied a force. The other early studies of the biological application of the optical tweezers can be named as; yeast cells

[4], blood cells [4], [5], plant cells [6]–[8], protozoa [1], studying DNA [9]–[11]. In 1997, a group of researchers at Rockefeller University used an optical tweezer for DNA manipulation by attaching a DNA to polystyrene beads and then by trapping the attached bead they manipulate the DNA [12]. Dr. Richard Dickinson had studied cell adhesion and migration at the University of Minnesota [13].

Single optical tweezers let the study of the mechanical properties of the biological cell membranes [14]. Recently, advancement in optical tweezers not only made it as a powerful tool in the field of biophysics, biophotonics and biomedical but also used as in a tool for clinical studies and neuroscience and surgery too. Neuroscience takes an advantage from these evolutions to record, modulate and manipulate the physiological activity of neurons. Optical tweezers can be count as one of the non-contact tools for the optical surgery. It can be used for axonal manipulation that enables researchers to pull the filopodium and influence the transport of intra-axonal organelles by use of microparticles as a handle [15]. Another advancement of Tweezers is, in the cell surgery, that has a high

potential in the microinjection [16], [17], micropositioning [18], micro gripping

[19]extraction and modification, and pre-implantation genetic diagnosis (PGD). Advance cell surgery research had been done at the University of Hong Kong by utilizing two optical traps. Optical traps were generated by robotically controlled holographic optical tweezers (HOT) to the rotation the cell [20]. Difato and his colleagues at the Italian

Institute Technology developed the system for combining optical tweezers and a laser dissector with electrophysiological tools. In this system, optical tweezers apply mechano- chemical stimuli to the cells and laser dissector can change the neuronal connection [21].

Besides all of these progress, researchers make this technology more advanced and decrease the applications day by day.

Figure 2- 2µm Microsphere in an optical Trap

CHAPTER III

THEORY AND APPLIED FORCE

3.1 THEORY OF OPTICAL TWEEZERS

The non-invasive and non-contact characteristics of the optical tweezers enable for an accurate positioning, measurement, and control of the trapped microscopic objects.

On the objects that have the same wavelength as light pN force can be applied with sub- pN resolution. There are various methods of force spectroscopy techniques to investigate the biological system such as atomic force microscopy (AFM), optical, magnetic [22] and microneedle manipulation including the other techniques of spatiotemporal resolution to manipulate objects. Among all these methods, optical tweezers have shown better accuracy and performance. The spatial-temporal sensitivity of the AFM to the motion of the tethered object is less than tweezers; However, the excreted force is much larger.

Consequently, optical tweezers have the most flexibility due to the adequate control throughout a comprehensive range of applied forces as well as the ability of 3D

measurement of motion in the vast range of small molecules to the whole living cells.

Years after the discovery of the laser, Ashkin stated that laser has the energy to accelerate the particles in the scale of microscopic for about times because of the gravity, and the force can be measured with these small particles. Ashkin did the experiment on the transparent particles because they do not absorb the light. Hence, they can avoid thermal effects and deflect the light as they have a higher index of refraction comparing with the surrounding fluid. Ashkin experiment showed that the particles were stretched into the beam axis, and they accelerate in the same direction as light, which is an indication of two mechanisms of pulling and pushing the particle into the trap and upwards. Therefore, the analysis is based on the reflection of the beam at the surface of the object. This reflection produces a force that is a radiation pressure. When a beam is focusing on a certain point, gradient force should be considered, and it is mandatory for understanding the trapping procedure [23]. Optical tweezers use tightly focused laser beams to trap and move particles [24] that are originally known as ‘’gradient force optical trap’’. The main feature of the optical trapping is focusing of the beam that enables us to use the intrinsic characteristic of the light to pull a high refractive index objects into high- intensity regions.

Light can transfer momentum to objects based on the electromagnetic theory of

Maxwell. The force is depending on the velocity in the medium and can be calculated for a single ray of the power (P) as:

� ∝ �/� (3.1) Where, υ = , nm is the medium index of refractive and C is the velocity of light in the vacuum. The magnitude of exerted force by light can be found by the assumption of an 12

incident light beam on a plane mirror perpendicularly.

Every photon has a momentum of ℏ�, where � is the light wave vector and ℏ is

Planck’s constant divided by 2π, � = . The optical force changing one of the

magnitude or direction of the momentum vector, therefore, � = . The momentum of

−ℏk needed when a photon is reflecting. The transferred momentum to the mirror equals to �� = 2ℏ� and the magnitude is:

� � �� = 2ℏ� = 2ℏ = 2 � � (3.2) Where E is the energy of a photon (E = ℏω) and � is the angular frequency. Exerted force from a beam with N photons per seconds incident on the mirror can write based on the second law of the Newton:

1 �� = 2 = 2 � �� (3.3) As already mentioned, light carries momentum and this momentum changes due to the change of the wave vector during refraction. Hence, based on the momentum conservation of the combined system the object also experiences a momentum change against the propagation (Newton’s Second Law) of light. This is a proof that a force acts on an object to change its momentum [25]. There are two qualitative descriptions regarding the gradient force. The first is the dipole momentum induction from the electric field of the beam to the trapped particle, which is then dragged to the region with the highest field. The second description is based on the momentum of the diverging and converging beam. For every part of the beam only the components of the beam, which

they are lateral to the beam axis contributes to the momentum. The Force that applies to the particle originated from the change in the momentum of the photon, and they decomposed to the gradient and scattering forces so, the momentum of the collimated beam is more than the converging and diverging beam. For any changes in the beam, even convergence or divergence momentum reduces and pushes the object in the same direction as propagation. A particle can be considered as a weak positive lens, hence, at the situation that beam converge, the convergence will increase and pushed toward the focus. If the beam is converging meaning that the object is passed the focused and cause the beam less divergent, and the object will be pulled towards the focus [25].

Figure 3- Changing in the momentum of the beam cause gradient force. (Left) If the light convergence increases before the focus reduces its momentum the net optical force acting on the particle should be equal to zero and the resulting force pushes the particle

3.2 OPTICAL FORCES

Optical trapping is based on the transfer of the momentum between the beam of radiation and the object. The beam can transfer the momentum from the beam to the trapped particle. The photon refraction will be separate the medium and object when they

pass through the boundary. This refraction results from a trap in a three-dimensional environment. The outcome is directly depending on the relationship between the index of the refraction of the object (np), and the environment or medium (nm), which it is immersed. In order to trapping; the particle index of refraction should be larger than the medium index of refraction (np > nm). Snell’s Law will be used once a beam of light passes through a boundary between the two media with the various index of refractions

with a ratio of . Based on the Snell’s law:

� �� = � �� (3.4)

Trapped bead is aligned along the incident beam and below the focal point of the objective lens. In this case, when the beam passes through the bead it refracted away from the axis of the incident beam and resulting to the momentum transfer from the deflected photons to the bead. Conservation of the momentum can depict the both magnitude and direction of this momentum. This force points in the opposite direction from the change in the light momentum that can be broken into two separate components known as scattering and gradient force. Scattering force (F) is parallel to the original direction of the beam as it left the object. F Can be known as the force that particles exert when it hits the bead and pushing it in. Gradient force (F) is perpendicular to the scattering force and its magnitude can describe by the vector relation:

� = � + � (3.5)

Resulting force on the bead can achieve by diminishing to a competition of the forces between significant elements of the total scattering and gradient force (F and F)

� = � + � (3.6)

Bead behaves differently when the focal point is at the top or below the center of the bead. When the incident beam hit the bead from the bottom of the normal position the resulting gradient force will push the bead up, and when the beam hits the top, the resulting gradient force will press the bead down. In both cases, the net force pushes the bead toward the focal point. Another important factor is the numerical aperture (N.A.).

The edge of the bead should be focused at an enough steep angle. The scattering force components will dominate the both scattering, and gradient relationship and pushing the particle out of the focal point. Hence, using the maximum NA can be beneficial to get the most out of the trapping force.

Force generated in every case based on the fact that photon carries an energy hν and momentum . If a photon absorbs by an object, the momentum transferred from a light beam with power P leads to the refraction force F on an object:

� � � = (3.7) �

Where, c is the light velocity and nis the refractive index of the medium. The efficiency of any particular configuration can be described based Q that is dimensionless quantity.

Hence, the generated force by the optical tweezers is [26] :

�� = � (3.8) �

Optical forces can be calculated based on the geometrical optical regime or, in other words, the size of the particle. This force can be divided in three; Rayleigh where size of the particle is much smaller than the wavelength of light (r ≪ λ), ray optics regime where

the radius of the particle is much larger than the wavelength of light (r ≫ λ) and Mie

Regime is where the size of the particle and the wavelength of light are comparable (r ∼

λ) [27]. The strongly focused laser beam can act like a 3D optical trap and based on the distance from the trap intensity will change; nearer to the trap center the intensity of the laser is larger. Once, the refractive index of a particle is greater than a surrounding medium refractive index; a particle can trap due to the intensity of light.

3.2.1 RAYLEIGHT SCATTERING

Optical tweezers are the single-beam gradient trap and originally designed for the particles much smaller than the wavelength of the beam. This gradient force allows optical tweezers to manipulate dielectric particles in aqueous solutions. The particle can be known as a point dipole, and Rayleigh scattering approximation used where the polarization is , � = �� ; � is the electronic polarizability and � is a homogeneous electric field.

� − � � − 1 � = 4�� = 4�� ( ) (3.9) � + 2 � � + 2

Where n is the relative refraction index , a is radius of a particle and � is the dielectric constant in the vacuum constant. Therefore, the dipole momentum equals to:

� − 1 � ⃗ = 4�� ( ) � � + 2 (3.10)

The laser beam is a linearly polarized Gaussian beam with beam waist radius ω0 at the focus. The electric field polarization direction for the laser is parallel to the x-axis. The center of the beam is at the origin and r⃗ = (x, y, z) is the center of the Nanosphere. The wavefront of the Gaussian beam is flat at the focus, and it is waist that is 1/e2 radius spreads as [28]:

�� = �[ 1 + ( ) ] �� (3.11)

In equation (3.11), � = �/� is the laser wavelength in the medium. The Rayleigh range defined as the distance over which the radius of the beam propagated by a factor of

2 and given by:

�� = (3.12) �

The Gaussian intensity distribution is:

2� � �, � = � �( )/ = �( )/ �� (3.13)

In the equation (3.13), � = �(�) and P is the power of the laser beam. The numerical aperture (1/e2 points in k-space) of a Gaussian beam is

� �� = = � (�/��) �� (3.14)

The optical force separated into two scattering and gradient force where scattering is a non-conservative force and F⃗scat (r⃗) ∝ I (�) and the gradient is a conservative force and

F⃗grad(r⃗) ∝ �� (�). Gradient force is the force that forms a trapping potential for a nanosphere and tends to push the Nanosphere out of the trap. Once gradient force gets large than the scattering force, therefore, a stable trap will be formed.

Scattering Force:

An atom or a molecule absorbs after emits photon, and they scattered in all directions while all the incident photons are traveling to the forward. Based of the conservation of the momentum the change of the photon will cause a forward force known as scattering force:

� � � � = � � � � (3.20)

where � = �� ( ) is the scattering cross section and � demonstrating the direction of the beam and I r is the intensity of the beam [58].

� 8� � − 1 �� (3.16) � � = � � ( ) � � � = ( )� � 3� � + 2 6��

�� − 1 � � = 128 � (3.17) 3� � + 2 �

Gradient Force:

Gradient force is the second rising force, and it appears because of the Lorentz force acting on the dipole that induced by the electromagnetic field. The gradient force on an induced dipole is:

� = � � (3.18)

�� = (� . �) � + × � (3.19) ��

In the equation (3.18) and (3.19), � is the electric field vector of the laser light

Substitution of equation (3.18) to (3.19):

� = � �. � � + � � ( �× � ) (3.20)

As a result of �× � = 0 from Maxwell equation:

1 � � = ∝ �� = ��(�) 2 2 (3.21)

�� = 2 �� + 2� × (�× �) (3.22)

The gradient force is the time-averaged version:

1 � = � 2 (3.23)

1 1 � � = � = �� = �� 2 4 (3.24)

Yields to,

2�� − 1 (3.25) � = ��(� � � + 2

As a consequence of acting with the particle as a dielectric dipole, the force is linearly proportional to the gradient intensity that is the reason that particle moves toward the region of higher intensity and that is the reason of gradient force name. Trapping occur when the scattering force is much smaller than the gradient force in the axial direction, and the particle is displaced a little downstream, of the laser focus [29].

Trapping potential that forms from the gradient force:

2�� − 1 � � = − �(�) (3.26) 3 � + 2

The total applied force on a sphere equals to the summation of the gradient and scattering force. In order to have a stable trap, the minimum force along the propagation axis should be negative; otherwise the force of the laser will always push the Nanosphere forward, and the trap will not form. The scattering force proportional to � and gradient force to � , therefore, the scattering force decrease much faster in compare with the size of the Nanosphere.

3.2.2 RAY OPTICS APPROXIMATION

Once the light wavelength in compare to the particle diameter is much smaller, the Ray approximation is used. A beam of light can decompose to the bundle of rays and each ray in this situation has an individual power. A ray described as a straight line in media with a homogeneous refractive index that follows Snell’s law of refraction because it happens on a border of two various refractive indices and Fresnel’s equations that occurs because of the reflection and refraction. Once a ray is refracted parts of its momentum is transferred from the ray to the particle. Summing all momentum changes from each ray will result to the net force that acts on a particle.

Figure 4- Optical forces on a dielectric sphere in Ray Regime. � and � are trapping rays. This is due to the refraction the direction and as a result of the changes of the light momentum and forces �� and �� generated. F is the sum of this two forces is restoring in axial and transverse direction so that focus (f) of two ray and the center of the sphere coincident [30].

Based on the � = = ℎ/�, The momentum change per seconds is equal to the force that is acting on a particle. The force on an object that hit with N photons is [30]:

(3.27)

�� = � = �∆� �

Gradient force and Scattering force can be calculated based on the Fresnel’s equation.

�� 2� − 2� + � �� 2� � = 1 + � �� 2� − � � 1 + � + 2� �� 2� (3.28) � � = � � � � �� 2� − 2� + � �� 2� � � � = � �� 2� − � = � (3.29) � 1 + � + 2� �� 2� �

Where p is the ray power, � is the incident ray angle and � is the refracted ray angle.

is the momentum per second which transferred by the ray. The Fresnel reflection and transmission coefficients are R and T, which at an interaction the fraction of light being reflected or transmitted [30].

Also, the net force is:

� � � � � = � + � = � (3.30) � �

dimensionless efficiency factor � can be calculated

� = � + � (3.31)

Figure 5- Qs, Qg and Qt magnitude shown in the YZ plane following the direction. Length of the arrows showing the force. A, B and C showing the forces. A) Gradient B) Scattering and C) Total force

3.2.3 GENERALIZED LORENTZ MIE THEORY (�~�)

In the case that particle has a diameter that is comparable to the wavelength, neither of Rayleigh nor Ray optics can be used. In this intermediate regime, an electromagnetic interaction must be applied [31]. The time average force can be represented by:

� = < �� > (3.32)

1 1 � = � �� + �� + �� (3.33) 2 �

Where the outward standard units vector � and the integral is over the surface that

brackets, denote a temporal average. All six components of electromagnetic (EM) field can be calculated. For the harmonic wave of EM [E (i) and H (i)], fields of the complex exponential assumed as e-iωt, where ω is frequency and later omitted from the subsequent time-dependent terms. The incident EM field can be considered as polarized at the x-axis.

In this case EM field can be described as:

∗ � = �� 3.34

� = 0 3.35

∗ () � = −(2� �/�)� 3.36

� = 0 3.37

� = �� 3.38

∗ � = − � 3.39

Where � is the permittivity of the background medium, � = � �, � = �/�, � =

1/(� + 2�), � = �� (−�� ) and � = . In these equations � is the beam waist radius, � is the wave vector of light in vacuum, � is the background permittivity medium and � = � � is the wave vector of light in the background medium, and

E0 is the electric field amplitude at the Gaussian beam focal point.

3.3 FORCE CALIBRATION

The potential of the trap can assume harmonic and defined with:

� = −�� (3.40)

Where � is the trap stiffness that enables to find the force as a function of position.

Three methods can apply with the same goal, which is finding a spring constant, �.

Spring constant describes the force that applied to an object, and it moves away from the trap. Energy of a harmonic spring has the quadratic relate RMS fluctuations in x to trap stiffness with equipartition theorem:

1 1 � � = � � (3.41) 2 2

Equation (3.41) illustrates that the stiffness can be determined independently from the

Stokes drag, that can cause significant error because of the hydrodynamic effects given the microsphere’s proximity to the surface for these experiments. Implementation of the above equation can be found by fitting the fluctuations of the x in frequency space.

At the x direction the Langevian equation can be written for the x direction �(�) as:

�(�) − �� − �� = 0 (3.42)

where � � indicates Brownian thermal noise, � is the trap stiffness to be determined and � is the drag on the bead. By applying the Fourier transform equation:

�(�) − �� − �� = 0 (3.43)

Then the power spectrum can be calculated for the fluctuation of the x as:

� � � � = (3.44) � + ��

The first technique is Equipartition theorem on time domain data. The amplitude of the traps position fluctuates inside the trapping beam and gives a fast estimation of the trap stiffness. The second method, power spectrum analysis, is the same data, but the analysis takes place in the frequency domain. The last method, drag forces, the specimen carrying the trapped particle is transferred at a known velocity to determine the drag force that is wanted to overcome the trapping force. This procedure is best for determining the greatest force that may be employed by the trap but performs a mediocre job of trap calibration.

3.4 QPD POSITION DETECTION

Figure 6- QPD diagram that used in our experiments

An accurate position detection of the trapped particle is necessary to find an optical force. The simplest way to determine the position of the trap is to guide the laser onto the quadrant photodiode. Laser beam scattered from a particle and is reflected by a dichroic mirror to the Quadrant Photo Diode (QPD) and it consist of 4 photodiodes in a quadrant formation that allows the calculation of the X and Y position. An incident light on each

QPD generates voltage along x and y-direction (�and �), which they are proportional to the position of X and Y around the center of the trap. Once there isn’t anything in the trap the laser beam is focused on the center of the QPD, and, therefore, the Voltages are zero and by moving the trap slightly away from the center of the trap causing a change in the

X and Y voltage. The position of the data and the center of the trap also can show the exerted force on the trap.

CHAPTER IV

MOTILE AND NONMOTILE CILIA

4.1 CILIA

Cilia first observed in 1674-1675 by Antoni van Leeuwnhoen in a letter to Royal

Society of London. According to quote from Dobell in 1932, Leeuwnhoen described ciliated protozoa as they provided with various extremely thin feet or legs, which were moved very quickly [32]. Cilia means hair or even eyelash and the term ‘’cilium’’ were first used in 1786 by Muller. The other term flagellum introduced by Dujardin in 1841 meaning whip [33]. Later in the mid 19th Century, flagellum being used once a cell has a single organelles and cilium when a cell has many similar organelles. The term ‘’Ciliated

Cell or Ciliated epithelium’’ refers to the cells that have many cilia on the apical surface

[34]. The other term “flagellated cell or epithelium’’ refers to the cells with a single organelle on the apical surface that they recently known as primary cilium. Since the 19th

century the most attention on the cilia for identifying them [35]. The motility of the cilia first describes in 1834 by Purkinje and Valentin. Later in mid-nineteenth century in 1898, nonmotile, solitary cilia, first seen by Zimmermann [36]. After nucleus, Cilia is one of the earliest cell organelles that recognized. Recently, cilia attract attentions due to the medical implications. It is emanating from centriole/centrosome complex of the cell hence it is part of it. These interests initiated since 1997 because of the unknown characteristic of it.

The Primary Cilium knew as a nonmotile, solitary cilium that can be found in all mammalian cell [37]. Primary Cilia linked to the multiple signaling pathways and based on the cell type they thought to function as chemosensors, mechanosensors or in some cases even both [35]. Cilia is mainly constructed from a microtubule axoneme that is nucleating from the basal body and terminated at the tip enclosed by a membrane that is connected to the plasma membrane [38]. The axoneme is a cylindrical array of nine doublet microtubules (MT) which extend from the triplet microtubule arrangement of the mother centriole or basal body [39]. In the cilia, structure microtubules play an important role where they provide the structural rigidity and help to provide the motion of the cilia.

Microtubules usually comes with the molecular motors that are proteins designed to travel along the microtubule, usually to help to transport something [40].

The central pair of microtubules are biochemically, and structurally asymmetric is present in the center of the ring and extends from the axoneme [41].

Cilia is divided in two motile and nonmotile cilia. Motile cilia have an axoneme with nine microtubules doublets that shaped in a ring with a central doublet pair (9+2). They appear

in multiples on the surface of the cell, and they beat with each other to provide unidirectional fluid flow [38].

Microtubules composed of an A tubule which is a one complete microtubule and linked to the B tubule that is the second incomplete microtubule (the B tubule) [69] Which here

A tubule consists of 13 tubulin protofilaments, and B tubule compromising from 10 protofilaments [42].

In motile cilia doublets can slide on each other because the crosslink dynein motor shape [43]. Hence, the outer and inner arms dynein-mediated the cilia motility that they control the ciliary beat frequency (CBF) and waveform [44].

The other type of the cilia, nonmotile also known as primary cilia is slightly different from the motile one and it has a simpler 9+0 microtubule configuration, lacking the central doublet pair, dynein arms, and radial spokes. They are usually present as single apical membrane extensions. The primary Cilium known as an non motile, solitary cilium that can be find in all differentiated mammalian cell [37]. Primary Cilia linked to the multiple signaling pathways and based on the cell type they thought to function as chemosensors, mechanosensors or in some cases even both [35]

Cilia contributes in many important cellular processes such as cell signaling [45].

Therefore, primary cilia known as a sensory organelle for not only detection but also transmission of signals from the extracellular environment to the cell too, which is vital for the homeostasis and function of a tissue [46].

Cilia signal transduction has two pros. First, adjusting ciliary localization of

signal transducers allows the modulation of the signaling pathway. Second, since there is a diffusion barrier between the cilium and cell body it is able to concentrate the signal transduction. Primary cilia can detect two physical and biochemical extracellular signals.

Primary cilia in collecting duct of kidneys act as mechanosensor. By a specific mechanism polycystin-1 (PC1), polycysin-2 (PC2) and fibrocystin convert mechanical stimuli to the calcium influx of the cell body [47].

The most important foundation of the cilia importance is they ability as a mechanosensors in the kidney tissue. Primary Cilia lining the epithelium of renal tubules control kidney tissue homeostasis and monitor the composition and flow rate of urine in the nephron. Cilia will bend because of the fluid flow and cause a change in the calcium intracellular levels. Occlusion of this flow cause defects in the assembly of the cilia [48].

Figure 7- Motile cilia Schematic [84]

4.2 PRIMARY CILIA

The primary cilium is almost ubiquitous organelle in vertebrates [49] most characteristically at the incidence of one per cell [50]. Primary cilium is an axoneme of nine doublet microtubules that extends from the basal body or motor centriole with the absence of the central pair (9+0), meaning they miss the molecular motors and axonemal dyneins which are responsible for the movement of the cilia [51]. Although, the embryonic immotile cilia have a dynein arms and counted as motile. Primary cilia appear during quiescence or the G1 phase of the cell cycle. The mother centriole, which, before ciliation, serves as a component of the centrosome and microtubule organizing center, differentiates into a basal body to nucleate a cilium [52].

primary cilium is multifunctional antenna that can sense both mechanical (fluid flow, pressure, touch, vibration) and chemical (light, odor, PDGF) variations in the extracellular environment [53]. The primary cilium is surrounded by a special membrane

[54] which is receptors for various signaling such as; Sonic hedgehog (Shh) [55] platelet- derived growth factor (PDGFR) [56] serotonin, and somatostatin localize [57]. Based on the cell type, primary ciliogenesis proceeds through two various ways like the ones that find in the lung or kidney, the basal body relocates to, and docks with, the apical surface of the plasma membrane, whereupon the axoneme assembles, protruding into the extracellular space [58], [59].

In a contrary, in mesenchymal cells, fibroblasts, and neuronal precursors, ciliary vesicles associate with the distal appendages of mother centrioles, and membrane biogenesis occurs in parallel with axoneme elongation as secondary vesicles are

recruited, and subsequently fuse, with the plasma membrane, exposing the cilium [60],

[61]. In both ways membrane biogenesis and vesicular trafficking are required.

Additionally, Primary cilia are required for the sensing of the shear stress in various developing organs like the kidneys and blood vessels. In endothelial cells (ECs), primary cilia bend as a result of the forces from the blood flow and are vital for flow sensing the same as control of angiogenesis. The multiple parameters guiding cilia bending reflect the forces constructed at the surface of the ECs and the mechanical properties of the endothelial cilia [62].

Figure 8- Left image is the schematic of the cilia in the cell [85] and right image showing the cilium in the shear flow that cause it to bend [53]

4.3 CILIOPATHY

Any abnormal or dysfunction of the cilia that caused from a genetic mutations encoding defective proteins therefore, any genetic harms that compromises the formation or function of the cilia will result to ciliopathies. Due to the reason that cilia can be find in almost any cells, any disorders can cause as constellation of features such as primarily retinal degeneration, renal disease, hearing loss, cerebral anomalies. The ciliopathic notation was initially recognized to a disease known as Bardet–Biedl syndrome (BBS) that can happen because of he BBS8 genetic mutations [63].

The other ciliopathies can be named as, congenital fibrocystic diseases of the liver and pancreas, diabetes, obesity and skeletal dysplasias [64], Joubert syndrome, Meckel-

Gruber syndrome and nephronophthisis. In addition to the genetic disorders to cilia genes chemical and mechanical stimuli can cause a change to the cilia structure [65]. In any organ disease can indicate in the context of ciliopathic dysfunction. The most prominent organs that can affected by cilia disorder includes the kidney, eye, liver and brain. The presence of the disease can be different and presenting at birth or even later in childhood and this is depending on the severity of the mutation besides the number of defective proteins encoded where more than one mutation in a ciliary gene occurs [64]. One of the most common diseases from the defects of the cilia is polycystic kidney disease (PKD).

PKD can appear due to an extra centrosome that results to the irregular cilium number; centrosome amplification affects the normal ciliary signaling. The extra centrosome will cause to the formation of the multiple primary cilia in one cell. Thus the presence of the numerous primary cilia in a cell will disrupt epithelial cell polarity and organization in

vitro. Additionally, these super ciliated cells display very slow progression through the cell cycle [66]. In the other words, PKD occurs because of the continuous formation of the the cysts and fluid filled cavities lined by epithelium.

Primary cilia in the kidney are present on most cells and it extends form the apical surface of the epithelium into the tubule. Autosomal dominant polycystic kidney disease

(ADPKD) can cause because of the mutations in PKD1 which is he gene encoding polycystin-1 and PKD2 with the gene polycystin-2. The other sever form of the PKD is

Autosomal recessive PKD (ARPKD) appears primarily in infancy and childhood is caused by a mutation in the polycystic kidney and hepatic disease1 (Pkhd1) gene [67].

Nephronophthisis, a form of PKD that is the most common genetic cause of renal failure through age 30, is caused by mutations in multiple different nephronophthisis (NPHP) genes [68]. All form of the PKD in both human and animal are associate with perturbations in renal primary cilia structure and function therefore the only one of preventing form the PKD is to keep the structure the primary cilia.

Figure 9- Healthy kidney versus kidney with PKD. Left is the schematic of the

normal kidney and right is the kidney with cyst (Polycystic Kidney) which is larger

than normal and cysts grown on it.

CHAPTER V

DEVELOPED MODEL OF THE PRIMARY CILIUM

5.1 CILIARY MECHANICS AND MODELS

Finding the mechanical properties of the cilium is beneficial to find the crucial role of the cilium including the mechanotransduction. Couple of studies during years by

Praetorious and Spring showed that the bending of the cilium in the kidney epithelial cells causes a drastic change in the extracellular Ca2+ and causes an increase in the concentration of the intracellular Ca2+. The increased Ca2+ concentration subsequently disappears as primary cilium removes [48], [69]. Two proteins Polycystin-1 (PC1) and polycystin-2 (PC2) which they encoding as pkd1 and pkd2. PC-2 is Ca2+ channel [70].

The polycystin-2 (PC2), protein respectively encoded as pkd2 causes the mechanosensory response of the cilium. PC2 is located at the base of the primary cilium and is a stretch activated cationic channel [71]

The cellular mechanosensing decreases as a result of the reduction in the length of the

primary cilium that occurs due to the orbital shaking of the cell. [72]. Any modification in the structure of the cilium cause an alteration in the mechanosensivity response of the cilium therefore, the primary cilium counts as antenna for extracellular physical signals

[73].

The mechanical behaviors of the cilia is just calculated in couple of studies. The first model of primary cilium described and calculated by Schwartz et al. They modeled a primary cilium as a thin elastic beam that is undergo substantial rotation the fluid drag force which acting thorough the cilium was constant. The flexural Rigidity EI quantified as evaluating the effective stiffness of the beam which counting for material and geometric [74]

In their model the fluid flow velocity that was a function of length was assumed constant and they did not measure for the identified linear velocity with distance from a no slip boundary. Later, in 2005 Liu et al. they used the same model with the consideration of the fluid flow profile. In this developed model the acting torque at the base of the primary cilium calculated but only for the small rotation [75]

Five years later Rydhom et al. described the finite element model of the primary cilium including the apical memberane. In this model the relationship amongst the shear stress as a result of the flow and the Ca2+ release calculated [76].In 2012 Young’s et al. suggested a model for the primary cilium as non linear rotational spring the details are appears by pairing the elastic beam with elastic shell [77]. In 2014 study developed by the same group which they suggested a model for the deflected primary cilia. In their study the primary cilia experiencing the fluid flow. I this model the 3D dynamics of the fluid including the large rotation beam formulation that counts for the cilium anchorage

rotation and fluid drag force at the high angles of the deflection [78].

The recent and more sophisticated model suggested at 2015, that the mechanical properties of the cilium calculated based on the resonant oscillation which the model showed that the primary cilium can be modeled as non linear rotatory spring[79].

The models provided essential perception to the current understanding of the primary cilium mechanics but still the more elaborated model including the initial shape, rotation and the reasonable fluid drag are necessary to fully understand the mechanics of the primary cilium in mechanosening of it.

Models will be shortly describing in AppendixA.

CHAPTER VI

METHODS AND MATERIALS

Various experiments had been done to measure the mechanical properties of the data. At the beginning microspheres with various diameters (1��, 2 ��, 0.5 ��) trapped by optical tweezers for the calibration. Afterwards, data acquired by trapping a microsphere

(mostly 2 ��) and drag it to the primary cilium for the manipulation. Finally, the cilium trapped with a non contact method without any attached microsphere.

6.1 Methods

All experiments were performed on epithelial cells. Experiments were carried out

with a Leica DM 6000 upright microscope equipped with both temperature and CO2 control (Solent Scientific incubation chamber) and a Point Grey Research ‘Flea’ digital 41

video-rate camera. Prior to experiments, the trap location was determined by trapping a small piece of cellular debris with the bright field imaging and labeling the position of the trap with a small piece of tape. A joystick (XY translation) was used to move a cilium to the vicinity of the trap. . The accuracy of the microscope stage (Prior Scientific H30XY2) was ±0.04 �m. Point Grey Instruments ‘Flea’ digital video-rate camera was used for the trap monitoring and image acquisition. The dynamics of the diffracted trapping beam were recorded using a quadrant photodiode (QPD). QPD (first sensor model QP50-6-

SD2) outputs the centroid location of the diffracted trapping beam, digitally sampled at

10 kS/s.

6.2 CELL CULTURE

The two cell lines used in this thesis are Madin-Darby canine Kidney (MDCK) and mouse cortical collecting duct (mCCD 1296 (d)) principal cells. mCCD cells derive from the heterozygous offspring of the Immortomouse (Charles River Laboratories,

Wilmington, MA, USA). The Immmortomouse has as a transgene a temperature-sensitive

SV40 large T antigen under the control of an interferon-� response element to provide experimental control over cell-cycle exit and differentitation (gain of function). To promote the development of a polarized epithelial phenotype, cells were cultured on collagen coated Millicell-CM inserts (inner diameter 30 mm, permeable support area 7

2 cm ; Millipore Corp, Billerica, MA). Cells were grown to e confluence at 33°C, 5% CO2 and then differentiated at 39°C, 5% CO2. The growth medium that we used was composed as below (all concentrations listed as final):

Dulbecco's Modified Eagle Medium without glucose and Ham’s F12 at a 1:1 ratio, 5 mM glucose, 5 �g/ml transferrin, 5 �g/ml insulin, 10 ng/ml epithelial growth factor

(EGF), 4 �g/ml dexamethasone, 15 mM 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES), 0.06% NaHCO3, 2 mM L-glutamine, 10 ng/ml mouse interferon-�, 50 �M ascorbic acid 2- phosphate, 20 nM selenium, 5%fetal bovine serum (FBS). For differentiation, FBS, EGF, insulin, and interferon- � were omitted from the apical medium and insulin, EGF, and interferon- � from the basal medium.

6.3 IMMUNOCYTOCHEMISTRY

To visualize the cilia, fluorescent microscopy was used as demonstrated in figure

10. Fixation and immunocytochemistry were performed using standard techniques. The cells were briefly fixed in 4% paraformaldehyde for 10 min. After rinsing, the monolayers were permeabilized for 10 min with a solution of 0.1% Triton-X and 0.5% saponin in a blocking buffer containing 5% donkey serum, 5% sheep serum, 1% bovine serum albumin (BSA), and 5% fetal bovine serum (FBS). The monolayers were then stained with a monoclonal mouse antibody against acetylated α-tubulin (Invitrogen,

Carlsbad, CA) and a polyclonal goat antibody against Polycystin-1 (Abcam, Cambridge,

UK) followed by an anti-mouse antibody labeled with AlexaFluor 488 (Invitrogen) and an anti-goat antibody labeled with AlexaFluor 594 (Invitrogen). The stained filter was cut out of the culture insert and transferred to a microscope slide, monolayer side up. The filter was mounted in VectaShield (Vector Labs, Burlingame, CA) with DAPI. A # 1 1⁄2 coverslip was placed on top of the monolayer. The slides were then sealed with nail polish and stored at 4oC for imaging.

Figure 10- En face images of mouse Collecting Duct (mCD) cells stained with antibody for acetylated tubulin (green) that appears the cilium and counter stained with wheat germ agglutinin for apical surface glycoproteins (red) and DAPI for nucleic acids (blue). X-Z slice of the primary cilia lying against the apical surface

6.4 OPTICAL TWEEZERS APPARATUS

The essential elements consist of a laser, steering optics, a dichroic mirror, the sample cell, and a microscope objective with a high numerical aperture (NA) [31]. For single beam optical tweezers, the gradient force must be large enough to overcome the scattering force. In a good approximation the gradient force is proportional to the spatial intensity gradient [80]. The high NA objective is required to achieve a small focus, and therefore, a steep intensity gradient. The beam expander is required to fully illuminate the back aperture of the objective and thus access the full NA of the objective. The other important factor is the wavelength of the optical tweezers that is chosen with consideration of possible optical damage and heating to the samples. In biological materials, the ideal trapping wavelengths range between 750 nm and 1200 nm [110]

Figure 11 shows the apparatus that used for our experiments.

The single beam 3D trap laser source was a Crystalaser IRCL-0.5W-1064, a diode- pumped Nd: YAG continuous-wave (CW) single mode laser providing 0.5W optical power from a 10W electrical power supply. The optical tweezer was aligned to the optical axis of the microscope (Leica DM6000B, Wetzlar, Germany) using a 5-degree-of- freedom (x-axis, y-axis, z-axis, pitch, and yaw) mount. The optical tweezers breadboard layout was constructed using Linos Microbench® optomechanical mounts. The beam expansion was achromatic doublets. The back aperture of the objective lens filled by expanding the laser beam. Two lenses were used and antireflection coated for 1064 nm.

The first lens has a focal length of 40mm and the other one 250mm. The focal lengths were chosen for the ease of use. The distance from the entry port of the microscope to the objective lens is 140 mm, allowing the second lens to be placed 100mm from the microscope body and the factor of laser expansion was 6X to fill the back aperture. The objective lens used was a Leica 63X NA 0.9 U-V-I HCX long working distance plan apochromatic dipping objective with a 2.2-millimeter working distance. Using an existing lateral port, the tweezers coupled into the microscope. A side-looking dichroic mirror

(Chroma Technology, Bellows Falls, Vermont) mounted on the fluorescence turret provides the ability to perform visible transillumination viewing while the tweezers are operating. A KG-1 IR cutoff filter (Newport, Irvine, California) inserted above the fluorescence turret prevents the observation of the tweezer spot by a camera during operation. The trapping beam applies a force to objects by moving the microscope sample stage (Prior ProScan II Motorized H101/2 Stage), the trap location does not move. To record the movement of a trapped object, a QPD (first sensor model QP50-6-SD2)

records the location of the trapping beam centroid. The QPD is located downstream from the condenser lens. Use of a dichroic mirror (Qoptic Microbench, Fairport, New York) and laser line filter (1064 nm, Edmund Optics, Barrington, New Jersey) ensures that only the Nd: YAG light is incident on the QPD. Intensities were converted to voltage readouts within the QPD and then transferred to a National Instruments data acquisition device which recorded voltages at a user-specified frequency and exported a digital record of particle positions to the host computer [82].

(i) (n)

(h) (a)

(b) (l) (c) (m) (j) (d) (e) (g) (f) (k)

Figure 11- Hardware configuration of the laser tweezer, microscope, and QPD data acquisition system. The solid line shows the laser beam path. Components labeled as follows: (a) Tweezer module (b) Side-looking dichroic mirror located in fluorescence turret (c) objective lense (d) Sample plane (e) Condenser lens (f) Dichrioic mirror (g) Quadrant photodiode (QPD) (h) Tube lens (i) Camera (j) 5 degree of freedom tweezer mount (k) Transillumination stage (l) Incubator (m) QPD data acquisition module (n) Computer

6.4.1 Major Components Description

In our Laboratory setup, Leica CTR6000 electronics box controls the microscope body and halogen illumination. It includes USB and AC power supply 90-250 V, 50-60

Hz shown in figure 12.

Figure 12- Leica CTR 6000 front side power supply

A XYZ ergo control was used to control the focus movement Z. In figure 13, number 4 is the buttons at the left and right. Right buttons are for coarse or fine focus control

Figure 13- Z controller

The pro scan II XY stage controller controls the motorized stage. The stage movement is controlled with a two axis joystick.

Figure 14- Prior PreScan II at the right and Ergonomic Joystick is at the left side laser source for the 3 D trap, 0.5-W diode-pumped Nd:YAG continuous-wave single- mode laser.

Figure 15- CrystaLaser (CL 2000 diode pumped crystal laser) laser shutter and the right and the power supply and the left

The Quadrant Photo Diode (QPD) used in our experiments was a QP-6SD which is a quad photodiode array including the current to voltage amplifiers. It provides 3 output voltages V1, V2, and V3; V1 is the sum of all four quadrant diode signals. The difference between the voltage analog intensities sensed by pairs of the diodes is the difference signals V2 and V3. QPD located downstream from the Condenser lens.

Figure 16- Right shows the location of the QPD that is downstream from the condenser lens and left is the schematic of the QPD.

CHAPTER VII

PRIMARY CILIUM TRAPPING

7.1 TRAPPING PROTOCOLE

In our experiment cilia are trapped directly within an optical trap, without the use of microspheres. First a small piece of floating cell debris was trapped to distinguish the location of the trap and marked with a small piece of tape on the monitor to mark the trap location. Following turning off the laser, bright field illumination was used; by moving the microscope stage, a cilium was moved to the trap location and focus adjusted to align the trapping plane to the distal tip of the primary cilium. The cilium was then laterally displaced slightly from the trap axis and position recorded using the

XY translation stage digital readout. The optical trap was turned on and QPD data acquired for several seconds. The laser was then turned off, another cilium was moved into position, and the procedure was repeated. Using the QPD output the spatial dynamics of the diffracted beam were recorded and analyzed based on the

[82]. By applying the trap to a cilium, the cilium can bend and initiate a

mechanotransduction-signaling cascade. Figure 17 is the demonstration of the

primary cilium in the trap.

Primary

δy

δz

Cell body z

Figure 17- A cilium is trapped and displaced from the center of the base by a distance “δy”; the flexible cilium deforms in response to the applied load. The resulting shape is shown when the trap is located at the distal tip of the cilium, but in general is located at the distal tip of the cilium, but in general is located a distance “δz” from the cell surface

Normally, it is difficult to see the primary cilium in the cell because the cilium extends out of the apical membrane along the optical axis of the microscope image. The primary cilium appears as a bright small circle in each cell, close to the nucleus. Once primary cilia are trapped, the output voltage of the x and y from the QPD resembles a harmonic oscillator.

CHAPTER VIII

RESULTS

8.1 ANALYSIS AND RESULT

The primary data acquired with the virtual instrument (VI) in LabView 2010

allowed us specify the sampling frequency and the duration of the data acquisition.

The VI records voltage outputs from the QPD and can display the voltage data in a

real time front panel while the data is converted and stored. Data is saved as .TDMS

binary files by the National Instruments LabView that was later converted to .MAT

files directly in MATLAB for further processing [82] . The called function, TDMS

(true, TDMSfileID), has been developed by a community of developers since

late 2009. The function can be found via the MATLAB Central File Exchange

and is offered open source to those who wish to make their own additions to

the development of the code. Here, version 9 of the software used. Figure 18

demonstrate the acquired QPD data in the National Instruments LabView that 52

can be recorded in .TDMS formats.

Figure 18- National Instrument LabView data acquisition software front view

The raw data are the time-series voltages at x and y direction. This output data provided at APPENDIXB. After processing in MATLAB the raw data is stored in separate .txt files. The MATLAB analysis outputs the trap’s spring constant, this is converted to a force through a prior calibration effort [107]. based on equation (8.1).

� = [9 × �(��)]. (8.1)

where � is the trap stiffness (output by MATLAB) and a is the diameter of the trapped particle. Similarly, the standard deviation (STD) of the computed spring constant is output by MATLAB as a consistency check. If a small floating particle falls into the trap, the computed stiffness will be very different as compared to trapping only the cilium. In our Experiment, the standard deviation of � and � were calculated as

1.1455×10and 9.1785×10, and the diameter of the cilia is about 0.2�� which by substitution in equation (8.1):

� = 9.75 � = 31.62

The average of the trap stiffness in x and y ( � and �) also calculated as 1.6717 ×

10 and 1.1849 × 10 . The mean square displacement (MSD) of the data also calculated and plotted by the software developed by Glaser et al. [82], figure 19 is the demonstration of the data with the MSD idealized curve fit. The MSD divided to two sections. The short-time section which is the inertial time scale and the long time limit section which corresponds to the restoring force of the optical trap.

Figure 19- The result of the data versus the mean square displacement (MSD) that demonstrate the short and long time sections.

The MSD, measures the displacement of the particle from its initial position [83].

�� (�) = 〈(�(� + �) − � (�))〉 (8.2)

In eqation (8.2) MSD is the function of lag time � . Because the optical trap confines the accessible space that a particle may diffuse through Brownian motion, the

MSD cannot grow indefinitely but reaches a plateau, rigorously calculated as:

2� � �� = [1 − � ] (8.3) �

From equation (8.3), we conclude that a particle freely diffuses within the optical potential at short times, but over long times it is confined by the trap restoring force. The long time section of the MSD depends on the spring constant �. The MSD in the short time section grows linearly therefore, �� = 2�� where D is the diffusion coefficient.

2� � lim �� = � → �

2� � lim �� = → �

MSD shows the maximum value of the trapped particle displacement by the value of the plateau. For convenience the .txt files are stored in an Excel file for further analysis.

Figure 20 and figure 21 illustrates some results of these primary data. Due to Brownian motion, diffuse motion appears in our raw data. The data of each sample were trimmed to regions of interest (from 1 to 1000 millivolts), and data was smoothened using a 1D

Savitsky-Golay filter with a window width of 21, and a fourth-degree smoothing polynomial that plotted in the MATLAB (The MathWorks INC.).

Figure 20- A sample of raw QPD output a) x-direction data b) y-direction data

Figure 21- Raw acquired data from the QPD. Left is the raw noisy data for the x direction and, right is the smoothed region of interested raw data

Another useful method that could be used for the purpose of smoothing the data is wavelength transform. Wavelength transform is applied to the same time domain data that acquired from QPD to eliminate the noise and make the data smoother. In wavelet transform method, based on the number of samples in the noisy signal, the primary data can be processed in any arbitrary levels (N=1,2,… ) and separates to the approximation and detailed signal (residual) for the better visualization and, as a result, elimination of the noise. This process is called decomposition. In our analysis symlet 4 (nearly symmetric wavelet) level 5 wavelet transform applied to the noisy signal. This Process performed ascending from level 1 (first transform) to level 5 (fifth transform). After separation of the signal into scaled signal and detail signals, we can start the process of noise elimination and filtering that is called thresholding. In general, there are two different thresholding methods. First, soft thresholding and second hard thresholding. In this study, soft thresholding was preferred because of its better performance in our system. In figure 22 first level of transformation marked with a5 (first approximation) and s5 (first residual) and so forth.

Figure 22- Decomposition of the signal in five level by wavelet transform. The decomposition process started from a1 in which decomposed to d1 and a2. This process is continuing until we get a5 and five detailed signals that shown at the right.

Figure 22 shown an experimental trap trajectory recorded for an optical trap.

Figure 23- X versus Y direction that shows the path of the trapped particle

The animated video of the cilia in an optical trap also plotted that shows the trap position and trajectory. Green dot is the Cilia and red is the trap.

Figure 24- Cilia in a trap animation

In order to calibrate of the optical tweezers, three methods can be used;

Equipartition theorem, Power spectrum and drag force. A histogram of the particle position is shown in the figure 25 and fitted to a Gaussian distribution that also depends on the spring constant. Brownian motion combined with the optical force confines the particle in the trap region. Thermally driven motion let us to achieve information related to the shape of the trap potential that is useful to calibrate optical traps. The probability distribution of the particle displacement in a certain time interval has a Gaussian distribution due to the harmonic potential of focused laser.

1 �(�) = �� (8.4) 2 In equilibrium conditions, the probability density of the particle position can be derived by Boltzmann statistics. In 2 dimensional movements, position probability density can be calculated as shown in equation (8.5):

�� −� �, � � �, � = � (8.5) ��

Where � is the normalization constant and � is the absolute temperature and � is the Boltzmann constant. Equation (8.5) shows that Brownian particles spend more time in the lower potential energy regions.

The probability is a Gaussian function:

() () (8.6) � �, � = � � � where � and �, are the stiffness of the trap, and (�, �) is the equilibrium position.

The width of the Gaussian-shaped histogram is directly related to � (the trap stiffness) under the condition that T is known. The width of the histogram can be easily calculated

by data tips at the figure that width/k can be calculated.

Xdata 3000

2000

Counts 1000

0 -0.16 -0.14 -0.12 -0.1 Modeled Data 3000

2000

Counts 1000 X: -0.1647 X: -0.09317 Y: 1 Y: 6.982 0 -0.16 -0.14 -0.12 -0.1

Figure 25- Histogram of the data with a Gaussian modeled fit

Oscillation amplitude was identified by finding local maxima of the discrete

Fourier transform of the data. For the � coordinate with Δ� intervals in time T data

Fourier transformed as:

(8.7) � = ∆� � �

where � is the x value at time � = �∆� and � = �∆� and N is the number of recorded value. As shown in figure 26, a spike at 50 Hz appears which shows the resonant frequency of the cilia.

Double Sided FFT - with FFTShift #10-6 One Sided Fourier Transform 4.5 18 X: 50 X: -50 X: 50 Y: 1.771e-05 4 Y: 4.208 Y: 4.208 16

3.5 14

3 12

2.5 10

2 8 DFT Values |DFT Values|

1.5 6

1 4

0.5 2

0 -600 -400 -200 0 200 400 600 0 100 200 300 400 500 600 700 Frequency (Hz) Frequency (Hz)

Figure 26- Fourier Transform of the data. At the right is the two sided power spectrum and left is the one sided Fourier transform which they show the peak resonant frequency at 50 Hz

The motion of the particle is related to the strength of the trap; in the back focal plane interferometry, the trapped object’s power spectrum of position is known. Power spectrum can be calculated as the square of the Fourier transform:

� ×� � = (8.8) � �

and, � = = 5000 Hz.

The power spectrum of the trapped particle position has a Lorentzian shape characteristic when the particle is held within a harmonic potential:

� 2� (8.9) � = � + �

where � is the corner frequency that in the Lorentzian equation is the free parameter that enables us to find k from fitting to the experimental data based on the equation k = 2��, where γ is the friction coefficient and D is the diffusion coefficient

and calculated based on the Einstein relation � = and k is the Boltzman constant and T is the temperature

(8.10) � = = . =

In equation (8.10), � = 2� � is the second free parameter and � = 2�� and is the corner frequency. � represents the frequency beyond the motion that purely diffused.

Spectrum: Frequency 2440.1779

3 3372.3808 10 2810.3173 2316.7982 1178.9624 Log y

2000 2500 3000 3500 4000 4500 5000 550060006500 Frequency

Figure 27- Power spectrum of the data. Left is the plot shown the resonance peaks of the microscope body and right is the two frequency peaks at the range between 2KHz to about 3KHz

Figure 27 is the result of the power spectrum of the trapped data from QPD that it demonstrates two noise peaks around 2 KHz and 3KHz which is the indication for the

movement of the cilia in the trap. The power spectrum is roughly constant from the second peak for the bandwidth of approximately 1 KHz.

8.2 Tweezers Calibration

To get the reliable and accurate results it is crucial to work with calibrated tweezers; therefore, it is mandatory to check the tweezers calibration before any experiments to prevent from further error in our experimental trials. Here, calibration performed by using polystyrene microspheres (Bangs Laboratories, Fishers, Indiana), phosphate-buffered saline (PBS, Cellgro, Pittsburgh, Pennsylvania) used for the dilution of the solution by the volume of 1:103. The microspheres solutions were placed within a microscope slide then laser was turned on and stage moved to trap any microsphere.

Flycapture used for the live cell imaging and visualizing the trap. Meanwhile, QPD recorded the data from the trap. QPD data were collected from the consistency checks in

10 kHz. Table demonstrates the consistency of the data from QPD which is a proof of the calibration of the system.

Object in the trap Index �� RUN NO. 1 1 3.52E-16 2.28E-17 2 7.16E-16 1.99E-17 �� polysteren 3 7.61E-16 5.68E-17 bead 4 5.18E-16 6.57E-17 5 7.61E-16 4.89E-17

6 7.18E-16 9.14E-17 7 7.23E-16 6.18E-17 8 7.25E-16 8.10E-17 9 7.07E-16 1.61E-16 Average 1.8094e-16 6.6466e-16 Standard Deviation 4.6533e-17 1.3809e-16 Force 0.0020 0.0021

Object in the trap Index �� RUN NO. 2 1 5.04E-16 1.79E-18 2 6.95E-16 1.25E-17 3 5.13E-16 2.85E-17 4 7.48E-16 3.54E-17 5 6.83E-16 8.76E-17 6 4.86E-16 4.34E-18 7 7.19E-16 8.96E-18 8 6.47E-16 7.93E-17 9 7.74E-16 1.38E-16 10 7.94E-16 7.86E-17 �� polysteren 11 7.10E-16 1.91E-18 bead 12 5.16E-16 1.33E-17 13 8.07E-16 4.11E-17 14 7.83E-16 4.18E-17 15 7.78E-16 2.87E-17 16 7.60E-16 1.48E-17 17 8.19E-16 2.25E-17 18 7.23E-16 2.14E-17 19 6.93E-16 1.05E-16 20 7.48E-16 7.72E-17 21 6.75E-16 6.89E-17

22 7.44E-16 1.06E-16 10 6.06E-16 1.28E-17 11 5.04E-16 1.79E-18 12 6.95E-16 1.25E-17 13 5.13E-16 2.85E-17 14 7.48E-16 3.54E-17 15 6.83E-16 8.76E-17 16 4.86E-16 4.34E-18 17 7.19E-16 8.96E-18 18 6.47E-16 7.93E-17 19 7.74E-16 1.38E-16 20 7.94E-16 7.86E-17 21 7.10E-16 1.91E-18 22 5.16E-16 1.33E-17 23 8.07E-16 4.11E-17 Average 1.4010e-16 6.9234e-16 Standard Deviation 9.0565e-17 1.0192e-16 Force 0.0020 0.0021

Object in the trap Index �� RUN NO. 3 1 3.33E-16 1.33E-16 2 7.42E-16 1.79E-16 3 6.70E-16 1.76E-16 4 5.87E-16 1.67E-16 5 7.09E-16 1.61E-16 6 7.81E-16 1.90E-16 �� polysteren bead 7 6.91E-16 1.88E-16 8 3.63E-16 1.84E-16 Average 2.0530e-16 6.0940e-16 Standard 2.4801e-17 1.7117e-16 Deviation Force 9.4982e-04 0.0028

Object in the trap Index �� RUN NO. 4 1 3.48E-16 6.55E-17 2 2.17E-16 1.80E-16 3 2.40E-16 2.26E-16 4 7.01E-16 1.93E-16 5 7.87E-16 1.41E-16 6 7.80E-16 2.15E-16 7 7.23E-16 8.77E-17 �� polysteren bead 8 7.48E-16 1.12E-16 9 7.87E-16 6.88E-17 10 7.74E-16 1.32E-16 Average 1.9896e-16 6.1043e-16 Standard 4.1945e-17 2.4012e-16 Deviation Force 0.0013 0.0034

Object in the trap Index �� RUN NO. 5 1 5.04E-16 1.79E-18 2 6.95E-16 1.25E-17 3 5.13E-16 2.85E-17 4 7.48E-16 3.54E-17 5 6.83E-16 8.76E-17 6 4.86E-16 4.34E-18 7 7.19E-16 8.96E-18 8 6.47E-16 7.93E-17 �� polysteren 9 7.74E-16 1.38E-16 bead 10 7.94E-16 7.86E-17 11 7.10E-16 1.91E-18 12 5.16E-16 1.33E-17 13 8.07E-16 4.11E-17 14 7.83E-16 4.18E-17 15 7.78E-16 2.87E-17 16 7.60E-16 1.48E-17 67

17 8.19E-16 2.25E-17 18 7.23E-16 2.14E-17 19 6.93E-16 1.05E-16 20 7.48E-16 7.72E-17 21 6.75E-16 6.89E-17 22 7.44E-16 1.06E-16 10 6.06E-16 1.28E-17 11 5.04E-16 1.79E-18 12 6.95E-16 1.25E-17 13 5.13E-16 2.85E-17 14 7.48E-16 3.54E-17 15 6.83E-16 8.76E-17 16 4.86E-16 4.34E-18 17 7.19E-16 8.96E-18 18 6.47E-16 7.93E-17 19 7.74E-16 1.38E-16 20 7.94E-16 7.86E-17 Average 1.5762e-16 5.3639e-16 Standard 5.3156e-17 1.6293e-16 Deviation Force 0.0015 0.0028

Table 1 - Data of the 5 runs for 2m beads at trap following the STD, Average and Force

CHAPTER IX

CONCLUSION

9.1 Conclusion and Future Work

Based on the chapter I the objective and motivation of this research is to find a

method to accurately measure the mechanical properties of the cilium. Measuring the

mechanical properties of the cilium is significant for the cure of growing list of the

diseases such as Polycystic kidney disease (PKD) and Bronchiectasis. The method

developed in our research suggests to accurately and precisely analyze the

experimental data to study the primary behavior of the cilium in the direct optical

trap. The resonant frequency from the trap was calculated around 50 Hz that enables

to find the mechanical properties of the cilium by resonant excitation. The potential

future research could be applying the same model to the motile cilia.

REFERENCES

[1] I. Veland, A. Awan, and L. Pedersen, “Primary cilia and signaling pathways in

mammalian development, health and disease,” Nephron …, 2009.

[2] A. Resnick, “Chronic fluid flow is an environmental modifier of renal epithelial

function,” PLoS One, 2011.

[3] F. Herzog, “A mechanical approach to study the bending of the primary cilium in

response to fluid flow,” 2010.

[4] A. Resnick, “Mechanical Properties of a Primary Cilium As Measured by

Resonant Oscillation,” Biophys. J., 2015.

[5] R. Quinlan, J. Tobin, and P. Beales, “Modeling ciliopathies: Primary cilia in

development and disease,” Curr. Top. Dev. Biol., 2008.

[6] M. R. Mahjoub, “The importance of a single primary cilium,” Organogenesis, vol.

9, no. 2, pp. 61–69, Oct. 2014.

[7] C. Battle and C. Ott, “Intracellular and extracellular forces drive primary cilia

movement,” Proc. …, 2015.

[8] J. C. Maxwell, A Treatise on Electricity and Magnetism, Volume 1. Clarendon

Press, 1881.

[9] K. Svoboda and S. Block, “Biological applications of optical forces,” Annu. Rev.

Biophys. …, 1994.

[10] P. Lebedew, “Untersuchungen über die Druckkräfte des Lichtes,” Ann. Phys.,

1901.

[11] E. Nichols and G. Hull, “A preliminary communication on the pressure of heat and

light radiation,” Phys. Rev. (Series I), 1901.

[12] A. Ashkin, “History of optical trapping and manipulation of small-neutral particle,

atoms, and molecules,” Sel. Top. Quantum Electron. IEEE …, 2000.

[13] M. Wördemann, Structured Light Fields. Berlin, Heidelberg: Springer Berlin

Heidelberg, 2012.

[14] M. Padgett and L. Allen, “Optical Tweezers And Spanners,” Physics World. 31-

Aug-1997.

[15] S. Block, “Making light work with optical tweezers.,” Nature, 1992.

[16] A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and

bacteria,” Science (80-. )., 1987.

[17] A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of single living

cells using infra-red laser beams,” Berichte der Bunsengesellschaft für …, 1989.

[18] A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys.

Rev. Lett., 1970.

[19] A. Ashkin and J. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys.

Lett., 1971.

[20] J. Liesener, M. Reicherter, T. Haist, and H. Tiziani, “Multi-functional optical

tweezers using computer-generated holograms,” Opt. Commun., 2000.

[21] J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,”

Opt. Commun., vol. 207, no. 1–6, pp. 169–175, Jun. 2002.

[22] L. Lin, G. Hong-Lian, H. Lu, and E. Qu, “The measurement of displacement and

optical force in multi-optical tweezers,” Chinese Phys. …, 2012.

[23] J. Yin, Y. Zhu, W. Wang, Y. Wang, and W. Jhe, “Optical potential for atom

guidance in a dark hollow laser beam,” JOSA B, 1998.

[24] A. O’Neil and M. Padgett, “Axial and lateral trapping efficiency of Laguerre–

Gaussian modes in inverted optical tweezers,” Opt. Commun., 2001.

[25] Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt.

Express, 2004.

[26] S. Smith and S. Bhalotra, “Inexpensive optical tweezers for undergraduate

laboratories,” Am. J. …, 1999.

[27] S. Seeger, S. Monajembashi, and K. Hutter, “Application of laser optical tweezers

in immunology and molecular genetics,” Cytometry, 1991.

[28] “Photonics Breakthrough for Silicon Chips - IEEE Spectrum.” [Online]. Available:

http://spectrum.ieee.org/semiconductors/devices/photonics-breakthrough-for-

silicon-chips/0. [Accessed: 31-Oct-2015].

[29] A. Ashkin, K. Schütze, and J. Dziedzic, “Force generation of organelle transport

measured in vivo by an infrared laser trap,” 1990.

[30] S. Block, D. Blair, and H. Berg, “Compliance of bacterial flagella measured with

optical tweezers,” 1989.

[31] J. Ando, G. Bautista, and N. Smith, “Optical trapping and surgery of living yeast

cells using a single laser,” Rev. Sci. …, 2008.

[32] M. Dao, C. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed

by optical tweezers,” J. Mech. Phys. Solids, 2003.

[33] A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,”

Proc. Natl. Acad. Sci., vol. 94, no. 10, pp. 4853–4860, May 1997.

[34] T. Ketelaar, N. de Ruijter, and S. Niehren, “Optical trapping in plant cells,” Plant

Cell Morphog., 2014.

[35] T. C. Vogelmann, “Plant Tissue Optics,” Annu. Rev. Plant Physiol. Plant Mol.

Biol., vol. 44, no. 1, pp. 231–251, Jun. 1993.

[36] T. Perkins, D. Smith, and S. Chu, “Relaxation of a single DNA molecule observed

by optical microscopy,” Science (80-. )., 1994.

[37] I. Heller, T. Hoekstra, and G. King, “Optical tweezers analysis of DNA–protein

complexes,” Chem. …, 2014.

[38] X. Bao, H. Lee, and S. Quake, “Behavior of complex knots in single DNA

molecules,” Phys. Rev. Lett., 2003.

[39] G. Shivashankar and A. Libchaber, “Single DNA molecule grafting and

manipulation using a combined atomic force microscope and an optical tweezer,”

Appl. Phys. Lett., 1997.

[40] R. Dickinson, “A generalized transport model for biased cell migration in an

anisotropic environment,” J. Math. Biol., 2000.

[41] H. Guo, Q. Cao, D. Ren, G. Liu, and J. Duan, “Measurements of leucocyte

membrane elasticity based on the optical tweezers,” Chinese Sci. …, 2003.

[42] M. Hamblin and P. Avci, Applications of Nanoscience in Photomedicine. 2015.

[43] Y. Sun and B. Nelson, “Biological cell injection using an autonomous

microrobotic system,” Int. J. Rob. Res., 2002.

[44] Y. Xie, D. Sun, and C. Liu, “A force control approach to a robot-assisted cell

microinjection system,” Int. J. …, 2010.

[45] S. Ralis, “Micropositioning of a weakly calibrated microassembly system using

coarse-to-fine visual servoing strategies,” … , IEEE Trans., 2000.

[46] M. Rakotondrabe and I. Ivan, “Development and force/position control of a new

hybrid thermo-piezoelectric microgripper dedicated to micromanipulation tasks,”

Autom. Sci. …, 2011.

[47] M. Xie, J. Mills, and X. Li, “Modelling and control of optical manipulation for cell

rotation,” Robot. Autom. ( …, 2015.

[48] F. Difato, E. Marconi, and A. Maccione, “Combining Optical Tweezers, Laser

Microdissectors and Multichannel Electrophysiology for the Non-Invasive Tracing

and Manipulation of Neural Activity,” Biophys. …, 2010.

[49] K. Neuman and A. Nagy, “Single-molecule force spectroscopy: optical tweezers,

magnetic tweezers and atomic force microscopy,” Nat. Methods, 2008.

[50] M. Rocha, “Optical tweezers for undergraduates: theoretical analysis and

experiments,” Am. J. Phys., 2009.

[51] M. Lee and M. Padgett, “Optical tweezers: a light touch,” J. Microsc., 2012.

[52] T. Nieminen and N. du Preez-Wilkinson, “Optical tweezers: Theory and

modelling,” J. Quant. …, 2014.

[53] J. E. Molloy and M. J. Padgett, “Lights, action: Optical tweezers,” Contemp. Phys.,

vol. 43, no. 4, pp. 241–258, Nov. 2010.

[54] D. Bonessi, K. Bonin, and T. Walker, “Optical forces on particles of arbitrary

shape and size,” J. Opt. A Pure …, 2007.

[55] P. C. D. Hobbs, Building Electro-Optical Systems: Making It all Work. John Wiley

& Sons, 2011.

[56] T. Li, Fundamental Tests of Physics with Optically Trapped Microspheres, vol. 2.

Springer Science & Business Media, 2012.

[57] A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in

the ray optics regime,” Biophys. J., 1992.

[58] K. C. Neuman and S. M. Block, “Optical trapping.,” Rev. Sci. Instrum., vol. 75, no.

9, pp. 2787–809, Sep. 2004.

[59] C. DOBELL, “ANTONY VAN LEEUWENHOEK AND HIS‘ LITTLE

ANIMALS.’.,” Am. J. Med. Sci., 1933.

[60] O. Müller and O. Fabricius, “Animalcula infusoria fluviatilia et marina, quae

detexit, systematice descripsit et ad vivum delineari curavit Otho Fridericus

Müller: Sistit opus hoc,” 1786.

[61] F. Dujardin, “Histoire naturelle des Zoophytes-Infusoires. 684 pp,” 1841.

[62] R. Bloodgood, “From central to rudimentary to primary: the history of an

underappreciated organelle whose time has come. The primary cilium,” Methods

Cell Biol., 2009.

[63] K. Zimmermann, “Beiträge zur Kenntniss einiger Drüsen und Epithelien,” Arch.

für mikroskopische Anat., 1898.

[64] D. WHEATLEY, “Expression of primary cilia in mammalian cells,” Cell Biol. …,

1996.

[65] D. Hoey, M. Downs, and C. Jacobs, “The mechanics of the primary cilium: an

intricate structure with complex function,” J. Biomech., 2012.

[66] C. Ethier and C. Simmons, Introductory biomechanics: from cells to organisms.

2007.

[67] I. Ibañez-Tallon, N. Heintz, and H. Omran, “To beat or not to beat: roles of cilia in

development and disease,” Hum. Mol. Genet., 2003.

[68] B. Alberts, A. Johnson, J. Lewis, and M. Raff, “Molecular Biology of the Cell

(Garland Science, New York, 2002),” There is no Corresp. …, 1997.

[69] M. Porter and W. Sale, “The 9+ 2 axoneme anchors multiple inner arm dyneins

and a network of kinases and phosphatases that control motility,” J. Cell Biol.,

2000.

[70] S. Christensen, L. Pedersen, L. Schneider, and P. Satir, “Sensory cilia and

integration of signal transduction in human health and disease,” Traffic, 2007.

[71] J. Davenport and B. Yoder, “An incredible decade for the primary cilium: a look at

a once-forgotten organelle,” Am. J. Physiol. …, 2005.

[72] M. Ascenzi, M. Lenox, and C. Farnum, “Analysis of the orientation of primary

cilia in growth plate cartilage: a mathematical method based on multiphoton

microscopical images,” J. Struct. Biol., 2007.

[73] J. R. (Joost) Broekhuis and E. M. U. M. C. Rotterdam, “Ciliary Length Control,”

Dec. 2012.

[74] H. Praetorius and K. Spring, “Bending the MDCK cell primary cilium increases

intracellular calcium,” J. Membr. Biol., 2001.

[75] G. Pazour and G. Witman, “The vertebrate primary cilium is a sensory organelle,”

Curr. Opin. Cell Biol., 2003.

[76] C. Anderson and A. Castillo, “Primary cilia: cellular sensors for the skeleton,”

Anat. …, 2008.

[77] S. Nonaka, Y. Tanaka, Y. Okada, and S. Takeda, “Randomization of left–right

asymmetry due to loss of nodal cilia generating leftward flow of extraembryonic

fluid in mice lacking KIF3B motor protein,” Cell, 1998.

[78] S. Kim and B. Dynlacht, “Assembling a primary cilium,” Curr. Opin. Cell Biol.,

2013.

[79] V. Singla and J. Reiter, “The primary cilium as the cell’s antenna: signaling at a

sensory organelle,” Science (80-. )., 2006.

[80] O. Vieira and K. Gaus, “FAPP2, cilium formation, and compartmentalization of

the apical membrane in polarized Madin–Darby canine kidney (MDCK) cells,”

Proc. …, 2006.

[81] R. Rohatgi, L. Milenkovic, and M. Scott, “Patched1 regulates hedgehog signaling

at the primary cilium,” Science (80-. )., 2007.

[82] L. Schneider, C. Clement, and S. Teilmann, “PDGFRαα signaling is regulated

through the primary cilium in fibroblasts,” Curr. Biol., 2005.

[83] M. Händel, S. Schulz, A. Stanarius, M. Schreff, M. Erdtmann-Vourliotis, H.

Schmidt, G. Wolf, and V. Höllt, “Selective targeting of somatostatin receptor 3 to

neuronal cilia,” M. Händel, S. Schulz, A. Stanarius, M. Schreff, M. Erdtmann-

Vourliotis, H. Schmidt, G. Wolf, V. Höllt. 1999. Sel. Target. Somatostat. Recept. 3

to neuronal cilia. Neurosci. 89 909-926., vol. 3, no. 89, pp. 909–926, 1999.

[84] S. Sorokin, “Reconstructions of centriole formation and ciliogenesis in mammalian

lungs,” J. Cell Sci., 1968.

[85] H. Latta, A. Maunsbach, and S. Madden, “Cilia in different segments of the rat

nephron,” J. Biophys. …, 1961.

[86] S. Sorokin, “Centrioles and the formation of rudimentary cilia by fibroblasts and

smooth muscle cells,” J. Cell Biol., 1962.

[87] J. Baudoin, L. Viou, P. Launay, and C. Luccardini, “Tangentially migrating

neurons assemble a primary cilium that promotes their reorientation to the cortical

plate,” Neuron, 2012.

[88] F. Boselli, J. Goetz, G. Charvin, and J. Vermot, “A quantitative approach to study

endothelial cilia bending stiffness during blood flow mechanodetection in vivo,”

Methods Cell Biol., 2015.

[89] S. Ansley, J. Badano, O. Blacque, and J. Hill, “Basal body dysfunction is a likely

cause of pleiotropic Bardet–Biedl syndrome,” Nature, 2003.

[90] A. Waters and P. Beales, “Ciliopathies: an expanding disease spectrum,” Pediatr.

Nephrol., 2011.

[91] K. Miyoshi and K. Kasahara, “Factors that influence primary cilium length,” Acta

Med …, 2011.

[92] L. Onuchic, L. Furu, and Y. Nagasawa, “PKHD1, the polycystic kidney and

hepatic disease 1 gene, encodes a novel large protein containing multiple

immunoglobulin-like plexin-transcription–factor,” Am. J. …, 2002.

[93] F. Hildebrandt and W. Zhou, “Nephronophthisis-associated ciliopathies,” J. Am.

Soc. …, 2007.

[94] H. Praetorius and K. Spring, “Removal of the MDCK cell primary cilium

abolishes flow sensing,” J. Membr. Biol., 2003.

[95] S. Nauli, F. Alenghat, Y. Luo, and E. Williams, “Polycystins 1 and 2 mediate

mechanosensation in the primary cilium of kidney cells,” Nat. …, 2003.

[96] A. Masyuk, T. Masyuk, and P. Splinter, “Cholangiocyte cilia detect changes in

luminal fluid flow and transmit them into intracellular Ca 2+ and cAMP

signaling,” Gastroenterology, 2006.

[97] A. Resnick and U. Hopfer, “Force-response considerations in ciliary

mechanosensation,” Biophys. J., 2007.

[98] K. Gardner, S. P. Arnoczky, and M. Lavagnino, “Effect of in vitro stress-

deprivation and cyclic loading on the length of tendon cell cilia in situ.,” J. Orthop.

Res., vol. 29, no. 4, pp. 582–7, May 2011.

[99] E. Schwartz and M. Leonard, “Analysis and modeling of the primary cilium

bending response to fluid shear,” Am. J. …, 1997.

[100] W. Liu and N. Murcia, “Mechanoregulation of intracellular Ca2+ concentration is

attenuated in collecting duct of monocilium-impaired orpk mice,” Am. J. …, 2005.

[101] S. Rydholm and G. Zwartz, “Mechanical properties of primary cilia regulate the

response to fluid flow,” Am. J. …, 2010.

[102] Y. Young, M. Downs, and C. Jacobs, “Dynamics of the primary cilium in shear

flow,” Biophys. J., 2012.

[103] M. Downs and A. Nguyen, “An experimental and computational analysis of

primary cilia deflection under fluid flow,” Comput. methods …, 2014.

[104] F. Ignatovich and L. Novotny, “Experimental study of nanoparticle detection by

optical gradient forces,” Rev. Sci. Instrum., 2003.

[105] T. Grzegorczyk, B. Kemp, and J. Kong, “Passive guiding and sorting of small

particles with optical binding forces,” Opt. Lett., 2006.

[106] C. Lant and A. Resnick, “Multi-function light microscopy module for the

International Space Station,” Sp. Technol. Appl. …, 2000.

[107] J. Glaser, D. Hoeprich, and A. Resnick, “Near real-time measurement of forces

applied by an optical trap to a rigid cylindrical object,” Opt. …, 2014.

[108] G. Pesce, G. Volpe, O. Maragó, and P. Jones, “Step-by-step guide to the

realization of advanced optical tweezers,” JOSA B, 2015.

[109] C. Poole, Z. ZHANG, and J. Ross, “The differential distribution of acetylated and

detyrosinated alpha-tubulin in the microtubular cytoskeleton and primary cilia of

hyaline cartilage chondrocytes,” J. Anat., 2001.

[110] Neuman, K. C., Chadd, E. H., Liou, G. F., Bergman, K., & Block, S. M. (1999).

Characterization of photodamage to Escherichia coli in optical traps. Biophysical

journal, 77(5), 2856-2863.

APPENDIX

APPENDIX A

PRIMARY CILIA AS A CLASSIC CANTILEVER BEAM

Basics of the Beam Deflection

The behavior of the beam can be showed by the Hooke’s law: � = �� where � is a � normal stress and � is the strain and and is the modulus of the elasticity or Young’s modulus. Stretching elastic beam is one direction and is accompanied by a compression in the perpendicular directions, which is known as Poisson’s ratio. It is possible to eliminate this effect when the length of the beam is larger than the cross section area.

�� = and �� = �� = ��

where M is the bending moment and � = is the curvature at any point, I is the moment of inertia of the beam cross section. Based on the Euler–Bernoulli law bending moment (M) is proportional to the alteration in the curvature produced by the action of the load which can be written as:

1 �� = = ��

where r is the radius of the curvature, E is the modulus of the elasticity and I is the

moment of inertia.

Euler Bernoulli is the relationship between the deflection of the beam and the force that

applied on it.

� �� = � ��

where q is the applied force to the beam. When the axial loading is not affected

the load above equation can be written as:

�� = �(�) ��

this equation is the description of the uniform, static beam.

� is the deflection be getting the derivations from it:

is the slope and � = −��( ) is the bending moment and – �� = � is

the shear force.

The boundary conditions at the fixed and free end can be describe as:

� = 0 �� = 0 (at fixed end)

�� = 0 (at free end)

Primary Cilium model as a cantilever Beam:

Primary cilium considered as an elastic thin, uniform cantilever beam with a cylinder cross section. Due to the reason that cilia is slender which means the ratio of the length to the diameter is large therefore it is feasible to model the cilium as a 1D homogenous uniform beam. The Euler Bernoulli equation for the pure bending is:

�� + � = � ��

where f is the applied force and � is the mass/unit length of the beam and EI is the mechanics of the primary cilium known as flexural rigidity having the unit of force*area

(f *a). The moment of inertia of the cilium is the same as cylinder with circular area:

� = �� = �� and we consider the polar coordinates and � = ��

�� = �� sin � �� = R 4

Regarding to find the natural frequency of the beam fore equals to zero (f = 0) therefore, the normal solution is to use the separation method � �, � = �(�)�(�) resulting to:

�� − = 0 � ��

the solution is:

� � = � cos �� + � sin �� + � cosh(��) + � cosh(��)

� � = � cos(��) + � sin(��)

where the oscillation frequency � related to the � by � = � . For the cantilever the slope and displacement are zero at the fixed end, while at the free end the moment and shear are zero by considering the foundry conditions:

At S = 0 At S = L

s = 0 (No movement) = 0 (Bending Moment = 0 )

= 0 (No Deflection) = 0 (Shear = 0)

Table 2- Boundary Conditions of the Beam

Based on the Boundary conditions � 0 = 0 , � 0 = 0, � 0 = 0 , � 0 = 0

� � = � sin �� + � cos �� + � sinh �� + � cosh ��

� � = � �sin �� + �� cos �� + � � sinh �� + �� cosh ��

� � = − �� sin �� + �� cos �� + � � sinh �� + �� cosh ��

0 1 0 1 � 1 0 1 0 � = 0 − sin �� − cos(��) sinh �� sinh(��) � − cos(��) sin(��) cosh(��) cosh(��) �

Determinant from the above matrix results to:

1 + cos(��) cosh(��) = 0

It proves that � = − � , and � and � results to : cos �� cosh �� = −1

which the roots are, � � = The time equation breaks down to

�� = � sin � � + � cos � � � �

So, the frequency in radian per seconds calculates as:

� �� = � �

By dividing the equation to 2� the frequency in Hz calculated:

� � �� = = 2� 2� � �

The frequency in the vacuum can be written as:

3.51 �� = = 3.51 � � �� and the frequency under the viscous effect can be considered as a virtual ass that affects on the cantilever beam. The resonant frequency relationship in both vacuum and viscous effect can be written as: [79]

�� = 3.51 � �� 1 + Γ � �� where Γ � is a hydrodynamic function for a cylinder:

−� �� 4� Γ � = −4�[ � ≈ − � �� −� �� ln −� ��

The approximation is at the limit of �� → 0.

Figure 28- Primary cilium modeled as a classical cantilevered

Primary Cilium as a cantilever beam with rotatory spring model:

As mentioned in the previous section the free vibration can be describes as:

�� + � = 0 ��

Cantilever beam moment of inertia is � = = where a is the radius and d is the diameter. The boundary conditions at this case is equals to:

�� = 0 At x= 0 è �� = −�( )

�� = 0 At x=L è �� = 0

In this case in:

�� − �� = �, � = , Therefore, the slop: � = �� = � = and the deformation can be calculated as:

� = , Therefore, the whole deformation is: +

L L

k k

Figure 29- Primary cilium modeled as a cantilevered beam with rotatory spring

APPENDIX B

TRAP STIFFNESS DATA ACQUIRED FROM QPD (Kx and Ky)

Table 2 is the demonstration of the time domain data that acquired from the QPD and analyzed in chapter 9. The number of the gathered data was large therefore, only the first

160 of them are shown here.

Test Object Index �� 1 -1.35E-01 -2.34E-03 1.00E+00 2 -1.36E-01 -2.33E-03 2.00E+00 3 -1.35E-01 -1.12E-03 3.00E+00 4 -1.35E-01 -3.55E-03 4.00E+00 5 -1.37E-01 -1.11E-03 5.00E+00 6 -1.37E-01 -1.12E-03 6.00E+00 7 -1.38E-01 -3.55E-03 7.00E+00 8 -1.34E-01 -2.33E-03 8.00E+00 Primary Cilium 9 -1.37E-01 -2.34E-03 9.00E+00 10 -1.36E-01 -2.33E-03 1.00E+01 11 -1.36E-01 -2.34E-03 1.10E+01 12 -1.39E-01 -2.34E-03 1.20E+01 13 -1.34E-01 -1.12E-03 1.30E+01 14 -1.36E-01 -2.34E-03 1.40E+01 15 -1.37E-01 -1.12E-03 1.50E+01 16 -1.37E-01 -1.12E-03 1.60E+01

17 -1.37E-01 -3.56E-03 1.70E+01 18 -1.37E-01 -3.56E-03 1.80E+01 19 -1.35E-01 -4.78E-03 1.90E+01 20 -1.37E-01 -1.12E-03 2.00E+01 21 -1.36E-01 -3.57E-03 2.10E+01 22 -1.36E-01 -3.58E-03 2.20E+01 23 -1.37E-01 -2.34E-03 2.30E+01 24 -1.35E-01 -2.35E-03 2.40E+01 25 -1.36E-01 -2.35E-03 2.50E+01 26 -1.35E-01 -3.58E-03 2.60E+01 27 -1.35E-01 -2.35E-03 2.70E+01

Test Object Index Kfit Kx Ky 28 -1.36E-01 -3.58E-03 2.80E+01 29 -1.36E-01 -2.35E-03 2.90E+01 30 -1.36E-01 -3.58E-03 3.00E+01 31 -1.35E-01 -3.58E-03 3.10E+01 32 -1.34E-01 -2.35E-03 3.20E+01 33 -1.35E-01 -3.58E-03 3.30E+01 34 -1.35E-01 -1.13E-03 3.40E+01 35 -1.37E-01 -3.58E-03 3.50E+01 36 -1.35E-01 -4.81E-03 3.60E+01 Primary Cilium 37 -1.33E-01 -3.59E-03 3.70E+01 38 -1.36E-01 -6.06E-03 3.80E+01 39 -1.33E-01 -1.13E-03 3.90E+01 40 -1.33E-01 -4.83E-03 4.00E+01 41 -1.37E-01 -3.59E-03 4.10E+01 42 -1.33E-01 -3.59E-03 4.20E+01 43 -1.36E-01 -8.54E-03 4.30E+01 44 -1.33E-01 -3.60E-03 4.40E+01 45 -1.34E-01 -4.83E-03 4.50E+01 46 -1.32E-01 -6.07E-03 4.60E+01

47 -1.33E-01 -7.31E-03 4.70E+01 48 -1.33E-01 -3.60E-03 4.80E+01 49 -1.33E-01 -6.07E-03 4.90E+01 50 -1.33E-01 -6.09E-03 5.00E+01 51 -1.31E-01 -7.32E-03 5.10E+01 52 -1.33E-01 -7.33E-03 5.20E+01 53 -1.30E-01 -7.34E-03 5.30E+01 54 -1.33E-01 -8.57E-03 5.40E+01 55 -1.31E-01 -7.34E-03 5.50E+01 56 -1.30E-01 -7.35E-03 5.60E+01 57 -1.32E-01 -7.35E-03 5.70E+01

Test Object Index � � � 58 -1.32E-01 -8.59E-03 5.90E+01 59 -1.29E-01 -7.37E-03 6.00E+01 60 -1.31E-01 -9.85E-03 6.10E+01 61 -1.32E-01 -7.36E-03 6.20E+01 62 -1.29E-01 -9.86E-03 6.30E+01 63 -1.31E-01 -9.87E-03 6.40E+01 64 -1.30E-01 -9.87E-03 6.50E+01 65 -1.29E-01 -8.64E-03 6.60E+01 66 -1.31E-01 -9.86E-03 6.70E+01 Primary Cilium 67 -1.30E-01 -9.90E-03 6.80E+01 68 -1.30E-01 -9.90E-03 6.90E+01 69 -1.28E-01 -9.91E-03 7.00E+01 70 -1.28E-01 -1.12E-02 7.10E+01 71 -1.28E-01 -1.12E-02 7.20E+01 72 -1.28E-01 -1.12E-02 7.30E+01 73 -1.28E-01 -1.12E-02 7.40E+01 74 -1.27E-01 -1.12E-02 7.50E+01 75 -1.27E-01 -1.24E-02 7.60E+01 76 -1.27E-01 -1.24E-02 7.70E+01

77 -1.26E-01 -1.25E-02 7.80E+01 78 -1.27E-01 -1.37E-02 7.90E+01 79 -1.26E-01 -1.38E-02 8.00E+01 80 -1.25E-01 -1.25E-02 8.10E+01 81 -1.26E-01 -1.50E-02 8.10E+01 82 -1.26E-01 -1.25E-02 8.20E+01 83 -1.26E-01 -1.50E-02 8.30E+01 84 -1.24E-01 -1.50E-02 8.40E+01 85 -1.25E-01 -1.51E-02 8.50E+01 86 -1.24E-01 -1.38E-02 8.60E+01 87 -1.23E-01 -1.76E-02 8.70E+01

Test Object Index �� 88 -1.24E-01 -1.64E-02 8.80E+01 89 -1.23E-01 -1.51E-02 8.90E+01 90 -1.22E-01 -1.76E-02 9.00E+01 91 -1.24E-01 -1.63E-02 9.10E+01 92 -1.23E-01 -1.64E-02 9.20E+01 93 -1.24E-01 -1.51E-02 9.30E+01 94 -1.24E-01 -1.64E-02 9.40E+01 95 -1.22E-01 -1.89E-02 9.50E+01 Primary Cilium 96 -1.22E-01 -1.76E-02 9.60E+01 97 -1.23E-01 -1.64E-02 9.70E+01 98 -1.22E-01 -1.77E-02 9.80E+01 99 -1.22E-01 -1.77E-02 9.90E+01 100 -1.22E-01 -1.77E-02 1.00E+02 101 -1.20E-01 -1.89E-02 1.01E+02 102 -1.22E-01 -1.77E-02 1.02E+02 103 -1.22E-01 -1.78E-02 1.03E+02 104 -1.22E-01 -1.90E-02 1.04E+02 105 -1.19E-01 -1.77E-02 1.05E+02

106 -1.20E-01 -1.90E-02 1.06E+02 107 -1.20E-01 -1.77E-02 1.07E+02 108 -1.21E-01 -1.90E-02 1.08E+02 109 -1.21E-01 -1.90E-02 1.09E+02 110 -1.21E-01 -1.90E-02 1.10E+02 111 -1.18E-01 -1.77E-02 1.11E+02 112 -1.20E-01 -2.03E-02 1.12E+02 113 -1.18E-01 -1.90E-02 1.13E+02 114 -1.20E-01 -1.90E-02 1.14E+02 115 -1.21E-01 -2.03E-02 1.15E+02 116 -1.20E-01 -1.90E-02 1.16E+02 117 -1.22E-01 -1.90E-02 1.17E+02

Test Object Index �� 118 -1.20E-01 -1.78E-02 1.18E+02 119 -1.21E-01 -2.41E-02 1.19E+02 120 -1.20E-01 -2.03E-02 1.20E+02 121 -1.18E-01 -1.91E-02 1.21E+02 122 -1.21E-01 -2.16E-02 1.22E+02 123 -1.20E-01 -2.03E-02 1.23E+02 124 -1.21E-01 -2.16E-02 1.24E+02 Primary Cilium 125 -1.19E-01 -2.03E-02 1.25E+02 126 -1.19E-01 -1.91E-02 1.26E+02 127 -1.20E-01 -1.78E-02 1.27E+02 128 -1.21E-01 -1.90E-02 1.28E+02 129 -1.21E-01 -2.03E-02 1.29E+02 130 -1.20E-01 -2.04E-02 1.30E+02 131 -1.20E-01 -2.04E-02 1.31E+02 132 -1.19E-01 -2.03E-02 1.32E+02

133 -1.19E-01 -2.03E-02 1.33E+02 134 -1.20E-01 -2.16E-02 1.34E+02 135 -1.20E-01 -1.91E-02 1.35E+02 136 -1.20E-01 -2.16E-02 1.36E+02 137 -1.19E-01 -1.91E-02 1.37E+02 138 -1.21E-01 -2.03E-02 1.38E+02 139 -1.20E-01 -2.03E-02 1.39E+02 140 -1.20E-01 -1.90E-02 1.40E+02 141 -1.21E-01 -2.03E-02 1.41E+02 142 -1.21E-01 -2.03E-02 1.42E+02 118 -1.20E-01 -1.78E-02 1.18E+02 119 -1.21E-01 -2.41E-02 1.19E+02 120 -1.20E-01 -2.03E-02 1.20E+02 121 -1.18E-01 -1.91E-02 1.21E+02 122 -1.21E-01 -2.16E-02 1.22E+02

Test Object Index Kfit Kx Ky 123 -1.20E-01 -2.03E-02 1.23E+02 124 -1.21E-01 -2.16E-02 1.24E+02 125 -1.19E-01 -2.03E-02 1.25E+02 126 -1.19E-01 -1.91E-02 1.26E+02 127 -1.20E-01 -1.78E-02 1.27E+02 128 -1.21E-01 -1.90E-02 1.28E+02 Primary Cilium 129 -1.21E-01 -2.03E-02 1.29E+02 130 -1.20E-01 -2.04E-02 1.30E+02 131 -1.20E-01 -2.04E-02 1.31E+02 132 -1.19E-01 -2.03E-02 1.32E+02 133 -1.19E-01 -2.03E-02 1.33E+02 134 -1.20E-01 -2.16E-02 1.34E+02 135 -1.20E-01 -1.91E-02 1.35E+02 136 -1.20E-01 -2.16E-02 1.36E+02

137 -1.19E-01 -1.91E-02 1.37E+02 138 -1.21E-01 -2.03E-02 1.38E+02 139 -1.20E-01 -2.03E-02 1.39E+02 140 -1.20E-01 -1.90E-02 1.40E+02 141 -1.21E-01 -2.03E-02 1.41E+02 142 -1.21E-01 -2.03E-02 1.42E+02 123 -1.20E-01 -2.03E-02 1.23E+02 124 -1.21E-01 -2.16E-02 1.24E+02 125 -1.19E-01 -2.03E-02 1.25E+02 126 -1.19E-01 -1.91E-02 1.26E+02 127 -1.20E-01 -1.78E-02 1.27E+02 128 -1.21E-01 -1.90E-02 1.28E+02 129 -1.21E-01 -2.03E-02 1.29E+02 130 -1.20E-01 -2.04E-02 1.30E+02 131 -1.20E-01 -2.04E-02 1.31E+02 132 -1.19E-01 -2.03E-02 1.32E+02

Test Object Index �� 133 -1.19E-01 -2.03E-02 1.33E+02 134 -1.20E-01 -2.16E-02 1.34E+02 135 -1.20E-01 -1.91E-02 1.35E+02 136 -1.20E-01 -2.16E-02 1.36E+02 137 -1.19E-01 -1.91E-02 1.37E+02 138 -1.21E-01 -2.03E-02 1.38E+02 Primary Cilium 139 -1.20E-01 -2.03E-02 1.39E+02 140 -1.20E-01 -1.90E-02 1.40E+02 141 -1.21E-01 -2.03E-02 1.41E+02 142 -1.21E-01 -2.03E-02 1.42E+02 143 -1.21E-01 -2.03E-02 1.43E+02 144 -1.22E-01 -2.02E-02 1.44E+02 145 -1.20E-01 -2.15E-02 1.45E+02

100

146 -1.22E-01 -2.14E-02 1.46E+02 147 -1.23E-01 -2.02E-02 1.47E+02 148 -1.23E-01 -2.14E-02 1.48E+02 149 -1.24E-01 -2.02E-02 1.49E+02 150 -1.23E-01 -2.01E-02 1.50E+02 151 -1.23E-01 -2.14E-02 1.51E+02 152 -1.24E-01 -2.26E-02 1.52E+02 153 -1.21E-01 -1.88E-02 1.53E+02 154 -1.23E-01 -1.88E-02 1.54E+02 155 -1.23E-01 -2.13E-02 1.55E+02 156 -1.23E-01 -2.26E-02 1.56E+02 157 -1.23E-01 -2.13E-02 1.57E+02 158 -1.23E-01 -2.00E-02 1.58E+02 159 -1.25E-01 -2.13E-02 1.59E+02 160 -1.26E-01 -2.01E-02 1.60E+02 Table 3- Raw QPD acquired data

101

102