Mechanics and Dynamics of Living Mammalian by Satish Kumar Gupta Bachelor of Technology in Mechanical Engineering National Institute of Technology, Durgapur, 2014 Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering

at the Massachusetts Institute of Technology June 2017

2017 Massachusetts Institute of Technology. All rights reserved.

Signature of Author... Signature red.acredacted Department of Mechanical Engineering May 12, 2017

Certifiedby...... Signature redacted Ming Guo Professor of Mechanical Engineering -- A Thesis Supervisor Signature redacted A ccepted b y ...... ------14 - - Rohan Abeyaratne Chairman, Department Committee on Graduate Students

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JUN 2 12017

LIBRARIES ARCHIVES 2 Mechanics and Dynamics of Living Mammalian Cytoplasm by Satish Kumar Gupta Submitted to the Department of Mechanical Engineering

on May 1 2 th, 2017 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mechanical Engineering ABSTRACT Passive microrheology, a method of calculating the frequency dependent complex moduli of a viscoelastic material has been widely accepted for systems at thermal equilibrium. However, cytoplasm of a living operates far from equilibrium and thus, the applicability of passive microrheology in living cells is often questioned. Active microrheology methods have been successfully used to measure mechanics of living cells however, they involve complicated experimentation and are highly invasive as they rely on application of an external force. In the first part of this thesis, we propose a high throughput, non-invasive method of extracting the mechanics of the cytoplasm using the fluctuations of tracer particles. Using experimental and theoretical analysis, we demonstrate that the cytoplasm of a living mammalian cell behaves as an equilibrium material at short time scales. This allows us to extract high frequency mechanics of the cytoplasm using the generalized Stokes-Einstein relationship. The results obtained are in excellent agreement with our independent optical tweezer measurements in this equilibrium regime.

Studies often assume cytoplasm as an isotropic material. However, under various physiological processes such as migration, blood flow on endothelial cells, it can undergo morphological changes which can induce significant redistribution of the . Evidence of induced anisotropy for cells under mechanical stimuli exists however, the role of cytoskeletal restructuring on mechanical anisotropy remains unclear. Moreover, the effect of this restructuring on intracellular dynamics and forces remains elusive. In the second part of this thesis, we confine the cells in different aspect ratio and measure the mechanics of the cytoplasm using optical tweezers in both longitudinal and transverse directions to quantify the degree of mechanical anisotropy. These active microrheology measurements are later combined with independent intracellular motion measurements to calculate the intracellular force spectrum using Force Spectrum Microscopy (FSM); from which the degree of anisotropy in dynamics and forces are quantified.

Thesis Supervisor: Ming Guo Title: Assistant Professor of Mechanical Engineering

3 4 Acknowledgements

I owe a debt of gratitude to Ming Guo, my thesis advisor, for the encouragement and help extended by him during the entire course of the work. I found a friend, philosopher and guide in him. His scientific acumen, analytical mind and methodical supervision have enabled me to complete this work in the present shape.

The Department of Mechanical engineering at MIT is an extraordinary place to study and it gives me immense pleasure to express my deep sense of appreciation and gratitude to all the members. I cannot thank Leslie and Joan enough for all the support and care they have provided me over these two years and made me feel at home. During the years I have spent here I have had numerous enlightening discussions with faculty members and peers. In particular, the deliberations with Roger Kamm, Gareth McKinley, Alan Grodzinsky have been have been irreplaceable.

This dissertation is incomplete without acknowledging the valuable suggestions I received from JiLiang Hu, Yiwei Li and YuLong Han. Thank you for being excellent colleagues and friends. I would like to thank members of Weitz lab at Harvard University for all the help and suggestions they have provided me over the years. In particular, working with Jing Xia, Yinan Shen, Helen Wu has been a pleasant experience.

I thank my friends, both old and new for making my life a lot of fun and inspiring me to become the best version of myself.

I would also like to thank Steve Wasserman for his invaluable guidance and suggestions he has offered me through many stimulating discussions on uncountable occasions during the research.

Finally, I would like to thank my family, in particular, my parents, grandparents and sisters for their unconditional love and support.

5 6 Table of Contents

Title Page...... 1 Abstract...... 3 Acknowledgements...... 5 Table of contents...... 7 List of Figures...... 9 Citations to Previously published work...... 13 Chapter 1. Introduction...... 15 1.1 Introduction and Motivation...... 15 Chapter 2. Materials and Methods...... 17 2.1 Cell culture, microinjection, and pharmacological Interventions...... 17 2.1.1 Cell Culture...... 17 2.1.2 Microinjection...... 17 2.1.3 Phagocytosis...... 18 2.1.4. Pharmacological Interventions...... 18 2.2. Micro-contact printing...... 18 2.3. Intracellular particle tracking...... 19 2.4. Active microrheology using optical tweezers...... 19 2.5 Immunofluorescence, microscopy and image processing...... 20 Chapter 3. Equilibrium and non-equilibrium cell mechanics...... 21 3.1 Introduction...... 21 3.2 Results and Discussion...... 23 3.3. Conclusion...... 33 Chapter 4. Anisotropic Mechanics and Dynamics of Cytoplasm...... 35 4.1 Introduction...... 35 4.2 Results...... 37 4.2.1 Cell aspect ratio modifies cytoskeletal organization...... 37 4.2.2. Cell aspect ratio induces anisotropy in cytoplasmic mechanics...... 40 4.2.3. Cell aspect ratio regulates cell volume and nuclear volume...... 42 4.2.4 Cell aspect ratio regulates anisotropy in intracellular motion...... 43 4.2.5 alignment modulates anisotropy in intracellular motion...... 45 4.2.6 Cell aspect ratio regulates anisotropy in intracellular force...... 44 4.3 Discussion...... 49 Bibliography...... 53

7 8 List of Figures

Figure 3.1. (a). Bright-field image of a living A7 cell with injected beads. (Scale bar: 10 pm.) (b). Typical trajectories of a 500 nm PEG coated particle in untreated and ATP depleted A7 cells. (Scale bar: 0.2im.) ...... 25

Figure 3.2. Two-dimensional MSD (Ar 2 (r)) of 500 nm tracer particles plotted against lag time on logarithmic scale in untreated A7 cells (red circle), ATP depleted A7 cells (black diamond) and noise floor (gray triangle)...... 25

Figure 3.3. (a). Schematic diagram of optical tweezers used to measure cytoplasmic moduli. (Inset): Schematic illustration of the cytoplasmic environment that the probe bead experiences. (b). Cytoplasmic moduli measured by active microrheology using optical tweezers for untreated A7 cells (red circles) and ATP Depleted A7 cells (black squares)...... 27

Figure 3.4. (a) Cytoplasmic moduli measured by active microrheology using optical tweezers for different concentrations of PEG300. (b) Two-dimensional MSD (Ar2 (r)) of tracer particles plotted against lag time on logarithmic scale for different PEG concentrations. (c) The MSD data depicted in (b) is scaled with K2 for different concentrations of PEG where K.= 8.6382, 12.059 and 16.678 Papm for 0% PEG300, 3% w/w PEG300 and 6% w/w PEG300 respectively obtained by fitting to equation 4. All curves collapse at long time scales. (d) The MSD data depicted in (b) is scaled with K. for different concentrations of PEG300 where K. is same as that used in (c). All curves collapse at short time scales...... 3 1

Figure 3.5. Comparison of cytoplasmic moduli of A7 cells measured by active microrheology using optical tweezers and passive microrheology for cells under two conditions, (a) with 0% w/w PEG 300 and (b) with 6% w/w PEG 300. Both methods show an excellent agreement at high frequencies for both untreated and osmotically compressed cells suggesting an equilibrium regime at short time scales...... 32

9 Figure 4.1. Geometric control of cell aspect ratio. (A-D) Fluorescent images of mEFs cultured with different aspect ratios (P ~ 1, 3, 5,10 respectively) using micro-contact printing stained for (red), microtubules (green) and nucleus (blue) (Scale bar: 5 pm). (F-I) Representative trajectories of a 500 nm endocytosed polystyrene bead in cells with different aspect ratios (Scale bar: 0.2pm). Movement of beads inside cells becomes highly anisotropic with increase in cell aspect ratio. (E) Reference frame used in our study ...... 38

Figure 4.2. Quantification of cytoskeletal anisotropy. (A and B) Histogram of actin and orientation as a function of aspect ratio, P. Data at each point represents the fraction of actin or microtubules aligned at a particular angle. Cells with low aspect ratio has an isotropic distribution of filaments however alignment of fibers in higher aspect ratio cells are biased in a particular direction. (C) Illustration of cells with different aspect ratios showing alignment of fibers and other . For low aspect ratio cells the fibers are randomly distributed in all directions resulting in isotropic movement of beads and organelles. Higher aspect ratio cells have higher movement of tracer particles and organelles in the direction of the microtubule alignm ent...... 39

Figure 4.3. Active microrheology measurements of intracellular mechanics using optical tweezers. (A and B) 500 nm polystyrene beads are endocytosed into mEFs and are trapped and subjected to sinusoidally varying force F at frequency f. The frequency dependent complex intracellular spring constant, K is calculated by measuring the resultant displacement of bead x. Longitudinal and transverse intracellular spring constant as a function of frequency follows power-law rheology for all aspect ratio ranges (P = 1-1.5, 1.5-3, 3-7, 7-12). (C) The variation of cytoplasmic stiffness, K, with aspect ratio at 10 Hz. With increase in aspect ratio, higher intracellular stiffness is observed in the longitudinal direction than transverse direction. (D) The mechanical anisotropy with increase in aspect ratio in terms of ratio of intracellular stiffness in longitudinal and transverse direction. Cells are mechanically anisotropic for higher aspect ratio cells. Error bars represent standard deviation (n = 15 )...... 4 1

Figure 4.4. (A and B) Cell volume and nuclear volume of cells as a function of cell aspect ratio. Both cell and nuclear volume decreases with an increase in cell aspect ratio. (C) Cell volume tracks nuclear volume. Increase in cell volume linearly increases nuclear volume. Error bars represent standard deviation (n = 25)...... 40 10 Figure 4.5. Intracellular movement of 500 nm endocytosed particles. (A and B) MSD (Ax2 (r)), in longitudinal and transverse direction of tracer particles are plotted against lag time on a log-log scale for different aspect ratio cells. (C) The MSD of beads in longitudinal and transverse direction at -r=1 s . MSD is observed to increase in longitudinal and decrease in transverse direction with an increase in aspect ratio. (D) Anisotropy in intracellular movement calculated in terms of ratio of MSD in longitudinal direction and transverse direction at r = 1 s increases with increase in aspect ratio. Error bars represent standard error of mean (n = 15)...... 4 4

Figure 4.6. (A-D) Intracellular movement of 500nm endocytosed particles treated in blebbistatin and nocodazole treated cells. MSD (Ax 2(v)), in longitudinal and transverse direction of tracer particles are plotted against lag time on a log-log scale for blebbistatin (A and B respectively) and nocodazole treated (C and D respectively) for different aspect ratio cells. Similar trend with reduced magnitude for MSD in different directions with aspect ratio is observed for blebbistatin treated cells as observed for untreated cells. For nocodazole treated cells, the MSD curves collapse for different aspect ratio in both directions with similar magnitude suggesting anisotropy in intracellular movement can possibly be attributed to alignment of m icrotubules in longitudinal direction...... 46

Figure 4.7. (A and B) Cytoplasmic force spectrum calculated from intracellular movement and active microrheology measurement using (F2 (f)) = IK(f)1 2 (r 2 (f)) in longitudinal and transverse direction. (C) The force acting on the tracer particles in longitudinal and transverse direction at f = 1 Hz. Force is observed to increase in longitudinal and almost remains unchanged in transverse direction with an increase in aspect ratio. (D) Anisotropy in intracellular dynamics is calculated in terms of ratio of force in longitudinal and transverse direction at f =1 Hz increases with increase in aspect ratio. Error bars: SEM (n= 15)...... 48

11 12 Citations to Previously published work

Chapter 3 is based on the manuscript:

"Equilibrium and out-of-equilibrium mechanics of living mammalian cytoplasm", Satish Kumar Gupta, Ming Guo, Submitted (2017)

Chapter 4 is based on the manuscript:

"Anisotropic mechanics and dynamics in living mammalian cytoplasm", Satish Kumar Gupta, Yiwei Li, Ming Guo, Submitted (2017)

13 14 Chapter 1

Introduction

In this chapter, we briefly discuss the significance ofstudying the mechanical behavior of cells and the forces at play in understandingcell biology. The motivation of conducting the studies presented in this thesis is established. Firstpart of the thesis introduces a new non-invasive, high-throughput method of measuring cell mechanics (chapter 3) and the second part of the thesis is devoted to understandingthe induction of anisotropy in both mechanics and dynamics of living cells (chapter4).

1.1 Introduction and Motivation

Eukaryotic cell is an active material comprising of numerous subcellular components that can actively tune their mechanics in response to external stimuli. There has been ample evidence suggesting that the mechanical properties of cells and cellular forces play a crucial role in regulating ranging from gene expression [1] to cell migration [2]. Consequently, there has been a strong interest among the scientific community to understand the role of mechanical forces and cellular mechanics in mechanosensation. However, in contrast to myriad of powerful tools available to characterize the biological processes, there are only a few methods available to measure the mechanical properties of cells [3-8]. Most of the methods rely on complex instrumentation and requires niche expertise for development and usage; restricting it's use to a handful of laboratories in the world. These methods typically involve application of an external force and recording the dynamic response of the cells to measure their rheology which make them highly invasive. Passive microrheology [9], a non-invasive method of measuring the viscoelastic properties from MSD of the tracer particles using the generalized Stokes- Einstein relation (GSER) has been proposed for living cells [10]. However, the Einstein component of GSER that connects thermal agitation to the frequency-dependent 15 mechanical property of the material assumes that the system is at thermal equilibrium. Cells, however, operate far from equilibrium [11-14] rendering the use of passive microrheology in cells inaccurate. Therefore, there is a need to develop new methodology to probe the mechanics of the cells that is easy to implement, non-invasive and that can be easily adopted by biology laboratories. Chapter 3 of this thesis introduces one such method. Using theory and experimentation, we show that living cells behave as an equilibrium material at short time scales and therefore, passive microrheology can be successfully deployed to extract the high frequency mechanics. Numerous studies have treated cells as an isotropic material assuming that cells have same mechanical properties in different directions [3-8]. However, cells can experience significant restructuring of the cytoskeleton while undergoing morphological changes inducing anisotropy in mechanics. Along with the mechanics, intracellular dynamics is also highly correlated to the structure of the cytoskeleton as the motor proteins work in conjunction with the cytoskeletal filaments. Chapter 4 of this thesis is dedicated to understanding the anisotropic behavior of both intracellular mechanics and dynamics of the cytoplasm while undergoing morphological changes. By quantifying the MSD of intracellular movement and independent micro-mechanical measurements we show that elongated cells depict significant anisotropic behavior in both mechanics and dynamics. However, control cells with aspect ratio, 1 ~ I demonstrated isotropicity. This study is critical in understanding biological processes such as cell migration, gene expression where cell morphology has been shown to play a critical role [15-17].

16 Chapter 2

Materials and Methods

In this chapter, we introduce the materials requiredand the experimentalprocedure we followedfor the studies presented in this thesis. All the imaging is done using a Leica TCS SP8 confocal microscope and the deconvolution is done using Huygens deconvolution software. Active microrheology measurements of intracellularmechanics is done using optical tweezers. Image processing is done either using a custom written MA TLAB code or ImageJ.

2.1 Cell culture, microinjection, and pharmacological Interventions

2.1.1 Cell Culture A7 cells [18] (gift from Tom Stossel lab at Harvard Medical School) are cultured in DMEM with 2% fetal calf serum, 8% newborn calf serum (Invitrogen, CA, USA), 10 mM HEPES buffer, 100 U/ml penicillin and 100 mg/ml streptomycin. Mouse embryonic fibroblasts (mEFs) [19] are cultured in Dulbecco's minimal essential medium (Corning, NY, USA) supplemented with 10% fetal calf serum (Gibco, Life Technologies, Gaithersburg, MD, USA) and 1% penicillin-streptomycin (Gibco, Life Technologies, Gaithersburg, MD, USA). All cells are maintained at 37*C and 5% C02 in humid conditions.

2.1.2 Microinjection Cells are injected with PEG-coated particles [20] of 0.5 micron in diameter diluted to a final concentration of 10' particles per mL in PBS using a glass needle and a FemtoJet microinjector (Eppendorf, Germany) mounted on a microscope. Each cell is injected only with up to 50 particles to reduce the interference with cell function.

17 2.1.3. Phagocytosis To allow the cells to internalize tracer particles, 500 nm fluorescent beads (Molecular

probes, Eugene, OR, USA) are mixed with culture media (at a concentration of 5 x 10' microspheres/mL) for 24 hours. Before imaging, beads that are not endocytosed are washed off with two washes using phosphate -buffered saline (PBS).

2.1.4. Pharmacological Interventions To inhibit the II activity, cells were treated with Blebbistatin (Toronto Research Chemicals, ON, Canada) at a working concentration of 25 gM for 30 min in the incubator. To depolymerize the microtubules, cells are treated with Nocodazole (Sigma Aldrich, MO, USA) at a working concentration of 20 pM for lh in the incubator.

2.2. Micro-contact printing Micro-contact printing is used to confine cells and culture them in different aspect ratios using the protocol described previously [21]. We culture the cells on micropatterned strips with different widths ranging from 10 pm to 40 gm to confine the cells in one direction while allowing it to spread unrestricted in the other direction; this results in cells with different aspect ratios. Polydimethylsiloxane (PDMS) (Sylgard 184; Dow Corning, MI, USA) precursor and curing agent are mixed homogeneously in 10:1 ratio and poured over the silicon wafer with micropatterned wells. To remove air bubbles from the PDMS mixture, the silicon wafer along with the PDMS mixture is degassed in the desiccator from 30 min and then is cured in the oven at 65 'C for 3 h. Solidified PDMS is peeled off from the silicon wafer and cut into stamps which are then oxidized using plasma. Later, 0.3 gg/mL of Collagen-I is poured over each stamp; extra solution is wiped with tissue and the stamp is allowed to dry for 15 min. After complete drying, the stamp is inverted onto the surface of a 35 mm dish (MatTek) with No. 1.5 glass coverslip at the bottom for 2 min and then gently removed. Before seeding cells, the unpatterned surface of the coverslip is treated with 1% pluronic F-127 for 5 min and then washed twice with PBS and cell culture medium.

18 2.3. Intracellular particle tracking Endocytosed fluorescent beads are imaged using a 63 x /1.2NA water immersion lens on a Leica TCS SP8. The motion of the fluorescent particles are recorded every 100 ms for 30 s and the images are processed using custom written particle tracking algorithm [22, 23] in MATLAB (The MathWorks, Natick, MA). Particle centers are found in each image with an accuracy of 20 nm. To avoid the cell-boundary effects and any possible interaction between the mechanically distinct cell cortex and nucleus, particles greater than 1 micron deep within the cell and away from both the thin lamellar region and the nucleus are imaged.

2.4. Active microrheology using optical tweezers The beam from a single-mode continuous wave (CW) Ytterbium fiber laser (10 W, 1064 nm; IPG Photonics, MA, USA) is steered through a series of Keplerian beam expanders to overfill the back aperture of a 100 x 1.45 numerical aperture microscope objective (CFI Plan Apo Lambda DM 100X Oil; Nikon Corp., Japan) to optically trap and manipulate 0.5 pm beads in the cytoplasm of living cells. Two- axis acousto-optic deflectors (IntraAction Corp., IL, USA) are used to manipulate the beam in the plane of the microscope glass slide to steer the beam and manipulate the trapped bead. For detection, the bead is centered on a high-resolution position detection quadrant detector (Thorlabs Inc., NJ, USA) and illuminated using brightfield illumination from a 100 W lamp. The linear region of the detector is calibrated by trapping a bead identical to those used in the cells in water and moving it across the detector using the acousto-optic deflectors in known step sizes. The trap stiffness is calibrated to 0.05 pN/nm using the mean-squared Brownian motion of a trapped bead in water at various laser power settings using the principle of energy equipartition as previously described [24]. A trapped bead is oscillated across a frequency range of 0.3-70 Hz using the acousto-optic deflectors, and the laser position and bead displacement are recorded simultaneously, from which the storage modulus G', representing the elastic portion and the loss modulus G", representing the viscous portion are determined.

19 2.5. Immunofluorescence, microscopy and image processing

Cells are fixed with 4% paraformaldehyde (Sigma Aldrich, MO, USA) and 0.1% Triton X- 100 (Sigma Aldrich, MO, USA) in PBS for 15 mins and then washed three times using PBS (Coming, NY, USA). Cells are then stained with rat anti-a-tubulin primary antibody (EMD Millipore, MA, USA), followed by Alexa Fluor 488 conjugated goat anti-rat (Invitrogen, CA, USA), using standard procedures. F-actin was stained using AlexaFluor 532 phalloidin (Molecular probes, Eugene, OR, USA) for 30 min at room temperature. Nucleus is labelled using DRAQ5 (Invitrogen, CA, USA). Cells are imaged using excitation from a 488, 552 and 638 nm laser line and a 63 x /1.2NA water immersion lens on a Leica TCS SP8 (Leica, Germany). Images were deconvolved using the Huygens deconvolution software (Huygens, Hilversum, Netherlands). To quantify the local fiber orientation, Orientationj, an imagej plugin is used which uses an algorithm based on structure tensors as described previously [25].

20 Chapter 3

Equilibrium and non-equilibrium cell mechanics

In this chapter, we introduce a high throughput, non-invasive method of measuring cytoplasmic mechanics from intracellularfluctuations. Living cells operate out of equilibrium and thus, passive microrheology is usually considered inaccurate. We show that living cells behave as equilibrium material at short time scales and thus, passive microrheology can be used to measure highfrequency mechanics of the cytoplasm.

3.1. Introduction

The cytoplasm of living cells is a crowded and highly dynamic environment, in which there is continuous motion [26], including vesicle traffic [27], cytoskeleton reorganization [28] and messenger RNA transport [29]. These dynamic processes are essential for life. Much of this intracellular movement is due to active processes that typically result in directed motion; for example, and motors transport cargo along microtubule tracks. This directional motion is fast and effective for rapid long-range transport in cells. At the same time, however, much of the motion in cells appears random and non-directed, for example, the seemingly random fluctuation of a majority of vesicles, organelles, and protein complexes [30-37]. Given the similarity of this motion to diffusion, it has often been interpreted as thermal Brownian motion, and has, in some cases, even been used to infer intracellular viscosity.

In systems that are in thermal equilibrium, small embedded objects typically experience random movement that are driven by thermal fluctuations. For example, in a pure viscous fluid, the probe particles will randomly diffuse; in this case, the mean square displacement (MSD) of these particles linearly increases with time, and is directly associated with the fluid viscosity through the Stokes-Einstein relationship [38]. In contrast, in a pure elastic material, the thermal fluctuation of probe particles will be

21 constrained by the elasticity of the matrix; in this case, the MSD of the movement is a constant which is set by equaling the thermal energy kBT with the elastic energy from the matrix deformation [9], where kB is the Boltzmann constant and T is the temperature. Using such energy balance argument, the elastic modulus of the material can be obtained. This picture is simplified for ideal materials, however, does highlight the physics underlying the relationship between material property and the thermal movement of embedded probe particles. If the material is viscoelastic, the thermal fluctuation of the probe particles will further complicate, with the MSD varying its time dependency non- monotonically at different characteristic time scales. Interestingly, the frequency dependent complex moduli of the viscoelastic material can also be calculated from the MSD using the generalized Stokes-Einstein relationship [9, 39]. This is typically referred as passive microrheology and its applicability has been demonstrated in various materials under thermal equilibrium [9, 40-43].

However, this analysis assumes equilibrium conditions [38], whereas living cells are far from equilibrium due to their many active processes powered by, for instance, adenosine triphosphate (ATP)-driven motors [26]. Indeed, recent experiments and theory have shown that motor activity can significantly enhance fluctuations of tracer particles in both reconstituted cytoskeletal networks and in living cells [13, 14, 44-47]. In this case, the movement of tracer particles does not only reflect the mechanical property of surrounding matrix, but also changes with the level of driving forces, which could originate from both thermal energy and biological activities. Thus, it is not clear how one could delineate the mechanical property of a living mammalian cytoplasm by solely watching the movement of embedded particles or endogenous organelles.

Besides influencing intracellular movements, the mechanical property of the cytoplasm also plays important roles in regulating many key cellular physiological functions, such as mechanotransduction [48], cell migration [49, 50], cancer [51, 52], and even stem cell fate [53, 54] . Thus, characterizing the mechanical properties of living mammalian cytoplasm, and their changes during biological processes is essential for us to understand fundamental cell physiology. Indeed, numerous methods have been 22 developed [3], including atomic force microscopy [4], micropipette aspiration [5], magnetic tweezers [6], optical tweezers [7, 8], etc. However, these methods rely on the application of external inputs, which often require direct contact with the cell, and are therefore invasive and have limited applicability. If we could obtain the mechanical information of the cytoplasm by solely watching its internal dynamics, it would enable us to characterize the cytoplasmic mechanics in more complicated environments and conditions, for example, in three dimensional matrix, native tissue, and even during the onset of disease in real time.

In this chapter, we present a direct quantification of random intracellular motion of injected sub-micron particles, and complement this by independent micromechanical measurements of the local cellular environment using optical tweezers. We observe two distinct regimes of mechanical behavior in living mammalian cytoplasm. At long time scale (r 0.1 s), corresponding to low frequency, the cytoplasm is out of equilibrium and the seemingly random intracellular motion is driven by active biological stress fluctuations in a nearly elastic cytoskeletal network; at short time scale (r 0.1 s), corresponding to high frequency, the cytoplasm is at thermal equilibrium instead and the random intracellular movement is driven by thermal fluctuation. Moreover, we directly extract the mechanical property of the cytoplasm of living A7 mammalian cells from the high frequency fluctuation of injected tracer particles; we find that it is in excellent agreement with the active microrheology measurement with optical tweezers at the same frequency range.

3.2. Results and Discussion To measure the fluctuating motion of components inside the cytoplasmic microenvironment of A7 cells, we inject 500 nm tracer particles and quantify their movement in terms of MSD utilizing confocal microscopy (figure 3. la). A short polyethylene-glycol (PEG) brush layer is attached to the colloidal tracer particles to prevent interactions with cytoskeletal network or proteins as suggested previously [20]. The size of the tracer particles is greater than the typical cytoskeletal

23 mesh size of about 50 nm [55, 56], so that the probes do not travel freely through the cytoskeletal network and their motion represents the fluctuations of the cytoplasm. We find the particle centers in each image, track their trajectories (figure 3.1 b) and measure the two-dimensional time- and ensemble-averaged MSD, (Ar2(r)), where,

Ar(r) = r(t +,r) - r(t). The dynamics of the complex cytoplasmic microenvironment is nontrivial owing to the fact that numerous active processes are operating at different time scales along with the omnipresent Brownian motion. At short time scales (zr 0.1 s), the MSD of the tracer particles is nearly constant in time; here, we note that value of this plateau is at least twice the measured noise floor with the same particle fixed on a coverslip. At longer time scales (r > 0.1 s), the MSD shows a linear dependence on time (figure 3.2). This long time scale behavior seems to be consistent with the Brownian motion of particles observed in a simple viscous liquid at thermal equilibrium. However, it has been shown that the cytoplasm is far from thermal equilibrium [11, 57], suggesting a source other than thermal energy for these observed seemingly random fluctuations. Indeed, the out of equilibrium nature of the intracellular motion has been observed in a variety of cellular systems [14, 46, 47, 58- 60]. To further demonstrate that this often misconstrued diffusion-like behavior does not have thermal origin, we deplete cells of ATP which inhibits motor and other enzymatic activities. It is observed that for ATP depleted cells, the MSD is nearly constant over the entire time scale having a magnitude comparable to MSD at short time scales for untreated cells; this result suggests that these diffusive-like fluctuations in the cytoplasm are due to ATP-dependent active processes. However, these intracellular fluctuating motions are governed by both the driving force and the mechanical resistance provided by the cytoplasmic environment. It is not clear how each of these factors are regulated by ATP dependent processes, thereby affecting intracellular fluctuation; for instance, are ATP dependent processes providing non- equilibrium driving force to push on intracellular objects, or relaxing the cytoplasmic material, thereby allowing intracellular objects to move under equilibrium condition? Therefore, to completely characterize the origin of intracellular fluctuations, it is vital

24 a b Untreated

Beads

ATP Depleted

Figure 3.1. (a). Bright-field image of a living A 7 cell with injected beads. (Scale bar: 10 Pm.)

(b). Typical trajectories of a 500 nm PEG coated particle in untreated and ATP depleted A 7 cells. (Scale bar: 0.2um.)

0 Untreated 10-1 * ATP depleted Noise floor

E

V

10-3

A AAAAA A A A A

10-2 10-1 100 101 T(sec)

Figure 3.2. Two-dimensional MSD (Ar 2(r)) of 500 nm tracerparticles plotted against

lag time on logarithmicscale in untreatedA 7 cells (red circle), A TP depleted A 7 cells (black diamond) and noisefloor (gray triangle).

25 to have a direct characterization of the mechanical environment of the cytoplasm. To measure the micromechanical properties of the cytoplasm, we perform active microrheology measurements using optical tweezers, as illustrated in figure 3.3 a. The same PEG coated particles, that we use for tracking motions, are optically trapped and manipulated using a laser trap. A trap stiffness of 0.05 pN/nm was maintained on the beads by keeping the laser power of the sample at roughly 200 mW. Trapped beads are oscillated across a frequency range of 0.3-70 Hz using acousto-optic deflectors and the laser position and particle displacement is recorded. This sinusoidally oscillating optical trap generates a force f(c) at the angular frequency, a, resulting in the displacement, r(w), of the bead and thus, the effective spring constant, K(w), of the intracellular environment can be calculated by K(w) = f(co)/ r(co) [7, 13]. We observe that the resultant displacement is practically in phase with the imposed force over the measured frequency range suggesting that the cytoplasm is predominantly elastic within the frequency range in our experiments. For a homogeneous, incompressible elastic material, generalization of the Stokes equation relates the displacement r of the probe particle of diameter d to the shear modulus G as r = F/3rGd, where using the classical Hooke's relation we get G = K/31rd [9, 61]. However, for materials with dissipation, the displacement is not in phase with the imposed force providing a complex shear modulus instead, given by G = G'+ G"where, G'is the elastic modulus, G" is the loss modulus. We find that the measured elastic modulus G'is significantly higher than the loss modulus G" within the measured frequency range (figure 3.3 b) . This confirms that the cytoplasm of living cells is predominantly elastic rather than viscous, and justifies the use of aforementioned generalized Stokes equation [13]. Interestingly, our measurements in ATP depleted cells show that the cytoplasmic mechanical property is indeed ATP dependent. Both elastic modulus and loss modulus G" decreases by a factor of 2 to 3 in ATP depleted cells as compared to the untreated cells [62] , however, the response is still elastic (figure 3.3 b). For both untreated and ATP depleted cells, a power-law frequency dependence of the elastic response, IG(a) oc 0' is observed which is consistent with earlier studies [7, 63]. However, the magnitude of the exponent p reduces from 0.15 to

26 a b

101 0 AG"

Actin filament 100 T oaiw Myosin 11 minifilament, * Lipid vesicle Mitochondria Tracer particle

1100 101 0)O Q20 10, 0 (rad/s) Figure 3.3. (a). Schematic diagram of optical tweezers used to measure cytoplasmic moduli. (Inset): Schematic illustration of the cytoplasmic environment that the probe bead experiences. (b). Cytoplasmic moduli measured by active microrheology using optical tweezersfor untreatedA 7 cells (red circles) and A TP Depleted A 7 cells (black squares).

0.10 upon ATP depletion. Furthermore, we note that the measured elastic modulus of the cytoplasm is about 1 Pa to 10 Pa over the measured frequency range, which is much lower compared to the elastic modulus of the cell cortex, -1 kPa [63, 64]. This can be attributed to the fact that the cell cortex has a denser cross-linked actin structure and the particles in the present investigation probe inside the cytoplasm, which is a less dense environment. The fluctuations of tracer particles appear diffusive at time scales greater than 0.1 s suggesting the cytoplasm is a viscous material, however, our micromechanical measurements using the same particles reveal that the cytoplasm is instead a weak elastic solid. This is indeed puzzling. Here, inert beads are directly injected into the cytoplasm of the cell which results in them evading the endocytic pathway; therefore, the beads do not undergo directional transport or adhere to the cytoskeletal structures. However, even in the absence of such directed transport, the acto-myosin contractility is known to result in bead movement. Previous studies using reconstituted actin network (predominantly 27 elastic) have shown that random fluctuations due to acto-myosin contractility caused by myosin II motors can lead to a similar diffusive-like behavior [13, 59]. To understand the observed random intracellular fluctuations in a weak elastic cytoplasm, we model the cytoplasm as a cross-linked semi-flexible filamentous network (such as actin cytoskeleton) with random contractile forces exerted by molecular motors (such as Myosin II). Although, numerous molecular motors are responsible for the activity in the cytoplasm, Myosin II is known to play a major role in acto-myosin contractility, which is important for muscle contraction, cell migration, cell division, tissue and stem cell fate [65, 66]. The forces generated by myosin motors individually have very short duty cycles and thus are incapable of producing directed motion, however, they polymerize in a solution to form aggregates and then give rise to coherent directed motion. These coherent forces commonly show a step function behavior operating for a time known as the processivity time of the motor, zr, during which the motor is attached

to the network [67]. Under the assumption that the processivity time follows Poisson distribution, the temporally averaged non-equilibrium active force fluctuation spectrum in frequency domain is given by [45, 57]:

2fo 2 (fa (a)) = 2f 2 (1)

For co >> l/z-, , equation 1 reduces to the form:

f 2 1 (act )) 0C 2 .(2)

To calculate the force experienced by the probe particle, we use the fundamental force displacement Hooke's relation, f = Kr, where, f is the driving force, r is the resulting displacement and K is the stiffness of the medium. However, as established above, the effective spring constant for the cytoplasm is frequency dependent and the forces are random, thus, we consider the quadratic form of the averaged quantities in the frequency domain. Hence, the frequency spectrum of the particle displacement can be given by:

(r2(Co)) =K(0))1 (f2 (0)).(3)

28 Our laser-tweezer experiments reveal that the cytoplasm is a weak elastic solid with the frequency dependent spring constant given by: K(o) ~ K, (-i) 6 . (4)

Thus, the frequency spectrum of the displacement of particle, (r2 (a)) , calculated from equation 3 utilizing K(co) and (f.,(w)) from equation 4 and equation 2 respectively is given by:

(r2(Co)) KC2 . (5) 2 K0

Therefore, the MSD in the time domain (r2 (r)) for times less than the processivity time is given by:

2 2 (Ar (r))= 2f (1 -e-")(r (co)) d c _2_ -r 2,r K, 6 In the case of Brownian (thermal) motion of the probe particles embedded in viscoelastic medium, the MSD can be calculated from the Generalized Stokes-Einstein Relation (GSER) [9]:

(Ar 2 kBT kBT7) 3iordG(co) icoK(co)' which takes the form of the classical Stokes-Einstein relationship for the case of purely viscous fluid given by:

2 (Ar (r)) = r, (8) 3rdri where q is the fluid viscosity, kB is the Boltzmann Constant and T is the temperature. Using equation 4, equation 7 reduces to the form given by:

2 ,) kB c-(P+1) (Ar (9) K0 which can give the MSD in time domain as:

(Ar 2 (,)) oB (10) K0

29 This dependence of MSD, (Ar2 (r)) oc r under thermal equilibrium is considerably different from that observed in non-equilibrium systems with active forces (equation 6). This is consistent with the trend observed at short time scales for untreated A7 cells as shown in figure 3.2; this implies that the motion in the short time scale regime is thermally driven in a viscoelastic media. For thermally driven fluctuations, the MSD of a particle is inversely proportional to KO (equation 10); in contrast, for actively driven fluctuations, it is inversely

proportional to K (equation 6). This stark difference in dependence of MSD on K can be used to further confirm the active and thermal origins of these fluctuations. To do so, we change the stiffness of the cytoplasm, K, through osmotic compression. This is achieved by adding different concentrations of PEG in to the culture medium. Elastic modulus G'and loss modulus G" of the cytoplasm under different PEG polymer concentrations (0% PEG300, 3% w/w PEG300 and 6% w/w PEG300) are measured as shown in figure 3.4 (a). Power law rheology is observed under all PEG concentrations in the cells; thus we obtain the value of cytoplasmic stiffness Ko by fitting the elastic component of the stiffness using K'(w)~ Kcwl, where K = 3rGd .We indeed find that Ko increases when the PEG concentration is increased. This increase in stiffness can be attributed to the reduction of cell volume through water efflux and consequent higher degree of molecular crowding [68]. Similar characteristics of MSD in untreated cells are also observed for cells under compression, however, a reduction in the amplitude is observed as the PEG concentration increases (figure 3.4 b). This is possibly due to the increase in cytoplasmic stiffness. The MSD curves are rescaled by K, and K' (K= 8.6382,

12.059 and 16.678 Papm for 0% PEG300, 3% w/w PEG300 and 6% w/w PEG300 respectively) to elucidate the origin of the short and long time scales behavior of MSD.

We find that all the curves collapse at short time scales when MSD is scaled by K (figure 3.4 d); this indicates that the random fluctuations corresponding to this time scale (r 0.1 s) is thermally dominated which is in accordance with equation 10.

30 a b 101

* 3% PEG 0 Isotonic U 3% PEG A$%PEG 101 A 6% PEG

10 E 10.2 A

100 10-3

1 00 101 102 10-2 10-1 100 10, w (rad/s) t (sec) C d 101 100 * Isotonic * Isotonic S 3% PEG * 3% PEG A 6% PEG A 6% PEG

L E o100 . 10.1

A A

V V A AA Thermal 10-1 (< A >cc I/K,) * gS 10-' . **4 102 101 10W 101 10-2 101 1c)0 101 T (ec) Figure 3.4. (a) Cytoplasmic moduli measured by active microrheology using optical tweezers for different concentrationsof PEG300. (b) Two-dimensional MSD (Ar2 (r)) of tracer particles plotted against lag time on logarithmic scalefor different PEG concentrations. (c) The MSD data depicted in (b) is scaled with K. for different concentrationsof PEG

where K. = 8.6382, 12.059 and 16.678 Paymfor 0% PEG300, 3% w/w PEG300 and 6% w/w PEG300 respectively obtainedby fitting to equation 4. All curves collapse at long time scales. (d) The MSD data depicted in (b) is scaled with K. for different concentrations of

PEG300 where K. is same as that used in (c). All curves collapse at short time scales.

Moreover, a similar curve collapse is observed at long time scales when the MSD is scaled by K. (figure 3.4 c); this indicates that at long time scales the diffusive like

31 behavior is actively driven which is in agreement with equation 6. These results confirm that living cells behave as equilibrium material at short time scales and an active non- equilibrium material at long time scales.

a b

10 'Out of Equilibrium Equlibrium Out of Equilibrium Equilibrium 10' so

100 -* U 0 U 0 700 0 0 100 O 00 d 10-1 U 0 0

10b

Optical1Tweezers 0 0 PaIvllirohoodogy 100 10 10 103 100 10 1P 103 w (radls) c (radls)

Figure 3.5. Comparison of cytoplasmic moduli of A7 cells measured by active microrheology using optical tweezers and passive microrheologyfor cells under two conditions, (a) with 0% w/w PEG 300 and (b) with 6% w/w PEG 300. Both methods show an excellent agreement at high frequenciesfor both untreated and osmotically compressed cells suggesting an equilibrium regime at short time scales.

Our results show that the intracellular fluctuations are dominated by thermal forces at short-time scales, thus we check if the mechanics of the cytoplasm at high frequency can be extracted from the intracellular fluctuations of the tracer particles. In this regard, we perform one particle passive microrheology to calculate the frequency dependent complex moduli from the MSD using the generalized Stokes-Einstein equation as described previously [9, 43]. An excellent agreement is observed between active and passive microrheology measurements for angular frequencies higher than -60 rad/s wherein thermal forces are dominant (figure 3.5 a). However, at lower frequencies when the cytoplasm is in the non-equilibrium regime driven by active forces, we observe that the mechanical properties measured using the two methods are distinct. Similar agreement is also observed for osmotically compressed cells (figure 3.5 b). These results

32 demonstrate that for a mammalian cytoplasm (A7 cells) the fluctuations at time scales shorter than 0.1 s are thermal driven and can be effectively used to measure the high frequency mechanics of the cytoplasm for frequencies corresponding to time scales less than 0.1 s. The frequency of transition from thermal dominated regime to active might change for different cellular systems however, by observing the power law change in MSD the transition lag time can be measured. We acknowledge that at this transition the forces could be of comparable magnitude however, if the time scales are smaller than the transition time, it is reasonable to assume that thermal forces are dominant and the fluctuations can be used to calculate the mechanics of the cytoplasm. It is worth mentioning that extracting the high frequency mechanical property using the short time scale MSD measurements is limited by the spatial resolution of the particle tracking. The spatial resolution of the present study is 20 nm, therefore for a 500 nm particle, the maximum complex modulus that can be measured is about 10 Pa (equation 7). It is however possible to measure the modulus of stiffer materials using smaller sized particles or other methods with better tracking resolution. Nonetheless, we show that despite living cells being in an active non-equilibrium state, passive microrheology can be used to extract valuable insights about the mechanical state of the cells at high frequencies.

3.3. Conclusion

In the present study, we show that the diffusive-like motion of tracer particles in living cells is due to actively driven intracellular fluctuations rather than thermal forces. A combination of intracellular fluctuation measurements and independently quantified micromechanical measurements is used to understand intracellular mechanics and dynamics in living mammalian cytoplasm. At short time scales (r 0.1 s), the random intracellular motion is driven by thermal fluctuations, while at long time scales (r 0.1 s ), the intracellular fluctuations are driven by active stress fluctuations in the cytoskeletal network. Finally, we show that passive microrheology, whose applicability has been challenged in living cells can be used to extract high frequency mechanical property of the cytoplasmic environment. The high frequency elastic modulus and loss modulus

33 calculated using passive microrheology is in agreement with that measured using active microrheology by optical tweezers. This is due to the fact that cytoplasm behaves as an equilibrium material at short time scales. Active microrheology has been successfully used to extract mechanical properties of non-equilibrium systems such as living cells, however, it often involves complicated setup, has low throughput, is invasive and has limited applicability in observing real time phenomena such as drug testing, embryo development, cancer metastasis, etc. The proposed high frequency passive microrheology is a high-throughput, non-invasive, inexpensive method of performing micromechanical measurements.

34 Chapter 4

Anisotropic Mechanics and Dynamics of Cytoplasm

In this chapter, we investigate the role of morphological changes on intracellular mechanics, dynamics and forces. We use optical tweezers and microscopic particle tracking to investigate the mechanics and dynamics inside the cytoplasmic microenvironment in directions perpendicular and parallel to the principal cell axis. Furthermore, we combine both these measurements to calculatespectrum of intracellular forces using ForceSpectrum Microscopy. We show that cytoplasm of a living mammalian cell becomes highly anisotropicwhen the aspect ratio of the cell deviates from 1.

4.1 Introduction

Cytoplasm is a complex active material wherein numerous biochemical processes occur which is critical for the functioning of a cell. Many of the biological processes such as, cell migration [49, 50], mechanotransduction [48], cancer metastasis [51, 52] involve mechanical processes and are known to be critically regulated by cell mechanics. Consequently, numerous techniques have been developed to probe the mechanical properties of cells [3-8]. Most of the studies report mechanical measurements of cells in terms of a stiffness wherein lies the inherent assumption that cells are isotropic [3-8, 69]. However, cytoplasm of a cell is a highly crowded, dynamic and heterogeneous microenvironment which under various physiological conditions can undergo morphological changes resulting in anisotropy. Evidence suggests that the cytoplasm experiences significant redistribution of its components under external mechanical stimuli typically observed during processes such as blood flow on endothelial cells [70, 71] or physiological processes such as cell migration [72]. This redistribution of the cytoskeleton comprising of actin, microtubule and intermediate filaments is governed by the morphological changes of the cell and can causes a mechanical anisotropy of the cytoplasm. For example, endothelial cells when subjected to continuous laminar flow shear stress, suffer directional anisotropy resulting in temporal and spatial changes in 35 cytoplasmic creep compliance in different directions [73]; smooth muscle cells under mechanical strain also modify their mechanics through cytoskeletal reorganization resulting in a mechanical anisotropy [74]. Therefore, a deeper insight of this mechanical anisotropy is critical in understanding the mechanism involved in cellular sensing and responding when subjected to external loads. Moreover, cytoskeletal reorganization not only regulates the mechanics of the cytoplasm but can also critically determine intracellular dynamics which is equally important for complete understanding of cytoplasmic physiological phenomena. Intracellular motion caused by collective activity of molecular motors within the cells is highly correlated with both mechanics and intracellular force as cells typically operate out-of-equilibrium [11-14]. Intracellular dynamics and force are known to drive important functions at the level of the whole cell such as division [75], migration [76], and contraction [66]. Motor proteins of the myosin superfamily form minifilaments and bind with actin filaments to cause acto-myosin contractility, whereas, families of motor proteins known as kinesin and dynein assist with cargo transport along the microtubules inside the cells [65, 77, 78]. As the motor proteins work in conjunction with the cytoskeletal fibers, their reorganization would perhaps influence the intracellular dynamics making them anisotropic as well. The anisotropy in mechanics during various physiological processes and its implications on different biological activities have been studied; in particular, the effect of mechanical cues such as mechanical strain [74], shear flow [73] or a combination of these mechanical stimuli have been studied [79]. Moreover, there has been evidence that cell-cell and cell- (ECM) interactions can also induce cell polarity, significantly affecting the internal organization of the cell and thereby playing a key role in developmental processes [80]. However, how the cytoskeletal reorganization results in mechanical anisotropy of cells is not well characterized. Moreover, how this spatial modification influences the internal dynamics and force which seems to be highly correlated to the intracellular organization remains unclear. In the present study, we investigate the effect of spatial restructuring of the cytoskeleton induced by morphological changes of the cells on intracellular mechanics and dynamics. We use micro-contact printing technique to confine the width of the cell while allowing

36 them to spread unrestricted in the other direction resulting in cells with different aspect ratios. We use optical tweezers and microscopic particle tracking to investigate the mechanics and dynamics inside the cytoplasmic microenvironment in directions perpendicular and parallel to the principal cell axis. We find that both mechanics of the intracellular environment and the motion of endocytosed tracer particles can be highly anisotropic depending on the cell morphology. Furthermore, we directly measure the spectrum of intracellular forces using force spectrum microscopy (FSM) [14] and find that the anisotropic cytoplasmic dynamics is governed by the forces due to activity of molecular motors and other active processes linked with microtubules.

4.2 Results

4.2.1 Cell aspect ratio modifies cytoskeletal organization.

To understand how morphological changes affects the cytoskeletal organization of the cytoplasm, mEFs are cultured in different aspect ratios, p = 1-1.5, 1.5-3, 3-7, 7-12 (figure 4.1 A-D) using micro-contact printing (see Materials and Methods). We stain actin and microtubules to quantify their local orientation distribution (see Materials and Methods). It is observed that for the control isotropic cells with aspect ratio, p = 1-1.5, both actin and microtubules are isotropically distributed with uniform fractions of fibers oriented in every direction (figure 4.2 A and B). As the aspect ratio of the cells increases, the distribution of the cytoskeletal fibers, namely, actin and microtubules become aligned preferentially in the longitudinal direction (figure 4.1 E). For cells with the highest aspect ratio achieved in our study, P = 7-12, we observe significant cytoskeletal remodeling; majority of actin and microtubules are aligned in the longitudinal direction as compared to the transverse direction. This confirms that cell shape can modify the cytoskeletal organization and can induce the network anisotropy of the cytoskeleton (figure 4.2 C).

37 A B C D E Reference Frame

CD

C 0

Transverse

F G H I p-1I 0-3 0-5 0-10 10105 90 75 s

16 ~~5

Figure 4.1. Geometric control of cell aspect ratio. (A-D) Fluorescentimages of mEFs cultured with different aspect ratios (1 ~ 1, 3, 5,10 respectively) using micro-contact printingstained for actin (red), microtubules (green) and nucleus (blue) (Scale bar: 5 pm). (F-I) Representative trajectories of a 500 nm endocytosed polystyrene bead in cells with different aspect ratios (Scale bar: 0.2pm). Movement of beads inside cells becomes highly anisotropicwith increasein cell aspect ratio. (E) Referenceframe used in our study.

38 A B

105 9075 OZI=1- 1.5 10 105 90 75 6 120 .% 60 0p=1.5 -3 106 135* 45 0 =3-7 135 45

150 30 150 3

165 15 185 15

180 - 0 180 0 0.01 0.02 0.005 0.010 0.015 Actin Microtubules C Actin filament Microtubule Myosin I minifilament Mitochondria Kinesin Dynein Lipid vesicle V Tracer particle

Figure 4.2. Quantification of cytoskeletal anisotropy. (A and B) Histogram of actin and microtubule orientation as a function of aspect ratio, fl. Data at each point represents the fraction of actin or microtubules aligned at a particularangle. Cells with low aspect ratio has an isotropic distribution offilaments however alignment of fibers in higher aspect ratio cells are biased in a particulardirection. (C) Illustration of cells with different aspect ratios showing alignment offibers and other organelles. Forlow aspectratio cells thefibers are randomly distributedin all directions resulting in isotropic movement of beads and organelles. Higher aspect ratio cells have higher movement of tracer particles and organelles in the direction of the microtubule alignment.

39 4.2.2 Cell aspect ratio induces anisotropy in cytoplasmic mechanics.

To investigate how the cytoskeletal reorganization modified due to changes in cell morphology alters the mechanical properties of the cells, active microrheology measurements are performed using optical tweezers to measure the micromechanical properties of the cytoplasm in the longitudinal and transverse directions. 500 nm diameter polystyrene beads are endocytosed into the cytoplasm of the cells. These beads go through the endocytic pathway and therefore are covered with lipid bi-layers. Consequently, occasionally they are directionally transported along microtubules, however, most of the time they exhibit random movement as shown previously [7, 81]. A bead is optically trapped and a sinusoidally oscillating force F(f) at the natural frequency, f across a frequency range of 1-70 Hz is applied using a piezo stage. This force results in the displacement, r(f), of the bead and thus, the effective spring constant of the intracellular environment can be calculated by K(f) = F,(f) / r(f) [7, 13]. All the measurements are made using particles away from both thin lamellar region and nucleus to prevent any contribution to the cytoplasmic stiffness from these mechanically distinct regions of the cells. For measurements in both directions within cells of different aspect ratios, an increase in the intracellular spring constant with frequency is observed which follows the power-law form, IK(f)I or IG(f)I oc f 'with a ranging from ~ 0.1 to 0.15

(figure 4.3 A and B). This weak power-law behavior is consistent with that observed previously for cells and biopolymer network [7, 13, 14, 63]. The cytoplasm of living cells has been shown as predominately elastic for the frequency range measured here[7, 14], therefore, the shear modulus G(f) relates to the intracellular stiffness K(f) by the generalized Stokes equation suggesting K(f) oc G(f) [7, 13, 14]. Although, a similar behavior in terms of frequency dependence is observed for all cases, the intracellular stiffness in both directions increases with an increase in the aspect ratio of the cells (figure 4.3 A and B). It is observed that for aspect ratio, 8 = 1-1.5, cells behave as isotropic isotropic material where, the intracellular stiffhess, K(f) is of the same magnit-

40 A B 12 12 11 Longitudinal Direction. 11 Transverse Direction 10 10 9 9 8 8 7 7 a. 6 IL6 I 5 15 p=1-1.5 * p=1-1.5 s 0=1.5-3 p.$1.5-3 3 A 0=3.7 3 A 0=3-7 * p.7-12 * P=7-12

100 10' 102 100 101 102 Frequency (Hz) Frequency (Hz) C D 9 1.4 U Longitudinal direction A Transverse direction 8 1.3

07 -+ 1.1 .26 11.01 . S ------5 ~0.9 4 0.8 2 4 6 8 10 2 4 6 8 10 Aspect Ratio (P) Aspect Ratio (P) Figure 4.3. Active microrheology measurements of intracellular mechanics using optical tweezers. (A and B) 500 nm polystyrene beads are endocytosed into mEFs and are trappedand subjected to sinusoidally varyingforceF atfrequencyf Thefrequency dependent complex intracellularspring constant, K is calculated by measuring the resultant displacement of bead x. Longitudinal and transverse intracellularspring constant as a function offrequency follows power-law rheology for all aspect ratio ranges (8 = 1-1.5, 1.5-3, 3-7, 7-12). (C) The variationof cytoplasmic stiffness, K, with aspect ratio at 10 Hz. With increase in aspect ratio, higher intracellularstiffness is observed in the longitudinaldirection than transverse direction. (D) The mechanical anisotropy with increase in aspect ratio in terms of ratio of intracellularstiffness in longitudinaland transverse direction. Cells are mechanically anisotropicfor higher aspect ratio cells. Errorbars represent standarddeviation (n =15).

41 -tude in both directions. However, cells with high aspect ratio demonstrate anisotropic behavior. Specifically, at 10 Hz, for cells with an aspect ratio, f = 7-12, the intracellular stiffness in longitudinal direction is 22% higher than that in transverse direction but for cells with aspect ratio, 8 = 1-1.5, they show similar magnitude of intracellular stiffness in both directions (figure 4.3 A and B). Furthermore, we quantify the mechanical anisotropy in terms of ratio of intracellular stiffness in longitudinal and transverse direction, KLongitudinal /KTranss measured at 10 Hz (figure 4.3 D). As mentioned earlier, we observe that for cells with aspect ratio f = 1-1.5, the cytoplasm behaves as an isotropic material showing that the ratio of the stiffness in different directions is ~1, however, as the aspect ratio of the cell increases, the ratio of intracellular stiffness or shear modulus in longitudinal and transverse direction increases suggesting that the cells become anisotropic. This can be explained by the fact that for cells with aspect ratio , = 1-1.5, the cytoskeletal fibers are uniformly distributed in all spatial directions as shown in figure 4.3 A and B, therefore, they behave as isotropic materials, however, increase in the cell aspect ratio introduces a bias on the distribution of the fibers causing a mechanical anisotropy.

4.2.3 Cell aspect ratio regulates cell volume and nuclear volume.

It has recently been shown that change in cell volume correlates with change in the mechanical property of both cytoplasm and cell cortex [68, 82] To check if cell aspect ratio also regulates cell and nuclear volume, we use CellTrackerTM and DRAQ5TM to label the cytoplasm and nucleus respectively and use three dimensional (3D) confocal microscopy to measure their volume for cells with different aspect ratios. We find that the volume of the cell decreases with the increase in the cell aspect ratio (figure 4.4 A). Similar trend of decreasing nuclear volume with aspect ratio is also observed (figure 4.4 B). Interestingly, we also find that as the aspect ratio of the cells increases, the nuclear volume decreases proportionally to cell volume (figure 4 C). This suggests that both cell volume and nuclear volume correlate with cell morphology in similar fashion.

42 A B C

...... 3500 16000 3000 14000 -C'14000, 1'12000 4. 12000 2500 010000. U200l

0 20008000 -

0 2 4 6 8 10 12 0 2 4 6 8 10 12 1200 1600 2000 2400 2800 Aspect Rato (0) Aspect Rato (0) Nuclear volume (pm)

Figure 4.4 (A and B) Cell volume and nuclear volume of cells as a function of cell aspect ratio. Both cell and nuclear volume decreases with an increase in cell aspect ratio. (C) Cell volume tracks nuclear volume. Increase in cell volume linearly increases nuclear volume. Error bars represent standarddeviation (n =25)

4.2.4 Cell aspect ratio regulates anisotropy in intracellular motion

To confirm that cytoskeletal reorganization indeed changes the intracellular motion inside the cytoplasm, we quantify the movement of 500 nm endocytosed particles for cells with different aspect ratios. Mean square displacement (MSD) of tracer particles in longitudinal and transverse directions is measured utilizing confocal microscopy. We find the centers of fluorescent particles in each image, track their trajectories (figure 4.1 F-I) and measure the one-dimensional time- and ensemble-averaged MSD, (Ax 2(r)), where, Ax(r) = x(t + v) -x(t) , in both directions. Particles imaged are greater than 1 micron deep within the cell and away from both the thin lamellar region and the nucleus to avoid any effects from the cell cortex and the mechanically distinct regions. The MSD in longitudinal direction monotonically increases with increase in the aspect ratio (figure 4.5 A). However, a reverse trend showing decrease in MSD with increase in aspect ratio in transverse direction is observed (figure 4.5 B). This anisotropic behavior of intracellular motion is predominant at long time scales. At lag time, r =1 S , the MSD increases by a factor of~2 in the longitudinal direction and reduces by ~1.6 in the transverse direction when the aspect ratio increases from P = 1-1.5 to f = 7-12 (figure 4.5 C).

43 A B

Longit'udinal Direction Transverse Direction

10-2 A 10'- .10 A A 0 a A *A 111 * .1 *A 0~~ * * "E AA * V 0A *AA A*a AE ILA 7 V dIIII* p.7A1 A 0.. 10-3 10-' Noe Psi7-1.5

0-1 100 101 100 10 T (sec) T (sec) C D 4.5 3.5 . Longitudinal direction A Transverse direction 4.0 3.0 3.5 2.5 -+ 3.0 A 2.5 1 2.0 v 2.0 1.5 -t 1.5 V 1.0 1.0 ------

0.5 0 2 4 6 8 10 2 4 6 8 10 Aspect Ratio (P) Aspect Ratio (0) Figure 4.5. Intracellularmovement of 500 nm endocytosed particles. (A and B) MSD (W2 ()), in longitudinal and transverse direction of tracer particles are plotted against lag time on a log-log scale for different aspect ratio cells. (C) The MSD of beads in longitudinaland transversedirection at r =1 s. MSD is observed to increase in longitudinaland decrease in transverse direction with an increase in aspect ratio. (D) Anisotropy in intracellular movement calculated in terms of ratio of MSD in longitudinaldirection and transverse direction at 'r=1 s increases with increase in aspect ratio. Errorbars representstandard error of mean (n =15)

We further quantify the anisotropy in intracellular motion in terms of ratio of MSD in

2 longitudinal and transverse direction, (Ax )Longitudinal /(AX2) Transverse at lag time T = I S

(figure 4.5 D). For cells with aspect ratio, p = 1-1.5, the intracellular motion appears to 44 be isotropic as the ratio of MSD in longitudinal and transverse direction,

2 2 (LX ) Longitudinal /(AX )Transverse is ~1; however, as the aspect ratio increases, this ratio deviates from 1 suggesting that the intracellular motion becomes anisotropic. Particularly, ratio of MSD in longitudinal and transverse direction,

2 (AX )LonLgitudinal /(2 Tratverse -3.5 for cells with aspect ratio, 8 = 7-12. These results show that the cytoskeletal reorganization induced by cell morphology not only causes mechanical anisotropy but also results in anisotropy of the intracellular movement.

4.2.5 Microtubules alignment modulates anisotropy in intracellular motion

As the particles are introduced into the cytoplasm by endocytosis, they are enveloped in a native phagosome [83] and thus, can interact with the cytoskeletal structure or adhere to motor proteins. Interaction with the cytoskeletal structures can sometimes lead to the tracers being caged and occasional tethering of the probe particles to the microtubules by motor proteins can cause directed transport. In addition, they also continuously fluctuate due to other motor activities and the omnipresent Brownian motion [7]. Majority of the intracellular fluctuations are typically attributed to a combination of thermal agitation and random active forces such as that generated by myosin II motors that bind with actin filaments to cause acto-myosin contractility; whereas, active directed intracellular transport is attributed to kinesin and dynein motor proteins that work along microtubules. In the present study, the MSD is quantified for lag times, r >0.1 s, hence, it is dominated by active forces of non-thermal origin [14]; this suggests that the anisotropicity in intracellular movement is possibly due to motor and other enzymatic activities. One of the major sources of intracellular fluctuations is acto-myosin contractility driven by myosin II motors [14, 60, 65, 66, 84].

45 A B

10.-2 Longitudinal Direction 10-2 Transverse Direction

"i 0 po.-. A p=3-7 A so E A pw3.7 *Pw7.12 .0AAE *g A *P.7-12

.11 - A *A AE * 600901 0-3

Cv0.

* p.1-1.5 V 100 . 0 . s=1.5-3 * A 1

100 10, T(sac) -C (sec) C D 10-2 Longitudinal Direction 102 Transverse Direction

* p=1-1.5 * 0=1.5-3 . P=1.5-3 A P=3-7 A p.3-7 A 0 =7-12 A *p.7-12

lo- 10-3 I &AAA&*111 s$log

101 100 101 101 100 10 T (sec) ' (sec)

Figure 4.6. (A-D) Intracellular movement of 500nm endocytosed particles treated in blebbistatin and nocodazole treated cells. MSD (Ax2 (v)), in longitudinal and transverse direction of tracerparticles are plotted against lag time on a log-log scalefor blebbistatin (A and B respectively) and nocodazole treated (C and D respectively) for different aspect ratio cells. Similar trend with reduced magnitudefor MSD in different directions with aspect ratio is observedfor blebbistatintreated cells as observedfor untreatedcells. Fornocodazole treated cells, the MSD curves collapse for different aspect ratio in both directions with similar magnitude suggesting anisotropy in intracellular movement can possibly be attributedto alignment of microtubules in longitudinaldirection.

To investigate if random intracellular fluctuations give rise to the observed anisotropic behavior of the intracellular motion, we use 25 pM blebbistatin to inhibit the activity of

46 myosin II motors. For all aspect ratios, a significant decrease in the magnitude of MSD of the tracer particles is observed in both directions after Myosin II inhibition (Figure 4.6 A and B). However, the MSD still increases in the longitudinal direction and decreases in the transverse direction with increase in aspect ratio, similar to the trend observed for untreated cells. This suggests that random intracellular fluctuations caused due to acto- myosin contractility is not a major player in causing anisotropic behavior of intracellular motion. Another possible source for this anisotropic behavior could be due to the contribution of directed transport along the microtubules. To test this hypothesis, we depolymerize the microtubule structure by treating cells with 20 pM of nocodazole. For nocodazole treated cells, all the MSD curves for different aspect ratios collapse in both longitudinal and transverse direction respectively (Figure 4.6 A and B). It is also observed that the MSD after nocodazole treatment exhibit largely subdiffusive behavior consistent with previous studies [85, 86]. Interestingly, the anisotropic behavior disappears and no significant difference in MSD is observed in between different directions. These results suggest that microtubules related dynamics is a major contributor to the observed anisotropy in movement.

4.2.6. Cell aspect ratio regulates anisotropy in intracellular force Our results suggest that cytoskeletal reorganization due to changes in cell morphology leads to an anisotropy in intracellular forces. To confirm, we use Force Spectrum Microscopy (FSM) to measure the spectrum of forces for cells with different aspect ratios in both longitudinal and transverse directions. FSM can be used to directly measure the spectrum of aggregate fluctuating forces that drive the intracellular motion by combining the MSD of tracer particles and independent micromechanical measurements of the intracellular environment using (F2 (f))= IK(f) 2 (r 2 (f)). The force in the longitudinal direction increases monotonically with increase in the aspect ratio of cells, however, no significant change in the magnitude of force in the transverse direction is observed with increase in the cell aspect ratio (figure 4.7 A and B). Particularly, at 1 Hz, the longitudinal force fluctuation of cells with aspect ratio, p = 7-12 is -5 times stronger as compared to cells with aspect ratio 0 =1-1.5, however, the transverse force fluctuation shows no signi- 47 A B

Longitudinal Direction Trar nsverse Direction 10-25 r Ii 1026 10-25 1 10-2 z z 10" 1 0-27 1 A r 1028 I - 1.5 I - 9 r 10-a 0 A 1 0 2 IL. V r--p=1-1.5 V 1030 r--3.1-1.5 I *-1.5-3 :- 0 z1.5 -3 10-31 - P=3-7 1031 r -- 0=3.- -3-07-12 - 0=7-12 10-32 10-32 1 180 101 1OU i1 1 Frequency (Hz) Frequency (Hz) C D

U Longitudinal direction A Transverse directon N 10

0 A 8

6 U-

+N 4 V L V 2 -'- L-+------'------0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Aspect Ratio (0) Aspect Ratio () Figure 4.7. (A and B) Cytoplasmic force spectrum calculated from intracellular

2 2 movement and active microrheology measurement using (F (f)) = IK(f)1 (r 2(f )) in longitudinaland transverse direction. (C) The force acting on the tracerparticles in longitudinal and transverse direction at f = 1 Hz. Force is observed to increase in longitudinaland almost remains unchanged in transverse direction with an increase in aspect ratio. (D) Anisotropy in intracellulardynamics is calculatedin terms of ratio offorce in longitudinaland transverse direction at f =1 Hz increases with increase in aspect ratio. Errorbars: SEM (n =15)

-ficant change (figure 4.7 C and D). Our force measurements also reveal an overall increase in the intracellular force when the cell aspect ratio increases. Furthermore, we

48 quantify the anisotropy in intracellular forces in terms of ratio of forces in longitudinal

2 and transverse direction, (F2 Longitudinal /(F ) .nsese at frequencyf= 1 Hz (figure 4.7 D).

The intracellular force fluctuations appear to be isotropic for cells with aspect ratio, P = 1-1.5, as the ratio of force in the longitudinal and transverse direction,

2 (F ) Longitudinal /(F2 )Transverse is ~1; however, the intracellular force fluctuations becomes anisotropic as the cell aspect ratio increases. The ratio of force in the longitudinal and transverse direction increases to -12 for cells with aspect ratio, p = 7-12. This shows that the cytoskeletal reorganization induced by cell morphology results in anisotropic forces.

4.3 Discussion

Cytoplasm of a living cell experiences significant redistribution of the cytoskeletal components such as actin and microtubules while undergoing morphological changes, in particular when the cell shape deviates from isotropicity. This induces an anisotropic behavior in both mechanics and dynamics of the cytoplasm which becomes evident in elongated cells. We use micro-contact printing to confine cells in different aspect ratios and first measure the local orientation of actin filaments and microtubules. Control cells with aspect ratio, p = 1-1.5, have randomly distributed actin filaments and microtubules suggesting an isotropic distribution, however, as the aspect ratio increases, fibers preferentially align in the longitudinal direction (figure 4.2). This causes a structural anisotropy of the cytoplasm resulting in a directionally dependent intracellular mechanics and dynamics. Our active microrheology measurements using optical tweezers show that control cells with aspect ratio, p = 1-1.5, have a similar value of intracellular stiffness in both longitudinal and transverse direction indicating an isotropic behavior. As the cell aspect ratio increases, the intracellular mechanics deviates from isotropicity showing an increase in stiffness in both longitudinal and transverse directions with different rates; intracellular stiffness increases faster in the longitudinal direction in comparison to the transverse direction with increase in cell aspect ratio (figure 4.3). This can be explained by the fact that mechanical stress in the plane parallel to the cytoskeletal fibers primarily results in the stretching of the fibers whereas in the plane perpendicular to the fibers the

49 deformation is dominated by bending. The bending modulus of major cytoskeletal fibers, such as F-actin and microtubule, has been shown to be significantly lower compared to its stretching elastic modulus and thus, results in a greater stiffness in the longitudinal direction for elongated cells [87-90]. Moreover, to investigate the potential cause of the increase in stiffness in both directions, we measure the volume of cells with different aspect ratios. We find that an increase in the cell aspect ratio results in a reduction of cell volume (figure 4.4). The observed increase in stiffness with reduction in cell volume is consistent with previous findings where cell volume reduction due to cellular water efflux increased the cytoplasmic stiffness by increasing the concentration of the intracellular components [68. 82]. Moreover, we find that with increase in the aspect ratio of cells, the nucleus also becomes elongated and the volume of nucleus decreases. Interestingly, the nuclear volume remains proportional to the cell volume (figure 4.4 C). The reduction in nuclear volume can possibly have implications in gene expression suggesting that cell morphology change may affect cell biology through changes in nuclear shape and volume. Indeed, previous studies have shown that cell and nuclear shape do play a role in influencing biological processes [15, 91-94]. It is evident that changes in cell morphology induces cytoskeletal remodeling (figure 4.5) and as molecular motors work in conjunction with the cytoskeletal fibers, this could possibly change the intracellular movement. By quantifying the motion of 500 nm tracer particles in terms of MSD, we show that the intracellular movement also becomes anisotropic for elongated cells. The cells with aspect ratio, p = 1-1.5, behaves as an isotropic material as the MSD in both longitudinal and transverse direction is of similar magnitude. However, as the cell aspect ratio increases we observe a marked increase of MSD in the longitudinal direction and decrease in the transverse direction demonstrating that the intracellular motion becomes anisotropic (figure 4.5). This behavior of MSD can be explained with our aggregate intracellular force measurements quantified using FSM. The intracellular force in the longitudinal direction increases with increasing aspect ratio. In fact, this increase in the force which drives the intracellular movement is more significant compared to the increase in resistance quantified in terms of stiffness, thereby,

50 increasing the MSD in the longitudinal direction with increase in aspect ratio. The force in the transverse direction, however, remains constant as the aspect ratio increases therefore, increase in stiffness in this direction reduces the MSD correspondingly. FSM also reveals that for the control cells with aspect ratio P = 1-1.5, the intracellular forces in longitudinal and transverse direction are of comparable magnitude; this result further confirms that these cells have isotropic dynamics (figure 4.7). However, as the aspect ratio of the cells increases, they deviate from isotropicity with an increase in intracellular forces in the longitudinal direction with no significant change in the transverse direction (Figure 7) showing that anisotropy in intracellular force fluctuations can be caused as a result of changes in cell morphology. Furthermore, to check the origin of the anisotropy in intracellular fluctuations we first treat the cells with blebbistatin to inhibit the activity of myosin II motors which are generally responsible for acto-myosin contractility. Blebbistatin treated cells show a significantly reduced MSD of tracer beads, however, the anisotropic behavior observed with change in aspect ratio remains, similar to that of untreated cells (figure 4.6 A and B). This suggests that activity of myosin II motors or acto-myosin contractility indeed contribute to intracellular fluctuations, however, is not a major player in regulating anisotropic movement in the cell. This result is consistent with previous findings that myosin II activity results in random fluctuating movement in both living cells and reconstituted actin networks [13, 14, 44, 45]. However, when we depolymerize the microtubules using nocodazole, we observe that the MSD significantly reduces and exhibits a subdiffusive behavior consistent with previous observations [85, 86]. This is because the beads are endocytosed into the cell and in the absence of directed transport there is a higher chance of them being caged within the cellular structures. More interestingly, the MSDs depict similar magnitude in both directions for all cells with varying aspect ratios (figure 4.6 C and D); these results indicate that the anisotropy in intracellular movement observed for elongated cells could be as a result of forces due to molecular motors working along the microtubules. In conclusion, our results systematically show that cell morphology is a critical regulator of anisotropicity of mechanics, dynamics, and forces within the cytoplasm. We

51 demonstrate that the anisotropy in mechanics arises as a consequence of the alignment of cytoskeletal components and the anisotropy in dynamics is majorly due to the generation of anisotropic forces produced by molecular motors working in combination with the microtubules. Our results suggest that it is important to consider the directional dependence of intracellular mechanics, dynamics and forces under the conditions when the cell shape deviates from isotropicity. In particular, it could have major implications in processes such as cancer cell migration, division, chemotaxis, embryogenesis where cell polarity is induced.

52 Bibliography

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