Theoretical study of stick-slip dynamics at the cell leading edge and cellular mechanosensing

De, Partho Sakha (2022) Theoretical study of stick-slip dynamics at the cell leading edge and cellular mechanosensing. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Partho Sakha De (15RS027)) 15RS027.pdf - Submitted Version Restricted to Repository staff only Download (12MB)

Abstract

Eukaryotic animal cells interact with the extracellular matrix through the formation of multimolecular protein assemblies known as focal adhesions, which serve the purpose of transmitting forces arising in the cell interior from acto-myosin contraction to the extracellular matrix. These adhesions form a physical linkage between the cell interior and extracellular matrix and play a major role in the execution of many cellular functions such as cell crawling, cell spread, substrate rigidity sensing and many other associated phenomena dependent on them such as wound healing, morphogenesis, durotaxis, embryonic development, cancer spread, tissue regeneration among others. The key players involved in this process are actin filaments, myosin motors and focal adhesions. Other phenomena observed in these processes include the likes of retrograde actin flow caused by myosin activity, force-dependent dissociation and binding of transmembrane receptor proteins with substrate ligands to form adhesion complexes and stick-slip motion emerging from the interplay between them. Stick-slip motion, which is strongly dependent on the stiffness of the extracellular matrix, has been observed at the leading edge of a crawling cell. Earlier modelling attempts at this phenomenon had presented working models for this phenomenon on typically elastic substrates. In this thesis, we develop a theoretical model for the dynamics at the leading edge of a cell. Our model is based on a pair of coupled reaction-diffusion equations representing the spatio-temporal evolution of the receptor-ligand densities at the cell leading edge and the reaction between them leading to the formation of focal adhesions at the cell-substrate interface. The model incorporates known phenomena such as retrograde flow of actin, myosin contractility, force-dependent assembly, and disassembly of focal adhesions coupled with cell-substrate interaction. The extracellular matrix in our model has been considered a Kelvin-Voight viscoelastic element to better represent the physical properties of the extracellular matrix. Our model not only captures the usually observed stick-slip motion at the cell leading edge but also highlights how the nature of the single bond force determines the nature of stick-slip jumps on substrates of varying rigidity. Our theory also provides an analytical understanding of how various parameters such as substrate stiffness, myosin activity, retrograde flow affect the duration of the stick-slip cycles. Interestingly, our model also predicts the existence of an ‘optimum’ substrate viscosity akin to already known ‘optimum’ substrate elastic stiffness that corresponds to the observation of maximum cell traction force and minimum actin retrograde flow, which had been hitherto unexplored. Transmission of acto-myosin contractile force to the substrate is essential for a variety of biological processes such as cell migration, cell spread, cell differentiation, cancer progression, et cetera. Focal adhesions arrest the retrograde flow of actin, which allows for the cell protrusions to propagate further by the force of actin polymerisation. Two entirely distinct responses of these focal adhesions with respect to variation in substrate stiffness are known. These responses give rise to the actin retrograde flow and the cell traction force to display either a biphasic or a monotonic dependence with increasing substrate rigidity. In the biphasic case, we observe maximum cell traction/ minimum actin flow at an intermediate value of extracellular matrix stiffness. Whereas in the monotonic case, traction force increases monotonically, and actin flow decreases monotonically with increasing substrate rigidity. In this thesis, we present a theoretical model for adhesion complexes at the cell leading edge, incorporating the novel approach of a force loading rate sensitive binding of the focal adhesion assembly. This model exhibits both the experimentally observed biphasic and monotonic dependence of actin flow and cell traction with increasing substrate rigidity. The competition between two system timescales, namely the binding timescale and the adhesion cluster lifetime timescale, at high substrate rigidities is found to be the determining factor behind the biphasic or monotonic behaviour. A few rudimentary calculations involving competition between the relevant timescales was found to give a good analytical approximation of the ’optimum’ substrate rigidity for the biphasic case. We also further investigated how substrate viscoelastic properties regulate these behaviours and modulate the cell response, including loss of cell sensitivity to variation in substrate viscosity on stiff substrates and vice-versa. The occurrence of stick-slip phenomena at the leading edge of a crawling cell is quite well known. Power law distributions have also been observed to arise in systems that exhibit stickslip motion. The emergence of a power law distribution in event sizes suggests that the physical mechanisms behind small and large events across multiple length scales are governed by the same physical laws. In this thesis, we study the statistical distribution of the bond breaking avalanche sizes occurring during the stick-slip motion at the cell leading edge. For this purpose, we develop the master equation of our stochastic model, simulate it using the Kinetic Monte Carlo method, and study the distribution of bond breaking event sizes over many stick-slip cycles. Here, we observe that the majority of the event sizes are distributed according to a power law. However, extreme events of large sizes appear as Dragon Kings (DK). These DK events correspond to the system-wide bond breaking events occurring in the ‘slip’ phase of the stick-slip cycle. Taking long time series data over numerous stick-slip cycles also shows that the DK event sizes are normally distributed. In this thesis, we investigated the effect of various cell and substrate parameters on the power law exponents and the distribution of the DK events. The scaling relations for the smaller events in the power law and those in the Gaussian are found to be different. Surface viscoelasticity was also found to cause the disappearance of the DK points in the distribution, allowing a power law to be sufficient to explain the distribution of bond breaking events of all sizes. Apart from substrate elastic stiffness and viscous properties, the density of ligands on the substrate have also been known to affect the behaviour and fate of the adhesions, thus modulating cell response. In the final part of this thesis, we study how the variation of substrate ligand density affects the response of the adhesion complexes and how substrate ligand distribution affects cell response to substrate elastic modulus. For this purpose, we simulate using the Kinetic Monte Carlo method, a modified version of the stochastic model, which has been tweaked to take into account the variation in the distribution of ligands on the substrate. From our simulations, we observe that similar to experimental observations; there exists an intermediate ‘optimum’ substrate ligand density which results in the most efficient transmission of cell cytoskeletal force to the substrate. This intermediate substrate ligand density results in maximum cell traction and minimum actin flow being observed across the adhesion cluster. Stark differences have been observed in cell response to variation in substrate ligand density and substrate stiffness, depending on the nature of force dependent bond dissociation pathways, namely catch versus slip adhesion bonds.

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