Cell Mechanics: From Cytoskeletal Dynamics to Tissue-Scale Mechanical Phenomena

This dissertation explores the mechanics of living cells, integrating the role of intracellular activity to capture the emergent mechanical behavior of cells. The topics covered in this dissertation fall into three broad categories : (a) intracellular mechanics, (b) interaction of cells with the extracellular matrix and (c) collective mechanics of multicellular colonies. In part (a) I propose theoretical models for motor-filament interactions in the cell cytoskeleton, which is the site for mechanical force generation in cells. The models predict in a unified manner how contractility, dynamic instabilities and mechanical waves arise in the cytoskeleton by tuning the activity of molecular motors. The results presented in (a) holds relevance to a variety of cellular systems that behave elastically at long time scales, such as muscle sarcomeres, actomyosin stress fibers, adherent cells. In part (b) I introduce a continuum mechanical model for cells adherent to two-dimensional extracellular matrix, and discuss how cells can sense mechanical and geometrical cues from its surrounding matrix. The model provides an important step towards a unified theoretical description of the dependence of traction forces on cell size, actomyosin activity, matrix depth and stiffness, strength of focal adhesions and makes experimentally testable predictions. In part (c) we combine experiment and theory to reveal how intercellular adhesions modulate forces transmitted to the extracellular matrix. We find that In the absence of cadherin-based adhesions, cells within a colony appear to act independently, whereas with strong cadherin-based adhesions, the cell colony behaves like a liquid droplet wetting the substrate underneath. This work defines the importance of intercellular adhesions in coordinating mechanical activity of cell monolayers and has implications for the mechanical regulation of tissues during development, homeostasis, and disease

Controlling cell-matrix traction forces by extracellular geometry

We present a minimal continuum model of strongly adhering cells as active contractile isotropic media and use the model to study the effect of the geometry of the adhesion patch in controlling the spatial distribution of traction and cellular stresses. Activity is introduced as a contractile, hence negative, spatially homogeneous contribution to the pressure. The model shows that patterning of adhesion regions can be used to control traction stress distribution and yields several results consistent with experimental observations. Specifically, the cell spread area is found to increase with substrate stiffness and an analytic expression for the dependence is obtained for circular cells. The correlation between the magnitude of traction stresses and cell boundary curvature is also demonstrated and analyzed.Comment: 12 pages, 4 figure

Contractile stresses in cohesive cell layers on finite-thickness substrates

Using a minimal model of cells or cohesive cell layers as continuum active elastic media, we examine the effect of substrate thickness and stiffness on traction forces exerted by strongly adhering cells. We obtain a simple expression for the length scale controlling the spatial variation of stresses in terms of cell and substrate parameters that describes the crossover between the thin and thick substrate limits. Our model is an important step towards a unified theoretical description of the dependence of traction forces on cell or colony size, acto-myosin contractility, substrate depth and stiffness, and strength of focal adhesions, and makes experimentally testable predictions.Comment: 5 pages, 3 figure

Tension Remodeling Controls Topological Transitions in Epithelial Tissues

Cell neighbor exchanges play a critical role in regulating tissue fluidity during epithelial morphogenesis and repair. In vivo, these neighbor exchanges are often hindered by the formation of transiently stable four-fold vertices, which can develop into complex multicellular rosettes where five or more cell junctions meet. Despite their importance, the mechanical origins of multicellular rosettes have remained elusive, and current cellular models lack the ability to explain their formation and maintenance. Here we present a dynamic vertex model of epithelial tissues with strain-dependent tension remodeling and mechanical memory dissipation. We show that an increase in cell junction tension upon contraction and reduction in tension upon extension can stabilize higher-order vertices, temporarily stalling cell rearrangements. On the other hand, inducing mechanical memory dissipation via relaxation of junction strain and stress promotes the resolution of higher-order vertices, facilitating cell neighbor exchanges. We demonstrate that by tuning the rates of tension remodeling and mechanical memory dissipation, we can control topological transitions and tissue material properties, recapitulating complex cellular topologies seen in developing organisms.Comment: 31 pages; 4 movies. To view movies, please download and extract the gzipped tar source file listed under "Other formats

Size-regulated symmetry breaking in reaction-diffusion models of developmental transitions

The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organization. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction-diffusion driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analyzing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer-, or switch-like dynamics. By relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions.Comment: 11 pages, 5 figures, Perspective Articl