Session B26: Mechanics of Cells and Tissues Across Scales II

Force generation and self-organization in mitosis

Life on earth depends on cells’ ability to duplicate. In order to divide successfully, cells must solve fascinating physics problems. A key step in cell division is ensuring that each of the daughter cells inherits a single copy of the genetic material. In eukaryotes, a self-organized machine called the mitotic spindle physically move the chromosomes. The spindle is composed of microtubules, molecular motors, and associated molecules. We are using theory, simulation, and experiment to understand how the mitotic spindle self-assembles and achieves the correct size, and how the spindle organizes and moves chromosomes. This talk will discuss how force is generated by motors, crosslinkers, and chromosomes over time during mitosis to correctly assemble the spindle. Depending on the dynamics of spindle molecules and microtubule-chromosome attachments, overall spindle length can be relatively constant in time, or undergo large fluctuations. I will explain our current understanding of spindle length stabilization.

  

Intrinsic time-scales of active forces control the dynamics of soft living matter

Living cells are crowded with active agents which consume energy and perform work on their surrounding environment, constantly keeping the system out of thermodynamic equilibrium. These locally exerted active forces are propagated to larger distances by the cytoskeleton and the cytoplasm. Such activity is believed to play an important role in vital intracellular processes such as transport. The active agents involved in these processes - molecular motors - are characterized by their intrinsic correlation time, typically of the order of seconds. While the significance of these correlation times is not well understood, we argue that they may be tuned to improve the efficiency of particular processes taking place in the cell. We investigate this by analyzing a model comprised of elastic network embedded in a viscous fluid and driven by a collection of stochastic, time-correlated forces. We show how the interplay between the correlation times of the active agents and the relaxation times of the system can lead to qualitatively different behaviors at different length scales.   

Mechanical properties of intermediate filament networks under compression

Cell motility is a fundamental process that contributes to building and maintaining tissues as well as the progression of diseases such as fibrosis and cancer. The material properties of cells and tissues are a central feature of this process. The mammalian cytoskeleton is made up of a network of (semi-)flexible biopolymers, including actin, microtubules, and intermediate filaments. While the mechanical responses of fibrous biopolymer networks to shear deformation have been studied in great detail, their response to uniaxial loading remains poorly understood. Here, we study the mechanical response of reconstituted polymer networks comprised of the intermediate filament proteins vimentin and keratin using a parallel-plate rheometer. Our results indicate that reconstituted vimentin and keratin networks stiffen under axial compression, with cation concentration mediating network crosslinking. This stiffening contrasts with other biopolymer networks which compression soften but coincides with the compression stiffening behavior of cells themselves. These results motivate future work in cytoskeletal mechanics as well as the general phenomenon of compression stiffening in biopolymer environments.   

Cytoskeletal Regulation of Three-Dimensional Epithelial Cell Shape

Three-dimensional force distribution within the actin cytoskeleton of epithelial tissue regulates cell shape. While two-dimensional cell shape has been well characterized and heavily studied, three-dimensional cell shape regulation is less well understood despite its critical role in large scale epithelial processes such as invagination. By examining the relationship between cell height, density and biological components of the actin cytoskeleton, we explore the mechanisms by which epithelial cells regulate shape and volume. We observe that while cell density is not a strong indicator of epithelial height, osmotic shock drastically decreases both tissue height and cell volume while leaving the lateral shape of cells in the tissue undisturbed.
  

Physical limits to sensing material properties

Constitutive relations describe how materials respond to external stimuli such as forces. All materials respond heterogeneously at small scales, which limits what a localized sensor can discern about the global constitution of a material. In this talk, I will present the limits to the precision of such constitutional sensing for sensors embedded in disordered media. Our results reveal how one can construct microscopic devices capable of sensing near these physical limits, e.g. for medical diagnostics. I will show how our theoretical framework can be applied to an experimental system by estimating a bound on the precision of cellular mechanosensing in a biopolymer network.   

Cell shape as a window into cell state

The shape of an adherent cell spread on a surface depends upon the biophysical properties of the cytoskeleton. However these are controlled by biochemical circuits and ultimately by gene expression. While shape of a single cell is dynamic, enough evidence has accumulated that cells in the same state adopt shapes that are, in a statistical sense, similar to each other, and distinguishable from cells in different states. If we could understand the major determinants of cell shape, we may be able to infer aspects of cell state merely by observing cell shape. We have imaged thousands of cells in different experimental conditions and have developed a large number of morphological parameters to quantify cell shape and cytoskeletal morphology. Using these we show that quantifiers of cell shape and cytoskeletal texture can be used to discriminate between different cell states. Projections of the data to lower-dimensional shape space can be used to distinguish between similar and dissimilar changes in shape. Pharmacological drugs that perturb the cytoskeletal can help to identify some of the biochemical circuits that control cell shape. Linking results of our experiments and data analysis with previous molecular biology studies on cytoskeletal proteins that affect cell shape, coupled with mathematical modeling, allow us to deconstruct some of the determinants of cell shape.   

The Morphodynamics of 3D Migrating Cancer Cells

During cancer cell migration, cells on a 2D surface experience uniform mechanical cues whereas in a fibrous 3D environment there exists heterogeneity at cellular and sub-cellular levels, leading to dramatically different invasion strategies. Here, we physically characterize morphodynamics (the temporal fluctuations of cell shape) rather than real-space migration alone. By studying morphodynamics, we show that 3D cell migration is accompanied by spontaneous and rapid shape changes regulated by the extra-cellular matrix (ECM), in contrast to 2D migration. We employ machine learning to classify cell shape into five different morphological phenotypes corresponding to different migration modes. We systematically characterize the phenotype evolutions including occurrence probability, dwell time, transition flux, and 3D migrational characteristics. By tuning ECM density, pore-size, and fiber-alignment, we show local mechanical influence on migration mode switching. We find mechanosensing mediated by rho-signaling is important to the resultant morphodynamics. We demonstrate cell morphodynamics as an information-rich biomarker that is directly regulated by cell mechanosensing and contributes critically to the cell motility.   

Switching between optimum substrate rigidity and focal adhesion reinforcement at the cell leading edge

It’s well known that substrate mechanical properties strongly influence cell behaviour and fate. There exists two well documented but contrasting responses of cells to substrate rigidity, namely the biphasic and the monotonic relationship of traction force and retrograde flow velocity with substrate stiffness. We have developed a theoretical model for the dynamics at the leading edge of a cell placed on a viscoelastic substrate, involving a pair of coupled reaction-diffusion equations. Motivated by experiments, the association and dissociation rates of focal adhesions are taken to be force dependent. Our model not only captures the experimentally observed stick-slip dynamics at the cell edge, but also can predict switching between both the biphasic relationship i.e. the presence of an optimum substrate stiffness where the retrograde flow is minimum and traction force is maximum; and the monotonic relationship between retrograde flow, traction force and substrate stiffness. Besides, our theory also elucidates the role played by substrate viscosity, predicts the presence of optimum viscosity as well as states the condition under which cellular rigidity sensing is lost.

Stick-slip dynamics of migrating cells on viscoelastic substrates
P. S. De and R. De
Phys. Rev. E 100, 012409 (2019)   

Mechanics of endocytosis under large osmotic pressure

In this talk, I will discuss membrane deformations powered by a point force under the condition of high pressure and low tension, which is rarely studied but directly relevant for endocytosis in yeast cells with a cell wall. I will show that the force-height relationship of membrane deformations under this condition is drastically different from that under conditions of high tension and low pressure. In addition, the boundary conditions at the attachment points of the membrane with the cell wall have dramatic effects on the force-height relationship. In particular, if the membrane is allowed to freely rotate at the attachment points, proteins that induced membrane curvature can lift the membrane off the cell wall without any external forces. This result is in sharp contrast with the conclusion of a previous study which adopted boundary conditions that fix the angle between the membrane and the cell wall at the attachment points. I will also discuss possible ways to pull the membrane off the cell wall against the high osmotic pressure with a small amount of force that can be provided by actin polymerization.   

Plasticity in vertex model of epithelial tissues

In order to properly develop living organisms are required to change and maintain shape. These properties exists in a class of materials called amorphous solids such as colloidal gels, emulsions and foams: they respond elastically when exposed to low external stress but at a critical value of stress they yield and permanently change shape, allowing them to retain the memory of past stresses. Could such plasticity play a role during biological morphogenesis? Motivated by this question in this work we study plastic properties of vertex model of epithelial tissues, in which mechanical properties of cells are prescribed and emerging tissue mechanics is obtained from their collective behaviour. We investigate mechanical properties of elementary plastic event, a so called T1 transition in which two pairs of cells exchange neighborship. We demonstrate that they are analogous to plastic events in amorphous solids and find that elastic interactions among T1 transitions lead to non-linear steady state rheology and mechanical stability in the vertex model that are the same as found in mesoscopic models of amorphous solids. Finally, we devise observables quantifying a ’distance’ to the critical stress in flowing vertex model and epithelial tissues.   

Loops versus lines and the compression stiffening of cells

Tissues exhibit a nonlinear phenomenon known as compression stiffening: an increase in moduli with increasing uniaxial compressive strain. Does such a phenomenon exist in single cells, which are the building blocks of tissues? One expects an individual cell to compression soften since the semiflexible biopolymer cytoskeletal network maintains the mechanical integrity of the cell. To the contrary, we find that mouse embryonic fibroblasts (mEFs) compression stiffen. To understand this finding, we uncover potential mechanisms for compression stiffening. First, we study a single semiflexible polymer loop modeling the actomyosin cortex enclosing a viscous medium modeled as an incompressible fluid. Second, we study a two-dimensional semiflexible polymer network interspersed with area-conserving loops, which are a proxy for vesicles and fluid-based organelles. Third, we study two-dimensional fiber networks with angular-constraining crosslinks. We find for the fiber network with area-conserving loops model that the stress-strain curves are sensitive to the packing fraction and size distribution of the area-conserving loops, thereby creating a mechanical fingerprint across different cell types. We make comparisons of these models with fibrin network experiments interlaced with beads.