Reversible elastic phase field approach and application to cell monolayers

The role of the nucleus for cell mechanics: an elastic phase field approach

The nucleus of eukaryotic cells typically makes up around 30% of the cell volume and has significantly different mechanics, which can make it effectively up to ten times stiffer than the surrounding cytoplasm. Therefore it is an important element for cell mechanics, but a quantitative understanding of its mechanical role during whole cell dynamics is largely missing. Here we demonstrate that elastic phase fields can be used to describe dynamical cell processes in adhesive or confining environments in which the nucleus acts as a stiff inclusion in an elastic cytoplasm. We first introduce and verify our computational method and then study several prevalent cell-mechanical measurement methods. For cells on adhesive patterns, we find that nuclear stress is shielded by the adhesive pattern. For cell compression between two parallel plates, we obtain force-compression curves that allow us to extract an effective modulus for the cell-nucleus composite. For micropipette aspiration, the effect of the nucleus on the effective modulus is found to be much weaker, highlighting the complicated interplay between extracellular geometry and cell mechanics that is captured by our approach. We also show that our phase field approach can be used to investigate the effects of Kelvin-Voigt-type viscoelasticity and cortical tension.

The analytical solution to the migration of an epithelial monolayer with a circular spreading front and its implications in the gap closure process

The coordinated behaviors of epithelial cells are widely observed in tissue development, such as re-epithelialization, tumor growth, and morphogenesis. In these processes, cells either migrate collectively or organize themselves into specific structures to serve certain purposes. In this work, we study a spreading epithelial monolayer whose migrating front encloses a circular gap in the monolayer center. Such tissue is usually used to mimic the wound healing process in vitro. We model the epithelial sheet as a layer of active viscous polar fluid. With an axisymmetric assumption, the model can be analytically solved under two special conditions, suggesting two possible spreading modes for the epithelial monolayer. Based on these two sets of analytical solutions, we assess the velocity of the spreading front affected by the gap size, the active intercellular contractility, and the purse-string contraction acting on the spreading edge. Several critical values exist in the model parameters for the initiation of the gap closure process, and the purse-string contraction plays a vital role in governing the gap closure kinetics. Finally, the instability of the morphology of the spreading front was studied. Numerical calculations show how the perturbated velocities and the growth rates vary with respect to different model parameters.

Cell size and actin architecture determine force generation in optogenetically activated cells

Adherent cells use actomyosin contractility to generate mechanical force and to sense the physical properties of their environment, with dramatic consequences for migration, division, differentiation, and fate. However, the organization of the actomyosin system within cells is highly variable, with its assembly and function being controlled by small GTPases from the Rho family. To understand better how activation of these regulators translates into cell-scale force generation in the context of different physical environments, here we combine recent advances in non-neuronal optogenetics with micropatterning and traction force microscopy on soft elastic substrates. We find that, after whole-cell RhoA activation by the CRY2/CIBN optogenetic system with a short pulse of 100 ms, single cells contract on a minute timescale in proportion to their original traction force, before returning to their original tension setpoint with near perfect precision, on a longer timescale of several minutes. To decouple the biochemical and mechanical elements of this response, we introduce a mathematical model that is parametrized by fits to the dynamics of the substrate deformation energy. We find that the RhoA response builds up quickly on a timescale of 20 s, but decays slowly on a timescale of 50 s. The larger the cells and the more polarized their actin cytoskeleton, the more substrate deformation energy is generated. RhoA activation starts to saturate if optogenetic pulse length exceeds 50 ms, revealing the intrinsic limits of biochemical activation. Together our results suggest that adherent cells establish tensional homeostasis by the RhoA system, but that the setpoint and the dynamics around it are strongly determined by cell size and the architecture of the actin cytoskeleton, which both are controlled by the extracellular environment.