A Dynamic Biochemomechanical Model of Geometry-Confined Cell Spreading

On the significance of membrane unfolding in mechanosensitive cell spreading: Its individual and synergistic effects

Mechanosensitivity of cell spread area to substrate stiffness has been established both through experiments and different types of mathematical models of varying complexity including both the mechanics and biochemical reactions in the cell. What has not been addressed in previous mathematical models is the role of cell membrane dynamics on cell spreading, and an investigation of this issue is the goal of this work. We start with a simple mechanical model of cell spreading on a deformable substrate and progressively layer mechanisms to account for the traction dependent growth of focal adhesions, focal adhesion induced actin polymerization, membrane unfolding/exocytosis and contractility. This layering approach is intended to progressively help in understanding the role each mechanism plays in reproducing experimentally observed cell spread areas. To model membrane unfolding we introduce a novel approach based on defining an active rate of membrane deformation that is dependent on membrane tension. Our modeling approach allows us to show that tension-dependent membrane unfolding plays a critical role in achieving the large cell spread areas experimentally observed on stiff substrates. We also demonstrate that coupling between membrane unfolding and focal adhesion induced polymerization works synergistically to further enhance cell spread area sensitivity to substrate stiffness. This enhancement has to do with the fact that the peripheral velocity of spreading cells is associated with contributions from the different mechanisms by either enhancing the polymerization velocity at the leading edge or slowing down of the retrograde flow of actin within the cell. The temporal evolution of this balance in the model corresponds to the three-phase behavior observed experimentally during spreading. In the initial phase membrane unfolding is found to be particularly important.

Biomechanical model of cells probing the myosin-II-independent mechanosensing mechanism

Mechanosensing of cells to extracellular matrix (ECM) is highly active and plays a crucial role in various physiological processes. Growing numbers of studies provide evidence that cell sensitivity to ECM stiffness is a complex stress-strain feedback process. However, the mechanisms that rule this process are still not fully known. Here, an alternative mechanosensing scheme of cells, which is different from the previous myosin-II-based mechanisms, is proposed by employing the tension in cortical cytoskeletons (CSKs) as a force module to probe the substrate. The molecular mechanotransduction from cortical CSKs, through actin filaments and focal adhesions, and finally to the substrate, is mechanically modeled to scale the dynamic traction forces of cells. The developed model captures the characteristic spread of cells with respect to ECM stiffness whereby the spread is fully developed on a stiff substrate but not on a soft one. Furthermore, durotactic migration of cells on an elastic-gradient substrate is successfully modeled by the current method. The cells are concluded to migrate, actuated by the polarized traction forces from the stiffness gradient of the substrate and the stiffness matching between cells and substrate. Finally, the cells are proposed to actively target the preferred substrate by following a rule of mechanical matching between cells and substrate. This study provides a theoretical tool to advance our knowledge regarding the passive mechanical properties and the active sensing of cells, and further promotes the discovery of mechanosensing mechanisms as well as the material design for embryonic development and tissue homeostasis.

Mesoscopic dynamic model of epithelial cell division with cell-cell junction effects

Cell division is central for embryonic development, tissue morphogenesis, and tumor growth. Experiments have evidenced that mitotic cell division is manipulated by the intercellular cues such as cell-cell junctions. However, it still remains unclear how these cortical-associated cues mechanically affect the mitotic spindle machinery, which determines the position and orientation of the cell division. In this paper, a mesoscopic dynamic cell division model is established to explore the integrated regulations of cortical polarity, microtubule pulling forces, cell deformability, and internal osmotic pressure. We show that the distributed pulling forces of astral microtubules play a key role in encoding the instructive cortical cues to orient and position the spindle of a dividing cell. The present model can not only predict the spindle orientation and position, but also capture the morphological evolution of cell rounding. The theoretical results agree well with relevant experiments both qualitatively and quantitatively. This work sheds light on the mechanical linkage between cell cortex and mitotic spindle, and holds potential in regulating cell division and sculpting tissue morphology.

An Active Biomechanical Model of Cell Adhesion Actuated by Intracellular Tensioning-Taxis

Cell adhesion to the extracellular matrix (ECM) is highly active and plays a crucial role in various physiological functions. The active response of cells to physicochemical cues has been universally discovered in multiple microenvironments. However, the mechanisms to rule these active behaviors of cells are still poorly understood. Here, we establish an active model to probe the biomechanical mechanisms governing cell adhesion. The framework of cells is modeled as a tensional integrity that is maintained by cytoskeletons and extracellular matrices. Active movement of the cell model is self-driven by its intrinsic tendency to intracellular tensioning, defined as tensioning-taxis in this study. Tensioning-taxis is quantified as driving potential to actuate cell adhesion, and the traction forces are solved by our proposed numerical method of local free energy adaptation. The modeling results account for the active adhesion of cells with dynamic protruding of leading edge and power-law development of mechanical properties. Furthermore, the morphogenesis of cells evolves actively depending on actin filaments alignments by a predicted mechanism of scaling and directing traction forces. The proposed model provides a quantitative way to investigate the active mechanisms of cell adhesion and holds the potential to guide studies of more complex adhesion and motion of cells coupled with multiple external cues.

Actin stress fiber dynamics in laterally confined cells

Multiple cellular processes are affected by spatial constraints from the extracellular matrix and neighboring cells. In vitro experiments using defined micro-patterning allow for in-depth analysis and a better understanding of how these constraints impact cellular behavior and functioning. Herein we focused on the analysis of actin cytoskeleton dynamics as a major determinant of mechanotransduction mechanisms in cells. We seeded primary human umbilical vein endothelial cells onto stripe-like cell-adhesive micro-patterns with varying widths and then monitored and quantified the dynamic reorganization of actin stress fibers, including fiber velocities, orientation and density, within these live cells using the cell permeable F-actin marker SiR-actin. Although characteristic parameters describing the overall stress fiber architecture (average orientation and density) were nearly constant throughout the observation time interval of 60 min, we observed permanent transport and turnover of individual actin stress fibers. Stress fibers were more strongly oriented along stripe direction with decreasing stripe width, (5° on 20 μm patterns and 10° on 40 μm patterns), together with an overall narrowing of the distribution of fiber orientation. Fiber dynamics was characterized by a directed movement from the cell edges towards the cell center, where fiber dissolution frequently took place. By kymograph analysis, we found median fiber velocities in the range of 0.2 μm/min with a weak dependence on pattern width. Taken together, these data suggest that cell geometry determines actin fiber orientation, while it also affects actin fiber transport and turnover.