We formulated a spatially resolved model to estimate forces exerted by a polymerizing actin meshwork on an invagination of the plasma membrane during endocytosis in yeast cells. The model, which approximates the actin meshwork as a visco-active gel exerting forces on a rigid spherocylinder representing the endocytic invagination, is tightly constrained by experimental data. Simulations of the model produce forces that can overcome resistance of turgor pressure in yeast cells. Strong forces emerge due to the high density of polymerized actin in the vicinity of the invagination and because of entanglement of the meshwork due to its dendritic structure and cross-linking. The model predicts forces orthogonal to the invagination that are consistent with formation of a flask shape, which would diminish the net force due to turgor pressure. Simulations of the model with either two rings of nucleation-promoting factors (NPFs) as in fission yeast or a single ring of NPFs as in budding yeast produce enough force to elongate the invagination against the turgor pressure.

To understand shapes and movements of cells undergoing lamellipodial motility, we systematically explore minimal free-boundary models of actin-myosin contractility consisting of the force-balance and myosin transport equations. The models account for isotropic contraction proportional to myosin density, viscous stresses in the actin network, and constant-strength viscous-like adhesion. The contraction generates a spatially graded centripetal actin flow, which in turn reinforces the contraction via myosin redistribution and causes retraction of the lamellipodial boundary. Actin protrusion at the boundary counters the retraction, and the balance of the protrusion and retraction shapes the lamellipodium. The model analysis shows that initiation of motility critically depends on three dimensionless parameter combinations, which represent myosin-dependent contractility, a characteristic viscosity-adhesion length, and a rate of actin protrusion. When the contractility is sufficiently strong, cells break symmetry and move steadily along either straight or circular trajectories, and the motile behavior is sensitive to conditions at the cell boundary. Scanning of a model parameter space shows that the contractile mechanism of motility supports robust cell turning in conditions where short viscosity-adhesion lengths and fast protrusion cause an accumulation of myosin in a small region at the cell rear, destabilizing the axial symmetry of a moving cell.

Electroporation is of interest for many drug-delivery and gene-therapy applications. Prior studies have shown that a two-pulse-electroporation protocol consisting of a short-duration, high-voltage first pulse followed by a longer, low-voltage second pulse can increase delivery efficiency and preserve viability. In this work the effects of the field strength of the first and second pulses and the inter-pulse delay time on the delivery of two different-sized Fluorescein-Dextran (FD) conjugates are investigated. A series of two-pulse-electroporation experiments were performed on 3T3-mouse fibroblast cells, with an alternating-current first pulse to permeabilize the cell, followed by a direct-current second pulse. The protocols were rationally designed to best separate the mechanisms of permeabilization and electrophoretic transport. The results showed that the delivery of FD varied strongly with the strength of the first pulse and the size of the target molecule. The delivered FD concentration also decreased linearly with the logarithm of the inter-pulse delay. The data indicate that membrane resealing after electropermeabilization occurs rapidly, but that a non-negligible fraction of the pores can be reopened by the second pulse for delay times on the order of hundreds of seconds. The role of the second pulse is hypothesized to be more than just electrophoresis, with a minimum threshold field strength required to reopen nano-sized pores or defects remaining from the first pulse. These results suggest that membrane electroporation, sealing, and re-poration is a complex process that has both short-term and long-term components, which may in part explain the wide variation in membrane-resealing times reported in the literature.

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Cytokinesis is the fundamental and ancient cellular process by which one cell physically divides into two. Cytokinesis in animal and fungal cells is achieved by contraction of an actomyosin cytoskeletal ring assembled in the cell cortex, typically at the cell equator. Cytokinesis is essential for the development of fertilized eggs into multicellular organisms and for homeostatic replenishment of cells. Correct execution of cytokinesis is also necessary for genome stability and the evasion of diseases including cancer. Cytokinesis has fascinated scientists for well over a century, but its speed and dynamics make experiments challenging to perform and interpret. The presence of redundant mechanisms is also a challenge to understand cytokinesis, leaving many fundamental questions unresolved. For example, how does a disordered cytoskeletal network transform into a coherent ring? What are the long-distance effects of localized contractility? Here, we provide a general introduction to 'modeling for biologists', and review how agent-based modeling and continuum mechanics modeling have helped to address these questions.