Modeling the dynamics of actin and myosin during bleb stabilization.

The actin cortex is very dynamic during migration of eukaryotes. In cells that use blebs as leading-edge protrusions, the cortex reforms beneath the cell membrane (bleb cortex) and completely disassembles at the site of bleb initiation. Remnants of the actin cortex at the site of bleb nucleation are referred to as the actin scar. We refer to the combined process of cortex reformation along with the degradation of the actin scar during bleb-based cell migration as bleb stabilization. The molecular factors that regulate the dynamic reorganization of the cortex are not fully understood. Myosin motor protein activity has been shown to be necessary for blebbing, with its major role associated with pressure generation to drive bleb expansion. Here, we examine the role of myosin in regulating cortex dynamics during bleb stabilization. Analysis of microscopy data from protein localization experiments in Dictyostelium discoideum cells reveals a rapid formation of the bleb's cortex with a delay in myosin accumulation. In the degrading actin scar, myosin is observed to accumulate before active degradation of the cortex begins. Through a combination of mathematical modeling and data fitting, we identify that myosin helps regulate the equilibrium concentration of actin in the bleb cortex during its reformation by increasing its dissasembly rate. Our modeling and analysis also suggests that cortex degradation is driven primarily by an exponential decrease in actin assembly rate rather than increased myosin activity. We attribute the decrease in actin assembly to the separation of the cell membrane from the cortex after bleb nucleation.

In vitro experiments and kinetic models of Arabidopsis pollen hydration mechanics show that MSL8 is not a simple tension-gated osmoregulator.

Pollen, a neighbor-less cell containing the male gametes, undergoes mechanical challenges during plant sexual reproduction, including desiccation and rehydration. It was previously shown that the pollen-specific mechanosensitive ion channel MscS-like (MSL)8 is essential for pollen survival during hydration and proposed that it functions as a tension-gated osmoregulator. Here, we test this hypothesis with a combination of mathematical modeling and laboratory experiments. Time-lapse imaging revealed that wild-type pollen grains swell, and then they stabilize in volume rapidly during hydration. msl8 mutant pollen grains, however, continue to expand and eventually burst. We found that a mathematical model, wherein MSL8 acts as a simple-tension-gated osmoregulator, does not replicate this behavior. A better fit was obtained from variations of the model, wherein MSL8 inactivates independent of its membrane tension gating threshold or MSL8 strengthens the cell wall without osmotic regulation. Experimental and computational testing of several perturbations, including hydration in an osmolyte-rich solution, hyper-desiccation of the grains, and MSL8-YFP overexpression, indicated that the cell wall strengthening model best simulated experimental responses. Finally, the expression of a nonconducting MSL8 variant did not complement the msl8 overexpansion phenotype. These data indicate that contrary to our hypothesis and to the current understanding of MS ion channel function in bacteria, MSL8 does not act as a simple membrane tension-gated osmoregulator. Instead, they support a model wherein ion flux through MSL8 is required to alter pollen cell wall properties. These results demonstrate the utility of pollen as a cellular scale model system and illustrate how mathematical models can correct intuitive hypotheses.

Computational estimates of mechanical constraints on cell migration through the extracellular matrix.

Cell migration through a three-dimensional (3D) extracellular matrix (ECM) underlies important physiological phenomena and is based on a variety of mechanical strategies depending on the cell type and the properties of the ECM. By using computer simulations of the cell's mid-plane, we investigate two such migration mechanisms-'push-pull' (forming a finger-like protrusion, adhering to an ECM node, and pulling the cell body forward) and 'rear-squeezing' (pushing the cell body through the ECM by contracting the cell cortex and ECM at the cell rear). We present a computational model that accounts for both elastic deformation and forces of the ECM, an active cell cortex and nucleus, and for hydrodynamic forces and flow of the extracellular fluid, cytoplasm, and nucleoplasm. We find that relations between three mechanical parameters-the cortex's contractile force, nuclear elasticity, and ECM rigidity-determine the effectiveness of cell migration through the dense ECM. The cell can migrate persistently even if its cortical contraction cannot deform a near-rigid ECM, but then the contraction of the cortex has to be able to sufficiently deform the nucleus. The cell can also migrate even if it fails to deform a stiff nucleus, but then it has to be able to sufficiently deform the ECM. Simulation results show that nuclear stiffness limits the cell migration more than the ECM rigidity. Simulations show the rear-squeezing mechanism of motility results in more robust migration with larger cell displacements than those with the push-pull mechanism over a range of parameter values. Additionally, results show that the rear-squeezing mechanism is aided by hydrodynamics through a pressure gradient.

Unite to divide - how models and biological experimentation have come together to reveal mechanisms of cytokinesis.

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.

Intracellular Pressure Dynamics in Blebbing Cells.

Blebs are pressure-driven protrusions that play an important role in cell migration, particularly in three-dimensional environments. A bleb is initiated when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol toward the area of detachment and local expansion of the cell membrane. Recent experiments involving blebbing cells have led to conflicting hypotheses regarding the timescale of intracellular pressure propagation. The interpretation of one set of experiments supports a poroelastic model of the cytoplasm that leads to slow pressure equilibration when compared to the timescale of bleb expansion. A different study concludes that pressure equilibrates faster than the timescale of bleb expansion. To address this discrepancy, a dynamic computational model of the cell was developed that includes mechanics of and the interactions among the cytoplasm, the actin cortex, the cell membrane, and the cytoskeleton. The model results quantify the relationship among cytoplasmic rheology, pressure, and bleb expansion dynamics, and provide a more detailed picture of intracellular pressure dynamics. This study shows the elastic response of the cytoplasm relieves pressure and limits bleb size, and that both permeability and elasticity of the cytoplasm determine bleb expansion time. Our model with a poroelastic cytoplasm shows that pressure disturbances from bleb initiation propagate faster than the timescale of bleb expansion and that pressure equilibrates slower than the timescale of bleb expansion. The multiple timescales in intracellular pressure dynamics explain the apparent discrepancy in the interpretation of experimental results.

A computational model of bleb formation.

Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent interest has focused on cells that use blebbing for migrating through 3D fibrous matrices. In particular, metastatic cancer cells have been shown to use blebs for motility. A dynamic computational model of the cell is presented that includes mechanics of and the interactions between the intracellular fluid, the actin cortex and the cell membrane. The computational model is used to explore the relative roles in bleb formation time of cytoplasmic viscosity and drag between the cortex and the cytosol. A regime of values for the drag coefficient and cytoplasmic viscosity values that match bleb formation timescales is presented. The model results are then used to predict the Darcy permeability and the volume fraction of the cortex.

SIMULATING BIOCHEMICAL SIGNALING NETWORKS IN COMPLEX MOVING GEOMETRIES.

Signaling networks regulate cellular responses to environmental stimuli through cascades of protein interactions. External signals can trigger cells to polarize and move in a specific direction. During migration, spatially localized activity of proteins is maintained. To investigate the effects of morphological changes on intracellular signaling, we developed a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods to simulate the resulting advection-reaction-diffusion system. We then apply the method to several biochemical reaction networks in changing geometries. We found that a Turing instability can develop exclusively by cell deformations that maintain constant area. For a Turing system with a geometry-dependent single or double peak solution, simulations in a dynamically changing geometry suggest that a single peak solution is the only stable one, independent of the oscillation frequency. The method is also applied to a model of a signaling network in a migrating fibroblast.

A Cut Cell Method for Simulating Spatial Models of Biochemical Reaction Networks in Arbitrary Geometries.

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through the network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian cut cells and is second order in space and time. We use our method to simulate several models of signaling systems in realistic cell morphologies obtained from live cell images and examine the effects of geometry on signal transduction.