Response of an actin filament network model under cyclic stretching through a coarse grained Monte Carlo approach.

Cells are complex, dynamic systems that actively adapt to various stimuli including mechanical alterations. Central to understanding cellular response to mechanical stimulation is the organization of the cytoskeleton and its actin filament network. In this manuscript, we present a minimalistic network Monte Carlo based approach to model actin filament organization under cyclic stretching. Utilizing a coarse-grained model, a filament network is prescribed within a two-dimensional circular space through nodal connections. When cyclically stretched, the model demonstrates that a perpendicular alignment of the filaments to the direction of stretch emerges in response to nodal repositioning to minimize net nodal forces from filament stress states. In addition, the filaments in the network rearrange and redistribute themselves to reduce the overall stress by decreasing their individual stresses. In parallel, we cyclically stretch NIH 3T3 fibroblasts and find a similar cytoskeletal response. With this work, we test the hypothesis that a first-principles mechanical model of filament assembly in a confined space is by itself capable of yielding the remodeling behavior observed experimentally. Identifying minimal mechanisms sufficient to reproduce mechanical influences on cellular structure has important implications in a diversity of fields, including biology, physics, medicine, computer science, and engineering.

Evaluating spatial constraints in cellular assembly processes using a monte carlo approach.

Biomolecular behavior commonly involves complex sets of interacting components that are challenging to understand through solution-based chemical theories. Molecular assembly is especially intriguing in the cellular environment because of its links to cell structure in processes such as chemotaxis. We use a coarse-grained Monte Carlo simulation to elucidate the importance of spatial constraints in molecular assembly. We have performed a study of actin filament polymerization through this space-aware probabilistic lattice-based model. Quantitative results are compared with nonspatial models and show convergence over a wide parameter space, but marked divergence over realistic levels corresponding to macromolecular crowding inside cells and localized actin concentrations found at the leading edge during cell motility. These conclusions have direct implications for cell shape and structure, as well as tumor cell migration.

Structurally governed cell mechanotransduction through multiscale modeling.

Mechanotransduction has been divided into mechanotransmission, mechanosensing, and mechanoresponse, although how a cell performs all three functions using the same set of structural components is still highly debated. Here, we bridge the gap between emerging molecular and systems-level understandings of mechanotransduction through a multiscale model linking these three phases. Our model incorporates a discrete network of actin filaments and associated proteins that responds to stretching through geometric relaxation. We assess three potential activating mechanisms at mechanosensitive crosslinks as inputs to a mixture model of molecular release and benchmark each using experimental data of mechanically-induced Rho GTPase FilGAP release from actin-filamin crosslinks. Our results suggest that filamin-FilGAP mechanotransduction response is best explained by a bandpass mechanism favoring release when crosslinking angles fall outside of a specific range. Our model further investigates the difference between ordered versus disordered networks and finds that a more disordered actin network may allow a cell to more finely tune control of molecular release enabling a more robust response.

Spatial patterning of cell proliferation and differentiation depends on mechanical stress magnitude.

Mechanical stress has been proposed as a major regulator of tissue morphogenesis; however, it remains unclear what is the exact mechanical signal that leads to local tissue pattern formation. We explored this question by using a micropatterned cell aggregate model in which NIH 3T3 fibroblasts were cultured on micropatterned adhesive islands and formed cell aggregates (or "cell islands") of triangular, square, and circular shapes. We found that the cell islands generated high levels of mechanical stresses at their perimeters compared to their inner regions. Regardless of the shape of cell islands, the mechanical stress patterns corresponded to both cell proliferation and differentiation patterns, meaning that high level of cell proliferation and differentiation occurred at the locations where mechanical stresses were also high. When mechanical stretching was applied to cell islands to elevate overall mechanical stress magnitudes, cell proliferation and differentiation generally increased with the relatively higher mechanical stresses, but neither cell proliferation nor differentiation patterns followed the new mechanical stress pattern. Thus, our findings indicate that a certain range of mechanical stress magnitudes, termed window stress threshold, drives formation of cell proliferation and differentiation patterns and hence possibly functions as a morphogenetic cue for local tissue pattern formation in vivo.

Understanding actin organization in cell structure through lattice based Monte Carlo simulations.

Understanding the connection between mechanics and cell structure requires the exploration of the key molecular constituents responsible for cell shape and motility. One of these molecular bridges is the cytoskeleton, which is involved with intracellular organization and mechanotransduction. In order to examine the structure in cells, we have developed a computational technique that is able to probe the self-assembly of actin filaments through a lattice based Monte Carlo method. We have modeled the polymerization of these filaments based upon the interactions of globular actin through a probabilistic model encompassing both inert and active proteins. The results show similar response to classic ordinary differential equations at low molecular concentrations, but a bi-phasic divergence at realistic concentrations for living mammalian cells. Further, by introducing localized mobility parameters, we are able to simulate molecular gradients that are observed in nonhomogeneous protein distributions in vivo. The method and results have potential applications in cell and molecular biology as well as self-assembly for organic and inorganic systems.