Computational Analysis of Viscoelastic Properties of Crosslinked Actin Networks

Abstract

Mechanical force plays an important role in the physiology of eukaryotic cells whose dominant structural constituent is the actin cytoskeleton composed mainly of actin and actin crosslinking proteins (ACPs). Thus, knowledge of rheological properties of actin networks is crucial for understanding the mechanics and processes of cells. We used Brownian dynamics simulations to study the viscoelasticity of crosslinked actin networks. Two methods were employed, bulk rheology and segment-tracking rheology, where the former measures the stress in response to an applied shear strain, and the latter analyzes thermal fluctuations of individual actin segments of the network. It was demonstrated that the storage shear modulus (G′) increases more by the addition of ACPs that form orthogonal crosslinks than by those that form parallel bundles. In networks with orthogonal crosslinks, as crosslink density increases, the power law exponent of G′ as a function of the oscillation frequency decreases from 0.75, which reflects the transverse thermal motion of actin filaments, to near zero at low frequency. Under increasing prestrain, the network becomes more elastic, and three regimes of behavior are observed, each dominated by different mechanisms: bending of actin filaments, bending of ACPs, and at the highest prestrain tested (55%), stretching of actin filaments and ACPs. In the last case, only a small portion of actin filaments connected via highly stressed ACPs support the strain. We thus introduce the concept of a ‘supportive framework,’ as a subset of the full network, which is responsible for high elasticity. Notably, entropic effects due to thermal fluctuations appear to be important only at relatively low prestrains and when the average crosslinking distance is comparable to or greater than the persistence length of the filament. Taken together, our results suggest that viscoelasticity of the actin network is attributable to different mechanisms depending on the amount of prestrain.

Actin filament curvature biases branching direction

“…Growth of one specialized cytoskeletal structure, the branched actin network (6)(7)(8), produces forces that act on cellular membranes to help them protrude or change shape (9)(10)(11)(12) and plays an important role in cell motility, the trafficking of cellular membranes including endocytosis, and the motility of intracellular pathogens (13,14). When this protrusive growth is opposed by resistance from the surrounding cytoskeleton or plasma membrane, the actin network compresses, and filaments in the network bend (15)(16)(17)(18). In vitro studies have shown that compressive forces applied to branched networks cannot only reversibly deform them (15) but can also alter their density (19) and growth velocity (10,11), suggesting that their architecture may respond actively to mechanical forces.…”

Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

“…Harjanto et al [168] used an approach where the cells can degrade, deposit, or pull on local fibers, depending on the fiber density around each cell. We note that the fibers themselves in principle are not inert stiff structures but have their specific dynamics which can be modeled as well using e.g., Brownian dynamics [169].…”

“…Also they cannot give detailed information of the mechanical signals (tensile, compressive forces, shear forces) that are transmitted by the ECM via integrin receptors linked with the cytoplasm and CSK. On the other hand, detailed models that focus on the mechanics of the CSK as such (e.g., [169]) may be unable to capture the behavior of the whole cell. An intermediate scale model is thus desirable to bridge this gap.…”

Shear-induced force transmission in a multicomponent, multicell model of the endothelium

“…Moreover, several models of the cytoskeleton have been constructed to investigate the hypothesis that this interconnected filamentous structure can act as a mechano-signal transmitter [44][45][46][47][48][49][50][51][52][53][54][55][56]. Shafrir & [46] proposed a two-dimensional model of the cytoskeleton as a random network of rigid rods representing the actin laments and linear Hookean springs representing the actin cross-linkers.…”

“…However, they assumed that the plasma and nuclear membranes are rigid and immobile, which is unrealistic. Later, more sophisticated models that focused on understanding the rheology of the actin network were presented [45,53,55,56]. The main concern of these studies was to connect these network models to the plasma and nuclear membranes.…”