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      Computational Analysis of Viscoelastic Properties of Crosslinked Actin Networks

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          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.

          Author Summary

          The actin cytoskeleton provides structural integrity to a cell, is highly dynamic, and plays a central role in a wide variety of phenomena such as migration and the sensation of external forces. For years, researchers have studied the mechanics of the cytoskeleton by creating actin gels in the laboratory in combination with proteins that bridge between and reinforce the actin gel found inside cells. These gels, however, failed to replicate many aspects of cell behavior. Recent studies have shown that tension within the cytoskeleton contributes to the observed stiffness of cells. Still, our understanding of cytoskeletal mechanics is incomplete, and many observed phenomena cannot be explained by existing models. Here, we simulate a three-dimensional network containing actin filaments linked together by other proteins. We studied the relative contributions of thermal fluctuations of the network and the stiffness of filaments and linking proteins. Under conditions that replicate those in a cell, properties of the linking proteins are surprisingly significant, as is the stiffness of the actin filament to stretching. Thermal fluctuations are relatively unimportant, but become more so at low levels of resting tension. At high tensions, a small fraction of filaments support a majority of the load.

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          Most cited references36

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          Cellular mechanotransduction: putting all the pieces together again.

          Analysis of cellular mechanotransduction, the mechanism by which cells convert mechanical signals into biochemical responses, has focused on identification of critical mechanosensitive molecules and cellular components. Stretch-activated ion channels, caveolae, integrins, cadherins, growth factor receptors, myosin motors, cytoskeletal filaments, nuclei, extracellular matrix, and numerous other structures and signaling molecules have all been shown to contribute to the mechanotransduction response. However, little is known about how these different molecules function within the structural context of living cells, tissues, and organs to produce the orchestrated cellular behaviors required for mechanosensation, embryogenesis, and physiological control. Recent work from a wide range of fields reveals that organ, tissue, and cell anatomy are as important for mechanotransduction as individual mechanosensitive proteins and that our bodies use structural hierarchies (systems within systems) composed of interconnected networks that span from the macroscale to the nanoscale in order to focus stresses on specific mechanotransducer molecules. The presence of isometric tension (prestress) at all levels of these multiscale networks ensures that various molecular scale mechanochemical transduction mechanisms proceed simultaneously and produce a concerted response. Future research in this area will therefore require analysis, understanding, and modeling of tensionally integrated (tensegrity) systems of mechanochemical control.
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            Scaling the microrheology of living cells.

            We report a scaling law that governs both the elastic and frictional properties of a wide variety of living cell types, over a wide range of time scales and under a variety of biological interventions. This scaling identifies these cells as soft glassy materials existing close to a glass transition, and implies that cytoskeletal proteins may regulate cell mechanical properties mainly by modulating the effective noise temperature of the matrix. The practical implications are that the effective noise temperature is an easily quantified measure of the ability of the cytoskeleton to deform, flow, and reorganize.
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              Microrheology of human lung epithelial cells measured by atomic force microscopy.

              Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G(*)(omega)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1-100 Hz) and at different loading forces (0.1-0.9 nN) with atomic force microscopy. G(*)(omega) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G'(omega) increased with frequency following a power law with exponent approximately 0.2. The loss modulus G"(omega) was approximately 2/3 lower and increased similarly to G'(omega) up to approximately 10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G'(omega) and G"(omega). G(*)(omega) conformed to the power-law model with a structural damping coefficient of approximately 0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                July 2009
                July 2009
                17 July 2009
                : 5
                : 7
                : e1000439
                Affiliations
                [1 ]Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
                [2 ]Department of Biomedical Engineering, Texas A&M University, College Station, Texas, United States of America
                [3 ]Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
                University of California, Berkeley, United States of America
                Author notes

                Conceived and designed the experiments: TK WH HL RDK. Performed the experiments: TK HL. Analyzed the data: TK WH HL. Wrote the paper: TK WH HL RDK.

                Article
                09-PLCB-RA-0032R2
                10.1371/journal.pcbi.1000439
                2703781
                19609348
                d903122a-b422-45e2-a3e6-1032afe53536
                Kim et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                History
                : 9 January 2009
                : 15 June 2009
                Page count
                Pages: 13
                Categories
                Research Article
                Biophysics/Theory and Simulation
                Cell Biology/Cytoskeleton

                Quantitative & Systems biology
                Quantitative & Systems biology

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