Effect of Crosslinking on the Elastic Properties of the Cytoskeleton: A 3D Discrete Modeling Approach
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Effect of Crosslinking on the Elastic Properties of the Cytoskeleton: A 3D Discrete Modeling Approach Florent Dalmas1 and Camilla Mohrdieck2 1 Institut de Chemie et des Matériaux Paris-Est (ICMPE), CNRS-UMR 7182, 2-8 rue Henri Dunant, Thiais, 94320, France 2 Inst. of Physical Metallurgy, Universitaet Stuttgart, Heisenbergstrasse 3, Stuttgart, 70569, Germany
ABSTRACT In living eukaryotic cells a crosslinked network of polymer fibers, the cytoskeleton, endows the cells with structural integrity and mechanical stability and flexibility. To understand the mechanisms that are at the base of these functions, it is important to know in what way the microstructure and the mechanical behavior of the cytoskeleton change as a function of the type and the density of crosslinking molecules. To address this issue, we have developed a new modeling approach based on the discretization of polymeric fibers that are modeled as homogeneous straight beams in a constant volume. Crosslinks between adjacent fibers are taken into account by creating additional beams between the fibers if their spacing is smaller than a meaningful upper bound. By varying their geometrical and mechanical properties, the influence of the crosslinks on the shear modulus of the network can be studied systematically. Our simulations predict interesting new scaling behaviors that depend on the degree of crosslinking. INTRODUCTION The cytoskeleton is the internal protein network of eukaryotic cells that is responsible for many cellular properties and functions. A major constituent of the cytoskeleton is the polymer actin that polymerizes to form semi-flexible filaments. In-vivo, actin filaments assemble into microstructures of very different topologies ranging from random networks consisting of short filaments (~ 0.1µm) to highly aligned filamentous structures that can span the entire cell (~ 1020 µm). Local changes in the topology can be induced by chemical or mechanical stimuli, such as forces, and can take place within a few seconds. Much of this structural and dynamic flexibility is due to various crosslinking proteins that tether actin filaments in specific ways and with protein-specific on and off rates. Although many experimental studies of the mechanical behavior of cells and in vitro actin networks (for a review see [1]) have been conducted, a quantitative analysis of the effect of individual crosslinker properties, such as their elastic stiffness, on the cytoskeleton is lacking so far. This is mainly due to the fact that the elastic and kinematic properties of single actin-crosslinking molecules have only recently begun to be measured. Computer simulations can thus provide a powerful tool to complement the quantitative study of the mechanical behavior of crosslinked networks. They allow us to vary the geometrical and mechanical properties of the crosslinking proteins individually and systematically and also enable us to simulate the concerted action of several different crosslinker types, which mimics
the situation in cells. In this work,
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