Cytoskeleton and Cell Motility
V.1 Coordinators
V.2 Participants
V.3 Introduction
V.4 Specific Research Objectives
V.5 Background and Significance
V.6 Research Plan V.7 Relation with Organogenesis (project 3) and Biological Networks (project 1)
V.8 Timeline
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V.6.v Subproject 5 - Computational Modeling of the Actin Cytoskeleton:
We will take two different approaches to modeling the actin cytoskeleton:
V.6.v.a Hybrid Stochastic/Reaction-Diffusion Model:The dynamic polymerization and depolymerization of the actin cytoskeleton forms a tree-like network in which the angle between the edges is 70° (Figure V.10). We propose to use a linked binary tree to represent the cytoskeleton computationally. Each structure in this tree contains complete information on the number and state of hydrolysis of the actin monomers which composed it to represent a polymeric segment. The nodes of the tree form a specific and important subset of the cytoskeleton, where that capping (represented computationally by the state of hydrolysis of the terminating monomers in the segment) polymerization and depolymerization of the nodes occur. The probability of polymerization will depend of the local concentration of actin monomers, so the data structures will have to store dynamically the spatial coordinates of the nodes. We calculate the local concentration of free actin monomers at these points by solving the diffusion equation for their concentration subject to no flux boundary conditions at the membrane boundaries and sinks at the cytoskeletal nodes. The source of new actin consists of a distributed intracellular source and the depolymerizing cytoskeleton. To model the addition of new filaments to the cytoskeleton due to extracellular stimuli which activate WASp/Scar proteins to form an Arp2/3 complex and bind to the cytoskeleton to create new branches we will add new data structures stochastically to the tree. This addition will depend on the local concentration of Arp2/3 complexes which also obey a diffusion equation with a time dependent membrane-localized source, dependent on the strength and duration of the extracellular stimulus.
From the data structure for the tree and the spatial distribution of actin and Arp2/3 complexes we can update the dynamically evolving tree. We need to specify rates for a number of processes including (but not limited to):
1. Addition of actin monomers to the tree nodes, which depends on the local concentration of free monomer.2. Hydrolysis of ATP to ADP monomers. These rates depend on the state of hydrolysis of the neighboring monomers.
3. The rate of addition of new branches to the dynamically evolving tree, which depends on the local concentration of nucleating Arp2/3 complex.
This model neglects the effects of localized calcium, calcium-induced regulation and mechanical stimulation on cytoskeletal growth (Lockhart, 1965; Odell et al., 1981; Oster et al., 1983; Oster and Odell, 1984; Goodwin and Trainor, 1988; Erxleben, 1993; Chen and Grinnel, 1995; Tanaka et al., 1994) which can lead to very nonlinear elastic strain and rheology.