Abstract
Actin filaments are critical components of the eukaryotic cytoskeleton, playing important roles in a number of cellular functions, such as cell migration, organelle transport, and mechanosensation. They are helical polymers with a well-defined polarity, composed of globular subunits that bind nucleotides in one of three hydrolysis states (ATP, ADP-Pi, or ADP). Mean-field models of the dynamics of actin polymerization have succeeded in, among other things, determining the nucleotide profile of an average filament and resolving the mechanisms of accessory proteins. However, these models require numerical solution of a high-dimensional system of nonlinear ordinary differential equations. By truncating a set of recursion equations, the Brooks–Carlsson (BC) model reduces dimensionality to 11, but it still remains nonlinear and does not admit an analytical solution, hence, significantly hindering understanding of its resulting dynamics. In this work, by taking advantage of the fast timescales of the hydrolysis states of the filament tips, we propose two model reduction schemes: the quasi steady-state approximation model is five-dimensional and nonlinear, whereas the constant tip (CT) model is five-dimensional and linear, resulting from the approximation that the tip states are not dynamic variables. We provide an exact solution of the CT model and use it to shed light on the dynamical behaviors of the full BC model, highlighting the relative ordering of the timescales of various collective processes, and explaining some unusual dependence of the steady-state behavior on initial conditions.
Highlights
Actin filaments are an integral part of the cytoskeleton and are involved in functions such as controlling cell shape, cell motility, organelle redistribution, and mechanical coupling with the cellular environment
Unpolymerized actin monomers are referred to as G-actin, while polymerized actin monomers are referred to as F-actin. But they are more modeled as linear chains, which is a realistic approximation if one assumes that the reaction propensities of a given F-actin monomer is determined only by the nucleotide bound by that monomer and not by the monomer’s neighbors
In our modeling we have included the reverses of kinetically dominant forward reactions, and we have set the rate constants of these reactions to be equal to something on the order of the corresponding forward reaction rate constants multiplied by a small parameter
Summary
Actin filaments are an integral part of the cytoskeleton and are involved in functions such as controlling cell shape, cell motility, organelle redistribution, and mechanical coupling with the cellular environment. These filaments are formed of globular monomers which polymerize in a nonequilibrium process that in vivo is modulated by an array of accessory proteins. They are helical and polar, with distinct plus (“barbed”) and minus (“pointed”) ends at which monomers have different rates of association and dissocation [1]. It is of interest to be able to predict the hydrolysis state of the nucleotide bound to each actin monomer in a filament, or at least the fraction of actin monomers bound to nucleotides in a certain hydrolysis state
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