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Modeling actin dynamics

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Abstract Actin monomers assemble into filaments that structurally support cells as well as drive membrane protrusion for cell movement. Within cells, some actin structures are very dynamic and turn over rapidly, while others are very stable. Even purified actin filament dynamics are complex, and researchers have often turned to mathematical models in order to interpret data, test hypotheses, make predictions, and deepen understanding. Models of actin dynamics can be broadly divided into time‐dependent models and time‐independent models. Most commonly, time‐independent models use numerical solutions of sets of differential equations to explore the effects of key parameters on the actin cycle at steady state. Recent examples have been used to predict the nucleotide profile of steady‐state filaments and to illuminate the mechanisms behind profilin's effects on actin dynamics. Time‐dependent models of actin dynamics have been either Monte Carlo simulations, which track individual filaments at various levels of detail or less commonly stochastic models, which have been explored and solved analytically. These Monte Carlo and stochastic models have recently been used to investigate filament length diffusion, filament length distributions, annealing and fragmentation, and pyrene fluorescence overshoots. We do not review force production/protrusion models as they tend to reduce the complexity of actin dynamics to a single 'elongation rate' and because these models have been recently well reviewed.1. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under: Models of Systems Properties and Processes > Cellular Models

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Factors influencing actin assembly and disassembly rate constants. (a) Filament end: barbed ends have higher on and off rates than pointed ends. (b) Bound nucleotide: all on and off rates depend on whether the actin subunit has bound adenosine triphosphate (ATP), adenosine diphosphate (ADP), or ADP with bound inorganic phosphate (ADP‐Pi). ATP‐actin assembles fastest at both ends and disassembles fastest at the pointed end. ADP‐actin disassembles fastest at the barbed end. ADP‐Pi‐actin assembles at similar rates to ADP‐actin at both ends, but disassembles much more slowly than either other species. In addition, it appears that the assembly rate for ATP‐actin at the pointed end depends on the nucleotide binding state of the existing filament tip, with faster assembly onto an existing ATP‐actin subunit and slower assembly onto a non‐ATP‐bound tip7. (c) Filament age: during dilution‐induced filament depolymerization, newly polymerized filaments disassemble rapidly, primarily from their barbed ends, whereas aged filaments disassemble slowly, primarily from their pointed ends2. (d) Actin binding proteins: proteins that bind to actin monomers or filaments can block assembly (e.g., capping protein or thymosin β4), sever filaments (e.g., ADF/cofilins), enhance assembly (e.g., formin and profilin‐actin), or even nucleate new filaments from the sides of existing filaments (Arp2/3 complex). T = ATP‐actin, D = ADP‐actin, Y = ADP‐Pi‐actin, CP = capping protein, B = thymosin β4, AC = ADF/cofilin, ARP = Arp2/3 complex, P = profilin and F = formin.

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