Monte Carlo simulation and theoretical analysis of self-assembled semiflexible equilibrium polymers Open Access

Lu, Xinjiang (2007)

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Grand canonical Monte Carlo simulations of a simple model semiflexible equilibrium polymer system, consisting of hard sphere monomers reversibly self-assembling into chains of arbitrary length, have been performed using a novel sampling method to add or remove multiple monomers during a single MC move. Systems with two different persistence lengths and a range of bond association constants have been studied. We find first-order lyotropic phase transitions between isotropic and nematic phases near the concentrations predicted by a statistical thermodynamic theory, but with significantly narrower coexistence regions. A possible contribution to the discrepancy between theory and simulation is that the length distribution of chains in the nematic phase is bi-exponential, differing from the simple exponential distribution found in the isotropic phase and predicted from a mean-field treatment of the nematic. The additional short length-scale characterizing the distribution appears to arise from the lower orientational order of short chains. The dependence of this length-scale on chemical potential, bond association constant, and total monomer concentration has been examined. Using grand canonical Monte Carlo simulations we study the equilibrium properties of actin self-assembly. The statistics of actin polymerization is described by a mechanism involving monomer activation and chain propagation with bond association constants derived from experimental free energy parameters. For efficiency in representing systems of extremely long, stiff chains we use a coarse-graining based on spherocylinders. We present results pertaining to the isotropic-nematic transition in this equilibrium biopolymer system. We have also used Monte Carlo simulations to study the bundle formation in self-assembled semiflexible chain polymers with inter-chain attractions. Approximate phase diagrams are obtained for varied physical parameters, such as the chain flexibility, bonded and non-bonded interactions. The attraction induced microphase separation results in an equilibrium between a bundle and isotropic short chains. The chain length distribution of the phase separated system, as well as the bundle's shape and aspect ratio, etc. are presented and discussed. Our simulation results are analyzed and compared with related experimental and theoretical work. We also observed toroids and branched bundles during the course of our simulations.

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Contents List of Figures List of Tables Introduction Monte Carlo methods and ensembles Metropolis algorithm Biased sampling methods Ensembles Actin protein: a model system for polymers Thesis outline Monte Carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers Introduction Methods Model description Polydisperse insertion, removal, and resizing (PDIRR) moves Justification of PDIRR algorithm Data analysis Other simulation details Performance of the PDIIR method Results on semiflexible equilibrium polymers Simulation results for Kassoc = 5000 General comparison between simulation and theory Disordering of short chains in the nematic phase Summary Monte Carlo simulation of actin self-assembly Introduction Simulation model Mechanism and thermodynamics of actin polymerization Simulation results and discussion Comparison with the sphere-chain model The phase transition of actin filaments The length distribution Summary Monte Carlo simulation of self-assembled polymer chains with inter- chain attractions Introduction Model Results and discussions Phase behavior and diagram Chain length distributions Analysis of the bundles Aspect ratio of the bundle Convergence issues The effect of the simulation box size Comparison with grand canonical Monte Carlo simulations Conclusion Bibliography

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