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To Build Viruses: A Markov Chain Monte Carlo Algorithm for Simulating Viral Assembly Kinetics
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| Organization: | Indiana University |
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Wolfram Technology Conference 2015
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Champaign, Illinois USA
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Icosahedral virus capsids are roughly spherical shells built of multiples of 60 self-assembling subunits. Despite such complexity, capsid assembly kinetics are simulated using a modified reaction kinetics framework with additional biophysical parameters, namely a microscopic forward rate constant, an energy term governing relative disassociation rates, and combinatorics terms distinguishing microscopic and macroscopic binding affinities. Mathematical models are increasingly consistent with experiment. Prediction of capsid and intermediate activity in vitro & per-species kinetics characterization are primary goals of this work. We present a suite of generalizable utilities for conducting simulation of capsid assembly using large systems of coupled, autonomous-differential (‘rate’) equations. These enable modeling of large viruses such as Hepatitis B Virus (HBV), an icosahedral virus whose capsid of 120 subunits, each assumed to add sequentially. Subunits are represented by, for HBV, 120 vertices of a tetravalent (k-regular, k = 4) graph, whose edges represent dimer-dimer contacts. A binomial rule system distinguishes between physically distinct intermediates, which constitute the full set assembly pathways. As each enumerated intermediate requires a state variable (ie. equation), complexity of large-scale modeling is prohibitive. In thoroughly enumerated, smaller systems of the same form, approximation techniques demonstrably remedy prohibition via use of most-stable subsets. With larger systems a biased Markov Chain Monte Carlo algorithm provides a means to selectively enumerate thermodynamically relevant subsets. Computational effort allows construction of models directly related to experimentally observed phenomena. Icosahedral virus capsids are roughly spherical shells built of multiples of 60 self-assembling subunits. Despite such complexity, capsid assembly kinetics are simulated using a modified reaction kinetics framework with additional biophysical parameters, namely a microscopic forward rate constant, an energy term governing relative disassociation rates, and combinatorics terms distinguishing microscopic and macroscopic binding affinities. Mathematical models are increasingly consistent with experiment. Prediction of capsid and intermediate activity in vitro & per-species kinetics characterization are primary goals of this work.
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To Build Viruses: A Markov Chain Monte Carlo Algorithm for Simulating Viral Assembly Kinetics
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| 1445373183.nb (8 MB) - Mathematica Notebook |
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