Modeling Virus Self-Assembly Pathways Using Computational Algebra and Geometry

We develop a tractable model for elucidating the assembly pathways by which an icosahedral viral shell forms from 60 identical constituent protein monomers. This poorly understood process a remarkable example of macromolecular self-assembly occuring in nature and possesses many features that are desirable while engineering self-assembly at the nanoscale. The model uses static geometric constraints to represent the driving (weak) forces that cause a viral shell to assemble and hold it together. The goal is to answer focused questions about the structural properties of a successful assembly pathway. Pathways and their properties are carefully defined and computed using computational algebra and geometry, specifically by crucial modifications to state of the art methods for geometric constraint decomposition. The model is analyzable and refinable and avoids expensive dynamics. It has a provably tractable and accurate computational simulation and that its predictions are roughly consistent with known information about viral shell assembly. Overall the paper’s new contributions are: (a) elucidation of a new model of virus assembly illustrating a strong, direct, mutually beneficial interplay between the concepts underlying macromolecular assembly and a wide variety of established as well as novel concepts from combinatorial and computational algebra, geometry and algebraic complexity; and (b) crucial modifications to existing geometric constraint decomposition methods to obtain a tractable and accurate simulation of the model. Organization of Paper –Introduction and Motivation –Geometric Constraints Background –The Virus Assembly Model: Pathways and Effort –A Tractable and Accurate Simulation supported in part by NSF-EIA 0218435.