Counting and Enumeration of Self-assembly Pathways for Symmetric Macromolecular Structures

Abstract

We consider the problem of explicitly enumerating and counting the assembly pathways by which an icosahedral viral shell forms from identical constituent protein monomers. This poorly understood assembly process is a remarkable example of symmetric macromolecular self-assembly occuring in nature and possesses many features that are desirable while engineering self-assembly at the nanoscale. We use the new model of 24;25 that employs a static geometric constraint graph to represent the driving (weak) forces that cause a viral shell to assemble and hold it together. The model was developed to answer focused questions about the structural properties of the most probable types of successful assembly pathways. Specifically, the model reduces the study of pathway types and their probabilities to the study of the orbits of the automorphism group of the underlying geometric constraint graph, acting on the set of pathways. Since these are highly symmetric polyhedral graphs, it seems a viable approach to explicitly enumerate these orbits and count their sizes. The contribution of this paper is to isolate and simplify the core combinatorial questions, list related work and indicate the advantages of an explicit enumerative approach.

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Cite this paper

@inproceedings{Sitharam2004CountingAE, title={Counting and Enumeration of Self-assembly Pathways for Symmetric Macromolecular Structures}, author={Meera Sitharam}, year={2004} }