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Generation and Assembly of Virus-Specific Nucleocapsids of the Respiratory Syncytial Virus
Published on: July 27, 2021
Enumeration of viral capsid assembly pathways: tree orbits under permutation group action
Miklós Bóna1, Meera Sitharam, Andrew Vince
1Department of Mathematics, University of Florida, Gainesville, 32611, USA. bona@ufl.edu
Bulletin of Mathematical Biology
|December 22, 2010
Summary
This study uses combinatorics and group theory to model viral shell assembly. It provides a formula and algorithm to count assembly pathways, clarifying symmetry
Area of Science:
- Computational Biology
- Biophysics
- Mathematical Biology
Background:
- The geometric structure of icosahedral viral capsids is understood, but the assembly process remains unclear.
- Viral capsids are modeled as polyhedra with facets representing monomers.
- Assembly pathways are modeled as rooted trees, with leaves as facets and the root as the assembled capsid.
Purpose of the Study:
- To apply combinatorics and group theory to understand viral capsid assembly.
- To enumerate orbits of trees under finite group actions, relevant to symmetric macromolecular assembly.
- To clarify the impact of symmetry on the probability and number of viral assembly pathways.
Main Methods:
- Modeling the viral capsid assembly process using rooted trees.
- Applying group theory to analyze the action of finite groups on labeled trees.
- Developing a formula for the number of orbits of trees under group action.
- Designing a linear-time algorithm to find the stabilizer of a tree in a group.
Main Results:
- A formula is derived for the number of orbits of each size in the action of a finite group G on the set of labeled trees T(x).
- A simple, linear-time algorithm is presented to efficiently find the stabilizer of a tree within the group action.
- These combinatorial results provide insights into the role of symmetry in biological assembly processes.
Conclusions:
- The study provides mathematical tools to analyze complex assembly processes, such as those in icosahedral viruses.
- The developed methods offer a general framework for studying any finite, symmetric macromolecular assembly.
- The findings contribute to understanding how symmetry influences the pathways and probabilities of biological self-assembly.
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