Icosahedral viral shell assembly starting from identical protein monomers is an outstanding but poorly understood example of symmetric macromolecularself-assembly occuring in nature. We propose to develop and biochemically validate a novel multiscale mathematical and computational model and associated software tools to answer focused questions about viral shell assembly pathways. The proposed approach is based on 3 novel ingredients. (i) Formalization of carefully focused questions about the structureof assembly pathways, which depend only on static geometric and symmetry constraints. Avoidance of dynamics facilitates computational tractability and an intuitive theory of pathway structure. (ii) Development of a modular, two-scale virus assembly model that makes the mathematics transparent and leads to new directions in geometric complexity and algebraic combinatorics. (iii)Independent biochemical validation of the 2 separate scales of the model, using known data as well as new experiments.
An array of applications in nanoscience and engineering, biosensor and gene therapy follow from effective models of symmetric macromolecular assembly pathways. Such models would additionally help arrest viral self-assembly and hence numerous plant and animal diseases. Opensource software built atop the PI's FRONTIER geometric constraint solving opensource software suite, and benchmark virus data will be developed for prediction and visualization of self-assembly pathways and for rigorous comparisons. The grant will foster a closely interacting, interdisciplinary group of students and will expose each of them to research in mathematics, structural biology, theoretical computer science, algorithms and software development. Outreach is planned via an interdisciplinary workshop at DIMACS or at IMA and in university press releases.
