Elasticity Theory of Macromolecular Aggregates

We present a version of continuum elasticity theory applicable to aggregates of functional biomolecules at length scales comparable to that of the component molecules. Unlike classical elasticity theory, the stress and strain fields have mathematical discontinuities along the interfaces of the macromolecules, due to conformational incompatibility and large scale conformational transitions. The method is applied to the P-II to EI shape transition of the protein shell of the virus HK97. We show that protein residual stresses generated by incompatibility drive a “reverse buckling” transition from an icosahedral to a dodecahedral shape via a “critical” spherical shape, which can be identified as the P-II state.