| Symmetry is a common feature in nature. Large biological macromolecules (> 100 kD) tend to assemble from multiple subunits and spatially arranged in symmetric ways. The topological symmetry not only results in coding efficiency and error control, but also characterizes the equilibrium dynamics of the biomolecular system. Coarse-grained normal mode analyses have been broadly used in recent years to elucidate the relation between structure, dynamics and function. Further insights into collective motions can be gained by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the molecular structure. We solved the elastic wave equation analytically for the case of spherical symmetry, yielding a symmetry-based classification of vibrational motions accessible to the structures together with explicit predictions of their vibrational frequencies. Applications to biomolecular assemblies have shown that the continuum models with spherical symmetry efficiently provide insights into collective motions that are otherwise obtained by detailed elastic network models. Additionally, to understand the mechanism of functions associated with structural changes between different conformations, the transition pathways between these conformations have been explored with the help of elastic network models. Although there are many computational methods for exploring the conformational transitions of proteins, these are usually applicable to small-to-moderate size proteins, and the task of exploring the transition pathways becomes prohibitively expensive in the case of supramolecular systems of the order of megadaltons. Coarse-grained models that lend themselves to analytical solutions appear to be the only possible means of approaching such cases. Motivated by the utility of elastic network models for describing the collective dynamics of biomolecular systems, and by the growing theoretical and experimental evidence in support of the intrinsic accessibility of functional substates under native state conditions, we developed a new method, adaptive anisotropic network model (aANM), for exploring the functional transitions of large biomolecular systems. Application to bacterial chaperonin GroEL, and comparisons with experimental data, and with results from other theoretical and/or computational approaches, support the utility of aANM as a computationally efficient, yet physically plausible, tool for unraveling the potential transition pathways sampled by large complexes/assemblies. |
