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Rigid-Cluster Models of Conformational Transitions in Macromolecular Machines and Assemblies

Moon K. Kim ^*, Robert L. Jernigan  and Gregory S. Chirikjian 

^* Department of Mechanical and Industrial Engineering, University of Massachusetts at Amherst, Amherst, Massachusetts; Laurence H. Baker Center for Bioinformatics and Biological Statistics, Iowa State University, Ames, Iowa; and Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland

Correspondence: Address reprint requests to Professor Gregory S. Chirikjian, Tel.: 410-516-7127; E-mail: gregc{at}jhu.edu.

We present a rigid-body-based technique (called rigid-cluster elastic network interpolation) to generate feasible transition pathways between two distinct conformations of a macromolecular assembly. Many biological molecules and assemblies consist of domains which act more or less as rigid bodies during large conformational changes. These collective motions are thought to be strongly related with the functions of a system. This fact encourages us to simply model a macromolecule or assembly as a set of rigid bodies which are interconnected with distance constraints. In previous articles, we developed coarse-grained elastic network interpolation (ENI) in which, for example, only C atoms are selected as representatives in each residue of a protein. We interpolate distance differences of two conformations in ENI by using a simple quadratic cost function, and the feasible conformations are generated without steric conflicts. Rigid-cluster interpolation is an extension of the ENI method with rigid-clusters replacing point masses. Now the intermediate conformations in an anharmonic pathway can be determined by the translational and rotational displacements of large clusters in such a way that distance constraints are observed. We present the derivation of the rigid-cluster model and apply it to a variety of macromolecular assemblies. Rigid-cluster ENI is then modified for a hybrid model represented by a mixture of rigid clusters and point masses. Simulation results show that both rigid-cluster and hybrid ENI methods generate sterically feasible pathways of large systems in a very short time. For example, the HK97 virus capsid is an icosahedral symmetric assembly composed of 60 identical asymmetric units. Its original Hessian matrix size for a C coarse-grained model is >(300,000)². However, it reduces to (84)² when we apply the rigid-cluster model with icosahedral symmetry constraints. The computational cost of the interpolation no longer scales heavily with the size of structures; instead, it depends strongly on the minimal number of rigid clusters into which the system can be decomposed.

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