A Civil Engineering Model of Protein Conformational Change

We present a variational approach for the simulation of large conformational changes of proteins (including multiple protein chains/ligands) which takes advantage of their cross-linked one-dimensional nature, a structure which often occurs in civil engineering. Conformational changes are computed by incremental energy minimisation. We use an efficient finite element method for finding equilibria of complexes composed of inter-linked chains; this method is based on recent advances in the description of one-dimensional elasticity. Protein backbone elasticity, van der Waals repulsions, hydrogen bonds and salt bridges are taken into account, together with user-defined geometric distance constraints that may be imposed for purposes of simulating various binding processes based on chemical knowledge. These computational methods have been integrated into a system, Proteinmorphosis, which includes interactive visualisation. The conformational change of calmodulin upon peptide binding is examined as a first experiment. Allostery in hemoglobin, which consists of a cooperative oxygen binding mechanism, is a second, more sophisticated, numerical experiment. Different modelling strategies are designed to understand the allostery. The results for both molecules are consistent with existing hypotheses, and reproduce the known atomic positions after binding to within the experimental error. The modelling system is part of an on-going program to model structural biology, from protein structure to cell and tissue properties.