The goals of this pilot project are to assess and further develop quantified measures for the degree of flexibility and rigidity in protein structure that characterize biologically relevant long-time and large-scale motions. The large approach employed here is to view the protein fold as a bar-joint framework, where covalent bonds, salt bridges and hydrogen bonds are represented as distance constraints, and dihedral angles associated with resonant and peptide bonds are locked.. Mechanical properties of the framework will be calculated exactly by invoking concepts from graph rigidity following previous work. To account for the large variability in hydrogen bond strength a given protein structure will be modeled as a statistical ensemble of frameworks using a product measure that is a function of bond energies, and a hierarchical representation of mechanical stability will be generated. Correlation matrices will be introduced to quantify the degree of coupling between pairs of dihedral angles. The complete set of dihedral angles will be partitioned into subsets that identify regions that are flexible, rigid and strained at each hierarchical level. The detailed micro-mechanical information will be used to identify structural mechanics that help regulate protein function such as induced conformation changes upon ligand binding. Obtaining insight into structure-function relationships is important in drug design and protein engineering, such as application to site-directed mutagenesis.
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