Rigidity theory for biomolecules: concepts, software, and applications

The mechanical heterogeneity of biomolecular structures is intimately linked to their diverse biological functions. Applying rigidity theory to biomolecules identifies this heterogeneous composition of flexible and rigid regions, which can aid in the understanding of biomolecular stability and long-ranged information transfer through biomolecules, and yield valuable information for rational drug design and protein engineering. We review fundamental concepts in rigidity theory, ways to represent biomolecules as constraint networks, and methodological and algorithmic developments for analyzing such networks and linking the results to biomolecular function. Software packages for performing rigidity analyses on biomolecules in an efficient, automated way are described, as are rigidity analyses on biomolecules including the ribosome, viruses, or transmembrane proteins. The analyses address questions of allosteric mechanisms, mutation effects on (thermo-) stability, protein (un-) folding, and coarse-graining of biomolecules. We advocate that the application of rigidity theory to biomolecules has matured in such a way that it could be broadly applied as a computational biophysical method to scrutinize biomolecular function from a structure-based point of view and to complement approaches focused on biomolecular dynamics. We discuss possibilities to improve constraint network representations and to perform large-scale and prospective studies. (C) 2017 John Wiley & Sons, Ltd