Rigidity and flexible motion in biomolecules

It has been known since Maxwell that a count of degrees of freedom and constraints can establish if a  structure is, overall, floppy, rigid or stressed (overconstrained). The "pebble game" algorithm can rapidly identify the rigid and stressed regions of a two-dimensional framework. The "Molecular Framework Conjecture"  states that the "pebble game" is valid for networks with nearest-neighbour and next-nearest-neighbour constraints, or equivalently, to frameworks with fixed bond lengths and angles and variable dihedral angles.  So, we can apply rigidity analysis to protein structures (as obtained from X-ray or neutron crystallography)  and identify rigid substructures. Rigidity analysis provides a natural coarse-graining for a simplified model of protein motion. This in turn allows us to address flexible (slow, low-energy) motions in proteins using the technique of "geometric simulation". Finally, I will show an example of synergy between

molecular-dynamics simulation and geometric simulation in the field of protein structure prediction.