Counting out to the flexibility of molecules.

We outline the mathematical models, and the related counting algorithms, that are the basis for fast computations to predict biomolecular flexibility and rigidity. Within these mathematical models, we describe the snap-shot flexibility (instantaneous motions) of biomolecules, extracted from a single snap-shot of the molecule and the connection to larger finite motions. We illustrate the results and techniques with direct analysis of simple secondary structures. Understanding these basic ideas clarifies both the limits and the power of the algorithms, as well as the prospects for extensions and refinements of these algorithms.