Arguably, the dynamics of protein folding is THE problem of modern mathematical biology. Here is a recent achievement:
In short, a supercomputer is built that uses a physical model of atom interactions to model protein folding. This is great, of course, and really exiting, but here is an extract:
Simulating the basic pancreatic trypsin inhibitor over the course of a millisecond took Anton about 100 days
Which undoubtedly means that any numerical experiments with protein folding are beyond our reach. Yet? I believe that approach by brute force is the wrong one here. In a similar vein, as no one calculates pressure of a gas, using differential equations for all the molecules, but instead uses statistical physics to predict the average effects of random behavior, a completely new approach is needed to model the protein folding.