We investigate the folding, binding and evolution of proteins using a computational approach that is largely based on simplified models of proteins. The models we use range from the simplest, two-dimensional HP (hydrophobic-polar) lattice models to more realistic models with various levels of coarse-graining. One of the most promising approaches is discrete molecular dynamics (DMD), which increases the time scale of molecular dynamics simulations by several orders of magnitude. The problems under study include folding, amyloid formation, the coupling between folding and binding, disorder-to-order transitions, and the evolution of protein structures from fragments corresponding to structural motifs.

Discrete (or discontinuous) molecular dynamics (DMD) is an old but significantly underutilized method to simulate macromolecular systems. DMD uses a step potential with discrete energy values. Instead of integrating the equations of motion using a final time step, an event-driven algorithm is employed, and the dynamics simplifies to a series of collision events separated by ballistic runs. This results in a speedup of several orders of magnitude relative to conventional molecular dynamics.

Because no DMD simulation engine is available, commercially or otherwise, we developed our own program, consisting of ~8000 lines of C source code.

The DMD algorithm requires forcefields developed specially for DMD. We introduced several united-atom forcefields for various simplified models. First, we tested the algorithm and the forcefields on polyalanine peptides, successfully reproducing helix-beta transitions and beta sheet formation.

On test systems, the simulation results were found to strongly depend on forcefield parameters including atomic radii. We describe a new procedure to optimize atomic radii to reproduce the expected energy map of short peptides on a Ramachandran plots. For a potential function including hydrogen bonds, hydrophobic interactions, salt bridges and interactions between aromatic groups, we optimized the weights of the energy terms by maximizing the correlation between the energy and the deviation of the structure of a small protein from the native state. Folding simulations were carried out on Trp cage, a 20-residue miniprotein. Using the optimized energy function, we folded the peptide to within 2 Å rmsd from the native structure.

Experimental results with certain Trp cage mutants indicate that the protein can form amyloid-like fibrils when exposed to heat treatment. Spectroscopical data are insufficient to determine the exact structure of the fibrils. Current data suggest that a small amount of alpha helix may be present; this may indicate domain swapping but a fibril assembled from short beta strands is also possible. DMD simulations with several chains were carried out in an attempt to set up a reasonable hypothesis regarding the structure of fib