Thesis by Alan Martin Mathiowetz
Advisor: William A. Goddard III
In order to increase the efficiency of protein simulations, both deterministic and stochastic methods can be formulated in terms of the most important degrees of freedom in polypeptide and protein systems: the torsions. Two such methods are presented here. The first is Newton-Euler Inverse Mass Operator (NEIMO) Dynamics, an internal-coordinate molecular dynamics method originally designed to study the dynamics of general multibody systems. The second is the Probability Grid Monte Carlo (PGMC) method, developed for searching the conformational space of polypeptides using a weighted sampling of the most favorable dihedral angles.
The first use of the NEIMO Dynamics method for studying molecular systems is reported here. The method is used to study the dynamics of a wide range of peptide and protein systems. These range from the pentapeptide Met-enkephalin to the crystallographic asymmetric unit of the tomato bushy stunt virus (TBSV), an assembly of three chains totaling 893 residues. Bond lengths and angles do not vary during the dynamics simulations; this enables timesteps larger than 10 femtoseconds to be used for small peptides, a substantial improvement over Cartesian coordinate molecular dynamics. Timesteps of 10 fs do not work well for NEIMO simulations of large proteins because of unacceptably large energy fluctuations. However, timesteps of 2-5 fs give acceptable results, even for very large systems. The NEIMO method is applied to TBSV coat proteins, in an investigation of the effect of Ca ions on the coat stability.
The PGMC method provides efficient conformational searches for polypeptide systems by assigning probabilities to different discrete values of the , , and dihedral angles. These probabilities were derived by investigation of the protein structures in the Brookhaven Protein Database. The PGMC method is applied successfully to several important problems in protein modeling: studies of the low-energy conformations of a peptide, prediction of the all-atom conformation of a protein from its C coordinates alone, and the prediction of antibody loop conformations. The success of the C modeling is further extended by its application to structures with coordinates constrained to a lattice, through the use of a simple C Forcefield.