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.