3 research outputs found
Equipartition Principle for Internal Coordinate Molecular Dynamics
The <i>principle of equipartition of (kinetic) energy</i> for all-atom Cartesian molecular dynamics states that each momentum
phase space coordinate on the average has <i>kT</i>/2 of
kinetic energy in a canonical ensemble. This principle is used in
molecular dynamics simulations to initialize velocities, and to calculate
statistical properties such as entropy. Internal coordinate molecular
dynamics (ICMD) models differ from Cartesian models in that the overall
kinetic energy depends on the generalized coordinates and includes
cross-terms. Due to this coupled structure, no such equipartition
principle holds for ICMD models. In this paper, we introduce noncanonical <i>modal coordinates</i> to recover some of the structural simplicity
of Cartesian models and develop a new equipartition principle for
ICMD models. We derive low-order recursive computational algorithms
for transforming between the modal and physical coordinates. The equipartition
principle in modal coordinates provides a rigorous method for initializing
velocities in ICMD simulations, thus replacing the <i>ad hoc</i> methods used until now. It also sets the basis for calculating conformational
entropy using internal coordinates
Protein Structure Refinement of CASP Target Proteins Using GNEIMO Torsional Dynamics Method
A longstanding
challenge in using computational methods for protein
structure prediction is the refinement of low-resolution structural
models derived from comparative modeling methods into highly accurate
atomistic models useful for detailed structural studies. Previously,
we have developed and demonstrated the utility of the internal coordinate
molecular dynamics (MD) technique, generalized NewtonâEuler
inverse mass operator (GNEIMO), for refinement of small proteins.
Using GNEIMO, the high-frequency degrees of freedom are frozen and
the protein is modeled as a collection of rigid clusters connected
by torsional hinges. This physical model allows larger integration
time steps and focuses the conformational search in the low frequency
torsional degrees of freedom. Here, we have applied GNEIMO with temperature
replica exchange to refine low-resolution protein models of 30 proteins
taken from the continuous assessment of structure prediction (CASP)
competition. We have shown that GNEIMO torsional MD method leads to
refinement of up to 1.3 Ă
in the root-mean-square deviation in
coordinates for 30 CASP target proteins without using any experimental
data as restraints in performing the GNEIMO simulations. This is in
contrast with the unconstrained all-atom Cartesian MD method performed
under the same conditions, where refinement requires the use of restraints
during the simulations
Structure Refinement of Protein Low Resolution Models Using the GNEIMO Constrained Dynamics Method
The challenge in protein structure prediction using homology
modeling
is the lack of reliable methods to refine the low resolution homology
models. Unconstrained all-atom molecular dynamics (MD) does not serve
well for structure refinement due to its limited conformational search.
We have developed and tested the constrained MD method, based on the
generalized NewtonâEuler inverse mass operator (GNEIMO) algorithm
for protein structure refinement. In this method, the high-frequency
degrees of freedom are replaced with hard holonomic constraints and
a protein is modeled as a collection of rigid body clusters connected
by flexible torsional hinges. This allows larger integration time
steps and enhances the conformational search space. In this work,
we have demonstrated the use of torsional GNEIMO method without using
any experimental data as constraints, for protein structure refinement
starting from low-resolution decoy sets derived from homology methods.
In the eight proteins with three decoys for each, we observed an improvement
of âŒ2 Ă
in the rmsd in coordinates to the known experimental
structures of these proteins. The GNEIMO trajectories also showed
enrichment in the population density of native-like conformations.
In addition, we demonstrated structural refinement using a âfreeze
and thawâ clustering scheme with the GNEIMO framework as a
viable tool for enhancing localized conformational search. We have
derived a robust protocol based on the GNEIMO replica exchange method
for protein structure refinement that can be readily extended to other
proteins and possibly applicable for high throughput protein structure
refinement