Computational Approaches in Peptide and Protein Design: An Overview - Peptide and Protein Design for Biopharmaceutical Applications - page 20

2.2.2.3 Sampling

Sampling of peptide conformational space The most thermodynami-
cally stable conformational state of a molecular system is, obviously, the
one with the lowest free energy (the global minimum-energy conformer).
However, energy minimizations performed using MM find only values of
potential energy; to calculate values of free energy, one needs to know the
entire multidimensional potential surface, or at least all local low-energy
conformers, in order to estimate the partition function and calculate the
entropic contribution to the free energy. In this regard, sampling of
peptide conformational space is, in fact, mapping of the energy surface
of the peptide in search of the local energy minima.
Several strategies have been developed to map the potential energy sur-
face and to find local minima. Stochastic methods such as Monte Carlo can
be employed not only to find local minima, but also to estimate local
fluctuations inside a given minimum. Molecular dynamics can also be
used to explore the potential energy surface, often with some enhance-
ments such as simulated annealing or replica exchange to help overcome
energy barriers between minima, i.e. kinetic barriers related to conforma-
tional dynamics. Systematic, or grid, search samples conformations in a
regular fashion in the space of parameters (usually by dihedral torsional
angles) that are incremented. In a sense, the same approach is represented
by various build-up procedures, whose aim is to explore the conforma-
tional states of the entire peptide molecule by systematically combining
results of conformational samplings for fragments of this peptide. These
different methods of conformational sampling are briefly discussed below.

Examples of systematic sampling Systematic search consists of sys-
tematic generation of all possible conformations at the selected torsional
grid, in order to determine the set of sterically allowed ones. Therefore,
systematic search is the most exhaustive way of sampling the conforma-
tional space, but due to its combinatorial nature the number of confor-
mations considered increases enormously with an increase of torsional
space dimensionality. Also, since the energetics of the molecular system
are very sensitive to interatomic distances, a conformation generated at,
say, the 10 increment may be sterically disallowed, but very close to a
minimum, so relaxation of the structure by allowing a torsional angle to
vary by 1 or less may find the missing minimum. However, the compu-
tational cost for that systematic change would be prohibitive. Indeed,
using a 10 grid for, say, a seven-rotatable bond problem, the entire
number of conformations explored will be 7 36 (2.65 10 30 ), whereas at