MMC, like MD, is based on statistical physics; but rather than
using Newtonian theory to model motions, Monte-Carlo random
numbers are used to generate changes to the model which are then
filtered with a Metropolis test to ensure sampling from the Boltz-
mann distribution.
MD and MMC are favored for different types of simulation
such as MMC for gas-phase or low-density models or calculations
of chemical potential. Generally MD is used for condensed phase
systems where collective motions are important. However, there
are some areas of overlap such as calculation of binding free-
energies. Furthermore, hybrid methods are becoming increasingly
popular as they offer great combinations of features [13]. Here we
will focus on MD simulations as we are mainly interested in
condensed phase simulations of proteins.3 Fundamental Challenges in Simulations of Conformational Change
The fundamental challenges of using dynamic simulation to explore
protein conformational transitions are related to the two interre-
lated limitations of molecular dynamics.- Model quality: It is difficult to produce a dynamic model which
is able to capture all aspects of the interactions of proteins yet
sufficiently simple such that it can be sampled rapidly. - Timescales: The protein conformational transitions of interest
often take place on slower timescales than what we are able to
sample with a suitable dynamic model.
3.1 Model Resolution Within the field of biosimulation various resolutions of model are
available from quantum mechanical (QM) to coarse-grained.
The QM level is the most detailed representation which
includes electronic structure. Dynamical simulations at the QM
level is carried out with either Born–Oppenheimer molecular
dynamics (BOMD) using the time-independent Schro ̈dinger equa-
tion or Car–Parrinello molecular dynamics (CPMD) which explic-
itly includes the electron dynamics. QM dynamics is normally
restricted to small chemical systems (seeNote 4). Well known
hybrid models (QM/MM) are also too slow for work on the slow
protein transitions of interest in many drug targets, and are gener-
ally used for models of enzyme reactions.
In terms of protein model resolution, after QM we have classi-
cal mechanics, which for proteins means molecular mechanics
(MM). Atomistic MM generally refers to Lifson like models or
force fields with van der Waals (VDW) spheres for atoms, point
charges and springs controlling bond angles and dihedrals [14](see
Note 5). In addition, modern atomistic simulations have periodic-
boundary conditions and provision for long-range electrostatics.
342 Benjamin P. Cossins et al.