Chemistry Reference
In-Depth Information
has been proposed recently to overcome this shortcoming.
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This method
computes a non-Markovian hopping between configuration space hyper-
planes, the so-called milestones. The assumption being made is that there
exists an equilibrium distribution on each milestone. The kinetics of a process
is obtained by starting an equilibrium configuration on a milestone and mea-
suring the time distribution needed to reach the forward or backward mile-
stones using short MD simulations. These time distributions are then used
to compute the global kinetics through a non-Markovian model. The algo-
rithm needs a reaction coordinate to define the hyperplanes. That reaction
coordinate can be an MEP or an SDEL trajectory. The equilibrium sampling
is performed in the neighborhood of the curvilinear path describing the reac-
tion coordinate. Milestoning can also be used to compute free energy profiles
along reaction coordinates.
140,141
Milestoning makes the assumption that only
one reaction coordinate (slow variable) exists in the system. The validity of the
simulation results can be assessed by monitoring the rate as a function of the
separation between the milestones, which can be changed from run to run.
A similar algorithm is partial path transition interface sampling
(PPTIS).
142
This method is based on transition interface sampling (TIS),
64,68
which maps the phase space of the system with many interfaces (similar to
the milestones) characterized by a one-dimensional reaction coordinate. In
PPTIS rates are computed using a Markovian state model, i.e., by assuming
a loss of correlation during interface hopping. This algorithm is aimed at com-
puting the kinetics of two-state exponential process in equilibrium.
Use of milestoning or PPTIS may provide a way to recover the informa-
tion that is lost when the high-frequency motions of the molecular system are
filtered out by an SDEL trajectory. Hence, correct kinetic and thermodynamic
properties might be extracted from the simulations. For very long and diffusive
processes, like those associated with the folding of large proteins, computation
of these properties will still be challenging because the transitions between
hyperplanes or interfaces require longer MD simulations. At that point, a com-
bination of MTS with these path methods could be used to improve efficiency
and speed.
CONCLUSION
Computational methods used to extend the time scale of atomically
detailed simulations have improved in the last 15 years. Accurate MTS simula-
tions, with computational gains up to a factor of 10, have extended the applic-
ability of molecular dynamics simulations and refinements in the computation
of medium-range forces could provide stable results with increasing speedups. It
is apparent that stability limitations will prevent the extension of these algo-
rithms to the range of time scales that are needed to study many processes of
interest, however. On the other hand, reaction path approaches can be used
