Chemistry Reference
In-Depth Information
the transition, and, umbrella sampling can be used to compute the rate in
Eq. [23].
The molecular processes typically studied with TPS involve a transition
over a single, albeit significant barrier. TPS is more efficient than standard MD
because the reactive trajectories (computed by TPS) are much shorter through
phase space than the time it takes between successive transitions; more (reac-
tive) trajectories are therefore computed with TPS than with normal MD
methods.
The TPS methodology has been applied successfully to evaluate time-
dependent events, such as chemical reactions and conformational chan-
ges.
65,68,70-74
Application of this algorithm to complex systems with rugged
energy surfaces, however, requires the identification of basin states separated
by several barriers with different heights. For these systems, the assumption of
time-scale separation between the transition time and the incubation time is
not easy to justify. For these complex systems, the reactive trajectories can
be long, and the sampling will be limited by the time step used in the simula-
tion. Defining the reaction coordinate or a physical descriptor that allows for
the identification of the different basin and transition states present during
transitions of complex molecules can be cumbersome.
75
Maximization of the Diffusive Flux (MaxFlux)
MaxFlux is a time-independent algorithm that seeks a path that maximizes
the diffusive flux (or minimizes the mean first-passage time) between two config-
urations at a given temperature. The algorithm is based on the work of
Berkowitz and co-workers
76
who derived the optimal transition connecting
reactant and product using a variational principle. If the transition is described
as a stochastic process, the flux of particles along the optimal path is given by
tan
t
g
Ð
exp
j
/
½
25
ð
b
V
Þ
dl
where
V
is the potential of mean force of the system,
g
is an isotropic and spa-
tially independent friction coefficient,
k
B
T
,and
dl
is an infinitesimal
length element along the path. In MaxFlux, the line integral in the denomina-
tor of Eq. [25] is minimized using a self-penalty walk method.
77
MaxFlux has been used to study conformational transitions in peptides
and aggregate formation by Straub et al.
78,79
Itcanalsobeusedtodescribe
slow processes controlled by diffusion.
76
A difficulty with MaxFlux is
the necessity to specify the phenomenological friction constant. Themagnitude
of the friction constant strongly influences computed rates, and it affects the
transition pathways. Equation [25] is maximized with global optimization
algorithms that are both time-consuming and dependent on the initial guess
for the pathway.
b
¼
1
=
