ct301005b_si_001.mpg (3.53 MB)
Accelerating Convergence in Molecular Dynamics Simulations of Solutes in Lipid Membranes by Conducting a Random Walk along the Bilayer Normal
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posted on 2013-08-13, 00:00 authored by Chris Neale, Chris Madill, Sarah Rauscher, Régis PomèsAll
molecular dynamics simulations are susceptible to sampling
errors, which degrade the accuracy and precision of observed values.
The statistical convergence of simulations containing atomistic lipid
bilayers is limited by the slow relaxation of the lipid phase, which
can exceed hundreds of nanoseconds. These long conformational autocorrelation
times are exacerbated in the presence of charged solutes, which can
induce significant distortions of the bilayer structure. Such long
relaxation times represent hidden barriers that induce systematic
sampling errors in simulations of solute insertion. To identify optimal
methods for enhancing sampling efficiency, we quantitatively evaluate
convergence rates using generalized ensemble sampling algorithms in
calculations of the potential of mean force for the insertion of the
ionic side chain analog of arginine in a lipid bilayer. Umbrella sampling
(US) is used to restrain solute insertion depth along the bilayer
normal, the order parameter commonly used in simulations of molecular
solutes in lipid bilayers. When US simulations are modified to conduct
random walks along the bilayer normal using a Hamiltonian exchange
algorithm, systematic sampling errors are eliminated more rapidly
and the rate of statistical convergence of the standard free energy
of binding of the solute to the lipid bilayer is increased 3-fold.
We compute the ratio of the replica flux transmitted across a defined
region of the order parameter to the replica flux that entered that
region in Hamiltonian exchange simulations. We show that this quantity,
the transmission factor, identifies sampling barriers in degrees of
freedom orthogonal to the order parameter. The transmission factor
is used to estimate the depth-dependent conformational autocorrelation
times of the simulation system, some of which exceed the simulation
time, and thereby identify solute insertion depths that are prone
to systematic sampling errors and estimate the lower bound of the
amount of sampling that is required to resolve these sampling errors.
Finally, we extend our simulations and verify that the conformational
autocorrelation times estimated by the transmission factor accurately
predict correlation times that exceed the simulation time scalesomething
that, to our knowledge, has never before been achieved.
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Keywords
side chain analoglipid bilayersolute insertion depthsMolecular Dynamics Simulationsatomistic lipid bilayerssampling errorsHamiltonian exchange algorithmensemble sampling algorithmsorder parameterHamiltonian exchange simulationstransmission factorsolute insertion depthreplica fluxautocorrelation times
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