168 research outputs found
Estimation of the infinitesimal generator by square-root approximation
For the analysis of molecular processes, the estimation of time-scales, i.e.,
transition rates, is very important. Estimating the transition rates between
molecular conformations is -- from a mathematical point of view -- an invariant
subspace projection problem. A certain infinitesimal generator acting on
function space is projected to a low-dimensional rate matrix. This projection
can be performed in two steps. First, the infinitesimal generator is
discretized, then the invariant subspace is approxi-mated and used for the
subspace projection. In our approach, the discretization will be based on a
Voronoi tessellation of the conformational space. We will show that the
discretized infinitesimal generator can simply be approximated by the geometric
average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct
correla-tion between the potential energy surface of molecular structures and
the transition rates of conformational changes. We present results for a
2d-diffusion process and Alanine dipeptide
Publisher’s Note: “Density-based cluster algorithms for the identification of core sets” [J. Chem. Phys. 145, 164104 (2016)]
Original Article: J. Chem. Phys. 145, 164104 (2016) This article was
originally published online on 26 October 2016 with an error in the second
author’s name. “Bettina G. Lemke” should be “Bettina G. Keller.” AIP
Publishing apologizes for this error. All online versions of the article were
corrected on 27 October 2016; the article is correct as it appears in the
printed version of the journal
GROMACS Stochastic Dynamics and BAOAB are equivalent configurational sampling algorithms
Two of the most widely used Langevin integrators for molecular dynamics
simulations are the GROMACS Stochastic Dynamics (GSD) integrator and the
splitting method BAOAB. We show that the GROMACS Stochastic Dynamics integrator
is equal to the less frequently used splitting method BAOA. It immediately
follows that GSD and BAOAB sample the same configurations and have the same
high configurational accuracy. Our numerical results indicate that GSD/BAOA has
higher kinetic accuracy than BAOAB
Fluorinated Protein–Ligand Complexes: A Computational Perspective
Fluorine is an element renowned for its unique properties. Its powerful capability to modulate molecular properties makes it an attractive substituent for protein binding ligands; however, the rational design of fluorination can be challenging with effects on interactions and binding energies being difficult to predict. In this Perspective, we highlight how computational methods help us to understand the role of fluorine in protein–ligand binding with a focus on molecular simulation. We underline the importance of an accurate force field, present fluoride channels as a showcase for biomolecular interactions with fluorine, and discuss fluorine specific interactions like the ability to form hydrogen bonds and interactions with aryl groups. We put special emphasis on the disruption of water networks and entropic effects
Path probability ratios for Langevin dynamics -- exact and approximate
Path reweighting is a principally exact method to estimate dynamic properties
from biased simulations - provided that the path probability ratio matches the
stochastic integrator used in the simulation. Previously reported path
probability ratios match the Euler-Maruyama scheme for overdamped Langevin
dynamics. Since MD simulations use Langevin dynamics rather than overdamped
Langevin dynamics, this severely impedes the application of path reweighting
methods. Here, we derive the path probability ratio for Langevin dynamics
propagated by a variant of the Langevin Leapfrog integrator. This new path
probability ratio allows for exact reweighting of Langevin dynamics propagated
by this integrator. We also show that a previously derived approximate path
probability ratio differs from the exact only by
, and thus yields highly accurate dynamic
reweighting results. ( is the integration time step, is the
collision rate.) The results are tested and the efficiency of path-reweighting
is explored using butane as an example
Thermal isomerization rates in retinal analogues using Ab-Initio molecular dynamics
For a detailed understanding of chemical processes in nature and industry, we need accurate models of chemical reactions in complex environments. While Eyring transition state theory is commonly used for modeling chemical reactions, it is most accurate for small molecules in the gas phase. A wide range of alternative rate theories exist that can better capture reactions involving complex molecules and environmental effects. However, they require that the chemical reaction is sampled by molecular dynamics simulations. This is a formidable challenge since the accessible simulation timescales are many orders of magnitude smaller than typical timescales of chemical reactions. To overcome these limitations, rare event methods involving enhanced molecular dynamics sampling are employed. In this work, thermal isomerization of retinal is studied using tight-binding density functional theory. Results from transition state theory are compared to those obtained from enhanced sampling. Rates obtained from dynamical reweighting using infrequent metadynamics simulations were in close agreement with those from transition state theory. Meanwhile, rates obtained from application of Kramers' rate equation to a sampled free energy profile along a torsional dihedral reaction coordinate were found to be up to three orders of magnitude higher. This discrepancy raises concerns about applying rate methods to one-dimensional reaction coordinates in chemical reactions
Prebound State Discovered in the Unbinding Pathway of Fluorinated Variants of the Trypsin–BPTI Complex Using Random Acceleration Molecular Dynamics Simulations
The serine protease trypsin forms a tightly bound inhibitor complex with the bovine pancreatic trypsin inhibitor (BPTI). The complex is stabilized by the P1 residue Lys15, which interacts with negatively charged amino acids at the bottom of the S1 pocket. Truncating the P1 residue of wildtype BPTI to α-aminobutyric acid (Abu) leaves a complex with moderate inhibitor strength, which is held in place by additional hydrogen bonds at the protein–protein interface. Fluorination of the Abu residue partially restores the inhibitor strength. The mechanism with which fluorination can restore the inhibitor strength is unknown, and accurate computational investigation requires knowledge of the binding and unbinding pathways. The preferred unbinding pathway is likely to be complex, as encounter states have been described before, and unrestrained umbrella sampling simulations of these complexes suggest additional energetic minima. Here, we use random acceleration molecular dynamics to find a new metastable state in the unbinding pathway of Abu-BPTI variants and wildtype BPTI from trypsin, which we call the prebound state. The prebound state and the fully bound state differ by a substantial shift in the position, a slight shift in the orientation of the BPTI variants, and changes in the interaction pattern. Particularly important is the breaking of three hydrogen bonds around Arg17. Fluorination of the P1 residue lowers the energy barrier of the transition between the fully bound state and prebound state and also lowers the energy minimum of the prebound state. While the effect of fluorination is in general difficult to quantify, here, it is in part caused by favorable stabilization of a hydrogen bond between Gln194 and Cys14. The interaction pattern of the prebound state offers insights into the inhibitory mechanism of BPTI and might add valuable information for the design of serine protease inhibitors
Implementation of Girsanov Reweighting in OpenMM and Deeptime
Classical molecular dynamics (MD) simulations provide invaluable insights into complex molecular systems but face limitations in capturing phenomena occurring on time scales beyond their reach. To bridge this gap, various enhanced sampling techniques have been developed, which are complemented by reweighting techniques to recover the unbiased dynamics. Girsanov reweighting is a reweighting technique that reweights simulation paths, generated by a stochastic MD integrator, without evoking an effective model of the dynamics. Instead, it calculates the relative path probability density at the time resolution of the MD integrator. Efficient implementation of Girsanov reweighting requires that the reweighting factors are calculated on-the-fly during the simulations and thus needs to be implemented within the MD integrator. Here, we present a comprehensive guide for implementing Girsanov reweighting into MD simulations. We demonstrate the implementation in the MD simulation package OpenMM by extending the library openmmtools. Additionally, we implemented a reweighted Markov state model estimator within the time series analysis package Deeptime
Grid-based state space exploration for molecular binding
Binding processes are difficult to sample with molecular-dynamics (MD)
simulations. In particular, the state space exploration is often incomplete.
Evaluating the molecular interaction energy on a grid circumvents this problem
but is heavily limited by state space dimensionality. Here, we make the first
steps towards a low-dimensional grid-based model of molecular binding. We
discretise the state space of relative positions and orientations of the two
molecules under the rigid body assumption.The corresponding program is
published as the Python package molgri. For the rotational component of the
grids, we test algorithms based on Euler angles, polyhedra and quaternions, of
which the polyhedra-based are the most uniform. The program outputs a sequence
of molecular structures that can be easily processed by standard MD programs to
calculate grid point energies. We demonstrate the grid-based approach on two
molecular systems: a water dimer and a coiled-coil protein interacting with a
chloride anion. For the second system we relax the rigid-body assumption and
improve the accuracy of the grid point energies by an energy minimisation. In
both cases, oriented bonding patterns and energies confirm expectations from
chemical intuition and MD simulations. We also demonstrate how analysis of
energy contributions on a grid can be performed and demonstrate that
electrostatically-driven association is sufficiently resolved by point-energy
calculations. Overall, grid-based models of molecular binding are potentially a
powerful complement to molecular sampling approaches, and we see the potential
to expand the method to quantum chemistry and flexible docking applications.Comment: 13 pages, 7 figure
A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models
Dynamical reweighting methods permit to estimate kinetic observables of a
stochastic process governed by a target potential from
trajectories that have been generated at a different potential . In this
article, we present Girsanov reweighting and Square Root Approximation (SqRA):
the first method reweights path probabilities exploiting the Girsanov theorem
and can be applied to Markov State Models (MSMs) to reweight transition
probabilities; the second method was originally developed to discretize the
Fokker-Planck operator into a transition rate matrix, but here we implement it
into a reweighting scheme for transition rates. We begin by reviewing the
theoretical background of the methods, then present two applications relevant
to Molecular Dynamics (MD), highlighting their strengths and weaknesses
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