384 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
Publisherâs Note: âDensity-based cluster algorithms for the identification of core setsâ [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
authorâs name. âBettina G. Lemkeâ should be âBettina G. Keller.â 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
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
Biomolecular structure refinement based on adaptive restraints using local-elevation simulation
Introducing experimental values as restraints into molecular dynamics (MD) simulation to bias the values of particular molecular properties, such as nuclear Overhauser effect intensities or distances, dipolar couplings, 3 J-coupling constants, chemical shifts or crystallographic structure factors, towards experimental values is a widely used structure refinement method. Because multiple torsion angle values Ï correspond to the same 3 J-coupling constant and high-energy barriers are separating those, restraining 3 J-coupling constants remains difficult. A method to adaptively enforce restraints using a local elevation (LE) potential energy function is presented and applied to 3 J-coupling constant restraining in an MD simulation of hen egg-white lysozyme (HEWL). The method succesfully enhances sampling of the restrained torsion angles until the 37 experimental 3 J-coupling constant values are reached, thereby also improving the agreement with the 1,630 experimental NOE atom-atom distance upper bounds. Afterwards the torsional angles Ï are kept restrained by the built-up local-elevation potential energie
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
Recommended from our members
Estimation of the infinitesimal generator by square-root approximation
For the analysis of molecular processes, the estimation of time-scales, i.e., tran-
sition rates, is very important. Estimating the transition rates between molecular
conformations is - from a mathematical point of view - an invariant subspace projec-
tion 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 ap-
proximated 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 ge-
ometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a
direct correlation 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
On using oscillating time-dependent restraints in MD simulation
The use of time-dependent restraints in molecular simulation in order to generate a conformational ensemble for molecules that is in accordance with measured ensemble averages for particular observable quantities is investigated. Using a model system consisting of liquid butane and the cyclic peptide antamanide the reproduction of particular average 3 J-coupling constant values in a molecular dynamics simulation is analysed. It is shown that the multiple-valuedness and the sizeable gradients of the Karplus curve relating 3 J-coupling constants measured in NMR experiments to the corresponding torsional-angle values cause severe problems when trying to restrain a 3 J-coupling constant to a value close to the extrema of the Karplus curve. The introduction of a factor oscillating with time into the restraining penalty function alleviates this problem and enhances the restrained conformational samplin
Transdisciplinary transformative change: an analysis of some best practices and barriers, and the potential of critical social science in getting us there
Biodiversity experts now widely acknowledge that transformative change is best supported through transdisciplinary collaborations. Yet, such collaborations rarely successfully occur in major biodiversity research institutions and those that do rarely achieve the paradigmatic effects they aim to deliver. To gain some insight into this global phenomenon, we surveyed Swiss-based researchers and non-academic stakeholders addressing global change and biodiversity. In this article, we connect our findings to global patterns in transdisciplinary transformative change initiatives (TTCIs) and heuristically divide collaboration barriers into two categories: lack of resources and lack of vital functional elements. Two of the major themes that emerged from this research were the continued difficulties with (1) establishing a common âlanguageâ, understanding, and goals, and (2) meaningful pluralization of knowledge in transdisciplinary collaborations aimed at addressing global change and biodiversity loss. The former is widely cited in the literature as contributing to the failure of TTCIs in the form of incoherent problem-framing, while the latter is often identified as contributing to the lack of structural transformative change (e.g., paradigmatic shifts) in completed initiatives. Another major theme reflected in TTCI literature was limited time. Moreover, based on our own extensive inter- and transdisciplinary experience, we agree with other experts that there is a persistent lack of understanding of the potential contributions of critical social science (CSS) to TTCIs. We thus argue that enhancing resource availability for TTCIs, especially tools for improving CSS literacy, could save time and support both problem-framing alignment and delivery of the structural/paradigmatic changes we aspire to
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