407 research outputs found
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Improving double-ended transition state searches for soft-matter systems.
Transitions between different stable configurations of biomolecules are important in understanding disease mechanisms, structure-function relations, and novel molecular-scale engineering. The corresponding pathways can be characterized efficiently using geometry optimization schemes based on double-ended transition state searches. An interpolation is first constructed between the known states and then refined, yielding a band that contains transition state candidates. Here, we analyze an example where various interpolation schemes lead to bands with a single step transition, but the correct pathway actually proceeds via an intervening, low-energy minimum. We compare a number of different interpolation schemes for this problem. We systematically alter the number of discrete images in the interpolations and the spring constants used in the optimization and test two schemes for adjusting the spring constants and image distribution, resulting in a total of 2760 different connection attempts. Our results confirm that optimized bands are not necessarily a good description of the transition pathways in themselves, and further refinement to actually converge transition states and establish their connectivity is required. We see an improvement in the optimized bands if we employ the adjustment of spring constants with doubly-nudged elastic band and a smaller improvement from the image redistribution. The example we consider is representative of numerous cases we have encountered in a wide variety of molecular and condensed matter systems
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Kinetics of Molecular Diffusion and Self-Assembly: Glycine on Cu{110}
Machine learning prediction for classification of outcomes in local minimisation
Machine learning schemes are employed to predict which local minimum will result from local energy minimisation of random starting configurations for a triatomic cluster. The input data consists of structural information at one or more of the configurations in optimisation sequences that converge to one of four distinct local minima. The ability to make reliable predictions, in terms of the energy or other properties of interest, could save significant computational resources in sampling procedures that involve systematic geometry optimisation. Results are compared for two energy minimisation schemes, and for neural network and quadratic functions of the inputs
The Energy Landscape, Folding Pathways and the Kinetics of a Knotted Protein
The folding pathway and rate coefficients of the folding of a knotted protein
are calculated for a potential energy function with minimal energetic
frustration. A kinetic transition network is constructed using the discrete
path sampling approach, and the resulting potential energy surface is
visualized by constructing disconnectivity graphs. Owing to topological
constraints, the low-lying portion of the landscape consists of three distinct
regions, corresponding to the native knotted state and to configurations where
either the N- or C-terminus is not yet folded into the knot. The fastest
folding pathways from denatured states exhibit early formation of the
N-terminus portion of the knot and a rate-determining step where the C-terminus
is incorporated. The low-lying minima with the N-terminus knotted and the
C-terminus free therefore constitute an off-pathway intermediate for this
model. The insertion of both the N- and C-termini into the knot occur late in
the folding process, creating large energy barriers that are the rate limiting
steps in the folding process. When compared to other protein folding proteins
of a similar length, this system folds over six orders of magnitude more
slowly.Comment: 19 page
Kinetic Analysis of Discrete Path Sampling Stationary Point Databases
Analysing stationary point databases to extract phenomenological rate
constants can become time-consuming for systems with large potential energy
barriers. In the present contribution we analyse several different approaches
to this problem. First, we show how the original rate constant prescription
within the discrete path sampling approach can be rewritten in terms of
committor probabilities. Two alternative formulations are then derived in which
the steady-state assumption for intervening minima is removed, providing both a
more accurate kinetic analysis, and a measure of whether a two-state
description is appropriate. The first approach involves running additional
short kinetic Monte Carlo (KMC) trajectories, which are used to calculate
waiting times. Here we introduce `leapfrog' moves to second-neighbour minima,
which prevent the KMC trajectory oscillating between structures separated by
low barriers. In the second approach we successively remove minima from the
intervening set, renormalising the branching probabilities and waiting times to
preserve the mean first-passage times of interest. Regrouping the local minima
appropriately is also shown to speed up the kinetic analysis dramatically at
low temperatures. Applications are described where rates are extracted for
databases containing tens of thousands of stationary points, with effective
barriers that are several hundred times kT.Comment: 28 pages, 1 figure, 4 table
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