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

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

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

Equilibrium molecular thermodynamics from Kirkwood sampling.

We present two methods for barrierless equilibrium sampling of molecular systems based on the recently proposed Kirkwood method (J. Chem. Phys. 2009, 130, 134102). Kirkwood sampling employs low-order correlations among internal coordinates of a molecule for random (or non-Markovian) sampling of the high dimensional conformational space. This is a geometrical sampling method independent of the potential energy surface. The first method is a variant of biased Monte Carlo, where Kirkwood sampling is used for generating trial Monte Carlo moves. Using this method, equilibrium distributions corresponding to different temperatures and potential energy functions can be generated from a given set of low-order correlations. Since Kirkwood samples are generated independently, this method is ideally suited for massively parallel distributed computing. The second approach is a variant of reservoir replica exchange, where Kirkwood sampling is used to construct a reservoir of conformations, which exchanges conformations with the replicas performing equilibrium sampling corresponding to different thermodynamic states. Coupling with the Kirkwood reservoir enhances sampling by facilitating global jumps in the conformational space. The efficiency of both methods depends on the overlap of the Kirkwood distribution with the target equilibrium distribution. We present proof-of-concept results for a model nine-atom linear molecule and alanine dipeptide.This research was funded by the European Research Council and EPSRC grant EP/I001352/1. Y.O. was supported, in part, by the JSPS Grant-in-Aid for Scientific Research on Innovative Areas (“Dynamical Ordering and Integrated Functions”).This is the final published version. It first appeared at http://pubs.acs.org/doi/abs/10.1021/acs.jpcb.5b01800

Watson–Crick and Sugar-Edge Base Pairing of Cytosine in the Gas Phase: UV and Infrared Spectra of Cytosine·2-Pyridone

While keto-amino cytosine is the dominant species in aqueous solution, spectroscopic studies in molecular beams and in noble gas matrices show that other cytosine tautomers prevail in apolar environments. Each of these offers two or three H-bonding sites (Watson–Crick, wobble, sugar-edge). The mass- and isomer-specific S1 ← S0 vibronic spectra of cytosine·2-pyridone (Cyt·2PY) and 1-methylcytosine·2PY are measured using UV laser resonant two-photon ionization (R2PI), UV/UV depletion, and IR depletion spectroscopy. The UV spectra of the Watson–Crick and sugar-edge isomers of Cyt·2PY are separated using UV/UV spectral hole-burning. Five different isomers of Cyt·2PY are observed in a supersonic beam. We show that the Watson–Crick and sugar-edge dimers of keto-amino cytosine with 2PY are the most abundant in the beam, although keto-amino-cytosine is only the third most abundant tautomer in the gas phase. We identify the different isomers by combining three different diagnostic tools: (1) methylation of the cytosine N1–H group prevents formation of both the sugar-edge and wobble isomers and gives the Watson–Crick isomer exclusively. (2) The calculated ground state binding and dissociation energies, relative gas-phase abundances, excitation and the ionization energies are in agreement with the assignment of the dominant Cyt·2PY isomers to the Watson–Crick and sugar-edge complexes of keto-amino cytosine. (3) The comparison of calculated ground state vibrational frequencies to the experimental IR spectra in the carbonyl stretch and NH/OH/CH stretch ranges strengthen this identification

Quasi-continuous Interpolation Scheme for Pathways between Distant Configurations

A quasi-continuous interpolation (QCI) scheme is introduced for characterizing physically realistic initial pathways from which to initiate transition state searches and construct kinetic transition networks. Applications are presented for peptides, proteins, and a morphological transformation in an atomic cluster. The first step in each case involves end point alignment, and we describe the use of a shortest augmenting path algorithm for optimizing permutational isomers. The QCI procedure then employs an interpolating potential, which preserves the covalent bonding framework for the biomolecules and includes repulsive terms between unconstrained atoms. This potential is used to identify an interpolating path by minimizing contributions from a connected set of images, including terms corresponding to minima in the interatomic distances between them. This procedure detects unphysical geometries in the line segments between images. The most difficult cases, where linear interpolation would involve chain crossings, are treated by growing the structure an atom at a time using the interpolating potential. To test the QCI procedure, we carry through a series of benchmark calculations where the initial interpolation is coupled to explicit transition state searches to produce complete pathways between specified local minima.This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/H042660/1]This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in the Journal of Chemical Theory and Computation, copyright © American Chemical Society after peer review. To access the final edited and published work see http://dx.doi.org/10.1021/ct300483

An ab initio and AIM investigation into the hydration of 2-thioxanthine

<p>Abstract</p> <p>Background</p> <p>Hydration is a universal phenomenon in nature. The interactions between biomolecules and water of hydration play a pivotal role in molecular biology. 2-Thioxanthine (2TX), a thio-modified nucleic acid base, is of significant interest as a DNA inhibitor yet its interactions with hydration water have not been investigated either computationally or experimentally. Here in, we reported an <it>ab initio </it>study of the hydration of 2TX, revealing water can form seven hydrated complexes.</p> <p>Results</p> <p>Hydrogen-bond (H-bond) interactions in 1:1 complexes of 2TX with water are studied at the MP2/6-311G(d, p) and B3LYP/6-311G(d, p) levels. Seven 2TX^...H₂O hydrogen bonded complexes have been theoretically identified and reported for the first time. The proton affinities (PAs) of the O, S, and N atoms and deprotonantion enthalpies (DPEs) of different N-H bonds in 2TX are calculated, factors surrounding why the seven complexes have different hydrogen bond energies are discussed. The theoretical infrared and NMR spectra of hydrated 2TX complexes are reported to probe the characteristics of the proposed H-bonds. An improper blue-shifting H-bond with a shortened C-H bond was found in one case. NBO and AIM analysis were carried out to explain the formation of improper blue-shifting H-bonds, and the H-bonding characteristics are discussed.</p> <p>Conclusion</p> <p>2TX can interact with water by five different H-bonding regimes, N-H^...O, O-H^...N, O-H^...O, O-H^...S and C-H^...O, all of which are medium strength hydrogen bonds. The most stable H-bond complex has a closed structure with two hydrogen bonds (N(7)-H^...O and O-H^...O), whereas the least stable one has an open structure with one H-bond. The interaction energies of the studied complexes are correlated to the PA and DPE involved in H-bond formation. After formation of H-bonds, the calculated IR and NMR spectra of the 2TX-water complexes change greatly, which serves to identify the hydration of 2TX.</p

The effect of size and composition on structural transitions in monometallic nanoparticles

Predicting the morphological stability of nanoparticles is an essential step towards the accurate modelling of their chemophysical properties. Here we investigate solid–solid transitions in monometallic clusters of 0.5–2.0 nm diameter at finite temperatures and we report the complex dependence of the rearrangement mechanism on the nanoparticle’s composition and size. The concerted Lipscomb’s Diamond-Square-Diamond mechanisms which connects the decahedral or the cuboctahedral to the icosahedral basins, take place only below a material dependent critical size above which surface diffusion prevails and leads to low-symmetry and defected shapes still belonging to the initial basin