Publications by authors named "David J Wales"

200 Publications

Dynamical Signatures of Multifunnel Energy Landscapes.

Authors:
David J Wales

J Phys Chem Lett 2022 Jul 8;13(27):6349-6358. Epub 2022 Jul 8.

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.

Multifunctional systems, such as molecular switches, exhibit multifunnel energy landscapes associated with the alternative functional states. In this contribution the multifunnel organization is decoded from dynamical signatures in the first passage time distribution between reactants and products. Characteristic relaxation rates are revealed by analyzing the kinetics as a function of the observation time scale, which scans the underlying distribution. Extracting the corresponding dynamical signatures provides direct insight into the organization of the molecular energy landscape, which will facilitate a rational design of target functionality. Examples are illustrated for multifunnel landscapes in biomolecular systems and an atomic cluster.
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http://dx.doi.org/10.1021/acs.jpclett.2c01258DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9289951PMC
July 2022

Evaluating Geometric Definitions of Stacking for RNA Dinucleoside Monophosphates Using Molecular Mechanics Calculations.

J Chem Theory Comput 2022 Jun 2;18(6):3637-3653. Epub 2022 Jun 2.

Department of Chemistry and Biochemistry, Florida Atlantic University, Jupiter, Florida 33458, United States.

RNA modulation via small molecules is a novel approach in pharmacotherapies, where the determination of the structural properties of RNA motifs is considered a promising way to develop drugs capable of targeting RNA structures to control diseases. However, due to the complexity and dynamic nature of RNA molecules, the determination of RNA structures using experimental approaches is not always feasible, and computational models employing force fields can provide important insight. The quality of the force field will determine how well the predictions are compared to experimental observables. Stacking in nucleic acids is one such structural property, originating mainly from London dispersion forces, which are quantum mechanical and are included in molecular mechanics force fields through nonbonded interactions. Geometric descriptions are utilized to decide if two residues are stacked and hence to calculate the stacking free energies for RNA dinucleoside monophosphates (DNMPs) through statistical mechanics for comparison with experimental thermodynamics data. Here, we benchmark four different stacking definitions using molecular dynamics (MD) trajectories for 16 RNA DNMPs produced by two different force fields (RNA-IL and ff99OL3) and show that our stacking definition better correlates with the experimental thermodynamics data. While predictions within an accuracy of 0.2 kcal/mol at 300 K were observed in RNA CC, CU, UC, AG, GA, and GG, stacked states of purine-pyrimidine and pyrimidine-purine DNMPs, respectively, were typically underpredicted and overpredicted. Additionally, population distributions of RNA UU DNMPs were poorly predicted by both force fields, implying a requirement for further force field revisions. We further discuss the differences predicted by each RNA force field. Finally, we show that discrete path sampling (DPS) calculations can provide valuable information and complement the MD simulations. We propose the use of experimental thermodynamics data for RNA DNMPs as benchmarks for testing RNA force fields.
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http://dx.doi.org/10.1021/acs.jctc.2c00178DOI Listing
June 2022

Energy Landscapes for Base-Flipping in a Model DNA Duplex.

J Phys Chem B 2022 04 15;126(16):3012-3028. Epub 2022 Apr 15.

Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, U.K.

We explore the process of base-flipping for four central bases, adenine, guanine, cytosine, and thymine, in a deoxyribonucleic acid (DNA) duplex using the energy landscape perspective. NMR imino-proton exchange and fluorescence correlation spectroscopy studies have been used in previous experiments to obtain lifetimes for bases in paired and extrahelical states. However, the difference of almost 4 orders of magnitude in the base-flipping rates obtained by the two methods implies that they are exploring different pathways and possibly different open states. Our results support the previous suggestion that minor groove opening may be favored by distortions in the DNA backbone and reveal links between sequence effects and the direction of opening, i.e., whether the base flips toward the major or the minor groove side. In particular, base flipping along the minor groove pathway was found to align toward the 5' side of the backbone. We find that bases align toward the 3' side of the backbone when flipping along the major groove pathway. However, in some cases for cytosine and thymine, the base flipping along the major groove pathway also aligns toward the 5' side. The sequence effect may be caused by the polar interactions between the flipping-base and its neighboring bases on either of the strands. For guanine flipping toward the minor groove side, we find that the equilibrium constant for opening is large compared to flipping via the major groove. We find that the estimated rates of base opening, and hence the lifetimes of the closed state, obtained for thymine flipping through small and large angles along the major groove differ by 6 orders of magnitude, whereas for thymine flipping through small angles along the minor groove and large angles along the major groove, the rates differ by 3 orders of magnitude.
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http://dx.doi.org/10.1021/acs.jpcb.2c00340DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9098180PMC
April 2022

Energy Landscapes of Carbon Clusters from Tight-Binding Quantum Potentials.

J Phys Chem A 2022 Apr 7;126(15):2342-2352. Epub 2022 Apr 7.

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

We calculate transformation pathways between fullerene and octahedral carbon clusters and between a buckyball and its bowl-shaped isomer. The energies and gradients are provided by efficient tight-binding potentials, which are interfaced to our Energy Landscape exploration software. From the global energy landscape, we extract the mechanistic and kinetic parameters as a function of temperature, and compare our results to selected density functional theory (DFT) (PBE/cc-pVTZ) benchmarks. Infrared spectra are calculated to provide data for experimental identification of the clusters and differentiation of their isomers. Our results suggest that the formation of buckyballs from a buckybowl will be suppressed at elevated temperatures (above around 5250 K) due to entropic effects, which may provide useful insight into the detection of cosmic fullerenes.
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http://dx.doi.org/10.1021/acs.jpca.2c00834DOI Listing
April 2022

The Energy Landscape Perspective: Encoding Structure and Function for Biomolecules.

Front Mol Biosci 2022 27;9:820792. Epub 2022 Jan 27.

Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom.

The energy landscape perspective is outlined with particular reference to biomolecules that perform multiple functions. We associate these multifunctional molecules with multifunnel energy landscapes, illustrated by some selected examples, where understanding the organisation of the landscape has provided new insight into function. Conformational selection and induced fit may provide alternative routes to realisation of multifunctionality, exploiting the possibility of environmental control and distinct binding modes.
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http://dx.doi.org/10.3389/fmolb.2022.820792DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8829389PMC
January 2022

Nearly reducible finite Markov chains: Theory and algorithms.

J Chem Phys 2021 Oct;155(14):140901

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Finite Markov chains, memoryless random walks on complex networks, appear commonly as models for stochastic dynamics in condensed matter physics, biophysics, ecology, epidemiology, economics, and elsewhere. Here, we review exact numerical methods for the analysis of arbitrary discrete- and continuous-time Markovian networks. We focus on numerically stable methods that are required to treat nearly reducible Markov chains, which exhibit a separation of characteristic timescales and are therefore ill-conditioned. In this metastable regime, dense linear algebra methods are afflicted by propagation of error in the finite precision arithmetic, and the kinetic Monte Carlo algorithm to simulate paths is unfeasibly inefficient. Furthermore, iterative eigendecomposition methods fail to converge without the use of nontrivial and system-specific preconditioning techniques. An alternative approach is provided by state reduction procedures, which do not require additional a priori knowledge of the Markov chain. Macroscopic dynamical quantities, such as moments of the first passage time distribution for a transition to an absorbing state, and microscopic properties, such as the stationary, committor, and visitation probabilities for nodes, can be computed robustly using state reduction algorithms. The related kinetic path sampling algorithm allows for efficient sampling of trajectories on a nearly reducible Markov chain. Thus, all of the information required to determine the kinetically relevant transition mechanisms, and to identify the states that have a dominant effect on the global dynamics, can be computed reliably even for computationally challenging models. Rare events are a ubiquitous feature of realistic dynamical systems, and so the methods described herein are valuable in many practical applications.
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http://dx.doi.org/10.1063/5.0060978DOI Listing
October 2021

Energy landscapes for a modified repulsive Weeks-Chandler-Andersen potential.

J Phys Condens Matter 2021 Nov 2;34(3). Epub 2021 Nov 2.

Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

The short-range nature of the repulsive Weeks-Chandler-Anderson (WCA) potential can create free particles/rattlers in a condensed system. The presence of rattlers complicates the analysis of the energy landscape due to extra zero-frequency normal modes. By employing a long-range Gaussian tail modification, we remove the rattlers without changing the structure and the dynamics of the system, and successfully describe the potential energy landscape in terms of minima and transition states. This coarse-grained description of the landscape and the dynamical properties of the modified potential exhibit characteristic signatures of glass-forming liquids. However, we show that despite having qualitatively similar behaviour, the modified WCA potential is less frustrated compared to its attractive counterpart.
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http://dx.doi.org/10.1088/1361-648X/ac2f6dDOI Listing
November 2021

The energy landscapes of bidisperse particle assemblies on a sphere.

Soft Matter 2021 Oct 20;17(40):9019-9027. Epub 2021 Oct 20.

Yusuf Hamied Department of Chemistry, Lensfield Road, Cambridge, CB2 1EW, UK.

The interplay between crystalline ordering, curvature, and size dispersity make the packing of bidisperse mixtures of particles on a sphere a varied and complex phenomenon. These structures have functional significance in a broad range of systems, such as cellular organisation in spherical epithelia, catalytic activity in binary colloidosomes, and chemical activity in heterofullerenes. In this contribution, we elucidate the potential energy landscapes for systems of repulsive, bidisperse particles confined to the surface of a sphere. It is commonly asserted that particle size dispersity destroys ordered arrangements, leading to glassy landscapes. Surprisingly, across a range of compositions, we find highly ordered global minima. Moreover, a minority of small particles is able to passivate defects, stabilising bidisperse global minima relative to monodisperse systems. However, our landscape analysis also reveals that bidispersity introduces numerous defective, low-lying states that are expected to cause broken ergodicity in corresponding experimental and computational systems. Probing the global minimum structures further, particle segregation is energetically preferred at intermediate compositions, contrasting with the approximate icosahedral global packing at either end of the composition range. Finally, changing the composition has a dramatic effect on the heat capacity: systems with low-symmetry global minima have melting temperatures an order of magnitude lower than monodisperse or high-symmetry systems. This observation may provide a further example of the principle of maximum symmetry: higher symmetry global minima exhibit a larger energy separation from the minima that define the high-entropy phase-like region of configuration space, raising the transition temperature.
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http://dx.doi.org/10.1039/d1sm01140eDOI Listing
October 2021

Minimal Design Principles for Icosahedral Virus Capsids.

ACS Nano 2021 09 7;15(9):14873-14884. Epub 2021 Sep 7.

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

The geometrical structures of single- and multiple-shell icosahedral virus capsids are reproduced as the targets that minimize the cost corresponding to relatively simple design functions. Capsid subunits are first identified as building blocks at a given coarse-grained scale and then represented in these functions as point particles located on an appropriate number of concentric spherical surfaces. Minimal design cost is assigned to optimal spherical packings of the particles. The cost functions are inspired by the packings favored for the Thomson problem, which minimize the electrostatic potential energy between identical charged particles. In some cases, icosahedral symmetry constraints are incorporated as external fields acting on the particles. The simplest cost functions can be obtained by separating particles in disjoint nonequivalent sets with distinct interactions, or by introducing interacting holes (the absence of particles). These functions can be adapted to reproduce any capsid structure found in real viruses. Structures absent in Nature require significantly more complex designs. Measures of information content and complexity are assigned to both the cost functions and the capsid geometries. In terms of these measures, icosahedral structures and the corresponding cost functions are the simplest solutions.
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http://dx.doi.org/10.1021/acsnano.1c04952DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8939845PMC
September 2021

Numerical analysis of first-passage processes in finite Markov chains exhibiting metastability.

Phys Rev E 2021 Jul;104(1-2):015301

Department of Chemistry, University of Cambridge, Lensfield Road, and Cambridge CB2 1EW, United Kingdom.

We describe state-reduction algorithms for the analysis of first-passage processes in discrete- and continuous-time finite Markov chains. We present a formulation of the graph transformation algorithm that allows for the evaluation of exact mean first-passage times, stationary probabilities, and committor probabilities for all nonabsorbing nodes of a Markov chain in a single computation. Calculation of the committor probabilities within the state-reduction formalism is readily generalizable to the first hitting problem for any number of alternative target states. We then show that a state-reduction algorithm can be formulated to compute the expected number of times that each node is visited along a first-passage path. Hence, all properties required to analyze the first-passage path ensemble (FPPE) at both a microscopic and macroscopic level of detail, including the mean and variance of the first-passage time distribution, can be computed using state-reduction methods. In particular, we derive expressions for the probability that a node is visited along a direct transition path, which proceeds without returning to the initial state, considering both the nonequilibrium and equilibrium (steady-state) FPPEs. The reactive visitation probability provides a rigorous metric to quantify the dynamical importance of a node for the productive transition between two endpoint states and thus allows the local states that facilitate the dominant transition mechanisms to be readily identified. The state-reduction procedures remain numerically stable even for Markov chains exhibiting metastability, which can be severely ill-conditioned. The rare event regime is frequently encountered in realistic models of dynamical processes, and our methodology therefore provides valuable tools for the analysis of Markov chains in practical applications. We illustrate our approach with numerical results for a kinetic network representing a structural transition in an atomic cluster.
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http://dx.doi.org/10.1103/PhysRevE.104.015301DOI Listing
July 2021

Graph transformation and shortest paths algorithms for finite Markov chains.

Phys Rev E 2021 Jun;103(6-1):063306

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

The graph transformation (GT) algorithm robustly computes the mean first-passage time to an absorbing state in a finite Markov chain. Here we present a concise overview of the iterative and block formulations of the GT procedure and generalize the GT formalism to the case of any path property that is a sum of contributions from individual transitions. In particular, we examine the path action, which directly relates to the path probability, and analyze the first-passage path ensemble for a model Markov chain that is metastable and therefore numerically challenging. We compare the mean first-passage path action, obtained using GT, with the full path action probability distribution simulated efficiently using kinetic path sampling, and with values for the highest-probability paths determined by the recursive enumeration algorithm (REA). In Markov chains representing realistic dynamical processes, the probability distributions of first-passage path properties are typically fat-tailed and therefore difficult to converge by sampling, which motivates the use of exact and numerically stable approaches to compute the expectation. We find that the kinetic relevance of the set of highest-probability paths depends strongly on the metastability of the Markov chain, and so the properties of the dominant first-passage paths may be unrepresentative of the global dynamics. Use of a global measure for edge costs in the REA, based on net productive fluxes, allows the total reactive flux to be decomposed into a finite set of contributions from simple flux paths. By considering transition flux paths, a detailed quantitative analysis of the relative importance of competing dynamical processes is possible even in the metastable regime.
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http://dx.doi.org/10.1103/PhysRevE.103.063306DOI Listing
June 2021

Side-Chain Polarity Modulates the Intrinsic Conformational Landscape of Model Dipeptides.

J Phys Chem B 2021 06 26;125(22):5809-5822. Epub 2021 May 26.

Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

The intrinsic conformational preferences of small peptides may provide additional insight into the thermodynamics and kinetics of protein folding. In this study, we explore the underlying energy landscapes of two model peptides, namely, Ac-Ala-NH and Ac-Ser-NH, using geometry-optimization-based tools developed within the context of energy landscape theory. We analyze not only how side-chain polarity influences the structural preferences of the dipeptides, but also other emergent properties of the landscape, including heat capacity profiles, and kinetics of conformational rearrangements. The contrasting topographies of the free energy landscape agree with recent results from Fourier transform microwave spectroscopy experiments, where Ac-Ala-NH was found to exist as a mixture of two conformers, while Ac-Ser-NH remained structurally locked, despite exhibiting an apparently rich conformational landscape.
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http://dx.doi.org/10.1021/acs.jpcb.1c02412DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8279551PMC
June 2021

Surface Chirality Influences Molecular Rotation upon Desorption.

Phys Rev Lett 2021 Apr;126(16):166101

Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Chiral surfaces offer great potential as a medium for enantioselective synthesis or separation, yet their dynamic enantiospecific interactions with adsorbates are not well understood. Here, the influence of chiral surfaces on the molecular rotations of desorbing molecules is investigated. Formic acid desorption from Cu{531} and Cu{110} serve as model systems for desorption processes of an achiral adsorbate from a chiral and an achiral surface. Our first-principles molecular dynamics study reveals a much larger and more directed angular momentum for molecules desorbing from the chiral surface and a clear preference for one sense of rotation. This result provides new insight into desorption and adsorption processes and propensities on chiral surfaces.
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http://dx.doi.org/10.1103/PhysRevLett.126.166101DOI Listing
April 2021

Crystal Structure Prediction for Benzene Using Basin-Hopping Global Optimization.

J Phys Chem A 2021 May 21;125(17):3776-3784. Epub 2021 Apr 21.

Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Organic molecules can be stable in distinct crystalline forms, known as polymorphs, which have significant consequences for industrial applications. Here, we predict the polymorphs of crystalline benzene computationally for an accurate anisotropic model parametrized to reproduce electronic structure calculations. We adapt the basin-hopping global optimization procedure to the case of crystalline unit cells, simultaneously optimizing the molecular coordinates and unit cell parameters to locate multiple low-energy structures from a variety of crystal space groups. We rapidly locate all the well-established experimental polymorphs of benzene, each of which corresponds to a single local energy minimum of the model. Our results show that basin-hopping can be both an efficient and effective tool for polymorphic crystal structure prediction, requiring no experimental knowledge of cell parameters or symmetry.
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http://dx.doi.org/10.1021/acs.jpca.1c00903DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8279651PMC
May 2021

Development of ReaxFF Reactive Force Field for Aqueous Iron-Sulfur Clusters with Applications to Stability and Reactivity in Water.

J Chem Inf Model 2021 03 22;61(3):1204-1214. Epub 2021 Feb 22.

Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road,Cambridge CB2 1EW, United Kingdom.

Iron-sulfur clusters serve unique roles in biochemistry, geochemistry, and renewable energy technologies. However, a full theoretical understanding of their structures and properties is still lacking. To facilitate large-scale reactive molecular dynamics simulations of iron-sulfur clusters in aqueous environments, a ReaxFF reactive force field is developed, based on an extensive set of quantum chemical calculations. This force field compares favorably with the reference calculations on gas-phase species and significantly improves on a previous ReaxFF parametrization. We employ the new potential to study the stability and reactivity of iron-sulfur clusters in explicit water with constant-temperature reactive molecular dynamics. The aqueous species exhibit a dynamic, temperature-dependent behavior, in good agreement with previous much more costly ab initio simulations.
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http://dx.doi.org/10.1021/acs.jcim.0c01292DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8028049PMC
March 2021

Optimal dimensionality reduction of Markov chains using graph transformation.

J Chem Phys 2020 Dec;153(24):244108

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Markov chains can accurately model the state-to-state dynamics of a wide range of complex systems, but the underlying transition matrix is ill-conditioned when the dynamics feature a separation of timescales. Graph transformation (GT) provides a numerically stable method to compute exact mean first passage times (MFPTs) between states, which are the usual dynamical observables in continuous-time Markov chains (CTMCs). Here, we generalize the GT algorithm to discrete-time Markov chains (DTMCs), which are commonly estimated from simulation data, for example, in the Markov state model approach. We then consider the dimensionality reduction of CTMCs and DTMCs, which aids model interpretation and facilitates more expensive computations, including sampling of pathways. We perform a detailed numerical analysis of existing methods to compute the optimal reduced CTMC, given a partitioning of the network into metastable communities (macrostates) of nodes (microstates). We show that approaches based on linear algebra encounter numerical problems that arise from the requisite metastability. We propose an alternative approach using GT to compute the matrix of intermicrostate MFPTs in the original Markov chain, from which a matrix of weighted intermacrostate MFPTs can be obtained. We also propose an approximation to the weighted-MFPT matrix in the strongly metastable limit. Inversion of the weighted-MFPT matrix, which is better conditioned than the matrices that must be inverted in alternative dimensionality reduction schemes, then yields the optimal reduced Markov chain. The superior numerical stability of the GT approach therefore enables us to realize optimal Markovian coarse-graining of systems with rare event dynamics.
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http://dx.doi.org/10.1063/5.0025174DOI Listing
December 2020

Energy Landscapes for Electronic Structure.

J Chem Theory Comput 2021 Jan 28;17(1):151-169. Epub 2020 Dec 28.

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.

Orbital-optimized multiple self-consistent-field (SCF) solutions are increasingly being interpreted as mean-field approximations of diabatic or excited electronic states. However, surprisingly little is known about the topology of the electronic energy landscape from which these multiple solutions emerge. In this contribution, we extend energy landscape methods, developed for investigating molecular potential energy surfaces, to investigate and understand the structure of the electronic SCF energy surface. Using analytic gradients and Hessians, we systematically identify every real SCF minimum for the prototypical H molecule with the 3-21G basis set, and the index-1 saddles that connect these minima. The resulting SCF energy landscape has a double-funnel structure, with no high-energy local minima. The effect of molecular symmetry on the pathways is analyzed, and we demonstrate how the SCF energy landscape changes with the basis set, SCF potential, molecular structure, and spin state. These results provide guiding principles for the future development of algorithms to systematically identify multiple SCF solutions from an orbital optimization perspective.
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http://dx.doi.org/10.1021/acs.jctc.0c00772DOI Listing
January 2021

Systematic Evaluation of ReaxFF Reactive Force Fields for Biochemical Applications.

J Chem Theory Comput 2021 Jan 18;17(1):497-514. Epub 2020 Dec 18.

Yusuf Hamied Department of Chemistry, University of Cambridge, Lens_eld Road, Cambridge CB2 1EW, U.K.

Four established ReaxFF force fields, trained on biochemical systems, have been systematically benchmarked on 20 proteinogenic amino acids and 11 dipeptides. The force fields were compared with respect to geometries, energetics, and atomic charges of conformers for the amino acids. To assess the performance with respect to reactivity, the condensation reactions for the formation of dipeptides were investigated by calculating the reaction energetics and pathways. We found systematic errors in the torsion angles for the amino acids, with deviations over 100°, and a generally incorrect account of relative energies for amino acid conformers. In describing the reactivity, only one of the force fields could reproduce the reaction energies of amino acid condensations quantitatively. All four force fields predict unphysical mechanisms for these reactions, involving highly unstable intermediate structures, proton transfers involving aliphatic protons, and even five-coordinate carbon atoms. The corresponding energy landscapes exhibit fluctuations on small length scales and artificial minima.
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http://dx.doi.org/10.1021/acs.jctc.0c01043DOI Listing
January 2021

Energy Landscape for the Membrane Fusion Pathway in Influenza A Hemagglutinin From Discrete Path Sampling.

Front Chem 2020 25;8:575195. Epub 2020 Sep 25.

Department of Chemistry, University of Cambridge, Cambridge, United Kingdom.

The conformational change associated with membrane fusion for Influenza A Hemagglutinin is investigated with a model based upon pre- and post-fusion structures of the HA2 component. We employ computational methods based on the potential energy landscape framework to obtain an initial path connecting these two end points, which provides the starting point for refinement of a kinetic transition network. Here we employ discrete path sampling, which provides access to the experimental time and length scales via geometry optimization techniques to identify local minima and the transition states that connect them. We then analyse the distinct phases of the predicted pathway in terms of structure and energetics, and compare with available experimental data and previous simulations. Our results provide the foundations for future work, which will address the effect of mutations, changes in pH, and incorporation of additional components, especially the HA1 chain and the fusion peptide.
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http://dx.doi.org/10.3389/fchem.2020.575195DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7546250PMC
September 2020

Rare events and first passage time statistics from the energy landscape.

J Chem Phys 2020 Oct;153(13):134115

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

We analyze the probability distribution of rare first passage times corresponding to transitions between product and reactant states in a kinetic transition network. The mean first passage times and the corresponding rate constants are analyzed in detail for two model landscapes and the double funnel landscape corresponding to an atomic cluster. Evaluation schemes based on eigendecomposition and kinetic path sampling, which both allow access to the first passage time distribution, are benchmarked against mean first passage times calculated using graph transformation. Numerical precision issues severely limit the useful temperature range for eigendecomposition, but kinetic path sampling is capable of extending the first passage time analysis to lower temperatures, where the kinetics of interest constitute rare events. We then investigate the influence of free energy based state regrouping schemes for the underlying network. Alternative formulations of the effective transition rates for a given regrouping are compared in detail to determine their numerical stability and capability to reproduce the true kinetics, including recent coarse-graining approaches that preserve occupancy cross correlation functions. We find that appropriate regrouping of states under the simplest local equilibrium approximation can provide reduced transition networks with useful accuracy at somewhat lower temperatures. Finally, a method is provided to systematically interpolate between the local equilibrium approximation and exact intergroup dynamics. Spectral analysis is applied to each grouping of states, employing a moment-based mode selection criterion to produce a reduced state space, which does not require any spectral gap to exist, but reduces to gap-based coarse graining as a special case. Implementations of the developed methods are freely available online.
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http://dx.doi.org/10.1063/5.0016244DOI Listing
October 2020

Fragility and correlated dynamics in supercooled liquids.

J Chem Phys 2020 Sep;153(12):124501

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

A connection between the super-Arrhenius behavior of dynamical properties and the correlated dynamics for supercooled liquids is examined for a well known glass forming binary Lennard-Jones mixture and its repulsive counterpart, the Weeks-Chandler-Andersen potential, over a range of densities. When considering short time nonergodic trajectory segments of a longer ergodic trajectory, we observe that, independent of the potentials and densities, the apparent diffusivity follows Arrhenius behavior until low temperatures. Comparing the two potentials, where the ergodic diffusivities are known to be rather different, we find that the short-time nonergodic part is similar throughout the temperature range. By including a correlation factor in the nonergodic diffusivity, a rescaled value is calculated, which provides a reasonable estimate of the true ergodic diffusivity. The true diffusion coefficient and the correction factor collapse to a master plot for all densities at any given time interval. Hence, our results confirm a strong connection between fragility and dynamical correlation.
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http://dx.doi.org/10.1063/5.0015091DOI Listing
September 2020

Archetypal landscapes for deep neural networks.

Proc Natl Acad Sci U S A 2020 09 25;117(36):21857-21864. Epub 2020 Aug 25.

Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom.

The predictive capabilities of deep neural networks (DNNs) continue to evolve to increasingly impressive levels. However, it is still unclear how training procedures for DNNs succeed in finding parameters that produce good results for such high-dimensional and nonconvex loss functions. In particular, we wish to understand why simple optimization schemes, such as stochastic gradient descent, do not end up trapped in local minima with high loss values that would not yield useful predictions. We explain the optimizability of DNNs by characterizing the local minima and transition states of the loss-function landscape (LFL) along with their connectivity. We show that the LFL of a DNN in the shallow network or data-abundant limit is funneled, and thus easy to optimize. Crucially, in the opposite low-data/deep limit, although the number of minima increases, the landscape is characterized by many minima with similar loss values separated by low barriers. This organization is different from the hierarchical landscapes of structural glass formers and explains why minimization procedures commonly employed by the machine-learning community can navigate the LFL successfully and reach low-lying solutions.
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http://dx.doi.org/10.1073/pnas.1919995117DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7486703PMC
September 2020

Protein energy landscape exploration with structure-based models.

Curr Opin Struct Biol 2020 10 12;64:145-151. Epub 2020 Aug 12.

Simons Centre for the Study of Living Machines, National Centre for Biological Sciences, Bangalore 560 065, India. Electronic address:

Exploring the multi-dimensional energy landscape of a large protein in detail is a computational challenge. Such investigations may include analysis of multiple folding pathways, rate constants for important conformational transitions, locating intermediate states populated during folding, estimating energetic and entropic barriers that separate populated basins, and visualising a high-dimensional surface. The complexity of the landscape can be simplified through coarse-grained structure-based models (SBMs). These widely used coarse-grained representations of proteins provide a minimalist approximation to the free energy landscape, which subsumes the folding behaviour of many single-domain proteins. Here we describe the combination of SBMs with discrete path sampling (DPS), and show how this approach can provide details of the landscape and folding pathways. Combining SBMs and DPS provides an efficient framework for sampling the protein free energy landscape and for calculating various kinetic and thermodynamic quantities.
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http://dx.doi.org/10.1016/j.sbi.2020.07.003DOI Listing
October 2020

Efficient and exact sampling of transition path ensembles on Markovian networks.

J Chem Phys 2020 Jul;153(2):024121

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

The problem of flickering trajectories in standard kinetic Monte Carlo (kMC) simulations prohibits sampling of the transition path ensembles (TPEs) on Markovian networks representing many slow dynamical processes of interest. In the present contribution, we overcome this problem using knowledge of the metastable macrostates, determined by an unsupervised community detection algorithm, to perform enhanced sampling kMC simulations. We implement two accelerated kMC methods to simulate the nonequilibrium stochastic dynamics on arbitrary Markovian networks, namely, weighted ensemble (WE) sampling and kinetic path sampling (kPS). WE-kMC utilizes resampling in pathway space to maintain an ensemble of representative trajectories covering the state space, and kPS utilizes graph transformation to simplify the description of an escape trajectory from a trapping energy basin. Both methods sample individual trajectories governed by the linear master equation with the correct statistical frequency. We demonstrate that they allow for efficient estimation of the time-dependent occupation probability distributions for the metastable macrostates, and of TPE statistics, such as committor functions and first passage time distributions. kPS is particularly attractive, since its efficiency is essentially independent of the degree of metastability, and we suggest how the algorithm could be coupled with other enhanced sampling methodologies. We illustrate our approach with results for a network representing the folding transition of a tryptophan zipper peptide, which exhibits a separation of characteristic timescales. We highlight some salient features of the dynamics, most notably, strong deviations from two-state behavior, and the existence of multiple competing mechanisms.
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http://dx.doi.org/10.1063/5.0012128DOI Listing
July 2020

A well-behaved theoretical framework for ReaxFF reactive force fields.

J Chem Phys 2020 Jul;153(2):021102

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

In recent work, we have presented a new ReaxFF formulation with a superior conservation of energy in reactive molecular dynamics simulations. The key ingredient in the approach involved the tapering of bond order and bond distance discontinuities using Hermite polynomials. This Communication extends the previous formulation by alleviating additional sources of numerical instability in the original formalism. These "numerical pathologies" are rooted in the counting of lone-pair electrons, the sum of bond orders between atoms that form a valence angle, and the definition of a torsional potential. Based on a theoretical analysis, new functions that mitigate these limitations are designed and validated. The extent of their transferability with previous parameterizations is discussed. The new enhancements provide further gains in numerical stability to facilitate exploration of reactive energy landscapes.
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http://dx.doi.org/10.1063/5.0013906DOI Listing
July 2020

Energy Landscapes of Deoxyxylo- and Xylo-Nucleic Acid Octamers.

J Phys Chem B 2020 05 6;124(20):4062-4068. Epub 2020 May 6.

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Artificial analogues of the natural nucleic acids have attracted interest as a diverse class of information storage molecules capable of self-replication. In this study, we use the computational potential energy landscape framework to investigate the structural and dynamical properties of xylo- and deoxyxylo-nucleic acids (XyNA and dXyNA), which are derived from their respective RNA and DNA analogues by inversion of a single chiral center in the sugar moiety of the nucleotides. For an octameric XyNA sequence and the analogue dXyNA, we observe facile conformational transitions between a left-handed helix, which is the free energy global minimum, and a ladder-type structure with approximately zero helicity. The competing ensembles are better separated in the dXyNA, making it a more suitable candidate for a molecular switch, whereas the XyNA exhibits additional flexibility. Both energy landscapes exhibit greater frustration than we observe in RNA or DNA, in agreement with the higher degree of optimization expected from the principle of minimal frustration in evolved biomolecules.
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http://dx.doi.org/10.1021/acs.jpcb.0c01420DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7304908PMC
May 2020

Affinity-Selected Bicyclic Peptide G-Quadruplex Ligands Mimic a Protein-like Binding Mechanism.

J Am Chem Soc 2020 05 21;142(18):8367-8373. Epub 2020 Apr 21.

Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW Cambridge, U.K.

The study of G-quadruplexes (G4s) in a cellular context has demonstrated links between these nucleic acid secondary structures, gene expression, and DNA replication. Ligands that bind to the G4 structure therefore present an excellent opportunity for influencing gene expression through the targeting of a nucleic acid structure rather than sequence. Here, we explore cyclic peptides as an alternative class of G4 ligands. Specifically, we describe the development of G4-binding bicyclic peptides selected by phage display. Selected bicyclic peptides display submicromolar affinity to G4 structures and high selectivity over double helix DNA. Molecular simulations of the bicyclic peptide-G4 complexes corroborate the experimental binding strengths and reveal molecular insights into G4 recognition by bicyclic peptides via the precise positioning of amino acid side chains, a binding mechanism reminiscent of endogenous G4-binding proteins. Overall, our results demonstrate that selection of (bi)cyclic peptides unlocks a valuable chemical space for targeting nucleic acid structures.
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http://dx.doi.org/10.1021/jacs.0c01879DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7212521PMC
May 2020

Defining, Calculating, and Converging Observables of a Kinetic Transition Network.

J Chem Theory Comput 2020 Apr 19;16(4):2661-2679. Epub 2020 Mar 19.

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Kinetic transition networks (KTNs) of local minima and transition states are able to capture the dynamics of numerous systems in chemistry, biology, and materials science. However, extracting observables is numerically challenging for large networks and generally will be sensitive to additional computational discovery. To have any measure of convergence for observables, these sensitivities must be regularly calculated. We present a matrix formulation of the discrete path sampling framework for KTNs, deriving expressions for branching probabilities, transition rates, and waiting times. Using the concept of the quasi-stationary distribution, a clear hierarchy of expressions for network observables is established, from exact results to steady-state approximations. We use these results in combination with the graph transformation method to derive the sensitivity, with respect to perturbations of the known KTN, giving explicit terms for the pairwise sensitivity and discussing the pathwise sensitivity. These results provide guidelines for converging the network, with respect to additional sampling, focusing on the estimates obtained for the overall rate coefficients between product and reactant states. We demonstrate this procedure for transitions in the double-funnel landscape of the 38-atom Lennard-Jones cluster.
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http://dx.doi.org/10.1021/acs.jctc.9b01211DOI Listing
April 2020

Counterion-Trapped-Molecules: From High Polarity and Enriched IR Spectra to Induced Isomerization.

Chemphyschem 2020 02 16;21(4):348-355. Epub 2020 Jan 16.

Department of Chemistry, University of Cambridge, Cambridge, CB2 1EW, United Kingdom.

We report extensive computational studies of some novel intermolecular systems and their properties. Recombination of alkali-halide counterions separated by a noncovalently trapped hydrocarbon molecule is prevented by significant potential energy barriers, resulting in unusual metastable insertion complexes. These systems are extremely polar, while the inserted molecule is strongly counter-polarized, leading to significant cooperative nonadditivity effects. The compression and electric field produced by the counterions favours isomerization of the trapped molecule via a significant reduction of the barriers to bond rearrangement, in a field-induced mechanochemical process. The predicted IR intensity spectra clearly reflect (1) formation of the insertion complex, rather than simple attachment of alkali halide, and (2) isomerization of the trapped molecule, thus allowing experimental access to these events.
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http://dx.doi.org/10.1002/cphc.201901112DOI Listing
February 2020

A multifunnel energy landscape encodes the competing α-helix and β-hairpin conformations for a designed peptide.

Phys Chem Chem Phys 2020 Jan;22(3):1359-1370

Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW, UK.

Depending on the amino acid sequence, as well as the local environment, some peptides have the capability to fold into multiple secondary structures. Conformational switching between such structures is a key element of protein folding and aggregation. Specifically, understanding the molecular mechanism underlying the transition from an α-helix to a β-hairpin is critical because it is thought to be a harbinger of amyloid assembly. In this study, we explore the energy landscape for an 18-residue peptide (DP5), designed by Araki and Tamura to exhibit equal propensities for the α-helical and β-hairpin forms. We find that the degeneracy is encoded in the multifunnel nature of the underlying free energy landscape. In agreement with experiment, we also observe that mutation of tyrosine at position 12 to serine shifts the equilibrium in favor of the α-helix conformation, by altering the landscape topography. The transition from the α-helix to the β-hairpin is a complex stepwise process, and occurs via collapsed coil-like intermediates. Our findings suggest that even a single mutation can tune the emergent features of the landscape, providing an efficient route to protein design. Interestingly, the transition pathways for the conformational switch seem to be minimally perturbed upon mutation, suggesting that there could be universal microscopic features that are conserved among different switch-competent protein sequences.
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http://dx.doi.org/10.1039/c9cp04778fDOI Listing
January 2020
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