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Blow KE, Tribello GA, Sosso GC, Quigley D. Interplay of multiple clusters and initial interface positioning for forward flux sampling simulations of crystal nucleation. J Chem Phys 2023; 158:2895225. [PMID: 37290068 DOI: 10.1063/5.0152343] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 05/19/2023] [Indexed: 06/10/2023] Open
Abstract
Forward flux sampling (FFS) is a path sampling technique widely used in computer simulations of crystal nucleation from the melt. In such studies, the order parameter underpinning the progress of the FFS algorithm is often the size of the largest crystalline nucleus. In this work, we investigate the effects of two computational aspects of FFS simulations, using the prototypical Lennard-Jones liquid as our computational test bed. First, we quantify the impact of the positioning of the liquid basin and first interface in the space of the order parameter. In particular, we demonstrate that these choices are key to ensuring the consistency of the FFS results. Second, we focus on the frequently encountered scenario where the population of crystalline nuclei is such that there are multiple clusters of size comparable to the largest one. We demonstrate the contribution of clusters other than the largest cluster to the initial flux; however, we also show that they can be safely ignored for the purposes of converging a full FFS calculation. We also investigate the impact of different clusters merging, a process that appears to be facilitated by substantial spatial correlations-at least at the supercooling considered here. Importantly, all of our results have been obtained as a function of system size, thus contributing to the ongoing discussion on the impact of finite size effects on simulations of crystal nucleation. Overall, this work either provides or justifies several practical guidelines for performing FFS simulations that can also be applied to more complex and/or computationally expensive models.
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Affiliation(s)
- Katarina E Blow
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Gareth A Tribello
- Centre for Quantum Materials and Technologies, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
| | - Gabriele C Sosso
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - David Quigley
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
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Kalwarczyk T, Bielec K, Burdzy K, Holyst R. Influence of molecular rebinding on the reaction rate of complex formation. Phys Chem Chem Phys 2021; 23:19343-19351. [PMID: 34524310 DOI: 10.1039/d1cp02820k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We simulated Brownian diffusion and reaction-diffusion processes to study the influence of molecular rebinding on the reaction rates of bimolecular reactions. We found that the number of rebinding events, Nreb, is proportional to the target's size and inversely proportional to the diffusion coefficient D and simulation time-step Δt. We found the proportionality constant close to π-1/2. We confirmed that Nreb is defined as a ratio of the activation-limited rate constant ka to the diffusion-limited rate constant, kD. We provide the formula describing the reactivity coefficient κ, modelling the transient-native complex transition for the activation-controlled reaction rates. We show that κ is proportional to (D/Δt)1/2. Finally, we apply our rebinding-including reaction rate model to the real reactions of photoacid dissociation and protein association. Based on literature data for both types of reactions, we found the Δt time-scale. We show that for the photodissociation of a proton, the Δt is equal to 171 ± 18 fs and the average number of rebinding events is approximately equal to 40. For proteins, Δt is of the order of 100 ps with around 20 rebinding events. In both cases the timescale is similar to the timescale of fluctuation of the solvent molecules surrounding the reactants; vibrations and bending in the case of photoacid dissociation and diffusional motion for proteins.
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Affiliation(s)
- Tomasz Kalwarczyk
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
| | - Krzysztof Bielec
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
| | - Krzysztof Burdzy
- Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA
| | - Robert Holyst
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
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Elber R, Fathizadeh A, Ma P, Wang H. Modeling molecular kinetics with Milestoning. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1512] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Ron Elber
- Department of Chemistry, The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
| | - Arman Fathizadeh
- The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
| | - Piao Ma
- Department of Chemistry University of Texas at Austin Austin Texas USA
| | - Hao Wang
- The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
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4
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Wang H, Huang N, Dangerfield T, Johnson KA, Gao J, Elber R. Exploring the Reaction Mechanism of HIV Reverse Transcriptase with a Nucleotide Substrate. J Phys Chem B 2020; 124:4270-4283. [PMID: 32364738 DOI: 10.1021/acs.jpcb.0c02632] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Enzymatic reactions consist of several steps: (i) a weak binding event of the substrate to the enzyme, (ii) an induced fit or a protein conformational transition upon ligand binding, (iii) the chemical reaction, and (iv) the release of the product. Here we focus on step iii of the reaction of a DNA polymerase, HIV RT, with a nucleotide. We determine the rate and the free energy profile for the addition of a nucleotide to a DNA strand using a combination of a QM/MM model, the string method, and exact Milestoning. The barrier height and the time scale of the reaction are consistent with experiment. We show that the observables (free energies and mean first passage time) converge rapidly, as a function of the Milestoning iteration number. We also consider the substitution of an oxygen of the incoming nucleotide by a nonbridging sulfur atom and its impact on the enzymatic reaction. This substitution has been suggested in the past as a tool to examine the influence of the chemical step on the overall rate. Our joint computational and experimental study suggests that the impact of the substitution is small. Computationally, the differences between the two are within the estimated error bars. Experiments suggest a small difference. Finally, we examine step i, the weak binding of the nucleotide to the protein surface. We suggest that this step has only a small contribution to the selectivity of the enzyme. Comments are made on the impact of these steps on the overall mechanism.
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Affiliation(s)
- Hao Wang
- Oden Institute for Computational Engineering and Sciences, University of Texas, Austin Texas 78712, United States
| | - Nathan Huang
- Department of Molecular Biosciences, University of Texas, Austin, Texas 78712, United States
| | - Tyler Dangerfield
- Department of Molecular Biosciences, University of Texas, Austin, Texas 78712, United States
| | - Kenneth A Johnson
- Department of Molecular Biosciences, University of Texas, Austin, Texas 78712, United States
| | - Jiali Gao
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas, Austin Texas 78712, United States.,Department of Chemistry, University of Texas, Austin, Texas 78712, United States
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Hussain S, Haji-Akbari A. Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook. J Chem Phys 2020; 152:060901. [DOI: 10.1063/1.5127780] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Sarwar Hussain
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
| | - Amir Haji-Akbari
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, USA
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Brotzakis ZF, Bolhuis PG. Unbiased Atomistic Insight into the Mechanisms and Solvent Role for Globular Protein Dimer Dissociation. J Phys Chem B 2019; 123:1883-1895. [PMID: 30714378 PMCID: PMC6581425 DOI: 10.1021/acs.jpcb.8b10005] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2018] [Revised: 01/30/2019] [Indexed: 12/18/2022]
Abstract
Association and dissociation of proteins are fundamental processes in nature. Although simple to understand conceptually, the details of the underlying mechanisms and role of the solvent are poorly understood. Here, we investigate the dissociation of the hydrophilic β-lactoglobulin dimer by employing transition path sampling. Analysis of the sampled path ensembles reveals a variety of mechanisms: (1) a direct aligned dissociation (2) a hopping and rebinding transition followed by unbinding, and (3) a sliding transition before unbinding. Reaction coordinate and transition-state analysis predicts that, besides native contact and neighboring salt-bridge interactions, solvent degrees of freedom play an important role in the dissociation process. Bridging waters, hydrogen-bonded to both proteins, support contacts in the native state and nearby lying transition-state regions, whereas they exhibit faster dynamics in further lying transition-state regions, rendering the proteins more mobile and assisting in rebinding. Analysis of the structure and dynamics of the solvent molecules reveals that the dry native interface induces enhanced populations of both disordered hydration water near hydrophilic residues and tetrahedrally ordered hydration water nearby hydrophobic residues. Although not exhaustive, our sampling of rare unbiased reactive molecular dynamics trajectories enhances the understanding of protein dissociation via complex pathways including (multiple) rebinding events.
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Affiliation(s)
| | - P. G. Bolhuis
- Van’t Hoff Institute
for Molecular Sciences, Universiteit van
Amsterdam, Science Park 904, 1090 GD Amsterdam, The Netherlands
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DeFever RS, Sarupria S. Contour forward flux sampling: Sampling rare events along multiple collective variables. J Chem Phys 2019; 150:024103. [PMID: 30646707 DOI: 10.1063/1.5063358] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Many rare event transitions involve multiple collective variables (CVs), and the most appropriate combination of CVs is generally unknown a priori. We thus introduce a new method, contour forward flux sampling (cFFS), to study rare events with multiple CVs simultaneously. cFFS places nonlinear interfaces on-the-fly from the collective progress of the simulations, without any prior knowledge of the energy landscape or appropriate combination of CVs. We demonstrate cFFS on analytical potential energy surfaces and a conformational change in alanine dipeptide.
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Affiliation(s)
- Ryan S DeFever
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
| | - Sapna Sarupria
- Department of Chemical and Biomolecular Engineering, Clemson University, Clemson, South Carolina 29634, USA
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Vijaykumar A, ten Wolde PR, Bolhuis PG. Generalised expressions for the association and dissociation rate constants of molecules with multiple binding sites. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1473653] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Adithya Vijaykumar
- NWO Institute AMOLF, Amsterdam, Netherlands
- van't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, Netherlands
| | | | - Peter G. Bolhuis
- van't Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, Netherlands
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