1
|
Wang R, Ji X, Wang H, Liu W. Kinetic Network in Milestoning: Clustering, Reduction, and Transition Path Analysis. J Chem Theory Comput 2024; 20:5439-5450. [PMID: 38885437 DOI: 10.1021/acs.jctc.4c00510] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/20/2024]
Abstract
We present a reduction of the Milestoning (ReM) algorithm to analyze the high-dimensional Milestoning kinetic network. The algorithm reduces the Milestoning network to low dimensions but preserves essential kinetic information, such as local residence time, exit time, and mean first passage time between any two states. This is achieved in three steps. First, nodes (milestones) in the high-dimensional Milestoning network are grouped into clusters based on the metastability identified by an auxiliary continuous-time Markov chain. Our clustering method is applicable not only to time-reversible networks but also to nonreversible networks generated from practical simulations with statistical fluctuations. Second, a reduced network is established via network transformation, containing only the core sets of clusters as nodes. Finally, transition pathways are analyzed in the reduced network based on the transition path theory. The algorithm is illustrated using a toy model and a solvated alanine dipeptide in two and four dihedral angles.
Collapse
Affiliation(s)
- Ru Wang
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Xiaojun Ji
- Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, Shandong 266237, P. R. China
- Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Hao Wang
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, School of Chemistry and Chemical Engineering, Shandong University, Qingdao, Shandong 266237, P. R. China
| |
Collapse
|
2
|
Wang R, Wang H, Liu W, Elber R. Approximating First Hitting Point Distribution in Milestoning for Rare Event Kinetics. J Chem Theory Comput 2023; 19:6816-6826. [PMID: 37695680 DOI: 10.1021/acs.jctc.3c00315] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/13/2023]
Abstract
Milestoning is an efficient method for rare event kinetics calculation using short trajectory parallelization. Mean first passage time (MFPT) is the key kinetic output of Milestoning, whose accuracy crucially depends on the initial distribution of the short trajectory ensemble. The true initial distribution, i.e., the first hitting point distribution (FHPD), has no analytic expression in the general case. Here, we introduce two algorithms, local passage time weighted Milestoning (LPT-M) and Bayesian inference Milestoning (BI-M), to accurately and efficiently approximate FHPD for systems at equilibrium condition. Starting from sampling the Boltzmann distribution on milestones, we calculate the proper weighting factor for the short trajectory ensemble. The methods are tested on two model examples for illustration purpose. Both methods improve significantly over the widely used classical Milestoning (CM) method in terms of the accuracy of MFPT. In particular, BI-M covers the directional Milestoning method as a special case in deterministic Hamiltonian dynamics. LPT-M is especially advantageous in terms of computational costs and robustness with respect to the increasing number of intermediate milestones. Furthermore, a locally iterative correction algorithm for nonequilibrium stationary FHPD is developed for exact MFPT calculation, which can be combined with LPT-M/BI-M and is much cheaper than the exact Milestoning (ExM) method.
Collapse
Affiliation(s)
- Ru Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Hao Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, P. R. China
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, United States
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| |
Collapse
|
3
|
Aristoff D, Copperman J, Simpson G, Webber RJ, Zuckerman DM. Weighted ensemble: Recent mathematical developments. J Chem Phys 2023; 158:014108. [PMID: 36610976 PMCID: PMC9822651 DOI: 10.1063/5.0110873] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 12/04/2022] [Indexed: 12/12/2022] Open
Abstract
Weighted ensemble (WE) is an enhanced sampling method based on periodically replicating and pruning trajectories generated in parallel. WE has grown increasingly popular for computational biochemistry problems due, in part, to improved hardware and accessible software implementations. Algorithmic and analytical improvements have played an important role, and progress has accelerated in recent years. Here, we discuss and elaborate on the WE method from a mathematical perspective, highlighting recent results that enhance the computational efficiency. The mathematical theory reveals a new strategy for optimizing trajectory management that approaches the best possible variance while generalizing to systems of arbitrary dimension.
Collapse
Affiliation(s)
- D. Aristoff
- Mathematics, Colorado State University, Fort Collins, CO 80521 USA
| | - J. Copperman
- Biomedical Engineering, Oregon Health and Science University, Portland, OR 97239 USA
| | - G. Simpson
- Mathematics, Drexel University, Philadelphia, Pennsylvania 19104 USA
| | - R. J. Webber
- Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 USA
| | - D. M. Zuckerman
- Biomedical Engineering, Oregon Health and Science University, Portland, OR 97239 USA
| |
Collapse
|
4
|
Baudel M, Guyader A, Lelièvre T. On the Hill relation and the mean reaction time for metastable processes. Stoch Process Their Appl 2022. [DOI: 10.1016/j.spa.2022.10.014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
|
5
|
Jas GS, Childs EW, Middaugh CR, Kuczera K. Dissecting Multiple Pathways in the Relaxation Dynamics of Helix <==> Coil Transitions with Optimum Dimensionality Reduction. Biomolecules 2021; 11:1351. [PMID: 34572564 PMCID: PMC8471320 DOI: 10.3390/biom11091351] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Revised: 09/07/2021] [Accepted: 09/09/2021] [Indexed: 11/16/2022] Open
Abstract
Fast kinetic experiments with dramatically improved time resolution have contributed significantly to understanding the fundamental processes in protein folding pathways involving the formation of a-helices and b-hairpin, contact formation, and overall collapse of the peptide chain. Interpretation of experimental results through application of a simple statistical mechanical model was key to this understanding. Atomistic description of all events observed in the experimental findings was challenging. Recent advancements in theory, more sophisticated algorithms, and a true long-term trajectory made way for an atomically detailed description of kinetics, examining folding pathways, validating experimental results, and reporting new findings for a wide range of molecular processes in biophysical chemistry. This review describes how optimum dimensionality reduction theory can construct a simplified coarse-grained model with low dimensionality involving a kinetic matrix that captures novel insights into folding pathways. A set of metastable states derived from molecular dynamics analysis generate an optimally reduced dimensionality rate matrix following transition pathway analysis. Analysis of the actual long-term simulation trajectory extracts a relaxation time directly comparable to the experimental results and confirms the validity of the combined approach. The application of the theory is discussed and illustrated using several examples of helix <==> coil transition pathways. This paper focuses primarily on a combined approach of time-resolved experiments and long-term molecular dynamics simulation from our ongoing work.
Collapse
Affiliation(s)
- Gouri S. Jas
- Department of Pharmaceutical Chemistry, The University of Kansas, Lawrence, KS 66047, USA;
| | - Ed W. Childs
- Department of Surgery, Morehouse School of Medicine, Atlanta, GA 30310, USA;
| | - C. Russell Middaugh
- Department of Pharmaceutical Chemistry, The University of Kansas, Lawrence, KS 66047, USA;
| | - Krzysztof Kuczera
- Department of Chemistry, The University of Kansas, Lawrence, KS 66045, USA;
- Department of Molecular Biosciences, The University of Kansas, Lawrence, KS 66045, USA
| |
Collapse
|
6
|
Arasteh S, Zhang BW, Levy RM. Protein Loop Conformational Free Energy Changes via an Alchemical Path without Reaction Coordinates. J Phys Chem Lett 2021; 12:4368-4377. [PMID: 33938761 PMCID: PMC8170697 DOI: 10.1021/acs.jpclett.1c00778] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We introduce a method called restrain-free energy perturbation-release 2.0 (R-FEP-R 2.0) to estimate conformational free energy changes of protein loops via an alchemical path. R-FEP-R 2.0 is a generalization of the method called restrain-free energy perturbation-release (R-FEP-R) that can only estimate conformational free energy changes of protein side chains but not loops. The reorganization of protein loops is a central feature of many biological processes. Unlike other advanced sampling algorithms such as umbrella sampling and metadynamics, R-FEP-R and R-FEP-R 2.0 do not require predetermined collective coordinates and transition pathways that connect the two endpoint conformational states. The R-FEP-R 2.0 method was applied to estimate the conformational free energy change of a β-turn flip in the protein ubiquitin. The result obtained by R-FEP-R 2.0 agrees with the benchmarks very well. We also comment on problems commonly encountered when applying umbrella sampling to calculate protein conformational free energy changes.
Collapse
Affiliation(s)
- Shima Arasteh
- Center for Biophysics and Computational Biology and Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Bin W Zhang
- Center for Biophysics and Computational Biology and Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Ronald M Levy
- Center for Biophysics and Computational Biology and Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| |
Collapse
|
7
|
Strahan J, Antoszewski A, Lorpaiboon C, Vani BP, Weare J, Dinner AR. Long-Time-Scale Predictions from Short-Trajectory Data: A Benchmark Analysis of the Trp-Cage Miniprotein. J Chem Theory Comput 2021; 17:2948-2963. [PMID: 33908762 DOI: 10.1021/acs.jctc.0c00933] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Elucidating physical mechanisms with statistical confidence from molecular dynamics simulations can be challenging owing to the many degrees of freedom that contribute to collective motions. To address this issue, we recently introduced a dynamical Galerkin approximation (DGA) [Thiede, E. H. J. Chem. Phys., 150, 2019, 244111], in which chemical kinetic statistics that satisfy equations of dynamical operators are represented by a basis expansion. Here, we reformulate this approach, clarifying (and reducing) the dependence on the choice of lag time. We present a new projection of the reactive current onto collective variables and provide improved estimators for rates and committors. We also present simple procedures for constructing suitable smoothly varying basis functions from arbitrary molecular features. To evaluate estimators and basis sets numerically, we generate and carefully validate a data set of short trajectories for the unfolding and folding of the trp-cage miniprotein, a well-studied system. Our analysis demonstrates a comprehensive strategy for characterizing reaction pathways quantitatively.
Collapse
Affiliation(s)
- John Strahan
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Adam Antoszewski
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Chatipat Lorpaiboon
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Bodhi P Vani
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Jonathan Weare
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
| | - Aaron R Dinner
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| |
Collapse
|
8
|
Length Dependent Folding Kinetics of Alanine-Based Helical Peptides from Optimal Dimensionality Reduction. Life (Basel) 2021; 11:life11050385. [PMID: 33923197 PMCID: PMC8170890 DOI: 10.3390/life11050385] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Revised: 04/19/2021] [Accepted: 04/21/2021] [Indexed: 01/23/2023] Open
Abstract
We present a computer simulation study of helix folding in alanine homopeptides (ALA)n of length n = 5, 8, 15, and 21 residues. Based on multi-microsecond molecular dynamics simulations at room temperature, we found helix populations and relaxation times increasing from about 6% and ~2 ns for ALA5 to about 60% and ~500 ns for ALA21, and folding free energies decreasing linearly with the increasing number of residues. The helix folding was analyzed with the Optimal Dimensionality Reduction method, yielding coarse-grained kinetic models that provided a detailed representation of the folding process. The shorter peptides, ALA5 and ALA8, tended to convert directly from coil to helix, while ALA15 and ALA21 traveled through several intermediates. Coarse-grained aggregate states representing the helix, coil, and intermediates were heterogeneous, encompassing multiple peptide conformations. The folding involved multiple pathways and interesting intermediate states were present on the folding paths, with partially formed helices, turns, and compact coils. Statistically, helix initiation was favored at both termini, and the helix was most stable in the central region. Importantly, we found the presence of underlying universal local dynamics in helical peptides with correlated transitions for neighboring hydrogen bonds. Overall, the structural and dynamical parameters extracted from the trajectories are in good agreement with experimental observables, providing microscopic insights into the complex helix folding kinetics.
Collapse
|
9
|
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
| |
Collapse
|
10
|
Elber R. Milestoning: An Efficient Approach for Atomically Detailed Simulations of Kinetics in Biophysics. Annu Rev Biophys 2020; 49:69-85. [PMID: 32375019 DOI: 10.1146/annurev-biophys-121219-081528] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.
Collapse
Affiliation(s)
- Ron Elber
- Oden Institute for Computational Engineering and Sciences, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA;
| |
Collapse
|
11
|
Ma P, Elber R, Makarov DE. Value of Temporal Information When Analyzing Reaction Coordinates. J Chem Theory Comput 2020; 16:6077-6090. [PMID: 32841001 PMCID: PMC7881391 DOI: 10.1021/acs.jctc.0c00678] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Reaction coordinates chart pathways from reactants to products of chemical reactions. Determination of reaction coordinates from ensembles of molecular trajectories has thus been the focus of many studies. A widely used and insightful choice of a reaction coordinate is the committor function, defined as the probability that a trajectory will reach the product before the reactant. Here, we consider alternatives to the committor function that add useful mechanistic information, the mean first passage time, and the exit time to the product. We further derive a simple relationship between the functions of the committor, the mean first passage time, and the exit time. We illustrate the diversity of mechanisms predicted by alternative reaction coordinates with several toy problems and with a simple model of protein searching for a specific DNA motif.
Collapse
Affiliation(s)
- Piao Ma
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Ron Elber
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
- Oden Institute for Computational Engineering and Sciences, Austin, Texas 78712, United States
| | - Dmitrii E Makarov
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
- Oden Institute for Computational Engineering and Sciences, Austin, Texas 78712, United States
| |
Collapse
|
12
|
Loper J, Zhou G, Geman S. Capacities and efficient computation of first-passage probabilities. Phys Rev E 2020; 102:023304. [PMID: 32942394 DOI: 10.1103/physreve.102.023304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2019] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
A reversible diffusion process is initialized at position x_{0} and run until it first hits any of several targets. What is the probability that it terminates at a particular target? We propose a computationally efficient approach for estimating this probability, focused on those situations in which it takes a long time to hit any target. In these cases, direct simulation of the hitting probabilities becomes prohibitively expensive. On the other hand, if the timescales are sufficiently long, then the system will essentially "forget" its initial condition before it encounters a target. In these cases the hitting probabilities can be accurately approximated using only local simulations around each target, obviating the need for direct simulations. In empirical tests, we find that these local estimates can be computed in the same time it would take to compute a single direct simulation, but that they achieve an accuracy that would require thousands of direct simulation runs.
Collapse
Affiliation(s)
- Jackson Loper
- Data Science Institute, Columbia University, 10027 New York, New York, USA
| | - Guangyao Zhou
- Division of Applied Mathematics, Brown University, Providence, 02912 Rhode Island, USA
| | - Stuart Geman
- Division of Applied Mathematics, Brown University, Providence, 02912 Rhode Island, USA
| |
Collapse
|
13
|
Berezhkovskii AM, Szabo A. Committors, first-passage times, fluxes, Markov states, milestones, and all that. J Chem Phys 2019; 150:054106. [PMID: 30736684 PMCID: PMC6910584 DOI: 10.1063/1.5079742] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Accepted: 01/05/2019] [Indexed: 11/14/2022] Open
Abstract
Milestoning on a one-dimensional potential starts by choosing a set of points, called milestones, and initiating short trajectories from each milestone, which are terminated when they reach an adjacent milestone for the first time. From the average duration of these trajectories and the probabilities of where they terminate, a rate matrix can be constructed and then used to calculate the mean first-passage time (MFPT) between any two milestones. All these MFPT's turn out to be exact. Here we adopt a point of view from which this remarkable result is not unexpected. In addition, we clarify the nature of the "states" whose interconversion is described by the rate matrix constructed using information obtained from short trajectories and provide a microscopic expression for the "equilibrium population" of these states in terms of equilibrium averages of the committors.
Collapse
Affiliation(s)
- Alexander M. Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Attila Szabo
- Laboratory of Chemical Physics, National institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 208192, USA
| |
Collapse
|
14
|
He P, Zhang BW, Arasteh S, Wang L, Abel R, Levy RM. Conformational Free Energy Changes via an Alchemical Path without Reaction Coordinates. J Phys Chem Lett 2018; 9:4428-4435. [PMID: 30024165 PMCID: PMC6092130 DOI: 10.1021/acs.jpclett.8b01851] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We introduce a novel method called restrain-free energy perturbation-release (R-FEP-R) to estimate conformational free energy changes via an alchemical path, which for some conformational landscapes like those associated with cellular signaling proteins in the kinase family is more direct and readily converged than the corresponding free energy changes along the physical path. The R-FEP-R method was developed from the dual topology free energy perturbation method that is widely applied to estimate the binding free energy difference between two ligands. In R-FEP-R, the free energy change between two conformational basins is calculated by free energy perturbations that remove those atoms involved in the conformational change from their initial conformational basin while simultaneously growing them back according to the final conformational basin. Both the initial and final dual topology states are unphysical, but they are designed in a way such that the unphysical contributions to the initial and final partition functions cancel. Compared with other advanced sampling algorithms such as umbrella sampling and metadynamics, the R-FEP-R method does not require predetermined transition pathways or reaction coordinates that connect the two conformational states. As a first illustration, the R-FEP-R method was applied to calculate the free energy change between conformational basins for alanine dipeptide in solution and for a side chain in the binding pocket of T4 lysozyme. The results obtained by R-FEP-R agree with the benchmarks very well.
Collapse
Affiliation(s)
- Peng He
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Bin W. Zhang
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Shima Arasteh
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Lingle Wang
- Schrödinger, Inc., 120 West 45th Street, New York, New York 10036, United States
| | - Robert Abel
- Schrödinger, Inc., 120 West 45th Street, New York, New York 10036, United States
| | - Ronald M. Levy
- Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122, United States
| |
Collapse
|
15
|
Abstract
The kinetics of biochemical and biophysical events determined the course of life processes and attracted considerable interest and research. For example, modeling of biological networks and cellular responses relies on the availability of information on rate coefficients. Atomically detailed simulations hold the promise of supplementing experimental data to obtain a more complete kinetic picture. However, simulations at biological time scales are challenging. Typical computer resources are insufficient to provide the ensemble of trajectories at the correct length that is required for straightforward calculations of time scales. In the last years, new technologies emerged that make atomically detailed simulations of rate coefficients possible. Instead of computing complete trajectories from reactants to products, these approaches launch a large number of short trajectories at different positions. Since the trajectories are short, they are computed trivially in parallel on modern computer architecture. The starting and termination positions of the short trajectories are chosen, following statistical mechanics theory, to enhance efficiency. These trajectories are analyzed. The analysis produces accurate estimates of time scales as long as hours. The theory of Milestoning that exploits the use of short trajectories is discussed, and several applications are described.
Collapse
|