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Zolaktaf S, Dannenberg F, Schmidt M, Condon A, Winfree E. Predicting DNA kinetics with a truncated continuous-time Markov chain method. Comput Biol Chem 2023; 104:107837. [PMID: 36858009 DOI: 10.1016/j.compbiolchem.2023.107837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Revised: 02/05/2023] [Accepted: 02/21/2023] [Indexed: 03/03/2023]
Abstract
Predicting the kinetics of reactions involving nucleic acid strands is a fundamental task in biology and biotechnology. Reaction kinetics can be modeled as an elementary step continuous-time Markov chain, where states correspond to secondary structures and transitions correspond to base pair formation and breakage. Since the number of states in the Markov chain could be large, rates are determined by estimating the mean first passage time from sampled trajectories. As a result, the cost of kinetic predictions becomes prohibitively expensive for rare events with extremely long trajectories. Also problematic are scenarios where multiple predictions are needed for the same reaction, e.g., under different environmental conditions, or when calibrating model parameters, because a new set of trajectories is needed multiple times. We propose a new method, called pathway elaboration, to handle these scenarios. Pathway elaboration builds a truncated continuous-time Markov chain through both biased and unbiased sampling. The resulting Markov chain has moderate state space size, so matrix methods can efficiently compute reaction rates, even for rare events. Also the transition rates of the truncated Markov chain can easily be adapted when model or environmental parameters are perturbed, making model calibration feasible. We illustrate the utility of pathway elaboration on toehold-mediated strand displacement reactions, show that it well-approximates trajectory-based predictions of unbiased elementary step models on a wide range of reaction types for which such predictions are feasible, and demonstrate that it performs better than alternative truncation-based approaches that are applicable for mean first passage time estimation. Finally, in a small study, we use pathway elaboration to optimize the Metropolis kinetic model of Multistrand, an elementary step simulator, showing that the optimized parameters greatly improve reaction rate predictions. Our framework and dataset are available at https://github.com/DNA-and-Natural-Algorithms-Group/PathwayElaboration.
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Affiliation(s)
| | | | - Mark Schmidt
- University of British Columbia, Canada; Canada CIFAR AI Chair (Amii), Canada.
| | | | - Erik Winfree
- California Institute of Technology, United States of America.
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Bolhuis PG, Swenson DWH. Transition Path Sampling as Markov Chain Monte Carlo of Trajectories: Recent Algorithms, Software, Applications, and Future Outlook. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202000237] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Peter G. Bolhuis
- Amsterdam Center for Multiscale Modeling van 't Hoff Institute for Molecular Sciences University of Amsterdam PO Box 94157 1090 GD Amsterdam The Netherlands
| | - David W. H. Swenson
- Centre Blaise Pascal Ecole Normale Superieure 46, allée d'Italie 69364 Lyon Cedex 07 France
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3
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Sharpe DJ, Wales DJ. Efficient and exact sampling of transition path ensembles on Markovian networks. J Chem Phys 2020; 153:024121. [DOI: 10.1063/5.0012128] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Daniel J. Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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4
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Yappert R, Kamat K, Peters B. The overdamped transmission coefficient: Recovering the true mean first passage time from an inaccurate reaction coordinate. J Chem Phys 2019; 151:184108. [DOI: 10.1063/1.5117237] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- Ryan Yappert
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Kartik Kamat
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Baron Peters
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Brotzakis ZF, Bolhuis PG. Approximating free energy and committor landscapes in standard transition path sampling using virtual interface exchange. J Chem Phys 2019; 151:174111. [DOI: 10.1063/1.5119252] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Z. Faidon Brotzakis
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Peter G. Bolhuis
- Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
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6
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Joswiak MN, Doherty MF, Peters B. Critical length of a one-dimensional nucleus. J Chem Phys 2016; 145:211916. [DOI: 10.1063/1.4962448] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Mark N. Joswiak
- Department of Chemical Engineering, University of California-Santa Barbara, Santa Barbara, California 93106, USA
| | - Michael F. Doherty
- Department of Chemical Engineering, University of California-Santa Barbara, Santa Barbara, California 93106, USA
| | - Baron Peters
- Department of Chemical Engineering, University of California-Santa Barbara, Santa Barbara, California 93106, USA
- Department of Chemistry and Biochemistry, University of California-Santa Barbara, Santa Barbara, California 93106, USA
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Mullen RG, Shea JE, Peters B. Easy Transition Path Sampling Methods: Flexible-Length Aimless Shooting and Permutation Shooting. J Chem Theory Comput 2015; 11:2421-8. [DOI: 10.1021/acs.jctc.5b00032] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ryan Gotchy Mullen
- Department of Chemical Engineering, ‡Department of Chemistry & Biochemistry, §Department of Physics, University of California, Santa Barbara, California 93106, United States
| | - Joan-Emma Shea
- Department of Chemical Engineering, ‡Department of Chemistry & Biochemistry, §Department of Physics, University of California, Santa Barbara, California 93106, United States
| | - Baron Peters
- Department of Chemical Engineering, ‡Department of Chemistry & Biochemistry, §Department of Physics, University of California, Santa Barbara, California 93106, United States
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Affiliation(s)
- Baron Peters
- Department
of Chemical Engineering, University of California, Santa Barbara, California 93106, United States
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
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Athènes M, Bulatov VV. Path factorization approach to stochastic simulations. PHYSICAL REVIEW LETTERS 2014; 113:230601. [PMID: 25526107 DOI: 10.1103/physrevlett.113.230601] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2014] [Indexed: 06/04/2023]
Abstract
The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still preserving exact statistics of escape paths from the trapping basins. The method is based on path factorization of the evolution operator and requires no prior knowledge of the underlying energy landscape. The efficiency of the new method is demonstrated in simulations of anomalous diffusion and phase separation in a binary alloy, two stochastic models presenting severe kinetic trapping.
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Affiliation(s)
- Manuel Athènes
- CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette, France
| | - Vasily V Bulatov
- Lawrence Livermore National Laboratory, Livermore, California 94551, USA
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Peter EK, Shea JE. A hybrid MD-kMC algorithm for folding proteins in explicit solvent. Phys Chem Chem Phys 2014; 16:6430-40. [PMID: 24499973 DOI: 10.1039/c3cp55251a] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a novel hybrid MD-kMC algorithm that is capable of efficiently folding proteins in explicit solvent. We apply this algorithm to the folding of a small protein, Trp-Cage. Different kMC move sets that capture different possible rate limiting steps are implemented. The first uses secondary structure formation as a relevant rate event (a combination of dihedral rotations and hydrogen-bonding formation and breakage). The second uses tertiary structure formation events through formation of contacts via translational moves. Both methods fold the protein, but via different mechanisms and with different folding kinetics. The first method leads to folding via a structured helical state, with kinetics fit by a single exponential. The second method leads to folding via a collapsed loop, with kinetics poorly fit by single or double exponentials. In both cases, folding times are faster than experimentally reported values, The secondary and tertiary move sets are integrated in a third MD-kMC implementation, which now leads to folding of the protein via both pathways, with single and double-exponential fits to the rates, and to folding rates in good agreement with experimental values. The competition between secondary and tertiary structure leads to a longer search for the helix-rich intermediate in the case of the first pathway, and to the emergence of a kinetically trapped long-lived molten-globule collapsed state in the case of the second pathway. The algorithm presented not only captures experimentally observed folding intermediates and kinetics, but yields insights into the relative roles of local and global interactions in determining folding mechanisms and rates.
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Affiliation(s)
- Emanuel Karl Peter
- University of California Santa Barbara, Department of Chemistry and Biochemistry, Department of Physics, Santa Barbara, CA 93106, USA.
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Athènes M, Marinica MC, Jourdan T. Estimating time-correlation functions by sampling and unbiasing dynamically activated events. J Chem Phys 2012. [PMID: 23181294 DOI: 10.1063/1.4766458] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
Transition path sampling is a rare-event method that estimates state-to-state time-correlation functions in many-body systems from samples of short trajectories. In this framework, it is proposed to bias the importance function using the lowest Jacobian eigenvalue moduli along the dynamical trajectory. A lowest eigenvalue modulus is related to the lowest eigenvalue of the Hessian matrix and is evaluated here using the Lanczos algorithm as in activation-relaxation techniques. This results in favoring the sampling of activated trajectories and enhancing the occurrence of the rare reactive trajectories of interest, those corresponding to transitions between locally stable states. Estimating the time-correlation functions involves unbiasing the sample of simulated trajectories which is done using the multi-state Bennett acceptance ratio (MBAR) method. To assess the performance of our procedure, we compute the time-correlation function associated with the migration of a vacancy in α-iron. The derivative of the estimated time-correlation function yields a migration rate in agreement with the one given by transition state theory. Besides, we show that the information relative to rejected trajectories can be recycled within MBAR, resulting in a substantial speed-up. Unlike original transition path-sampling, our approach does not require computing the reversible work to confine the trajectory endpoints to a reactive state.
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Affiliation(s)
- Manuel Athènes
- CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette, France
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