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Wang B, Jackson S, Nakano A, Nomura KI, Vashishta P, Kalia R, Stevens M. Neural Network for Principle of Least Action. J Chem Inf Model 2022; 62:3346-3351. [PMID: 35786887 PMCID: PMC9326973 DOI: 10.1021/acs.jcim.2c00515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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The principle of
least action is the cornerstone of classical mechanics,
theory of relativity, quantum mechanics, and thermodynamics. Here,
we describe how a neural network (NN) learns to find the trajectory
for a Lennard-Jones (LJ) system that maintains balance in minimizing
the Onsager–Machlup (OM) action and maintaining the energy
conservation. The phase-space trajectory thus calculated is in excellent
agreement with the corresponding results from the “ground-truth”
molecular dynamics (MD) simulation. Furthermore, we show that the
NN can easily find structural transformation pathways for LJ clusters,
for example, the basin-hopping transformation of an LJ38 from an incomplete Mackay icosahedron to a truncated face-centered
cubic octahedron. Unlike MD, the NN computes atomic trajectories over
the entire temporal domain in one fell swoop, and the NN time step
is a factor of 20 larger than the MD time step. The NN approach to
OM action is quite general and can be adapted to model morphometrics
in a variety of applications.
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Affiliation(s)
- Beibei Wang
- Collaboratory for Advanced Computing and Simulations, University of Southern California, Los Angeles, California 90089, United States
| | - Shane Jackson
- Collaboratory for Advanced Computing and Simulations, University of Southern California, Los Angeles, California 90089, United States
| | - Aiichiro Nakano
- Collaboratory for Advanced Computing and Simulations, University of Southern California, Los Angeles, California 90089, United States
| | - Ken-Ichi Nomura
- Collaboratory for Advanced Computing and Simulations, University of Southern California, Los Angeles, California 90089, United States
| | - Priya Vashishta
- Collaboratory for Advanced Computing and Simulations, University of Southern California, Los Angeles, California 90089, United States
| | - Rajiv Kalia
- Collaboratory for Advanced Computing and Simulations, University of Southern California, Los Angeles, California 90089, United States
| | - Mark Stevens
- Center for Integrated Nanotechnologies, Sandia National Laboratory, Albuquerque, New Mexico 87185, United States
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2
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Radhakrishnan R. A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects. AIChE J 2021; 67:e17026. [PMID: 33790479 PMCID: PMC7988612 DOI: 10.1002/aic.17026] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 08/09/2020] [Accepted: 08/13/2020] [Indexed: 01/14/2023]
Abstract
Research problems in the domains of physical, engineering, biological sciences often span multiple time and length scales, owing to the complexity of information transfer underlying mechanisms. Multiscale modeling (MSM) and high-performance computing (HPC) have emerged as indispensable tools for tackling such complex problems. We review the foundations, historical developments, and current paradigms in MSM. A paradigm shift in MSM implementations is being fueled by the rapid advances and emerging paradigms in HPC at the dawn of exascale computing. Moreover, amidst the explosion of data science, engineering, and medicine, machine learning (ML) integrated with MSM is poised to enhance the capabilities of standard MSM approaches significantly, particularly in the face of increasing problem complexity. The potential to blend MSM, HPC, and ML presents opportunities for unbound innovation and promises to represent the future of MSM and explainable ML that will likely define the fields in the 21st century.
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Affiliation(s)
- Ravi Radhakrishnan
- Department of Chemical and Biomolecular EngineeringPenn Institute for Computational Science, University of PennsylvaniaPhiladelphiaPhiladelphiaUSA
- Department of BioengineeringPenn Institute for Computational Science, University of PennsylvaniaPhiladelphiaPhiladelphiaUSA
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3
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Lee J, Brooks BR. Direct global optimization of Onsager-Machlup action using Action-CSA. Chem Phys 2020. [DOI: 10.1016/j.chemphys.2020.110768] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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4
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Lee J, Lee IH, Joung I, Lee J, Brooks BR. Finding multiple reaction pathways via global optimization of action. Nat Commun 2017; 8:15443. [PMID: 28548089 PMCID: PMC5458546 DOI: 10.1038/ncomms15443] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2016] [Accepted: 03/24/2017] [Indexed: 12/25/2022] Open
Abstract
Global searching for reaction pathways is a long-standing challenge in computational chemistry and biology. Most existing approaches perform only local searches due to computational complexity. Here we present a computational approach, Action-CSA, to find multiple diverse reaction pathways connecting fixed initial and final states through global optimization of the Onsager-Machlup action using the conformational space annealing (CSA) method. Action-CSA successfully overcomes large energy barriers via crossovers and mutations of pathways and finds all possible pathways of small systems without initial guesses on pathways. The rank order and the transition time distribution of multiple pathways are in good agreement with those of long Langevin dynamics simulations. The lowest action folding pathway of FSD-1 is consistent with recent experiments. The results show that Action-CSA is an efficient and robust computational approach to study the multiple pathways of complex reactions and large-scale conformational changes.
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Affiliation(s)
- Juyong Lee
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH), Bethesda, Maryland 20892, USA
| | - In-Ho Lee
- Center for Materials Genome, Korea Research Institute of Standards and Science, Daejeon 34113, Republic of Korea
- Center for In Silico Protein Science, School of Computational Science, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - InSuk Joung
- Center for In Silico Protein Science, School of Computational Science, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
- School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Jooyoung Lee
- Center for In Silico Protein Science, School of Computational Science, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
- School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Bernard R. Brooks
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute (NHLBI), National Institutes of Health (NIH), Bethesda, Maryland 20892, USA
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5
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Abstract
Atomically detailed computer simulations of complex molecular events attracted the imagination of many researchers in the field as providing comprehensive information on chemical, biological, and physical processes. However, one of the greatest limitations of these simulations is of time scales. The physical time scales accessible to straightforward simulations are too short to address many interesting and important molecular events. In the last decade significant advances were made in different directions (theory, software, and hardware) that significantly expand the capabilities and accuracies of these techniques. This perspective describes and critically examines some of these advances.
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Affiliation(s)
- Ron Elber
- Department of Chemistry, The Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA
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6
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Giambaşu GM, Lee TS, Scott WG, York DM. Mapping L1 ligase ribozyme conformational switch. J Mol Biol 2012; 423:106-22. [PMID: 22771572 DOI: 10.1016/j.jmb.2012.06.035] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2012] [Revised: 05/21/2012] [Accepted: 06/25/2012] [Indexed: 01/10/2023]
Abstract
L1 ligase (L1L) molecular switch is an in vitro optimized synthetic allosteric ribozyme that catalyzes the regioselective formation of a 5'-to-3' phosphodiester bond, a reaction for which there is no known naturally occurring RNA catalyst. L1L serves as a proof of principle that RNA can catalyze a critical reaction for prebiotic RNA self-replication according to the RNA world hypothesis. L1L crystal structure captures two distinct conformations that differ by a reorientation of one of the stems by around 80Å and are presumed to correspond to the active and inactive state, respectively. It is of great interest to understand the nature of these two states in solution and the pathway for their interconversion. In this study, we use explicit solvent molecular simulation together with a novel enhanced sampling method that utilizes concepts from network theory to map out the conformational transition between active and inactive states of L1L. We find that the overall switching mechanism can be described as a three-state/two-step process. The first step involves a large-amplitude swing that reorients stem C. The second step involves the allosteric activation of the catalytic site through distant contacts with stem C. Using a conformational space network representation of the L1L switch transition, it is shown that the connection between the three states follows different topographical patterns: the stem C swing step passes through a narrow region of the conformational space network, whereas the allosteric activation step covers a much wider region and a more diverse set of pathways through the network.
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Affiliation(s)
- George M Giambaşu
- BioMaPS Institute and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA
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7
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Jas GS, Hegefeld W, Májek P, Kuczera K, Elber R. Experiments and comprehensive simulations of the formation of a helical turn. J Phys Chem B 2012; 116:6598-610. [PMID: 22335541 PMCID: PMC3361543 DOI: 10.1021/jp211645s] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
We investigate the kinetics and thermodynamics of a helical turn formation in the peptide Ac-WAAAH-NH(2). NMR measurements indicate that this peptide has significant tendency to form a structure of a helical turn, while temperature dependent CD establishes the helix fraction at different temperatures. Molecular dynamics and milestoning simulations agree with experimental observables and suggest an atomically detailed picture for the turn formation. Using a network representation, two alternative mechanisms of folding are identified: (i) a direct co-operative mechanism from the unfolded to the folded state without intermediate formation of hydrogen bonds and (ii) an indirect mechanism with structural intermediates with two residues in a helical conformation. This picture is consistent with kinetic measurements that reveal two experimental time scales of sub-nanosecond and several nanoseconds.
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Affiliation(s)
- Gouri S. Jas
- Department of Chemistry, Biochemistry, and Institute of Biomedical Studies, Baylor University, Waco, TX 76706
| | - Wendy Hegefeld
- Department of Chemistry, Biochemistry, and Institute of Biomedical Studies, Baylor University, Waco, TX 76706
| | - Peter Májek
- Institute of Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, TX 78712
| | - Krzysztof Kuczera
- Departments of Chemistry and Molecular Biosciences, The University of Kansas, Lawrence, KS 66045
| | - Ron Elber
- Institute of Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, TX 78712
- Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, TX 78712
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8
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LIM WILBER, FENG YUANPING. AN OVERVIEW OF THE STRETCHED INTERMEDIATE MODEL OF B–Z DNA TRANSITION. ACTA ACUST UNITED AC 2011. [DOI: 10.1142/s1793048006000185] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Recently, the stretched intermediate model was proposed for the B–Z deoxyribonucleic acid (DNA) transition based on simulation results carried out using the Stochastic Difference Equation (SDE) that showed unwinding and elongation of the oligomer during the transition. This model has proven to be successful in resolving the steric dilemma in short oligomers. However, extending the simulation method to larger DNA strands may prove to be computationally challenging. Such difficulty has led us to adopt a mean field approach using phenomenological interaction potentials to simulate the transition. Like the atomistic approach, the SDE simulations based on the mean field approach, also suggest the presence of a stretched intermediate during the transition.
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Affiliation(s)
- WILBER LIM
- Department of Physics, Faculty of Science, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
| | - YUAN PING FENG
- Department of Physics, Faculty of Science, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
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9
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Fuchigami S, Fujisaki H, Matsunaga Y, Kidera A. Protein Functional Motions: Basic Concepts and Computational Methodologies. ADVANCING THEORY FOR KINETICS AND DYNAMICS OF COMPLEX, MANY-DIMENSIONAL SYSTEMS: CLUSTERS AND PROTEINS 2011. [DOI: 10.1002/9781118087817.ch2] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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10
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Kirmizialtin S, Elber R. Revisiting and computing reaction coordinates with Directional Milestoning. J Phys Chem A 2011; 115:6137-48. [PMID: 21500798 PMCID: PMC3116089 DOI: 10.1021/jp111093c] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
The method of Directional Milestoning is revisited. We start from an exact and more general expression and state the conditions and validity of the memory-loss approximation. An algorithm to compute a reaction coordinate from Directional Milestoning data is presented. The reaction coordinate is calculated as a set of discrete jumps between Milestones that maximizes the flux between two stable states. As an application we consider a conformational transition in solvated adenosine. We compare a long molecular dynamic trajectory with Directional Milestoning and discuss the differences between the maximum flux path and minimum energy coordinates.
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Affiliation(s)
- Serdal Kirmizialtin
- Department of Chemistry and Biochemistry, Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA
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11
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Wang J, Zhang K, Wang E. Kinetic paths, time scale, and underlying landscapes: A path integral framework to study global natures of nonequilibrium systems and networks. J Chem Phys 2010; 133:125103. [DOI: 10.1063/1.3478547] [Citation(s) in RCA: 85] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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13
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Fujisaki H, Shiga M, Kidera A. Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways. J Chem Phys 2010; 132:134101. [PMID: 20387915 DOI: 10.1063/1.3372802] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.
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Affiliation(s)
- Hiroshi Fujisaki
- Department of Physics, Nippon Medical School, 2-297-2 Kosugi-cho, Nakahara, Kawasaki 211-0063, Japan.
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14
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15
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Brokaw JB, Haas KR, Chu JW. Reaction Path Optimization with Holonomic Constraints and Kinetic Energy Potentials. J Chem Theory Comput 2009; 5:2050-61. [DOI: 10.1021/ct9001398] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jason B. Brokaw
- Department of Chemistry and Department of Chemical Engineering, University of California, Berkeley, California 94720
| | - Kevin R. Haas
- Department of Chemistry and Department of Chemical Engineering, University of California, Berkeley, California 94720
| | - Jhih-Wei Chu
- Department of Chemistry and Department of Chemical Engineering, University of California, Berkeley, California 94720
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16
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Mills M, Andricioaei I. An experimentally guided umbrella sampling protocol for biomolecules. J Chem Phys 2009; 129:114101. [PMID: 19044944 DOI: 10.1063/1.2976440] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a simple method for utilizing experimental data to improve the efficiency of numerical calculations of free energy profiles from molecular dynamics simulations. The method involves umbrella sampling simulations with restraining potentials based on a known approximate estimate of the free energy profile derived solely from experimental data. The use of the experimental data results in optimal restraining potentials, guides the simulation along relevant pathways, and decreases overall computational time. In demonstration of the method, two systems are showcased. First, guided, unguided (regular) umbrella sampling simulations and exhaustive sampling simulations are compared to each other in the calculation of the free energy profile for the distance between the ends of a pentapeptide. The guided simulation use restraints based on a simulated "experimental" potential of mean force of the end-to-end distance that would be measured by fluorescence resonance energy transfer (obtained from exhaustive sampling). Statistical analysis shows a dramatic improvement in efficiency for a 5 window guided umbrella sampling over 5 and 17 window unguided umbrella sampling simulations. Moreover, the form of the potential of mean force for the guided simulations evolves, as one approaches convergence, along the same milestones as the extensive simulations, but exponentially faster. Second, the method is further validated by replicating the forced unfolding pathway of the titin I27 domain using guiding umbrella sampling potentials determined from actual single molecule pulling data. Comparison with unguided umbrella sampling reveals that the use of guided sampling encourages unfolding simulations to converge faster to a forced unfolding pathway that agrees with previous results and produces a more accurate potential of mean force.
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Affiliation(s)
- Maria Mills
- Department of Chemistry, University of California, Irvine, California 92697, USA
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17
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18
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Affiliation(s)
- Alexander V. Zhukov
- Department of Physics Education and Department of Physics, Pusan National University, Pusan 609-735, Korea
| | - Sang Wook Kim
- Department of Physics Education and Department of Physics, Pusan National University, Pusan 609-735, Korea
| | - Thomas F. George
- Office of the Chancellor and Center for Nanoscience, Department of Chemistry & Biochemistry and Department of Physics & Astronomy, University of Missouri-St. Louis, St. Louis, Missouri 63121
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19
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MacFadyen J, Wereszczynski J, Andricioaei I. Directionally negative friction: A method for enhanced sampling of rare event kinetics. J Chem Phys 2008; 128:114112. [DOI: 10.1063/1.2841102] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Nummela J, Yassin F, Andricioaei I. Entropy-energy decomposition from nonequilibrium work trajectories. J Chem Phys 2008; 128:024104. [DOI: 10.1063/1.2817332] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin. Proc Natl Acad Sci U S A 2007; 104:18043-8. [PMID: 17984047 DOI: 10.1073/pnas.0706349104] [Citation(s) in RCA: 99] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The computational sampling of rare, large-scale, conformational transitions in proteins is a well appreciated challenge-for which a number of potentially efficient path-sampling methodologies have been proposed. Here, we study a large-scale transition in a united-residue model of calmodulin using the "weighted ensemble" (WE) approach of Huber and Kim. Because of the model's relative simplicity, we are able to compare our results with brute-force simulations. The comparison indicates that the WE approach quantitatively reproduces the brute-force results, as assessed by considering (i) the reaction rate, (ii) the distribution of event durations, and (iii) structural distributions describing the heterogeneity of the paths. Importantly, the WE method is readily applied to more chemically accurate models, and by studying a series of lower temperatures, our results suggest that the WE method can increase efficiency by orders of magnitude in more challenging systems.
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22
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Nummela J, Andricioaei I. Exact low-force kinetics from high-force single-molecule unfolding events. Biophys J 2007; 93:3373-81. [PMID: 17704183 PMCID: PMC2072064 DOI: 10.1529/biophysj.107.111658] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Mechanical forces play a key role in crucial cellular processes involving force-bearing biomolecules, as well as in novel single-molecule pulling experiments. We present an exact method that enables one to extrapolate, to low (or zero) forces, entire time-correlation functions and kinetic rate constants from the conformational dynamics either simulated numerically or measured experimentally at a single, relatively higher, external force. The method has twofold relevance: 1), to extrapolate the kinetics at physiological force conditions from molecular dynamics trajectories generated at higher forces that accelerate conformational transitions; and 2), to extrapolate unfolding rates from experimental force-extension single-molecule curves. The theoretical formalism, based on stochastic path integral weights of Langevin trajectories, is presented for the constant-force, constant loading rate, and constant-velocity modes of the pulling experiments. For the first relevance, applications are described for simulating the conformational isomerization of alanine dipeptide; and for the second relevance, the single-molecule pulling of RNA is considered. The ability to assign a weight to each trace in the single-molecule data also suggests a means to quantitatively compare unfolding pathways under different conditions.
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Affiliation(s)
- Jeremiah Nummela
- Department of Chemistry, Center for Computational Medicine and Biology, University of Michigan, Ann Arbor, Michigan, USA
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23
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MacFadyen J, Andricioaei I. A skewed-momenta method to efficiently generate conformational-transition trajectories. J Chem Phys 2007; 123:074107. [PMID: 16229559 DOI: 10.1063/1.2000242] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
We present a novel computational method, the skewed-momenta method (Skew'M), which applies a bias to the Maxwell distribution of initial momenta used to generate ensembles of trajectories. As a result, conformational transitions are accentuated and kinetic properties are calculated more effectively. The connection to the related puddle jumping method is discussed. A reweighting scheme permits the exact calculation of kinetic properties. Applications are presented for the rapid calculation of rate constants for molecular isomerization, and for the efficient reconstruction of free-energy profiles using a straightforward modification of the Jarzynski identity.
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Affiliation(s)
- James MacFadyen
- Department of Chemistry and The Program in Bioinformatics, University of Michigan, Ann Arbor, Michigan 48109, USA
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24
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Mossa A, Clementi C. Supersymmetric Langevin equation to explore free-energy landscapes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:046707. [PMID: 17501016 DOI: 10.1103/physreve.75.046707] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2006] [Revised: 02/15/2007] [Indexed: 05/15/2023]
Abstract
The recently discovered supersymmetric generalizations of the Langevin dynamics and Kramers equation can be utilized for the exploration of free-energy landscapes of systems whose large time-scale separation hampers the usefulness of standard molecular dynamics techniques. The first realistic application is here presented. The system chosen is a minimalist model for a short alanine peptide exhibiting a helix-coil transition.
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Affiliation(s)
- Alessandro Mossa
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005, USA
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25
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Zhang BW, Jasnow D, Zuckerman DM. Transition-event durations in one-dimensional activated processes. J Chem Phys 2007; 126:074504. [PMID: 17328617 DOI: 10.1063/1.2434966] [Citation(s) in RCA: 84] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Despite their importance in activated processes, transition-event durations--which are much shorter than first passage times--have not received a complete theoretical treatment. The authors therefore study the distribution rhob(t) of durations of transition events over a barrier in a one-dimensional system undergoing overdamped Langevin dynamics. The authors show that rhob(t) is determined by a Fokker-Planck equation with absorbing boundary conditions and obtain a number of results, including (i) the analytic form of the asymptotic short-time transient behavior, which is universal and independent of the potential function; (ii) the first nonuniversal correction to the short-time behavior leading to an estimate of a key physical time scale; (iii) following previous work, a recursive formulation for calculating, exactly, all moments of rhob based solely on the potential function-along with approximations for the distribution based on a small number of moments; and (iv) a high-barrier approximation to the long-time (t-->infinity) behavior of rhob(t). The authors also find that the mean event duration does not depend simply on the barrier-top frequency (curvature) but is sensitive to details of the potential. All of the analytic results are confirmed by transition-path-sampling simulations implemented in a novel way. Finally, the authors discuss which aspects of the duration distribution are expected to be general for more complex systems.
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Affiliation(s)
- Bin W Zhang
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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27
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Chapter 2 Extending Atomistic Time Scale Simulations by Optimization of the Action. ACTA ACUST UNITED AC 2007. [DOI: 10.1016/s1574-1400(07)03002-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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28
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Yang H, Wu H, Li D, Han L, Huo S. Temperature-Dependent Probabilistic Roadmap Algorithm for Calculating Variationally Optimized Conformational Transition Pathways. J Chem Theory Comput 2006; 3:17-25. [DOI: 10.1021/ct0502054] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Haijun Yang
- Gustaf H. Carlson School of Chemistry and Biochemistry and Department of Mathematics and Computer Science, Clark University, 950 Main Street, Worcester, Massachusetts 01610
| | - Hao Wu
- Gustaf H. Carlson School of Chemistry and Biochemistry and Department of Mathematics and Computer Science, Clark University, 950 Main Street, Worcester, Massachusetts 01610
| | - Dawei Li
- Gustaf H. Carlson School of Chemistry and Biochemistry and Department of Mathematics and Computer Science, Clark University, 950 Main Street, Worcester, Massachusetts 01610
| | - Li Han
- Gustaf H. Carlson School of Chemistry and Biochemistry and Department of Mathematics and Computer Science, Clark University, 950 Main Street, Worcester, Massachusetts 01610
| | - Shuanghong Huo
- Gustaf H. Carlson School of Chemistry and Biochemistry and Department of Mathematics and Computer Science, Clark University, 950 Main Street, Worcester, Massachusetts 01610
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29
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Radhakrishnan R, Schlick T. Correct and incorrect nucleotide incorporation pathways in DNA polymerase beta. Biochem Biophys Res Commun 2006; 350:521-9. [PMID: 17022941 PMCID: PMC1976263 DOI: 10.1016/j.bbrc.2006.09.059] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2006] [Accepted: 09/13/2006] [Indexed: 10/24/2022]
Abstract
Tracking the structural and energetic changes in the pathways of DNA replication and repair is central to the understanding of these important processes. Here we report favorable mechanisms of the polymerase-catalyzed phosphoryl transfer reactions corresponding to correct and incorrect nucleotide incorporations in the DNA by using a novel protocol involving energy minimizations, dynamics simulations, quasi-harmonic free energy calculations, and mixed quantum mechanics/molecular mechanics dynamics simulations. Though the pathway proposed may not be unique and invites variations, geometric and energetic arguments support the series of transient intermediates in the phosphoryl transfer pathways uncovered here for both the G:C and G:A systems involving a Grotthuss hopping mechanism of proton transfer between water molecules and the three conserved aspartate residues in pol beta's active-site. In the G:C system, the rate-limiting step is the initial proton hop with a free energy of activation of at least 17 kcal/mol, which corresponds closely to measured k(pol) values. Fidelity discrimination in pol beta can be explained by a significant loss of stability of the closed ternary complex of the enzyme in the G:A system and much higher activation energy of the initial step of nucleophilic attack, namely deprotonation of terminal DNA primer O3'H group. Thus, subtle differences in the enzyme active-site between matched and mismatched base pairs generate significant differences in catalytic performance.
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Affiliation(s)
- Ravi Radhakrishnan
- Department of Bioengineering, University of Pennsylvania, 240 Skirkanich Hall, 210 S. 33rd Street, Philadelphia, PA,
| | - Tamar Schlick
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012,
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30
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Wang J, Zhang K, Lu H, Wang E. Quantifying the kinetic paths of flexible biomolecular recognition. Biophys J 2006; 91:866-72. [PMID: 16617073 PMCID: PMC1563758 DOI: 10.1529/biophysj.105.074716] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2005] [Accepted: 02/06/2006] [Indexed: 11/18/2022] Open
Abstract
Biomolecular recognition often involves large conformational changes, sometimes even local unfolding. The identification of kinetic pathways has become a central issue in understanding the nature of binding. A new approach is proposed here to study the dynamics of this binding-folding process through the establishment of a path-integral framework on the underlying energy landscape. The dominant kinetic paths of binding and folding can be determined and quantified. The significant coupling between the binding and folding of biomolecules often exists in many important cellular processes. In this case, the corresponding kinetic paths of binding are shown to be intimately correlated with those of folding and the dynamics becomes quite cooperative. This implies that binding and folding happen concurrently. When the coupling between binding and folding is weak (strong), the kinetic process usually starts with significant folding (binding) first, with the binding (folding) later proceeding to the end. The kinetic rate can be obtained through the contributions from the dominant paths. The rate is shown to have a bell-shaped dependence on temperature in the concentration-saturated regime consistent with experiment. The changes of the kinetics that occur upon changing the parameters of the underlying binding-folding energy landscape are studied.
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Affiliation(s)
- Jin Wang
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin, China
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31
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Khavrutskii IV, Byrd RH, Brooks CL. A line integral reaction path approximation for large systems via nonlinear constrained optimization: Application to alanine dipeptide and the β hairpin of protein G. J Chem Phys 2006; 124:194903. [PMID: 16729840 DOI: 10.1063/1.2194544] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A variation of the line integral method of Elber with self-avoiding walk has been implemented using a state of the art nonlinear constrained optimization procedure. The new implementation appears to be robust in finding approximate reaction paths for small and large systems. Exact transition states and intermediates for the resulting paths can easily be pinpointed with subsequent application of the conjugate peak refinement method [S. Fischer and M. Karplus, Chem. Phys. Lett. 194, 252 (1992)] and unconstrained minimization, respectively. Unlike previous implementations utilizing a penalty function approach, the present implementation generates an exact solution of the underlying problem. Most importantly, this formulation does not require an initial guess for the path, which makes it particularly useful for studying complex molecular rearrangements. The method has been applied to conformational rearrangements of the alanine dipeptide in the gas phase and in water, and folding of the beta hairpin of protein G in water. In the latter case a procedure was developed to systematically sample the potential energy surface underlying folding and reconstruct folding pathways within the nearest-neighbor hopping approximation.
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Affiliation(s)
- Ilja V Khavrutskii
- Department of Molecular Biology, The Scripps Research Institute, La Jolla, CA 92037, USA
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32
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Adcock SA, McCammon JA. Molecular dynamics: survey of methods for simulating the activity of proteins. Chem Rev 2006; 106:1589-615. [PMID: 16683746 PMCID: PMC2547409 DOI: 10.1021/cr040426m] [Citation(s) in RCA: 757] [Impact Index Per Article: 42.1] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Stewart A. Adcock
- NSF Center for Theoretical Biological Physics, Department of Chemistry and Biochemistry, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0365
| | - J. Andrew McCammon
- NSF Center for Theoretical Biological Physics, Department of Chemistry and Biochemistry, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0365
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33
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Wang J, Zhang K, Lu H, Wang E. Dominant kinetic paths on biomolecular binding-folding energy landscape. PHYSICAL REVIEW LETTERS 2006; 96:168101. [PMID: 16712278 DOI: 10.1103/physrevlett.96.168101] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2005] [Indexed: 05/09/2023]
Abstract
The identification of kinetic pathways is a central issue in understanding the nature of flexible binding. A new approach is proposed here to study the dynamics of this binding-folding process through the establishment of a path integral framework on the underlying energy landscape. The dominant kinetic paths of binding and folding can be determined and quantified. In this case, the corresponding kinetic paths of binding are shown to be intimately correlated with those of folding and the dynamics becomes quite cooperative. The kinetic time can be obtained through the contributions from the dominant paths and has a U-shape dependence on temperature.
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Affiliation(s)
- Jin Wang
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130021, People's Republic of China.
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34
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35
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Xing C, Andricioaei I. On the calculation of time correlation functions by potential scaling. J Chem Phys 2006; 124:034110. [PMID: 16438570 DOI: 10.1063/1.2159476] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present and analyze a general method to calculate time correlation functions from molecular dynamics on scaled potentials for complex systems for which simulation is affected by broken ergodicity. Depending on the value of the scaling factor, correlations can be calculated for times that can be orders of magnitude longer than those accessible to direct simulations. We show that the exact value of the time correlation functions of the original system (i.e., with unscaled potential) can be obtained, in principle, using an action-reweighting scheme based on a stochastic path-integral formalism. Two tests (involving a bistable potential model and a dipeptide bond-vector orientational relaxation) are exemplified to showcase the strengths, as well as the limitations of the approach, and a procedure for the estimation of the time-dependent standard deviation error is outlined.
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Affiliation(s)
- Chenyue Xing
- Department of Chemistry and The Program in Bioinformatics, University of Michigan, Ann Arbor, Michigan 48109, USA
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36
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37
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Abstract
Thermodynamic and dynamic properties of biomolecules can be calculated using a coarse-grained approach based upon sampling stationary points of the underlying potential energy surface. The superposition approximation provides an overall partition function as a sum of contributions from the local minima, and hence functions such as internal energy, entropy, free energy and the heat capacity. To obtain rates we must also sample transition states that link the local minima, and the discrete path sampling method provides a systematic means to achieve this goal. A coarse-grained picture is also helpful in locating the global minimum using the basin-hopping approach. Here we can exploit a fictitious dynamics between the basins of attraction of local minima, since the objective is to find the lowest minimum, rather than to reproduce the thermodynamics or dynamics.
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Affiliation(s)
- David J Wales
- Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, UK.
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38
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Waalkens H, Burbanks A, Wiggins S. A formula to compute the microcanonical volume of reactive initial conditions in transition state theory. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/0305-4470/38/45/l03] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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39
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Abstract
We propose a new approach to activated protein folding dynamics via a diffusive path integral framework. The important issues of kinetic paths in this situation can be directly addressed. This leads to the identification of the kinetic paths of the activated folding process, and provides a direct tool and language for the theoretical and experimental community to understand the problem better. The kinetic paths giving the dominant contributions to the long-time folding activation dynamics can be quantitatively determined. These are shown to be the instanton paths. The contributions of these instanton paths to the kinetics lead to the "bell-like" shape folding rate dependence on temperature, which is in good agreement with folding kinetic experiments and simulations. The connections to other approaches as well as the experiments of the protein folding kinetics are discussed.
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Affiliation(s)
- Jin Wang
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130021, People's Republic of China.
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40
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Abstract
There have been numerous attempts to describe the mechanism of B-Z transition. Our simulations based on the stochastic difference equation with length algorithm show that a short DNA oligomer will tend to unwind and overstretch during the transition. The overstretching of DNA is then understood from the Zhou, Zhang, and Ou-Yang model. Unlike the Harvey model, the stretched intermediate model does not pose any steric dilemma; we are able to show that the chain sense reversal progresses spontaneously using the stretched intermediate model. A nonlinear DNA model is used to describe the origins and mechanism of base rotation in the stretched intermediate state of DNA. We also propose an experiment that can verify the existence of a stretched intermediate state during B-Z transition, thus opening up fresh grounds for experimentation in this field.
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Affiliation(s)
- Wilber Lim
- Department of Physics, Faculty of Science, National University of Singapore, Singapore 117542.
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41
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Cárdenas AE, Elber R. Atomically detailed simulations of helix formation with the stochastic difference equation. Biophys J 2004; 85:2919-39. [PMID: 14581195 PMCID: PMC1303571 DOI: 10.1016/s0006-3495(03)74713-4] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022] Open
Abstract
An algorithm is described to compute approximate classical trajectories as a boundary value problem with an integration step in the arc length. High-frequency motions are filtered out when a large integration step is used, maintaining the stability of the algorithm. At the limit of high filtering (large steps), but still offering an accurate description of the continuous path, the trajectory approaches the steepest descent path (SDP). The steepest descent path is widely used as a reaction coordinate in chemical systems. At intermediate step sizes, some inertial motions remain, interpolating between reaction coordinates and exact classical trajectories. Numerical studies of spatial and energetic properties of meta-trajectories are carried out. Two systems are considered here: valine dipeptide and the folding of a small helical protein. Although thermodynamic properties of meta-trajectories are affected by the filtering, the ordering of events remains similar for substantial differences in trajectory resolution.
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Affiliation(s)
- Alfredo E Cárdenas
- Department of Computer Science, Cornell University, Ithaca, New York 14850, USA
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42
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Zuckerman DM. Simulation of an Ensemble of Conformational Transitions in a United-Residue Model of Calmodulin. J Phys Chem B 2004. [DOI: 10.1021/jp0370730] [Citation(s) in RCA: 76] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daniel M. Zuckerman
- Center for Computational Biology & Bioinformatics, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, and Department of Environmental & Occupational Health, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
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43
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Somasi S, Khomami B, Lovett R. A density functional view of transition state theory: Simulating the rates at which Si adatoms hop on a silicon surface. J Chem Phys 2003. [DOI: 10.1063/1.1615472] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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44
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Abstract
The vast range of time scales (from nanoseconds to seconds) during protein folding is a challenge for experiments and computations. To make concrete predictions on folding mechanisms, atomically detailed simulations of protein folding, using potentials derived from chemical physics principles, are desired. However, due to their computational complexity, straightforward molecular dynamics simulations of protein folding are impossible today. An alternative algorithm is used that makes it possible to compute approximate atomically detailed long time trajectories (the Stochastic Difference Equation in Length). This algorithm is used to compute 26 atomically detailed folding trajectories of cytochrome c (a millisecond process). The early collapse of the protein chain (with marginal formation of secondary structure), and the earlier formation of the N and C helices (compare to the 60's helix) are consistent with the experiment. The existence of an energy barrier upon entry to the molten globule is examined as well. In addition to (favorable) comparison to experiments, we show that non-native contacts drive the formation of the molten globule. In contrast to popular folding models, the non-native contacts do not form off-pathway kinetic traps in cytochrome c.
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Affiliation(s)
- Alfredo E Cárdenas
- Department of Computer Science, Cornell University, Ithaca, New York 14853, USA
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45
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Brutovsky B, Mülders T, Kneller GR. Accelerating molecular dynamics simulations by linear prediction of time series. J Chem Phys 2003. [DOI: 10.1063/1.1559033] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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Kleinjung J, Fraternali F, Martin SR, Bayley PM. Thermal unfolding simulations of apo-calmodulin using leap-dynamics. Proteins 2003; 50:648-56. [PMID: 12577271 DOI: 10.1002/prot.10331] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The simulation method leap-dynamics (LD) has been applied to protein thermal unfolding simulations to investigate domain-specific unfolding behavior. Thermal unfolding simulations of the 148-residue protein apo-calmodulin with implicit solvent were performed at temperatures 290 K, 325 K, and 360 K and compared with the corresponding molecular dynamics trajectories in terms of a number of calculated conformational parameters. The main experimental results of unfolding are reproduced in showing the lower stability of the C-domain: at 290 K, both the N- and C-domains are essentially stable; at 325 K, the C-domain unfolds, whereas the N-domain remains folded; and at 360 K, both domains unfold extensively. This behavior could not be reproduced by molecular dynamics simulations alone under the same conditions. These results show an encouraging degree of convergence between experiment and LD simulation. The simulations are able to describe the overall plasticity of the apo-calmodulin structure and to reveal details such as reversible folding/unfolding events within single helices. The results show that by using the combined application of a fast and efficient sampling routine with a detailed molecular dynamics force field, unfolding simulations of proteins at atomic resolution are within the scope of current computational power.
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Affiliation(s)
- Jens Kleinjung
- Division of Mathematical Biology, National Institute for Medical Research, London, United Kingdom.
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47
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Andricioaei I, Dinner AR, Karplus M. Self-guided enhanced sampling methods for thermodynamic averages. J Chem Phys 2003. [DOI: 10.1063/1.1528893] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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48
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Siva K, Elber R. Ion permeation through the gramicidin channel: atomically detailed modeling by the Stochastic Difference Equation. Proteins 2003; 50:63-80. [PMID: 12471600 DOI: 10.1002/prot.10256] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Atomically detailed descriptions of ionic solution, membrane, and the gramicidin channel are used to compute molecular dynamics trajectories of ion permeation. The microsecond trajectories are calculated with the Stochastic Difference Equation (SDE), which provides approximate solutions to the equations of motions (with filtered high-frequency modes) of extended timescales. The relative permeations of lithium, sodium, and potassium are estimated by using a novel, kinetic cycle protocol and are compared with experiment. The transport through native gramicidin and one fluoro-valine variant is considered as well. Qualitative agreement between theory and experiment is obtained. The faster permeation rate of sodium compared to lithium is reproduced in the calculations. The calculations also reproduce the slower diffusion through a gramicidin with fluorinated valine compared to native gramicidin. The calculations are inconclusive about the relative rates of potassium and sodium. The experiment suggests that potassium permeates more quickly. We directly probe the kinetics of a biophysical process at a relevant time window without reducing the atomically detailed description of the system. The calculations were able to capture subtle balances between binding and diffusion that determine permeation rates. The same model gave the correct ordering of diffusion rates for cases in which electrostatic binding has opposite effects and must be supplemented by dynamic factors. Diffusion rates are faster when favorable electrostatic interactions of ions in the channel (compared to the solvent) are observed. Studies of a gramicidin variant suggest an opposite effect, in which permeation is faster for the less polar channel, indicating dynamic effects. Although both trends can be explained qualitatively, it is not possible to predict (before doing the SDE calculations) which factor is more important.
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Affiliation(s)
- Koneshan Siva
- Department of Computer Science, Cornell University, Ithaca, New York, USA
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49
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Baffico L, Bernard S, Maday Y, Turinici G, Zérah G. Parallel-in-time molecular-dynamics simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:057701. [PMID: 12513644 DOI: 10.1103/physreve.66.057701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2002] [Indexed: 05/24/2023]
Abstract
While there have been many progress in the field of multiscale simulations in the space domain, in particular, due to efficient parallelization techniques, much less is known in the way to perform similar approaches in the time domain. In this paper we show on two examples that, provided we can describe in a rough but still accurate way the system under consideration, it is indeed possible to parallelize molecular dynamics simulations in time by using the recently introduced pararealalgorithm. The technique is most useful for ab initio simulations.
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Affiliation(s)
- L Baffico
- Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte Courrier 187, 75252 Paris Cedex 05, France
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50
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Abstract
Molecular dynamics trajectories of large biological molecules are restricted to nanoseconds. We describe a computational method, based on optimization of a functional, to extend the time of molecular simulations by orders of magnitude. Variants of our technique have already produced microsecond and millisecond trajectories. The large steps enable feasible computations of atomically detailed approximate trajectories. Numerical examples are provided: (i) a conformational change in blocked glycine peptide and (ii) helix formation of an alanine-rich peptide.
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Affiliation(s)
- Ron Elber
- Department of Computer Science, Upson Hall 4130, Cornell University, Ithaca, New York 14853, USA.
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