Computing time scales from reaction coordinates by milestoning

Faradjian, A.; Elber, Ron

doi:10.1063/1.1738640

Cited by 610 publications

(727 citation statements)

References 8 publications

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“…An algorithm to determine the time scales of complex processes following predetermined milestones along the reaction coordinate was recently developed but has not been tested yet on complex biomolecular processes. 72 , was used to retain the coordinates of protein residues and DNA sequences in place during these preparations. The hydroxyl group was also added to the 3′ terminus of the primer DNA strand.…”

Section: Sdelmentioning

confidence: 99%

Conformational Transition Pathway of Polymerase β/DNA upon Binding Correct Incoming Substrate

Arora

Schlick

2005

J. Phys. Chem. B

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The closing conformational transition of wild-type polymerase bound to DNA template/primer before the chemical step (nucleotidyl transfer reaction) is simulated using the stochastic difference equation (in length version, "SDEL") algorithm that approximates long-time dynamics. The order of the events and the intermediate states during pol 's closing pathway are identified and compared to a separate study of pol using transition path sampling (TPS) (Radhakrishnan, R.; Schlick, T. Proc. Natl. Acad. Sci. USA 2004, 101, 5970-5975). Results highlight the cooperative and subtle conformational changes in the pol active site upon binding the correct substrate that may help explain DNA replication and repair fidelity. These changes involve key residues that differentiate the open from the closed conformation (Asp192, Arg258, Phe272), as well as residues contacting the DNA template/primer strand near the active site (Tyr271, Arg283, Thr292, Tyr296) and residues contacting the and γ phosphates of the incoming nucleotide (Ser180, Arg183, Gly189). This study compliments experimental observations by providing detailed atomistic views of the intermediates along the polymerase closing pathway and by suggesting additional key residues that regulate events prior to or during the chemical reaction. We also show general agreement between two sampling methods (the stochastic difference equation and transition path sampling) and identify methodological challenges involved in the former method relevant to large-scale biomolecular applications. Specifically, SDEL is very quick relative to TPS for obtaining an approximate path of medium resolution and providing qualitative information on the sequence of events; however, associated free energies are likely very costly to obtain because this will require both successful further refinement of the path segments close to the bottlenecks and large computational time.

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Section: Sdelmentioning

confidence: 99%

Conformational Transition Pathway of Polymerase β/DNA upon Binding Correct Incoming Substrate

Arora

Schlick

2005

J. Phys. Chem. B

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“…In this paper we have shown that this exit probability has intrinsic value and can allow for the precise computation of the statistics of switching times, escape times and completion times for more complicated trajectories. Unlike previous analyses of stochastic switch rates that utilize Monte Carlo type approaches [12][13][14][15][16][17], the current method directly approximates the transient solution to the master equation and provides otherwise unachievable precision guarantees on the switch time distribution. At present this precision comes at a cost of adverse complexity scaling.…”

Section: Resultsmentioning

confidence: 99%

“…As a few representative examples, these methods include Transition Path Sampling [12], Transition Interface Sampling [13], and various approaches of transition path sampling with multiple interfaces [14][15][16][17]. By concentrating on trajectories that eventually result in switches and interrupting the the vast majority trajectories that do not, these approaches are far more efficient than a standard brute force Monte Carlo approach like the SSA.…”

Section: Introductionmentioning

confidence: 99%

Transient analysis of stochastic switches and trajectories with applications to gene regulatory networks

Munsky

Khammash

2008

IET Syst. Biol.

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Many gene regulatory networks are modeled at the mesoscopic scale, where chemical populations change according to a discrete state (jump) Markov process. The chemical master equation (CME) for such a process is typically infinite dimensional and unlikely to be computationally tractable without reduction. The recently proposed Finite State Projection (FSP) technique allows for a bulk reduction of the CME while explicitly keeping track of its own approximation error. In previous work, this error has been reduced in order to obtain more accurate CME solutions for many biological examples. In this paper, we show that this "error" has far more significance than simply the distance between the approximate and exact solutions of the CME. In particular, we show that this error term serves as an exact measure of the rate of first transition from one system region to another. We demonstrate how this term may 1 be used to (i) directly determine the statistical distributions for stochastic switch rates, escape times, trajectory periods, and trajectory bifurcations, and (ii) evaluate how likely it is that a system will express certain behaviors during certain intervals of time. We also present two systems-theory based FSP model reduction approaches that are particularly useful in such studies. We illustrate the benefits of this approach to analyze the switching behavior of a stochastic model of Gardner's genetic toggle switch.

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“…Finally, to complete this study with a look at the rates for each folding stage, one would need to reintroduce a time scale to the trajectories. This can be accomplished by the Milestoning technique 43 currently available for use in the MOIL package.…”

Section: Chapter 6 Conclusionmentioning

confidence: 99%

A study of Barstar folding events using boundary value simulations

Yunger

2007

Physica A: Statistical Mechanics and its Applications

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This study revolves around a computational algorithm called SDEL (Stochastic Difference Equation in Length) that generates approximate protein folding trajectories on the atomically detailed resolution scale. The protein studied is Barstar-a barnase inhibitor. Because of the protein's interesting structure (four alpha helices, three beta strands) and relatively small size (89 residues), Barstar is an optimal choice for running complete folding trajectories on a computer. 12 pathways were generated with SDEL, starting from a structurally wide selection of unfolded conformations, yet all ending with the native configuration. We tracked hydrogen bonds, dihedral angles, native and non-native contacts, and energetic along these folding pathways. The resulting trajectories show: 1) Barstar follows the Hydrophobic Collapse folding scenario, 2) native α-helices begin forming earlier in the trajectory than the β-sheets, 3) particular residues maintain a propensity for helical structure in their unfolded state, and 4) specific non-native contacts persist during the folding trajectory. Strong correlations were found between the SDEL pathways and data from NMR, CD, and other experimental studies.

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Computing time scales from reaction coordinates by milestoning

Cited by 610 publications

References 8 publications

Conformational Transition Pathway of Polymerase β/DNA upon Binding Correct Incoming Substrate

Conformational Transition Pathway of Polymerase β/DNA upon Binding Correct Incoming Substrate

Transient analysis of stochastic switches and trajectories with applications to gene regulatory networks

A study of Barstar folding events using boundary value simulations

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