Elaborating Transition Interface Sampling Methods

Erp, Titus S. van; Bolhuis, Peter G.

doi:10.1002/chin.200447267

Cited by 14 publications

(25 citation statements)

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“…The rate constants can be efficiently computed using the transition interface sampling (TIS) framework [15,16], in which a collective variable is used to describe a foliation of hyper-surfaces or interfaces. A TIS simulation collects trajectories that leave the reactant stable state, and cross a specific interface.…”

Section: Introductionmentioning

confidence: 99%

On the Relation Between Projections of the Reweighted Path Ensemble

Bolhuis

Lechner

2011

J Stat Phys

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We derive several distribution functions for the recently introduced reweighted path ensemble [Rogal et al. in J. Chem. Phys. 133:174109, 2010]: the configurational and path densities, the reactive current, and the generalized committors for the different path types. We relate these distributions to the free energy and to the expressions for the rate constant in the transition state theory, the reactive flux method, the transition path (interface) sampling framework, and the Bayesian path statistics. In addition, we compute the transmission coefficient (distribution) from the reweighted path ensemble. Finally, we derive the path sampling shooting point distributions. For a simple two dimensional Langevin model we illustrate how these novel distributions can be used as analysis tools in rare event simulations.

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Section: Introductionmentioning

confidence: 99%

On the Relation Between Projections of the Reweighted Path Ensemble

Bolhuis

Lechner

2011

J Stat Phys

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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%

“…4). First, the lines correspond to solutions where (13) has been solved as a single large system of 1496 ODEs. In the second approach, the system has been analyzed as two separate sub-systems defined by the triplets SY S 1 = (A ON , P ON , C 1 )…”

Section: Q4mentioning

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%

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

Munsky

Khammash

2008

IET Systems Biology

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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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“…The rate of the system can be obtained via (22) k IJ = ϕ I Pðλ 0J jλ 1I Þ, [2] where ϕ I is the flux out of the stable state I and Pðλ 0J jλ1IÞ is the crossing probability from the first interface of state I to the first interface of state J, which can be factorized into the crossing probability Pðλ mI jλ 1I Þ and Pðλ 0J jλ mI Þ. The flux is easily calculated with a standard DMC run, or from the minus interface ensemble (22)(23)(24). The crossing probabilities are usually very small and therefore difficult to obtain.…”

Section: Simulation Settingsmentioning

confidence: 99%

Rotational diffusion affects the dynamical self-assembly pathways of patchy particles

Newton

Groenewold

Kegel

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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Predicting the self-assembly kinetics of particles with anisotropic interactions, such as colloidal patchy particles or proteins with multiple binding sites, is important for the design of novel hightech materials, as well as for understanding biological systems, e.g., viruses or regulatory networks. Often stochastic in nature, such self-assembly processes are fundamentally governed by rotational and translational diffusion. Whereas the rotational diffusion constant of particles is usually considered to be coupled to the translational diffusion via the Stokes-Einstein relation, in the past decade it has become clear that they can be independently altered by molecular crowding agents or via external fields. Because virus capsids naturally assemble in crowded environments such as the cell cytoplasm but also in aqueous solution in vitro, it is important to investigate how varying the rotational diffusion with respect to transitional diffusion alters the kinetic pathways of self-assembly. Kinetic trapping in malformed or intermediate structures often impedes a direct simulation approach of a kinetic network by dramatically slowing down the relaxation to the designed ground state. However, using recently developed path-sampling techniques, we can sample and analyze the entire self-assembly kinetic network of simple patchy particle systems. For assembly of a designed cluster of patchy particles we find that changing the rotational diffusion does not change the equilibrium constants, but significantly affects the dynamical pathways, and enhances (suppresses) the overall relaxation process and the yield of the target structure, by avoiding (encountering) frustrated states. Besides insight, this finding provides a design principle for improved control of nanoparticle self-assembly.kinetic networks | colloids | globular proteins | transition path sampling I n nature, self-assembled complex structures and networks often provide function. Prime examples are virus capsids, where capsomer proteins with specific interaction sites self-assemble into various structures, such as icosahedrons and dodecahedrons. Protein complexes can spontaneously form in the living cell, e.g., in signal transduction networks. Self-assembly of small designed building blocks can provide novel (bio)materials with desired properties. Such building blocks can consist of proteins, synthetic polypeptides, but also of colloidal particles. Particularly, the advent of novel synthesis routes for colloidal particles with a valence, so-called "patchy particles" opened up avenues for designing colloidal superstructures. Numerous experimental, theoretical, and numerical studies have enabled understanding of the phase behavior of these particles, predicting not only interesting building blocks for new functional materials, but also demonstrating new physics (1-5). Design principles for colloidal superstructures can predict which structure is the most thermodynamically favorable state (6). However, the fact that kinetics often trumps thermodynamics can hamper such...

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Elaborating Transition Interface Sampling Methods

Cited by 14 publications

References 48 publications

On the Relation Between Projections of the Reweighted Path Ensemble

On the Relation Between Projections of the Reweighted Path Ensemble

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

Rotational diffusion affects the dynamical self-assembly pathways of patchy particles

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