The stochastic separatrix and the reaction coordinate for complex systems

Antoniou, Dimitri; Schwartz, Steven D.

doi:10.1063/1.3123162

Cited by 48 publications

(84 citation statements)

References 17 publications

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“…55 An important attribute of TPS is that it does not require a priori knowledge of the reaction coordinate; one can obtain important macroscopic variables that define the reaction coordinate from analysis of the reactive pathways obtained from TPS calculations. 31,71,72 TPS simulations require that the stable states between which the reaction occurs be identified in terms of one or more "nonoverlapping" order parameters. Here, we used two order parameters referred to as OP1 and OP2.…”

Section: B Transition Path Sampling Simulationsmentioning

confidence: 99%

α-helix to β-hairpin transition of human amylin monomer

Singh

Chiu

Reddy

et al. 2013

The Journal of Chemical Physics

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The human islet amylin polypeptide is produced along with insulin by pancreatic islets. Under some circumstances, amylin can aggregate to form amyloid fibrils, whose presence in pancreatic cells is a common pathological feature of Type II diabetes. A growing body of evidence indicates that small, early stage aggregates of amylin are cytotoxic. A better understanding of the early stages of the amylin aggregation process and, in particular, of the nucleation events leading to fibril growth could help identify therapeutic strategies. Recent studies have shown that, in dilute solution, human amylin can adopt an α-helical conformation, a β-hairpin conformation, or an unstructured coil conformation. While such states have comparable free energies, the β-hairpin state exhibits a large propensity towards aggregation. In this work, we present a detailed computational analysis of the folding pathways that arise between the various conformational states of human amylin in water. A free energy surface for amylin in explicit water is first constructed by resorting to advanced sampling techniques. Extensive transition path sampling simulations are then employed to identify the preferred folding mechanisms between distinct minima on that surface. Our results reveal that the α-helical conformer of amylin undergoes a transformation into the β-hairpin monomer through one of two mechanisms. In the first, misfolding begins through formation of specific contacts near the turn region, and proceeds via a zipping mechanism. In the second, misfolding occurs through an unstructured coil intermediate. The transition states for these processes are identified. Taken together, the findings presented in this work suggest that the inter-conversion of amylin between an α-helix and a β-hairpin is an activated process and could constitute the nucleation event for fibril growth.

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Section: B Transition Path Sampling Simulationsmentioning

confidence: 99%

α-helix to β-hairpin transition of human amylin monomer

Singh

Chiu

Reddy

et al. 2013

The Journal of Chemical Physics

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“…[19][20][21][22][23] Peters et al proposed the likelihood maximization method [19][20][21] to identify reaction coordinates based on one-time committor realizations from transition path sampling with aimless shooting. Antoniou et al identified components of the reaction coordinate first by analysing the variance of coordinates at the separatrix 22 -the isocommittor surface where the configurations have equal probability to relax to either of the stable basins, and then by kernel principal component analysis. 23 Methods that do not rely on evaluating committor are available as well.…”

Section: Introductionmentioning

confidence: 99%

A benchmark for reaction coordinates in the transition path ensemble

2016

The Journal of Chemical Physics

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The molecular mechanism of a reaction is embedded in its transition path ensemble, the complete collection of reactive trajectories. Utilizing the information in the transition path ensemble alone, we developed a novel metric, which we termed the emergent potential energy, for distinguishing reaction coordinates from the bath modes. The emergent potential energy can be understood as the average energy cost for making a displacement of a coordinate in the transition path ensemble. Where displacing a bath mode invokes essentially no cost, it costs significantly to move the reaction coordinate. Based on some general assumptions of the behaviors of reaction and bath coordinates in the transition path ensemble, we proved theoretically with statistical mechanics that the emergent potential energy could serve as a benchmark of reaction coordinates and demonstrated its effectiveness by applying it to a prototypical system of biomolecular dynamics. Using the emergent potential energy as guidance, we developed a committor-free and intuition-independent method for identifying reaction coordinates in complex systems. We expect this method to be applicable to a wide range of reaction processes in complex biomolecular systems. C 2016 AIP Publishing LLC. [http://dx

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“…The transition state ensemble or the stochastic separatrix is a hypersurface in the configuration space on which there is no change in the progression of the reaction. [82] To characterise the behaviour of coordinates on the stochastic separatrix, Antoniou and Schwartz [82] plotted the distributions of all the coordinates and examined the width of their distributions on the separatrix in model systems of a double-well potential coupled to a single and multiple oscillators. They found that the variation of the reaction coordinate is significantly smaller than that of the non-reactive coordinates.…”

Section: Committor-based Methodsmentioning

confidence: 99%

“…The method assumes a narrow transition state region and is, therefore, mainly applicable to systems with fast barrier crossing, but not so much to systems with diffusive barrier crossing. [82,83]…”

Section: Committor-based Methodsmentioning

confidence: 99%

“…For the first question, the GNN method [19] requires a database that contains accurate committor information over the entire range from 0 to 1, whereas the kernel PCA method [24,82] only requires information around the committor value of 0.5, which reduced the computational cost considerably but may also limit the applicability of the method to reactions with high barrier and ballistic dynamics. The likelihood maximisation method reduced the computational cost at the expense of the accuracy of committor information in the database, which could potentially limit the reliability of the reaction coordinates selected by the method.…”

Section: Conclusion and Prospectivesmentioning

confidence: 99%

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Recent developments in methods for identifying reaction coordinates

2014

Molecular Simulation

109

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In the study of rare events in complex systems with many degrees of freedom, a key element is to identify the reaction coordinates of a given process. Over recent years, a number of methods and protocols have been developed to extract the reaction coordinates based on limited information from molecular dynamics simulations. In this review, we provide a brief survey over a number of major methods developed in the past decade, some of which are discussed in greater detail, to provide an overview of the problems that are partially solved and challenges that still remain. A particular emphasis has been placed on methods for identifying reaction coordinates that are related to the committor.

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The stochastic separatrix and the reaction coordinate for complex systems

Cited by 48 publications

References 17 publications

α-helix to β-hairpin transition of human amylin monomer

α-helix to β-hairpin transition of human amylin monomer

A benchmark for reaction coordinates in the transition path ensemble

Recent developments in methods for identifying reaction coordinates

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