Nonparametric variational optimization of reaction coordinates

Banushkina, Polina; Krivov, Sergei V.

doi:10.1063/1.4935180

Cited by 27 publications

(60 citation statements)

References 62 publications

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“…Indeed the algorithm proposed in the present work is similar to these previous studies. It is also similar in spirit to references [25,26]. However, there are conceptual and algorithmic differences between these investigations, which are discussed later in the article.…”

Section: Methodssupporting

confidence: 55%

“…However, it is limited to a small number of degrees of freedom since the complexity of the solution increases exponentially with the dimensionality of the system. Studies of committors [26,28–30] in systems with high dimension use estimates based on trajectory sampling. Trajectory-based formulation makes it possible to use arbitrary dynamics and not limit the choice to overdamped Langevin.…”

Section: Methodsmentioning

confidence: 99%

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Calculating Iso-Committor Surfaces as Optimal Reaction Coordinates with Milestoning

Elber

Bello-Rivas

et al. 2017

Entropy

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Reaction coordinates are vital tools for qualitative and quantitative analysis of molecular processes. They provide a simple picture of reaction progress and essential input for calculations of free energies and rates. Iso-committor surfaces are considered the optimal reaction coordinate. We present an algorithm to compute efficiently a sequence of isocommittor surfaces. These surfaces are considered an optimal reaction coordinate. The algorithm analyzes Milestoning results to determine the committor function. It requires only the transition probabilities between the milestones, and not transition times. We discuss the following numerical examples: (i) a transition in the Mueller potential; (ii) a conformational change of a solvated peptide; and (iii) cholesterol aggregation in membranes.

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Section: Methodssupporting

confidence: 55%

Section: Methodsmentioning

confidence: 99%

Calculating Iso-Committor Surfaces as Optimal Reaction Coordinates with Milestoning

Elber

Bello-Rivas

et al. 2017

Entropy

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“…In the protein folding example, we see that deflation can obscure a long-timescale process from a kinetic model in order to facilitate further analysis that is desired to be independent of that process. In MD simulations, the dominant processes may not be the same as the processes of interest due to low sampling or force field artifacts 8,9 . Thus, deflation presents a systematic way of removing the effects of these undesired modes on model building.…”

Section: Discussionmentioning

confidence: 99%

Deflation reveals dynamical structure in nondominant reaction coordinates

Husic

Noé

2019

The Journal of Chemical Physics

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The output of molecular dynamics simulations is high-dimensional, and the degrees of freedom among the atoms are related in intricate ways. Therefore, a variety of analysis frameworks have been introduced in order to distill complex motions into lower-dimensional representations that model the system dynamics. These dynamical models have been developed to optimally approximate the system's global kinetics. However, the separate aims of optimizing global kinetics and modeling a process of interest diverge when the process of interest is not the slowest process in the system. Here, we introduce deflation into state-of-the-art methods in molecular kinetics in order to preserve the use of variational optimization tools when the slowest dynamical mode is not the same as the one we seek to model and understand. First, we showcase deflation for a simple toy system and introduce the deflated variational approach to Markov processes (dVAMP). Using dVAMP, we show that nondominant reaction coordinates produced using deflation are more informative than their counterparts generated without deflation. Then, we examine a protein folding system in which the slowest dynamical mode is not folding. Following a dVAMP analysis, we show that deflation can be used to obscure this undesired slow process from a kinetic model, in this case a VAMPnet. The incorporation of deflation into current methods opens the door for enhanced sampling strategies and more flexible, targeted model building.arXiv:1907.04101v1 [q-bio.BM]

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“…Integrating Eq. over r one obtains

true {false\int}_{0}^{1} Z_{C, 1} ((),, r, Δ t) d r = 1 false/ 2 true \underset{i}{false\sum} {[r (Δ t + i Δ t) - r (i Δ t)]}^{2} = 1 false/ 2 (〈〉, Δ r^{2} ((), Δ t)) ((), N Δ t_{0}) false/ Δ t

(〈〉, Δ r^{2} ((), Δ t)) = 2 Δ t false/ ((), N Δ t_{0}) (〈〉, Z_{C, 1} ((), Δ t))

which means that if 〈 Z C ,1 (Δ t )〉 is constant (increases with Δ t , decreases with Δ t ) the equilibrium mean squared displacement grows linearly (faster than linear, slower than linear) with time . For the committor one specifically obtains 〈Δ q 2 (Δ t )〉 = 2 ΔtJ AB .…”

Section: The Committor As An Optimal Rcmentioning

confidence: 99%

“…Then, one numerically optimizes the weights w ij or the cutoff distances

r_{i j}^{0}

for contacts by optimizing a particular functional, so that in the end, the putative RC accurately approximates the committor. The following optimization functionals have been suggested: the probability of being on a transition path, the likelihood functional, the cut profiles, and the total squared displacement (TSD) …”

Section: Validation and Determination Of Optimal Rcsmentioning

confidence: 99%

Optimal reaction coordinates

Banushkina

Krivov

2016

WIREs Comput Mol Sci

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The dynamic behavior of complex systems with many degrees of freedom is often analyzed by projection onto one or a few reaction coordinates. The dynamics is then described in a simple and intuitive way as diffusion on the associated free energy profile. In order to use such a picture for a quantitative description of the dynamics one needs to select the coordinate in an optimal way so as to minimize non-Markovian effects due to the projection. For equilibrium dynamics between two boundary states (e.g., a reaction) the optimal coordinate is known as the committor or the pfold coordinate in protein folding studies. While the dynamics projected on the committor is not Markovian, many important quantities of the original multidimensional dynamics on an arbitrarily complex landscape can be computed exactly. Here we summarize the derivation of this result, discuss different approaches to determine and validate the committor coordinate and present three illustrative applications: protein folding, the game of chess, and patient recovery dynamics after kidney transplant.

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Nonparametric variational optimization of reaction coordinates

Cited by 27 publications

References 62 publications

Calculating Iso-Committor Surfaces as Optimal Reaction Coordinates with Milestoning

Calculating Iso-Committor Surfaces as Optimal Reaction Coordinates with Milestoning

Deflation reveals dynamical structure in nondominant reaction coordinates

Optimal reaction coordinates

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