Advances in milestoning. II. Calculating time-correlation functions from milestoning using stochastic path integrals

Grazioli, Gianmarc; Andricioaei, Ioan

doi:10.1063/1.5037482

Cited by 10 publications

(11 citation statements)

References 20 publications

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“…So p 0 = (0, 1, 0, 0, 0). Recently Grazioli and Andricioaei have shown that time correlation functions can also be calculated by using the transition kernel and the first passage time distribution between milestones 75 . For that, a move from milestone i to j is proposed with probability p i→ j where…”

Section: A Milestoningmentioning

confidence: 99%

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Weighted Ensemble Milestoning (WEM): A Combined Approach for Rare Event Simulations

Ray,

Andricioaei

2019

Preprint

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Direct simulation of rare events using atomistic molecular dynamics is a significant challenge in computational biophysics. Well established enhanced sampling techniques like umbrella sampling, metadynamics and adaptive-biasing forces are able to calculate the free energy landscapes for rare events involving barrier crossing. But developing methods for obtaining kinetics of long timescale processes from molecular dynamics simulation is still an emerging area of science. Milestoning and weighted ensemble (WE) are two different path sampling based strategies which have shown promises for computing timescales of complex biomolecular processes. Nevertheless, both require a significant investment of computational resources. We have combined WE and milestoning, in a novel way, to calculate experimental observables in orders of magnitude less CPU and wall-clock time. Our method uses WE simulation to converge the transition probability and first passage times between milestones, followed by the utilization of the theoretical framework of milestoning to extract thermodynamic and kinetic properties of the entire process. We tested our method for a simple one dimensional double well potential, an eleven dimensional potential energy surface with energy barrier, and on a molecular system of alanine dipeptide. We were able to recover the free energy profiles, time correlation functions, and mean first passage times for barrier crossing events at a significantly small computational cost. Our method promises to extend the applicability of molecular dynamics simulation to the slow dynamics of large systems which are beyond the scope of present day computer power.

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Section: A Milestoningmentioning

confidence: 99%

“…Moreover, Grazioli and Andricioaei have developed an enhanced milestoning protocol by applying biasing force to obtain quick convergence for milestone to milestone trajectories 19 . They also have come up with a strategy to calculate time correlation functions from milestoning simulation using stochastic path integral 75 .…”

Section: Introductionmentioning

confidence: 99%

Weighted Ensemble Milestoning (WEM): A Combined Approach for Rare Event Simulations

Ray,

Andricioaei

2019

Preprint

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“…Developed independently about 16 years ago, the milestoning technique of Elber and coworkers 39 is another powerful method that can be used to compute timescales, as well as free energy profiles along suitably chosen directions in con-figuration space. In a recent work, the mathematical details of milestoning theory have been clarified 40 , allowing the calculation of many thermodynamic and kinetic properties including mean first passage times 41,42 , free energy profiles [43][44][45] , committor probabilities 46 , and time-correlation functions 47 .…”

Section: Introductionmentioning

confidence: 99%

Kinetics and Free Energy of Ligand Dissociation Using Weighted Ensemble Milestoning

Ray,

Gokey,

Mobley

et al. 2020

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We consider the recently developed weighted ensemble milestoning (WEM) scheme [J. Chem. Phys. 152, 234114 (2020)], and test its capability of simulating ligand-receptor dissociation dynamics. We performed WEM simulations on the following host-guest systems: Na+/Cl-ion pair and 4-hydroxy-2-butanone (BUT) ligand with FK506 binding protein (FKBP). As proof or principle, we show that the WEM formalism reproduces the Na+/Cl-ion pair dissociation timescale and the free energy profile obtained from long conventional MD simulation. To increase accuracy of WEM calculations applied to kinetics and thermodynamics in protein-ligand binding, we introduced a modified WEM scheme called weighted ensemble milestoning with restraint release (WEM-RR), which can increase the number of starting points per milestone without adding additional computational cost. WEM-RR calculations obtained a ligand residence time and binding free energy in agreement with experimental and previous computational results. Moreover, using the milestoning framework, the binding time and rate constants, dissociation constant and the committor probabilities could also be calculated at a low computational cost. We also present an analytical approach for estimating the association rate constant (k on ) when binding is primarily diffusion driven. We show that the WEM method can efficiently calculate multiple experimental observables describing ligand-receptor binding/unbinding and is a promising candidate for computer-aided inhibitor design.

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“…In practice, previous milestoning calculations have been limited to calculating the constant flux values representative of the system at equilibrium, which can be thought of as the long time flux values lim t→∞ P s (t). A method for calculating the time-dependent flux through a given milestone P s (t) can be found in the companion paper to this article, also in this publication [13]. The aim of the technique we present in this paper is to increase the computational speed of the milestoning method via the addition of an artificial constant force (F wind ) along the vector pointing from the initial state to the final state for each pair of milestones in the simulation, causing the system to arrive at the destination configuration in far fewer time steps than if it were left to Brownian dynam-ics alone.…”

Section: Introductionmentioning

confidence: 99%

Advances in milestoning. I. Enhanced sampling via wind-assisted reweighted milestoning (WARM)

Grazioli

Andricioaei

2018

The Journal of Chemical Physics

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The milestoning algorithm of Elber and co-workers creates a framework for computing the time scale of processes that are too long and too complex to be studied using simply brute force simulations. The fundamental objects involved in the milestoning algorithm are the first passage time distributions () between adjacent conformational milestones and. The method proposed herein aims to further enhance milestoning (or other interface based sampling methods) by employing an artificially applied force, akin to a wind that blows the trajectories from their initial to their final states, and by subsequently applying corrective weights to the trajectories to yield the true first passage time distributions () in a fraction of the computation time required for unassisted calculations. The re-weighting method is rooted in the formalism of stochastic path integrals. The theoretical basis for the technique and numerical examples are presented.

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Advances in milestoning. II. Calculating time-correlation functions from milestoning using stochastic path integrals

Cited by 10 publications

References 20 publications

Weighted Ensemble Milestoning (WEM): A Combined Approach for Rare Event Simulations

Weighted Ensemble Milestoning (WEM): A Combined Approach for Rare Event Simulations

Kinetics and Free Energy of Ligand Dissociation Using Weighted Ensemble Milestoning

Advances in milestoning. I. Enhanced sampling via wind-assisted reweighted milestoning (WARM)

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