Extracting the diffusion tensor from molecular dynamics simulation with Milestoning

Mugnai, Mauro L.; Elber, Ron

doi:10.1063/1.4904882

Cited by 14 publications

(21 citation statements)

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“…For example, modeling permeation using the Smoluchowski Equation (SE) in a space of more than one curvilinear variable requires a non-trivial coordinate transformation from the Cartesian to the curvilinear space and an estimate of a non-diagonal diffusion tensor. 31 This is the case for the variables d 1 and d 2 . One should also keep in mind that the use of overdamped dynamics is an approximation.…”

Section: Methodsmentioning

confidence: 94%

Ion Permeation through a Phospholipid Membrane: Transition State, Path Splitting, and Calculation of Permeability

Fathizadeh

Elber

2018

J. Chem. Theory Comput.

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We investigate the thermodynamics and kinetics of the permeation of a potassium ion through a phospholipid membrane. We illustrate that the conventional reaction coordinate (the position of the ion along the normal to the membrane plane) is insufficient to capture essential elements of the process. It is necessary to add coarse variables that measure membrane distortion. New coarse variables are suggested and a two-dimensional coarse-space is proposed to describe the permeation. We illustrate path splitting and two transition states of comparable barrier heights. The alternative pathways differ by the extent of water solvation of the ion-phosphate pairs. The permeation process cannot be described by a local one-dimensional reaction coordinate and a network formulation is more appropriate. We use Milestoning with Voronoi tessellation in two dimensions to quantify the equilibrium and rate of the permeation of the positively charged ion. The permeation coefficient is computed and compared favorably to experiment.

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Section: Methodsmentioning

confidence: 94%

Ion Permeation through a Phospholipid Membrane: Transition State, Path Splitting, and Calculation of Permeability

Fathizadeh

Elber

2018

J. Chem. Theory Comput.

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“…25,26 This correction can be achieved by introducing a position-dependent diffusion coefficient, 27 since the gradient of the free-energy landscape itself is not sufficient to predict the relative rates of molecular motions on the one-dimensional reaction coordinate. The key limitation of this approach is that the transition-path trajectories that we wish to predict are required as input, either to determine the coordinate-dependence of the diffusion coefficient 26,28–30 or to find a projection for which the apparent diffusive behavior is coordinate-independent. 31,32 It is also unclear whether a single optimized one-dimensional coordinate can always be found for large proteins, which may have more complicated or parallel folding pathways.…”

Section: Introductionmentioning

confidence: 99%

Accurate Protein-Folding Transition-Path Statistics from a Simple Free-Energy Landscape

Jacobs

Shakhnovich

2018

J. Phys. Chem. B

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A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths-the rare trajectories that transit between the folded and unfolded ensembles-using only thermodynamic information, such as a low-dimensional equilibrium free-energy landscape. However, commonly used one-dimensional landscapes typically fall short of this aim, because an empirical coordinate-dependent diffusion coefficient has to be fit to transition-path trajectory data in order to reproduce the transition-path dynamics. We show that an alternative, first-principles free-energy landscape predicts transition-path statistics that agree well with simulations and single-molecule experiments without requiring dynamical data as an input. This "topological configuration" model assumes that distinct, native-like substructures assemble on a time scale that is slower than native-contact formation but faster than the folding of the entire protein. Using only equilibrium simulation data to determine the free energies of these coarse-grained intermediate states, we predict a broad distribution of transition-path transit times that agrees well with the transition-path durations observed in simulations. We further show that both the distribution of finite-time displacements on a one-dimensional order parameter and the ensemble of transition-path trajectories generated by the model are consistent with the simulated transition paths. These results indicate that a landscape based on transient folding intermediates, which are often hidden by one-dimensional projections, can form the basis of a predictive model of protein-folding transition-path dynamics.

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“…Milestoning is a technique that is similar to the theory used in MSMs and can serve as an alternative approach to investigating biomolecular events, such as conformational sampling (West et al, 2007 ; Mugnai and Elber, 2015 ), diffusion (Mugnai and Elber, 2015 ), and membrane permeation (Cardenas et al, 2012 ), among others. Milestoning retrieves the kinetics as well as the thermodynamics of chemical processes (Vanden-Eijnden et al, 2008 ; Májek and Elber, 2010 ; Kirmizialtin and Elber, 2011 ), and can make use of extensive parallelization.…”

Section: Investigating Intermolecular Interactionsmentioning

confidence: 99%

Bridging scales through multiscale modeling: a case study on protein kinase A

et al. 2015

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The goal of multiscale modeling in biology is to use structurally based physico-chemical models to integrate across temporal and spatial scales of biology and thereby improve mechanistic understanding of, for example, how a single mutation can alter organism-scale phenotypes. This approach may also inform therapeutic strategies or identify candidate drug targets that might otherwise have been overlooked. However, in many cases, it remains unclear how best to synthesize information obtained from various scales and analysis approaches, such as atomistic molecular models, Markov state models (MSM), subcellular network models, and whole cell models. In this paper, we use protein kinase A (PKA) activation as a case study to explore how computational methods that model different physical scales can complement each other and integrate into an improved multiscale representation of the biological mechanisms. Using measured crystal structures, we show how molecular dynamics (MD) simulations coupled with atomic-scale MSMs can provide conformations for Brownian dynamics (BD) simulations to feed transitional states and kinetic parameters into protein-scale MSMs. We discuss how milestoning can give reaction probabilities and forward-rate constants of cAMP association events by seamlessly integrating MD and BD simulation scales. These rate constants coupled with MSMs provide a robust representation of the free energy landscape, enabling access to kinetic, and thermodynamic parameters unavailable from current experimental data. These approaches have helped to illuminate the cooperative nature of PKA activation in response to distinct cAMP binding events. Collectively, this approach exemplifies a general strategy for multiscale model development that is applicable to a wide range of biological problems.

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Extracting the diffusion tensor from molecular dynamics simulation with Milestoning

Cited by 14 publications

References 50 publications

Ion Permeation through a Phospholipid Membrane: Transition State, Path Splitting, and Calculation of Permeability

Ion Permeation through a Phospholipid Membrane: Transition State, Path Splitting, and Calculation of Permeability

Accurate Protein-Folding Transition-Path Statistics from a Simple Free-Energy Landscape

Bridging scales through multiscale modeling: a case study on protein kinase A

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