The Adaptive Path Collective Variable: A Versatile Biasing Approach to Compute the Average Transition Path and Free Energy of Molecular Transitions

2019 ◽  
pp. 255-290
Author(s):  
Alberto Pérez de Alba Ortíz ◽  
Jocelyne Vreede ◽  
Bernd Ensing
Keyword(s):  
Free Energy ◽  
Collective Variable ◽  
Transition Path ◽  
Average Transition

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

2018 ◽  
Vol 122 (49) ◽  
pp. 11126-11136 ◽  
Author(s):  
William M. Jacobs ◽  
Eugene I. Shakhnovich
Keyword(s):  
Free Energy ◽  
Protein Folding ◽  
Energy Landscape ◽  
Free Energy Landscape ◽  
Transition Path

scholarly journals Thermodynamic and Kinetic Characterization of Protein Conformational Dynamics within a Riemannian Framework

2021 ◽  
Author(s):  
Curtis Goolsby ◽  
Ashkan Fakharzadeh ◽  
Mahmoud Moradi
Keyword(s):  
Free Energy ◽  
Transition Rate ◽  
Conformational Dynamics ◽  
Diffusion Constant ◽  
Minimum Free Energy ◽  
Umbrella Sampling ◽  
Potential Of Mean Force ◽  
Collective Variable ◽  
Bayesian Estimator ◽  
Riemannian Framework

AbstractWe have formulated a Riemannian framework for describing the geometry of collective variable spaces of biomolecules within the context of molecular dynamics (MD) simulations. The formalism provides a theoretical framework to develop enhanced sampling techniques, path-finding algorithms, and transition rate estimators consistent with a Riemannian treatment of the collective variable space, where the quantities of interest such as the potential of mean force (PMF) and minimum free energy path (MFEP) remain invariant under coordinate transformation. Specific algorithms within this framework are discussed such as the Riemannian umbrella sampling, the Riemannian string method, and a Riemannian-Bayesian estimator of free energy and diffusion constant, which can be used to estimate the transition rate along an MFEP.

scholarly journals Adaptive free energy sampling in multidimensional collective variable space using boxed molecular dynamics

2016 ◽  
Vol 195 ◽  
pp. 395-419 ◽  
Author(s):  
Mike O'Connor ◽  
Emanuele Paci ◽  
Simon McIntosh-Smith ◽  
David R. Glowacki
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Rare Event ◽  
Potential Of Mean Force ◽  
Good Evidence ◽  
Collective Variable ◽  
Rigid Body Dynamics ◽  
Free Energy Surface ◽  
Molecular Configuration ◽  
Free Energy Sampling

The past decade has seen the development of a new class of rare event methods in which molecular configuration space is divided into a set of boundaries/interfaces, and then short trajectories are run between boundaries. For all these methods, an important concern is how to generate boundaries. In this paper, we outline an algorithm for adaptively generating boundaries along a free energy surface in multi-dimensional collective variable (CV) space, building on the boxed molecular dynamics (BXD) rare event algorithm. BXD is a simple technique for accelerating the simulation of rare events and free energy sampling which has proven useful for calculating kinetics and free energy profiles in reactive and non-reactive molecular dynamics (MD) simulations across a range of systems, in both NVT and NVE ensembles. Two key developments outlined in this paper make it possible to automate BXD, and to adaptively map free energy and kinetics in complex systems. First, we have generalized BXD to multidimensional CV space. Using strategies from rigid-body dynamics, we have derived a simple and general velocity-reflection procedure that conserves energy for arbitrary collective variable definitions in multiple dimensions, and show that it is straightforward to apply BXD to sampling in multidimensional CV space so long as the Cartesian gradients ∇CV are available. Second, we have modified BXD to undertake on-the-fly statistical analysis during a trajectory, harnessing the information content latent in the dynamics to automatically determine boundary locations. Such automation not only makes BXD considerably easier to use; it also guarantees optimal boundaries, speeding up convergence. We have tested the multidimensional adaptive BXD procedure by calculating the potential of mean force for a chemical reaction recently investigated using both experimental and computational approaches – i.e., F + CD3CN → DF + D2CN in both the gas phase and a strongly coupled explicit CD3CN solvent. The results obtained using multidimensional adaptive BXD agree well with previously published experimental and computational results, providing good evidence for its reliability.

High-resolution free energy landscape analysis of protein folding

2015 ◽  
Vol 43 (2) ◽  
pp. 157-161 ◽  
Author(s):  
Polina V. Banushkina ◽  
Sergei V. Krivov
Keyword(s):  
Free Energy ◽  
Protein Folding ◽  
High Resolution ◽  
Energy Landscape ◽  
Quantitative Description ◽  
Free Energy Landscape ◽  
Transition Path ◽  
Exponential Factor ◽  
Basic Properties ◽  
Folding Dynamics

The free energy landscape can provide a quantitative description of folding dynamics, if determined as a function of an optimally chosen reaction coordinate. The profile together with the optimal coordinate allows one to directly determine such basic properties of folding dynamics as the configurations of the minima and transition states, the heights of the barriers, the value of the pre-exponential factor and its relation to the transition path times. In the present study, we review the framework, in particular, the approach to determine such an optimal coordinate, and its application to the analysis of simulated protein folding dynamics.

scholarly journals Measurement of Average Transition-Path Time for Protein Folding in Single Molecule FRET Experiments

2012 ◽  
Vol 102 (3) ◽  
pp. 217a-218a
Author(s):  
Hoi Sung Chung ◽  
Irina V. Gopich ◽  
Kevin McHale ◽  
John M. Louis ◽  
William A. Eaton
Keyword(s):  
Protein Folding ◽  
Single Molecule ◽  
Transition Path ◽  
Single Molecule Fret ◽  
Average Transition

scholarly journals Thermodynamic and Kinetic Characterization of Protein Conformational Dynamics within a Riemannian Diffusion Formalism

2019 ◽  
Author(s):  
Curtis Goolsby ◽  
Ashkan Fakharzadeh ◽  
Mahmoud Moradi
Keyword(s):  
Free Energy ◽  
Transition Rate ◽  
Conformational Dynamics ◽  
Diffusion Constant ◽  
Minimum Free Energy ◽  
Umbrella Sampling ◽  
Collective Variable ◽  
Bayesian Estimator ◽  
Variable Space ◽  
Dynamics Simulations

AbstractWe have formulated a Riemannian framework for describing the geometry of collective variable spaces of biomolecules within the context of collective variable based molecular dynamics simulations. The formalism provides a theoretical framework to develop enhanced sampling techniques, path-finding algorithms, and transition rate estimators consistent with a Riemannian treatment of the collective variable space, where the quantities of interest such as the potential of the mean force, minimum free energy path, the diffusion constant, and the transition rate remain invariant under coordinate transformation due to the Riemannian treatment of the collective variable space. Specific algorithms within this framework are discussed such as the Riemannian umbrella sampling, the Riemannian string method, and a Riemannian-Bayesian estimator of free energy and diffusion constant, which can be used to estimate the transition rate along a minimum free energy path.

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