Entropy in bimolecular simulations: A comprehensive review of atomic fluctuations-based methods

Kassem, Summer M.; Ahmed, Marawan; El‐Sheikh, Said M.; Barakat, Khaled

doi:10.1016/j.jmgm.2015.09.010

Cited by 32 publications

(23 citation statements)

References 101 publications

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“…A number of methods have been developed to estimate S int or DS int (44,51). Below, we briefly sketch the QHA (40,41), BQH (42)(43)(44), and MIE (45) methods used in this article.…”

Section: Solute Entropy and Coordinate Systemmentioning

confidence: 99%

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Drake

Pettitt

2018

Biophysical Journal

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Conformational entropy is expected to contribute significantly to the thermodynamics of structural transitions in intrinsically disordered proteins or regions in response to protein/ligand binding, posttranslational modifications, and environmental changes. We calculated the backbone (dihedral) conformational entropy of oligoglycine (Gly), a protein backbone mimic and model intrinsically disordered region, as a function of chain length (N=3, 4, 5, 10, and 15) from simulations using three different approaches. The backbone conformational entropy scales linearly with chain length with a slope consistent with the entropy of folding of well-structured proteins. The entropic contributions of second-order dihedral correlations are predominantly through intraresidue ϕ-ψ pairs, suggesting that oligoglycine may be thermodynamically modeled as a system of independent glycine residues. We find the backbone conformational entropy to be largely independent of global structural parameters, like the end-to-end distance and radius of gyration. We introduce a framework referred to herein as "ensemble confinement" to estimate the loss (gain) of conformational free energy and its entropic component when individual residues are constrained to (released from) particular regions of the ϕ-ψ map. Quantitatively, we show that our protein backbone model resists ordering/folding with a significant, unfavorable ensemble confinement free energy because of the loss of a substantial portion of the absolute backbone entropy. Proteins can couple this free-energy reservoir to distal binding events as a regulatory mechanism to promote or suppress binding.

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“…A number of methods have been developed to estimate S int or DS int (44,51). Below, we briefly sketch the QHA (40,41), BQH (42)(43)(44), and MIE (45) methods used in this article.…”

Section: Solute Entropy and Coordinate Systemmentioning

confidence: 99%

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Drake

Pettitt

2018

Biophysical Journal

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“…The field of entropy calculations has progressed substantially over the past few decades. [2][3][4][5][6][7][8][9] Probability distributions may be extracted from equilibrium simulations as a function of one or a few dimensions for a wide range of coordinates or order parameters. Such approaches, however, usually only give part of the total entropy, neglect correlations and require an arbitrary choice of coordinates.…”

Section: Introductionmentioning

confidence: 99%

Entropy of flexible liquids from hierarchical force–torque covariance and coordination

et al. 2018

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New theory is presented to calculate the entropy of a liquid of flexible molecules from a molecular dynamics simulation. Entropy is expressed in two terms: a vibrational term, representing the average number of configurations and momentum states in an energy well, and a topographical term, representing the effective number of energy wells. The vibrational term is derived in a hierarchical manner from two force-torque covariance matrices, one at the molecular level and one at the united-atom level. The topographical term comprises conformations and orientations, which are derived from the dihedral distributions and 1 coordination numbers, respectively. The method is tested on fourteen liquids, ranging from argon to cyclohexane. For most molecules our results lie within the experimental range, and are slightly higher than those by the 2PT method, the only other method currently capable of directly calculating entropy for such systems. As well as providing an efficient and practical way to calculate entropy, the theory serves to give a comprehensive characterization and quantification of molecular structure.

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“…We then present a fast and accurate method of calculating entropy changes in proteins subject to pairwise interactions. Calculation of entropy of proteins is not new and has already been investigated by several authors [ 26 – 28 , 49 , 50 ] at different levels of approximation. Our method of entropy calculation is motivated by the recent finding that the distribution functions for the magnitude of fluctuations of residues in globular proteins can be derived from a universal function [ 51 ].…”

Section: Introductionmentioning

confidence: 99%

Entropy Transfer between Residue Pairs and Allostery in Proteins: Quantifying Allosteric Communication in Ubiquitin

Hacisuleyman

Erman

2017

PLoS Comput Biol

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It has recently been proposed by Gunasakaran et al. that allostery may be an intrinsic property of all proteins. Here, we develop a computational method that can determine and quantify allosteric activity in any given protein. Based on Schreiber's transfer entropy formulation, our approach leads to an information transfer landscape for the protein that shows the presence of entropy sinks and sources and explains how pairs of residues communicate with each other using entropy transfer. The model can identify the residues that drive the fluctuations of others. We apply the model to Ubiquitin, whose allosteric activity has not been emphasized until recently, and show that there are indeed systematic pathways of entropy and information transfer between residues that correlate well with the activities of the protein. We use 600 nanosecond molecular dynamics trajectories for Ubiquitin and its complex with human polymerase iota and evaluate entropy transfer between all pairs of residues of Ubiquitin and quantify the binding susceptibility changes upon complex formation. We explain the complex formation propensities of Ubiquitin in terms of entropy transfer. Important residues taking part in allosteric communication in Ubiquitin predicted by our approach are in agreement with results of NMR relaxation dispersion experiments. Finally, we show that time delayed correlation of fluctuations of two interacting residues possesses an intrinsic causality that tells which residue controls the interaction and which one is controlled. Our work shows that time delayed correlations, entropy transfer and causality are the required new concepts for explaining allosteric communication in proteins.

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Entropy in bimolecular simulations: A comprehensive review of atomic fluctuations-based methods

Cited by 32 publications

References 101 publications

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Entropy of flexible liquids from hierarchical force–torque covariance and coordination

Entropy Transfer between Residue Pairs and Allostery in Proteins: Quantifying Allosteric Communication in Ubiquitin

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