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

Goolsby, Curtis; Fakharzadeh, Ashkan; Moradi, Mahmoud

doi:10.1101/707711

Cited by 3 publications

(4 citation statements)

References 67 publications

(84 reference statements)

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“…There have also been attempts to include the orientational degrees of freedom ,, and to consider the transient subdiffusive mode. , Apart from mass transport, there have been attempts to describe, for example, the kinetics of proteins − and biocomplexes . It has also been suggested that the position-dependent diffusion constant can be used to eliminate the ambiguity related to the choice of reaction coordinates in interpreting the PMF. , …”

Section: Introductionmentioning

confidence: 99%

Position-Dependent Diffusion Constant of Molecules in Heterogeneous Systems as Evaluated by the Local Mean Squared Displacement

Nagai

Tsurumaki

Urano

et al. 2020

J. Chem. Theory Comput.

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The authors propose a novel method to evaluate the position-dependent diffusion constant by analyzing unperturbed segments of a trajectory determined by the additional flat-bottom potential. The accuracy of this novel method is first established by studying homogeneous systems, where the reference value can be obtained by the Einstein relation. The applicability of this new method to heterogeneous systems is then demonstrated by studying a hydrophobic solute near a hydrophobic wall. The proposed method is also comprehensively compared with popular conventional methods, whereby the significance of the present method is illustrated. The novel method is powerful and useful for studying kinetics in heterogeneous systems based on molecular dynamics calculations.

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Section: Introductionmentioning

confidence: 99%

Position-Dependent Diffusion Constant of Molecules in Heterogeneous Systems as Evaluated by the Local Mean Squared Displacement

Nagai

Tsurumaki

Urano

et al. 2020

J. Chem. Theory Comput.

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“…Other possibilities considered include, for example, a “tilt” of MerF into the membrane plane, which may expose MerF's Cys21/22 to the periplasm. The true reaction coordinate, which typically is a concerted motion of the protein(s), likely involves all of these simpler descriptors . Thus, our choice of variables to bias may limit the physical relevance of the obtained free energies.…”

Section: Discussionmentioning

confidence: 99%

A Minimal Membrane Metal Transport System: Dynamics and Energetics of mer Proteins

et al. 2019

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The mer operon in bacteria encodes a set of proteins and enzymes that impart resistance to environmental mercury toxicity by importing Hg 2+ and reducing it to volatile Hg(0). Because the reduction occurs in the cytoplasm, mercuric ions must first be transported across the cytoplasmic membrane by one of a few known transporters. MerF is the smallest of these, containing only two transmembrane helices and two pairs of vicinal cysteines that coordinate mercuric ions. In this work, we use molecular dynamics simulations to characterize the dynamics of MerF in its apo and Hg 2+ -bound states. We find that the apo state positions one of the cysteine pairs closer to the periplasmic side of the membrane, while in the bound state the same pair approaches the cytoplasmic side. This finding is consistent with the functional requirement of accepting Hg 2+ from the periplasmic space, sequestering it on acceptance, and transferring it to the cytoplasm. Conformational changes in the TM helices facilitate the functional interaction of the two cysteine pairs. Free-energy calculations provide a barrier of 16 kcal/mol for the association of the periplasmic Hg 2+ -bound protein MerP with MerF and 7 kcal/mol for the subsequent association of MerF's two cysteine pairs. Despite the significant conformational changes required to move the binding site across the membrane, coarse-grained simulations of multiple copies of MerF support the expectation that it functions as a monomer. Our results demonstrate how conformational changes and binding thermodynamics could lead to such a small membrane protein acting as an ion transporter. Published 2019.

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“…This second quantity has also been termed the Riemannian effective potential. 54,55 Several papers have laid out the very subtle differences in these two definitions, 17,54 with an examination of the coarea formula being perhaps the clearest way to see the relationship. 17 The derivatives of both quantities can still be related to the mean force along the collective variable, with proper corrections for changes of variables which are beyond the scope of this summary.…”

Section: Theory: Fes Estimation From Biasedmentioning

confidence: 99%

“…The “geometric FES”, in contrast, is defined as where Σ(ξ⃗) is the surface of constant ξ⃗, and dΩ is the phase space volume of this surface, and thus is the logarithm of probability density of the surface Σ(ξ⃗). This second quantity has also been termed the Riemannian effective potential. , Several papers have laid out the very subtle differences in these two definitions, , with an examination of the coarea formula being perhaps the clearest way to see the relationship . The derivatives of both quantities can still be related to the mean force along the collective variable, with proper corrections for changes of variables which are beyond the scope of this summary. , …”

Section: Theory: Fes Estimation From Biased Sampled Datamentioning

confidence: 99%

Statistically Optimal Continuous Free Energy Surfaces from Biased Simulations and Multistate Reweighting

Shirts

Ferguson

2020

J. Chem. Theory Comput.

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Free energies as a function of a selected set of collective variables are commonly computed in molecular simulation and of significant value in understanding and engineering molecular behavior. These free energy surfaces are most commonly estimated using variants of histogramming techniques, but such approaches obscure two important facets of these functions. First, the empirical observations along the collective variable are defined by an ensemble of discrete observations, and the coarsening of these observations into a histogram bin incurs unnecessary loss of information. Second, the free energy surface is itself almost always a continuous function, and its representation by a histogram introduces inherent approximations due to the discretization. In this study, we relate the observed discrete observations from biased simulations to the inferred underlying continuous probability distribution over the collective variables and derive histogram-free techniques for estimating this free energy surface. We reformulate free energy surface estimation as minimization of a Kullback–Leibler divergence between a continuous trial function and the discrete empirical distribution and show that this is equivalent to likelihood maximization of a trial function given a set of sampled data. We then present a fully Bayesian treatment of this formalism, which enables the incorporation of powerful Bayesian tools such as the inclusion of regularizing priors, uncertainty quantification, and model selection techniques. We demonstrate this new formalism in the analysis of umbrella sampling simulations for the χ torsion of a valine side chain in the L99A mutant of T4 lysozyme with benzene bound in the cavity.

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

Cited by 3 publications

References 67 publications

Position-Dependent Diffusion Constant of Molecules in Heterogeneous Systems as Evaluated by the Local Mean Squared Displacement

Position-Dependent Diffusion Constant of Molecules in Heterogeneous Systems as Evaluated by the Local Mean Squared Displacement

A Minimal Membrane Metal Transport System: Dynamics and Energetics of mer Proteins

Statistically Optimal Continuous Free Energy Surfaces from Biased Simulations and Multistate Reweighting

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