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Toward a General Yet Effective Computational Approach for Diffusive Problems: Variable Diffusion Tensor and DVR Solution of the Smoluchowski Equation along a General One-Dimensional Coordinate.

ABSTRACT: A generalization to arbitrary large amplitude motions of a recent approach to the evaluation of diffusion tensors [ J. Comput. Chem. , 2009 , 30 , 2 - 13 ] is presented and implemented in a widely available package for electronic structure computations. A fully black-box tool is obtained, which, starting from the generation of geometric structures along different kinds of paths, proceeds toward the evaluation of an effective diffusion tensor and to the solution of one-dimensional Smoluchowski equations by a robust numerical approach rooted in the discrete variable representation (DVR). Application to a number of case studies shows that the results issuing from our approach are identical to those delivered by previous software (in particular DiTe) for rigid scans along a dihedral angle, but can be improved by employing relaxed scans (i.e., constrained geometry optimizations) or even more general large amplitude paths. The theoretical and numerical background is robust and general enough to allow quite straightforward extensions in several directions (e.g., inclusion of reactive paths, solution of Fokker-Planck or stochastic Liouville equations, multidimensional problems, free-energy rather than electronic-energy driven processes).

SUBMITTER: Piserchia A

PROVIDER: S-EPMC5603279 | biostudies-literature | 2016 Aug

REPOSITORIES: biostudies-literature

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Toward a General Yet Effective Computational Approach for Diffusive Problems: Variable Diffusion Tensor and DVR Solution of the Smoluchowski Equation along a General One-Dimensional Coordinate.

Piserchia Andrea A Barone Vincenzo V

Journal of chemical theory and computation 20160725 8

A generalization to arbitrary large amplitude motions of a recent approach to the evaluation of diffusion tensors [ J. Comput. Chem. , 2009 , 30 , 2 - 13 ] is presented and implemented in a widely available package for electronic structure computations. A fully black-box tool is obtained, which, starting from the generation of geometric structures along different kinds of paths, proceeds toward the evaluation of an effective diffusion tensor and to the solution of one-dimensional Smoluchowski eq ...[more]

PMID: 27403666

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Project description:The macroscopic diffusion constant for a charged diffuser is in part dependent on (1) the volume excluded by solute "obstacles" and (2) long-range interactions between those obstacles and the diffuser. Increasing excluded volume reduces transport of the diffuser, while long-range interactions can either increase or decrease diffusivity, depending on the nature of the potential. We previously demonstrated [P. M. Kekenes-Huskey et al., Biophys. J. 105, 2130 (2013)] using homogenization theory that the configuration of molecular-scale obstacles can both hinder diffusion and induce diffusional anisotropy for small ions. As the density of molecular obstacles increases, van der Waals (vdW) and electrostatic interactions between obstacle and a diffuser become significant and can strongly influence the latter's diffusivity, which was neglected in our original model. Here, we extend this methodology to include a fixed (time-independent) potential of mean force, through homogenization of the Smoluchowski equation. We consider the diffusion of ions in crowded, hydrophilic environments at physiological ionic strengths and find that electrostatic and vdW interactions can enhance or depress effective diffusion rates for attractive or repulsive forces, respectively. Additionally, we show that the observed diffusion rate may be reduced independent of non-specific electrostatic and vdW interactions by treating obstacles that exhibit specific binding interactions as "buffers" that absorb free diffusers. Finally, we demonstrate that effective diffusion rates are sensitive to distribution of surface charge on a globular protein, Troponin C, suggesting that the use of molecular structures with atomistic-scale resolution can account for electrostatic influences on substrate transport. This approach offers new insight into the influence of molecular-scale, long-range interactions on transport of charged species, particularly for diffusion-influenced signaling events occurring in crowded cellular environments.

Project description:BackgroundDynamic diffusion magnetic resonance imaging (ddMRI) metrics can assess transient microstructural alterations in tissue diffusivity but requires additional scan time hindering its clinical application.PurposeTo determine whether a diffusion gradient table can simultaneously acquire data to estimate dynamic and diffusion tensor imaging (DTI) metrics.Study typeProspective.SubjectsSeven healthy subjects, 39 epilepsy patients (15 female, 31 male, age ± 15).Field strength/sequenceTwo-dimensional diffusion MRI (b = 1000 s/mm2 ) at a field strength of 3 T. Sessions in healthy subjects-standard ddMRI (30 directions), standard DTI (15 and 30 directions), and nested cubes scans (15 and 30 directions). Sessions in epilepsy patients-two 30 direction (standard ddMRI, 10 nested cubes) or two 15 direction scans (standard DTI, 5 nested cubes).AssessmentFifteen direction DTI was repeated twice for within-session test-retest measurements in healthy subjects. Bland-Altman analysis computed bias and limits of agreement for DTI metrics using test-retest scans and standard 15 direction vs. 5 nested cubes scans. Intraclass correlation (ICC) analysis compared tensor metrics between 15 direction DTI scans (standard vs. 5 nested cubes) and the coefficients of variation (CoV) of trace and apparent diffusion coefficient (ADC) between 30 direction ddMRI scans (standard vs. 10 nested cubes).Statistical testsBland-Altman and ICC analysis using a P-value of 0.05 for statistical significance.ResultsCorrelations of mean diffusivity (MD), axial diffusivity (AD), and radial diffusivity (RD) were strong and significant in gray (ICC > 0.95) and white matter (ICC > 0.95) between standard vs. nested cubes DTI acquisitions. Correlation of white matter fractional anisotropy was also strong (ICC > 0.95) and significant. ICCs of the CoV of dynamic ADC measured using repeated cubes and nested cubes acquisitions were modest (ICC >0.60), but significant in gray matter.ConclusionA nested cubes diffusion gradient table produces tensor-based and dynamic diffusion measurements in a single acquisition.Level of evidence2 TECHNICAL EFFICACY: Stage 1.

Dataset Information

Toward a General Yet Effective Computational Approach for Diffusive Problems: Variable Diffusion Tensor and DVR Solution of the Smoluchowski Equation along a General One-Dimensional Coordinate.

Publications

Toward a General Yet Effective Computational Approach for Diffusive Problems: Variable Diffusion Tensor and DVR Solution of the Smoluchowski Equation along a General One-Dimensional Coordinate.

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