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Dispersion terms and analysis of size- and charge dependence in an enhanced Poisson-Boltzmann approach.

ABSTRACT: We implement a well-established concept to consider dispersion effects within a Poisson-Boltzmann approach of continuum solvation of proteins. The theoretical framework is particularly suited for boundary element methods. Free parameters are determined by comparison to experimental data as well as high-level quantum mechanical reference calculations. The method is general and can be easily extended in several directions. The model is tested on various chemical substances and found to yield good-quality estimates of the solvation free energy without obvious indication of any introduced bias. Once optimized, the model is applied to a series of proteins, and factors such as protein size or partial charge assignments are studied.

SUBMITTER: Kar P

PROVIDER: S-EPMC2536643 | biostudies-literature | 2007 Aug

REPOSITORIES: biostudies-literature

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Dispersion terms and analysis of size- and charge dependence in an enhanced Poisson-Boltzmann approach.

Kar Parimal P Seel Max M Hansmann Ulrich H E UH Höfinger Siegfried S

The journal of physical chemistry. B 20070712 30

We implement a well-established concept to consider dispersion effects within a Poisson-Boltzmann approach of continuum solvation of proteins. The theoretical framework is particularly suited for boundary element methods. Free parameters are determined by comparison to experimental data as well as high-level quantum mechanical reference calculations. The method is general and can be easily extended in several directions. The model is tested on various chemical substances and found to yield good- ...[more]

PMID: 17628098

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Project description:The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

Project description:Proper modeling of nonspecific salt-mediated electrostatic interactions is essential to understanding the binding of charged ligands to nucleic acids. Because the linear Poisson-Boltzmann equation (PBE) and the more approximate generalized Born approach are applied routinely to nucleic acids and their interactions with charged ligands, the reliability of these methods is examined vis-à-vis an efficient nonlinear PBE method. For moderate salt concentrations, the negative derivative, SK(pred), of the electrostatic binding free energy, DeltaG(el), with respect to the logarithm of the 1:1 salt concentration, [M(+)], for 33 cationic minor groove drugs binding to AT-rich DNA sequences is shown to be consistently negative and virtually constant over the salt range considered (0.1-0.4 M NaCl). The magnitude of SK(pred) is approximately equal to the charge on the drug, as predicted by counterion condensation theory (CCT) and observed in thermodynamic binding studies. The linear PBE is shown to overestimate the magnitude of SK(pred), whereas the nonlinear PBE closely matches the experimental results. The PBE predictions of SK(pred) were not correlated with DeltaG(el) in the presence of a dielectric discontinuity, as would be expected from the CCT. Because this correlation does not hold, parameterizing the PBE predictions of DeltaG(el) against the reported experimental data is not possible. Moreover, the common practice of extracting the electrostatic and nonelectrostatic contributions to the binding of charged ligands to biopolyelectrolytes based on the simple relation between experimental SK values and the electrostatic binding free energy that is based on CCT is called into question by the results presented here. Although the rigid-docking nonlinear PB calculations provide reliable predictions of SK(pred), at least for the charged ligand-nucleic acid complexes studied here, accurate estimates of DeltaG(el) will require further development in theoretical and experimental approaches.

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Dispersion terms and analysis of size- and charge dependence in an enhanced Poisson-Boltzmann approach.

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Dispersion terms and analysis of size- and charge dependence in an enhanced Poisson-Boltzmann approach.

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