Optimization of 3D Poisson-Nernst-Planck model for fast evaluation of diverse protein channels

Abstract

International audienceWe show the accuracy and applicability of our fast algorithmic implementation of a three-dimensional Poisson-Nernst-Planck (3D-PNP) flow model for characterizing different protein channels. Due to its high computational efficiency, our model can predict the full current-voltage characteristics of a channel within minutes, based on the experimental 3D structure of the channel or its computational model structure. Compared with other methods, such as Brownian dynamics, which currently needs a few weeks of the computational time, or even much more demanding molecular dynamics modeling, 3D-PNP is the only available method for a function-based evaluation of very numerous tentative structural channel models. Flow model tests of our algorithm and its optimal parametrization are provided for five native channels whose experimental structures are available in the protein data bank (PDB) in an open conductive state, and whose experimental current-voltage characteristics have been published. The channels represent very different geometric and structural properties, which makes it the widest test to date of the accuracy of 3D-PNP on real channels. We test whether the channel conductance, rectification, and charge selectivity obtained from the flow model, could be sufficiently sensitive to single-point mutations, related to unsignificant changes in the channel structure. Our results show that the classical 3D-PNP model, under proper parametrization, is able to achieve a qualitative agreement with experimental data for a majority of the tested characteristics and channels, including channels with narrow and irregular conductivity pores. We propose that although the standard PNP model cannot provide insight into complex physical phenomena due to its intrinsic limitations, its semiquantitative agreement is achievable for rectification and selectivity at a level sufficient for the bioinformatical purpose of selecting the best structural models with a great advantage of a very short computational time

Fast assessment of structural models of ion channels based on their predicted current-voltage characteristics

“…The outcome of the tests was consistent with our previous analysis of these channels by means of the classical 3D PNP . Not surprisingly, 3D PNP was the most efficient in assessment of candidate models in cases when characteristics calculated for experimentally solved structures were in good agreement with experimental characteristics.…”

“…Eventually, the first scenario has been applied to three other ion channels: MthK, GLIC and alpha‐hemolysin. The functional characteristics of the experimentally solved structures of these channels have been calculated using 3D PNP Solver in a previous study …”

“…ratio of cation to anion current) and rectification of the current. When applied to the reference structure, the electrodiffusion model properly predicted outward rectification of the channel and virtually infinite cation to anion selectivity (above 100:1) while total currents were underestimated 3–4‐fold (Table ) …”

Theoretical frameworks for multiscale modeling and simulation

“…One step down the resolution hierarchy are models that treat the conducting ions explicitly by Brownian dynamics simulations, but the channel protein, membrane, and solvent as static dielectric continuum [75,76]. A further approximation is to replace the discrete ions of each species by a continuous charge density and treat ion-ion interactions in a mean-field way; the resulting Poisson-Nernst-Planck model continues to find use [77–79]. Lastly one can model ion permeation as the diffusion of one or a few ions in a 1- or 3-dimensional potential of mean force [80–83]; this potential of mean force can be obtained from all-atom molecular dynamics simulations.…”

Automated Procedure for Contact-Map-Based Protein Structure Reconstruction

“…For instance, Memoir (Ebejer et al 2013) a program, which was specially designed to predict membrane proteins, provides models with average Root Mean Square Deviation (RMSD) of 2.57 Å. Prediction of transmembrane structures, especially ionic channels, will further allow for modeling their conductivity characteristics using biophysical models (e.g., Dyrka et al 2008; Dyrka et al 2013) and finally prediction of their cellular functionality (e.g., Jafri and Kotulska 2006). Currently, the major challenge in this field is to predict the protein structure, without prior knowledge of homologous structures.…”