In this work we propose a force-field scheme for the self-consistent particle-based simulation of electrolytic solutions. Within this approach, the electrostatic interactions are modeled with a particle-particle-particlemesh (P 3 M) algorithm, where the long-range components of the force are resolved in real space with an iterative multi-grid Poisson solver. Simulations are performed where the solute ions are treated as Brownian particles governed by the full Langevin equation, while the effects of the solvent are accounted for with the implicit solvent model. The main motivation of this work is to efficiently extend the modeling capability of the standard particlebased approaches to liquid systems characterized by a spatially inhomogeneous charge distribution and realistic, non-periodic boundary conditions. Examples of such systems are large polymer chains, biological membranes, and ion channels.

In this work, we study the suitability of a P3M force field scheme coupled with a Brownian dynamics simulation engine for the accurate modelling of charge transport in ion channels. The proposed simulation algorithm (Aboud et al 2004 J. Comput. Electron. 3 117–33) is briefly discussed, and its validation for the electrodynamic description of aqueous solutions (Marreiro et al 2005 J. Comput. Electron. 4 179–83; 2006 J. Comput. Electron. at press) is presented. The algorithm is applied to the simulation of ion channel systems where the influence of the dielectric representation and the diffusion coefficients are computed and compared to experimental (Van Der Straaten et al 2003 J. Comput. Electron. 2 29–47) and simulated (Van Der Straaten et al 2003 J. Comput. Electron. 2 29–47; Miedema et al 2004 Biophys. J. 87 3137–47) data. The results show that while the bulk parameters do not correctly apply to the channel, the model can be refined by a careful choice of parameters in order to yield accurate charge transport properties while remaining extremely effective from the computational viewpoint.

In this work, an error analysis methodology is applied to the study of various integration schemes used in Brownian Dynamics simulations of ion channels. Three algorithms have been compared for the integration of the full Langevin Equation [1]. A first-order Euler scheme [2], the Verlet-like algorithm proposed by [3], and a novel Predictor/Corrector (PC) scheme [4] have been implemented and analyzed using our assessment methodology [5]. Our results show that a significant increase in the integration timestep, and a subsequent reduction in computational cost and improvement in efficiency, can be achieved with the second order Verlet-like and PC schemes, while maintaining an excellent accuracy for the description of both structure and dynamics of the electrolyte solution. This work extends the analysis developed in [5] to dynamic properties of the solution as well as structural aspects of inhomogeneous systems such as a lipid membrane.

The particle-particle-particle-mesh (P 3 M) force field scheme [1], [2] is an efficient approach to account for both the long-range and short-range electrostatic interactions in the simulation of biological systems. Resolving the particle-mesh term in real-space [2], [3] improves the original approach of Hockney et al. [1] by allowing for the inclusion of non-periodic boundary conditions. To date, the P 3 M method has not been fully utilized by the computational biophysics community due to a lack of rigorous analysis of the computational error associated with the P 3 M approach [4]. Performing such an analysis is the main goal of this work. The P 3 M approach is based on a separation of the Coulomb interaction into a long-range and short-range component by a smooth function f (r),which is chosen in such a way that the first term represents the long-range interaction and the second term results in a short-range one. Within the proposed P 3 M formalism, the long-range force, or particle-mesh force, is calculated with an extremely efficient finite difference multi-grid Poisson solver in real space [3]. The function f (r) is then related to the "shape" of the particle used to assign its charge to the real space grid, and to interpolate the corresponding force at the particle position. The short-range force is composed of two parts that are both determined within a small domain. The first term is the particle-particle force and is computed by a direct summation of the pair-wise interaction of close neighbors, including the van der Waals interactions. The second part of the short-range calculation is a correction term, which accounts for the portion of the interaction already included in the solution of Poisson's equation. This correction term, or "reference" force, is calculated analytically and stored in a look-up table [1]. The ability of the reference force to reproduce the force calculated with the Poisson solver within the short-range domain determines the accuracy of the P 3 M method. Figure 1 shows a plot of the particle-particle, reference, and particle-mesh forces between two ions in a 0.5 M KCl solution as a function of ion separation. The triangular-shaped cloud (TSC) [1] assignment scheme is used and the mesh spacing is 1 nm. As can be seen, within the short-range domain (defined here as a sphere with a 2 nm radius) the reference force and particle-mesh force cancel and the short-range ion interaction is defined exclusively by the particle-particle interaction as it should be.In order to further assess the accuracy of the P 3 M approach, the radial distribution function (RDF) of the ionic population [5] is calculated with Brownian dynamics for bulk electrolyte solutions, and compared with the analytic solution of the Ornstein-Zernike equation [6], using the hypernetted-chain closure relation [7]. The RDF is shown in Fig. 2 for several simulation parameters. For the parameters corresponding to Fig. 1 there is excellent agreement between the computed RDF (TSC, Grid 1.0 nm) and the analytic values. For simul...

A fully self-consistent 3D Poisson P 3 M Brownian dynamics solver is used to investigate the role of the long-range electrostatic forces on the selectivity and conductivity of OmpF porin. Our simulations show that even with zero applied bias, the long-range interactions are an important component of the total potential energy. In addition, the long-range force due to mobile carriers is shown to play a role in facilitating the flow of anions through the OmpF channel by screening the effect of the negative fixed charge of the protein.