An ambitious project is taking place [1,2] in which a fast and efficient software solution is being developed for studying ion permeation and substrate translocation across a nanopore, i.e., artificial or biological channel.

Among the large number of computational methods for studying ion and substrate permeation across biological and artificial pores, most of them can be divided into three different categories: at the continuum level, the Poisson-Nernst-Planck model; Brownian dynamics (BD), in which the environment is typically represented by a structureless dielectric medium; and all-atom molecular dynamics (MD) which is a fully microscopic description with all atoms treated explicitly. Here, we have developed an hybrid MD-BD scheme that incorporates a forces field description for the dynamics of explicit atoms and several boundary conditions to mimic canonical and grand canonical ensembles.

This project is part of the Translocation consortium (www.translocation.eu) and has received support from the Innovative Medicines Joint Under-taking under Grant Agreement No. 115525, resources which are composed of financial contribution from the European Unions seventh framework programme (FP7/2007-2013) and EFPIA companies in kind contribution. The work in Calgary was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (Discovery Grant RGPIN-315019 to S.Y.N.) and the Alberta Innovates Technology Futures (AITF) Strategic Chair in BioMolecular Simulations (Centre for Molecular Simulation).

References

[1] P.M. De Biase, C, J. F. Solano et al, J. Chem. Theory Comput. 8, 2540 (2012).
[2] C. J. F. Solano et al, J. Chem. Theory Comput. 12, 2401 (2016).
[3] C. J. F. Solano, J. D. Prajapati, K. R. Pothula and U. Kleinekathöfer, J. Chem. Theory Comput. 14, 6701 (2018).

The string method (SM) [1,2] has been implemented for finding minimum free energy paths (MFEPs) on a given free energy surface (FES). Since metadynamics [3] allows for estimating the FES and deriving its gradient, MFEPs can be computed efficiently using the SM. In addition, other enhanced sampling methods could be also combined with the SM by including minor modifications in this code. Given an initial guess for a curve on the FES, the SM finds the closest MFEP by moving a discrete set of points on the curve by the steepest descent on the free energy landscape. At the same time, the points are kept at constant distance from each other.

A time-independent and locally convergent FES estimator [4] for metadynamics has been also implemented in this code. Thereby, this FES estimator can be calculated at any position in the collective variable space.

References

[1] L. Maragliano et al, J. Chem. Phys. 125, 024106 (2006).
[2] L. Maragliano et al, Chem. Phys. Lett. 446, 182-190 (2007).
[3] A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. USA 99, 12562 (2002).
[4] P. Tiwary and M. Parrinello, J. Phys. Chem. B 119, 736-742 (2014).

The Tiwary-Parrinello reweighting technique [1] is implemented in this Phyton script.

References

[1] P. Tiwary and M. Parrinello, J. Phys. Chem. B 119, 736-742 (2014).

A collective diffusion model based on the linear response theory has been defined that enables one to determine the ion channel conductance from equilibrium simulations [1]. Here, this model is implemented in an efficient algorithm.

References

[1] Y. Liu and F. Zhu, Biophys. J. 104, 368 (2013).

Th ion diffusion profiles are central input parameters in many theoretical description of permeation process across membrane channels. Here, an algorithm is implemented that enables one to compute the self-diffusion constant of ions at different positions along the channel axis from molecular dynamics data [1].

References

[1] W. Im and B. Roux, J. Mol. Biol. 319, 1177 (2002).

A set of algorithms described in [1] are implemented for estimating the structural and transport properties as from molecular dynamics simulations using Lucretius code [2].

References

[1] C. J. F. Solano, S. Jeremias, E. Paillard, D. Beljonne and R. Lazzaroni, J. Chem. Phys. 139, 034502 (2013).
[2] C. Ayyagari, D. Bredov, O. Borodin and G. D. Smith, Lucretius, MD simulation code.

Computer simulations of physical systems by Monte Carlo methods or molecular dynamics typically produce raw data in the form of finitie series of correlated data. When stationary states are investigated, the first step in data analysis consists in computing time averages. Since such averages are over finite times, they are fluctuating quantities. So the next step in the data analysis consists in estimating the variance of finite time averages. Here, a code is provided that enables one to estimate the error on averages of correlated data [1,2].

References

[1] H. Flyvbjerg and H. G. Petersen, J. Chem. Phys. 91, 461–466 (1989).
[2] M. P. Allen and D. J. Tildesley, Computer simulation of liquids. Oxford: Clarendon Press
(1987).

In the quantum chemistry group of Oviedo University (Spain), PROMOLDEN code was designed to perform the topological analysis of the electron density according to the quantum theory of atoms in molecules (QTAIM). Here, an auxiliary code of PROMOLDEN, which has been termed as RHOLM, is introduced. This code enables one to generate the QTAIM multipole moments and apply different methodologies for studying the convergence of the multipole expansion for Coulomb interactions [1].

References

[1] C. J. F. Solano, A. M. Pendás, E. Francisco, M. A. Blanco and P. L. A. Popelier, J. Chem. Phys, 132, 194110 (2010).

The generalized perturbed ion (gPI) method [1] has been developed in the quantum chemistry group of Oviedo University (Spain). This quantum local method, which is based on the theory of separability of many-electrons system, allows for a description of ionic systems such as crystals, finite clusters and crystal defects or impurities. gPI code enables one to include polarization effects of the electron density for the ions. To this end, every spatial orbital transform according to one of the irreducible representations belonging to the symmetry point group for the ion.

References

[1] C. J. F. Solano, PhD Thesis (2009).