In a multiscale modeling approach, we present computer simulation results for a rectifying bipolar nanopore at two modeling levels. In an all-atom model, we use explicit water to simulate ion transport directly with the molecular dynamics technique. In a reduced model, we use implicit water and apply the Local Equilibrium Monte Carlo method together with the Nernst-Planck transport equation. This hybrid method makes the fast calculation of ion transport possible at the price of lost details. We show that the implicit-water model is an appropriate representation of the explicit-water model when we look at the system at the device (i.e., input vs. output) level. The two models produce qualitatively similar behavior of the electrical current for different voltages and model parameters. Looking at the details of concentration and potential profiles, we find profound differences between the two models. These differences, however, do not influence the basic behavior of the model as a device because they do not influence the z-dependence of the concentration profiles which are the main determinants of current. These results then address an old paradox: how do reduced models, whose assumptions should break down in a nanoscale device, predict experimental data? Our simulations show that reduced models can still capture the overall device physics correctly, even though they get some important aspects of the molecular-scale physics quite wrong; reduced models work because they include the physics that is necessary from the point of view of device function. Therefore, reduced models can suffice for general device understanding and device design, but more detailed models might be needed for molecular level understanding.

We report a multiscale modeling study for charged cylindrical nanopores using three modeling levels that include (1) an all-atom explicit-water model studied with molecular dynamics (MD), and reduced models with implicit water containing (2) hard-sphere ions studied with the Local Equilibrium Monte Carlo simulation method (computing ionic correlations accurately), and (3) point ions studied with Poisson-Nernst-Planck (PNP) theory (mean-field approximation). We show that reduced models are able to reproduce device functions (rectification and selectivity) for a wide variety of charge patterns; that is, reduced models are useful in understanding the mesoscale physics of the device (i.e., how the current is produced). We also analyze the relationship of the reduced implicit-water models with the explicit-water model and show that diffusion coefficients in the reduced models can be used as adjustable parameters with which the results of the explicit-and implicit-water models can be related. We find that the values of the diffusion coefficients are sensitive to the net charge of the pore, but are relatively transferable to different voltages and charge patterns with the same total charge. Multiscale analysis of the effect of surface charge pattern on a nanopore's rectification and selectivity properties: from all-atom model to Poisson-Nernst-Planck -4/15

We provide a systematic comparative analysis of various simulation methods for studying steady-state diffusive transport of molecular systems. The methods differ in two respects: (1) the actual method with which the dynamics of the system is handled can be a direct simulation technique [molecular dynamics (MD) and dynamic Monte Carlo (DMC)] or can be an indirect transport equation [the Nernst-Planck (NP) equation], while (2) the driving force of the steady-state transport can be maintained with control cells on the two sides of the transport region [dual control volume (DCV) technique] or it can be maintained in the whole simulation domain with the local equilibrium Monte Carlo (LEMC) technique, where the space is divided into small subvolumes, different chemical potentials are assigned to each, and grand canonical Monte Carlo simulations are performed for them separately. The various combinations of the transport-methods with the driving-force methods have advantages and disadvantages. The MD+DCV and DMC+DCV methods are widely used to study membrane transport. The LEMC method has been introduced with the NP+LEMC technique, which was proved to be a fast, but somewhat empirical method to study diffusion [D. Boda and D. Gillespie, J. Chem. Theor. Comput. 8, 824 (2012)]. In this paper, we introduce the DMC+LEMC method and show that the resulting DMC+LEMC technique has the advantage over the DMC+DCV method that it provides better sampling for the flux, while it has the advantage over the NP+LEMC method that it simulates dynamics directly instead of hiding it in an external adjustable parameter, the diffusion coefficient. The information gained from the DMC+LEMC simulation can be used to construct diffusion coefficient profiles for the NP+LEMC calculations, so a simultaneous application of the two methods is advantageous.

We study a rectifying mutant of the OmpF porin ion channel using both all-atom and reduced models. The mutant was created by Miedema et al. [Nano Lett., 2007, 7, 2886 on the basis of the N-P semiconductor diode, in which an N-P junction is formed. The mutant contains a pore region with positive amino acids on the left-hand side and negative amino acids on the right-hand side. Experiments show that this mutant rectifies. Although we do not know the structure of this mutant, we can build an all-atom model for it on the basis of the structure of the wild type channel. Interestingly, molecular dynamics simulations for this all-atom model do not produce rectification. A reduced model that contains only the important degrees of freedom (the positive and negative amino acids and free ions in an implicit solvent), on the other hand, exhibits rectification. Our calculations for the reduced model (using the Nernst-Planck equation coupled to Local Equilibrium Monte Carlo simulations) reveal a rectification mechanism that is different from that seen for semiconductor diodes. The basic reason is that the ions are different in nature from electrons and holes (they do not recombine). We provide explanations for the failure of the all-atom model including the effect of all the other atoms in the system as a noise that inhibits the response of ions (that would be necessary for rectification) to the polarizing external field.

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