Ion fluxes through nanopores and transmembrane channels

Accuracy of TIP4P/2005 and SPC/Fw Water Models

Water is used as the main solvent in model systems containing bioorganic molecules. Choosing the right water model is an important step in the study of the biophysical and biochemical processes that occur in cells. In the present work, we perform molecular dynamics simulations using two distinct force fields for water: the rigid model TIP4P/2005, where only intermolecular interactions are considered, and the flexible model SPC/Fw, where intramolecular interactions are also taken into account. The simulations aim to determine the effect of the inclusion of intramolecular interactions on the accuracy of calculated properties of bulk water (density and thermal expansion coefficient, self-diffusion coefficients, shear viscosity, radial distribution functions, and dielectric constant), as compared to experimental results, over a temperature range between 250 and 370 K. We find that the results of the rigid model present the smallest deviations relative to experiments for most of the calculated quantities, except for the shear viscosity of supercooled water and the water dielectric constant, where the flexible model presents better agreement with experiments.

Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores

In many practical applications, ions are the primary charge carrier and must move through either semipermeable membranes or through pores, which mimic ion channels in biological systems. In analogy to electronic devices, the "iontronic" ones use electric fields to induce the charge motion. However, unlike the electrons that move through a conductor, motion of ions is usually associated with simultaneous solvent flow. A study of electroosmotic flow through narrow pores is an outstanding challenge that lies at the interface of non-equilibrium statistical mechanics and fluid dynamics. In this paper, we will review recent works that use dissipative particle dynamics simulations to tackle this difficult problem. We will also present a classical density functional theory (DFT) based on the hypernetted-chain approximation (HNC), which allows us to calculate the velocity of electroosmotic flows inside nanopores containing 1 : 1 or 2 : 1 electrolyte solution. The theoretical results will be compared with simulations. In simulations, the electrostatic interactions are treated using the recently introduced pseudo-1D Ewald summation method. The zeta potentials calculated from the location of the shear plane of a pure solvent are found to agree reasonably well with the Smoluchowski equation. However, the quantitative structure of the fluid velocity profiles deviates significantly from the predictions of the Smoluchowski equation in the case of charged pores with 2 : 1 electrolyte. For low to moderate surface charge densities, the DFT allows us to accurately calculate the electrostatic potential profiles and the zeta potentials inside the nanopores. For pores with 1 : 1 electrolyte, the agreement between theory and simulation is particularly good for large ions, for which steric effects dominate over the ionic electrostatic correlations. The electroosmotic flow is found to depend very strongly on the ionic radii. In the case of pores containing 2 : 1 electrolyte, we observe a reentrant transition in which the electroosmotic flow first reverses and then returns to normal as the surface change density of the pore is increased.

Functionalized carbon nanocones performance in water harvesting

In this work, we investigate the water capture process for functionalized carbon nanocones (CNCs) through molecular dynamic simulations in the following three scenarios: a single CNC in contact with a reservoir containing liquid water, a single CNC in contact with a water vapor reservoir, and a combination of more than one CNC in contact with vapor. We found that water flows through the nanocones when in contact with the liquid reservoir if the nanocone tip presents hydrophilic functionalization. In contact with steam, we observed the formation of droplets at the base of the nanocone only when hydrophilic functionalization is present. Then, water flows through in a linear manner, a process that is more efficient than that in the liquid reservoir regime. The scalability of the process is tested by analyzing the water flow through more than one nanocone. The results suggest that the distance between the nanocones is a fundamental ingredient for the efficiency of water harvesting.

Breakdown of electroneutrality in nanopores

Ion transport in extremely narrow nanochannels has gained increasing interest in recent years due to unique physical properties at the nanoscale and the technological advances that allow us to study them. It is tempting to approach this confined regime with the theoretical tools and knowledge developed for membranes and microfluidic devices, and naively apply continuum models, such as the Poisson-Nernst-Planck and Navier-Stokes equations. However, it turns out that some of the most basic principles we take for granted in larger systems, such as the complete screening of surface charge by counter-ions, can break down under extreme confinement. We show that in a truly one-dimensional system of ions interacting with three-dimensional electrostatic interactions, the screening length is exponentially large, and can easily exceed the macroscopic length of a nanotube. Without screening, electroneutrality breaks down within the nanotube, with fundamental consequences for ion transport and electrokinetic phenomena. In this work, we build a general theoretical framework for electroneutrality breakdown in nanopores, focusing on the most interesting case of a one-dimensional nanotube, and show how it provides an elegant interpretation for the peculiar scaling observed in experimental measurements of ionic conductance in carbon nanotubes.

Integral Representation of Electrostatic Interactions inside a Lipid Membrane

Interactions between charges and dipoles inside a lipid membrane are partially screened. The screening arises both from the polarization of water and from the structure of the electric double layer formed by the salt ions outside the membrane. Assuming that the membrane can be represented as a dielectric slab of low dielectric constant sandwiched by an aqueous solution containing mobile ions, a theoretical model is developed to quantify the strength of electrostatic interactions inside a lipid membrane that is valid in the linear limit of Poisson-Boltzmann theory. We determine the electrostatic potential produced by a single point charge that resides inside the slab and from that calculate charge-charge and dipole-dipole interactions as a function of separation. Our approach yields integral representations for these interactions that can easily be evaluated numerically for any choice of parameters and be further simplified in limiting cases.

Salt parameterization can drastically affect the results from classical atomistic simulations of water desalination by MoS2 nanopores

Water scarcity is a reality in our world, and scenarios predicted by leading scientists in this area indicate that it will worsen in the next decades. However, new technologies based on low-cost seawater desalination can prevent the worst scenarios, providing fresh water for humanity. With this goal, membranes based on nanoporous materials have been suggested in recent years. One of the materials suggested is MoS₂, and classical Molecular Dynamics (MD) simulation is one of the most powerful tools to explore these nanomaterials. However, distinct force fields employed in MD simulations are parameterized based on distinct experimental quantities. In this paper, we compare two models of salt that were built based on distinct properties of water-salt mixtures. One model fits the hydration free energy and lattice properties, and the second fits the crystal density and the density and the dielectric constant of water and salt mixtures. To compare the models, MD simulations for salty water flow through nanopores of two sizes were used - one pore big enough to accommodate hydrated ions, and one smaller in which the ion has to dehydrate to enter - and two rigid water models from the TIP4P family - TIP4P/2005 and TIP4P/ε. Our results indicate that the water permeability and salt rejection by the membrane are more influenced by the salt model than by the water model, especially for the narrow pore. In fact, completely distinct mechanisms were observed, and they are related to the characteristics employed in the ion model parameterization. The results show that not only can the water model influence the outcomes, but the ion model plays a crucial role when the pore is small enough.

Coulomb interaction rules timescales in potassium ion channel tunneling

Assuming the selectivity filter of KcsA potassium ion channel may exhibit quantum coherence, we extend a previous model by Vaziri and Plenio (2010 New J. Phys. 12 085001) to take into account Coulomb repulsion between potassium ions. We show that typical ion transit timescales are determined by this interaction, which imposes optimal input/output parameter ranges. Also, as observed in other examples of quantum tunneling in biological systems, the addition of moderate noise helps coherent ion transport.

Diffusion of Charged Species in Liquids

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Influence of disordered porous media on the anomalous properties of a simple water model

The thermodynamic, dynamic, and structural behavior of a water-like system confined in a matrix is analyzed for increasing confining geometries. The liquid is modeled by a two-dimensional associating lattice gas model that exhibits density and diffusion anomalies, similar to the anomalies present in liquid water. The matrix is a triangular lattice in which fixed obstacles impose restrictions to the occupation of the particles. We show that obstacles shorten all lines, including the phase coexistence, the critical and the anomalous lines. The inclusion of a very dense matrix not only suppresses the anomalies but also the liquid-liquid critical point.

Potassium ions in the cavity of a KcsA channel model

The high rate of ion flux and selectivity of potassium channels has been attributed to the conformation and dynamics of the ions in the filter which connects the channel cavity and the extracellular environment. The cavity serves as the reservoir for potassium ions diffusing from the intracellular medium. The cavity is believed to decrease the dielectric barrier for the ions to enter the filter. We study here the equilibrium and dynamic properties of potassium ions entering the water-filled cavity of a KcsA channel model. Atomistic molecular dynamics simulations that are supplemented by electrostatic calculations reveal the important role of water molecules and the partially charged protein helices at the bottom of the cavity in overcoming the energy barrier and stabilizing the potassium ion in the cavity. We further show that the average time for a potassium ion to enter the cavity is much shorter than the conduction rate of a potassium passing through the filter, and this time duration is insensitive over a wide range of the membrane potential. The conclusions drawn from the study of the channel model are applicable in generalized contexts, including the entry of ions in artificial ion channels and other confined geometries.

Enhanced permeation of single-file water molecules across a noncylindrical nanochannel

We utilize molecular dynamics simulations to study the effect of noncylindrical shapes of a nanochannel (which are inspired from the shape of real biological water nanochannels) on the permeation of single-file water molecules across the nanochannel. Compared with the cylindrical shape that has been tremendously adopted in the literature, the noncylindrical shapes play a crucial role in enhancing water permeation. Remarkably, the maximal enhancement ratio reaches a value of 6.28 (enhancement behavior). Meanwhile, the enhancement becomes saturated when the volume of the noncylindrical shape continues to increase (saturation behavior). The analysis of average diffusivity of water molecules helps to reveal the mechanism underlying the two behaviors whereas Poiseuille's law fails to explain them. These results pave a way for designing high-flow nanochannels and provide insight into water permeation across biological water nanochannels.