Ben Corry

Tests of Continuum Theories as Models of Ion Channels. II. Poisson–Nernst–Planck Theory versus Brownian Dynamics

We test the validity of the mean-field approximation in Poisson-Nernst-Planck theory by contrasting its predictions with those of Brownian dynamics simulations in schematic cylindrical channels and in a realistic potassium channel. Equivalence of the two theories in bulk situations is demonstrated in a control study. In simple cylindrical channels, considerable differences are found between the two theories with regard to the concentration profiles in the channel and its conductance properties. These differences are at a maximum in narrow channels with a radius smaller than the Debye length and diminish with increasing radius. Convergence occurs when the channel radius is over 2 Debye lengths. These tests unequivocally demonstrate that the mean-field approximation in the Poisson-Nernst-Planck theory breaks down in narrow ion channels that have radii smaller than the Debye length.

Mechanisms of permeation and selectivity in calcium channels.

The mechanisms underlying ion transport and selectivity in calcium channels are examined using electrostatic calculations and Brownian dynamics simulations. We model the channel as a rigid structure with fixed charges in the walls, representing glutamate residues thought to be responsible for ion selectivity. Potential energy profiles obtained from multi-ion electrostatic calculations provide insights into ion permeation and many other observed features of L-type calcium channels. These qualitative explanations are confirmed by the results of Brownian dynamics simulations, which closely reproduce several experimental observations. These include the current-voltage curves, current-concentration relationship, block of monovalent currents by divalent ions, the anomalous mole fraction effect between sodium and calcium ions, attenuation of calcium current by external sodium ions, and the effects of mutating glutamate residues in the amino acid sequence.

Continuum electrostatics fails to describe ion permeation in the gramicidin channel.

We investigate the validity of continuum electrostatics in the gramicidin A channel using a recently determined high-resolution structure. The potential and electric field acting on ions in and around the channel are computed by solving Poissons equation. These are then used in Brownian dynamics simulations to obtain concentration profiles and the current passing through the channel. We show that regardless of the effective dielectric constant used for water in the channel or the channel protein, it is not possible to reproduce all the experimental data on gramicidin A; thus, continuum electrostatics cannot provide a valid framework for the description of ion dynamics in gramicidin channels. Using experimental data and molecular dynamics simulations as guides, we have constructed potential energy profiles that can satisfactorily describe the available physiological data. These profiles provide useful benchmarks for future potential of mean force calculations of permeating ions from molecular dynamics simulations of gramicidin A. They also offer a convenient starting point for studying structure-function relationships in modified gramicidin channels.

Dielectric Self-Energy in Poisson-Boltzmann and Poisson-Nernst-Planck Models of Ion Channels

We demonstrated previously that the two continuum theories widely used in modeling biological ion channels give unreliable results when the radius of the conduit is less than two Debye lengths. The reason for this failure is the neglect of surface charges on the protein wall induced by permeating ions. Here we attempt to improve the accuracy of the Poisson-Boltzmann and Poisson-Nernst-Planck theories, when applied to channel-like environments, by including a specific dielectric self-energy term to overcome spurious shielding effects inherent in these theories. By comparing results with Brownian dynamics simulations, we show that the inclusion of an additional term in the equations yields significant qualitative improvements. The modified theories perform well in very wide and very narrow channels, but are less successful at intermediate sizes. The situation is worse in multi-ion channels because of the inability of the continuum theories to handle the ion-to-ion interactions correctly. Thus, further work is required if these continuum theories are to be reliably salvaged for quantitative studies of biological ion channels in all situations.

Bioinspired Graphene Nanopores with Voltage-Tunable Ion Selectivity for Na+ and K+

Biological protein channels have many remarkable properties such as gating, high permeability, and selectivity, which have motivated researchers to mimic their functions for practical applications. Herein, using molecular dynamics simulations, we design bioinspired nanopores in graphene sheets that can discriminate between Na(+) and K(+), two ions with very similar properties. The simulation results show that, under transmembrane voltage bias, a nanopore containing four carbonyl groups to mimic the selectivity filter of the KcsA K(+) channel preferentially conducts K(+) over Na(+). A nanopore functionalized by four negatively charged carboxylate groups to mimic the selectivity filter of the NavAb Na(+) channel selectively binds Na(+) but transports K(+) over Na(+). Surprisingly, the ion selectivity of the smaller diameter pore containing three carboxylate groups can be tuned by changing the magnitude of the applied voltage bias. Under lower voltage bias, it transports ions in a single-file manner and exhibits Na(+) selectivity, dictated by the knock-on ion conduction and selective blockage by Na(+). Under higher voltage bias, the nanopore is K(+)-selective, as the blockage by Na(+) is destabilized and the stronger affinity for carboxylate groups slows the passage of Na(+) compared with K(+). The computational design of biomimetic ion-selective nanopores helps to understand the mechanisms of selectivity in biological ion channels and may also lead to a wide range of potential applications such as sensitive ion sensors, nanofiltration membranes for Na(+)/K(+) separation, and voltage-tunable nanofluidic devices.

Conduction mechanisms of chloride ions in ClC-type channels

The conduction properties of ClC-0 and ClC-1 chloride channels are examined using electrostatic calculations and three-dimensional Brownian dynamics simulations. We create an open-state configuration of the prokaryotic ClC Cl(-) channel using its known crystallographic structure as a basis. Two residues that are occluding the channel are slowly pushed outward with molecular dynamics to create a continuous ion-conducting path with the minimum radius of 2.5 A. Then, retaining the same pore shape, the prokaryotic ClC channel is converted to either ClC-0 or ClC-1 by replacing all the nonconserved dipole-containing and charged amino acid residues. Employing open-state ClC-0 and ClC-1 channel models, current-voltage curves consistent with experimental measurements are obtained. We find that conduction in these pores involves three ions. We locate the binding sites, as well as pinpointing the rate-limiting steps in conduction, and make testable predictions about how the single channel current across ClC-0 and ClC-1 will vary as the ionic concentrations are increased. Finally, we demonstrate that a ClC-0 homology model created from an alternative sequence alignment fails to replicate any of the experimental observations.

An improved open-channel structure of MscL determined from FRET confocal microscopy and simulation

Mechanosensitive channels act as molecular transducers of mechanical force exerted on the membrane of living cells by opening in response to membrane bilayer deformations occurring in physiological processes such as touch, hearing, blood pressure regulation, and osmoregulation. Here, we determine the likely structure of the open state of the mechanosensitive channel of large conductance using a combination of patch clamp, fluorescence resonance energy transfer (FRET) spectroscopy, data from previous electron paramagnetic resonance experiments, and molecular and Brownian dynamics simulations. We show that structural rearrangements of the protein can be measured in similar conditions as patch clamp recordings while controlling the state of the pore in its natural lipid environment by modifying the lateral pressure distribution via the lipid bilayer. Transition to the open state is less dramatic than previously proposed, while the N terminus remains anchored at the surface of the membrane where it can either guide the tilt of or directly translate membrane tension to the conformation of the pore-lining helix. Combining FRET data obtained in physiological conditions with simulations is likely to be of great value for studying conformational changes in a range of multimeric membrane proteins.

Mechanisms of Valence Selectivity in Biological Ion Channels

Abstract.Transmembrane ion channels play a crucial role in the existence of all living organisms. They partition the exterior from the interior of the cell, maintain the proper ionic gradient across the cell membrane and facilitate signaling between cells. To perform these functions, ion channels must be highly selective, allowing some types of ions to pass while blocking the passage of others. Here we review a number of studies that have helped to elucidate the mechanisms by which ion channels discriminate between ions of differing charge, focusing on four channel families as examples: gramicidin, ClC chloride, voltage-gated calcium and potassium channels. The recent availability of high-resolution structural data has meant that the specific inter-atomic interactions responsible for valence selectivity can be pinpointed. Not surprisingly, electrostatic considerations have been shown to play an important role in ion specificity, although many details of the origins of this discrimination remain to be determined.

Reservoir boundaries in Brownian dynamics simulations of ion channels.

Brownian dynamics (BD) simulations provide a practical method for the calculation of ion channel conductance from a given structure. There has been much debate about the implementation of reservoir boundaries in BD simulations in recent years, with claims that the use of improper boundaries could have large effects on the calculated conductance values. Here we compare the simple stochastic boundary that we have been using in our BD simulations with the recently proposed grand canonical Monte Carlo method. We also compare different methods of creating transmembrane potentials. Our results confirm that the treatment of the reservoir boundaries is mostly irrelevant to the conductance properties of an ion channel as long as the reservoirs are large enough.

Anomalous decline of water transport in covalently modified carbon nanotube membranes

Carbon nanotube membranes have been shown to rapidly transport liquids; but progressive hydrophilic modification--contrary to expectations--induces a drastic reduction of water flow. Enhanced electrostatic interaction and the disruption of the mechanically smooth graphitic walls is the determinant of this behavior. These results have critical implications in the design of nanofluidic devices.