The Role of the Dielectric Barrier in Narrow Biological Channels: a Novel Composite Approach to Modeling Single-channel Currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory

Tuning ion coordination preferences to enable selective permeation

Potassium (K-) channels catalyze K+ ion permeation across cellular membranes while simultaneously discriminating their permeation over Na+ ions by more than a factor of a thousand. Structural studies show bare K+ ions occupying the narrowest channel regions in a state of high coordination by all 8 surrounding oxygen ligands from the channel walls. As in most channels, the driving force for selectivity occurs when one ion is preferentially stabilized or destabilized by the channel compared to water. In the common view of mechanism, made vivid by textbook graphics, the driving force for selectivity in K- channels arises by a fit, whereby the channel induces K+ ions to leave water by offering an environment like water for K+, in terms of both energy and local structure. The implication that knowledge of local ion coordination in a liquid environment translates to design parameters in a protein ion channel, producing similar energetic stabilities, has gone unchallenged, presumably due in part to lack of consensus regarding ion coordination structures in liquid water. Growing evidence that smaller numbers and different arrangements of ligands coordinate K+ ions in liquid water, however, raises new questions regarding mechanism: how and why should ion coordination preferences change, and how does that alter the current notions of ion selectivity? Our studies lead to a new channelcentric paradigm for the mechanism of K+ ion channel selectivity. Because the channel environment is not liquid-like, the channel necessarily induces local structural changes in ion coordination preferences that enable structural and energetic differentiation between ions.Comment: Main manuscript: 12 pages, 6 figures. Supplementary information: 10 pages, 7 figure

The influence of geometry, surface character and flexibility on the permeation of ions and water through biological pores

A hydrophobic constriction site can act as an efficient barrier to ion and water permeation if its diameter is less than the diameter of an ion's first hydration shell. This hydrophobic gating mechanism is thought to operate in a number of ion channels, e.g. the nicotinic receptor, bacterial mechanosensitive channels (MscL and MscS) and perhaps in some potassium channels (e.g. KcsA, MthK, and KvAP). Simplified pore models allow one to investigate the primary characteristics of a conduction pathway, namely its geometry (shape, pore length, and radius), the chemical character of the pore wall surface, and its local flexibility and surface roughness. Our extended (ca. 0.1 \mu s) molecular dynamic simulations show that a short hydrophobic pore is closed to water for radii smaller than 0.45 nm. By increasing the polarity of the pore wall (and thus reducing its hydrophobicity) the transition radius can be decreased until for hydrophilic pores liquid water is stable down to a radius comparable to a water molecule's radius. Ions behave similarly but the transition from conducting to non-conducting pores is even steeper and occurs at a radius of 0.65 nm for hydrophobic pores. The presence of water vapour in a constriction zone indicates a barrier for ion permeation. A thermodynamic model can explain the behaviour of water in nanopores in terms of the surface tensions, which leads to a simple measure of "hydrophobicity" in this context. Furthermore, increased local flexibility decreases the permeability of polar species. An increase in temperature has the same effect, and we hypothesise that both effects can be explained by a decrease in the effective solvent-surface attraction which in turn leads to an increase in the solvent-wall surface free energy.Comment: Peer reviewed article appeared in Physical Biology http://www.iop.org/EJ/abstract/1478-3975/1/1/005

EXFI: a low cost Fault Injection System for embedded Microprocessor-based Boards

Evaluating the faulty behavior of low-cost embedded microprocessor-based boards is an increasingly important issue, due to their adoption in many safety critical systems. The architecture of a complete Fault Injection environment is proposed, integrating a module for generating a collapsed list of faults, and another for performing their injection and gathering the results. To address this issue, the paper describes a software-implemented Fault Injection approach based on the Trace Exception Mode available in most microprocessors. The authors describe EXFI, a prototypical system implementing the approach, and provide data about some sample benchmark applications. The main advantages of EXFI are the low cost, the good portability, and the high efficienc

Potentials of mean force in acidic proton transfer reactions in constrained geometries

Free energy barriers associated with the transfer of an excess proton in water and related to the potentials of mean force in proton transfer episodes have been computed in a wide range of thermodynamic states, from low-density amorphous ices to high-temperature liquids under the critical point for unconstrained and constrained systems. The latter were represented by set-ups placed inside hydrophobic graphene slabs at the nanometric scale allocating a few water layers, namely one or two in the narrowest case. Water–proton and carbon–proton forces were modelled with a Multi-State Empirical Valence Bond method. As a general trend, a competition between the effects of confinement and temperature is observed on the local hydrogen-bonded structures around the lone proton and, consequently, on the mean force exerted by its environment on the water molecule carrying the proton. Free energy barriers estimated from the computed potentials of mean force tend to rise with the combined effect of increasing temperatures and the packing effect due to a larger extent of hydrophobic confinement. The main reason observed for such enhancement of the free energy barriers was the breaking of the second coordination shell around the lone proton.Postprint (author's final draft

The Ca2+Ca^{2+}-activated Cl−Cl^- current ensures robust and reliable signal amplification in vertebrate olfactory receptor neurons

Activation of most primary sensory neurons results in transduction currents that are carried by cations. One notable exception is the vertebrate olfactory receptor neuron (ORN), where the transduction current is carried largely by the anion $Cl^-$. However, it remains unclear why ORNs use an anionic current for signal amplification. We have sought to provide clarification on this topic by studying the so far neglected dynamics of $Na^+$, $Ca^{2+}$, $K^+$ and $Cl^-$ in the small space of olfactory cilia during an odorant response. Using computational modeling and simulations we compared the outcomes of signal amplification based on either $Cl^-$ or $Na^+$ currents. We found that amplification produced by $Na^+$ influx instead of a $Cl^-$ efflux is problematic due to several reasons: First, the $Na^+$ current amplitude varies greatly depending on mucosal ion concentration changes. Second, a $Na^+$ current leads to a large increase in the ciliary $Na^+$ concentration during an odorant response. This increase inhibits and even reverses $Ca^{2+}$ clearance by $Na^+/Ca^{2+}/K^+$ exchange, which is essential for response termination. Finally, a $Na^+$ current increases the ciliary osmotic pressure, which could cause swelling to damage the cilia. By contrast, a transduction pathway based on $Cl^-$ efflux circumvents these problems and renders the odorant response robust and reliable.Comment: 31 pages, 10 figures (including SI