Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

Dynamics of Ion Channels via Non-Hermitian Quantum Mechanics

We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.

Ionic Coulomb blockade and the determinants of selectivity in the NaChBac bacterial sodium channel

Mutation-induced transformations of conductivity and selectivity in NaChBac bacterial channels are studied experimentally and interpreted within the framework of ionic Coulomb blockade (ICB), while also taking account of resonant quantised dehydration (QD) and site protonation. Site-directed mutagenesis and whole-cell patch-clamp experiments are used to investigate how the fixed charge Q_f at the selectivity filter (SF) affects both valence selectivity and same-charge selectivity. The new ICB/QD model predicts that increasing ∣Q_f∣ should lead to a shift in selectivity sequences toward larger ion sizes, in agreement with the present experiments and with earlier work. Comparison of the model with experimental data leads to the introduction of an effective charge Q_f^∗ at the SF, which was found to differ between Aspartate and Glutamate charged rings, and also to depend on position within the SF. It is suggested that protonation of the residues within the restricted space of the SF is important in significantly reducing the effective charge of the EEEE ring. Values of Q_f^∗ derived from experiments on divalent blockade agree well with expectations based on the ICB/QD model and have led to the first demonstration of ICB oscillations in Ca²⁺ conduction as a function of the fixed charge. Preliminary studies of the dependence of Ca²⁺ conduction on pH are qualitatively consistent with the predictions of the model.

Exploring the pore charge dependence of K+ and Cl- permeation across a graphene monolayer: a molecular dynamics study

Selective permeation through graphene nanopores is attracting increasing interest as an efficient and cost-effective technique for water desalination and purification. In this work, using umbrella sampling and molecular dynamics simulations with constant electric field, we analyze the influence of pore charge on potassium and chloride ion permeation. As pore charge is increased, the barrier of the potential of mean force (PMF) gradually decreases until it turns into a well split in two subminima. While in the case of K+ this pattern can be explained as an increasing electrostatic compensation of the desolvation cost, in the case of Cl- the pattern can be attributed to the accumulation of a concentration polarization layer of potassium ions screening pore charge. The analysis of potassium PMFs in terms of forces revealed a conflicting influence on permeation of van der Waals and electrostatic forces that both undergo an inversion of their direction as pore charge is increased. Even if the most important transition involves the interplay between the electrostatic forces exerted by graphene and water, the simulations also revealed an important role of the changing distribution of potassium and chloride ions. The influence of pore charge on the orientation of water molecules was also found to affect the van der Waals forces they exert on potassium.

Different roles for aspartates and glutamates for cation permeation in bacterial sodium channels

A key driving force for ion channel selectivity is represented by the negative charge of the Selectivity Filter carried by aspartate (D) and glutamate (E) residues. However, the structural effects and specific properties of D and E residues have not been extensively studied. In order to investigate this issue we studied the mutants of NaChBac channel with all possible combinations of D and E in the charged rings in position 191 and 192. Electrophysiological measurements showed significant Ca²⁺ currents only when position 191 was occupied by E. Equilibrium Molecular Dynamics simulations revealed the existence of two binding sites, corresponding to the charged rings and another one, more internal, at the level of L190. The simulations showed that the ion in the innermost site can interact with the residue in position 191 only when this is glutamate. Based on the MD simulations, we suggest that a D in position 191 leads to a high affinity Ca²⁺ block site resulting from a significant drop in the free energy of binding for an ion moving between the binding sites; in contrast, the free energy change is more gradual when an E residue occupies position 191, resulting in Ca²⁺ permeability. This scenario is consistent with the model of ion channel selectivity through stepwise changes in binding affinity proposed by Dang and McCleskey. Our study also highlights the importance of the structure of the selectivity filter which should contribute to the development of more detailed physical models for ion channel selectivity.

Sodium Binding Sites and Permeation Mechanism in the NaChBac Channel: A Molecular Dynamics Study

NaChBac was the first discovered bacterial sodium voltage-dependent channel, yet computational studies are still limited due to the lack of a crystal structure. In this work, a pore-only construct built using the NavMs template was investigated using unbiased molecular dynamics and metadynamics. The potential of mean force (PMF) from the unbiased run features four minima, three of which correspond to sites IN, CEN, and HFS discovered in NavAb. During the run, the selectivity filter (SF) is spontaneously occupied by two ions, and frequent access of a third one is often observed. In the innermost sites IN and CEN, Na⁺ is fully hydrated by six water molecules and occupies an on-axis position. In site HFS sodium interacts with a glutamate and a serine from the same subunit and is forced to adopt an off-axis placement. Metadynamics simulations biasing one and two ions show an energy barrier in the SF that prevents single-ion permeation. An analysis of the permeation mechanism was performed both computing minimum energy paths in the axial-axial PMF and through a combination of Markov state modeling and transition path theory. Both approaches reveal a knock-on mechanism involving at least two but possibly three ions. The currents predicted from the unbiased simulation using linear response theory are in excellent agreement with single-channel patch-clamp recordings.

Ion selectivity strategies of sodium channel selectivity filters

CONSPECTUS: Sodium ion channels selectively transport Na(+) cations across the cell membrane. These integral parts of the cell machinery are implicated in regulating the cardiac, skeletal and smooth muscle contraction, nerve impulses, salt and water homeostasis, as well as pain and taste perception. Their malfunction often results in various channelopathies of the heart, brain, skeletal muscles, and lung; thus, sodium channels are key drug targets for various disorders including cardiac arrhythmias, heart attack, stroke, migraine, epilepsy, pain, cancer, and autoimmune disorders. The ability of sodium channels to discriminate the native Na(+) among other competing ions in the surrounding fluids is crucial for proper cellular functions. The selectivity filter (SF), the narrowest part of the channel's open pore, lined with amino acid residues that specifically interact with the permeating ion, plays a major role in determining Na(+) selectivity. Different sodium channels have different SFs, which vary in the symmetry, number, charge, arrangement, and chemical type of the metal-ligating groups and pore size: epithelial/degenerin/acid-sensing ion channels have generally trimeric SFs lined with three conserved neutral serines and/or backbone carbonyls; eukaryotic sodium channels have EKEE, EEKE, DKEA, and DEKA SFs with an invariant positively charged lysine from the second or third domain; and bacterial voltage-gated sodium (Nav) channels exhibit symmetrical EEEE SFs, reminiscent of eukaryotic voltage-gated calcium channels. How do these different sodium channel SFs achieve high selectivity for Na(+) over its key rivals, K(+) and Ca(2+)? What factors govern the metal competition in these SFs and which of these factors are exploited to achieve Na(+) selectivity in the different sodium channel SFs? The free energies for replacing K(+) or Ca(2+) bound inside different model SFs with Na(+), evaluated by a combination of density functional theory and continuum dielectric calculations, have shed light on these questions. The SFs of epithelial and eukaryotic Nav channels select Na(+) by providing an optimal number and ligating strength of metal ligands as well as a rigid pore whose size fits the cognate Na(+) ideally. On the other hand, the SFs of bacterial Nav channels select Na(+), as the protein matrix attenuates ion-protein interactions relative to ion-solvent interactions by enlarging the pore and allowing water to enter, so the ion interacts indirectly with the conserved glutamates via bridging water molecules. This shows how these various SFs have adapted to the specific physicochemical properties of the native ion, using different strategies to select Na(+) among its contenders.

Channel-facilitated diffusion boosted by particle binding at the channel entrance

We investigate single-file diffusion of Brownian particles in arrays of closely confining microchannels permeated by a variety of attractive optical potentials and connecting two baths with equal particle concentration. We simultaneously test free diffusion in the channel, diffusion in optical traps coupled in the center of the channel, and diffusion in traps extending into the baths. We found that both classes of attractive optical potentials enhance the translocation rate through the channel with respect to free diffusion. Surprisingly, for the latter class of potentials we measure a 40-fold enhancement in the translocation rate with respect to free diffusion and find a sublinear power law dependence of the translocation rate on the average number of particles in the channel. Our results reveal the function of particle binding at the channel entrances for diffusive transport and open the way to a better understanding of membrane transport and design of synthetic membranes with enhanced diffusion rate.