Effects of the protonation state of the EEEE motif of a bacterial Na(+)-channel on conduction and pore structure

Ion channel selectivity through ion-modulated changes of selectivity filter pKa values

In bacterial voltage-gated sodium channels, the passage of ions through the pore is controlled by a selectivity filter (SF) composed of four glutamate residues. The mechanism of selectivity has been the subject of intense research, with suggested mechanisms based on steric effects, and ion-triggered conformational change. Here, we propose an alternative mechanism based on ion-triggered shifts in pKa values of SF glutamates. We study the NavMs channel for which the open channel structure is available. Our free-energy calculations based on molecular dynamics simulations suggest that pKa values of the four glutamates are higher in solution of K+ ions than in solution of Na+ ions. Higher pKa in the presence of K+ stems primarily from the higher population of dunked conformations of the protonated Glu sidechain, which exhibit a higher pKa shift. Since pKa values are close to the physiological pH, this results in predominant population of the fully deprotonated state of glutamates in Na+ solution, while protonated states are predominantly populated in K+ solution. Through molecular dynamics simulations we calculate that the deprotonated state is the most conductive, the singly protonated state is less conductive, and the doubly protonated state has significantly reduced conductance. Thus, we propose that a significant component of selectivity is achieved through ion-triggered shifts in the protonation state, which favors more conductive states for Na+ ions and less conductive states for K+ ions. This mechanism also suggests a strong pH dependence of selectivity, which has been experimentally observed in structurally similar NaChBac channels.

The insights into calcium ion selectivity provided by ancestral prokaryotic ion channels

Prokaryotic channels play an important role in the structural biology of ion channels. At the end of the 20^th century, the first structure of a prokaryotic ion channel was revealed. Subsequently, the reporting of structures of various prokaryotic ion channels have provided fundamental insights into the structure of ion channels of higher organisms. Voltage-dependent Ca²⁺ channels (Cavs) are indispensable for coupling action potentials with Ca²⁺ signaling. Similar to other proteins, Cavs were predicted to have a prokaryotic counterpart; however, it has taken more than 20 years for one to be identified. The homotetrameric channel obtained from Meiothermus ruber generates the calcium ion specific current, so it is named as CavMr. Its selectivity filter contains a smaller number of negatively charged residues than mutant Cavs generated from other prokaryotic channels. CavMr belonged to a different cluster of phylogenetic trees than canonical prokaryotic cation channels. The glycine residue of the CavMr selectivity filter is a determinant for calcium selectivity. This glycine residue is conserved among eukaryotic Cavs, suggesting that there is a universal mechanism for calcium selectivity. A family of homotetrameric channels has also been identified from eukaryotic unicellular algae, and the investigation of these channels can help to understand the mechanism for ion selection that is conserved from prokaryotes to eukaryotes.

Determinants of conductance of a bacterial voltage-gated sodium channel

Through molecular dynamics (MD) and free energy simulations in electric fields, we examine the factors influencing conductance of bacterial voltage-gated sodium channel Na_vMs. The channel utilizes four glutamic acid residues in the selectivity filter (SF). Previously, we have shown, through constant pH and free energy calculations of pKa values, that fully deprotonated, singly protonated, and doubly protonated states are all feasible at physiological pH, depending on how many ions are bound in the SF. With 173 MD simulations of 450 or 500 ns and additional free energy simulations, we determine that the conductance is highest for the deprotonated state and decreases with each additional proton bound. We also determine that the pKa value of the four glutamic residues for the transition between deprotonated and singly protonated states is close to the physiological pH and that there is a small voltage dependence. The pKa value and conductance trends are in agreement with experimental work on bacterial Na_v channels, which show a decrease in maximal conductance with lowering of pH, with pKa in the physiological range. We examine binding sites for Na⁺ in the SF, compare with previous work, and note a dependence on starting structures. We find that narrowing of the gate backbone to values lower than the crystal structure's backbone radius reduces the conductance, whereas increasing the gate radius further does not affect the conductance. Simulations with some amount of negatively charged lipids as opposed to purely neutral lipids increases the conductance, as do simulations at higher voltages.

Physics of Selective Conduction and Point Mutation in Biological Ion Channels

We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutation. We derive an effective grand-canonical ensemble and generalized Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K^{+} channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical.

Application of a Statistical and Linear Response Theory to Multi-Ion Na+ Conduction in NaChBac

Biological ion channels are fundamental to maintaining life. In this manuscript we apply our recently developed statistical and linear response theory to investigate Na+ conduction through the prokaryotic Na+ channel NaChBac. This work is extended theoretically by the derivation of ionic conductivity and current in an electrochemical gradient, thus enabling us to compare to a range of whole-cell data sets performed on this channel. Furthermore, we also compare the magnitudes of the currents and populations at each binding site to previously published single-channel recordings and molecular dynamics simulations respectively. In doing so, we find excellent agreement between theory and data, with predicted energy barriers at each of the four binding sites of ∼4,2.9,3.6, and 4kT.

Changes in Ion Selectivity Following the Asymmetrical Addition of Charge to the Selectivity Filter of Bacterial Sodium Channels

Voltage-gated sodium channels (NaVs) play fundamental roles in eukaryotes, but their exceptional size hinders their structural resolution. Bacterial NaVs are simplified homologues of their eukaryotic counterparts, but their use as models of eukaryotic Na⁺ channels is limited by their homotetrameric structure at odds with the asymmetric Selectivity Filter (SF) of eukaryotic NaVs. This work aims at mimicking the SF of eukaryotic NaVs by engineering radial asymmetry into the SF of bacterial channels. This goal was pursued with two approaches: the co-expression of different monomers of the NaChBac bacterial channel to induce the random assembly of heterotetramers, and the concatenation of four bacterial monomers to form a concatemer that can be targeted by site-specific mutagenesis. Patch-clamp measurements and Molecular Dynamics simulations showed that an additional gating charge in the SF leads to a significant increase in Na⁺ and a modest increase in the Ca²⁺ conductance in the NavMs concatemer in agreement with the behavior of the population of random heterotetramers with the highest proportion of channels with charge -5e. We thus showed that charge, despite being important, is not the only determinant of conduction and selectivity, and we created new tools extending the use of bacterial channels as models of eukaryotic counterparts.

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.

Bases of Bacterial Sodium Channel Selectivity Among Organic Cations

Hille’s (1971) seminal study of organic cation selectivity of eukaryotic voltage-gated sodium channels showed a sharp size cut-off for ion permeation, such that no ion possessing a methyl group was permeant. Using the prokaryotic channel, NaChBac, we found some similarity and two peculiar differences in the selectivity profiles for small polyatomic cations. First, we identified a diverse group of minimally permeant cations for wildtype NaChBac, ranging in sizes from ammonium to guanidinium and tetramethylammonium; and second, for both ammonium and hydrazinium, the charge-conserving selectivity filter mutation (E191D) yielded substantial increases in relative permeability (P_X/P_Na). The relative permeabilities varied inversely with relative K_d calculated from 1D Potential of Mean Force profiles (PMFs) for the single cations traversing the channel. Several of the cations bound more strongly than Na⁺, and hence appear to act as blockers, as well as charge carriers. Consistent with experimental observations, the E191D mutation had little impact on Na⁺ binding to the selectivity filter, but disrupted the binding of ammonium and hydrazinium, consequently facilitating ion permeation across the NaChBac-like filter. We concluded that for prokaryotic sodium channels, a fine balance among filter size, binding affinity, occupancy, and flexibility seems to contribute to observed functional differences.

Molecular Dynamics of Ion Conduction through the Selectivity Filter of the NaVAb Sodium Channel

The determination of the atomic structures of voltage-gated bacterial sodium channels using X-ray crystallography has provided a first view of this family of membrane proteins. Molecular dynamics simulations offer one approach to clarify the underlying mechanism of permeation and selectivity in these channels. However, it appears that the intracellular gate of the pore domain is either closed or only open partially in the available X-ray structures. The lack of structure with a fully open intracellular gate poses a special challenge to computational studies aimed at simulating ion conduction. To circumvent this problem, we simulated a model of the Na_VAb channel in which the transmembrane S5 and S6 helices of the pore domain have been truncated to provide direct open access to the intracellular entryway to the pore. Molecular dynamics simulations were carried out over a range of membrane potential and ion concentration of sodium and potassium. The simulations show that the Na_VAb selectivity filter is essentially a cationic pore supporting the conduction of ions at a rate comparable to aqueous diffusion with no significant selectivity for sodium. Conductance and selectivity vary as a function of ion concentration for both cations. Permeation occurs primarily via a knock-on mechanism for both sodium and potassium, although the ion ordering in single file along the pore is not strictly maintained. The character of the outward current appears quite different from the inward current, with a buildup on ions in the selectivity filter prior to escape toward the extracellular side, indicating the presence of a rectification effect that is overcome by nonphysiological applied voltages.

Role of the Interaction Motif in Maintaining the Open Gate of an Open Sodium Channel

Voltage-gated sodium channels undergo transitions between open, closed, and inactivated states, enabling regulation of the translocation of sodium ions across membranes. A recently published crystal structure of the full-length prokaryotic NavMs crystal structure in the activated open conformation has revealed the presence of a novel motif consisting of an extensive network of salt bridges involving residues in the voltage sensor, S4-S5 linker, pore, and C-terminal domains. This motif has been proposed to be responsible for maintaining an open conformation that enables ion translocation through the channel. In this study, we have used long-time molecular dynamics calculations without artificial restraints to demonstrate that the interaction network of full-length NavMs indeed prevents a rapid collapse and closure of the gate, in marked difference to earlier studies of the pore-only construct in which the gate had to be restrained to remain open. Interestingly, a frequently discussed "hydrophobic gating" mechanism at nanoscopic level is also observed in our simulations, in which the discontinuous water wire close to the gate region leads to an energetic barrier for ion conduction. In addition, we demonstrate the effects of in silico mutations of several of the key residues in the motif on the open channel's stability and functioning, correlating them with existing functional studies on this channel and homologous disease-associated mutations in human sodium channels; we also examine the effects of truncating/removing the voltage sensor and C-terminal domains in maintaining an open gate.

Selective ion permeation involves complexation with carboxylates and lysine in a model human sodium channel

Bacterial and human voltage-gated sodium channels (Navs) exhibit similar cation selectivity, despite their distinct EEEE and DEKA selectivity filter signature sequences. Recent high-resolution structures for bacterial Navs have allowed us to learn about ion conduction mechanisms in these simpler homo-tetrameric channels, but our understanding of the function of their mammalian counterparts remains limited. To probe these conduction mechanisms, a model of the human Nav1.2 channel has been constructed by grafting residues of its selectivity filter and external vestibular region onto the bacterial NavRh channel with atomic-resolution structure. Multi-μs fully atomistic simulations capture long time-scale ion and protein movements associated with the permeation of Na+ and K+ ions, and their differences. We observe a Na+ ion knock-on conduction mechanism facilitated by low energy multi-carboxylate/multi-Na+ complexes, akin to the bacterial channels. These complexes involve both the DEKA and vestibular EEDD rings, acting to draw multiple Na+ into the selectivity filter and promote permeation. When the DEKA ring lysine is protonated, we observe that its ammonium group is actively participating in Na+ permeation, presuming the role of another ion. It participates in the formation of a stable complex involving carboxylates that collectively bind both Na+ and the Lys ammonium group in a high-field strength site, permitting pass-by translocation of Na+. In contrast, multiple K+ ion complexes with the DEKA and EEDD rings are disfavored by up to 8.3 kcal/mol, with the K+-lysine-carboxylate complex non-existent. As a result, lysine acts as an electrostatic plug that partially blocks the flow of K+ ions, which must instead wait for isomerization of lysine downward to clear the path for K+ passage. These distinct mechanisms give us insight into the nature of ion conduction and selectivity in human Nav channels, while uncovering high field strength carboxylate binding complexes that define the more general phenomenon of Na+-selective ion transport in nature.

Bias-Exchange Metadynamics Simulations: An Efficient Strategy for the Analysis of Conduction and Selectivity in Ion Channels

Conduction through ion channels possesses two interesting features: (i) different ionic species are selected with high-selectivity and (ii) ions travel across the channel with rates approaching free-diffusion. Molecular dynamics simulations have the potential to reveal how these processes take place at the atomic level. However, analysis of conduction and selectivity at atomistic detail is still hampered by the short time scales accessible by computer simulations. Several algorithms have been developed to "accelerate" sampling along the slow degrees of freedom of the process under study and thus to probe longer time scales. In these algorithms, the slow degrees of freedom need to be defined in advance, which is a well-known shortcoming. In the particular case of ion conduction, preliminary assumptions about the number and type of ions participating in the permeation process need to be made. In this study, a novel approach for the analysis of conduction and selectivity based on bias-exchange metadynamics simulations was tested. This approach was compared with umbrella sampling simulations, using a model of a Na(+)-selective channel. Analogous conclusions resulted from both techniques, but the computational cost of bias-exchange simulations was lower. In addition, with bias-exchange metadynamics it was possible to calculate free energy profiles in the presence of a variable number and type of permeating ions. This approach might facilitate the definition of the set of collective variables required to analyze conduction and selectivity in ion channels.

Lysine and the Na+/K+ Selectivity in Mammalian Voltage-Gated Sodium Channels

Voltage-gated sodium (Na_v) channels are critical in the generation and transmission of neuronal signals in mammals. The crystal structures of several prokaryotic Na_v channels determined in recent years inspire the mechanistic studies on their selection upon the permeable cations (especially between Na⁺ and K⁺ ions), a property that is proposed to be mainly determined by residues in the selectivity filter. However, the mechanism of cation selection in mammalian Na_v channels lacks direct explanation at atomic level due to the difference in amino acid sequences between mammalian and prokaryotic Na_v homologues, especially at the constriction site where the DEKA motif has been identified to determine the Na⁺/K⁺ selectivity in mammalian Na_v channels but is completely absent in the prokaryotic counterparts. Among the DEKA residues, Lys is of the most importance since its mutation to Arg abolishes the Na⁺/K⁺ selectivity. In this work, we modeled the pore domain of mammalian Na_v channels by mutating the four residues at the constriction site of a prokaryotic Na_v channel (Na_vRh) to DEKA, and then mechanistically investigated the contribution of Lys in cation selection using molecular dynamics simulations. The DERA mutant was generated as a comparison to understand the loss of ion selectivity caused by the K-to-R mutation. Simulations and free energy calculations on the mutants indicate that Lys facilitates Na⁺/K⁺ selection by electrostatically repelling the cation to a highly Na⁺-selective location sandwiched by the carboxylate groups of Asp and Glu at the constriction site. In contrast, the electrostatic repulsion is substantially weakened when Lys is mutated to Arg, because of two intrinsic properties of the Arg side chain: the planar geometric design and the sparse charge distribution of the guanidine group.

Computational Study of Binding of μ-Conotoxin GIIIA to Bacterial Sodium Channels NaVAb and NaVRh

Structures of several voltage-gated sodium (NaV) channels from bacteria have been determined recently, but the same feat might not be achieved for the mammalian counterparts in the near future. Thus, at present, computational studies of the mammalian NaV channels have to be performed using homology models based on the bacterial crystal structures. A successful homology model for the mammalian NaV1.4 channel was recently constructed using the extensive mutation data for binding of μ-conotoxin GIIIA to NaV1.4, which was further validated through studies of binding of other μ-conotoxins and ion permeation. Understanding the similarities and differences between the bacterial and mammalian NaV channels is an important issue, and the NaV1.4-GIIIA system provides a good opportunity for such a comparison. To this end, we study the binding of GIIIA to the bacterial channels NaVAb and NaVRh. The complex structures are obtained using docking and molecular dynamics simulations, and the dissociation of GIIIA is studied through umbrella sampling simulations. The results are compared to those obtained from the NaV1.4-GIIIA system, and the differences in the binding modes arising from the changes in the selectivity filters are highlighted.

Voltage-Gated Sodium Channels: Mechanistic Insights From Atomistic Molecular Dynamics Simulations

The permeation of ions and other molecules across biological membranes is an inherent requirement of all cellular organisms. Ion channels, in particular, are responsible for the conduction of charged species, hence modulating the propagation of electrical signals. Despite the universal physiological implications of this property, the molecular functioning of ion channels remains ambiguous. The combination of atomistic structural data with computational methodologies, such as molecular dynamics (MD) simulations, is now considered routine to investigate structure-function relationships in biological systems. A fuller understanding of conduction, selectivity, and gating, therefore, is steadily emerging due to the applicability of these techniques to ion channels. However, because their structure is known at atomic resolution, studies have consistently been biased toward K(+) channels, thus the molecular determinants of ionic selectivity, activation, and drug blockage in Na(+) channels are often overlooked. The recent increase of available crystallographic data has eminently encouraged the investigation of voltage-gated sodium (NaV) channels via computational methods. Here, we present an overview of simulation studies that have contributed to our understanding of key principles that underlie ionic conduction and selectivity in Na(+) channels, in comparison to the K(+) channel analogs.

Molecular basis of ion permeability in a voltage-gated sodium channel

Voltage‐gated sodium channels are essential for electrical signalling across cell membranes. They exhibit strong selectivities for sodium ions over other cations, enabling the finely tuned cascade of events associated with action potentials. This paper describes the ion permeability characteristics and the crystal structure of a prokaryotic sodium channel, showing for the first time the detailed locations of sodium ions in the selectivity filter of a sodium channel. Electrostatic calculations based on the structure are consistent with the relative cation permeability ratios (Na⁺ ≈ Li⁺ ≫ K⁺, Ca²⁺, Mg²⁺) measured for these channels. In an E178D selectivity filter mutant constructed to have altered ion selectivities, the sodium ion binding site nearest the extracellular side is missing. Unlike potassium ions in potassium channels, the sodium ions in these channels appear to be hydrated and are associated with side chains of the selectivity filter residues, rather than polypeptide backbones.

Mechanism of Ion Permeation in Mammalian Voltage-Gated Sodium Channels

Recent determination of the crystal structures of bacterial voltage-gated sodium (NaV) channels have raised hopes that modeling of the mammalian counterparts could soon be achieved. However, there are substantial differences between the pore domains of the bacterial and mammalian NaV channels, which necessitates careful validation of mammalian homology models constructed from the bacterial NaV structures. Such a validated homology model for the NaV1.4 channel was constructed recently using the extensive mutagenesis data available for binding of μ-conotoxins. Here we use this NaV1.4 model to study the ion permeation mechanism in mammalian NaV channels. Linking of the DEKA residues in the selectivity filter with residues in the neighboring domains is found to be important for keeping the permeation pathway open. Molecular dynamics simulations and potential of mean force calculations reveal that there is a binding site for a Na+ ion just inside the DEKA locus, and 1-2 Na+ ions can occupy the vestibule near the EEDD ring. These sites are separated by a low free energy barrier, suggesting that inward conduction occurs when a Na+ ion in the vestibule goes over the free energy barrier and pushes the Na+ ion in the filter to the intracellular cavity, consistent with the classical knock-on mechanism. The NaV1.4 model also provides a good description of the observed Na+/K+ selectivity.

Theoretical and simulation studies on voltage-gated sodium channels

Voltage-gated sodium (Na_v) channels are indispensable membrane elements for the generation and propagation of electric signals in excitable cells. The successes in the crystallographic studies on prokaryotic Na_v channels in recent years greatly promote the mechanistic investigation of these proteins and their eukaryotic counterparts. In this paper, we mainly review the progress in computational studies, especially the simulation studies, on these proteins in the past years.