Electrostatic basis of valence selectivity in cationic channels

P-Loop Channels: Experimental Structures, and Physics-Based and Neural Networks-Based Models

The superfamily of P-loop channels includes potassium, sodium, and calcium channels, as well as TRP channels and ionotropic glutamate receptors. A rapidly increasing number of crystal and cryo-EM structures have revealed conserved and variable elements of the channel structures. Intriguing differences are seen in transmembrane helices of channels, which may include π-helical bulges. The bulges reorient residues in the helices and thus strongly affect their intersegment contacts and patterns of ligand-sensing residues. Comparison of the experimental structures suggests that some π-bulges are dynamic: they may appear and disappear upon channel gating and ligand binding. The AlphaFold2 models represent a recent breakthrough in the computational prediction of protein structures. We compared some crystal and cryo-EM structures of P-loop channels with respective AlphaFold2 models. Folding of the regions, which are resolved experimentally, is generally similar to that predicted in the AlphaFold2 models. The models also reproduce some subtle but significant differences between various P-loop channels. However, patterns of π-bulges do not necessarily coincide in the experimental and AlphaFold2 structures. Given the importance of dynamic π-bulges, further studies involving experimental and theoretical approaches are necessary to understand the cause of the discrepancy.

Selecting ions by size in a calcium channel: the ryanodine receptor case study

Many calcium channels can distinguish between ions of the same charge but different size. For example, when cations are in direct competition with each other, the ryanodine receptor (RyR) calcium channel preferentially conducts smaller cations such as Li(+) and Na(+) over larger ones such as K(+) and Cs(+). Here, we analyze the physical basis for this preference using a previously established model of RyR permeation and selectivity. Like other calcium channels, RyR has four aspartate residues in its GGGIGDE selectivity filter. These aspartates have their terminal carboxyl group in the pore lumen, which take up much of the available space for permeating ions. We find that small ions are preferred by RyR because they can fit into this crowded environment more easily.

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

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

Computational methods of studying the binding of toxins from venomous animals to biological ion channels: theory and applications

The discovery of new drugs that selectively block or modulate ion channels has great potential to provide new treatments for a host of conditions. One promising avenue revolves around modifying or mimicking certain naturally occurring ion channel modulator toxins. This strategy appears to offer the prospect of designing drugs that are both potent and specific. The use of computational modeling is crucial to this endeavor, as it has the potential to provide lower cost alternatives for exploring the effects of new compounds on ion channels. In addition, computational modeling can provide structural information and theoretical understanding that is not easily derivable from experimental results. In this review, we look at the theory and computational methods that are applicable to the study of ion channel modulators. The first section provides an introduction to various theoretical concepts, including force-fields and the statistical mechanics of binding. We then look at various computational techniques available to the researcher, including molecular dynamics, brownian dynamics, and molecular docking systems. The latter section of the review explores applications of these techniques, concentrating on pore blocker and gating modifier toxins of potassium and sodium channels. After first discussing the structural features of these channels, and their modes of block, we provide an in-depth review of past computational work that has been carried out. Finally, we discuss prospects for future developments in the field.

Na(+)/Ca(2+) selectivity in the bacterial voltage-gated sodium channel NavAb

The recent publication of a number of high resolution bacterial voltage-gated sodium channel structures has opened the door for the mechanisms employed by these channels to distinguish between ions to be elucidated. The way these channels select between Na⁺ and K⁺ has been investigated in computational studies, but the selectivity for Na⁺ over Ca²⁺ has not yet been studied in this way. Here we use molecular dynamics simulations to calculate the energetics of Na⁺ and Ca²⁺ transport through the channel. Single ion profiles show that Ca²⁺ experiences a large barrier midway through the selectivity filter that is not seen by Na⁺. This barrier is caused by the need for Ca²⁺ to partly dehydrate to pass through this region and the lack of compensating interactions with the protein. Multi-ion profiles show that ions can pass each other in the channel, which is why the presence of Ca²⁺ does not block Na⁺ conduction despite binding more strongly in the pore.

Competition among Ca2+, Mg2+, and Na+ for model ion channel selectivity filters: determinants of ion selectivity

Because voltage-gated ion channels play critical biological roles, understanding how they can discriminate the native metal ion from rival cations in the milieu is of great interest. Although Ca(2+), Mg(2+), and Na(+) are present in comparable concentrations outside the cell, the factors governing the competition among these cations for the selectivity filter of voltage-gated Ca(2+) ion channel remain unclear. Using density functional theory combined with continuum dielectric methods, we evaluate the effect of (1) the number, chemical type, and charge of the ligands lining the pore, (2) the pore's rigidity, size, symmetry, and solvent accessibility, and (3) the Ca(2+) hydration number outside the selectivity filter on the competition among Ca(2+), Mg(2+), and Na(+) in model selectivity filters. The calculations show how the outcome of this competition depends on the interplay between electronic and solvation effects. Selectivity for monovalent Na(+) over divalent Ca(2+)/Mg(2+) is achieved when solvation effects outweigh electrostatic effects; thus filters comprising a few weak charge-donating groups such as Ser/Thr side chains, where electrostatic effects are relatively weak and are easily overcome by solvation effects, are Na(+)-selective. In contrast, selectivity for divalent Ca(2+)/Mg(2+) over monovalent Na(+) is achieved when metal-ligand electrostatic effects outweigh solvation effects. The key differences in selectivity between Mg(2+) and Ca(2+) lie in the pore size, oligomericity, and solvent accessibility. The results, which are consistent with available experimental data, reveal how the structure and composition of the ion channel selectivity pore had adapted to the specific physicochemical properties of the native metal ion to enhance the competitiveness of the native metal toward rival cations.

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al.

Solvation free energies of glutamate and its metal complexes: a computer simulation study

Most biological ion channels demonstrate a high degree of selectivity for one type of ion more than others, and in many cases, how they control attaining this is still not clear. So we have studied on some metal ion compounds of glutamate. The Glutamate and its meal ion compounds (Ca(2+), Na(+), K(+) and Li(+)) were first modeled by ab initio calculations and then Monte Carlo simulation was used to calculate solvation free energies and also the complexes free energies for the related structures. The results indicated that Glutamate-Ca(2+) have more stability in water than other metal ion. Also, it was found out that the more movement in ions; less stability of the structure would result. This trend can be seen both in gas and liquid phase.

Protein structure and ionic selectivity in calcium channels: selectivity filter size, not shape, matters

Calcium channels have highly charged selectivity filters (4 COO(-) groups) that attract cations in to balance this charge and minimize free energy, forcing the cations (Na(+) and Ca(2+)) to compete for space in the filter. A reduced model was developed to better understand the mechanism of ion selectivity in calcium channels. The charge/space competition (CSC) mechanism implies that Ca(2+) is more efficient in balancing the charge of the filter because it provides twice the charge as Na(+) while occupying the same space. The CSC mechanism further implies that the main determinant of Ca(2+) versus Na(+) selectivity is the density of charged particles in the selectivity filter, i.e., the volume of the filter (after fixing the number of charged groups in the filter). In this paper we test this hypothesis by changing filter length and/or radius (shape) of the cylindrical selectivity filter of our reduced model. We show that varying volume and shape together has substantially stronger effects than varying shape alone with volume fixed. Our simulations show the importance of depletion zones of ions in determining channel conductance calculated with the integrated Nernst-Planck equation. We show that confining the protein side chains with soft or hard walls does not influence selectivity.

Determinants of K+ vs Na+ selectivity in potassium channels

Ion channels, specialized pore-forming proteins, are an indispensable component of the nervous system and play a crucial role in regulating cardiac, skeletal, and smooth muscle contraction. Potassium ion channels, controlling the action potential of a number of excitable cells, are characterized by a remarkable ability to select K(+) over Na(+). Although the molecular basis for this striking ion selectivity has been a subject of extensive investigations using both experimental and theoretical methods, the following outstanding questions remain: (a) To what extent is the number of water molecules bound to the permeating ion (i.e., the hydration number) important for the K(+)/Na(+) competition? (b) Are the chemical type and number of coordinating groups lining the pore critical for the selectivity process? (c) Apart from providing cation-ligating groups, do the channel walls play any other role in the selectivity process? This work reveals that the pore's selectivity for K(+) over Na(+) increases with (i) increasing hydration number of K(+) relative to that of Na(+), (ii) increasing number of K(+)-coordinating dipoles, (iii) increasing number of Na(+)-coordinating dipoles, and (iv) decreasing magnitude of the coordinating dipoles provided by the pore. Thus, a high K(+)/Na(+) selectivity in K(+) channels could be achieved from a combination of several favorable factors involving the native ion, the metal-coordinating ligands, and the protein matrix, viz., (a) an octahydrated permeating K(+), (b) a pore lined with 8 carbonyl ligands, and (c) finely tuned physicomechanical properties of the channel walls providing a low dielectric medium favoring a high hydration number for the permeating K(+) and enough stiffness to force the competing Na(+) to adopt an unfavorable 8-fold coordination. This implies that optimal K(+)/Na(+) selectivity in K(+) channels generally does not arise from solely structural or energetic consideration. The factors affecting ion selectivity revealed herein help to rationalize why valinomycin and the KcsA ion channels are highly K(+)-selective, whereas the NaK channel is nonselective. The calculations predict that other pores containing a different number/chemical type of coordinating groups from those observed in potassium channels could also select K(+) over Na(+).

Molecular basis for cation selectivity in claudin-2-based paracellular pores: identification of an electrostatic interaction site

Paracellular ion transport in epithelia is mediated by pores formed by members of the claudin family. The degree of selectivity and the molecular mechanism of ion permeation through claudin pores are poorly understood. By expressing a high-conductance claudin isoform, claudin-2, in high-resistance Madin-Darby canine kidney cells under the control of an inducible promoter, we were able to quantitate claudin pore permeability. Claudin-2 pores were found to be narrow, fluid filled, and cation selective. Charge selectivity was mediated by the electrostatic interaction of partially dehydrated permeating cations with a negatively charged site within the pore that is formed by the side chain carboxyl group of aspartate-65. Thus, paracellular pores use intrapore electrostatic binding sites to achieve a high conductance with a high degree of charge selectivity.

The anomalous mole fraction effect in calcium channels: a measure of preferential selectivity

The cause of the anomalous mole fraction effect (AMFE) in calcium-selective ion channels is studied. An AMFE occurs when the conductance through a channel is lower in a mixture of salts than in the pure salts at the same concentration. The textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. Instead of this, we find that at its most basic level an AMFE reflects a channel's preferential binding selectivity for one ion species over another. The AMFE is explained by considering the charged and uncharged regions of the pore as electrical resistors in series: the AMFE is produced by these regions of high and low ion concentration changing differently with mole fraction due to the preferential ion selectivity. This is demonstrated with simulations of a model L-type calcium channel and a mathematical analysis of a simplistic point-charge model. The particle simulations reproduce the experimental data of two L-type channel AMFEs. Conditions under which an AMFE may be found experimentally are discussed. The resistors-in-series model provides a fundamentally different explanation of the AMFE than the traditional theory and does not require single filing, multiple occupancy, or momentum-correlated ion motion.

Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study

A model of the ryanodine receptor (RyR) calcium channel is used to study the energetics of binding selectivity of Ca(2+) versus monovalent cations. RyR is a calcium-selective channel with a DDDD locus in the selectivity filter, similar to the EEEE locus of the L-type calcium channel. While the affinity of RyR for Ca(2+) is in the millimolar range (as opposed to the micromolar range of the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity. A Poisson-Nernst-Planck/density functional theory model of RyR is used to calculate the energetics of selectivity. Ca(2+) versus monovalent selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded volume of ions in the crowded selectivity filter. While electrostatic terms dominate the selectivity, the much smaller excluded-volume term also plays a substantial role. In the D4899N and D4938N mutations of RyR that are analyzed, substantial changes in specific components of the chemical potential profiles are found far from the mutation site. These changes result in the significant reduction of Ca(2+) selectivity found in both theory and experiments.

Effects of exogenous electromagnetic fields on a simplified ion channel model

In this paper, we calculate the effect of an exogenous perturbation (an electromagnetic field [EMF] oscillating in the range of microwave frequencies in the range of 1 GHz) on the flux of two ion species through a cylindrical ion channel, implementing a continuous model, the Poisson-Smoluchowski system of equations, to study the dynamics of charged particle density inside the channel. The method was validated through comparison with Brownian dynamics simulations, supposed to be more accurate but computationally more demanding, obtaining a very good agreement. No EMF effects were observed for low field intensities below the level for thermal effects, as the highly viscous regime and the simplicity of the channel do not exhibit resonance phenomena. For high intensities of the external field (>10(5) V/m), we observed slightly different behavior of ion concentration oscillations and ion currents as a function of EMF orientation with respect to the channel axis.

Volume exclusion in calcium selective channels

Another research group has proposed an interesting model for calcium channel selectivity. However, on the basis of their reported results we find it impossible to assess the merits of their model because their results and claims concerning selectivity are based on an extrapolation over four orders of magnitude to low Ca(2+) concentration. Their results and claims have been presented in several articles and reviews in several journals and, thus, need attention. In this article, we first establish that we obtain results on electrostatics and channel occupancies similar to the high-concentration simulations they present. We then perform grand canonical ensemble simulations that enable us to study micromolar Ca(2+) concentrations. We find that their model channel is only weakly Ca(2+) selective. A crucial problem with their model appears to be the placement of the negatively charged glutamate structural elements in fixed positions inside the protein rather than as flexible units inside the filter.

Ca2+ selectivity of the sarcoplasmic reticulum Ca2+-ATPase at the enzyme-water interface and in the Ca2+ entrance channel

The sarcoplasmic reticulum (SR) Ca(2+)-ATPase, a P-type transmembrane protein, can transport Ca(2+) from the cytoplasmic to the luminal side over other cations specifically. The proposed Ca(2+) entrance channel, composed of the main-chain carbonyl oxygen and side-chain carboxyl oxygen atoms of the amino acids, opens on the enzyme surface, just above the biphospholipid layer membrane-water interface, where Trp residues are frequently found. In this work, the physicochemical nature of Ca(2+) selectivity over Mg(2+) on the surface of the SR Ca(2+)-ATPase has been investigated using the density functional theory (DFT) method. The selection process can be regarded as the first step of the specificity of the enzyme to transport Ca(2+). Subsequently, the specificity of the entrance channel to conduct Ca(2+) over other cations has also been explored. As revealed by thermodynamic analyses, either the aromatic or the aliphatic amino acid residues distributed on the surface of Ca(2+)-ATPase have a bigger affinity to Mg(2+) than to Ca(2+), resulting in a concentration decrease of free Mg(2+) in the local region. Thus, Ca(2+) can transport into the Ca(2+)-entrance channel more easily. Whereafter, for a small quantity of Mg(2+) entering this channel accompanying the Ca(2+) current, the strong electrostatic interactions between Mg(2+) and the ligands will limit the activity of this metal ion, which facilitates the weakly bonded Ca(2+) passing through the channel at a relatively high rate, as suggested by the "sticky-pore" hypothesis. Furthermore, the corresponding theoretical investigations have demonstrated that the increase of the ligand electronegativity can enhance their discrimination between these two cations effectively.

The effect of protein dielectric coefficient on the ionic selectivity of a calcium channel

Calcium-selective ion channels are known to have carboxylate-rich selectivity filters, a common motif that is primarily responsible for their high Ca(2+) affinity. Different Ca(2+) affinities ranging from micromolar (the L-type Ca channel) to millimolar (the ryanodine receptor channel) are closely related to the different physiological functions of these channels. To understand the physical mechanism for this range of affinities given similar amino acids in their selectivity filters, we use grand canonical Monte Carlo simulations to assess the binding of monovalent and divalent ions in the selectivity filter of a model Ca channel. We use a reduced model where the electolyte is modeled by hard-sphere ions embedded in a continuum dielectric solvent, while the interior of protein surrounding the channel is allowed to have a dielectric coefficient different from that of the electrolyte. The induced charges that appear on the protein/lumen interface are calculated by the induced charge computation method [Boda et al., Phys. Rev. E 69, 046702 (2004)]. It is shown that decreasing the dielectric coefficient of the protein attracts more cations into the pore because the protein's carboxyl groups induce negative charges on the dielectric boundary. As the density of the hard-sphere ions increases in the filter, Ca(2+) is absorbed into the filter with higher probability than Na(+) because Ca(2+) provides twice the charge to neutralize the negative charge of the pore (both structural carboxylate oxygens and induced charges) than Na(+) while occupying about the same space (the charge/space competition mechanism). As a result, Ca(2+) affinity is improved an order of magnitude by decreasing the protein dielectric coefficient from 80 to 5. Our results indicate that adjusting the dielectric properties of the protein surrounding the permeation pathway is a possible way for evolution to regulate the Ca(2+) affinity of the common four-carboxylate motif.

Combined effect of pore radius and protein dielectric coefficient on the selectivity of a calcium channel

Calcium-selective ion channels often contain a selectivity filter made of similar amino acids, rich in carboxlylates, although the Ca2+ affinities of these channels range from micromolar to millimolar. To understand the physical mechanism for this range of affinities, we use grand canonical Monte Carlo simulations to study the competition of Na+ and Ca2+ in the selectivity filter of a reduced model of a Ca channel. We show that Ca2+ affinity is increased dramatically when both the volume and dielectric coefficient of the protein are reduced.

Ion conductance vs. pore gating and selectivity in KcsA channel: Modeling achievements and perspectives

KcsA potassium channel belongs to a wide family of allosteric proteins that switch between closed and open states conformations in response to a stimulus, and act as a regulator of cation activity in living cells. The gating mechanism and cation selectivity of such channels have been extensively studied in the literature, with a revival emphasis these latter years, due to the publication of the crystallized structure of KcsA. Despite the increasing number of research and review papers on these topics, quantitative interpretation of these processes at the atomic scale is far from achieved. On the basis of available experimental and theoretical data, and by including our recent results, we review the progresses in this field of activity and discuss the weaknesses that should be corrected. In this spirit, we partition the channel into the filter, cavity, extra and intracellular media, in order to analyze separately the specificity of each region. Special emphasis is brought to the study of an open state for the channel and to the different properties generated by the opening. The influence of water as a structural and dynamical component of the channel properties in closed and open states, as well as in the sequential motions of the cations, is analyzed using molecular dynamics simulations and ab initio calculations. The polarization and charge transfer effects on the ions' dynamics and kinetics are discussed in terms of partial charge models.

Ca2+ selectivity of a chemically modified OmpF with reduced pore volume

We studied an E. coli OmpF mutant (LECE) containing both an EEEE-like locus, typical of Ca(2+) channels, and an accessible and reactive cysteine. After chemical modification with the cysteine-specific, negatively charged (-1e) reagents MTSES or glutathione, this LECE mutant was tested for Ca(2+) versus alkali metal selectivity. Selectivity was measured by conductance and zero-current potential. Conductance measurements showed that glutathione-modified LECE had reduced conductance at Ca(2+) mole fractions <10(-3). MTSES-modified LECE did not. Apparently, the LECE protein is (somehow) a better Ca(2+) chelator after modification with the larger glutathione. Zero-current potential measurements revealed a Ca(2+) versus monovalent cation selectivity that was highest in the presence of Li(+) and lowest in the presence of Cs(+). Our data clearly show that after the binding of Ca(2+) the LECE pore (even with the bulky glutathione present) is spacious enough to allow monovalent cations to pass. Theoretical computations based on density functional theory combined with Poisson-Nernst-Planck theory and a reduced pore model suggest a functional separation of ionic pathways in the pore, one that is specific for small and highly charged ions, and one that accepts preferentially large ions, such as Cs(+).

Probing ion-channel pores one proton at a time

Although membrane proteins often rely on ionizable residues for structure and function, their ionization states under physiological conditions largely elude experimental estimation. To gain insight into the effect of the local microenvironment on the proton affinity of ionizable residues, we have engineered individual lysines, histidines and arginines along the alpha-helical lining of the transmembrane pore of the nicotinic acetylcholine receptor. We can detect individual proton binding-unbinding reactions electrophysiologically at the level of a single proton on a single side chain as brief blocking-unblocking events of the passing cation current. Kinetic analysis of these fluctuations yields the position-dependent rates of proton transfer, from which the corresponding pK(a) values and shifts in pK(a) can be calculated. Here we present a self-consistent, residue-by-residue description of the microenvironment around the pore-lining transmembrane alpha-helices (M2) in the open-channel conformation, in terms of the excess free energy that is required to keep the engineered basic side chains protonated relative to bulk water. A comparison with closed-channel data leads us to propose that the rotation of M2, which is frequently invoked as a hallmark of the gating mechanism of Cys-loop receptors, is minimal, if any.

Understanding ion channel selectivity and gating and their role in cellular signalling

Ion channels play an essential role in the communication between and within cells. Here some of the different ion channel proteins and the roles they perform are introduced, before a discussion of the mechanisms by which they discriminate between different ion types and open and close to allow the passage of ions at the appropriate times.