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.     

Intrinsic electrostatic potential in the BK channel pore: role in determining single channel conductance and block

The internal vestibule of large-conductance Ca(2+) voltage-activated K(+) (BK) channels contains a ring of eight negative charges not present in K(+) channels of lower conductance (Glu386 and Glu389 in hSlo) that modulates channel conductance through an electrostatic mechanism (Brelidze, T.I., X. Niu, and K.L. Magleby. 2003. Proc. Natl. Acad. Sci. USA. 100:9017-9022). In BK channels there are also two acidic amino acid residues in an extracellular loop (Asp326 and Glu329 in hSlo). To determine the electrostatic influence of these charges on channel conductance, we expressed wild-type BK channels and mutants E386N/E389N, D326N, E329Q, and D326N/E329Q channels on Xenopus laevis oocytes, and measured the expressed currents under patch clamp. Contribution of E329 to the conductance is negligible and single channel conductance of D326N/E329Q channels measured at 0 mV in symmetrical 110 mM K(+) was 18% lower than the control. Current-voltage curves displayed weak outward rectification for D326N and the double mutant. The conductance differences between the mutants and wild-type BK were caused by an electrostatic effect since they were enhanced at low K(+) (30 mM) and vanished at high K(+) (1 M K(+)). We determine the electrostatic potential change, Deltaphi, caused by the charge neutralization using TEA(+) block for the extracellular charges and Ba(2+) for intracellular charges. We measured 13 +/- 2 mV for Deltaphi at the TEA(+) site when turning off the extracellular charges, and 17 +/- 2 mV for the Deltaphi at the Ba(2+) site when the intracellular charges were turned off. To understand the electrostatic effect of charge neutralizations, we determined Deltaphi using a BK channel molecular model embedded in a lipid bilayer and solving the Poisson-Boltzmann equation. The model explains the experimental results adequately and, in particular, gives an economical explanation to the differential effect on the conductance of the neutralization of charges D326 and E329.     

Energy barriers for passage of ions through channels. Exact solution of two electrostatic problems

Exact solutions are given to two electrostatic problems relevant to ion permeation through pores in membranes. The first assesses the importance of the pore forming molecule as a dielectric shield. It is shown on the basis of structural and dielectric considerations alone (neglecting effects attributable to possible charge distribution at the interior surface of the pre-former) that the minimum electrostatic barrier for monovalent ion passage through a gramicidin-like channel is 11 kT. It is further shown that given favorable circumstances, dielectric shielding might dramatically reduce the barrier to ion passage through potassium channels. The second problem considers the error introduced by treating ions as point charges. It is shown that for structureless pores the point charge approximation introduces no meaningful error, even if the ratio of ion radius to pore radius is as great as 0.95.     

A model of sodium channels

We have explored the permeation and blockage of ions in sodium channels, relating the channel structure to function using electrostatic profiles and Brownian dynamics simulations. The model used resembles the KcsA potassium channel with an added external vestibule and a shorter selectivity filter. The electrostatic energy landscape seen by permeating ions is determined by solving Poisson's equation. The two charged amino acid rings of Glu-Glu-Asp-Asp (EEDD) and Asp-Glu-Lys-Ala (DEKA) around the selectivity filter region are seen to play a crucial role in making the channel sodium selective, and strongly binding calcium ions such that they block the channel. Our model closely reproduces a range of experimental data including the current-voltage curves, current-concentration curves and blockage of monovalent ions by divalent ions.     

The sliding-helix voltage sensor: mesoscale views of a robust structure–function relationship

The voltage sensor (VS) domain of voltage-gated ion channels underlies the electrical excitability of living cells. We simulate a mesoscale model of the VS domain to determine the functional consequences of some of its physical elements. Our mesoscale model is based on VS charges, linear dielectrics, and whole-body motion, applied to an S4 "sliding helix." The electrostatics under voltage-clamped boundary conditions are solved consistently using a boundary-element method. Based on electrostatic configurational energy, statistical-mechanical expectations of the experimentally observable relation between displaced charge and membrane voltage are predicted. Consequences of the model are investigated for variations of S4 configuration (α- and 3(10)-helical), countercharge alignment with S4 charges, protein polarizability, geometry of the gating canal, screening of S4 charges by the baths, and fixed charges located at the bath interfaces. The sliding-helix VS domain has an inherent electrostatic stability in the explored parameter space: countercharges present in the region of weak dielectric always retain an equivalent S4 charge in that region but allow sliding movements displacing 3-4 e (0). That movement is sensitive to small energy variations (<2?kT) along the path dependent on a number of electrostatic parameters tested in our simulations. These simulations show how the slope of the relation between displaced charge and voltage could be tuned in a channel.     

A model of sodium channels

We have explored the permeation and blockage of ions in sodium channels, relating the channel structure to function using electrostatic profiles and Brownian dynamics simulations. The model used resembles the KcsA potassium channel with an added external vestibule and a shorter selectivity filter. The electrostatic energy landscape seen by permeating ions is determined by solving Poisson's equation. The two charged amino acid rings of Glu-Glu-Asp-Asp (EEDD) and Asp-Glu-Lys-Ala (DEKA) around the selectivity filter region are seen to play a crucial role in making the channel sodium selective, and strongly binding calcium ions such that they block the channel. Our model closely reproduces a range of experimental data including the current-voltage curves, current-concentration curves and blockage of monovalent ions by divalent ions.     

Environment of the gating charges in the Kv1.2 Shaker potassium channel

Recently, the structure of the Shaker channel Kv1.2 has been determined at a 2.9-angstroms resolution. This opens new possibilities in deciphering the mechanism underlying the function of voltage-gated potassium (Kv) channels. Molecular dynamics simulations of the channel, embedded in a membrane environment show that the channel is in its open state and that the gating charges carried by S4 are exposed to the solvent. The hydrated environment of S4 favors a local collapse of the electrostatic potential, which generates high electric-field gradients around the arginine gating charges. Comparison to experiments suggests furthermore that activation of the channel requires mainly a lateral displacement of S4. Overall, the results agree with the transporter model devised for Kv channels from electrophysiology experiments, and provide a possible pathway for the mechanistic response to membrane depolarization.     

Influence of protein flexibility on the electrostatic energy landscape in gramicidin A

We describe an electrostatic model of the gramicidin A channel that allows protein atoms to move in response to the presence of a permeating ion. To do this, molecular dynamics simulations are carried out with a permeating ion at various positions within the channel. Then an ensemble of atomic coordinates taken from the simulations are used to construct energy profiles using macroscopic electrostatic calculations. The energy profiles constructed are compared to experimentally-determined conductance data by inserting them into Brownian dynamics simulations. We find that the energy landscape seen by a permeating ion changes significantly when we allow the protein atoms to move rather than using a rigid protein structure. However, the model developed cannot satisfactorily reproduce all of the experimental data. Thus, even when protein atoms are allowed to move, the dielectric model used in our electrostatic calculations breaks down when modeling the gramicidin channel.     

Conduction through the inward rectifier potassium channel, Kir2.1, is increased by negatively charged extracellular residues

Ion channel conductance can be influenced by electrostatic effects originating from fixed "surface" charges that are remote from the selectivity filter. To explore whether surface charges contribute to the conductance properties of Kir2.1 channels, unitary conductance was measured in cell-attached recordings of Chinese hamster ovary (CHO) cells transfected with Kir2.1 channels over a range of K+ activities (4.6-293.5 mM) using single-channel measurements as well as nonstationary fluctuation analysis for low K+ activities. K+ ion concentrations were shown to equilibrate across the cell membrane in our studies using the voltage-sensitive dye DiBAC4(5). The dependence of gamma on the K+ activity (a(K)) was fit well by a modified Langmuir binding isotherm, with a nonzero intercept as a(K) approaches 0 mM, suggesting electrostatic surface charge effects. Following the addition of 100 mM N-methyl-D-glucamine (NMG+), a nonpermeant, nonblocking cation or following pretreatment with 50 mM trimethyloxonium (TMO), a carboxylic acid esterifying agent, the gamma-a(K) relationship did not show nonzero intercepts, suggesting the presence of surface charges formed by glutamate or aspartate residues. Consistent with surface charges in Kir2.1 channels, the rates of current decay induced by Ba2+ block were slowed with the addition of NMG or TMO. Using a molecular model of Kir2.1 channels, three candidate negatively charged residues were identified near the extracellular mouth of the pore and mutated to cysteine (E125C, D152C, and E153C). E153C channels, but not E125C or D152C channels, showed hyperbolic gamma-a(K) relationships going through the origin. Moreover, the addition of MTSES to restore the negative charges in E53C channels reestablished wild-type conductance properties. Our results demonstrate that E153 contributes to the conductance properties of Kir2.1 channels by acting as a surface charge.     

Ion channels formed by chemical analogs of gramicidin A.

Channel-forming peptides such as gramicidin A offer the opportunity to study the relationship between chemical structure and transport properties of an ion channel. This article summarizes a number of recent experiments with chemical analogs and derivatives of gramicidin A using artificial lipid bilayer membranes. The introduction of negative charges near the channel mouth leads to an increase in the cation transport rate. Hybrid channels consisting of a neutral and a negatively charged or of a positively and a negatively charged half-channel may be formed. The current-voltage characteristic of these hybrid channels exhibits a pronounced asymmetry.Experiments with charged derivatives of gramicidin A have been used in order to distinguish between different structural models of the dimeric channel; these studies strongly support Urry's model of a single-stranded, head-to-head associated helical dimer. In a further set of experiments gramicidin analogs with modified amino acid sequence were studied. It was found that a single substitution (tryptophan replaced by phenylalanine) leads to marked changes in the conductance of the channel. Analogs with a simplified amino acid sequence such as (L-Trp-D-Leu)7-L-Trp or L-Trp-Gly-(L-Trp-D-Leu)6-L-Trp are able to form cation permeable channels with similar properties as gramicidin A.     

Permeation of ions across the potassium channel: brownian dynamics studies

The physical mechanisms underlying the transport of ions across a model potassium channel are described. The shape of the model channel corresponds closely to that deduced from crystallography. From electrostatic calculations, we show that an ion permeating the channel, in the absence of any residual charges, encounters an insurmountable energy barrier arising from induced surface charges. Carbonyl groups along the selectivity filter, helix dipoles near the oval chamber, and mouth dipoles near the channel entrances together transform the energy barrier into a deep energy well. Two ions are attracted to this well, and their presence in the channel permits ions to diffuse across it under the influence of an electric field. Using Brownian dynamics simulations, we determine the magnitude of currents flowing across the channel under various conditions. The conductance increases with increasing dipole strength and reaches its maximum rapidly; a further increase in dipole strength causes a steady decrease in the channel conductance. The current also decreases systematically when the effective dielectric constant of the channel is lowered. The conductance with the optimal choice of dipoles reproduces the experimental value when the dielectric constant of the channel is assumed to be 60. The current-voltage relationship obtained with symmetrical solutions is linear when the applied potential is less than approximately 100 mV but deviates from Ohm's law at a higher applied potential. The reversal potentials obtained with asymmetrical solutions are in agreement with those predicted by the Nernst equation. The conductance exhibits the saturation property observed experimentally. We discuss the implications of these findings for the transport of ions across the potassium channels and membrane channels in general.     

Molecular determinants of electrical rectification of single channel conductance in gap junctions formed by connexins 26 and 32.

The fully open state of heterotypic gap junction channels formed by pairing cells expressing connexin 32 (Cx32) with those expressing connexin 26 (Cx26) rectifies in a way that cannot be predicted from the current-voltage (I-V) relation of either homotypic channel. Using a molecular genetic analysis, we demonstrate that charged amino acids positioned in the amino terminus (M1 and D2) and first extracellular loop (E42) are major determinants of the current-voltage relation of the fully open state of homotypic and heterotypic channels formed by Cx26 and Cx32. The observed I-V relations of wild-type and mutant channels were closely approximated by those obtained with the electrodiffusive model of Chen and Eisenberg (Chen, D., and R. Eisenberg. 1993. Biophys. J. 64:1405-1421), which solves the Poisson-Nernst-Plank equations in one dimension using charge distribution models inferred from the molecular analyses. The rectification of the Cx32/Cx26 heterotypic channel results from the asymmetry in the number and position of charged residues. The model required the incorporation of a partial charge located near the channel surface to approximate the linear I-V relation observed for the Cx32*Cx26E1 homotypic channel. The best candidate amino acid providing this partial charge is the conserved tryptophan residue (W3). Incorporation of the partial charge of residue W3 and the negative charge of the Cx32E41 residue into the charge profile used in the Poisson-Nernst-Plank model of homotypic Cx32 and heterotypic Cx26/Cx32 channels resulted in I-V relations that closely resembled the observed I-V relations of these channels. We further demonstrate that some channel substates rectify. We suggest that the conformational changes associated with transjunctional voltage (V(j))-dependent gating to these substates involves a narrowing of the cytoplasmic entry of the channel that increases the electrostatic effect of charges in the amino terminus. The rectification that is observed in the Cx32/Cx26 heterotypic channel is similar although less steep than that reported for some rectifying electrical synapses. We propose that a similar electrostatic mechanism, which results in rectification through the open and substates of heterotypic channels, is sufficient to explain the properties of steeply rectifying electrical synapses.     

Cytochrome c decelerates channel kinetics of negatively charged gramicidin due to electrostatic interaction

The effect of cytochrome c on the kinetic properties of ion channels formed by O-pyromellitylgramicidin (OPg), the negatively charged analogue of gramicidin A (gA), in bilayer lipid membranes was studied by the method of sensitized photoinactivation. The addition of cytochrome c to both sides of the membrane caused substantial deceleration of the photoinactivation kinetics of OPg channels which expose three negative charges to the aqueous phase at both sides of the membrane. By contrast, the gA photoinactivation kinetics was unaltered by the addition of cytochrome c. Based on the sensitivity of the observed effect to the ionic strength of the bathing solution, the cytochrome c-induced deceleration of the OPg photoinactivation kinetics reflecting the increase in the OPg channel lifetime was ascribed to electrostatic interaction of positive charges of cytochrome c with negative charges of OPg that resulted in channel clustering. Formation of clusters of OPg channels was previously inferred to explain the polylysine effect on the OPg channel kinetics. The decelerating effect of cytochrome c on OPg channels was observed only at a high number of OPg channels in the membrane, thus suggesting that the interaction between cytochrome c and the charged transmembrane protein requires sufficiently high negative charge density on the surface of the membrane.     

Model Hydrophobic Ion Exchange Membrane

Two models of hydrophobic ion exchange membranes were examined theoretically with regard to the characteristics of cellulose acetate-nitrate membranes saturated with hydrophobic solvents. The first model, consisting of fixed negative sites dispersed in a homogeneous medium of low dielectric constant, was shown to be invalid for the experimental membranes. The second model, consisting of fixed negative sites in an aqueous channel surrounded by a medium of low dielectric constant, explains many properties of the cellulose acetate-nitrate hydrophobic membranes and was analyzed in some detail. Organic cations can enter the membranes through the hydrophobic phase as well as through the aqueous channels. The mechanism of counterion movement in such a model is assumed to consist of exchange of vacancies and or double-occupied sites positions. The presence of the medium of low dielectric constant around the aqueous channel increases the “self”-energy of the ions in the channel and the electrostatic interaction between a fixed site and a counterion in the membrane. Both these factors can account for the marked dependence of ion mobility in the aqueous channels on the dielectric constant of the surrounding medium. The model predicts membrane preference for monovalent counterions over divalent ones.     

How do ionic channel properties depend on the structure of polyene antibiotic molecules?

A study has been made of the properties of ionic channels formed in phospholipid-cholesterol bilayers by polyene antibiotics of various molecular structures. Properties of channels created by natural antibiotics with different structures of the lactone ring (amphotericin B-nystatin-mycoheptin) as well as by some derivatives of amphotericin B modified with respect to the amino and carboxyl groups are compared. Neutralization of one or both charges of the amphotericin B molecule (both by chemical modification and by pH shift) increases the probability of the channel to be in a nonconducting state. An increase of cholesterol concentration in the membrane produces an opposite effect. It is assumed that the electrostatic interaction of the amino group of an antibiotic molecule with the carboxyl group of an adjacent one stabilized the channel. Conductance and selectivity of an open channel are not influenced by changes in the charged groups. These properties strongly depend on the structure of the polar chain of the lactone ring. For example, the appearance of one more carbonyl group in the mycoheptin molecule results in a sharply decreasing anion permeability of channels. An antibiotic concentration which is necessary to observe single channels depends on the polyene chain structure: this is about 10(-7) M for tetraene nystatin and 2.10(-8) M for heptaene amphotericin B an mycoheptin.     

Strong electrolyte continuum theory solution for equilibrium profiles, diffusion limitation, and conductance in charged ion channels.

The solution for the ion flux through a membrane channel that incorporates the electrolyte nature of the aqueous solution is a difficult theoretical problem that, until now, has not been properly formulated. The difficulty arises from the complicated electrostatic problem presented by a high dielectric aqueous channel piercing a low dielectric lipid membrane. The problem is greatly simplified by assuming that the ratio of the dielectric constant of the water to that of the lipid is infinite. It is shown that this is a good approximation for most channels of biological interest. This assumption allows one to derive simple analytical expressions for the Born image potential and the potential from a fixed charge in the channel, and it leads to a differential equation for the potential from the background electrolyte. This leads to a rigorous solution for the ion flux or the equilibrium potential based on a combination of the Nernst-Planck equation and strong electrolyte theory (i.e., Gouy-Chapman or Debye-Huckel). This approach is illustrated by solving the system of equations for the specific case of a large channel containing fixed negative charges. The following characteristics of this channels are discussed: anion and mono- and divalent cation conductance, saturation of current with increasing concentration, current-voltage relationship, influence of location and valence of fixed charge, and interaction between ions. The qualitative behavior of this channel is similar to that of the acetylcholine receptor channel.     

Proteins,channels and crowded ions

Ion channels are proteins with a hole down their middle that control a vast range of biological function in health and disease. Selectivity is an important biological function determined by the open channel, which does not change conformation on the biological time scale. The challenge is to predict the function—the current of ions of different types and concentrations through a variety of channels—from structure, given fundamental physical laws. Walls of ion channels, like active sites of enzymes, often contain several fixed charges. Those fixed charges demand counter ions nearby, and the density of those counter ions is very high, greater than 5 molar, because of the tiny volumes of the channel's pore. Physical chemists can now calculate the free energy per mole of salt solutions (e.g. the activity coefficient) from infinite dilution to saturation, even in ionic melts. Such calculations of a model of the L-type calcium channel show that the large energies needed to crowd charges into the channel can account for the substantial selectivity and complex properties found experimentally. The properties of such crowded charge are likely to be an important determinant of the properties of proteins in general because channels are nearly enzymes.     

Molecular design of PhoE porin and its functional consequences

The three-dimensional structure of PhoE porin from Escherichia coli, negatively stained with uranyl acetate, has been determined by electron crystallographic techniques to a resolution of about 18 A. The structure shows that PhoE porin consists of trimeric stain-filled channels as the basic unit. The trimeric channels converge as they transverse the membrane but they do not merge. Our three-dimensional structure of PhoE porin indicates that there is a short, narrower segment of channel, which extends beyond the visible strain-filled portion of the channel. The map of glucose-embedded PhoE porin in projection normal to the membrane has also been determined to a resolution of 6.5 A. The projected map shows trimeric ring-like structures, which are presumably cylindrical domains of beta-sheet. At the 3-fold symmetry axis of the trimer, there is a low density region, which is suggested to be a site of lipopolysaccharide that is required for channel and bacteriophage receptor activities. The structural model of the PhoE monomer consists of a flattened cylinder with a large water-filled vestibule about 35 A long with an elliptically shaped opening that is 27 A along the major axis and 18 A along the minor axis. The vestibule has a narrower extension about 10 A long with an average diameter of about 10 A. The vestibule wall is formed by beta-sheet, which may have a large fraction of the beta-strands oriented normal to membrane. Our structural model provides a clue as to how the surface charges on the outer membrane may regulate the permeation of ionic solutes through the channel.     

Long-pore Electrostatics in Inward-rectifier Potassium Channels

Inward-rectifier potassium (Kir) channels differ from the canonical K⁺ channel structure in that they possess a long extended pore (~85 Å) for ion conduction that reaches deeply into the cytoplasm. This unique structural feature is presumably involved in regulating functional properties specific to Kir channels, such as conductance, rectification block, and ligand-dependent gating. To elucidate the underpinnings of these functional roles, we examine the electrostatics of an ion along this extended pore. Homology models are constructed based on the open-state model of KirBac1.1 for four mammalian Kir channels: Kir1.1/ROMK, Kir2.1/IRK, Kir3.1/GIRK, and Kir6.2/KATP. By solving the Poisson-Boltzmann equation, the electrostatic free energy of a K⁺ ion is determined along each pore, revealing that mammalian Kir channels provide a favorable environment for cations and suggesting the existence of high-density regions in the cytoplasmic domain and cavity. The contribution from the reaction field (the self-energy arising from the dielectric polarization induced by the ion's charge in the complex geometry of the pore) is unfavorable inside the long pore. However, this is well compensated by the electrostatic interaction with the static field arising from the protein charges and shielded by the dielectric surrounding. Decomposition of the static field provides a list of residues that display remarkable correspondence with existing mutagenesis data identifying amino acids that affect conduction and rectification. Many of these residues demonstrate interactions with the ion over long distances, up to 40 Å, suggesting that mutations potentially affect ion or blocker energetics over the entire pore. These results provide a foundation for understanding ion interactions in Kir channels and extend to the study of ion permeation, block, and gating in long, cation-specific pores.