Electroelastic coupling between membrane surface fluctuations and membrane-embedded charges: continuum multidielectric treatment.

The coupling of electric fields and charges with membrane-water interfacial fluctuations affects membrane electroporation, ionic conductance, and voltage gating. A modified continuum model is introduced to study charge interaction with membrane-water interfacial fluctuations in multidielectric environments. By surrounding a point charge with a low dielectric sphere, the linear Poisson-Boltzmann equation is directly solved by calculating the reaction field potential via a method that eliminates singularity contributions. This allows treatment of charges located at dielectric boundaries. Two complementary mechanisms governing charge-fluctuation interactions are considered: (1) electroelastic deformation (EED), treating the membrane as an elastic slab (smectic bilayer model), and (2) electrohydrophobic solvation (EHS), accounting for water penetration into the membrane's hydrophobic core. EED often leads to large membrane thickness perturbations, far larger than those consistent with elastic model descriptions [M. B. Partenskii, G. V. Miloshevsky, and P. C. Jordan, Isr. J. Chem. 47, 385 (2007)]. We argue that a switch from EED to EHS can be energetically advantageous at intermediate perturbation amplitudes. Both perturbation mechanisms are simulated by introducing adjustable shapes optimized by the kinetic Monte Carlo reaction path following approach [G. V. Miloshevsky and P. C. Jordan, J. Chem. Phys. 122, 214901 (2005)]. The resulting energy profiles agree with those of recent atomistic molecular dynamics studies on translating a charged residue across a lipid bilayer [S. Dorairaj and T. W. Allen, Proc. Natl. Acad. Sci. U.S.A. 104, 4943 (2007)].

Shape-Dependent Global Deformation Modes of Large Protein Structures.

Conformational changes are central to the functioning of pore-forming proteins that open and close their molecular gates in response to external stimuli such as pH, ionic strength, membrane voltage or ligand binding. Normal mode analysis (NMA) is used to identify and characterize the slowest motions in the gA, KcsA, ClC-ec1, LacY and LeuT(Aa) proteins at the onset of gating. Global deformation modes of the essentially cylindrical gA, KcsA, LacY and LeuT(Aa) biomolecules are reminiscent of global twisting, transverse and longitudinal motions in a homogeneous elastic rod. The ClC-ec1 protein executes a splaying motion in the plane perpendicular to the lipid bilayer. These global collective deformations are determined by protein shape. New methods, all-atom Monte Carlo Normal Mode Following and its simplification using a rotation-translation of protein blocks (RTB), are described and applied to gain insight into the nature of gating transitions in gA and KcsA. These studies demonstrate the severe limitations of standard NMA in characterizing the structural rearrangements associated with gating transitions. Comparison of all-atom and RTB transition pathways in gA clearly illustrates the impact of the rigid protein block approximation and the need to include all degrees of freedom and their relaxation in computational studies of protein gating. The effects of atomic level structure, pH, hydrogen bonding and charged residues on the large scale conformational changes associated with gating transitions are discussed.

Antiport mechanism for Cl(-)/H(+) in ClC-ec1 from normal-mode analysis.

ClC chloride channels and transporters play major roles in cellular excitability, epithelial salt transport, volume, pH, and blood pressure regulation. One family member, ClC-ec1 from Escherichia coli, has been structurally resolved crystallographically and subjected to intensive mutagenetic, crystallographic, and electrophysiological studies. It functions as a Cl(-)/H(+) antiporter, not a Cl(-) channel; however, the molecular mechanism for Cl(-)/H(+) exchange is largely unknown. Using all-atom normal-mode analysis to explore possible mechanisms for this antiport, we propose that Cl(-)/H(+) exchange involves a conformational cycle of alternating exposure of Cl(-) and H(+) binding sites of both ClC pores to the two sides of the membrane. Both pores switch simultaneously from facing outward to facing inward, reminiscent of the standard alternating-access mechanism, which may have direct implications for eukaryotic Cl(-)/H(+) transporters and Cl(-) channels.

"Squishy capacitor" model for electrical double layers and the stability of charged interfaces.

Negative capacitance (NC), predicted by various electrical double layer (EDL) theories, is critically reviewed. Physically possible for individual components of the EDL, the compact or diffuse layer, it is strictly prohibited for the whole EDL or for an electrochemical cell with two electrodes. However, NC is allowed for the artificial conditions of sigma control, where an EDL is described by the equilibrium electric response of electrolyte to a field of fixed, and typically uniform, surface charge-density distributions, sigma. The contradiction is only apparent; in fact local sigma cannot be set independently, but is established by the equilibrium response to physically controllable variables, i.e., applied voltage phi (phi control) or total surface charge q (q control). NC predictions in studies based on sigma control signify potential instabilities and phase transitions for physically realizable conditions. Building on our previous study of phi control [M. B. Partenskii and P. C. Jordan, Phys. Rev. E 77, 061117 (2008)], here we analyze critical behavior under q control, clarifying the basic picture using an exactly solvable "squishy capacitor" toy model. We find that phi can change discontinuously in the presence of a lateral transition, specify stability conditions for an electrochemical cell, analyze the origin of the EDL's critical point in terms of compact and diffuse serial contributions, and discuss perspectives and challenges for theoretical studies not limited by sigma control.

Conformational changes in the selectivity filter of the open-state KcsA channel: an energy minimization study.

Potassium channels switch between closed and open conformations and selectively conduct K(+) ions. There are at least two gates. The TM2 bundle at the intracellular site is the primary gate of KcsA, and rearrangements at the selectivity filter (SF) act as the second gate. The SF blocks ion flow via an inactivation process similar to C-type inactivation of voltage-gated K(+) channels. We recently generated the open-state conformation of the KcsA channel. We found no major, possibly inactivating, structural changes in the SF associated with this massive inner-pore rearrangement, which suggests that the gates might act independently. Here we energy-minimize the open state of wild-type and mutant KcsA, validating in silico structures of energy-minimized SFs by comparison with crystallographic structures, and use these data to gain insight into how mutation, ion depletion, and K(+) to Na(+) substitution influence SF conformation. Both E71 or D80 protonations/mutations and the presence/absence of protein-buried water molecule(s) modify the H-bonding network stabilizing the P-loops, spawning numerous SF conformations. We find that the inactivated state corresponds to conformations with a partially unoccupied or an entirely empty SF. These structures, involving modifications in all four P-loops, are stabilized by H-bonds between amide H and carbonyl O atoms from adjacent P-loops, which block ion passage. The inner portions of the P-loops are more rigid than the outer parts. Changes are localized to the outer binding sites, with innermost site S4 persisting in the inactivated state. Strong binding by Na(+) locally contracts the SF around Na(+), releasing ligands that do not participate in Na(+) coordination, and occluding the permeation pathway. K(+) selectivity primarily appears to arise from the inability of the SF to completely dehydrate Na(+) ions due to basic structural differences between liquid water and the "quasi-liquid" SF matrix.

Limitations and strengths of uniformly charged double-layer theory: physical significance of capacitance anomalies.

Theoretical studies of electrical double layers typically consider the response of ionic conductors to the field of uniform charge-density distributions sigma ("sigma -control"). Many such analyses predict apparent anomalies of differential capacitance, C , including divergences and negative values. To clarify misconceptions regarding these predictions, we critically reexamine some theoretical approaches dealing with the admissible sign of C . We examine the anomalies' origin and stress its relation to the artificiality of sigma-control. We show that calculations based on sigma-control can illuminate the nature of instabilities and phase transitions under the physically attainable conditions of potential control, where applied voltage phi rather than sigma is fixed. For illustration, we discuss the physical nature of the "ultimate anomaly," negative integral capacitance predicted by some recent analyses. We also show that sigma-control anomalies can explain some experimentally observed features of C(phi) .

Open-state conformation of the KcsA K+ channel: Monte Carlo normal mode following simulations.

Potassium channels fluctuate between closed and open states. The detailed mechanism of the conformational changes opening the intracellular pore in the K+ channel from Streptomyces lividans (KcsA) is unknown. Applying Monte Carlo normal mode following, we find that gating involves rotation and unwinding of the TM2 bundle, lateral movement of the TM2 helices away from the channel axis, and disappearance of the TM2 bundle. The open-state conformation of KcsA exhibits a very wide inner vestibule, with a radius approximately 5-7 A and inner helices bent at the A98-G99 hinge. Computed conformational changes demonstrate that spin labeling and X-ray experiments illuminate different stages in gating: transition begins with clockwise rotation of the TM2 helices ending at a final state with the TM2 bend hinged near residues A98-G99. The concordance between the computational and experimental results provides atomic-level insights into the structural rearrangements of the channel's inner pore.

The open state gating mechanism of gramicidin a requires relative opposed monomer rotation and simultaneous lateral displacement.

The gating mechanism of the open state of the gramicidin A (gA) channel is studied by using a new Monte Carlo Normal Mode Following (MC-NMF) technique, one applicable even without a target structure. The results demonstrate that the lowest-frequency normal mode (NM) at approximately 6.5 cm(-1) is the crucial mode that initiates dissociation. Perturbing the gA dimer in either direction along this NM leads to opposed, nearly rigid-body rotations of the gA monomers around the central pore axis. Tracking this NM by using the eigenvector-following technique reveals the channel's gating mechanism: dissociation via relative opposed monomer rotation and simultaneous lateral displacement. System evolution along the lowest-frequency eigenvector shows that the large-amplitude motions required for gating (dissociation) are not simple relative rigid-body motions of the monomers. Gating involves coupling intermonomer hydrogen bond breaking, backbone realignment, and relative monomer tilt with complex side chain reorganization at the intermonomer junction.

Permeation and gating in proteins: kinetic Monte Carlo reaction path following.

We present a new Monte Carlo technique, kinetic Monte Carlo reaction path following (kMCRPF), for the computer simulation of permeation and large-scale gating transitions in protein channels. It combines ideas from Metropolis Monte Carlo (MMC) and kinetic Monte Carlo (kMC) algorithms, and is particularly suitable when a reaction coordinate is well defined. Evolution of transition proceeds on the reaction coordinate by small jumps (kMC technique) toward the nearest lowest-energy uphill or downhill states, with the jumps thermally activated (constrained MMC). This approach permits navigation among potential minima on an energy surface, finding the minimum-energy paths and determining their associated free-energy profiles. The methodological and algorithmic strategies underlying the kMCRPF method are described. We have tested it using an analytical model and applied it to study permeation through the curvilinear ClC chloride and aquaporin pores and to gating in the gramicidin A channel. These studies of permeation and gating in real proteins provide extensive procedural tests of the method.

Fifty years of progress in ion channel research.

Fifty years ago, ion channels were but a reasonable hypothesis. I outline some major steps in transforming this idea from a plausible description of the biological assemblies responsible for controlling passive ion transport across membranes to established fact. Important electrophysiological, biochemical, molecular biological, structural, and theoretical tools are discussed in the context of the transition from studying whole cell preparations, containing many channels, to investigating single channel behavior. Six channel families are exemplified: the model peptide, gramicidin, the acetylcholine receptor, and the sodium, potassium, calcium, and chloride channels. Some questions of current interest are posed.

Semimicroscopic modeling of permeation energetics in ion channels.

The semimicroscopic (SMC) approach to modeling the energetics of ion permeation through biological channels provides an alternative perspective to standard molecular dynamics methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization and accounts for electronic polarization by embedding the channel in a milieu that, on average, describes this polarization. Ions, water, and selected peptide moieties are mobile and comprise the reorganizational contribution to dielectric stabilization. The conceptual advantages and limitations of the technique are described. Methodological details are outlined, stressing three convenient electrical geometries. Practical aspects of the SMC procedure are explained, highlighting the areas ripe for further development. Finally, some specific applications are considered.

Water and ion permeation in bAQP1 and GlpF channels: a kinetic Monte Carlo study.

The kinetic Monte Carlo reaction-path-following technique is applied to determine the lowest-energy water pathway and the coordinating amino acids in bAQP1 and GlpF channels, both treated as rigid. In bAQP1, water molecules pass through the pore between the asparagine-proline-alanine (NPA) and selectivity filter (SF) sites one at a time. The water chain is interrupted at the SF where one water forms three stable hydrogen bonds with protein atoms. In this SF, water's conformation depends on the protonation locus of H182. In GlpF, two water molecules bond simultaneously to the NPA asparagines and pass through the SF in zigzag fashion. No water single-file forms in rigid GlpF. To accommodate a single file of waters requires narrowing the GlpF pore. Our results reveal that in both proteins a proposed bipolar water arrangement is thermally disrupted in the NPA region, especially in the cytoplasmic part of the pore. The equilibrium hydrogen-bonded chain is occasionally interrupted in the hydrophobic zones adjacent to the NPA motifs. The permeation of alkali cations through bAQP1 and GlpF is barred due to a large free-energy barrier in the NPA region as well as a large energy barrier blocking entry from the cytoplasm. Permeation of halides is prevented due to two large energy barriers in the cytoplasmic and periplasmic pores as well as a large free-energy barrier barring entry from the periplasm. Our results, based on modeling charge permeation, support an electrostatic rather than orientational basis for proton exclusion. Binding within the aquaporin pore cannot compensate sufficiently for dehydration of the protonic charge; there is also an electrostatic barrier in the NPA region blocking proton transport. The highly ordered single file of waters, which is drastically interrupted at the SF of bAQP1, may also contribute to proton block.

Membrane inclusions as coupled harmonic oscillators: effects due to anisotropic membrane slope relaxation.

Membrane-mediated interaction between membrane-spanning peptides or protein segments plays an important role in their function and stability. Our rigorous "coupled harmonic oscillators" representation is extended to account for the complex boundary conditions permitting anisotropic relaxation of the membrane slope along the contours of the inclusions. Using this representation and applying a highly efficient finite-difference algorithm, we have analyzed the membrane-mediated interaction triggered by deformation of the hydrophobic tails of lipid molecules to match the lipophilic exterior of the inserted peptide. We establish that anisotropic relaxation crucially affects the interaction energy, leading to a short-range attraction between two inclusions, while conventional isotropic boundary conditions result in their strong repulsion. In a multi-inclusion cluster, this attraction is further enhanced and modified due to nonpairwise interactions. The results for dimyristoyl phosphatidylcholine and glyceryl monooleate membranes are compared, and the effects of the inclusion radius are considered. The possible role of slope relaxation in the reported stabilization of linked gramicidin channels and in proteins' functional cooperativity is outlined.

Ionic permeation free energy in gramicidin: a semimicroscopic perspective.

Ion permeation through the gramicidin channel is studied using a model that circumvents two major difficulties inherent to standard simulational methods. It exploits the timescale separation between electronic and structural contributions to dielectric stabilization, accounting for the influence of electronic polarization by embedding the channel in a dielectric milieu that describes this polarization in a mean sense. The explicit mobile moieties are the ion, multipolar waters, and the carbonyls and amides of the peptide backbone. The model treats the influence of aromatic residues and the membrane dipole potential. A new electrical geometry is introduced that treats long-range electrostatics exactly and avoids problems related to periodic boundary conditions. It permits the translocating ion to make a seamless transition from nearby electrolyte to the channel interior. Other degrees of freedom (more distant bulk electrolyte and nonpolar lipid) are treated as dielectric continua. Reasonable permeation free energy profiles are obtained for potassium, rubidium, and cesium; binding wells are shallow and the central barrier is small. Estimated cationic single-channel conductances are smaller than experiment, but only by factors between 2 (rubidium) and 50 (potassium). When applied to chloride the internal barrier is large, with a corresponding miniscule single-channel conductance. The estimated relative single-channel conductances of gramicidin A, B, and C agree well with experiment.

Permeation in ion channels: the interplay of structure and theory.

Combined with high-resolution atomic-level crystal structures of channel forming peptides, theory has become a powerful tool for illuminating factors influencing permeation. Here, advantages and limitations of the more familiar continuum and molecular modeling techniques are briefly outlined. These methods are applied to issues of permeation in two different channel families: gramicidin and K(+) channels. Using structural data, theory provides verifiable atomic-level insights into permeation dynamics, channel conductance and molecular selectivity mechanisms. Not only can theory confirm experimental inference, it can also sometimes provide structural perspectives in advance of experiment.

Anion pathway and potential energy profiles along curvilinear bacterial ClC Cl- pores: electrostatic effects of charged residues.

X-ray structures permit theoretical study of Cl(-) permeation along bacterial ClC Cl(-) pores. We determined the lowest energy curvilinear pathway, identified anion-coordinating amino acids, and calculated the electrostatic potential energy profiles. We find that all four bacterial ClC Cl(-) crystal structures correspond to closed states. E148 and S107 side chains form steric barriers on both sides of the crystal binding site in the StClC wild-type and EcClC wild-type crystals; both the EcClC(E148A) and EcClC(E148Q) mutants are blocked at the S107 site. We studied the effect that mutating the charge of some strongly conserved pore-lining amino acids has on the electrostatic potential energy profiles. When E148 is neutralized, it creates an electrostatic trap, binding the ion near midmembrane. This suggests a possible electrostatic mechanism for controlling anion flow: neutralize E148, displace the side chain of E148 from the pore pathway to relieve the steric barrier, then trap the anion at midmembrane, and finally either deprotonate E148 and block the pore (pore closure) or bring a second Cl(-) into the pore to promote anion flow (pore conductance). Side-chain displacement may arise by competition for the binding site between the oxygens of E148 and the anion moving down the electrostatic energy gradient. We also find that the charge state of E111 and E113 may electrostatically control anion conductance and occupancy of the binding site within the cytoplasmic pore.

Gating gramicidin channels in lipid bilayers: reaction coordinates and the mechanism of dissociation.

The dissociation of gramicidin A (gA) channels into monomers is the simplest example of a channel gating process. The initial steps in this process are studied via a computational model that simulates the reaction coordinate for dimer-monomer dissociation. The nonbonded interaction energy between the monomers is determined, allowing for their free relative translational and rotational motion. Lowest energy pathways and reaction coordinates of the gating process are determined. Partial rupture of the six hydrogen bonds (6HB) at the dimer junction takes place by coupling monomer rotation and lateral displacement. Coupling rotation with axial separation is far more expensive energetically. The transition state for channel dissociation occurs when monomers are displaced laterally by approximately 4-6 A, separated by approximately 1.6-2 A, and rotated by approximately 120 degrees, breaking two hydrogen bonds. In membranes with significant hydrophobic mismatch there is a much greater likelihood of forming 4HB and possibly even 2HB states. In the 4HB state the pore remains fully open and conductive. However, transitions from the 6HB to 4HB and 4HB to 2HB states take place via intermediates in which the gA pore is closed and nonconductive. These lateral monomer displacements give rise to transitory pore occlusion at the dimer junction, which provides a rationale for fast closure events (flickers). Local dynamics of gA monomers also leads to lateral and rotational diffusion of the whole gA dimer, giving rise to diffusional rotation of the dimer about the channel axis.