Permeation Models and Structure-Function Relationships in Ion Channels

Recent determination of the molecular structures of potassium andmechanosensitive channels from x-ray crystallography has led to arenewed interest in ion channels. The challenge for permeation modelsis to understand the functional properties of channels from the availablestructural information. Here we give a critical review of the three maincontenders, namely, continuum theories, Brownian dynamics and moleculardynamics. Continuum theories are shown to be invalid in a narrow channel environment because they ignore the self-energy of ions arising from theinduced charges on the dielectric boundary. Brownian and moleculardynamics are thus the only physically valid methods for studying thestructure-function relations in ion channels. Applications of thesemethods to potassium and calcium channels are presented, which illustratethe multi-ion nature of the permeation mechanism in selective biologicalchannels.     

Physics of Ion Channels

We review the basic physics involved in transport of ions across membrane channels in cells. Electrochemical forces that control the diffusion of ions are discussed both from microscopic and macroscopic perspectives. A case is made for use of Brownian dynamics as the minimal phenomenological model that provides a bridge between experiments and more fundamental theoretical approaches. Application of Brownian and molecular dynamics methods to channels with known molecular structures is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Switching substrate specificity of AMT/MEP/ Rh proteins

In organisms from all kingdoms of life, ammonia and its conjugated ion ammonium are transported across membranes by proteins of the AMT/Rh family. Efficient and successful growth often depends on sufficient ammonium nutrition. The proteins mediating this transport, the so called Ammonium Transporter (AMT) or Rhesus like (Rh) proteins, share a very similar trimeric overall structure and a high sequence similarity even throughout the kingdoms. Even though structural components of the transport mechanism, like an external substrate recruitment site, an essential twin histidine pore motif, a phenylalanine gate and the hydrophobic pore are strongly conserved and have been analyzed in detail by molecular dynamic simulations and mutational studies, the substrate(s), which pass the central pores of the AMT/Rh subunits, NH₄⁺, NH₃ + H⁺, NH₄⁺ + H⁺ or NH₃, are still a matter of debate for most proteins, including the best characterized AmtB protein from Escherichia coli. The lack of a robust expression system for functional analysis has hampered proof of structural and mutational studies, although the NH₃ transport function for Rh-like proteins is rarely disputed. In plant transporters belonging to the subfamily AMT1, transport is associated with electrical currents, while some plant transporters, notably of the AMT2 type, were suggested to transport NH₃ across the membrane, without associated ionic currents. Here we summarize data in favor of each substrate for the distinct AMT/Rh classes, discuss mutants and how they differ in structure and functionality. A common mechanism with deprotonation and subsequent NH₃ transport through the central subunit pore is suggested.     

Switching substrate specificity of AMT/MEP/ Rh proteins

In organisms from all kingdoms of life, ammonia and its conjugated ion ammonium are transported across membranes by proteins of the AMT/Rh family. Efficient and successful growth often depends on sufficient ammonium nutrition. The proteins mediating this transport, the so called Ammonium Transporter (AMT) or Rhesus like (Rh) proteins, share a very similar trimeric overall structure and a high sequence similarity even throughout the kingdoms. Even though structural components of the transport mechanism, like an external substrate recruitment site, an essential twin histidine pore motif, a phenylalanine gate and the hydrophobic pore are strongly conserved and have been analyzed in detail by molecular dynamic simulations and mutational studies, the substrate(s), which pass the central pores of the AMT/Rh subunits, NH₄⁺, NH₃ + H⁺, NH₄⁺ + H⁺ or NH₃, are still a matter of debate for most proteins, including the best characterized AmtB protein from Escherichia coli. The lack of a robust expression system for functional analysis has hampered proof of structural and mutational studies, although the NH₃ transport function for Rh-like proteins is rarely disputed. In plant transporters belonging to the subfamily AMT1, transport is associated with electrical currents, while some plant transporters, notably of the AMT2 type, were suggested to transport NH₃ across the membrane, without associated ionic currents. Here we summarize data in favor of each substrate for the distinct AMT/Rh classes, discuss mutants and how they differ in structure and functionality. A common mechanism with deprotonation and subsequent NH₃ transport through the central subunit pore is suggested.     

On the cyclotron resonance mechanism for magnetic field effects on transmembrane ion conductivity

The cyclotron resonance model, recently proposed to account for physiological response to weak environmental magnetic fields, is shown to violate the laws of classical mechanics. Further, it is argued that the ubiquitous presence of dynamic friction in fluid media precludes significant magnetic effects on membrane ion transport.     

Uphill transport of water by electroosmosis

Summary Lepismatidae are able to gain water from subsaturated atmosphere above a relative humidity of 45%, surmounting a water potential difference of at least 1.1×10⁸ Pa (1,100 bar). This extraordinary task is performed by the monolayered epithelium of the posterior rectum. The particle coat of the folded apical membrane of this epithelium suggests the presence of the electrogenic, lumen-directed cation transport, which is commonly found in insects. Assuming this kind of transport and considering the anatomy of the organ, a working hypothesis for this hyposmotic water transport has been developed: The electrogenic cation transport maintains the circulation of the transported ion species across the apical membrane; the voltagedriven inward current transfers water by electroosmosis against its chemical potential from the extracellular space into the cytoplasm. Voltage and current measurements and synchronous measurements of water flow across the epithelium of the posterior rectum ofLepisma saccharina strongly corroborate this hypothesis. The transepithelial voltage is up to 200 mV (lumen positive); the short-circuit current averages 200 A per cm² of the epithelium. Both depend acutely on oxidative metabolism as does spontaneous water uptake. Exogenous transepithelial current (I) induces, independently of anoxia, a proportional change in volume flow (J _v). The induced flow has the direction of the cation flow. Its mean coupling ratio (J _v/I) is 1.5×10^–9m³/A·sec corresponding to 7 to 8 H₂O per positive unit charge. Critical evaluation of experimental data reveals that water uptake by electroosmosis may quantitatively account forin vivo performance without requiring any unusual assumption.     

Local Control Model of Excitation–Contraction Coupling in Skeletal Muscle

The voltage-activated H⁺ selective conductance of rat alveolar epithelial cells was studied using whole-cell and excised-patch voltage-clamp techniques. The effects of substituting deuterium oxide, D₂O, for water, H₂O, on both the conductance and the pH dependence of gating were explored. D⁺ was able to permeate proton channels, but with a conductance only about 50% that of H⁺. The conductance in D₂O was reduced more than could be accounted for by bulk solvent isotope effects (i.e., the lower mobility of D⁺ than H⁺), suggesting that D⁺ interacts specifically with the channel during permeation. Evidently the H⁺ or D⁺ current is not diffusion limited, and the H⁺ channel does not behave like a water-filled pore. This result indirectly strengthens the hypothesis that H⁺ (or D⁺) and not OH⁻ is the ionic species carrying current. The voltage dependence of H⁺ channel gating characteristically is sensitive to pH_o and pH_i and was regulated by pD_o and pD_i in an analogous manner, shifting 40 mV/U change in the pD gradient. The time constant of H⁺ current activation was about three times slower (τ_act was larger) in D₂O than in H₂O. The size of the isotope effect is consistent with deuterium isotope effects for proton abstraction reactions, suggesting that H⁺ channel activation requires deprotonation of the channel. In contrast, deactivation (τ_tail) was slowed only by a factor ≤1.5 in D₂O. The results are interpreted within the context of a model for the regulation of H⁺ channel gating by mutually exclusive protonation at internal and external sites (Cherny, V.V., V.S. Markin, and T.E. DeCoursey. 1995. J. Gen. Physiol. 105:861–896). Most of the kinetic effects of D₂O can be explained if the pK _a of the external regulatory site is ∼0.5 pH U higher in D₂O.     

β-Barrel topology of Alzheimer's β-amyloid ion channels

Emerging evidence supports the ion channel mechanism for Alzheimer's disease pathophysiology wherein small β-amyloid (Aβ) oligomers insert into the cell membrane, forming toxic ion channels and destabilizing the cellular ionic homeostasis. Solid-state NMR-based data of amyloid oligomers in solution indicate that they consist of a double-layered β-sheets where each monomer folds into β-strand-turn-β-strand and the monomers are stacked atop each other. In the membrane, Aβ peptides are proposed to be β-type structures. Experimental structural data available from atomic force microscopy (AFM) imaging of Aβ oligomers in membranes reveal heterogeneous channel morphologies. Previously, we modeled the channels in a non-tilted organization, parallel with the cross-membrane normal. Here, we modeled a β-barrel-like organization. β-Barrels are common in transmembrane toxin pores, typically consisting of a monomeric chain forming a pore, organized in a single-layered β-sheet with antiparallel β-strands and a right-handed twist. Our explicit solvent molecular dynamics simulations of a range of channel sizes and polymorphic turns and comparisons of these with AFM image dimensions support a β-barrel channel organization. Different from the transmembrane β-barrels where the monomers are folded into a circular β-sheet with antiparallel β-strands stabilized by the connecting loops, these Aβ barrels consist of multimeric chains forming double β-sheets with parallel β-strands, where the strands of each monomer are connected by a turn. Although the Aβ barrels adopt the right-handed β-sheet twist, the barrels still break into heterogeneous, loosely attached subunits, in good agreement with AFM images and previous modeling. The subunits appear mobile, allowing unregulated, hence toxic, ion flux.     

Affinity and location of an internal K+ ion binding site in shaker K channels

We have examined the interaction between TEA and K+ ions in the pore of Shaker potassium channels. We found that the ability of external TEA to antagonize block of Shaker channels by internal TEA depended on internal K+ ions. In contrast, this antagonism was independent of external K+ concentrations between 0.2 and 40 mM. The external TEA antagonism of internal TEA block increased linearly with the concentration of internal K+ ions. In addition, block by external TEA was significantly enhanced by increases in the internal K+ concentration. These results suggested that external TEA ions do not directly antagonize internal TEA, but rather promote increased occupancy of an internal K+ site by inhibiting the emptying of that site to the external side of the pore. We found this mechanism to be quantitatively consistent with the results and revealed an intrinsic affinity of the site for K+ ions near 65 mM located approximately 7% into the membrane electric field from the internal end of the pore. We also found that the voltage dependence of block by internal TEA was influenced by internal K+ ions. The TEA site (at 0 internal K+) appeared to sense approximately 5% of the field from the internal end of the pore (essentially colocalized with the internal K+ site). These results lead to a refined picture of the number and location of ion binding sites at the inner end of the pore in Shaker K channels.     

A simple method for the simulation of steady-state diffusion through membranes: pressure-tuned,boundary-driven molecular dynamics

We present a novel molecular dynamics-based simulation technique for investigating gas transport through membranes. In our simulations, the main control parameters are the partial pressure for the components on the input side of the membrane and the total pressure on the output side. The essential point of our scheme is that this pressure control should be realised by adjusting the particle numbers in the input and output side control cells indirectly. Although this perturbation is applied sufficiently far from the membrane, the bulk-phase properties are well controlled in a simulation cell of common size. Numerical results are given for silicalite-1 membrane with permeating CH₄, CO₂, H₂ and N₂ gases as well as with binary mixtures of CO₂ with the other three components. To describe interactions between particles, we used the simple shifted and cut Lennard–Jones potential with parameters available in the literature. It is expected that the proposed technique can be applied to several other types of membranes and transported fluids in order to support the development of a deeper understanding of separation processes.     

Molecular Basis of Filtering Carbapenems by Porins from β-Lactam-resistant Clinical Strains of Escherichia coli

Integral membrane proteins known as porins are the major pathway by which hydrophilic antibiotics cross the outer membrane of Gram-negative bacteria. Single point mutations in porins can decrease the permeability of an antibiotic, either by reduction of channel size or modification of electrostatics in the channel, and thereby confer clinical resistance. Here, we investigate four mutant OmpC proteins from four different clinical isolates of Escherichia coli obtained sequentially from a single patient during a course of antimicrobial chemotherapy. OmpC porin from the first isolate (OmpC20) undergoes three consecutive and additive substitutions giving rise to OmpC26, OmpC28, and finally OmpC33. The permeability of two zwitterionic carbapenems, imipenem and meropenem, measured using liposome permeation assays and single channel electrophysiology differs significantly between OmpC20 and OmpC33. Molecular dynamic simulations show that the antibiotics must pass through the constriction zone of porins with a specific orientation, where the antibiotic dipole is aligned along the electric field inside the porin. We identify that changes in the vector of the electric field in the mutated porin, OmpC33, create an additional barrier by “trapping” the antibiotic in an unfavorable orientation in the constriction zone that suffers steric hindrance for the reorientation needed for its onward translocation. Identification and understanding the underlying molecular details of such a barrier to translocation will aid in the design of new antibiotics with improved permeation properties in Gram-negative bacteria.