Non-extensitivity and criticality of atomic hydropathicity around a voltage-gated sodium channel’s pore: a modeling study

Voltage-gated sodium channels (NavChs) are pore-forming membrane proteins that regulate the transport of sodium ions through the cell membrane. Understanding the structure and function of NavChs is of major biophysical, as well as clinical, importance given their key role in cellular pathophysiology. In this work, we provide a computational framework for modeling system-size-dependent, i.e., cumulative, atomic properties around a NavCh’s pore. We illustrate our methodologies on the bacterial NavAb channel captured in a closed-pore state where we demonstrate that the atomic environment around its pore exhibits a bi-phasic spatial organization dictated by the structural separation of the pore domains (PDs) from the voltage-sensing domains (VSDs). Accordingly, a mathematical model describing packing of atoms around NavAb’s pore is constructed that allows—under certain conservation conditions—for a power-law approximation of the cumulative hydropathic dipole field effect acting along NavAb’s pore. This verified the non-extensitivity hypothesis for the closed-pore NavAb channel and revealed a long-range hydropathic interactions law regulating atom-packing around the NavAb’s selectivity filter. Our model predicts a PDs-VSDs coupling energy of ∼282.1 kcal/mol corresponding to a global maximum of the atom-packing energy profile. Crucially, we demonstrate for the first time how critical phenomena can emerge in a single-channel structure as a consequence of the non-extensive character of its atomic porous environment.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10867-021-09565-w.     

Indication of an Anal Pore in Gnathostomulida

Two species of Haplognathia (Gnathostomulida, Filospermoidea) were examined by electron microscopy and found to possess a tissue connection between the posterior end of the intestine and the dorsal epidermis. This anal tissue connection is characterized by a thinned out epidermis, interdigitation of epidermal and intestinal cells, and the absence of the basement membrane. An open anal pore was not observed. It is possible that the anal tissue connection of Haplognathia serves as a functional anal pore. The implications of this discovery with respect to the various theories of early Metazoan evolution are discussed.     

Fusion and scission of membranes: Ubiquitous topological transformations in cells

The 2016 Nobel Prizes were awarded to Yoshinori Ohsumi for autophagy and to David Thouless, Duncan Haldane and Michael Kosterlitz for topological transitions. Both of these phenomena are intrinsically related when it comes to membranes. Here, we give a brief account on topological transformations of lipid membranes, commonly known as membrane fusion and membrane scission, and introduce the underlying topological invariant, the genus. The genus of a shape is a useful concept to distinguish unambiguously the processes of membrane fusion/scission and offers a simple method to describe complex, cellular membrane structures, such as fenestrated cristae. We distinguish and highlight the connection between topological transformations of lipid membranes and the recent awards, and point out the extraordinarily large number of topological changes during autophagy.      

Tracking S4 movement by gating pore currents in the bacterial sodium channel NaChBac

Voltage-gated sodium channels mediate the initiation and propagation of action potentials in excitable cells. Transmembrane segment S4 of voltage-gated sodium channels resides in a gating pore where it senses the membrane potential and controls channel gating. Substitution of individual S4 arginine gating charges (R1–R3) with smaller amino acids allows ionic currents to flow through the mutant gating pore, and these gating pore currents are pathogenic in some skeletal muscle periodic paralysis syndromes. The voltage dependence of gating pore currents provides information about the transmembrane position of the gating charges as S4 moves in response to membrane potential. Here we studied gating pore current in mutants of the homotetrameric bacterial sodium channel NaChBac in which individual arginine gating charges were replaced by cysteine. Gating pore current was observed for each mutant channel, but with different voltage-dependent properties. Mutating the first (R1C) or second (R2C) arginine to cysteine resulted in gating pore current at hyperpolarized membrane potentials, where the channels are in resting states, but not at depolarized potentials, where the channels are activated. Conversely, the R3C gating pore is closed at hyperpolarized membrane potentials and opens with channel activation. Negative conditioning pulses revealed time-dependent deactivation of the R3C gating pore at the most hyperpolarized potentials. Our results show sequential voltage dependence of activation of gating pore current from R1 to R3 and support stepwise outward movement of the substituted cysteines through the narrow portion of the gating pore that is sealed by the arginine side chains in the wild-type channel. This pattern of voltage dependence of gating pore current is consistent with a sliding movement of the S4 helix through the gating pore. Through comparison with high-resolution models of the voltage sensor of bacterial sodium channels, these results shed light on the structural basis for pathogenic gating pore currents in periodic paralysis syndromes.     

Structure of the lac carrier protein of Escherichia coli

Circular dichroic measurements on the lac carrier protein purified from the cytoplasmic membrane of Escherichia coli indicate that 85 +/- 5% of the amino acid residues comprising this integral membrane protein are arranged in helical secondary structures. Analysis of the sequential hydropathic character of this protein by the method of Kyte and Doolittle (J. Mol. Biol. (1982) 157, 105-132) indicates that the protein is composed of at least 12 hydrophobic segments with a mean length of 24 +/- 4 residues/segment. Approximately 70% of the 417 amino acids in the lac carrier are found in these domains. The hydropathic profile, together with the circular dichroic measurements, suggest that the 12 hydrophobic segments are largely in a helical conformation. If the segments are assumed to be alpha-helical, the mean length of each domain approximates the thickness of the most hydrophobic portion of the lipid bilayer. Based on these considerations, it is proposed that the lac carrier protein consists of at least 12 alpha-helical segments that traverse the membrane in a perpendicular sense, i.e. in a fashion similar to bacteriorhodopsin.     

Hydrophobic Regions in Myelin Proteins Characterized Through Analysis of "Hydropathic"Profiles

Computer-generated "hydropathic" profiles were constructed for graphic comparison of the amino acid sequences for P2 protein, 18.5 kilodalton (kDa) myelin basic protein (BP), and myelin proteolipid protein (PLP). Profiles were also obtained for cytochrome b5, a membrane protein known to be capable of reversible association with lipid bilayers and of a size comparable to that of the myelin BPs. Analysis of the PLP sequence produced profiles generally compatible with the suggestions that PLP has three transbilayer and two bilayer intercalating segments. Profiles for P2 and 18.5 kDa BP were found to contain hydrophilic segments separated by relatively short hydrophobic regions. Whereas hydropathic indices in hydrophobic regions of P2, 18.5 kDa BP, and PLP fall in the value ranges recently reported for cores of globular proteins and intrabilayer domains of membrane proteins, hydrophobic sections of P2 and 18.5 kDa BP have hydropathic indices similar to those in the hydrophobic core (transprotein) regions of globular proteins. None of them are comparable to the region of cytochrome b5 known to anchor that protein in its membrane or to the segments of PLP sequence proposed as intrabilayer domains. This comparison suggests that neither BP has structural characteristics compatible with insertion into the hydrocarbon core of the myelin lipid bilayer, a conclusion that is consistent with a recently published study that identified the bilayer penetrating proteins of myelin with a hydrophobic probe. The above findings suggest an enhancement for some details of myelin architecture and a cautious approach to interpreting data for BP intercalation into bilayers.     

Ion leakage through transient water pores in protein-free lipid membranes driven by transmembrane ionic charge imbalance

We have employed atomic-scale molecular dynamics simulations to address ion leakage through transient water pores in protein-free phospholipid membranes. Our results for phospholipid membranes in aqueous solution with NaCl and KCl salts show that the formation of transient water pores and the consequent ion leakage can be induced and be driven by a transmembrane ionic charge imbalance, an inherent feature in living cells. These processes take place if the gradient is large enough to develop a sufficiently significant potential difference across the membrane. The transport of cations and anions through the water pores is then seen; it discharges the transmembrane potential, considerably reduces the size of a water pore, and makes the water pore metastable, leading eventually to its sealing. The ion transport is found to be sensitive to the type of ions. It turns out that Na(+) and Cl(-) ions leak through a membrane at approximately the same ratio despite the fact that Na(+) ions are expected to experience a lower potential barrier for the permeation through the pore. This is because of strong interactions of sodium ions with the carbonyl region of a phospholipid membrane as well as with lipid headgroups forming pore "walls," considerably slowing down the permeation of sodium ions. In contrast, we observed a pronounced selectivity of a phospholipid membrane to the permeation of potassium ions as compared to chloride ions: Potassium ions, being larger than sodium ions, interact only weakly with phospholipid headgroups, so that these interactions are not able to compensate for a large difference in free-energy barriers for permeation of K(+) and Cl(-) ions. These findings are found to be robust to a choice of force-field parameters for ions (tested by Gromacs and Charmm force-fields for ions). What is more, a potassium ion is found to be able to permeate a membrane along an alternate, "water-defect-mediated" pathway without actual formation of a pore. The "water-defect-mediated" leakage involves formation of a single water defect only and is found to be at least one order of magnitude faster than the pore-mediated ion leakage.     

Nucleotide sequence of the melB gene and characteristics of deduced amino acid sequence of the melibiose carrier in Escherichia coli

The nucleotide sequence of the melB gene coding for the melibiose carrier in Escherichia coli has been determined. The melibiose carrier is predicted to consist of 469 amino acid residues, resulting in a protein with a molecular weight of 52,029. The predicted carrier protein is highly hydrophobic (70% nonpolar amino acid residues). The hydropathic profile suggests that there are 10 long hydrophobic segments in the primary structure of the carrier protein. Most of them seem to traverse the membrane. Although the hydropathic profile of the melibiose carrier is similar to that of the lactose carrier as a whole, homology in the primary structure between the two carriers is very low. Furthermore, no homology in the nucleotide sequence is found in the structural genes for the two carriers. However, the nucleotide sequences of the intergenic regions are very similar between the melibiose operon and the lactose operon. There is a typical intercistronic regulatory sequence in the 3'-flanking region of the melB as well as in that of the lacY, which suggests the presence of another gene downstream of the melB.     

A Model of Information Carried over a Neuron Soma

A series of cellular automata models of amino acid side chains on a neuron soma membrane have been created to simulate their hydropathic influences on adjacent water molecules. The presence of pathways, referred to as water wires, is identified. These pathways are invoked as passage ways across a neuron soma of proton hopping carrying the information from dendrites to the axon hillock.     

Hydropathic analysis and comparison of KcsA and Shaker potassium channels

The similarity in structure of potassium (K(+)) channels from different families has been revealed by only recently available crystallographic 3D structural data. The hydropathic analysis presented in this work illuminates whether homologous residues perform the same functions in channels that use different gating mechanisms. We calculated and compared the hydropathic profiles of two K(+) channels, KcsA and Kv1.2 (the latter a member of the Shaker family), at their pore-forming domain. Quantitative information describing important interactions stabilizing the protein beyond obvious secondary-structure elements was extracted from the analysis and applied as a template for subsequent molecular-dynamics (MD) analyses. For example, two key groups of interactions, defining the turns that connect the transmembrane helices and responsible for the orientation of the pore helix, were identified. Our results also indicate that Asp(80) and Asp(379) play a similar role in stabilizing the P-loop of KcsA and Kv1.2, respectively, but to significantly different extents.     

Elucidation of the stator organization in the V-ATPase of Neurospora crassa

V-ATPases are membrane protein complexes that pump protons in the lumen of various subcellular compartments at the expense of ATP. Proton pumping is done by a rotary mechanism that requires a static connection between the membrane pumping domain (V(0)) and the extrinsic catalytic head (V(1)). This static connection is composed of several known subunits of the V-ATPase, but their location and topological relationships are still a matter of controversy. Here, we propose a model for the V-ATPase of Neurospora crassa on the basis of single-particle analysis by electron microscopy. Comparison of the resulting map to that of the A-ATPase from Thermus thermophilus allows the positioning of two subunits in the static connecting region that are unique to eukaryotic V-ATPases (C and H). These two subunits seem to be located on opposite sides of a semicircular arrangement of the peripheral connecting elements, suggesting a role in stabilizing the stator in V-ATPases.     

Simplified bacterial "pore" channel provides insight into the assembly, stability, and structure of sodium channels

Eukaryotic sodium channels are important membrane proteins involved in ion permeation, homeostasis, and electrical signaling. They are long, multidomain proteins that do not express well in heterologous systems, and hence, structure/function and biochemical studies on purified sodium channel proteins have been limited. Bacteria produce smaller, homologous tetrameric single domain channels specific for the conductance of sodium ions. They consist of N-terminal voltage sensor and C-terminal pore subdomains. We designed a functional pore-only channel consisting of the final two transmembrane helices, the intervening P-region, and the C-terminal extramembranous region of the sodium channel from the marine bacterium Silicibacter pomeroyi. This sodium "pore" channel forms a tetrameric, folded structure that is capable of supporting sodium flux in phospholipid vesicles. The pore-only channel is more thermally stable than its full-length counterpart, suggesting that the voltage sensor subdomain may destabilize the full-length channel. The pore subdomains can assemble, fold, and function independently from the voltage sensor and exhibit similar ligand-blocking characteristics as the intact channel. The availability of this simple pore-only construct should enable high-level expression for the testing of potential new ligands and enhance our understanding of the structural features that govern sodium selectivity and permeability.     

Binding of the anticonvulsant drug lamotrigine and the neurotoxin batrachotoxin to voltage-gated sodium channels induces conformational changes associated with block and steady-state activation

Voltage-gated sodium channels are dynamic membrane proteins characterized by rapid conformational changes that switch the molecule between closed resting, activated, and inactivated states. Sodium channels are specifically blocked by the anticonvulsant drug lamotrigine, which preferentially binds to the channel pore in the inactivated open state. Batrachotoxin is a lipid-soluble alkaloid that causes steady-state activation and binds in the inner pore of the sodium channel with overlapping but distinct molecular determinants from those of lamotrigine. Using circular dichroism spectroscopy on purified voltage-gated sodium channels from Electrophorus electricus, the secondary structures associated with the mixture of states present at equilibrium in the absence of these ligands were compared with specific stabilized states in their presence. As the channel shifts to open states, there appears to be a significant change in secondary structure to a more alpha-helical conformation. The observed changes are consistent with increased order involving the S6 segments that form the pore, the domain III-IV linker, and the P-loops that form the outer pore and selectivity filter. A molecular model has been constructed for the sodium channel based on its homology with the pore-forming regions of bacterial potassium channels, and automated docking of the crystal structure of lamotrigine with this model produces a structure in which the close contacts of the drug are with the residues previously identified by mutational studies as forming the binding site for this drug.     

Evidence for existence of two acid groups controlling the conductance of sodium channel

The inhibition of the sodium current in nodal membrane at low pH external solutions was studied under voltage clamp conditions. Analysis of the data for membrane potentials from +10 to +150 mV shows that the inhibition of the Na+ currents at high positive potentials cannot be described by a titration curve of a single acid group. The data can be explained on assumption that the conductance of each sodium channel is controlled by two acid groups: one is located within the pore, the other just near the outer mouth of the pore. The affinity of both groups for H+ is estimated.     

Sodium flux ratio in voltage-clamped squid giant axons

The sodium flux ratio across the axolemma of internally perfused, voltage-clamped giant axons of Loligo pealei has been measured at various membrane potentials. The flux ratio exponent obtained from these measurements was about unity and independent of membrane voltage over the 50 mV range from about -20 to l mV. These results, combined with previous measurements of ion permeation through sodium channels, show that the sodium channel behaves like a multi-ion pore with two ion binding sites that are rarely simultaneously occupied by sodium.     

An analysis of conductance changes in squid axon

The membrane of the squid axon is considered on the basis of a pore model in which the distribution of the pore sizes strongly favors K⁺ transfer when there is no potential. Electrical asymmetry causes non-penetrating ions on the membrane capacitor to exert a mechanical force on both membrane surfaces and this force results in a deformation of the membrane pore system such that it assumes a distribution of sizes favoring the ions exerting mechanical force. The ions involved appear to be Ca⁺⁺ on the outside of the membrane and isethionate^-, (i^-) on the inside; as Ca⁺⁺ is equivalent in size to Na⁺, the charged membrane is potentially able to transfer Na⁺, when the ions deforming the membrane pore distribution are removed. A depolarization of the membrane leads to an opening of pores that will allow Na⁺ penetration and a release of the membrane from deformation. The pores revert to the zero-potential pore size distribution hence the Na permeability change is a transient. Calculation shows that the potassium conductance vs. displacement of membrane potential curve for the squid axon and the "inactivation" function, h, can be obtained directly from the assumed membrane distortion without the introduction of arbitrary parameters. The sodium conductance, because it is a transient, requires assumptions about the time constants with which ions unblock pores at the outside and the inside of the membrane.     

Properties of the fusion pore that forms during exocytosis of a mast cell secretory vesicle

During exocytosis, secretory vesicles of mast cells generate a current transient that marks the opening of the fusion pore, the first aqueous connection that forms between the vesicle lumen and the cell exterior. By recording and analyzing such current transients, we have tracked the conductance of the fusion pore over the first millisecond of its existence. The first opening of the pore occurs rapidly, generally within 100 microseconds at 23 degrees C. The electric conductance of the pore is a few hundred picosiemens at first, but gradually increases over the subsequent milliseconds. Evidently the pore opens abruptly and then dilates. The initial conductance of the pore suggests a diameter comparable to that of a large ion channel. From an analysis of "capacitance flicker" we infer that a pore can increase its diameter severalfold and still close again completely. This suggests that several early events in membrane fusion are reversible.     

Ion transport across transmembrane pores

To study the pore-mediated transport of ionic species across a lipid membrane, a series of molecular dynamics simulations have been performed of a dipalmitoyl-phosphatidyl-choline bilayer containing a preformed water pore in the presence of sodium and chloride ions. It is found that the stability of the transient water pores is greatly reduced in the presence of the ions. Specifically, the binding of sodium cations at the lipid/water interface increases the pore line tension, resulting in a destabilization of the pore. However, the application of mechanical stress opposes this effect. The flux of ions through these mechanically stabilized pores has been analyzed. Simulations indicate that the transport of the ions through the pores depends strongly on the size of the water channel. In the presence of small pores (radius <1.5 nm) permeation is slow, with both sodium and chloride permeating at similar rates. In the case in which the pores are larger (radius >1.5 nm), a crossover is observed to a regime where the anion flux is greatly enhanced. Based on these observations, a mechanism for the basal membrane permeability of ions is discussed.     

Effects of arginine density on the membrane-bound structure of a cationic antimicrobial peptide from solid-state NMR

Solid-state NMR spectroscopy is used to determine the membrane-bound topological structure of a cationic β-hairpin antimicrobial peptide in which the number of Arg residues has been halved. The parent peptide, PG-1, was previously found to form transmembrane β-barrels in anionic membranes where the Arg residues complex with the lipid phosphate groups to cause toroidal pore defects in the membrane. In comparison, the charge-attenuated and less active mutant studied here forms β-sheets that lie on the surface of the zwitterionic membrane and only partially insert into the anionic membrane. The mutant also exhibits much looser contact with the lipid headgroups. These results indicate that transmembrane insertion and tight Arg-phosphate association are two important elements for strong antimicrobial activities of this class of peptides. Comparison with other β-hairpin antimicrobial peptides studied so far further suggests a relative potency scale for the various mechanisms of action for the β-sheet family of antimicrobial peptides. The transmembrane insertion-toroidal pore mechanism is the most potent in disrupting the lipid bilayer, followed by the large-amplitude in-plane motional mechanism. The carpet model, where peptides aggregate on the membrane surface to cause lateral expansion and eventual micellization of the membrane, is a weaker mechanism of action.