Reverberation of excitation in neuronal networks interconnected through voltage-gated gap junction channels

We combined Hodgkin–Huxley equations and gating models of gap junction (GJ) channels to simulate the spread of excitation in two-dimensional networks composed of neurons interconnected by voltage-gated GJs. Each GJ channel contains two fast and slow gates, each exhibiting current–voltage (I-V) rectification and gating properties that depend on transjunctional voltage (V_j). The data obtained show how junctional conductance (g_j), which is necessary for synchronization of the neuronal network, depends on its size and the intrinsic firing rate of neurons. A phase shift between action potentials (APs) of neighboring neurons creates bipolar, short-lasting V_j spikes of approximately ±100 mV that induce V_j gating, leading to a small decay of g_j, which can accumulate into larger decays during bursting activity of neurons. We show that I-V rectification of GJs in local regions of the two-dimensional network of neurons can lead to unidirectional AP transfer and consequently to reverberation of excitation. This reverberation can be initiated by a single electrical pulse and terminated by a low-amplitude pulse applied in a specific window of reverberation cycle. Thus, the model accounts for the influence of dynamically modulatable electrical synapses in shaping the function of a neuronal network and the formation of reverberation, which, as proposed earlier, may be important for the development of short-term memory and its consolidation into long-term memory.     

Leak Current Rectification in Myxicola Giant Axons : Constant field and constant conductance components

Early leak current, i.e. for times similar to the time to peak of the transient current was measured in Myxicola giant axons in the presence of tetrodotoxin. The leak current-voltage relation rectifies, showing more current for strong depolarizing pulses than expected from symmetry around the holding potential. A satisfactory practical approximation for most leak corrections is constant resting conductance. The leak current-voltage curve rectifies less than expected from the constant field equation. These curves cannot be reconstructed by summing the constant field currents for sodium and potassium using a P_Na/P_K ratio obtained in the usual way, from zero current constant field fits to resting membrane potential data. Nor can they be reconstructed by summing the constant field current for potassium with that for any other single ion. They can be reconstructed, however, by summing the constant field current for potassium with a constant conductance component. It is concluded that the leak current and the resting membrane potential, therefore, are determined by multiple ionic components, at least three and possibly many. Arguments are presented suggesting that ion permeability ratios obtained in the usual way, by fitting the constant field equation to resting membrane potential data should be viewed with skepticism.     

Effect of Ethanol on the Sodium and Potassium Conductances of the Squid Axon Membrane

The effects of ethanol on squid giant axons were studied by means of the sucrose-gap technique. The membrane action potential height is moderately reduced and the duration sometimes shortened by ethanol in sea water. Voltage clamp experiments showed that ethanol in sea water reduced the maximum membrane conductances for sodium (g'_Na) and potassium (g'_K). In experiments with multiple application of ethyl alcohol to the same spot of membrane, a reduction of g'_Na to 82 per cent and of g'_K to 80 per cent of their value in sea water was brought about by 3 per cent ethanol (by volume) while 6 per cent caused a decrease of g'_Na to 59 per cent and of g'_K to 69 per cent. Ethanol has no significant effect on the steady-state inactivation of g_Na (as a function of conditioning membrane potential) or on such kinetic parameters as τ_h or the time course of turning on gi g_Na and g_K. It is concluded that ethanol mainly reduces g_Na and g_K in the Hodgkin-Huxley terminology.     

Extracellular charge adsorption influences intracellular electrochemical homeostasis in amphibian skeletal muscle

The membrane potential measured by intracellular electrodes, E_m, is the sum of the transmembrane potential difference (E₁) between inner and outer cell membrane surfaces and a smaller potential difference (E₂) between a volume containing fixed charges on or near the outer membrane surface and the bulk extracellular space. This study investigates the influence of E₂ upon transmembrane ion fluxes, and hence cellular electrochemical homeostasis, using an integrative approach that combines computational and experimental methods. First, analytic equations were developed to calculate the influence of charges constrained within a three-dimensional glycocalyceal matrix enveloping the cell membrane outer surface upon local electrical potentials and ion concentrations. Electron microscopy confirmed predictions of these equations that extracellular charge adsorption influences glycocalyceal volume. Second, the novel analytic glycocalyx formulation was incorporated into the charge-difference cellular model of Fraser and Huang to simulate the influence of extracellular fixed charges upon intracellular ionic homeostasis. Experimental measurements of E_m supported the resulting predictions that an increased magnitude of extracellular fixed charge increases net transmembrane ionic leak currents, resulting in either a compensatory increase in Na⁺/K⁺-ATPase activity, or, in cells with reduced Na⁺/K⁺-ATPase activity, a partial dissipation of transmembrane ionic gradients and depolarization of E_m.     

Conditions of appearance of local response and action potential in a simple mathematical model of nerve

A simple mathematical model of a nerve fibre is proposed. According to the model the current-voltage relation for the peak Na-current is represented as a broken line. It is shown that within the potential range, where the differential (slope) Na-conductance isnegative but its absolutevalue is smaller than the membrane conductance, the fibre gives a subthreshold local response. Within the range, where differential Na-conductance is negative and has absolute value larger than the membrane conductance, the action potential arises, the rise being independent on the strength of the stimulus and conditioned only by the membrane parameters. A simple formula is obtained which describes the relation between the strength of the threshold stimulus, I, and its duration, t₀. There are two parameters in this formula, which can be measured independently: the time constant of the membrane and the lag-period in the Na-current. Insertion of these parameters into the formula allows one to construct a theoretical I-t₀ curve in good agreement with experiment.     

Associative learning in a network model of Hermissenda crassicornis

A time-varying Resistance-Capacitance (RC) circuit computer model was constructed based on known membrane and synaptic properties of the visualvestibular network of the marine snail Hermissenda crassicornis. Specific biophysical properties and synaptic connections of identified neurons are represented as lumped parameters (circuit elements) in the model; in the computer simulation, differential equations are approximated by difference equations. The model's output, membrane potential, an indirect measure of firing frequency, closely parallels the behavioral and electrophysiologic outputs of Hermissenda in response to the same input stimuli presented during and after associative learning. The parallelism of the computer modeled and the biologic outputs suggests that the model captures the features necessary and sufficient for associative learning.     

Application of the Hodgkin-Huxley equations to an electric field model for interaction between excitable cells

We previously described a model for the electrical transfer of excitation from one cell to the next which utilized the electric potential generated in the junctional cleft between the cells. Low-resistance connections between the cells were not used in the model, and it was assumed that the junctional membranes were excitable. This model was analyzed for the static case without capacitances and for the dynamic case in which capacitances were part of the circuit elements. For simplicity, the Na⁺ resistance (R_Na), after a threshold potential was exceeded, was allowed to decrease exponentially (to 1% of its initial value) within 0·25–1·0 ms, and possible changes in the K⁺ resistance were ignored. In this paper, we have incorporated the Hodgkin-Huxley equations into the operation of the lumped membrane units for the electrical equivalent circuit of the cell membrane. The parameters varied are the membrane capacitances, resistances, maximum Na⁺ conductance ($\text{g}{}_{\mathrm{<mtext>Na</mtext>}}$), and the radial cleft resistance (R_jc). We demonstrated that our model worked very well, i.e. the successful transfer of action potentials was achieved, with the membrane units following Hodgkin-Huxley dynamics for changes in g_Na and g_K. The calculations indicate that transmission is facilitated when the junctional units have a higher $\text{g}{}_{\mathrm{<mtext>Na</mtext>}}$ and a lower capacitance and when R_jc is elevated. Lowering the resistance of the junctional membrane units several fold, relative to the surface membrane units, also facilitated transmission; however, the absolute resistance of the junctional membrane was still well above the maximum value that would allow sufficient local-circuit current to flow to effect transmission. Thus, the electric field model provides an alternative means of cell-to-cell propagation between myocardial cells which is electrical in nature but does not require the presence of low-resistance connections between cells.     

A modified cable formalism for modeling neuronal membranes at high frequencies

Intracellular recordings of cortical neurons in vivo display intense subthreshold membrane potential (V_m) activity. The power spectral density of the V_m displays a power-law structure at high frequencies (>50 Hz) with a slope of ∼−2.5. This type of frequency scaling cannot be accounted for by traditional models, as either single-compartment models or models based on reconstructed cell morphologies display a frequency scaling with a slope close to −4. This slope is due to the fact that the membrane resistance is short-circuited by the capacitance for high frequencies, a situation which may not be realistic. Here, we integrate nonideal capacitors in cable equations to reflect the fact that the capacitance cannot be charged instantaneously. We show that the resulting nonideal cable model can be solved analytically using Fourier transforms. Numerical simulations using a ball-and-stick model yield membrane potential activity with similar frequency scaling as in the experiments. We also discuss the consequences of using nonideal capacitors on other cellular properties such as the transmission of high frequencies, which is boosted in nonideal cables, or voltage attenuation in dendrites. These results suggest that cable equations based on nonideal capacitors should be used to capture the behavior of neuronal membranes at high frequencies.     

Thermodynamic resolution of the iron-sulfur centers of the succinic dehydrogenase of Rhodopseudomonas sphaeroides.

A single alkaline wash removes most of the succinic dehydrogenase activity from chromatophores of Rhodopseudomonas sphaeroides. Three iron-sulfur centers are also removed by this washing. Two of these are ferredoxin-like centers with electron paramagnetic resonance signals at g_v = 1.94 and midpoint potentials of +50 and ?250 mV at pH 7. The third is a high-potential iron-sulfur protein type signal centered at g 2.01 and a midpoint potential of +80 mV at pH 7. These centers have very similar properties to those of the well-characterized mammalian succinic dehydrogenase and account for the majority of iron-sulfur centers observed in chromatophores. Because it is so easily removed, it is concluded that succinic dehydrogenase is located on the outer surface of the chromatophore membrane, a conclusion supported by the fact that removal of the enzyme does not interfere with the kinetics of light-induced electron flow, nor does it allow cytochrome c₂ to escape from inside the chromatophore vesicles.     

A theoretical approach to cluster formation in biological membranes

A theoretical analysis of cluster formation within the lipid matrix of biological membranes is presented. Various models are analysed: (a) one-dimensional monolayer, (b) two-dimensional monolayer and (c) one dimensional bilayer. Furthermore, lipid-protein interactions are considered. The model is based on differential equations for the probabilities a_i and b₁ which characterize the occupation of the lattice site i by the lipids A and B, respectively. These differential equations are an approximation of the Master-equation. Steady states as well as time-dependent variations are analysed. Depending on the interaction energies of the two lipids, different stationary lipid distributions are obtained, including clusters of lipids A or B and alternating structures. The distributions may be dynamically stable or unstable. It is shown that phase transitions within the lipid matrix may be induced by alteration of the composition of the membrane, by changing the interaction energies of the lipids, by variation of the temperature or by lipid-protein interactions. The transitions between different stationary distributions are studied by use of bifurcation diagrams. The analysis of time-dependent states reveals that unstable structures of the membrane may be important for certain time periods. Consideration of the lipid bilayer leads to a great number of possible distributions, which may be symmetric or asymmetric with respect to the outer and inner leaflets of the membrane.     

Studies of the orientation of the mitochondrial redox carriers III. Orientation of the gx and gy axes of the hemes of cytochrome oxidase with respect to the plane of the membrane in oriented membrane multilayers

The EPR absorption properties of the hemes of cytochrome oxidase and their liganded derivatives were examined in oriented multilayers from isolated oxidase, mitochondrial membranes and membrane fragments of a bacterium, Paracoccus denitrificans. The hemes of the oxidase in all the systems investigated were oriented normal to the plane of the multilayers. The directions of the g signals corresponding to the g_x and g_y axes of the g tensor were found to be different in low-spin ferric heme in fully oxidized oxidase and in half-reduced liganded oxidase. It is suggested that this different orientation of g_x and g_y in fully oxidized oxidase and half-reduced liganded oxidase arises because the respective EPR signals belong to two different hemes, those of cytochrome a and a₃.     

Identification of a g equals 1.90 high-potential iron-sulfur protein in chloroplasts.

A new bound iron-sulfur protein has been identified in spinach chloroplasts. In the reduced form, this protein has an electron paramagnetic resonance spectrum at 20°K with g-values of 2.02 and 1.90. The midpoint oxidation-reduction potential (E_m) of the protein, which is pH-independent, is +290 mV. These properties are similar to those of the “Rieske” g = 1.90 iron-sulfur protein of mitochondrial Complex III.     

Melatonin Alters Fluid Phase Coexistence in POPC/DPPC/Cholesterol Membranes

The structure and biophysical properties of lipid membranes are important for cellular functions in health and disease. In Alzheimer’s disease, the neuronal membrane is a target for toxic amyloid-β (Aβ). Melatonin is an important pineal gland hormone that has been shown to protect against Aβ toxicity in cellular and animal studies, but the molecular mechanism of this protection is not fully understood. Melatonin is a small membrane-active molecule that has been shown to interact with model lipid membranes and alter the membrane biophysical properties, such as membrane molecular order and dynamics. This effect of melatonin has been previously studied in simple model bilayers with one or two lipid components. To make it more relevant to neuronal membranes, we used a more complex ternary lipid mixture as our membrane model. In this study, we used ²H-NMR to investigate the effect of melatonin on the phase behavior of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), and cholesterol lipid membranes. We used deuterium-labeled POPC-d₃₁ and DPPC-d₆₂,separately to probe the changes in hydrocarbon chain order as a function of temperature and melatonin concentration. We find that POPC/DPPC/cholesterol at molar proportions of 3:3:2 is close to liquid-disordered/liquid-ordered phase separation and that melatonin can induce phase separation in these ternary mixtures by preferentially incorporating into the disordered phase and increasing its level of disorder. At 5 mol% melatonin, we observed phase separation in samples with POPC-d₃₁, but not with DPPC-d₆₂, whereas at 10 mol% melatonin, phase separation was observed in both samples with either POPC-d₃₁ or DPPC-d₆₂. These results indicate that melatonin can have a strong effect on membrane structure and physical properties, which may provide some clues to understanding how melatonin protects against Aβ, and that choice of chain perdeuteration is an important consideration from a technical point of view.     

The Effects of Several Alcohols on the Properties of the Squid Giant Axon

The effects of several alcohols on the resting potential, action potential, and voltage-clamp currents of the squid giant axon have been measured. All the alcohols employed are similar in that they depress maximum sodium conductance much more than maximum potassium conductance. Octyl alcohol differs from the others (C₂ through C₅) in that it has less tendency to depolarize the axon. Depolarization is always accompanied by a decrease of g_K near the resting potential, such that the ratio g_K/g_leak is decreased. Steady-state inactivation of the sodium ion current is unaffected by alcohols, as is membrane capacity. Resting membrane conductance is usually decreased by alcohols. The findings are discussed in relation to work on monomolecular films.     

Filamin A Promotes Dynamin-dependent Internalization of Hyperpolarization-activated Cyclic Nucleotide-gated Type 1 (HCN1) Channels and Restricts Ih in Hippocampal Neurons

The actin-binding protein filamin A (FLNa) regulates neuronal migration during development, yet its roles in the mature brain remain largely obscure. Here, we probed the effects of FLNa on the regulation of ion channels that influence neuronal properties. We focused on the HCN1 channels that conduct I_h, a hyperpolarization-activated current crucial for shaping intrinsic neuronal properties. Whereas regulation of HCN1 channels by FLNa has been observed in melanoma cell lines, its physiological relevance to neuronal function and the underlying cellular pathways that govern this regulation remain unknown. Using a combination of mutational, pharmacological, and imaging approaches, we find here that FLNa facilitates a selective and reversible dynamin-dependent internalization of HCN1 channels in HEK293 cells. This internalization is accompanied by a redistribution of HCN1 channels on the cell surface, by accumulation of the channels in endosomal compartments, and by reduced I_h density. In hippocampal neurons, expression of a truncated dominant-negative FLNa enhances the expression of native HCN1. Furthermore, acute abrogation of HCN1-FLNa interaction in neurons, with the use of decoy peptides that mimic the FLNa-binding domain of HCN1, abolishes the punctate distribution of HCN1 channels in neuronal cell bodies, augments endogenous I_h, and enhances the rebound-response (“voltage-sag”) of the neuronal membrane to transient hyperpolarizing events. Together, these results support a major function of FLNa in modulating ion channel abundance and membrane trafficking in neurons, thereby shaping their biophysical properties and function.     

Analysis of the electron paramagnetic resonance spectrum of the cobalamin intermediate in ribonucleotide reduction

EPR absorption-derivative lineshapes have been computed and least-squares fitted to the spectrum of the intermediate derived from 5'-deoxy-5'-adenosyl-cobalamin in the ribonucleotide reductase reaction. A Gausian-type intrinsic lineshape was assumed and the effects of inhomogenous broadening, rotation of coordinate axes of the A-tensor relative to the g-tensor, angular dependence of transition probability and ligand hyperfine splitting have also been investigated.When the overall spectrum was computed as the sum of the linshapes corresponding to two distinct Co(II) species, A and B, each having rhombic asymmetry, the least squares procedure converged to a much better fit than with a single species, and matched almost all of the features of the experimental spectrum.The magnetic properties of A and B were compared with those of a series of other Co(II) complexes by a plot of g_|?g₆ versus ∥A₆∥?∥A_|∥. The results eliminate cobalt with 5-coordination to nitrogen for A and B, suggest low-spin cobalt complexes having strongly distorted 6-fold coordination. The possibility that the sixth, symmetry-decreasing ligand is the oxygen molecule is excluded by the chemistry of the system and by the EPR properties of previously reported cob(II)alamins. It is suggested that the sixth ligand is carbonyl, amide or sulfhydryl group of an enzyme sidechain which is inserted off-axis into the coordination position so as to exert the observed symmetry-lowering effect.     

Multiple equilibria and exotic behaviour in excitable membranes

The excitation equation for an excitable membrane dV/dt=F(V) may have multiple equilibria where F(V)=0, and these may be stable or unstable. We demonstrate multiple equilibria in the Hodgkin-Huxley equations when either g_K or [Ca²⁺]₀ is lowered in the presence of a hyperpolarising current density. Under these conditions molluscan somata exhibit exotic behaviours-endogenous paroxysmal depolarising shifts and complex multiple spikes reminiscent of the normal complex activity of some mammalian central neurones. Complex discharge waveforms can be an expression of membrane (differential) properties, rather than electrotonic, geometric (partial differential) behaviour.     

Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents

Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and their interactions in shaping the properties of impedance amplitude and phase in linearized biophysical models and demonstrate this approach in a two-dimensional linear model with two effective conductances g _L and g ₁. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g _L ???g ₁ parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g ₁ increases while the overall impedance is decreased, and an increase in the maximal impedance, without any change in the input resistance, as the ionic current time constant increases. We use the attribute diagrams to analyze resonance and phase of the linearization of two biophysical models that include resonant (I _h or slow potassium) and amplifying currents (persistent sodium). In the absence of amplifying currents, the two models behave similarly as the conductances of the resonant currents is increased whereas, with the amplifying current present, the two models have qualitatively opposite responses. This work provides a general method for decoding the effect of biophysical parameters on linear membrane resonance and phase by tracking trajectories, parametrized by the relevant biophysical parameter, in pre-constructed attribute diagrams.     

Formation of cristae and crista junctions in mitochondria depends on antagonism between Fcj1 and Su e/g

Crista junctions (CJs) are important for mitochondrial organization and function, but the molecular basis of their formation and architecture is obscure. We have identified and characterized a mitochondrial membrane protein in yeast, Fcj1 (formation of CJ protein 1), which is specifically enriched in CJs. Cells lacking Fcj1 lack CJs, exhibit concentric stacks of inner membrane in the mitochondrial matrix, and show increased levels of F₁F_O–ATP synthase (F₁F_O) supercomplexes. Overexpression of Fcj1 leads to increased CJ formation, branching of cristae, enlargement of CJ diameter, and reduced levels of F₁F_O supercomplexes. Impairment of F₁F_O oligomer formation by deletion of its subunits e/g (Su e/g) causes CJ diameter enlargement and reduction of cristae tip numbers and promotes cristae branching. Fcj1 and Su e/g genetically interact. We propose a model in which the antagonism between Fcj1 and Su e/g locally modulates the F₁F_O oligomeric state, thereby controlling membrane curvature of cristae to generate CJs and cristae tips.