Voltage-dependent Rate Constants Research Articles

Kinetic Analysis of the Effect of Charge Neutralization on Single-Molecule Electro-Diffusion between Two Energy Minima in a Protein Pore

The conductance of the pore formed by the bacterial toxin aerolysin shows complex modulation in the presence of a single blocking molecule, such as an oligonucleotide or a peptide, that can be attributed to the stochastic oscillation of the analyte molecule between two energy minima inside the pore. For adenine oligonucleotides, the statistics of these oscillations conform with a simple kinetic model where these minima are linked by voltage-dependent rate constants and correspond to two binding sites arranged sequentially along the pore's transmembrane axis.

Channel noise effects on neural synchronization

Synchronization in neural networks is believed to be linked to cognitive processes, while abnormal synchronization has been associated with disorders such as epilepsy and schizophrenia. We examine the synchronization of small Hodgkin–Huxley neuronal networks. The principal features of Hodgkin–Huxley neurons are protein channels in the neural membrane that transition between open and closed states with voltage dependent rate constants. The standard assumption of infinitely many channels neglects the fact that real neurons have finitely many channels, which leads to fluctuations in the membrane voltage and modifies neuronal spike times. These fluctuations are referred to as channel noise. We demonstrate that regardless of channel noise magnitude, neurons in the network reach a steady state synchronization level dependent only on the number of neurons in the network, equivalent to the steady state level of uncoupled Poisson neurons. The channel noise only affects the time to reach the steady state synchronization level.

A Microscopic Capacitor Model of Voltage Coupling in Membrane Proteins: Gating Charge Fluctuations in Ci-VSD

The voltage sensitivity of membrane proteins is reflected in the response of the voltage sensing domains (VSDs) to the changes in membrane potential. This response is implicated in the displacement of positively charged residues, associated with the conformational changes of VSDs. The displaced charges generate nonlinear (i.e., voltage-dependent) capacitance current called the gating current (and its corresponding gating charge), which is a key experimental quantity that characterizes voltage activation in VSMP. However, the relevant theoretical/computational approaches, aimed to correlate the structural information on VSMP to electrophysiological measurements, have been rather limited, posing a broad challenge in computer simulations of VSMP. Concomitant with the development of our coarse-graining (CG) model of voltage coupling, we apply our theoretical framework for the treatments of voltage effects in membrane proteins to modeling the VSMP activation, taking the VSDs (Ci-VSD) derived from the Ciona intestinalis voltage sensitive phosphatase (Ci-VSP) as a model system. Our CG model reproduces the observed gating charge of Ci-VSD activation in several different perspectives. In particular, a new closed-form expression of the gating charge is evaluated in both nonequilibrium and equilibrium ways, while considering the fluctuation-dissipation relation that connects a nonequilibrium measurement of the gating charge to an equilibrium measurement of charge fluctuations (i.e., the voltage-independent linear component of membrane capacitance). In turn, the expression uncovers a novel link that connects an equilibrium measurement of the voltage-independent linear capacitance to a nonequilibrium measurement of the voltage-dependent nonlinear capacitance (whose integral over voltage is equal to the gating charge). In addition, our CG model yields capacitor-like voltage dependent free energy parabolas, resulting in the free energy difference and the free energy barrier for the Ci-VSD activation at "zero" (depolarization) membrane potential. Significantly, the resultant voltage dependent energetics enables a direct evaluation of capacitance-voltage relationship (C-V curve) as well as charge-voltage relationship (Q-V curve) that is in a good agreement with the observed measurement of Ci-VSD voltage activation. Importantly, an extension of our kinetic/thermodynamic model of voltage dependent activation in VSMP allows for novel derivations of voltage-dependent rate constants, whose parameters are expressed by the intrinsic properties of VSMP. These novel closed-form expressions offer a physicochemical foundation for the semiempirical Eyring-type voltage dependent rate equations that have been the cornerstone for the phenomenological (kinetic) descriptions of gating and membrane currents in the mechanistic study of ion channels and transporters. Our extended theoretical framework developed in the present study has potential implications on the roles played by gating charge fluctuations for the spike generations in nerve cells within the framework of the Hodgkin-Huxley-type model.

PROBABILITY DISTRIBUTIONS OF MARKOVIAN SODIUM CHANNEL STATES DURING PROPAGATING AXONAL IMPULSES WITH OR WITHOUT RECOVERY SUPERNORMALITY

This study addressed a macroscopic neurophysiological phenomenon - supernormality during the recovery phase of propagating axonal impulses - in explicit chemical terms. Excitation was reconstructed numerically using the kinetic scheme of multiple-state probabilistic transitions within a population of voltage-dependent sodium channels (NaCh) derived by Vandenberg and Bezanilla ("PC" scheme). Each NaCh transition was characterized as a reversible Markov process with voltage-dependent rate constants associated with each respective directional transition. While recovery reconstructed with the Hodgkin-Huxley formalism included a supernormal period, the PC scheme did not. The present analysis showed that the occurrence and degree of supernormality with the PC scheme was determined by the relative speed of the transitions within the closed loop of the kinetic scheme; supernormality was promoted by speeding these kinetics. The analysis also showed that concurrent with supernormality, the faster loop kinetics caused (1) an elevation in the C(1) --> C(2) transitions, and (2) a reduction in the I(4) --> I(5) transitions. Thus, macroscopic functionality in information processing could be expressed in terms of probabilistic interstate transitions among a population of NaCh molecules.

Temperature Dependence of Steady-State and Presteady-State Kinetics of a Type IIb Na+/Pi Cotransporter

The temperature dependence of the transport kinetics of flounder Na(+)-coupled inorganic phosphate (P(i)) cotransporters (NaPi-IIb) expressed in Xenopus oocytes was investigated using radiotracer and electrophysiological assays. (32)P(i) uptake was strongly temperature-dependent and decreased by approximately 80% at a temperature change from 25 degrees C to 5 degrees C. The corresponding activation energy (E (a)) was approximately 14 kcal mol(-1) for the cotransport mode. The temperature dependence of the cotransport and leak modes was determined from electrogenic responses to 1 mM P(i) and phosphonoformic acid (PFA), respectively, under voltage clamp. The magnitude of the P(i)- and PFA-induced changes in holding current decreased with temperature. E (a) at -100 mV for the cotransport and leak modes was approximately 16 kcal mol(-1) and approximately 11 kcal mol(-1), respectively, which suggested that the leak is mediated by a carrier, rather than a channel, mechanism. Moreover, E (a) for cotransport was voltage-independent, suggesting that a major conformational change in the transport cycle is electroneutral. To identify partial reactions that confer temperature dependence, we acquired presteady-state currents at different temperatures with 0 mM P(i) over a range of external Na(+). The relaxation time constants increased, and the peak time constant shifted toward more positive potentials with decreasing temperature. Likewise, there was a depolarizing shift of the charge distribution, whereas the total available charge and apparent valency predicted from single Boltzmann fits were temperature-independent. These effects were explained by an increased temperature sensitivity of the Na(+)-debinding rate compared with the other voltage-dependent rate constants.

Functional characterization of the pentapeptide QYNAD on rNav1.2 channels and its NMR structure.

The endogenous pentapeptide QYNAD (Gln-Tyr-Asn-Ala-Asp) is present in human cerebrospinal fluid (CSF), and its concentration is increased in demyelinating diseases. QYNAD was synthesized and its action on the rNav1.2 voltage-gated sodium channel alpha-subunit was studied using whole-cell recordings in a heterologous expression system. The effects were seen only upon equilibration of the peptide in the external bath solution for at least 10 min before the commencement of whole-cell experiments. The steady-state activation curve showed a rightward shift of 10 mV, while the steady-state inactivation curve showed a leftward shift of 5 mV. Frequency-dependent inhibition of the sodium current amplitude was observed at 2-10 Hz, in the presence of external QYNAD, but was not seen when applied internally. Fits of the whole-cell sodium current traces by Hodgkin-Huxley equations revealed subtle changes in the voltage-dependent rate constants governing the transition of the activation and the inactivation gates. Two dimensional NMR spectroscopy revealed the absence of medium and long-range Nuclear Overhauser effects (NOEs), which indicates that the peptide does not adopt any canonical secondary structure in solution. In summary, our studies show that although the pentapeptide QYNAD does not have a defined structure in solution, it has defined actions on the rNav1.2 voltage-gated sodium channel isoform.

Timing and Efficacy of Ca2+Channel Activation in Hippocampal Mossy Fiber Boutons

The presynaptic Ca2+ signal is a key determinant of transmitter release at chemical synapses. In cortical synaptic terminals, however, little is known about the kinetic properties of the presynaptic Ca2+ channels. To investigate the timing and magnitude of the presynaptic Ca2+ inflow, we performed whole-cell patch-clamp recordings from mossy fiber boutons (MFBs) in rat hippocampus. MFBs showed large high-voltage-activated Ca(2+) currents, with a maximal amplitude of approximately 100 pA at a membrane potential of 0 mV. Both activation and deactivation were fast, with time constants in the submillisecond range at a temperature of approximately 23 degrees C. An MFB action potential (AP) applied as a voltage-clamp command evoked a transient Ca2+ current with an average amplitude of approximately 170 pA and a half-duration of 580 microsec. A prepulse to +40 mV had only minimal effects on the AP-evoked Ca2+ current, indicating that presynaptic APs open the voltage-gated Ca2+ channels very effectively. On the basis of the experimental data, we developed a kinetic model with four closed states and one open state, linked by voltage-dependent rate constants. Simulations of the Ca2+ current could reproduce the experimental data, including the large amplitude and rapid time course of the current evoked by MFB APs. Furthermore, the simulations indicate that the shape of the presynaptic AP and the gating kinetics of the Ca2+ channels are tuned to produce a maximal Ca2+ influx during a minimal period of time. The precise timing and high efficacy of Ca2+ channel activation at this cortical glutamatergic synapse may be important for synchronous transmitter release and temporal information processing.

A Nonselective High Conductance Channel in Bovine Pigmented Ciliary Epithelial Cells

An ion channel activated by hyperpolarization was identified in excised patches of bovine pigmented ciliary epithelial cells using the single channel patch clamp technique. In symmetrical NaGluconate, the channel had a maximum conductance of 285 pS. The channel was characterized by frequent flickery transitions between the fully open and closed levels. The channel did not discriminate very clearly between anions and cations; when the cytoplasmic face of excised patches was bathed in a dilute NaCl solution, the channel had a chloride-to-sodium permeability ratio (PCl/PNa) of 1.3. However, the channel showed a small anion selectivity (PCl/PNa = 3.7) when bathed in a concentrated NaCl solution. Gd3+ blocked the channel reversibly. Channel kinetics were characterised by slow (approximately min) voltage-dependent activation and inactivation rate constants. The channel was most active in the range-60 to -140 mV and showed a peak at -120 mV. A similar time- and voltage-dependent activation was also observed in cell-attached recordings. In conclusion, hyperpolarization of pigmented ciliary epithelial cell membrane patches activated a large conductance, nonselective ion channel. This combination of nonselectivity and hyperpolarizing activation is consistent with the involvement of this channel in ion loading from the blood into pigmented ciliary epithelial cells-the first phase in the secretion of aqueous humor.

Small inward rectifying K+ channels in coleoptiles: inhibition by external Ca2+ and function in cell elongation.

Plant growth requires a continuous supply of intracellular solutes in order to drive cell elongation. Ion fluxes through the plasma membrane provide a substantial portion of the required solutes. Here, patch clamp techniques have been used to investigate the electrical properties of the plasma membrane in protoplasts from the rapid growing tip of maize coleoptiles. Inward currents have been measured in the whole cell configuration from protoplasts of the outer epidermis and from the cortex. These currents are essentially mediated by K+ channels with a unitary conductance of about 12 pS. The activity of these channels was stimulated by negative membrane voltage and inhibited by extracellular Ca2+ and/or tetraethylammonium-CI (TEA). The kinetics of voltage- and Ca(2+)-gating of these channels have been determined experimentally in some detail (steady-state and relaxation kinetics). Various models have been tested for their ability to describe these experimental data in straightforward terms of mass action. As a first approach, the most appropriate model turned out to consist of an active state which can equilibrate with two inactive states via independent first order reactions: a fast inactivation/activation by Ca(2+)-binding and -release, respectively (rate constants >> 10(3) sec-1) and a slower inactivation/activation by positive/negative voltage, respectively (voltage-dependent rate constants in the range of 10(3) sec-1). With 10 mM K+ and 1 mM Ca2+ in the external solution, intact coleoptile cells have a membrane voltage (V) of -105 +/- 7 mV. At this V, the density and open probability of the inward-rectifying channels is sufficient to mediate K+ uptake required for cell elongation. Extracellular TEA or Ca2+, which inhibit the K+ inward conductance, also inhibit elongation of auxin-depleted coleoptile segments in acidic solution. The comparable effects of Ca2+ and TEA on both processes and the similar Ca2+ concentration required for half maximal inhibition of growth (4.3 mM Ca2+) and for conductance (1.2 mM Ca2+) suggest that K+ uptake through the inward rectifier provides essential amounts of solute for osmotic driven elongation of maize coleoptiles.

A molecular model of low-voltage-activated calcium conductance

1. T-type or low-voltage-activated Ca2+ channels (IT) expressed in the mammalian thalamus play an important physiological role in the induction of membrane potential oscillations and in the regulation of the timing of synaptic signaling. On the basis of recent molecular studies on Ca2+, Na+, and K+ channels, a structure-kinetic model has been proposed for IT. 2. The model considers that the pore-opening process of IT is governed by three of the four protein domains that are arranged asymmetrically across the membrane plane. The three cytoplasmic linkers connecting individual channel domains serve as inactivation gates. On a membrane voltage change, each domain may engage independently into a sequential, thermodynamically coupled conformational change, thereby causing channel activation and inactivation. 3. A linear Marcov chain reaction with coupled channel activation and inactivation was adopted to test the kinetic feasibility of this trimeric model in a single-compartmental thalamic cell. The differential equations for voltage-dependent rate constants and transitional rates were solved to produce macroscopic T-type Ca2+ current. 4. Our simulation results indicate that this novel structure-kinetic model produces excellent predictions of the macroscopic behaviors of IT, and, more importantly, it provides some new insights into the microscopic mechanism underlying channel recovery.

Voltage dependence of g-protein-mediated inhibition of high-voltage-activated calcium channels in rat pituitary melanotropes

Dopamine D 2 receptor stimulation inhibited high-threshold, slowly inactivating (L-type) barium curents of isolated, rat pituitary melanotropes in primary culture. The extent of inhibition depended on the concentration of LY 171555 applied. Current activation in the presence of LY 171555 was described by two time constants, a fast one, also observed under control conditions, and a slow one, induced by LY 171555. The slow time constant did not depend on the concentration of LY 171555. Guanosine-5′- O-(3-thiotriphosphate) (100μ M) induced a similar inhibition of the barium currents. Depolarizing propulses more positive than −20mV counteracted the inhibition induced by LY 171555 as well as guanosine-5′- O-(3-thiotriphosphate). The voltage dependence and time course of this disinhibition were obtained. The results suggest that the slow time course of activation during current inhibition reflects a voltage-dependent conversion of the channel from the inhibited state to an available state. This voltage dependence is probably an intrinsic property of the calcium channel. The voltage-dependent rate constants of a first-order kinetic model which describes the voltage-dependent inhibition and disinhibition were estimated.

A model of the electrophysiological properties of nucleus reticularis thalami neurons

A model of the electrophysiological properties of rodent nucleus reticularis thalami (NRT) neurons of the dorsal lateral thalamus was developed using Hodgkin-Huxley style equations. The model incorporated voltage-dependent rate constants and kinetics obtained from recent voltage-clamp experiments in vitro. The intrinsic electroresponsivity of the model cell was found to be similar to several empirical observations. Three distinct modes of oscillatory activity were identified: 1) a pattern of slow rhythmic burst firing (0.5-7 Hz) usually associated with membrane potentials negative to approximately -70 mV which resulted from the interplay of ITs and IK(Ca); 2) at membrane potentials from approximately -69 to -62 mV, rhythmic burst firing in the spindle frequency range (7-12 Hz) developed and was immediately followed by a tonic tail of single spike firing after several bursts. The initial bursting rhythm resulted from the interaction of ITs and IK(Ca), with a slow after-depolarization due to ICAN which mediated the later tonic firing; 3) with further depolarization of the membrane potential positive to approximately -61 mV, sustained tonic firing appeared in the 10-200-Hz frequency range depending on the amplitude of the injected current. The frequency of this firing was also dependent on the maximum conductance of the leak current, IK(leak), and an interaction between the fast currents involved in generating action potentials, INa(fast) and IK(DR), and the persistent Na+ current, INa(P). Transitions between different firing modes were identified and studied parametrically.

Ca channel kinetics during the spontaneous heart beat in embryonic chick ventricle cells

The ability of Ca ions to inhibit Ca channels presents one of the most intriguing problems in membrane biophysics. Because of this negative feedback, Ca channels can regulate the current that flows through them. The kinetics of the channels depend on voltage, and, because the voltage controls the current, a strong interaction exists between voltage dependence and Ca dependence. In addition to this interaction, the proximity of pores and the local concentration of ions also determine how effectively the Ca ions influence channel kinetics. The present article proposes a model that incorporates voltage-dependent kinetics, current-dependent kinetics, and channel clustering. We have based the model on previous voltage-clamp data and on Ca and Ba action currents measured during the action potential in beating heart cells. In general we observe that great variability exists in channel kinetics from patch to patch: Ba or Ca currents have low or high amplitudes and slow or fast kinetics during essentially the same voltage regime, either applied step-protocols or spontaneous cell action potentials. To explain this variability, we have postulated that Ca channels interact through shared ions. The model we propose expands on our previous model for Ba currents. We use the same voltage-dependent rate constants for the Ca currents that we did for the Ba currents. However, we vary the current-dependent rate constants according to the species of the conducting ion. The model reproduces the main features of our data, and we use it to predict Ca channel kinetics under physiological conditions. Preliminary reports of this work have appeared (DeFelice et al., 1991, Biophys. J. 59:551a; Risso et al., 1992, Biophys. J. 61:248a).

Steady-state kinetics of solitary batrachotoxin-treated sodium channels. Kinetics on a bounded continuum of polymer conformations

The underlying principles of the kinetics and equilibrium of a solitary sodium channel in the steady state are examined. Both the open and closed kinetics are postulated to result from round-trip excursions from a transition region that separates the openable and closed forms. Exponential behavior of the kinetics can have origins different from small-molecule systems. These differences suggest that the probability density functions (PDFs) that describe the time dependences of the open and closed forms arise from a distribution of rate constants. The distribution is likely to arise from a thermal modulation of the channel structure, and this provides a physical basis for the following three-variable equation: [formula; see text] Here, A0 is a scaling term, k is the mean rate constant, and sigma quantifies the Gaussian spread for the contributions of a range of effective rate constants. The maximum contribution is made by k, with rates faster and slower contributing less. (When sigma, the standard deviation of the spread, goes to zero, then p(f) = A0 e-kt.) The equation is applied to the single-channel steady-state probability density functions for batrachotoxin-treated sodium channels (1986. Keller et al. J. Gen. Physiol. 88: 1-23). The following characteristics are found: (a) The data for both open and closed forms of the channel are fit well with the above equation, which represents a Gaussian distribution of first-order rate processes. (b) The simple relationship [formula; see text] holds for the mean effective rat constants. Or, equivalently stated, the values of P open calculated from the k values closely agree with the P open values found directly from the PDF data. (c) In agreement with the known behavior of voltage-dependent rate constants, the voltage dependences of the mean effective rate constants for the opening and closing of the channel are equal and opposite over the voltage range studied. That is, [formula; see text] "Bursts" are related to the well-known cage effect of solution chemistry.

Global parameter optimization for cardiac potassium channel gating models

Quantitative ion channel model evaluation requires the estimation of voltage dependent rate constants. We have tested whether a unique set of rate constants can be reliably extracted from nonstationary macroscopic voltage clamp potassium current data. For many models, the rate constants derived independently at different membrane potentials are not unique. Therefore, our approach has been to use the exponential voltage dependence predicted from reaction rate theory (Stevens, C. F. 1978. Biophys. J. 22:295-306; Eyring, H., S. H. Lin, and S. M. Lin. 1980. Basic Chemical Kinetics. Wiley and Sons, New York) to couple the rate constants derived at different membrane potentials. This constrained the solution set of rate constants to only those that also obeyed this additional set of equations, which was sufficient to obtain a unique solution. We have tested this approach with data obtained from macroscopic delayed rectifier potassium channel currents in voltage-clamped guinea pig ventricular myocyte membranes. This potassium channel has relatively simple kinetics without an inactivation process and provided a convenient system to determine a globally optimized set of voltage-dependent rate constants for a Markov kinetic model. The ability of the fitting algorithm to extract rate constants from the macroscopic current data was tested using "data" synthesized from known rate constants. The simulated data sets were analyzed with the global fitting procedure and the fitted rate constants were compared with the rate constants used to generate the data. Monte Carlo methods were used to examine the accuracy of the estimated kinetic parameters. This global fitting approach provided a useful and convenient method for reliably extracting Markov rate constants from macroscopic voltage clamp data over a broad range of membrane potentials. The limitations of the method and the dependence on initial guesses are described.

"Caged calcium" in Aplysia pacemaker neurons. Characterization of calcium-activated potassium and nonspecific cation currents.

We have studied calcium-activated potassium current, IK(Ca), and calcium-activated nonspecific cation current, INS(Ca), in Aplysia bursting pacemaker neurons, using photolysis of a calcium chelator (nitr-5 or nitr-7) to release "caged calcium" intracellularly. A computer model of nitr photolysis, multiple buffer equilibration, and active calcium extrusion was developed to predict volume-average and front-surface calcium concentration transients. Changes in arsenazo III absorbance were used to measure calcium concentration changes caused by nitr photolysis in microcuvettes. Our model predicted the calcium increments caused by successive flashes, and their dependence on calcium loading, nitr concentration, and light intensity. Flashes also triggered the predicted calcium concentration jumps in neurons filled with nitr-arsenazo III mixtures. In physiological experiments, calcium-activated currents were recorded under voltage clamp in response to flashes of different intensity. Both IK(Ca) and INS(Ca) depended linearly without saturation upon calcium concentration jumps of 0.1-20 microM. Peak membrane currents in neurons exposed to repeated flashes first increased and then declined much like the arsenazo III absorbance changes in vitro, which also indicates a first-order calcium activation. Each flash-evoked current rose rapidly to a peak and decayed to half in 3-12 s. Our model mimicked this behavior when it included diffusion of calcium and nitr perpendicular to the surface of the neuron facing the flashlamp. Na/Ca exchange extruding about 1 pmol of calcium per square centimeter per second per micromolar free calcium appeared to speed the decline of calcium-activated membrane currents. Over a range of different membrane potentials, IK(Ca) and INS(Ca) decayed at similar rates, indicating similar calcium stoichiometries independent of voltage. IK(Ca), but not INS(Ca), relaxes exponentially to a different level when the voltage is suddenly changed. We have estimated voltage-dependent rate constants for a one-step first-order reaction scheme of the activation of IK(Ca) by calcium. After a depolarizing pulse, INS(Ca) decays at a rate that is well predicted by a model of diffusion of calcium away from the inner membrane surface after it has entered the cell, with active extrusion by surface pumps and uptake into organelles. IK(Ca) decays somewhat faster than INS(Ca) after a depolarization, because of its voltage-dependent relaxation combined with the decay of submembrane calcium. The interplay of these two currents accounts for the calcium-dependent outward-inward tail current sequence after a depolarization, and the corresponding afterpotentials after a burst

Kinetic model of the effects of electrogenic enzymes on the membrane potential

Electrogenic enzymes contribute to the electrical field existing across biological membranes by using a source of free energy to generate an ionic current. The model introduced here permits one to evaluate this contribution. Since the model incorporates the electrogenic enzyme in the form of a sequential kinetic diagram, it permits one to study the kinetic effects of the concentration of the enzyme, the substrates and the different ligands on the membrane potential. Ionic electrodiffusion is expressed in terms of a chemical reaction; ionic permeabilities are thus treated as voltage-dependent rate constants. We use the condition of global electroneutrality to obtain an expression for the electrical potential difference across the membrane; such expression constitutes an extension of the Goldman-Hodgkin-Katz equation. The enzyme-related terms appear in the equation as functions of the rate constants and the diverse concentrations. The model is used to analyze the case of a cell membrane traversed by Na+ and K+ by simple diffusion, and by electrogenic transport mediated by a Na+-K+ ATPase. The enzyme reaction is represented by the six-step scheme proposed by Chapman et al. (1983, J. membr. Biol. 74, 139-153). The main results of the numerical calculations are that, within a certain interval, the membrane potential difference depends linearly on the enzyme density and hyperbolically on the ATP concentration. A similar behavior has been experimentally observed for the electrogenic proton pump of Neurospora crassa. Thus, the model here can be useful in the explanation and prediction of effects of electrogenic enzymes on the membrane potential.

Delayed rectification in the calf cardiac Purkinje fiber. Evidence for multiple state kinetics

We have investigated the delayed rectifier current (Ix) in the calf cardiac Purkinje fiber using a conventional two-microelectrode voltage clamp arrangement. The deactivation of Ix was monitored by studying decaying current tails after the application of depolarizing voltage prepulses. The reversal potential (Vrev) of these Ix tails was measured as a function of prepulse magnitude and duration to test for possible permeant ion accumulation- or depletion-induced changes in Vrev. We found that prepulse-induced changes in Vrev were less than 5 mV, provided that prepulse durations were less than or equal to 3.5 s and magnitudes were less than or equal to +35 mV. We kept voltage pulse structures within these limits for the remainder of the experiments in this study. We studied the sensitivity of Vrev to variation in extracellular K+. The reversal potential for Ix is well described by a Goldman-Hodgkin-Katz relation for a channel permeable to Na+ and K+ with PNa/PK = 0.02. The deactivation of Ix was always found to be biexponential and the two components shared a common reversal potential. These results suggest that it is not necessary to postulate the existence of two populations of channels to account for the time course of the Ix tails. Rather, our results can quantitatively be reproduced by a model in which the Ix channel can exist in three (two closed, one open) conformational states connected by voltage dependent rate constants.

Mechanisms of quinidine-induced depression of maximum upstroke velocity in ovine cardiac Purkinje fibers.

A major advance in understanding how quinidine depresses maximum upstroke velocity (Vmax) is the Hondeghem-Katzung mathematical model which incorporates voltage-independent rate constants for binding to and unbinding from resting, open, and inactive Na channels, and a voltage shift of -40 mV for the Hodgkin-Huxley h-kinetics of quinidine-associated Na channels. Using a double microelectrode voltage clamp technique to control transmembrane voltage and apply conditioning pulses, we found that quinidine blockade increased as transmembrane voltage became more positive in the range -60 to +40 mV, and that the rate of quinidine dissociation increased as transmembrane voltage became more negative in the range -60 to -140 mV. The relationship of Vmax to transmembrane voltage obtained at drive cycles from 500 msec to 20 seconds conformed to the model modified to include voltage-dependent rate constants without the postulated -40-mV shift for quinidine-associated channels. Thus binding of quinidine to inactive Na channels and unbinding from resting channels are both voltage-dependent and can explain frequency and voltage dependent actions of quinidine on Vmax without any voltage shift for quinidine-associated channels.

Consistency between thermodynamics and the kinetics of n, m, and h in the hodgkin-huxley equations

The voltage-dependent rate constants of the Hodgkin-Huxley equations for the n, m, and h systems are tested for consistency with the Second Law of Thermodynamics as applied to the kinetic behaviour of independent particles moving in a closed thermodynamic system according to first-order rate laws. No consistency with Boltzmann distribution theory and classical thermodynamics is found for any of the n, m, or h rate constants without the additional proviso that the equivalent valencies of the n, m, and h particles are also voltage-dependent. A model is provided showing how non-linear membrane potential profiles could create an apparent voltage-dependent variation in the equivalent valency of particles experiencing only a fraction of the electric field. There is an unexplained discrepancy between the classical description of the m system and the more recent description of it in association with measurement of gating currents: the classical description requires voltage-dependent valency for thermodynamic consistency whereas the recent description is a thermodynamically formulated one that assumes constant valency independent of voltage for the independent m particles. The formulations presented become void if departures from first order independent behaviour are allowed.