A quantitative description of QX222 blockade of sodium channels in squid axons

The interaction of QX222, a quaternary ammonium derivative of lidocaine, with the Na channel was studied in internally perfused squid axons under voltage-clamped conditions. A use-dependent block was observed in response to repetitive depolarizing pulses. The time constant for block development and the steady state level of the block were increased with increasing frequency of stimulation from 0.1 to 10 Hz. Use-dependent block can be viewed as a net increase in the drug incorporation into Na channels with successive pulses. That is, net drug uptake by Na channels occurs during the depolarizing phase and net drug release occurs during the interpulse interval. The observed uptake rate of use-dependent block is shown to be a linear combination of the uptake rates associated with the depolarizing and resting potentials. Also, the steady state fraction of blocked channels is shown to be a linear combination of the state-dependent blockade equilibria. Drug-channel interactions are assumed to be dependent on gated control of the diffusion path between drug pool and the interior channel binding site. Drug ingress to the binding site can be inhibited by the channel gates (receptor guarding), while drug bound to the channel may become trapped by closure of the channel gates (trapping). On the basis of these assumptions, a simple procedure is proposed for estimating apparent rate constants governing the drug-channel binding reactions for two cases of channel blockade.(ABSTRACT TRUNCATED AT 250 WORDS)     

Kinetic analysis of the action of Leiurus scorpion alpha-toxin on ionic currents in myelinated nerve

The effects of a neurotoxin, purified from the venom of the scorpion Leiurus quinquestriatus, on the ionic currents of toad single myelinated fibers were studied under voltage-clamp conditions. Unlike previous investigations using crude scorpion venom, purified Leiurus toxin II alpha at high concentrations (200-400 nM) did not affect the K currents, nor did it reduce the peak Na current in the early stages of treatment. The activation of the Na channel was unaffected by the toxin, the activation time course remained unchanged, and the peak Na current vs. voltage relationship was not altered. In contrast, Na channel inactivation was considerably slowed and became incomplete. As a result, a steady state Na current was maintained during prolonged depolarizations of several seconds. These steady state Na currents had a different voltage dependence from peak Na currents and appeared to result from the opening of previously inactivated Na channels. The opening kinetics of the steady state current were exponential and had rates approximately 100-fold slower than the normal activation processes described for transitions from the resting state to the open state. In addition, the dependence of the peak Na current on the potential of preceding conditioning pulses was also dramatically altered by toxin treatment; this parameter reached a minimal value near a membrane potential of -50 mV and then increased continuously to a "plateau" value at potentials greater than +50 mV. The amplitude of this plateau was dependent on toxin concentration, reaching a maximum value equal to approximately 50% of the peak current; voltage-dependent reversal of the toxin's action limits the amplitude of the plateauing effect. The measured plateau effect was half-maximum at a toxin concentration of 12 nM, a value quite similar to the concentration producing half of the maximum slowing of Na channel inactivation. The results of Hill plots for these actions suggest that one toxin molecule binds to one Na channel. Thus, the binding of a single toxin molecule probably both produces the steady state currents and slows the Na channel inactivation. We propose that Leiurus toxin inhibits the conversion of the open state to inactivated states in a voltage-dependent manner, and thereby permits a fraction of the total Na permeability to remain at membrane potentials where inactivation is normally complete.     

Use-dependent inhibition of Na+ currents by benzocaine homologs.

Most local anesthetics (LAs) elicit use-dependent inhibition of Na+ currents when excitable membranes are stimulated repetitively. One exception to this rule is benzocaine, a neutral LA that fails to produce appreciable use-dependent inhibition. In this study, we have examined the use-dependent phenomenon of three benzocaine homologs: ethyl 4-diethylaminobenzoate, ethyl 4-ethoxybenzoate, and ethyl 4-hydroxybenzoate. Ethyl 4-hydroxybenzoate at 1 mM, like benzocaine, elicited little use-dependent inhibition of Na+ currents, whereas ethyl 4-diethylaminobenzoate at 0.15 mM and ethyl 4-ethoxybenzoate at 0.5 mM elicited substantial use-dependent inhibition--up to 55% of peak Na+ currents were inhibited by repetitive depolarizations at 5 Hz. Each of these compounds produced significant tonic block of Na+ currents at rest and shifted the steady-state inactivation curve (h infinity) toward the hyperpolarizing direction. Kinetic analyses showed that the decaying phase of Na+ currents during a depolarizing pulse was significantly accelerated by all drugs, thus suggesting that these drugs also block the activated channel. The recovery time course for the use-dependent inhibition of Na+ currents was relatively slow, with time constants of 6.8 and 4.4 s for ethyl 4-diethylaminobenzoate and ethyl 4-ethoxybenzoate, respectively. We conclude that benzocaine and 4-hydroxybenzoate interact with the open and inactivated channels during repetitive pulses, but during the interpulse the complex dissociates too fast to accumulate sufficient use-dependent block of Na+ currents. In contrast, ethyl 4-diethylaminobenzoate and ethyl 4-ethoxybenzoate dissociate slowly from their binding site and consequently elicit significant use-dependent block. A common LA binding site suffices to explain the presence and absence of use-dependent block by benzocaine homologs during repetitive pulses.     

Proton dependence of the partial reactions of the sodium-proton exchanger in renal brush border membranes.

The pre-steady state time dependence of Na+ accumulation by the Na(+)-H+ exchanger in renal brush border membrane vesicles was investigated at 0 degree C by a manual mixing technique using amiloride to quench the reaction. Dilution of acid-loaded (pHi 5.7) vesicles into an alkaline medium (pHo 7.7) containing 1 mM 22Na+ produced a time course of amiloride-sensitive Na+ uptake that consisted of three distinct phases: 1) a lag, 2) a monoexponential "burst," and 3) a linear or steady state phase. Experiments testing for the presence of 22Na+ backflux, residual Na+ binding to the membrane, and hysteresis were negative, lending support to the hypothesis that the burst phase corresponds to Na+ translocation during the initial turnover of Na(+)-H+ exchanger. Lowering the internal pH increased the amount of na+ uptake in each of the phases without affecting the apparent burst rate, whereas lowering the external pH inhibited Na+ uptake while increasing the duration of the lag phase. The pattern of inhibition produced by external H+ was of the simple competitive type, indicating that Na+ and H+ share a common binding site. Steady state Na+ uptake showed a sigmoidal dependence on internal pH (Hill coefficient = 1.67), consistent with the presence of an internal allosteric H+ activation site. Alkaline loading conditions (pHi 7.7), which favor desaturation of the internal H+ binding sites, completely abolished Na+ uptake in the steady state. In contrast, Na+ accumulation during the burst phase was reduced to 25% of an acid-loaded (pHi 5.7) control. The persistence of the burst phase and the disappearance of steady state Na+ uptake under alkaline loading conditions suggest that recycling of the H(+)-loaded exchanger is a late event in the transport cycle that follows Na+ translocation (ping-pong mechanism) and controls the steady state rate of Na+ accumulation. Activation of the recycling step involves sequential binding of H+ to the allosteric and transport sites, thus accounting for the cooperative dependence of steady state Na+ uptake on the internal [H+].     

Characterizing activity-dependent processes with a piecewise exponential model

The response of some biological processes is dependent on the frequency of stimulation. With first-order processes, the response is driven exponentially to an equilibrium determined by the value of the driving function. When the stimulus or driving function is viewed as switching between constant values the resulting response is piecewise exponential. With periodic excitation, the time course of a point fixed in time relative to the initiation time of each stimulus is shown to be exponential with a rate and steady state that are linearly dependent on the rates and equilibria associated with each component exponential. This linearity can be exploited and leads to a simple estimation procedure for the apparent state-dependent rates.     

Mathematical properties of pump-leak models of cell volume control and electrolyte balance

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.     

Erratum to: Mathematical properties of pump-leak models of cell volume control and electrolyte balance

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.     

Dynamic tension spectroscopy and strength of biomembranes

Rupturing fluid membrane vesicles with a steady ramp of micropipette suction produces a distribution of breakage tensions governed by the kinetic process of membrane failure. When plotted as a function of log(tension loading rate), the locations of distribution peaks define a dynamic tension spectrum with distinct regimes that reflect passage of prominent energy barriers along the kinetic pathway. Using tests on five types of giant phosphatidylcholine lipid vesicles over loading rates(tension/time) from 0.01-100 mN/m/s, we show that the kinetic process of membrane breakage can be modeled by a causal sequence of two thermally-activated transitions. At fast loading rates, a steep linear regime appears in each spectrum which implies that membrane failure starts with nucleation of a rare precursor defect. The slope and projected intercept of this regime are set by defect size and frequency of spontaneous formation, respectively. But at slow loading rates, each spectrum crosses over to a shallow-curved regime where rupture tension changes weakly with rate. This regime is predicted by the classical cavitation theory for opening an unstable hole in a two-dimensional film within the lifetime of the defect state. Under slow loading, membrane edge energy and the frequency scale for thermal fluctuations in hole size are the principal factors that govern the level of tension at failure. To critically test the model and obtain the parameters governing the rates of transition under stress, distributions of rupture tension were computed and matched to the measured histograms through solution of the kinetic master (Markov) equations for defect formation and annihilation or evolution to an unstable hole under a ramp of tension. As key predictors of membrane strength, the results for spontaneous frequencies of defect formation and hole edge energies were found to correlate with membrane thicknesses and elastic bending moduli, respectively.     

Characterization of the inward-rectifying potassium current in cat ventricular myocytes

Whole-cell membrane currents were measured in isolated cat ventricular myocytes using a suction-electrode voltage-clamp technique. An inward-rectifying current was identified that exhibited a time-dependent activation. The peak current appeared to have a linear voltage dependence at membrane potentials negative to the reversal potential. Inward current was sensitive to K channel blockers. In addition, varying the extracellular K+ concentration caused changes in the reversal potential and slope conductance expected for a K+ current. The voltage dependence of the chord conductance exhibited a sigmoidal relationship, increasing at more negative membrane potentials. Increasing the extracellular K+ concentration increased the maximal level of conductance and caused a shift in the relationship that was directly proportional to the change in reversal potential. Activation of the current followed a monoexponential time course, and the time constant of activation exhibited a monoexponential dependence on membrane potential. Increasing the extracellular K+ concentration caused a shift of this relationship that was directly proportional to the change in reversal potential. Inactivation of inward current became evident at more negative potentials, resulting in a negative slope region of the steady state current-voltage relationship between -140 and -180 mV. Steady state inactivation exhibited a sigmoidal voltage dependence, and recovery from inactivation followed a monoexponential time course. Removing extracellular Na+ caused a decrease in the slope of the steady state current-voltage relationship at potentials negative to -140 mV, as well as a decrease of the conductance of inward current. It was concluded that this current was IK1, the inward-rectifying K+ current found in multicellular cardiac preparations. The K+ and voltage sensitivity of IK1 activation resembled that found for the inward-rectifying K+ currents in frog skeletal muscle and various egg cell preparations. Inactivation of IK1 in isolated ventricular myocytes was viewed as being the result of two processes: the first involves a voltage-dependent change in conductance; the second involves depletion of K+ from extracellular spaces. The voltage-dependent component of inactivation was associated with the presence of extracellular Na+.     

On the relation between displacement currents and activation of the sodium conductance in the squid giant axon.

The early time course of the current passing across the membrane in squid giant axons in which the ionic currents have been blocked reveals substantial asymmetries during and after the application of hyperpolarizing and depolarizing voltage-clamp pulses of identical size. Since the integral of the 'on' and 'off' current transients is zero, these currents must result from charge movements confined to the membrane and, therefore, they are nonlinear displacement currents. The steady state rearrangement of the charges as a consequence of sudden displacements of the membrane potential is consistent with a Boltzmann distribution of charges between two states characterized by different energy levels. Following changes in membrane potential the charges undergo a first order transition between these states. The relaxation time constant for the transition at a given temperature is a function of membrane potential. We propose that these displacement currents arise from a redistribution of the charges involved in the sodium gating system.     

Voltage-dependent transient currents of human and rat 5-HT transporters (SERT) are blocked by HEPES and ion channel ligands

The hyperpolarization-activated transient current of mammalian 5-hydroxytryptamine transporters (SERT) expressed in Xenopus oocytes was studied. Human (h) and rat (r) SERT transient currents are blocked by HEPES with changes in the waveform kinetics, and the blockade of hSERT has use-dependent properties. HEPES also changes the time course of the prepriming step, especially for hSERT. Transient currents at hSERT and rSERT are also blocked by spermine and spermidine in the mM range, and by fluoxetine, cocaine, QX-314, and QX-222 in the microM range. These pharmacological and kinetic properties of transient current blockade emphasize the similarities between the transient current and phenomena at ion channels.     

The effect of membrane potential on initial velocity of GABA uptake and steady state distribution ratio in rat cortical synaptosomes

Initial velocity of synaptosomal GABA uptake and steady state distribution ratio (DR) have been measured as a function of medium potassium concentration ([K]_o) and in the presence of veratridine. Previous studies of the effect of [K]_o and veratridine on membrane potential have been utilized to relate GABA uptake to membrane potential. Both initial velocity of uptake and steady state DR are functions of membrane potential; initial velocity and ln DR are linearly related to membrane potential. Final DR is determined by the electrochemical potential gradient for the transported ions. Previous studies of the relation of [Na]_o to uptake have shown that either one or two sodium ions may be translocated with each GABA molecule. Present results are consistent with this assumption if it is also assumed that an anion is co-transported with each GABA molecule.     

Carotid baroreflex sensitivity and physical fitness in cycling tourists

Carotid baroreceptors were stimulated with neck suction in 47 healthy subjects. Pulse interval lengthening was measured and the time course of the response was evaluated. Eight intensities of neck chamber suction were applied to select a criterion for computing the "RR response" that gives a significant linear relationship with the magnitude of the stimuli in the highest number of individuals. The best criterion was the maximal RR prolongation within 5 seconds after the onset of the stimulus. The slope of this relationship was defined as baroreflex sensitivity. The effect of physical fitness on baroreceptor function was investigated in 24 cycling tourists with a wide range of peak oxygen uptake and training characteristics. Baroreflex sensitivity averaged 7.3 +/- 0.8 msec X mm Hg-1 and was not significantly related to age, weight, basal heart rate, peak oxygen uptake and ventilation and other training characteristics. The results suggest that in man the so defined sensitivity of the carotid baroreflex control of heart rate is not influenced by the level of physical fitness and therefore the measurement of these characteristics can be neglected in evaluating baroreflex sensitivity.     

Use-dependent block of sodium channels in frog myelinated nerve by tetrodotoxin and saxitoxin at negative holding potentials

Na+ currents were measured in myelinated frog nerve fibres in the presence of nanomolar concentrations of tetrodotoxin (TTX) or saxitoxin (STX) in the extracellular solution. The Na+ currents declined during a train of depolarizing pulses if the fibre was held at hyperpolarizing potentials between the pulses. At a pulse frequency of 0.8 Hz, the peak Na+ currents were reduced to 70 or 60% of the initial value in 9.3 nM TTX and 3.5 nM STX solutions, respectively. A decline of Na+ currents was also observed in two-pulse experiments. The peak Na+ current during a second test pulse did not depend on the duration (0.2 to 12 ms) of the first pulse. It decreased with increasing interval between the pulses, reached a minimum and increased again. The results are interpreted with a use-dependent blockage of Na+ channels by TTX or STX at negative holding potentials. The effects were described quantitatively, assuming a fast affinity increase of toxin receptors at Na+ channels triggered by Na+ activation followed by slow toxin binding to channels and relaxation of the receptor affinity.     

On the mechanism of proton transport by the neuronal excitatory amino acid carrier 1

Uptake of glutamate from the synaptic cleft is mediated by high affinity transporters and is driven by Na(+), K(+), and H(+) concentration gradients across the membrane. Here, we characterize the molecular mechanism of the intracellular pH change associated with glutamate transport by combining current recordings from excitatory amino acid carrier 1 (EAAC1)-expressing HEK293 cells with a rapid kinetic technique with a 100-micros time resolution. Under conditions of steady state transport, the affinity of EAAC1 for glutamate in both the forward and reverse modes is strongly dependent on the pH on the cis-side of the membrane, whereas the currents at saturating glutamate concentrations are hardly affected by the pH. Consistent with this, the kinetics of the pre-steady state currents, measured after saturating glutamate concentration jumps, are not a function of the pH. In addition, we determined the deuterium isotope effect on EAAC1 kinetics, which is in agreement with proton cotransport but not OH(-) countertransport. The results can be quantitatively explained with an ordered binding model that includes a rapid proton binding step to the empty transporter followed by glutamate binding and translocation of the proton-glutamate-transporter complex. The apparent pK of the extracellular proton binding site is approximately 8. This value is shifted to approximately 6.5 when the substrate binding site is exposed to the cytoplasm.     

Determination of unidirectional uptake rates for lipids across the intestinal brush border

An in vitro method is presented which measures valid, unidirectional uptake rates for lipids across the intestinal brush border. This method combines analysis by a newly devised, double isotope counting system for solubilized tissue with the use of a nonabsorbable marker to correct gross uptake determinations for contamination by adherent mucosal fluid. Of seven markers, only [(3)H]inulin measured adherent mucosal fluid volumes as much as 20% greater than the other markers. Diffusion of the nonabsorbable marker, as well as of the compound being studied, into the unstirred layer made the time course of uptake critically important. The time lag for diffusion of marker invalidates the use of 1-min incubation periods; however, a linear time course of uptake that intercepts essentially at zero was found for taurocholate and octanoate for periods of from 2 to 5 min. Working within this critical time period with jejunum, it was shown that tissue dry weight was an appropriate measure of the amount of tissue and that uptake rates for taurocholic, octanoic, and lauric acids were linear with respect to concentration. Tissue binding of compounds was not significant. The results demonstrate that careful use of the described method yields accurate measurement of unidirectional uptake rates of lipids across the brush border that are of critical importance in defining the characteristics of membrane penetration and the rate-limiting steps in fat and sterol absorption.     

Interactions of monovalent cations with sodium channels in squid axon. I. Modification of physiological inactivation gating

Inactivation of Na channels has been studied in voltage-clamped, internally perfused squid giant axons during changes in the ionic composition of the intracellular solution. Peak Na currents are reduced when tetramethylammonium ions (TMA+) are substituted for Cs ions internally. The reduction reflects a rapid, voltage-dependent block of a site in the channel by TMA+. The estimated fractional electrical distance for the site is 10% of the channel length from the internal surface. Na tail currents are slowed by TMA+ and exhibit kinetics similar to those seen during certain drug treatments. Steady state INa is simultaneously increased by TMA+, resulting in a "cross-over" of current traces with those in Cs+ and in greatly diminished inactivation at positive membrane potentials. Despite the effect on steady state inactivation, the time constants for entry into and exit from the inactivated state are not significantly different in TMA+ and Cs+. Increasing intracellular Na also reduces steady state inactivation in a dose-dependent manner. Ratios of steady state INa to peak INa vary from approximately 0.14 in Cs+- or K+-perfused axons to approximately 0.4 in TMA+- or Na+-perfused axons. These results are consistent with a scheme in which TMA+ or Na+ can interact with a binding site near the inner channel surface that may also be a binding or coordinating site for a natural inactivation particle. A simple competition between the ions and an inactivation particle is, however, not sufficient to account for the increase in steady state INa, and changes in the inactivation process itself must accompany the interaction of TMA+ and Na+ with the channel.     

Steady state kinetics of consecutive enzyme catalysed reactions involving single substrates: procedures for the interpretation of coupled assays

Sets of differential rate equations are written describing a linear sequence of reactions occurring in solution each catalysed by a control enzyme or one of the Michaelis-Menten type. It is shown that the solutions of these equations may be formulated as a set of Maclaurin polynomials, expressing the concentration of each reactant and of final product as a function of time. From arrays of such polynomials, general expressions are induced for the first non-zero term of the series. These are used to formulate a procedure (illustrated with an example simulated by numerical integration) by which results of coupled enzymic assays may be analysed in terms of maximal velocities and apparent Michaelis constants: correlation is made with other established methods for conducting coupled assays. The present procedure assumes a steady state of enzyme-substrate complexes but not of intermediate reactants.     

A steady state model for analyzing the cellular binding, internalization and degradation of polypeptide ligands

We demonstrate that the interaction of polypeptide ligands with cells under physiological conditions can be described by a set of steady state equations. These equations include four new rate constants: V_r, the rate of insertion of receptors into the cell membrane; K_e, the endocytotic rate constant of occupied receptors; K_t, the turnover rate constant of unoccupied receptors; and K_h, the rate constant of hydrolysis of internalized ligand. Several simple procedures are described for determining these constants. In experiments in which epidermal growth factor and human fibroblasts were used, the cell-ligand interactions followed the predictions of the steady state model. The utility of the steady state equations is demonstrated by establishing the kinetic basis of the commonly observed “down regulation” phenomenon and by quantitating the effect of methylamine on the endocytotic and degradation rates of epidermal growth factor. We also show that the slope of a “Scatchard plot” of steady state binding data is a complex constant including terms for the endocytotic rate of both occupied and unoccupied receptors. The X-intercept of such a plot is a function of the insertion rate of new receptors, the internalization rate of occupied receptors and the degradation rate of the internalized ligand. The steady state equations allow one to predict changes in cellular ligand binding resulting from alterations in the four rate constants. They also provide a foundation for computer simulations of ligand-cell interactions, which closely correspond to experimental data. These approaches should facilitate studies on the control of cellular activities by these polypeptide ligands.