Roles of mitochondria and temperature in the control of intracellular calcium in adult rat sensory neurons.

We recorded Ca2+ current and intracellular Ca2+ ([Ca2+](i)) in isolated adult rat dorsal root ganglion (DRG) neurons at 20 and 30 degrees C. In neurons bathed in tetraethylammonium and dialyzed with cesium, warming reduced resting [Ca2+](i) from 87 to 49 nM and the time constant of the decay of [Ca2+](i) transients (tau(r)) from 1.3 to 0.99s (Q(10)=1.4). The Buffer Index, the ratio between Ca2+ influx and Delta[Ca2+](i) (f I(ca)d(t)/Delta[Ca2+]i) , increased two- to threefold with warming. Neither inhibition of the plasma membrane Ca2+ -ATPase by intracellular sodium orthovanadate nor inhibition of Ca2+ uptake by the endoplasmic reticulum by thapsigargin plus ryanodine were necessary for the effects of warming on these parameters. In contrast, inhibition of the mitochondrial Ca2+ uniporter by intracellular ruthenium red largely reversed the effects of warming. Carbonyl cyanide 4-(trifluoromethoxy) phenylhydrazone (FCCP, 500 nM) increased resting [Ca2+](i) at 30 degrees C. Ten millimolar intracellular sodium prolonged the recovery of [Ca2+](i) transients to 10-40s. This effect was reversed by an inhibitor of mitochondrial Na(+)/Ca2+ -exchange (CGP 37157, 10 microM). Thus, mitochondrial Ca2+ uptake is necessary for the temperature-dependent increase in Ca2+ buffering and mitochondrial Ca2+ fluxes contribute to the control of [Ca2+](i) between 50 and 150 nM at 30 degrees C.

Calcium- and voltage-activated plateau currents of cardiac Purkinje fibers.

We have used the two-microelectrode voltage-clamp technique to investigate the components of membrane current that contribute to the formation of the early part of the plateau phase of the action potential of calf cardiac Purkinje fibers. 3,4-Diaminopyridine (50 microM) reduced the net transient outward current elicited by depolarizations to potentials positive to -30 mV but had no consistent effect on contraction. We attribute this effect to the blockade of a voltage-activated transient potassium current component. Ryanodine (1 microM), an inhibitor of sarcoplasmic reticulum calcium release and intracellular calcium oscillations in Purkinje fibers (Sutko, J.L., and J.L. Kenyon. 1983. Journal of General Physiology. 82:385-404), had complex effects on membrane currents as it abolished phasic contractions. At early times during a depolarization (5-30 ms), ryanodine reduced the net outward current. We attribute this effect to the loss of a component of calcium-activated potassium current caused by the inhibition of sarcoplasmic reticulum calcium release and the intracellular calcium transient. At later times during a depolarization (50-200 ms), ryanodine increased the net outward current. This effect was not seen in low-sodium solutions and we could not observe a reversal potential over a voltage range of -100 to +75 mV. These data suggest that the effect of ryanodine on the late membrane current is attributable to the loss of sodium-calcium exchange current caused by the inhibition of sarcoplasmic reticulum calcium release and the intracellular calcium transient. Neither effect of ryanodine was dependent on chloride ions, which suggests that chloride ions do not carry the ryanodine-sensitive current components. Strontium (2.7 mM replacing calcium) and caffeine (10 mM), two other treatments that interfere with sarcoplasmic reticulum function, had effects in common with ryanodine. This supports the hypothesis that the effects of ryanodine may be attributed to the inhibition of sarcoplasmic reticulum calcium release.

Ryanodine modification of cardiac muscle responses to potassium-free solutions. Evidence for inhibition of sarcoplasmic reticulum calcium release.

To test whether ryanodine blocks the release of calcium from the sarcoplasmic reticulum in cardiac muscle, we examined its effects on the aftercontractions and transient depolarizations or transient inward currents developed by guinea pig papillary muscles and voltage-clamped calf cardiac Purkinje fibers in potassium-free solutions. Ryanodine (0.1-1.0 microM) abolished or prevented aftercontractions and transient depolarizations by the papillary muscles without affecting any of the other sequelae of potassium removal. In the presence of 4.7 mM potassium and at a stimulation rate of 1 Hz, ryanodine had only a small variable effect on papillary muscle force development and action potential characteristics. In calf Purkinje fibers, ryanodine (1 nM-1 microM) completely blocked the aftercontractions and transient inward currents without altering the steady state current-voltage relationship. Ryanodine also abolished the twitch in potassium-free solutions, but it enhanced the tonic force during depolarizing voltage-clamp steps. This latter effect was dependent on the combination of ryanodine and potassium-free solutions. The slow inward current was not blocked by 1 microM ryanodine, but ryanodine did appear to abolish an outward current that remained in the presence of 0.5 mM 4-aminopyridine. Our observations are consistent with the hypothesis that ryanodine, by inhibiting the release of calcium from the sarcoplasmic reticulum, prevents the oscillations in intracellular calcium that activate the transient inward currents and aftercontractions associated with calcium overload states.

Influence of chloride, potassium, and tetraethylammonium on the early outward current of sheep cardiac Purkinje fibers.

In voltage clamp studies of cardiac Purkinje fibers, a large early outward current is consistently observed during depolarizations to voltages more positive than -20 mV. After the outward peak of the current, the total membrane current declines slowly. Dudel et al. (1967. Pfluegers Arch. Eur. J. Physiol. 294:197--212) reduced the extracellular chloride concentration and found that the outward peak and the decline of the current were abolished. They concluded that the total membrane current at these voltages was largely determined by a time- and voltage-dependent change in the membrane chloride conductance. We reinvestigated the chloride sensitivity of this current, taking care to minimize possible sources of error. When the extracellular chloride concentration was reduced to 8.6% of control, the principal effect was a 20% decrease in the peak amplitude of the outward current. This implies that the membrane chloride conductance is not the major determinant of the total current at these voltages. The reversal potential of current tails obtained after a short conditioning depolarization was not changed by alterations in the extracellular chloride or potassium concentrations. We suspect that the tail currents contain both inward and outward components, and that the apparent reversal potential of the net tail current largely reflects the kinetics of the outward component, so that this experiment does not rule out potassium as a possible charge carrier. The possibility that potassium carries much of the early outward current was further investigated using tetraethylammonium, which blocks potassium currents in nerve and skeletal muscle. This drug substantially reduced the early outward current, which suggests that much of the early outward current is carried by potassium ions.

4-Aminopyridine and the early outward current of sheep cardiac Purkinje fibers.

We have studied the effects of the potassium-blocking agent 4-aminopyridine (4-AP) on the action potential and membrane currents of the sheep cardiac Purkinje fiber. 4-AP slowed the rate of phase 1 repolarization and shifted the plateau of the action potential to less negative potentials. In the presence of 4-AP, the substitution of sodium methylsulfate or methanesulfonate for the NaCl of Tyrode's solution further slowed the rate of phase 1 repolarization, even though chloride replacement has no effect on the untreated preparation. In voltage clamp experiments, 4-AP rapidly and reversibly reduced the early peak of outward current that is seen when the Purkinje fiber membrane is voltage-clamped to potentials positive to -20 mV. In addition, 4-AP reduced the steady outward current seen at the end of clamp steps positive to -40 mV. 4-AP did not appear to change the slow inward current observed over the range of -60 to -40 mV, nor did it greatly change the current tails that have been used as a measure of the slow inward conductance at more positive potentials. 4-AP did not block the inward rectifying potassium currents, IK1 and IK2. A phasic outward current component that was insensitive to 4-AP was reduced by chloride replacement. We conclude that the early outward current has two components: a chloride-sensitive component plus a 4-AP-sensitive component. Since a portion of the steady-state current was sensitive to 4-AP, the early outward current either does not fully inactivate or 4-AP blocks a component of time-independent background current.

Delays in inactivation development and activation kinetics in myxicola giant axons.

Na inactivation was studied in Myxicola (two-pulse procedure, 6-ms gap between conditioning and test pulses). Inactivation developed with an initial delay (range 130-817 microseconds) followed by a simple exponential decline (time constant tau c). Delays (deviations from a simple exponential) are seen only for brief conditioning pulses were gNa is slightly activated. Hodgkin-Huxley kinetics with series resistance, Rs, predict deviations from a simple exponential only for conditioning pulses that substantially activate gNa. Reducing INa fivefold (Tris substitution) had no effect on either tau c or delay. Delay in not generated by Rs or by contamination from activation development. The slowest time constant in Na tails is approximately 1 ms (Goldman and Hahin, 1978) and the gap was 6 ms. Shortening the gap to 2 ms had no effect on either tau c or delay. Delay is a true property of the channel. Delay decreased with more positive conditioning potentials, and also decreased approximately proportionally with time to peak gNa during the conditioning pulse, as expected for sequentially coupled activation and inactivation. In a few cases the difference between Na current values for brief conditioning pulses and the tau c exponential could be measured. Difference values decayed exponentially with time constant tau m. The inactivation time course is described by a model that assumes a process with the kinetics of gNa activation as a precursor to inactivation.

Effects of low-chloride solutions on action potentials of sheep cardiac Purkinje fibers.

The rapid repolarization during phase 1 of the action potential of sheep cardiac purkinje fibers has been attributed to a time- and voltage-dependent chloride current. In part, this conclusion was based on experiments that showed a substantial slowing of phase 1 when larger, presumably impermeant, anions were substituted for chloride in tyrode's solution. We have re- examined the electrical effects of low-chloride solutions. We recorded action potentials of sheep cardiac purkinje fibers in normal tyrode's solution and in low-chloride solutions made by substituting sodium propionate, acetylglycinate, methylsulfate, or methanesulfonate for the NaCl of Tyrode's solution. Total calcium was adjusted to keep calcium ion activity of test solutions equal to that of control solutions. Propionate gave qualitatively variable results in preliminary experiments; it was not tested further. Low-chloride solutions made with the other anions gave much more consistent results: phase 1 and the notch that often occurs between phases 1 and 2 were usually unaffected, and the action potential duration usually increased. The only apparent change in the resting potential was a transient 3-6 mV depolarization when low-chloride solution was first admitted to the chamber, and a symmetrical transient hyperpolarization when chloride was returned to normal. If a time- and voltage-dependent chloride current exists in sheep cardiac purkinje fibers, our results suggest that it plays little role in generating phase 1 of the action potential.

Temperature dependencies of Ca2+ current, Ca(2+)-activated Cl- current and Ca2+ transients in sensory neurones.

We recorded Ca2+ current (ICa) and Ca(2+)-activated Cl- current (ICl(Ca)) in isolated chick dorsal root ganglion neurons. At room temperature, ICl(Ca) is activated by Ca2+ influx (e.g. ICa) or by caffeine-stimulated release of Ca2+ via ryanodine receptors. Warming from room temperature to 37 degrees C increased the amplitude of ICa as well as the amplitude and rate of deactivation of ICl(Ca) activated by Ca2+ influx. In contrast, the activation of ICl(Ca) by caffeine-stimulated release of Ca2+ from intracellular stores abruptly failed between 19 and 28 degrees C. Warning from 22 to 37 degrees C reduced the amplitude of [Ca2+]i transients (measured with Indo-1) in chick neurons by more than 50% and reduced [Ca2+]i transients in mouse neurons by more than 40%. We investigated the role of mitochondria in these phenomena using carbonyl cyanide p-(trifluoromethoxy) phenylhydrazone (FCCP) to inhibit mitochondrial Ca2+ uptake. 1-4 microM FCCP slowed the deactivation of ICa-activated ICl(Ca) at 20 degrees C and at 36 degrees C, having a greater effect at the higher temperature. In the presence of FCCP, the rate of deactivation of ICl(Ca) was relatively insensitive to temperature in this protocol. In contrast, FCCP had little effect on ICl(Ca) activated by caffeine at warmer temperatures (> 22 degrees C) but prolonged ICl(Ca) at cooler temperatures (< 22 degrees C). Thus, we find that warming reduces the ability of Ca2+ release to raise [Ca2+]i increases the effect of mitochondria on the deactivation of ICl(Ca) if ICl(Ca) is activated by Ca2+ influx, and reduces the effect of mitochondria if ICl(Ca) is activated by caffeine-stimulated Ca2+ release.

The spatial relationship between Ca2+ channels and Ca2+-activated channels and the function of Ca2+-buffering in avian sensory neurons.

In order to learn about the endogenous Ca2+-buffering in the cytoplasm of chick dorsal root ganglion (DRG) neurons and the distance separating the ryanodine receptor Ca2+ release channels (RyRs) from the plasma membrane, we monitored the amplitude and time course of Ca2+-activated Cl- currents (I(ClCa)) in protocols that manipulated Ca2+-buffering. I(ClCa)was activated by Ca2+ influx via voltage-gated Ca2+ channels or by Ca2+ release via RyRs activated by 10 mM caffeine. I(ClCa)was measured in neurons at 20 degrees C and 35 degrees C using the amphotericin perforated patch technique that preserves endogenous Ca2+-buffering, or at 20 degrees C in neurons dialyzed with pipette solutions designed to replace the endogenous Ca2+ buffers. The amplitude of I(ClCa)activated by Ca2+ influx or Ca2+ at 20 degrees C was similar in the amphotericin neurons and neurons dialyzed with an 'unbuffered' pipette solution containing 10 mM citrate and 3 mM ATP as the only Ca2+ binding molecules. Thus, endogenous mobile Ca2+ buffers are relatively unimportant in chick DRG neurons. Warming the neurons from 20 degrees C to 35 degrees C increased the amplitude and the rate of deactivation of I(ClCa)consistent with an increased rate of Ca2+ buffering by fixed endogenous Ca2+-buffers. Dialysis with 2 mM EGTA/0.1 microM free Ca2+ reduced the amplitude and increased the rate of deactivation of I(ClCa)activated by Ca2+ influx and abolished I(ClCa)activated by Ca2+ release. Dialysis with 2 mM BAPTA/0.1 microM free Ca2+ abolished I(ClCa)activated by Ca2+ influx or release. Dialysis with 42 mM HEEDTA/0.5 microM free Ca2+ caused the persistent activation of I(ClCa). Calculations using a Ca2+-diffusion model suggest that the voltage-gated Ca2+ channels and the Ca2+-activated Cl- channels are separated by 50-400 nm and that the RyRs are more than 600 nm from the plasma membrane.

Amplitude histograms can identify positively but not negatively coupled channels.

We investigated the ability of amplitude distributions to determine if the gating of a pair of channels is coupled. These distributions are expressed as probability density amplitude histograms with peaks corresponding to zero, one, or two open channels. If the channels gate independently, the areas under these peaks (A, B, and C, respectively) determine the open probabilities of the two channels (p(1) and p(2)). Manivannan et al. (Biophys J 1994;61:216) showed that if Delta=B(2)/AC was less than 4 then the channel gating is coupled. We defined a similar parameter, D=(B(2)/4)-AC. If D<0 then channel gating is coupled. However, amplitude histograms with D0 are consistent with both independent and coupled gating. We further present a simple model in which channels are assumed to be identical and can be positively or negatively coupled. Here, amplitude histograms determine q=(B+2C)/2 (open probability of the coupled channels) and r=-D (the coupling parameter). Thus, positively coupled channels (r0) produce amplitude histograms with D<0 whereas negatively coupled channels (r<0) produce amplitude histograms with D0.

Determination of channel open probabilities from multichannel data.

We developed a method for determining whether channels in a multichannel patch or bilayer have the same or statistically significantly different open probabilities. We use a maximum likelihood method to fit the distribution of (unbinned) current amplitudes and to provide estimates of individual channel open probabilities, single channel currents, and standard deviations of the channel currents. These parameters are used to compare models with increasing constraints on the open probabilities including the model where all channels have different open probabilities and the model where all channels have the same open probability. A chi 2 statistic is used to identify models that are statistically less likely to predict the data. The ability of multichannel data to determine individual open probabilities is limited by two factors: the signal to noise ratio of the record and the fact that changes in amplitude distributions caused by a 0.2 difference in open probabilities are comparable in magnitude to the variations caused by random channel gating. These limitations notwithstanding, we demonstrate the utility of our approach by using it to analyze the open probabilities of 3 large conductance Ca2(+)-activated K+ channels in an artificial lipid bilayer revealing the response of one of those channels to GTP gamma S.

Dorsal root ganglion neurons of embryonic chicks contain nitric oxide synthase and respond to nitric oxide.

We investigated the function of nitric oxide (NO) in dorsal root ganglion (DRG) neurons from 10 day embryonic chicks and adult birds. NADPH-diaphorase activity, a histochemical marker for nitric oxide synthase (NOS) in paraformaldehyde-fixed neurons, and NOS-like immunoreactivity were localized in all neurons in thoracic and lumbar ganglia from embryos. However, only a subset of neurons from adults contained NOS-like immunoreactivity and NADPH-diaphorase activity. Thus, embryonic chick DRG neurons have the potential to synthesize NO in response to elevated cytoplasmic Ca2+. We also investigated the ability of dissociated embryonic chick DRG neurons to respond to NO by examining the effects of NO donors and 8-bromoguanosine 3',5'-cyclic monophosphate (8-Br-cGMP) on Ca2+ current (ICa) using the amphotericin-permeabilized patch-clamp technique: sodium nitroprusside (5 microM) reduced ICa to 0.68 +/- 0.06 (mean +/- S.D., n = 5) of control, S-nitroso-N-acetylpenicillamine (1 microM) reduced ICa to 0.44 +/- 0.06 (n = 4) of control, while 8-Br-cGMP (1 mM) reduced ICa to 0.58 +/- 0.22 (n = 5) of control. ICa was reduced in every neuron tested and this effect was partially reversed after approximately 10 min of washing. Thus, ICa of embryonic chick DRG neurons is inhibited by NO, possibly by a cGMP-dependent mechanism. These results indicate that all DRG neurons in embryonic chicks contain NOS-like immunoreactivity and respond to NO. Further, the percentage of NADPH-diaphorase positive neurons is reduced during development.

Potassium currents in chick sensory neurons change with development.

We used the whole-cell configuration of the giga-seal voltage-clamp to study voltage-gated potassium currents in sensory neurons dissociated from dorsal root ganglia from embryonic and hatched chicks. Neurons from 8-, 10-, 14-, and 18-day-old embryos (E8, E10, E14, E18) and 1- to 5-day-old chicks were studied under conditions which inhibited inward currents and calcium-activated currents (tetrodotoxin, no added calcium, intracellular EGTA). At all ages, potassium currents were activated by depolarizations to potentials positive to -40 mV. At a given age the amount of inactivation of outward current during 50- to 100-ms steps varied from cell to cell; some cells showed no inactivation while in others the outward current declined to about half of the peak current. On average, the amount of inactivation was fairly stable at E8, E10, E18, and in hatched chicks but showed a transient increase at E14. In contrast, currents elicited by 50-ms test steps following 2-s conditioning steps showed an age dependent change. In E8 neurons, shifting the conditioning voltage from -100 to -90 mV had little or no effect on the current at the end of the test step while earlier outward current was reduced. In cells from older embryos or hatched chicks, similar conditioning voltages caused reductions of both early and late currents during the test step. The relative amount of late current inactivated by this protocol increased as the age of the chicks increased. In addition, the amount of variation in the inactivation properties was larger in cells from older embryos and hatched birds. The changes in outward current occur during a period in which new neurons are formed and existing neurons mature and establish function.

The reversal potential of Ca(2+)-activated Cl(-) currents indicates that chick sensory neurons accumulate intracellular Cl(-).

In order to establish the physiological role of the Ca(2+)-activated Cl(-) current (I(Cl(Ca))) of chick primary afferent neurons, I measured the reversal potential of this current using either the amphotericin perforated patch technique (that alters intracellular Cl(-)) or the gramicidin perforated patch technique (that does not perturb intracellular Cl(-)). In the amphotericin experiments at 35 degrees C, I(Cl(Ca)) reversed at the Cl(-) equilibrium potential (E(Cl)=-24 mV) set by the superfusate (147 mM Cl(-)) and the pipette solution (60 mM Cl(-)). In contrast, in the gramicidin experiments at 35 degrees C, I(Cl(Ca)) reversed at -42+/-2 mV, midway between E(Cl) of the solutions and E(Cl) expected if Cl(-) were passively distributed. Thus the gramicidin perforated patch technique monitors Cl(-) currents without perturbing intracellular Cl(-). Further, the data imply that chick dorsal root ganglia (DRG) neurons actively accumulate Cl(-). I(Cl(Ca)) reversed at the same potential (-46+/-3 mV) at 20 degrees C indicating that the non-equilibrium distribution of Cl(-) is maintained at the lower temperature. Thus, I(Cl(Ca)) is a depolarizing current that can contribute to the after-depolarization in chick DRG neurons and thereby alter Ca(2+) influx.

Alosetron and the rapid component of delayed rectifying potassium current in cardiac cells.

Some drugs acting on 5-hydroxytryptamine receptors inhibit the rapid component of delayed rectifying potassium currents (I(Kr)) in cardiac muscle cells. This is associated with lengthening of the QT interval in the cardiac cycle and can lead to fatal arrhythmias. We investigated whether alosetron, a novel 5HT3 antagonist proposed for treatment of irritable bowel syndrome (IBS), blocks I(Kr) in guinea pig cardiac myocytes. I(Kr) was isolated under whole-cell voltage clamp, and was identified by its sensitivity to the selective I(Kr) antagonist E4031. Cisapride (10(-6) M) inhibited the E4031-sensitive current while alosetron (10(-10)-10(-6) M) had no effect on I(Kr). We also found that alosetron did not inhibit I(Ks). Therefore, use of alosetron for treatment of IBS should not be confounded by long QT syndrome.

Template switching within exons 3 and 4 of KV11.1 (HERG) gives rise to a 5' truncated cDNA.

K(V)11.1 (HERG) channels contribute to membrane potential in a number of excitable cell types. We cloned a variant of K(V)11.1 from human jejunum containing a 171 bp deletion spanning exons 3 and 4. Expression of a full-length cDNA clone containing this deletion gave rise to protein that trafficked to the cell membrane and generated robust currents. The deletion occurred in a G/C-rich region and identical sequence elements of UGGUGG were located at the deletion boundaries. In recent studies these features have been implicated to cause deletions via template switching during cDNA synthesis. To examine this possibility we compared cDNAs from human brain, heart, and jejunum synthesized at lower (42 degrees C) and higher temperatures (70 degrees C). The 171 bp deletion was absent at the higher temperature. Our results suggest that the sequence and secondary structure of mRNA in the G/C rich region leads to template switching producing a cDNA product with a 171 bp deletion.

Internally perfused Myxicola giant axons showing long-term survival.

An improved method for internally perfusing the Myxicola giant axon based on removing the axoplasm by dispersing it in KCl-KF salt solutions is described. Proteolytic enzymes are not introduced. With this improved method perfused preparations show long-term stability of their electrical properties and the ability to generate action potentials for many hours. Mean initial values for resting membrane potential, action potential amplitude, and peak inward current were -68 mV, 118 mV, and 3.62 mA/cm2, respectively. Mean resting membrane resistance was 75% of that in intact axons. In one series of voltage clamp experiments, perfused preparations remained excitable for a mean period of 5 1/2 h, but this period could exceed 10 h. 4 min are needed for exchange of internal solutions. At least 50 mM KF is required both in the axoplasm liquefying solution and in the standard perfusate to obtain stable preparations.

An Excel-based model of Ca2+ diffusion and fura 2 measurements in a spherical cell.

We wrote a program that runs as a Microsoft Excel spreadsheet to calculate the diffusion of Ca2+ in a spherical cell in the presence of a fixed Ca2+ buffer and two diffusible Ca2+ buffers, one of which is considered to be a fluorescent Ca2+ indicator. We modeled Ca2+ diffusion during and after Ca2+ influx across the plasma membrane with parameters chosen to approximate amphibian sympathetic neurons, mammalian adrenal chromaffin cells, and rat dorsal root ganglion neurons. In each of these cell types, the model predicts that spatially averaged intracellular Ca2+ activity ([Ca2+]avg) rises to a high peak and starts to decline promptly on the termination of Ca2+ influx. We compared [Ca2+]avg with predictions of ratiometric Ca2+ measurements analyzed in two ways. Method 1 sums the fluorescence at each of the two excitation or emission wavelengths over the N compartments of the model, calculates the ratio of the summed signals, and converts this ratio to Ca2+ ([Ca2+]avg,M1). Method 2 sums the measured number of moles of Ca2+ in each of the N compartments and divides by the volume of the cell ([Ca2+]avg,M2). [Ca2+]avg,M1 peaks well after the termination of Ca2+ influx at a value substantially less than [Ca2+]avg because the summed signals do not reflect the averaged free Ca2+ if the signals come from compartments containing gradients in free Ca2+ spanning nonlinear regions of the relationship between free Ca2+ and the fluorescence signals. In contrast, [Ca2+]avg,M2 follows [Ca2+]avg closely.

Theory of the kinetic analysis of patch-clamp data.

This paper describes a theory of the kinetic analysis of patch-clamp data. We assume that channel gating is a Markov process that can be described by a model consisting of n kinetic states and n(n - 1) rate constants at each voltage, and that patch-clamp data describe the occupancy of x different conductance levels over time. In general, all the kinetic information in a set of patch-clamp data is found in either two-dimensional dwell time histograms describing the frequency of observation of sequential dwell times of durations tau 1 and tau 2 (Fredkin, D. R., M. Montal, and J. A. Rice, 1985, Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, vol. 1, 269-289) or in three-point joint probability functions describing the probability that a channel is in a given conductance at time t, and at time t + tau 1, and at time t + tau 1 + tau 2. For the special case of channels with a single open state plus multiple closed states, one-dimensional analyses provide all of the kinetic information. Stationary patch-clamp data have information that can be used to determine H rate constants, where H = n(n - 1) - G and G is the number of intraconductance rate constants. Thus, to calculate H rate constants, G rate constants must be fixed. In general there are multiple sets of G rate constants that can be fixed to allow the calculation of H rate constants although not every set of G rate constants will work. Arbitrary assignment of the G intraconductance rate constants equal to zero always provides a solution and the calculation of H rate constants. Nonstationary patch-clamp data have information for the determination of H rate constants at a reference voltage plus n(n - 1) rate constants at all test voltages. Thus, nonstationary data have extra information about the voltage dependencies of rate constants that can be used to rule out kinetic models that cannot be disqualified on the basis of stationary data.