Kinetics of homomeric GluR6 glutamate receptor channels.

We studied the kinetics of the unedited version of rat GluR6 glutamate (glu) receptor channels, GluR6Q, in outside-out patches using a system for submillisecond solution exchange. Half-maximum activation of the channels was reached with approximately 0.5 microM glu. The maximum slope of the double-logarithmic plot of the peak current versus glu was approximately 1.3, indicating that at least two binding steps are necessary to open the channels. Currents in response to a pulse of 10 microM glu had a short rise time (10-90% of peak current) of approximately 220 microseconds at approximately 20 degrees C. The rise time increased with falling glu concentration, reaching approximately 6.0 ms with 10 microM glu. In the continued presence of glu, the channels desensitized, and this desensitization can be described with a single time constant of approximately 7.0 ms for a pulse of 10 microM glu. The steady-state current in response to a long pulse of 10 microM glu was below 1/280th of the peak current. The time constant of desensitization was found to be independent of concentration between 30.0 and 0.3 microM glu, but to be increased for lower concentrations. After a short pulse of 1 ms duration and 10 or 0.3 microM glu, currents decayed with a time constant of approximately 2.5 ms. Recovery from desensitization after a pulse took approximately 5 s, and the half-time of recovery was approximately 2.2 s. Continuous application of low concentrations of glutamate reduced the peak currents in response to a pulse of 10 microM glu markedly. Fifty percent response reduction was observed in the continuous presence of approximately 0.3 microM glu. Our results for homomeric GluR6 agree with a cyclical reaction scheme developed for completely desensitizing, glu-activated channels on crayfish muscles.     

Flickering of a nicotinic ion channel to a subconductance state.

Nicotinic acetylcholine channels show bursts of activity where open channel currents are separated from each other by short closed periods called flickers. These flickers presumably represent transitions from the open state to the state preceding the first opening of a burst (doubly liganded, closed state). Using tissue cultured chick pectoral muscle, we have examined the amplitude distribution of flickers. Of those events sufficiently long to permit accurate measurement of the amplitude (approximately 25% of all flickers), approximately two-thirds had a mean current equal to 10% of the fully open channel. The remaining one-third did appear to close completely. The subconducting flicker state is not a requisite step preceding channel opening. We conclude that there are three types of flicker events: a short event (time constant approximately 0.1 ms) whose current distribution is uncertain and two longer events (time constant approximately 1 ms), one of which has a current approximately 10% of the main open state and the other of which has a current indistinguishable from zero. In contrast, the amplitude of flickers induced by the local anesthetic QX-222 is indistinguishable from zero.     

Comparison of excitatory currents activated by different transmitters on crustacean muscle. II. Glutamate-activated currents and comparison with acetylcholine currents present on the same muscle

The properties of glutamate-activated excitatory currents on the gm6 muscle from the foregut of the spiny lobsters Panulirus argus and interruptus and the crab Cancer borealis were examined using either noise analysis, analysis of synaptic current decays, or slow iontophoretic currents. The properties of acetylcholine currents activated in nonjunctional regions of the gm6 muscle were also examined. At 12 degrees C and -80 mV, the predominant time constant of power spectra from glutamate-activated current noise was approximately 7 ms and the elementary conductance was approximately 34 pS. At 12 degrees C and -80 mV, the predominant time constant of acetylcholine- activated channels was approximately 11 ms with a conductance of approximately 12 pS. Focally recorded glutamatergic extracellular synaptic currents on the gm6 muscle decayed with time constants of approximately 7-8 ms at 12 degrees C and -80 mV. The decay time constant was prolonged e-fold about every 225-mV hyperpolarization in membrane potential. The Q10 of the time constant of the synaptic current decay was approximately 2.6. The voltage dependence of the steady-state conductance increase activated by iontophoretic application of glutamate has the opposite direction of the steady-state conductance activated by cholinergic agonists when compared on the gm6 muscles. The glutamate-activated conductance increase is diminished with hyperpolarization. The properties of the marine crustacean glutamate channels are discussed in relation to glutamate channels in other organisms and to the acetylcholine channels found on the gm6 muscle and the gm1 muscle of the decapod foregut (Lingle and Auerbach, 1983).     

The excitatory glutamate-activated channel recorded in cell-attached and excised patches from the membranes of tail,leg and stomach muscles of crayfish

Summary Glutamate activated, excitatory single channel currents were recorded from 5 different muscles of crayfish (Austropotamobius torrentium) from abdomen, legs and stomach. Cell-attached and outside-out excised membrane patches with G-seals were studied. At –70 mV membrane potential and 19 °C, single channel currents activated by 0.5 mM glutamate had an amplitude of –7.6 pA, a mean open time of 0.22 ms and a mean burst length of 0.58 ms. These values did not show significant differences in all muscles investigated. The distributions of open times and of burst durations were described by single exponentials. The distributions of closed times could be fitted only by at least two exponentials. The short component of on average 0.1 ms represented closings within bursts, a longer component of on average 0.9 ms grouping of bursts. Burst durations (but not individual open times) increased with rising glutamate concentration: the relative open time of the channel was approximately proportional to glutamate concentration between 0.1 and 5 mM. The channels described above could not be activated by the glutamate analogues kainate and NMDA, but were about 10 times more sensitive to quisqualate than to glutamate. Quisqualate elicited single channel currents of the same amplitude as those triggered by glutamate. Compared at the same concentrations, channel open times and burst durations were about 4 times longer in quisqualate than in glutamate. A model describing the kinetics of the glutamate-activated excitatory channels is discussed. In addition, a type of Ca-independent, depolarization-activated K⁺-channel is reported.     

Glutamate activation of a single NMDA receptor-channel produces a cluster of channel openings.

Activations of the N-methyl-D-aspartate (NMDA) receptor by glutamate were studied in outside-out patches from CA1 cells in rat hippocampal slices. Very low glutamate concentrations (20-100 nM) were used so that individual receptor activations would be well separated. The shut-time distribution contained at least five components, only the longest component being obviously concentration dependent. The three briefest shut-time components had time constants of 56 microseconds, 0.68 ms and 10.1 ms; all of these were independent of glutamate concentration. An individual activation of the receptor therefore produces a long cluster of channel openings that contains longer gaps than have been reported for receptor activations by other fast neurotransmitters. In addition, (i) some activations may contain still longer (mean 78 ms) shut periods generating 'super clusters', and (ii) a significant amount of NMDA current may be carried by prolonged ('high P(open)') periods during which the channel is open for most of the time. Such periods occur intermittently even at these very low glutamate concentrations. It is suggested that the slow time course of the NMDA receptor-mediated synaptic currents may be determined mainly by the channel activation kinetics.     

Ionic currents in dispersed chemoreceptor cells of the mammalian carotid body

Ionic currents of enzymatically dispersed type I and type II cells of the carotid body have been studied using the whole cell variant of the patch-clamp technique. Type II cells only have a tiny, slowly activating outward potassium current. By contrast, in every type I chemoreceptor cell studied we found (a) sodium, (b) calcium, and (c) potassium currents. (a) The sodium current has a fast activation time course and an activation threshold at approximately -40 mV. At all voltages inactivation follows a single exponential time course. The time constant of inactivation is 0.67 ms at 0 mV. Half steady state inactivation occurs at a membrane potential of approximately -50 mV. (b) The calcium current is almost totally abolished when most of the external calcium is replaced by magnesium. The activation threshold of this current is at approximately -40 mV and at 0 mV it reaches a peak amplitude in 6-8 ms. The calcium current inactivates very slowly and only decreases to 27% of the maximal value at the end of 300-ms pulses to 40 mV. The calcium current was about two times larger when barium ions were used as charge carriers instead of calcium ions. Barium ions also shifted 15-20 mV toward negative voltages the conductance vs. voltage curve. Deactivation kinetics of the calcium current follows a biphasic time course well fitted by the sum of two exponentials. At -80 mV the slow component has a time constant of 1.3 +/- 0.4 ms whereas the fast component, with an amplitude about 20 times larger than the slow component, has a time constant of 0.16 +/- 0.03 ms. These results suggest that type I cells have predominantly fast deactivating calcium channels. The slow component of the tails may represent the activity of a small population of slowly deactivating calcium channels, although other possibilities are considered. (c) Potassium current seems to be mainly due to the activity of voltage-dependent potassium channels, but a small percentage of calcium-activated channels may also exist. This current activates slowly, reaches a peak amplitude in 5-10 ms, and thereafter slowly inactivates. Inactivation is almost complete in 250-300 ms. The potassium current is reversibly blocked by tetraethylammonium. Under current-clamp conditions type I cells can spontaneously fire large action potentials. These results indicate that type I cells are excitable and have a variety of ionic conductances. We suggest a possible participation of these conductances in chemoreception.     

Sodium and calcium currents in dispersed mammalian septal neurons

Voltage-gated Na+ and Ca2+ conductances of freshly dissociated septal neurons were studied in the whole-cell configuration of the patch-clamp technique. All cells exhibited a large Na+ current with characteristic fast activation and inactivation time courses. Half-time to peak current at -20 mV was 0.44 +/- 0.18 ms and maximal activation of Na+ conductance occurred at 0 mV or more positive membrane potentials. The average value was 91 +/- 32 nS (approximately 11 mS cm-2). At all membrane voltages inactivation was well fitted by a single exponential that had a time constant of 0.44 +/- 0.09 ms at 0 mV. Recovery from inactivation was complete in approximately 900 ms at -80 mV but in only 50 ms at -120 mV. The decay of Na+ tail currents had a single time constant that at -80 mV was faster than 100 microseconds. Depolarization of septal neurons also elicited a Ca2+ current that peaked in approximately 6-8 ms. Maximal peak Ca2+ current was obtained at 20 mV, and with 10 mM external Ca2+ the amplitude was 0.35 +/- 0.22 nA. During a maintained depolarization this current partially inactivated in the course of 200-300 ms. The Ca2+ current was due to the activity of two types of conductances with different deactivation kinetics. At -80 mV the closing time constants of slow (SD) and fast (FD) deactivating channels were, respectively, 1.99 +/- 0.2 and 0.11 +/- 0.03 ms (25 degrees C). The two kinds of channels also differed in their activation voltage, inactivation time course, slope of the conductance-voltage curve, and resistance to intracellular dialysis. The proportion of SD and FD channels varied from cell to cell, which may explain the differential electrophysiological responses of intracellularly recorded septal neurons.     

Rapid activation, desensitization, and resensitization of synaptic channels of crayfish muscle after glutamate pulses.

Completely desensitizing excitatory channels were activated in outside-out patches of crayfish muscle membrane by applying glutamate pulses with switching times of approximately 0.2 ms for concentration changes. Channels were almost completely activated with 10 mM glutamate. Maximum activation was reached within 0.4 ms with greater than or equal to 1 mM glutamate. Channel open probability decayed with a time constant of desensitization of 2 ms with 10 mM glutamate and more rapidly at lower glutamate concentrations. The rate of beginnings of bursts (average number of beginnings of bursts per time bin) decayed even faster but approximately in proportion to the glutamate concentration. The dose-response curve for the channel open probability and for the rate of bursts had a maximum double-logarithmic slope of 5.1 and 4.2, respectively. Channels desensitized completely without opening at very low or slowly rising glutamate concentrations. Desensitization thus originates from a closed channel state. Resensitization was tested by pairs of completely desensitizing glutamate pulses. Sensitivity to the second pulse returned rapidly at pulse intervals between 1 and 2 ms and was almost complete with an interval of 3 ms. Schemes of channel activation by up to five glutamate binding steps, with desensitization by glutamate binding from closed states, are discussed. At high agonist concentrations bursts are predominantly terminated by desensitization. Quantal currents are generated by pulses of greater than 1 mM glutamate, and their decay is determined by the duration of presence of glutamate and possibly by desensitization.     

Ion channels activated by L-glutamate and GABA in cultured cerebellar neurons of the rat

Glutamate and GABA-receptor channels were investigated in explants of rat cerebellum grown in cell culture. The patch-clamp technique was used to examine neurons under whole cell clamp and the properties of channels were derived by analysis of glutamate and GABA-evoked current noise. In addition, single channel currents activated by glutamate were recorded from isolated outside-out patches of membrane. We found evidence for at least two types of glutamate receptor-channels in cerebellar cells. Some neurons exhibited a channel of 50 pS conductance with a Lorentzian noise spectrum of 5.9 ms time constant. Single channels were readily resolved both in whole cell clamp and excised patches. Other neurons possessed low conductance channels which produced two component spectra. Estimates of the single channel conductance gave a value of about 140 fS. GABA channel noise obtained from these cells was also fitted by two component spectra which gave single channel conductance of 16 pS.     

A family of glutamatergic,excitatory channel types at the crayfish neuromuscular junction

Summary Outside-out patches from membrane of muscles of crayfish (Austropotamobius torrentium) were excised, and L-glutamate (glu) was applied to these patches in pulses of different duration, performing a concentration step within about 0.2 ms. While a uniform population of cationic channels is seen in equilibrium applications of glu, four kinetically different channel types were revealed by the pulse applications of glu. All these channel types had the same single channel conductance and durations of elementary short single channel openings and closings, and they thus form a family of channels. Type I, incompletely desensitizing channels reacted to a pulse of 10 mM glu with a peak open probability of 0.7 within 0.3 ms. Thereafter open probability decayed with a time constant of desensitization of about 5 ms, reaching a plateau of about 1/20 peak probability which was maintained as long as 10 mM glu were present. The peak probabilities of channel opening were proportional to approximately power 2.5 of the glu concentration, for low concentrations. Type II, completely desensitizing channels also were activated very rapidly by glu pulses, but their time constant of desensitization was 1–2 ms, and no channel openings were observed after more than 10 ms presence of a high glu concentration. The peak probabilities of channel opening rose with about the 5th power of glu concentration (for low concentrations). Type III, non-desensitizing channels, were observed relatively rarely. They were activated much more slowly and reached much lower probabilities of opening than type I and II channels. They did not show appreciable desensitization. Type IV, short-opening channels, develop sometimes from type I channels while recording, and may revert to the type I. Type IV channels show an additional open time component of 0.08 ms average duration, and a relatively long additional closed time of on average 1.3 ms. In addition to channel measurements, distributions of amplitudes and time courses of macroscopic quantal currents were determined. It is discussed in which way the different channel types may contribute to the quantal currents.     

Characterization of the calcium-activated chloride channel in isolated guinea-pig hepatocytes

Macroscopic and unitary currents through Ca(2+)-activated Cl- channels were examined in enzymatically isolated guinea-pig hepatocytes using whole-cell, excised outside-out and inside-out configurations of the patch-clamp technique. When K+ conductances were blocked and the intracellular Ca2+ concentration ([Ca2+]i) was set at 1 microM (pCa = 6), membrane currents were observed under whole-cell voltage-clamp conditions. The reversal potential of the current shifted by approximately 60 mV per 10-fold change in the external Cl- concentration. In addition, the current did not appear when Cl- was omitted from the internal and external solutions, indicating that the current was Cl- selective. The current was activated by increasing [Ca2+]i and was inactivated in Ca(2+)-free, 5 mM EGTA internal solution (pCa > 9). The current was inhibited by bath application of 9- anthracenecarboxylic acid (9-AC) and 4,4'-diisothiocyanatostilbene-2,2'- disulfonic acid (DIDS) in a voltage-dependent manner. In single channel recordings from outside-out patches, unitary current activity was observed, whose averaged slope conductance was 7.4 +/- 0.5 pS (n = 18). The single channel activity responded to extracellular Cl- changes as expected for a Cl- channel current. The open time distribution was best described by a single exponential function with mean open lifetime of 97.6 +/- 10.4 ms (n = 11), while at least two exponentials were required to fit the closed time distributions with a time constant for the fast component of 21.5 +/- 2.8 ms (n = 11) and that for the slow component of 411.9 +/- 52.0 ms (n = 11). In excised inside-out patch recordings, channel open probability was sensitive to [Ca2+]i. The relationship between [Ca2+]i and channel activity was fitted by the Hill equation with a Hill coefficient of 3.4 and the half-maximal activation was 0.48 microM. These results suggest that guinea-pig hepatocytes possess Ca(2+)-activated Cl- channels.     

Study of conductance changes of bilayer lipid membrane induced by electric field

Changes in the bilayer lipid membrane (BLM) conductance induced by electric field were studied. BLMs were formed from diphytanoylphosphocholine (DPhPC) solution in squalene. Certain time after a constant voltage (200-500 mV) was applied to the BLM in the voltage-clamp mode, the BLM conductance started to grow up to approximately 10 nS until the BLM ruptured. The conductance often changed abruptly (with the front duration of less than 33 micros) and then stabilized for a relatively long time (up to 10; 300 ms on average) thus resembling the ion channel activity. The mean amplitude of conductance steps was 650 pS. However, in some cases a slow conductance drift was recorded. When N-methyl-D-glucamine/glutamate ions were used instead of KCl, the conductance changes became 5 times smaller. We suggest that formation in the BLM of single pores approximately 1 nm in diameter should result in the observed changes in BLM conductance. The BLM conductance growth was due to consecutive opening of several such pores. When the electric field amplitude was abruptly decreased (down to 50-100 mV), the conductance dropped rapidly to the background value. When we increased the voltage again, the BLM conductance right after the increase depended on the time BLM spent under "weak" electric field. If this time exceeded 500 ms, the conductance was at the background level, but when the time was diminished, the conductance reached the value recorded before the voltage decrease. These data imply that the closure of the pores should lead to the formation in BLM of small defects (prepores) that can be easily transformed into pores when the voltage is increased. The lifetimes of such prepores did not exceed 500 ms.     

Outward current in single smooth muscle cells of the guinea pig taenia coli

In single myocytes of the guinea pig taenia coli, dispersed by enzymatic digestion, the late outward current is carried by K+. It has both a Ca2+-activated component and a voltage-dependent component which is resistant to external Co2+. The reversal potential is -84 mV, and the channel(s) for it are highly selective to K+. At 33 degrees C, the activation follows n2 kinetics, with a voltage-dependent time constant of 10.6 ms at 0 mV, which shortens to 1.7 ms at +70 mV. Deactivation follows a single-exponential time course, with a voltage-dependent time constant of 11 ms at -50 mV, which lengthens to 33 ms at -20 mV. During a 4.5-s maintained depolarization, IK inactivates, most of it into two exponential components, but there is a small noninactivating residue. It is surmised that during an action potential under physiological conditions, there is sufficient IK to cause repolarization.     

Characterization of slowly inactivating KV{alpha} current in rabbit pulmonary neuroepithelial bodies: effects of hypoxia and nicotine

Pulmonary neuroepithelial bodies (NEB) form innervated cell clusters that express voltage-activated currents and function as airway O(2) sensors. We investigated A-type K(+) currents in NEB cells using neonatal rabbit lung slice preparation. The whole cell K(+) current was slowly inactivating with activation threshold of approximately -30 mV. This current was blocked approximately 27% by blood-depressing substance I (BDS-I; 3 microM), a selective blocker of Kv3.4 subunit, and reduced approximately 20% by tetraethylammonium (TEA; 100 microM). The BDS-I-sensitive component had an average peak value of 189 +/- 14 pA and showed fast inactivation kinetics that could be fitted by one-component exponential function with a time constant of (tau1) 77 +/- 10 ms. This Kv slowly inactivating current was also blocked by heteropodatoxin-2 (HpTx-2; 0.2 microM), a blocker of Kv4 subunit. The HpTx-2-sensitive current had an average peak value of 234 +/- 23 pA with a time constant (tau) 82 +/- 11 ms. Hypoxia (Po(2) = 15-20 mmHg) inhibited the slowly inactivating K(+) current by approximately 47%, during voltage steps from -30 to +30 mV, and no further inhibition occurred when TEA was combined with hypoxia. Nicotine at concentrations of 50 and 100 microM suppressed the slowly inactivating K(+) current by approximately 24 and approximately 40%, respectively. This suppression was not reversed by mecamylamine suggesting a direct effect of nicotine on these K(+) channels. In situ hybridization experiments detected expression of mRNAs for Kv3.4 and Kv4.3 subunits, while double-label immunofluorescence confirmed membrane localization of respective channel proteins in NEB cells. These studies suggest that the hypoxia-sensitive current in NEB cells is carried by slowly inactivating A-type K(+) channels, which underlie their oxygen-sensitive potassium currents, and that exposure to nicotine may directly affect their function, contributing to smoking-related lung disease.     

Voltage-clamp studies on the canine Purkinje strand

Purkinje strands were excised from the left and right ventricles of adult mongrel dogs and cut to lengths of less than 2.0 mm in order to apply the two-microelectrodes voltage-clamp technique. A sizeable fraction of these preparations fully recover following dissection, with resting potentials more negative than--80 mV and upstroke velocities faster than 290 V s-1. Analysis of the voltage response to small current pulses shows that the short Purkinje strands can be treated as simple finite one-dimensional cables with ends of infinite resistance. The average length constant is 2.5 mm. In keeping with the relatively long length constant, insertion of a third microelectrode along the strand demonstrates a high degree of longitudinal homogeneity of the voltage clamp. Analysis of the capacity transient gives an estimate of the total capacity, normalized to cylindrical surface area, of 11.5 muF cm-2. The final decay of the capacity transient is a single exponential with an average time constant of 1 ms. A second slower component to the final decay of the capacity transient is absent in solutions of normal conductivity as well as in solutions of reduced (13%) conductivity. This suggests that the extracellular series resistance may be relatively small. The magnitude of the K+ depletion current was estimated by measuring the ratio of depletion current to instantaneous current. This ratio averaged 10%. These two results are consistent with the morphometric data described in the accompanying paper, which show that the canine preparation has wider extracellular clefts than the ungulate preparation. The existence of the full complement of inward and outward currents, including the pacemaker current, is demonstrated. The presence of wide clefts does not affect the potential at which the pacemaker current reverses (about--107 mV in 4 mM [K+] Tyrode solution), since the pacemaker current reverses at approximately the same potential in the canine Purkinje preparation as it does in the ungulate.     

Tail currents in the myelinated axon of Xenopus laevis suggest a two-open-state Na channel.

Na tail currents in the myelinated axon of Xenopus laevis were measured at -70 mV after steps to -10 mV. The tail currents were biexponential, comprising a fast and a slow component. The time constant of the slow tail component, analyzed in the time window 0.35-0.50 ms, was independent of step duration, and had a value of 0.23 ms. The amplitude, extrapolated back to time 0, varied, however, with step duration. It reached a peak after 0.7 ms and inactivated relatively slowly (at 2.1 ms the absolute value was reduced by approximately 30%). The amplitude of the fast component, estimated by subtracting the amplitude of the slow component from the calculated total tail current amplitude, reached a peak (three times larger than that of the slow component) after 0.5 ms and inactivated relatively fast (at 2.1 ms it was reduced by approximately 65%). The results were explained by a novel Na channel model, comprising two open states bifurcating from a common closed state and with separate inactivating pathways. A voltage-regulated use of the two pathways explains a number of findings reported in the literature.     

Inward current in single smooth muscle cells of the guinea pig taenia coli

Using the tight-seal voltage-clamp method, the ionic currents in the enzymatically dispersed single smooth muscle cells of the guinea pig taenia coli have been studied. In a physiological medium containing 3 mM Ca2+, the cells are gently tapering spindles, averaging 201 (length) x 8 microns (largest diameter in center of cell), with a volume of 5 pl. The average cell capacitance is 50 pF, and the specific membrane capacitance 1.15 microF/cm2. The input impedance of the resting cell is 1-2 G omega. Spatially uniform voltage-control prevails after the first 400 microseconds. There is much overlap of the inward and outward currents, but the inward current can be isolated by applying Cs+ internally to block all potassium currents. The inward current is carried by Ca2+. Activation begins at approximately -30 mV, maximum ICa occurs at +10-+20 mV, and the reversal potential is approximately +75 mV. The Ca2+ channel is permeable to Sr2+ and Ba2+, and to Cs+ moving outwards, but not to Na+ moving inwards. Activation and deactivation are very rapid at approximately 33 degrees C, with time-constants of less than 1 ms. Inactivation has a complex time course, resolvable into three exponential components, with average time constants (at 0 mV) of 7, 45, and 400 ms, which are affected differently by voltage. Steady-state inactivation is half-maximal at -30 mV for all components combined, but -36 mV for the fast component and -26 and -23 mV for the other two components. The presence of multiple forms of Ca2+ channel is inferred from the inactivation characteristics, not from activation properties. Recovery of the fast channel occurs with a time-constant of 72 ms (at +10 mV). Ca2+ influx during an action potential can transfer approximately 9 pC of charge, which could elevate intracellular Ca2+ concentration adequately for various physiological functions.     

The calcium-activated potassium channels of turtle hair cells

A major factor determining the electrical resonant frequency of turtle cochlear hair cells is the time course of the Ca-activated K current (Art, J. J., and R. Fettiplace. 1987. Journal of Physiology. 385:207- 242). We have examined the notion that this time course is dictated by the K channel kinetics by recording single Ca-activated K channels in inside-out patches from isolated cells. A hair cell's resonant frequency was estimated from its known correlation with the dimensions of the hair bundle. All cells possess BK channels with a similar unit conductance of approximately 320 pS but with different mean open times of 0.25-12 ms. The time constant of relaxation of the average single- channel current at -50 mV in 4 microM Ca varied between cells from 0.4 to 13 ms and was correlated with the hair bundle height. The magnitude and voltage dependence of the time constant agree with the expected behavior of the macroscopic K(Ca) current, whose speed may thus be limited by the channel kinetics. All BK channels had similar sensitivities to Ca which produced half-maximal activation for a concentration of approximately 2 microM at +50 mV and 12 microM at -50 mV. We estimate from the voltage dependence of the whole-cell K(Ca) current that the BK channels may be fully activated at -35 mV by a rise in intracellular Ca to 50 microM. BK channels were occasionally observed to switch between slow and fast gating modes which raises the possibility that the range of kinetics of BK channels observed in different hair cells reflects a common channel protein whose kinetics are regulated by an unidentified intracellular factor. Membrane patches also contained 30 pS SK channels which were approximately 5 times more Ca-sensitive than BK channels at -50 mV. The SK channels may underlie the inhibitory synaptic potential produced in hair cells by efferent stimulation.     

Two-dimensional probability density analysis of single channel currents from reconstituted acetylcholine receptors and sodium channels

Two-dimensional probability density analysis of single channel current recordings was applied to two purified channel proteins reconstituted in planar lipid bilayers: Torpedo acetylcholine receptors and voltage-sensitive sodium channels from rat brain. The information contained in the dynamic history of the gating process, i.e., the time sequence of opening and closing events was extracted from two-dimensional distributions of transitions between identifiable states. This approach allows one to identify kinetic models consistent with the observables. Gating of acetylcholine receptors expresses "memory" of the transition history: the receptor has two channel open (O) states; the residence time in each of them strongly depends on both the preceding open time and the intervening closed interval. Correspondingly, the residence time in the closed (C) states depends on both the preceding open time and the preceding closed time. This result confirms the scheme that considers, at least, two transition pathways between the open and closed states and extends the details of the model in that it defines that the short-lived open state is primarily entered from long-lived closed states while the long-lived open state is accessed mainly through short-lived closed states. Since ligand binding to the acetylcholine-binding sites is a reaction with channel closed states, we infer that the longest closed state (approximately 19 ms) is unliganded, the intermediate closed state (approximately 2 ms) is singly liganded and makes transitions to the short open state (approximately 0.5 ms) and the shortest closed state (approximately 0.4 ms) is doubly liganded and isomerizes to long open states (approximately 5 ms). This is the simplest interpretation consistent with available data. In contrast, sodium channels modified with batrachotoxin to eliminate inactivation show no correlation in the sequence of channel opening and closing events, i.e., have no memory of the transition history. This result is, therefore, consistent with any kinetic scheme that considers a single transition pathway between open and closed states, and confirms the C-C-O model previously inferred from one-dimensional distribution analysis. The strategy described should be of general validity in the analysis of single channel events from channel proteins in both natural and reconstituted membranes.     

Pairwise Comparisons of Mitochondrial DNA Sequences in Stable and Exponentially Growing Populations

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.