Biophysical properties of mouse connexin30 gap junction channels studied in transfected human HeLa cells

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1 9430 Journal of Physiology (1999), 519.3, pp Biophysical properties of mouse connexin30 gap junction channels studied in transfected human HeLa cells Virginijus Valiunas *, Dieter Manthey, Rolf Vogel *, Klaus Willecke and Robert Weingart * * Department of Physiology, University of Bern, B uhlplatz 5, CH-3012 Bern, Switzerland and Institute of Genetics, University of Bonn, R omerstrasse 164, D Bonn, Germany (Received 22 March 1999; accepted after revision 22 June 1999) 1. Human HeLa cells expressing mouse connexin30 (Cx30) were used to study the electrical properties of Cx30 gap junction channels. Experiments were performed on cell pairs with the dual voltage-clamp method. 2. The gap junction conductance (gj) at steady state showed a bell-shaped dependence on junctional voltage (Vj; Boltzmann fit: Vj,0 = 27mV, gj,min =0 15, z = 4). The instantaneous gj decreased slightly with increasing Vj. 3. The gap junction currents (Ij) declined with time following a single exponential. The time constants of Ij inactivation (ôé) decreased with increasing Vj. 4. Single channels exhibited a main state, a residual state and a closed state. The conductances ãj,main and ãj,residual were 179 and 48 ps, respectively (pipette solution, potassium aspartate; temperature, C; extrapolated to Vj = 0 mv). 5. The conductances ãj,residual and ãj,main showed a slight Vj dependence and were sensitive to temperature (QÔÑ values of 1 28 and 1 16, respectively). 6. Current transitions between open states (i.e. main state, substates, residual state) were fast (< 2 ms), while those between an open state and the closed state were slow (12 ms). 7. The open channel probability (Pï) at steady state decreased from 1 to 0 with increasing Vj (Boltzmann fit: Vj,0 = 37mV; z = 3). 8. Histograms of channel open times implied the presence of a single main state; histograms of channel closed times suggested the existence of two closed states (i.e. residual states). 9. We conclude that Cx30 channels are controlled by two types of gates, a fast one responsible for Vj gating involving transitions between open states (i.e. residual state, main state), and a slow one correlated with chemical gating involving transitions between the closed state and an open state. Our knowledge on functional aspects of gap junction channels has evolved quickly over the last decade. Progress has been closely associated with the availability of cdnas coding for various gap junction proteins of vertebrates, the connexins. Expression studies with injected Xenopus oocytes and transfected mammalian cells have shown that the functional diversity of gap junctions reflects the structural variety of connexins (see Bruzzone et al. 1996). Recently, a new mouse connexin has been identified and cloned by screening of a mouse genomic library (Dahl et al. 1996). This protein has a molecular mass of kda and hence was called connexin30 (Cx30). Northern blots of total RNA from mouse tissues have indicated that Cx30 is strongly expressed in adult brain as well as skin and is less abundant in uterus, lung and eye tissue. Small amounts of transcripts have been detected in testis and sciatic nerve. No Cx30 mrna has been found in liver. Sequence comparisons of nucleotides and amino acids suggest that mouse Cx30 is a close relative of mouse Cx26. There are few reports in the literature on functional aspects of Cx30 gap junctions. Injection of mouse Cx30 crna into Xenopus oocytes induced the formation of gap junctions susceptible to intercellular current flow and dye diffusion (Dahl et al. 1996). Neurobiotin diffusion experiments with transfected HeLa cells revealed that Cx30 forms heterotypic gap junction channels with Cx26, Cx30 3, Cx31, Cx40, Cx43, Cx45 and Cx50 (D. Manthey et al., in preparation). Electrophysiological studies on pairs of transfected HeLa

2 632 V. Valiunas, D. Manthey, R. Vogel, K. Willecke and R. Weingart J. Physiol cells revealed that Cx30 forms heterotypic gap junctions with Cx43 and Cx50 (Weingart et al. 1996b). It is interesting to note that Cx30 co-localises with Cx43 in adult rat astrocytes (Kunzelmann et al. 1999). The aim of this study has been to provide a comprehensive description of the biophysical properties of Cx30 gap junction channels. All experiments were carried out on HeLa cells transfected with mouse Cx30 cdna (Kunzelmann et al. 1999; D. Manthey et al., in preparation). Electrical measurements were performed on pairs of cells using the dual voltage-clamp method. This approach allowed us to examine microscopic currents (gap junctions consisting of single channels) and macroscopic currents (gap junctions consisting of many channels) in the same type of preparation. The data collected provide a physico-chemical basis for an understanding of the biological role of gap junction channels in astrocytes, ependymal cells and leptomeningeal cells, where Cx30 is co-expressed with Cx43. Preliminary reports have been published (Valiunas et al. 1996; Weingart et al. 1996b). METHODS Cells and culture conditions Experiments were carried out on human HeLa cells (human cervix carcinoma cells, ATCC code CCL2). Wild-type cells and transfected cells were grown in Dulbecco s modified Eagle s medium (DMEM) supplemented with 10 % fetal calf serum, 100 ìg ml streptomycin and 100 U ml penicillin (code 2212, Seromed, Fakola, Basel, Switzerland). The medium for HeLa transfectants also contained 1 ìg ml puromycin (Sigma, Dreisenhofen, Germany). The cells were passaged weekly, diluted 1:10 and kept at 37 C in a COµ incubator (5 % COµ, 95 % ambient air). To perform electrophysiological measurements, the cells were diluted ( ² 10É cells ml ) and seeded onto sterile glass coverslips placed in multiwell culture dishes ( 10ffi cells cm Â). Experiments were performed 1 3 days after plating. Transfection The mouse connexin30 coding sequence was amplified in a PCR reaction using the genomic mouse Cx30 exon 2 sequence (Dahl et al. 1996) as template (primers: 5'-GAATAAGCCTGCACGATGGAC-3' and 3'-GCACACCTACACTTGACCTTG-5'. The 827 bp PCR fragment was cloned at the Sma I site of the expression vector pbluescript SK (Stratagene, La Jolla, CA, USA) and completely sequenced on both strands. No Taq polymerase-induced nucleotide exchanges were detected in comparison with the original mouse Cx30 phage insert DNA (Dahl et al. 1996). A 850 bp EcoRIÏXba I fragment, containing the coding region of mouse Cx30, was cloned at the Eco RIÏXba I site of the transfection vector pbehpac18 (Horst et al. 1991) that contained the SV-40 early promotor, a polyadenylation signal and a gene conferring resistance to puromycin. HeLa cells were transfected with 20 ìg DNA of the Cx30 coding region in pbehpac18 by the calcium phosphate transfection protocol, as described by Chen & Okayama (1987). Forty-eight hours after exposure to the DNA calcium phosphate precipitate, 1 ìg ml puromycin was added to the medium. Clones were picked after 3 weeks and grown under selective conditions. The clones were checked by radioactive Northern blot analysis (Hennemann et al. 1992) with total RNA (20 ìg) and a Cx30 PCR fragment (590 bp, representing the nucleic acid residues from positions 25 to 615) as specific probes. Solutions Electrophysiological experiments were performed in modified Krebs Ringer solution (mò): NaCl, 140; KCl, 4; CaClµ, 2; MgClµ, 1; glucose, 5; pyruvate, 2; Hepes, 5 (ph 7 4). The patch pipettes were filled with saline containing (mò): potassium aspartate, 120; NaCl, 10; MgATP, 3; MgClµ, 1; CaClµ, 1; EGTA, 10 (pca 8); Hepes, 5 (ph 7 2); filtered through 0 22 ìm pores. SKF-525A hydrochloride (mol. wt. 390; Proadifen) was purchased from Biomed Research Laboratories (Plymouth, PA, USA). Electrical measurements Glass coverslips with adherent cells were transferred to an experimental chamber superfused with Krebs Ringer solution at C. The chamber was mounted on the stage of an inverted microscope (Diaphot-TMD, Nikon; Nippon Kogaku, Tokyo, Japan). Patch pipettes were pulled from glass capillaries (GC150TF-10; Clark Electromedical Instruments, Pangbourne, Berks, UK) with a horizontal puller (DMZ-Universal; Zeitz- Instrumente, Augsburg, Germany). When filled, the pipette resistances measured 3 5 MÙ. Experiments were carried out on cell pairs. A dual voltage-clamp method and whole-cell recording were used to control the membrane potential of both cells and to measure currents (Bukauskas et al. 1995a). Initially, the membrane potentials of cells 1 and 2 were clamped to the same value, V1 = Vµ. Vµ was then changed to establish a junctional voltage, Vj = Vµ V1. Currents recorded from cell 2 represent the sum of two components, a junctional current, Ij, and a membrane current, Im,2; the current gainedfromcell1correspondstoij. Signal recording and analysis Voltage and current signals were recorded on chart paper (Gould RS 3400; Gould Instruments, Minneapolis, MN, USA) and videotape (Neurocorder DR-886; Neuro Data Instruments, New York, NY, USA). For off-line analysis the current signals were filtered at 1 khz (8-pole Bessel; 3 db) and digitised at 5 khz with a 12-bit AÏD converter (IDA 12120; INDEC Systems, Capitola, CA, USA). Data acquisition and analysis was done with commercial (C-Lab; INDEC Systems) and custom-made software (Krisciukaitis, 1997). Curve fitting and statistical analysis were performed with SigmaPlot and SigmaStat, respectively (Jandel Scientific, Erkrath, Germany). The data are presented as means ± 1 s.e.m. Wild-type HeLa cells express an intrinsic connexin, conceivably Cx45, at an extremely low level (H ulser et al. 1997). Since the properties of Cx45 channels are so different from those of Cx30 channels, they would be readily detectable in HeLa cells transfected with Cx30. However, we did not see any such signals. For a more complete discussion of this issue, see Bukauskas et al. (1995a). RESULTS Expression of Cx30 DNA in HeLa transfectants The HeLa Cx30 transfectants together with HeLa wild-type cells were characterised by Northern blot analysis as shown in Fig. 1. The Cx30-transfected clone TD0 2 showed the expected hybridisation signal of 1 1 kb. The expression of Cx30 protein in this clone was verified by immunoblot (Kunzelmann et al. 1999) and immunofluorescence analysis (D. Manthey et al. in preparation). Functional communication

3 J. Physiol Connexin30 gap junction channels 633 through homotypic Cx30 gap junction channels in clone TD0 2 was demonstrated after microinjection of neurobiotin (D. Manthey et al., in preparation). For the subsequent electrophysiological experiments we used clone 2. Voltage dependence of gap junction currents To perform this set of experiments, macroscopic intercellular currents, Ij, were examined in 26 cell pairs. In 17 preparations the cells were coupled by gap junctions. They yielded a gap junction conductance, gj, of 2 7 ± 0 7 ns. The remaining nine cell pairs contained cytoplasmic bridges (Bukauskas et al. 1992). In these cases, gj was 18 0 ± 5 5 ns. To distinguish between gap junctions and cytoplasmic bridges, the preparations were routinely exposed to 75 ìò SKF-525A (Schmilinsky-Fluri et al. 1997). This impaired the current across gap junctions but did not affect the cytoplasmic bridges. The relationship between Vj and gj was studied systematically in eight cell pairs with gap junctions. To minimise series resistance problems, preparations with moderate coupling were selected (gj < 5 ns; see Bukauskas & Weingart, 1993). The protocol adopted was as follows. Both cells were clamped to the same holding potential, V1 = Vµ = 20 mv. Voltage pulses of long duration (10 40 s), different amplitudes (up to 110 mv) and either polarity were applied to cell 2 to impose a Vj. Figure 2A shows selected records from such an experiment. Hyperpolarisation of Vµ by 40 mv gave rise to an Ij exhibiting a time-dependent decay (I1, left-hand side). Subsequent depolarisation by the same amount led to a similar Ij of opposite polarity (I1, right-hand side). In between, small test pulses (12 5 mv; 200 ms; 1 Hz) were delivered to cell 2 (spikes in Vµ) to monitor the electrical stability of the preparation (spikes in I1). Figure 2B summarises the results from these experiments. The amplitude of Ij was determined at the beginning (Ij,inst; inst = instantaneous) and end (Ij,ss; ss = steady state) of each Vj pulse. The values of Ij,inst were normalised with respect to the amplitude of Ij associated with the small test pulse immediately before each Vj pulse. The corrected Ij,inst current was used to calculate the conductance, gj,inst = Figure 1. Northern blot analysis of total RNA from HeLa cells Total RNA was extracted from Cx30-transfected human HeLa cells and wild-type cells, electrophoresed, blotted onto nylon membrane, hybridised to a 32 P-labelled Cx30 probe (PCR fragment, nucleotide position ) under high stringency conditions and autoradiographed. Lines 1 5 correspond to different clones of Cx30-transfected HeLa cells and wild-type HeLa cells (wt). The different transcripts in lane 3 may have resulted from different transcriptional termination sites of several copies of the inserted plasmid DNA. The bar marks the location of the 1 1 kb band of Cx30 mrna. Figure 2. Dependence of intercellular coupling on transjunctional voltage (Vj) A, responses of gap junction currents (Ij) tovj. Records illustrate the membrane potential of cell 1 (V1) and cell 2 (Vµ) and the current measured from cell 1 (I1). Deflections in Vµ and I1 correspond to Vj and Ij, respectively. Long Vj pulses of ±40 mv gave rise to a time-dependent Ij. Short Vj pulses (downward deflections in Vµ) served to monitor the stability of Ij (upward deflections in I1). Holding potential, Vh = 20 mv. B, plot of normalised gj determined at the make (gj,inst; 1) and break (gj,ss; 0) of Vj pulses versus Vj. Each symbol corresponds to a single determination. Data from 8 cell pairs. 1, instantaneous data; for curve fitting procedure, see text. 0, steady-state data; continuous curve represents the best fit of data to the Boltzmann equation; Vj,0 = 28 5 and 26 4 mv, gj,min = 0 15 and 0 14, z = 4 1 and 3 9 for negative and positive Vj, respectively.

4 634 V. Valiunas, D. Manthey, R. Vogel, K. Willecke and R. Weingart J. Physiol Ij,instÏVj. Thevaluesofgj,inst were then plotted versus Vj (1) to obtain the relationship gj,inst =f(vj). The gj,inst data followed a curved relationship symmetrical with respect to Vj. The smooth curve represents the best fit of data to a function derived from our gap junction model (Vogel & Weingart, 1998; see eqn (29), adapted for a multi-channel case and normalised with respect to the conductance at Vj =0mV): Gj gj,inst =. (1) Vj Vj exp( ) +exp( ) VH(1 + exp(vjïvh)) VH(1 + exp( VjÏVH)) Gj is a dimensionless fitting parameter and VH is a decay constant (for a detailed description, see Vogel & Weingart, 1998). The analysis yielded the following values: Gj = 1 98; VH = mv. Starting from a maximum of 0 99 at Vj =0mV, gj,inst decreased with increasing Vj. At Vj = ±100 mv, it reached a value of about 0 9. The current Ij,ss was used to calculate the conductance gj,ss = Ij,ss ÏVj. Thevaluesofgj,ss were then normalised with respect to gj,inst prevailing at each Vj and plotted versus Vj (0) to obtain the relationship gj,ss Ïgj,inst =f(vj). The gj,ss Ïgj,inst data followed a bell-shaped relationship which was nearly symmetrical. At Vj =0mV, gj,ss Ïgj,inst was maximal. Between Vj values of10and40mv, it decreased toaquasi-constant value distinctly different from zero. The smooth curve represents the best fit of data to the Boltzmann equation: gj,ss 1 gj,min = + gj,min, (2) gj,inst 1 + exp(a(vj Vj,0)) where gj,min is the normalised conductance at large Vj and Vj,0 corresponds to the Vj at which gj,ss Ïgj,inst is halfmaximally inactivated. A is a constant which expresses the gating charge, zq(kt), where z is the equivalent number of unitary positive charges q moving through the electric field applied, and k and T are the Boltzmann constant and the temperature in Kelvin, respectively. The analysis yielded the following values: Vj,0 = 28 5 and 26 4mV, gj,min = 0 15 and 0 14, and z = 4 1 and 3 9 for negative and positive Vj values, respectively. Figure 3. Kinetic analysis of junctional currents A, plot of time constants of Ij inactivation (ôé) versus Vj. Each symbol corresponds to a mean value ± 1 s.e.m. Data from 8 cell pairs. The continuous curves represent the best fit of data to single exponentials; ôi,0 = 8 5 and 11 4 s and Vô = 27 4 and 24 4 mv for negative and positive Vj values, respectively. B, plot of rate constants of channel opening, á (0), and channel closing, â (1), versus Vj. The continuous curves correspond to the best fit of data to single exponentials; ë = 0 21 and 0 18, Aá = and 0 102, Aâ = and 0 049, and Vj,0 = 24 1 and 27 8 mv for negative and positive Vj values, respectively. Time-dependent inactivation of gap junction currents The current records indicated that Ij inactivates with time in a voltage-dependent manner. Inactivation was rapid at large Vj (see Fig. 2A) and slow or virtually absent at small Vj (not shown). To perform a systematic analysis, current records obtained at different Vj gradients were digitised and subjected to a least-squares curve-fitting procedure. It turned out that Ij inactivation obeys a mono-exponential time course: Ij(t) = (Ij(0) Ij,ss)exp( (tïôi)) + Ij,ss, (3) where Ij(0) is the current at time t =0andôéisthetime constant of Ij inactivation. Figure 3A summarises the collected ôé data from eight cell pairs. Individual values of ôé were averaged and plotted versus Vj. OvertheVj range examined, ôé decreased with increasing Vj irrespective of the voltage polarity. The smooth curves correspond to the best fit of data to a single exponential: ôi =ôi,0exp( (VjÏVô)), (4) where ôi,0 is the zero Vj intercept and Vô is the decay constant. The analysis yielded the following values: ôi,0 = 8 5 and 11 4 s, and Vô = 27 4 and 24 4 mv for negative and positive Vj values, respectively. If one assumes a two-state process (main state residual state) and takes into account that ãj,residual is different from zero (see Conductances of single channels ), the rate constants of channel opening (á) and closing (â) can be

5 J. Physiol Connexin30 gap junction channels 635 estimated from the formalism proposed by Harris et al. (1981). This analysis was performed using the data presented in Figs 2B and 3A. The values obtained were averaged and plotted versus Vj as shown in Fig. 3B. The graphs á = f(vj)(0)andâ=f(vj)(1)indicatethatatlowvj, ôé is governed by á whereas at large Vj, it is dominated by â. The continuous curves represent the best fit of data to the equations: á=ëexp( Aá(Vj Vj,0)), (5) â=ëexp( Aâ(Vj Vj,0)), (6) where Aá and Aâ express the voltage sensitivity of the rate constants and ë is the rate constant at which Vj = Vj,0 (i.e. á = â). The analysis yielded similar values for negative and positive voltages: ë = 0 21 and 0 18; Aá = and 0 102; Aâ = and 0 049; Vj,0 = 24 1 and 27 8 mv. If one combines eqns (5) and (6), an independent estimate of ôé can be obtained: ôi = 1Ï(á + â). (7) With this approach, we obtained the following values: for Vj = 50 and 50 mv, ôé = 1 52 and 1 79 s; for Vj = 100 and 100 mv, ôé = 0 19 and 0 16 s. These values are in good agreement with those extracted from the Ij records (see Fig. 3A). De novo formation of gap junction channels In three other cell pairs, we successfully observed the de novo formation of gap junction channels. Figure 4A illustrates a representative example. After establishing the whole-cell recording conditions, a sustained Vj of 40 mv was applied (V1 = 5mV; Vµ = 45 mv; not shown). Initially, there was no Ij, indicating that the cells were not coupled electrically. A few minutes later, a first channel begun to operate as shown by the paired records I1 and Iµ. They exhibited simultaneous transitions similar in amplitude and of opposite polarity and hence reflect gap junction events. Starting from zero current (continuous lines), Ij slowly increased to a plateau corresponding to the main state, Ij,main (upward deflection in I1; downward deflection in Iµ). The transition between the two levels lasted 80 ms. Subsequently, Ij exhibited fast transitions (< 2 ms) between Ij,main and Ij,residual (dashed lines). The latter was different from zero, indicating that the channel did not close completely.ananalysisofthesignalsinfig. 4A yielded the following single channel conductances: ãj,main = 156 ps, ãj,residual = 28 ps. Slow transitions associated with first channel openings have been observed previously in insect cells and transfected HeLa cells (Bukauskas & Weingart, 1994; Bukauskas et al. 1995a). Conductances of single channels To study single channel currents, we selected cell pairs with only one or two operational channels. This condition prevailed in weakly coupled pairs or in normally coupled pairs after advanced spontaneous uncoupling (27 cell pairs). In a few cases (6 cell pairs), 75 ìò SKF-525A was administered to a normally coupled pair to impair Ij and hence to resolve single channel events. As previously shown, this intervention does not affect the conductances of single gap junction channels (Valiunas et al. 1997). Figure 4B shows records from a weakly coupled cell pair. A voltage pulse was delivered repetitively to cell 2 ( 50 mv, 200 ms, 1 Hz) while the membrane potential of cell 1 was maintained at 20 mv (traces Vµ and V1). Initially, the cell pair had one operational channel (upper and middle I1 trace), i.e. the current signal exhibited fast transitions between Ij,main and Ij,residual (dashed line). Later on, two channels were present (lower I1 trace), i.e. the signal showed multiple transitions involving three discrete levels corresponding to 2 ²Ij,main, Ij,main + Ij,residual and 2 ²Ij,residual, respectively. For further analysis we used current records obtained with maintained and pulsed Vj gradients (compare A and B in Figure 4. Single channel activity of a cell pair whose gap junction contained a single channel A, sister current records documenting the de novo formation of a gap junction channel. Vj was maintained at 40 mv. Simultaneous transitions in I1 and Iµ reflect gap junction events (channel opening: upward deflections in I1, downward deflections in Iµ). The very first transition was slow and corresponds to the first opening after channel formation. The subsequent transitions were fast and represent channel flickering between the main state and the residual state (dashed lines). Continuous lines indicate the zero coupling current. B, single channel currents from a weakly coupled cell pair elicited by Vj pulses (V1 and Vµ) of 50 mv (top and middle I1 trace) and 75 mv (bottom IÔ trace). The coupling currents in the presence of one (top and middle I1 trace) and two channels (bottom I1 trace) exhibited fast transitions between the main state and the residual state.

6 636 V. Valiunas, D. Manthey, R. Vogel, K. Willecke and R. Weingart J. Physiol Fig. 4). Vj was varied between 25 and 100 mv. The conductances of the main and residual states were determined as the ratios Ij,mainÏVj and Ij,residualÏVj, respectively. The histogram in Fig. 5 summarises the data collected from seven cell pairs, plotting the number of events versus conductance. It shows two narrow distributions with no overlap. Both data groups exhibited a binomial distribution and hence were fitted with a Gaussian. The right-hand peak revealed a mean value of ± 0 8 ps (n = 221; range ps) and corresponds to ãj,main. The left-hand peak yielded a mean value of 26 4 ± 0 5 ps (n = 53; range ps) and corresponds to ãj,residual. The ratio ãj,residualïãj,main was Note that the data included in this analysis were gained at C. Influence of temperature on single channel conductances To explore the effect of temperature on channel conductances, we used cell pairs with a single operational channel. The temperatureofthebathsolutionwasalteredwithapeltier element and measured with a thermistor positioned close to the preparation, i.e mm (Bukauskas & Weingart, 1993). The experimental protocol involved repetitive application of Vj pulses (±50 mv or ±75 mv; 200 ms; 1 Hz) to one of the cells and assessment of Ij,main and Ij,residual. The mean values of ãj,main and ãj,residual were calculated and plotted on a logarithmic scale versus temperature. Figure 6 depicts the resulting graph (4 cell pairs). Over the temperature range examined, i.e C, ãj,main (1) and ãj,residual (0) increased with increasing temperature. The continuous lines were obtained by fitting the data to the equation: ãj(t) =ãj(23)q10(t 23)Ï10, (8) where T is the temperature in C, ãj(23) the conductance at 23 C, and QÔÑ the temperature coefficient. QÔÑ for ãj,main and ãj,residual turned out to be 1 16 ± (n = 427) and 1 27 ± (n = 170), respectively. Statistical analysis showed that the values of QÔÑ are significantly different from each other (Student s t test: P < 0 001). This suggests that ãj,main and ãj,residual exhibit a different temperature sensitivity. Hence, the ratio ãj,residualïãj,main is expected to be temperature dependent as well. At T values of 23 C (room temperature) and 37 C (body temperature) the ratios were (20 8 psï141 4 ps) and (29 1 ps/ ps), respectively. For comparison, the QÔÑ of aqueous KCl solution is (Robinson & Stokes, 1970). This suggests that in the case of the residual state, permeation of small ions may be slightly impaired by spatial andïor electrical constraints, whereas in the case of the main state it is not. A similar study with HeLa cells expressing Cx40 yielded QÔÑ values of 1 21 and Figure 5. Histogram of single channel conductances (ãj) gained from cell pairs with a single gap junction channel Data from 7 cell pairs were pooled in consecutive 5 ps bins. The number of observations was plotted versus ãj. The continuous curves represent the best fit of data to Gaussians. The left-hand distribution revealed a mean value of 26 4 ± 0 5 ps (n = 53) and reflects the conductance of the incompletely closed channel, ãj,residual. The right-hand distribution yielded a mean value of ± 0 8 ps (n = 221) and corresponds to the conductance of the fully open channel, ãj,main. Note that these experiments were carried out at C. Figure 6. Influence of temperature on single channel conductances (ãj) Plots of single channel conductances ãj,main (1)andãj,residual (0) on a logarithmic scale versus temperature. Symbols correspond to mean values ± 1 s.e.m. obtained from 426 and 170 measurements for ãj,main and ãj,residual, respectively. Data were collected during application of Vj pulses of 50 or 75 mv amplitude. Continuous lines were drawn by fitting the data to single exponentials. The temperature coefficients (QÔÑ) for ãj,main and ãj,residual were 1 16 and 1 27, respectively.

7 J. Physiol Connexin30 gap junction channels for ãj,main and ãj,residual, respectively (Bukauskas et al. 1995a). Voltage dependence of single channel conductances Next we explored the relationship between the single channel conductances and Vj. For this purpose, the values of ãj,main (1) andãj,residual (0) obtained at different Vj were sampled, averaged and plotted versus Vj. Theãj data for positive and negative voltages were symmetrical and hence were pooled. The number of observations at a given Vj varied from 16 to 207 (12 cell pairs). The values of ãj,residual collected at Vj =25mV were discarded because of the marginal signalïnoise ratio and the small number of observations. Figure 7 shows the resulting graph. Over the voltage range examined, i.e. up to ±100 mv,thevaluesof both ãj,main and ãj,residual decreased moderately with increasing Vj. The continuous lines correspond to the best fit of data to our gap junction model (Vogel & Weingart, 1998). In the case of ãj,residual data, the fitting procedure involved numerical calculations. This was necessary because no analytical solution is available. The procedure revealed the following values: ÃL = 39pS, VL = 127 mv. ÃL represents the conductance of a hemichannel in the low conductance state at Vj =0mV (for interpretation of VL, see Vogel & Weingart, 1998). In the case of the ãj,main data, the curve fitting was done with the equation: ÃH ãj,main =. (9) Vj exp( ) +exp( ) VH(1 + exp(vjïvh)) VH(1 + exp( VjÏVH)) ÃH corresponds to the conductance of a hemichannel in the high conductance state at Vj = 0 mv (for interpretation of VH, see Vogel & Weingart, 1998). The analysis yielded the following values: ÃH = 291 ps; VH = 253 mv. Since a gap junction channel consists of two hemichannels in series, ãj,main and ãj,residual at Vj =0mV can be calculated as ÃHÏ2 = 146 ps and (ÃH ²ÃL)/(ÃH +ÃL) = 34 4 ps, respectively. Note that the data described in this section were gained at C. Taking into account the values of QÔÑ (see Influence of temperature on single channel conductances ), ãj,main and ãj,residual at 37 C would be 179 and 48 ps, respectively. Fast versus slow current transitions Current transitions associated with single channel activity were usually fast. They were complete within the response time of the experimental set-up, i. e. < 2 ms (see Fig. 4B). This was true for the transitions between channel open states (i.e. the main state and the residual state). However, in conjunction with chemical uncoupling (see Conductances of single channels ), we also observed slow transitions. Ij exhibited slow transitions between a channel open state and the closed state late during wash-in and early during washout of 75 ìò SKF-525A, i.e. immediately before complete uncoupling and early during recovery from uncoupling. Vj Figure 7. Relationships between single channel conductances (ãj) and transjunctional voltage (Vj) Plots of the single channel conductances ãj,main (1)and ãj,residual (0) versus Vj. The symbols represent mean values obtained from 313 and 136 measurements, respectively; the bars for ± 1 s.e.m. lay within the size of the symbols. Data derived from negative and positive Vj were pooled. The continuous curves correspond to the best fit of data to equations derived from a mathematical model (for details, see text). Extrapolation to Vj = 0 mv led to ãj,main and ãj,residual values of 146 and 34 ps, respectively. Figure 8. Comparison of fast and slow channel transitions Sister current records I1 and Iµ illustrating the re-opening of a gap junction channel previously closed by exposure to 75 ìò SKF-525A. Vj was maintained at 50 mv (not shown). The first transition (closed state main state) was slow (see inset at expanded time scale), the second transition (main state residual state) was fast (see inset), and the third transition (residual state closed state) was slow. The values of ãj,main and ãj,residual were 140 ps and 25 ps, respectively. The short transitions in I1 resulted from depolarising test pulses applied to cell 1. Continuous lines indicate zero current, dashed lines indicate residual current.

8 638 V. Valiunas, D. Manthey, R. Vogel, K. Willecke and R. Weingart J. Physiol Figure 8 illustrates this finding. It shows the first reopening of a channel during wash-out. The signals I1 and Iµ were recorded at a maintained Vj of 50 mv (V1 = 45 mv, Vµ =5mV). The associated sequence of transitions involved a slow event ( 11 ms) between the closed state (continuous lines) and the main state, a fast event (< 2 ms) betweenthe main state and the residual state (dashed lines), and a slow event ( 36 ms) between the residual state and the closed state. The time course of the first two events becomes evident on the expanded time scale (see inset). At the beginning and end of the current traces, superimposed on the maintained Vj, a depolarising test pulse (200 mv, 75 mv) was administered repetitively to cell 1 giving rise to short current deflections in I1 but not in Iµ. This indicates that the baseline current level (continuous lines) reflects the channel closed state. The analysis of slow events in six cell pairs yielded a mean transition time of 12 ± 1 ms (n = 28). This implies that the channels possess two gating mechanisms, a biophysical one associated with fast transitions and a chemical one accompanied by slow transitions (Bukauskas & Weingart, 1994; Weingart & Bukauskas, 1997). Determination of main-state probability Cell pairs with a single gap junction channel were also used to study channel kinetics. At steady state, Ij mainly flickered between two discrete levels, i.e. Ij,main and Ij,residual. To determine the open channel probability, Pï, we used a protocol with Vj pulses of variable amplitude (up to 65 mv) and duration (20 80 s). The initial segment of each Ij record was discarded to avoid non-steady-state data. Figure 9 illustrates segments of such current traces recorded at Vj values of 25, 35, 40 and 55 mv (from top to bottom). The signals indicate that the dwell time in the main state was inversely related to Vj. At a small Vj, i.e. 25 mv, flickeringwasrareandthechannelwaspreferentiallyinthe main state. At a large Vj, i.e.55mv, flickering was also rare but the channel stayed mainly in the residual state (dashed line). At an intermediate Vj, i.e. 35 mv and 40 mv, the channel gradually altered from being in the main state to being in the residual state. The transitions between Ij,main and Ij,residual were always fast (i.e. < 2 ms). To calculate Pï, the times spent in the main state were determined and divided by the signal duration. The values of Pï obtained from three cell pairs were sampled, averaged and plotted versus Vj. Figure 10 shows the resulting graph. Pï decreased in a sigmoidal fashion between 1 and 0 when Vj was increased from 0 mv to 70 mv. The data points were fitted with the Boltzmann equation: 1 Po,min Pï = + Po,min, (10) 1+exp(A(Vj Vj,0)) where Po,min is the minimal Pï at large Vj and Vj,0 corresponds to the Vj at which Pï is half-maximal. The analysis yielded the following values: Vj,0 = 37 5 mv, Po,min =0,z =3. Steady-state kinetics of single channel currents Currents from preparations with a single channel indicated that Cx30 channels mainly flicker between the main state Figure 9. Effects of transjunctional voltage (Vj) on single channel activity Long-lasting segments of current records obtained from a cell pair with a single operational gap junction channel. The signals were recorded during steady-state conditions. Upward deflections correspond to channel openings. When Vj was increased from 25 to 35, 40 and 55 mv (from top to bottom), the channel spent progressively less time in the main state and more time in the residual state (dashed lines). Continuous lines refer to the zero coupling current. Figure 10. Dependence of main-state probability (Po,main) on transjunctional voltage (Vj) Values of Po,main were determined from long lasting current records (20 80 s) during steady-state conditions. The data were collected from cell pairs with a single operational gap junction channel. Data points represent mean values ± 1 s.e.m. from 3 preparations. The continuous curve represents the best fit of data to the Boltzmann equation, with Vj,0 = 37 5 mv, Po,main =0andz =3.

9 J. Physiol Connexin30 gap junction channels 639 and the residual state. Occasionally, these states were interrupted by short-lived substates. To study the underlying processes, we examined long segments of Ij records at steady state. The current traces were analysed for dwell times of the channel in the main and the residual states. Because of the rare occurrence and short duration, substates were ignored in this analysis. Figure 11 shows histograms of the open time prevailing at different Vj values, i.e mv (panel A), mv (panel B), mv (panel C) and mv (panel D). ThedataatVj values of and mv were pooled because of the low number of events (3 cell pairs). Over the time domains examined, the distributions of the open times were best approximated by single exponentials, implying that the channels possess a single open state. Curve fitting yielded time constants (ôï) of 4, 2, 0 67 and 0 4 s, respectively. While the determination of the channel open times was straightforward, the assessment of the channel closed times, i.e. the time spent in the residual state, posed problems. These arose from the limited response time of the experimental set-up (1 2 ms). This may have led to the situation that short-lived residual states were interpreted as substates. To eliminate this problem, channel closed times < 50 ms were excluded from the analysis. Another problem was the low number of events, especially at small Vj values. The resulting histograms (data not shown) indicated that the longest closed time increased with increasing Vj, i.e. from 6 s to 11, 42 and 56 s for Vj values of 10 25, 30 35, and mv, respectively. Furthermore, short closed times were more frequent than long ones at each Vj examined. At Vj values of and mv, the histograms allowed reliable curve fitting whereas at Vj values of and mv, the data were too scarce. The distributions in the former cases were best approximated by the sum of two exponentials. The analysis yielded the following time constants for the channel closed times: for Vj = mv, ôc1 = 0 3 s and ôc2 = 7 0 s; for Vj = mv, ôc1 = 0 23 s and ôc2 = 8 7 s. This suggests that the channels possess two residual states, one with a short lifetime and one with a long lifetime. The fitted curves in Fig. 11 correspond to the probability density function f(t) = âexp( ât), where â is the rate constant of channel closing and 1Ïâ represents the mean open time, i.e. the average time a channel spends in the main state. Likewise, the closed time histograms reflect the function f(t) = áexp( át),whereáistherateconstantof Figure 11. Histograms of channel open times Current traces of cell pairs with a single gap junction channel were analysed for dwell times in the main state (i.e. channel open times) at different Vj at steady state. The data from 3 cell pairs were sampled and plotted as frequency histograms. The continuous curves correspond to the best fit of data to single exponentials with the following time constants: A, ôï = 4 s(vj = mv); B, ôï = 2 s(vj = mv); C, ôï = 0 67 s (Vj = mv); D, ôï = 0 4 s (Vj = mv).

10 640 V. Valiunas, D. Manthey, R. Vogel, K. Willecke and R. Weingart J. Physiol channel opening and 1Ïá reflects the mean closed time, i.e. the average time a channel spends in the residual state. In Fig. 12A, the data on channel lifetimes obtained in this way were plotted versus Vj, revealing that both channel lifetimes are voltage dependent, i.e. the open times (1) decreased with increasing Vj and the closed times (0: ôc data; 8: ôc1 data; þ: ôc2 data) increased. However, the closed times should be regarded with caution because of the limited number of data points and observations. Channel lifetimes can also be determined from the dwell times and their frequency of occurrence (see Johnston & Wu, 1995). The channel open times obtained with this procedure were 4 5, 1 99, 0 8 and 0 5 s. These values are close to those deduced from the probability density function (4, 2, 0 67 and 0 4 s) (1, Fig. 12A). The continuous curves were obtained by fitting the open time (1) and closed time data (0) to exponentials with decay constants of 16 6 and 20 2, respectively. In conclusion, these data suggest that the channels stayed in the residual state more often and for longer periods as Vj was increased. Figure 12B shows plots of the rate constants of channel opening, á (0), á1 (8) and áµ (þ), and channel closing, â (1), versus Vj. The data were obtained from Fig. 12A. The data points for channel open times and closed times were best fitted by exponentials with decay constants of 16 9 and 16 8, respectively. The two curves cross each other at Vj = 32 7 mv. Figure 12. Steady-state kinetics of gap junction channels A, values of channel mean open times (i.e. main state; 1) were determined from the probability density function using the rate constant of channel closure, â, and plotted versus Vj. Likewise, values of channel mean closed times (i.e. residual state) were derived from the probability density function, with the rate constant of channel opening, á, and plotted versus Vj. The histograms of the channel closed times were approximated with the sum of two exponentials. This gave rise to two values for the channel mean closed time (0, single exponential with ôc; 8, first exponential with ôc1; þ, second exponential with ôc2). B, plots of the rate constants of channel opening, i.e. á (0), á1 (8) and áµ (þ), and channel closing, i.e. â(1), versus Vj (data obtained from Fig. 12A). DISCUSSION Basic properties of macroscopic gap junction currents Our data demonstrate that the current flow through Cx30 gap junctions is sensitive to Vj. Hence, these junctions resemble other vertebrate gap junctions (see Bruzzone et al. 1996). On the one hand, the relationship gj,inst =f(vj) indicated that Ij,inst is not constant (see Fig. 2B). It decreased slightly with increasing Vj of either polarity. This may reflect (i) a genuine property of the channels, (ii) interference from a Vm-sensitive gj,inst, or (iii) an artefact. The analysis of Ij records yielded similar values for Ij,inst when a graphical method or a curve fitting procedure was used. Hence, (iii) can be ignored. Explanation (ii) can also be ruled out since there was no indication of a sensitivity of Ij,inst to membrane potential (data not shown). Explanation (i) seems most likely. It is consistent with the single channel data, which indicated that ãj,main is sensitive to Vj (see Single channel properties ). Computer simulations with our gap junction model (Vogel & Weingart, 1998) showed an excellent fit with the Ij,inst measurements (see Fig. 2B). On the other hand, the relationship gj,ss Ïgj,inst = f(vj) revealed that Ij,ss decreases with increasing Vj without, however, reaching zero. The data described a bell-shaped relationship and were best approximated with Boltzmann s equation. This is compatible with the observation that channel gating is sensitive to Vj (see Determination of main-state probability ). In comparison with other gap junctions, the Boltzmann parameters for Cx30 channels suggest a strong voltage sensitivity (Vj,0 = 28 5 and 26 4 mv and z = 4 1 and 3 9 for negative and positive Vj values). Data previously gained from pairs of injected oocytes revealed a moderately lower Vj sensitivity (Vj,0 = 46 mvï38 mv; Dahl et al. 1996). The single channel measurements offer a plausible explanation for the incomplete decay of gj,ss at large Vj. They suggest that it reflects partial channel closure, i.e. gj,min is related to ãj,residual. This conclusion is consistent with the close match of the values for gj,min and ãj,residualïãj,main (0 15 and 0 14 for negative and positive Vj versus 0 15). It is also supported by the kinetic studies which

11 J. Physiol Connexin30 gap junction channels 641 demonstrated that the open channel probability, Pï, approaches zero at large Vj (see Fig. 10). This concept has been proposed before for other vertebrate gap junctions, e.g. Cx40 (Bukauskas et al. 1995a), Cx43 (Valiunas et al. 1997) and Cx46 (Sakai et al. 1998). For comparison, gap junctions whose connexins are structurally closely related to Cx30 exhibit the following properties. Cx26: Vj,0 = 93 mvï95 mv; gj,min = 0 31Ï0 34; z = 1 2Ï1 4 (Valiunas et al. 1998). Cx30 3: Vj,0 = 62 mv/ 64 mv; gj,min = 0 11Ï0 17; z = 2 4/2 4 (F. F. Bukauskas & R. Weingart, unpublished observation). Cx32: Vj,0 = 44 mv/ 44 mv; gj,min = 0 22Ï0 23; z = 2 6Ï2 5 (Valiunas et al. 1998). Hence, there is no obvious correlation between the amino acid chain length of connexins and the selected electrophysiological parameters. Kinetics of Ij inactivation Our experiments revealed that the time-dependent decay of Ij is best described by single exponentials with the time constant ôé, irrespective of the amplitude and polarity of Vj (see Fig. 3A). This is consistent with the presence of a single population of channels whose Vj-sensitive gating is controlled by a two-state process. Over the voltage range examined (i.e mv), the relationship ôé = f(vj) obeyed a monoexponential. The values of ôé decreased with increasing Vj in a manner symmetrical to Vj =0mV. The error bars in Fig. 3A indicate that the data scatter was inversely related to the amplitude of Vj. This means the uncertainty about the course of the function increased with decreasing Vj. Hence, it cannot be excluded that ôé declines again at very small Vj (see Moreno et al. 1995). If one considers a two-state process, i.e. open state residual state, the rate constants of channel opening (á) and closing (â) can be deduced from ôé, gj,ss, gj,inst and gj,min. The ensuing plots for á = f(vj) and â = f(vj) indicated that á, the rate constant of channel opening, is considerably less voltage dependent than â, the rate constant of channel closing (see Fig. 3B), i.e. á > â at Vj < Vj,0 and á < â at Vj > Vj,0. Hence, at high Vj the conductance state of the channels is primarily determined by the closing rate constant. The functions á = f(vj) and â = f(vj) cross each other at comparable Vj values, i.e. at 24 1 and 27 8 mv for negative and positive voltages, respectively. The values of Vj,0 deduced in this way agree with those determined from the relationship gj,ssïgj,inst =f(vj), i.e and 26 4 mv (see Fig. 2B). This close correspondence is somewhat unexpected. Early during Vj pulses (non-stationary condition), channel substates were seen at all voltages, late during Vj pulses (stationary condition), they were virtually absent (Weingart et al. 1996b). Hence, non-stationary data (i.e. á and â) are expected to lead to smaller values of Vj,0 than stationary data (i.e. gj,ssïgj,inst). The similarity of Vj,0 values suggests that substates do not contribute significantly to Ij inactivation. Previous studies with transfected RIN cells expressing Cx43 provided comparable Vj,0 values for non-stationary and stationary data ( 60 6 and 60 1 mv and 60 5 and 59 5 mv, respectively; deduced from Banach & Weingart, 1996). Similar results were obtained with SKHep1 cells expressing Cx45 (14mV and 13 4 mv;morenoet al. 1995). Single channel conductances HeLa cells expressing Cx30 channels exhibited several conductance states, a fully open state, ãj,main, a residual state, ãj,residual, several substates, ãj,substate, and a closed state, ãj,closed. Hence, they behave like other vertebrate gap junction channels (Weingart et al. 1996a; Valiunas et al. 1998; for an exception, see Valiunas et al. 1998). One series of experiments was performed at C. It yielded an average ãj,main of 163 ps and a ãj,residual of 26 ps. If one considers QÔÑ values of 1 16 and 1 27 for ãj,main and ãj,residual, respectively (see Fig. 6), this corresponds to conductances at room and body temperatures (23 and 37 C) of ãj,main = 141 and 174 ps and ãj,residual = 21 and 29 ps. Another series of experiments was carried out at C, the temperature mainly used in this study. It revealed a distinct Vj dependence for ãj,main and ãj,residual; both conductances decreased with increasing Vj (see Fig. 7). Extrapolation to Vj =0mV yielded a ãj,main of 146 ps and aãj,residual of 34 ps. If one takes into account the respective QÔÑ values, this leads to a ãj,main of 179 ps and a ãj,residual of 48 ps at 37 C. These values are in good agreement with those obtained from the first series of experiments (see above). The Vj sensitivity of ãj,main and ãj,residual is a novel finding for homotypic gap junction channels of vertebrates. It has been anticipated from investigations on heterotypic gap junction channels (Bukauskas & Weingart, 1995; Weingart et al. 1996a; see also Bukauskas et al. 1995b) and was predicted from our gap junction model (Vogel & Weingart, 1998). This property is based on the assumption that the conductances of hemichannels are voltage dependent (Bukauskas & Weingart, 1995; Weingart et al. 1996a). Recent studies on Cx30 hemichannels expressed in HeLa cells support this prediction (Valiunas & Weingart, 1997; V. Valiunas, R. Vogel & R. Weingart, in preparation). Hence, the Vj sensitivity of ãj,main and ãj,residual reflects the sum of a constant conductance of the non-gated hemichannel and a variable conductance of the gated hemichannel. The Vj sensitivity of the hemichannel conductances may arise from a rearrangement of charged amino acid residues of the connexins located inside the channel or at the mouth of the channel. Alternatively, cytoplasmic ions may provoke screening of surface charges during current flow through the channels. For comparison, a Vj-dependent ãj,residual has also been reported for insect gap junctions (Bukauskas & Weingart, 1994). Cx30 gap junction channels also exhibited several substates interposed between the main state and the residual state. These data will be presented in a separate paper (V. Valiunas & R. Weingart, in preparation; see also Weingart et al. 1996b; Valiunas et al. 1996). Closed states of Cx30 channels have been observed in conjunction with chemical

12 642 V. Valiunas, D. Manthey, R. Vogel, K. Willecke and R. Weingart J. Physiol interventions, e. g. exposure to lipophilic agents such as SKF-525A (see Fig. 8) or long-chain alkanols such as heptanol (data not shown). Current transitions involving the channel closed state (closed state residual state, closed state substates, closed state main state) were slow (12 ms; see Fast versus slow current transitions ) while those involving open states (main state substates, main state residual state, substate residual state) were fast (< 2 ms). Hence, Cx30 channels resemble other vertebrate gap junction channels such as Cx32 and Cx43 (Valiunas et al. 1997, 1998; Bukauskas & Peracchia, 1997). For comparison, the closely related connexins Cx26, Cx30 3, Cx31 and Cx32 form channels with a ãj,main of 102 ps (Valiunas et al. 1998), 73 ps (F. F. Bukauskas & R. Weingart, unpublished observation), 50 ps (Bukauskas & Weingart, 1995) and 31 ps (Valiunas et al. 1998), respectively. Hence, Cx30 channels do not fit into this sequence of values. This suggests that there is no correlation between ãj,main and the length of the C-terminus of the channel proteins. Single channel kinetics Cell pairs with a single gap junction channel have shown that the probability of being in the main state, Pï, decreased with increasing Vj (see Fig. 10). Over the voltage range explored, i.e. Vj = 70 to +70 mv, Pï declined in a sigmoidal manner from 1 to 0. Hence, gj,min cannot be explained by a partial decrease in Pï (see Basic properties of macroscopic gap junction currents ). It rather corresponds to the product of the number of operational channels, n, and ãj,residual. The analysis of the Pï data yielded a Vj,0 of 37 5 mv. This value is significantly larger than those gained from the relationship gj,ss Ïgj,inst =f(vj), i.e and 26 4 mv (see Fig. 2B). Several mechanisms may be responsible for this discrepancy: (i) involvement of substates, (ii) alteration of the driving force across the channels, and (iii) co-operativity between channels. With regard to (i), the following observations argue against a role of substates. Both data sets, the Pï and gj,ss Ïgj,inst values, were gained at steady state. Since identical experimental conditions are likely to disclose the same channel properties, this should result in similar values of Vj,0. Furthermore, substates were virtually absent at steady state (see Kinetics of Ij inactivation ). With respect to (ii), the two kinds of experiments were performed on cell pairs with single channels and many channels. Hence, Vj,0 may be affected by the number of channels involved. It has been proposed that tightly packed channels increase the channel access resistance and thereby lower the effective voltage gradient across the channels (Hall & Gourdie, 1995). However, this would shift Vj,0 towards larger values, the opposite of what we observed. (iii) Another possibility is that tightly packed channels lead to interactions between individual channels. In transfected HeLa cells the gap junction channels are mostly compacted in membrane plaques, although exceptions have been reported (H ulser et al. 1997). Hence, gating of a channel may affect the operation of adjacent channels. Such a mechanism would be consistent with the observation that Ij inactivation proceeds faster in the presence of many gap junction channels than a single one (V. Valiunas & R. Weingart, in preparation). For comparison, transfected HeLa cells expressing Cx40 yielded similar Vj,0 values for the Po and gj,ss Ïgj,inst = f(vj) data, i.e. 44 mv and 45 and 49 mv, respectively (Bukauskas et al. 1995a). A similar coincidence in Vj,0 has been reported for rat Schwann cells expressing Cx32 (Chanson et al. 1993). Single channel time histograms The analysis of single channel records at steady state enabled us to construct channel time histograms (see Fig. 11). Over the time domain explored, the distributions of the open times were best approximated by a single exponential, suggesting that the channels possess a single open state. Curve fitting yielded open time constants (ôï) of 4, 2, 0 67 and 0 4 s for Vj values of 17 5, 32 5, 42 5 and 52 5 mv, respectively. In contrast, the channel closed times were best described by the sum of two exponentials, indicating that the channels possess two residual states. Curve fitting yielded the following closed time constants: for Vj = 42 5 mv, ôc1 = 0 3 s and ôc2 = 7 0 s; for Vj = 52 5 mv, ôc1 = 0 23 s and ôc2 = 8 7 s. At a given Vj, short closed times were more abundant than long ones. A comparison of the open and closed times indicates that the former decreased with increasing Vj while the latter increased. On average, the channel open times were shorter than the closed times. The establishment of lifetime histograms was somewhat hampered by the presence of substates (Weingart et al. 1996b; Valiunas et al. 1996). However, because of their low incidence and short duration they were ignored in the present context. While this had no serious effect on the analysis of channel open times, it influenced the analysis of the channel closed times. The problem was that the short lifetimes of the substates (5 10 ms) made it difficult to distinguish residual states from substates. To circumvent this difficulty, events shorter than 50 ms were excluded, which lowered the number of observations. This rendered it impractical to do curve fitting at Vj = 17 5 mv and 22 5 mv. Using the channel lifetimes, we made an attempt to determine the rate constants of channel opening (á) and closing (â). The former involved the use of the probability density function (see Fig. 11), the latter the use of the channel dwell times and their frequency of occurrence. This procedure is a compromise for the missing histograms of the channel closed times at smaller voltages. It turned out that á decreases exponentially with increasing Vj while â increases (see Fig. 12B). This suggests that the channels stayed in the residual state more often and for longer periods as Vj was increased. This explains the decrease in Pï