The Journal of Neuroscience, February 1987, 7(2): 418431 Voltage-Dependent Gating of Single Sodium Channels from Mammalian Neuroblastoma Cells Richard W. Aldrich” and Charles F. Stevens Section of Molecular Neurobiology, Yale University School of Medicine, New Haven, Connecticut 06510 Single sodium channel currents have been studied in cell- depends quite strongly on voltage. After a step increase in mem- attached patches from the mouse neuroblastoma cell line brane potential, the time course of current flow is, under many NlEl15. Distributions of open duration, latency until first circumstances, dominated by channel opening rather than some opening, and the average probability of a channel being other process (such as inactivation or simple channel closing). open after a voltage step, p(f), were analyzed and com- The results reported here, including an analysis of channel pared to predicted distributions from various kinetic models behavior during tail currents, confirm and extend our earlier for voltage-dependent gating. It was found that, over most observations (Aldrich and Stevens, 1983; Aldrich et al., 1983). of the voltage range under which channel gating occurs, the Perhaps our most striking finding is that activation processes, slow steps in gating are opening transitions and that in- rather than inactivation, dominate macroscopic sodium channel activation of open channels is significantly faster than the kinetics over a surprisingly large voltage range. What has tra- decline in p(f) (7J. This view of gating is confirmed by com- ditionally been recognized as the kinetics of inactivation, then, parison of the kinetics of ensemble averages of single-chan- appears to be a manifestation of a slow component of the ac- nel currents obtained from step- and tail-current records at tivation process in the type of sodium channels we have studied. the same voltage. The probability of a channel reopening after having closed was calculated by comparing p(f) with Materials and Methods the convolution of the first-latency probability density and General methods. The data reported here were obtained with the single- the conditional probability of remaining open t milliseconds channel recording method from cell-attached patches on cultured neu- after opening. This reopening probability is small but slightly roblastoma cells of the type NlEl15. The cells were maintained in Delbecco’s modified Eaale’s medium ~1~s 5% fetal calf serum and arown voltage dependent over the voltage range where the mean at 37°C in a 5% CO, atmosphere. They were plated onto glass cov&slips open duration remains constant and 7,, changes consider- in 35 ml tissue culture dishes. Cells were used for patch-clamp exper- ably. The voltage dependence of open channel inactivation iments from 1 d to 2 weeks after plating. During this time the density and deactivation were calculated from the probability of re- of sodium channels (as judged by the number of channels per patch) increased. In some cases, the cells were plated into medium containing opening and the mean open duration. The equivalent gating 10% fetal calf serum. Cells in medium containing higher serum were charge for the inactivation rate is a few tenths of an elec- slower to differentiate and consequently had lower sodium channel den- tronic charge, whereas the equivalent charge for the closing sities during the first week after plating. No differences in sodium chan- rate is 2.5-3.5 electronic charges. nel behavior were seen between cells in high- and low-serum media. Pipette and bath solutions contained mammalian Ringer’s solution (150 mM NaCl, 5 mM KCl, 4 mM MgCl,, 2 mM CaCl,, 10 mM HEPES, pH Unraveling the molecular mechanisms of nerve excitation will 7.2). Because we have mostly analyzed data from cell attached patches, require precise knowledge of the states the sodium channel can the absolute value of the membrane potential is unknown. All potentials occupy and transition rates between these states. We have used are reported relative to the resting membrane potential. Holding po- single-channel recordings to develop a description of a small tential was maintained 60 or 70 mV more negative than the resting values. Test voltages were preceeded by a 300-msec-long step to very part of the sodium channel’s behavior, specifically to estimate negative voltages to remove inactivation: Prepulses to - 120, - 140, the rates at which channels leave the open state.We shall con- and - 160 mV (relative to rest) were equally effective in removing in- clude that channels have only a single kinetically defined open activation. Ensembles of 64 current records were collected with a given state, that the inactivation rate is significantly greater than the voltage pulse sequence. The pulse sequences were repeated once every deactivation (closing but not inactivating) rate over a wide volt- 800 msec. Current records were filtered with an 8 pole Bessel filter with a cutoff age range, and that the inactivation rate constant (from the open frequency of 2500 Hz and sampled once per 100 msec. Leak and ca- state) is only weakly voltage dependent, whereas deactivation pacitative current subtraction was achieved by subtracting a scaled av- erage of 32 current records obtained during steps to a voltage at which no channel openings occurred. Changes in the time course of ensemble Received Jan. 4, 1986; revised July 7, 1986; accepted Aug. 21, 1986. averages at a given voltage were taken as signs of experimental drift. We wish to thank Charles K. Sole for collaborating on some of the experiments Segments of data were analyzed only if they were free of drift. Tem- (data given in Fig. 6) and for help with the preparation of the figures; and Denis perature usually was 11°C but other temperatures have been used as Baylor for comments on the manuscript. This work was supported by National specified in the text. Institute of Health Grants NS23294 to R.W.A. and NS12961 to C.F.S. and a Missed events. The filter characteristics are such that the dwell time arant from The Chicaeo Comma&v Trust/Searle Scholar’s Proaram to R.W.A. Yang ~~~ Correspondence sh&ld be addressed to C. F. Stevens, Sect&n of Molecular at half-maximum response is, in the noise-free case, equal to the open Neurobiology, Yale University School of Medicine, 333 Cedar Street, New Haven, channel lifetime; for that reason, all open durations have been measured CT 06510. at the criterion level of 0.5 i., where i, is the single-channel current (see a Present address: Department of Neurobiology, Stanford University School of Colquhoun and Sigworth, 1983). Medicine, Stanford, CA 94305. When durations are measured in this way, 5 sorts of errors occur. (1) Copyright 0 1987 Society for Neuroscience 0270-6474/87/020418-14$02.00/O Some events are so brief that the filter response does not reach the The Journal of Neuroscience, February 1987. 7(2) 419 criterion level. This effect gives rise to missed events and makes the then O(t), the value of p(t) for this specialcase, is given by estimate of the mean open time longer than it should be because shorter events are systematically excluded. (2) If the noise level of the recording amplifier and electrode is large enough, noise crossings of the criterion PW = At)* w(t) level will occasionally be interpreted as openings. This effect causes open times to be underestimated because the shortest bins in the open where w(t) is the conditional probability that a channel is still time histogram will contain more entries than they should. (3) If the open t msecafter first opening without having closed.Whenever underlying event was too brief to give a full-sized filter response, the reopeningsoccur, p(t) will be greater than B(t), and the proba- dwell time above criterion will be less than the duration of the underlying bility of reopeningscan be estimated from the extent to which opening. (4) Fluctuations in current due to noise in the recording system can cross the criterion, leading to over- or underestimates ofthe duration p(t) exceeds P(t); p(t) can be estimated directly from single- of the underlying event. (5) The fact that the sampling interval is com- channel current averagesand $(t) can be calculated from first parable to some short open durations gives rise to a “scattering error” latenciesand the distribution of dwell time in the open state by in which events that should be entered in 1 bin of the histogram in fact using Eq. (3). appear in a neighboring bin. For example, if the sample interval is 100 We have shown previously that Eq. (3) for a(t) is actually a psec, an event with a duration of 150 psec (which should appear in the 100-200 psec bin) will be recorded half of the time as 100 psec long good approximation to the observed p(t) under at least some (exceeds criterion for 1 sample point) and half of the time as 200 psec circumstances, but we have not quantified the significanceof long (exceeds criterion for 200 psec). any deviations betweenpredictions and observations.Our goal, We have estimated the magnitude of these errors by simulations in then, is to estimate the reopeningprobability from the discrep- which square currents of the appropriate amplitude and with various durations were added to noise recorded during experiments under con- ancy betweenthed(t) predicted by Eq. (3) and the experimentally ditions that did not produce sodium channel openings. The simulated observedp(t). It will turn out that it is more convenient to work openings were then filtered and analyzed with the same computer pro- with the time integralsof p and fi than with the functions them- grams used for our experimental records.