Karl L. Magleby

Properties of single calcium‐activated potassium channels in cultured rat muscle

1. Properties of the Ca‐activated K channel were studied in excised patches of surface membrane from cultured rat muscle cells using single channel recording techniques.

Calcium-activated potassium channels

Abstract Ca 2+ -activated K + currents are found in most types of cells. Considerable progress has been made since the development of single channel recording techniques in identifying some of the channels underlying these currents. It is now apparent that there are many types of Ca 2+ -activated K + channels, which differ in their conductances and sensitivity to activation by both [Ca 2+ ] i and voltage. Ca 2+ -activated K + channels couple Ca 2+ metabolism and membrane potential to K + flux and membrane excitability. Ca 2+ -activated K + channels allow and modulate repetitive firing in some neurons and contribute to regulation of secretion in some endocrine and exocrine cells.

Kinetic states and modes of single large-conductance calcium-activated potassium channels in cultured rat skeletal muscle

1. Kinetic states and modes of a large‐conductance Ca2+‐activated K+ channel in excised patches of membrane from cultured rat skeletal muscle were studied with the patch clamp technique. Up to 10(6) open and shut intervals were analysed from each of seven different excised membrane patches containing a single channel. 2. Plots of the mean durations of consecutive groups of ten to fifty open and shut intervals were made to assess kinetic stability of the channel. Occasional abrupt decreases in the mean open interval duration from normal to different distinct levels, which were maintained for hundreds to thousands of consecutive intervals, indicated entry of the channel into different modes. 3. Four different kinetic modes were identified: normal mode, which included 96% of the intervals; intermediate open mode with 3.2% of the intervals; brief open mode with 0.5% of the intervals; and buzz mode with 0.1% of the intervals. The mean open interval durations were 61% of normal during the intermediate open mode, 12% of normal during the brief open mode, and 2.6% of normal during the buzz mode. 4. Most mode transitions were observed from the normal mode to one of the other modes and then back to normal. Sojourns in the normal mode lasted 5‐1000 s. Sojourns in the intermediate open, brief open, and buzz modes lasted 1.5‐150, 1‐7, and 0.01‐1 s, respectively. 5. During normal activity the distributions of interval durations were typically described by the sum of three to four exponential components for the open intervals and six to eight exponential components for the shut intervals, and this was the case for data obtained over a wide range of open channel probability resulting from different Ca2+i. These observations suggest that the channel can enter at least three to four open and six to eight shut states during normal activity. 6. The numbers of detected states for data sets of different sample sizes drawn from normal activity agreed with theoretical predictions, and were essentially independent of the segment of normal activity from which the data sets were drawn. These observations are consistent with relative stability of channel kinetics during normal activity. Detection of each additional open or shut state after the first was found to require a 3‐ to 10‐fold increase in the number of analysed events. 7. The intermediate open mode differed from the normal mode in that the longest open component of the four normal open components was absent.

Calcium dependence of open and shut interval distributions from calcium-activated potassium channels in cultured rat muscle.

The stochastic properties of single Ca‐activated K channels in excised patches of surface membrane from cultured rat muscle cells were studied using the patch‐clamp technique. The distribution of all open intervals was described by the sum of two exponential distributions of short and long mean open time, suggesting at least two major open‐channel states. Increasing the concentration of Ca at the inner membrane surface, [Ca]i, increased the mean duration of the long open distribution, while having little effect on the mean duration of the short open distribution. The frequency of openings to each distribution increased with [Ca]i. The rate of increase was a much steeper function of [Ca]i for openings in the long open distribution than for openings in the short open distribution; about 80% of the openings were to the long open distribution with 0.1 microM‐Cai, increasing to 97% with 1 microM‐Cai (+ 30 mV). These results suggest that openings in both open distributions are Ca‐dependent, with openings in the long open distribution requiring the binding of more Ca ions than openings in the short open distribution. The distribution of all shut intervals at 0.5 microM‐Cai and + 30 mV was described by the sum of three exponential distributions with mean durations of: 0.21 msec (short shut distribution), 1.90 msec (intermediate shut), and 44 msec (long shut). These results indicate that the channel typically enters at least three closed channel states during normal channel activity. In addition, a few longer shut intervals not accounted for by the above distributions suggested that there was a fourth infrequently occurring inactivated closed‐channel state. The mean duration of the distribution of long shut intervals decreased with a power of about 2 with increasing [Ca]i under conditions where most openings were to the long open state (+ 30 mV, 0.25‐1 microM‐Cai). This observation suggests that openings to the long open distribution typically require the binding of two or more Ca ions. The mean intermediate shut interval appeared to increase slightly with increasing [Ca]i while the mean short shut interval was relatively Cai‐independent. The percentage of all shut intervals that were short shut intervals increased with increasing [Ca]i while the percentage of long shut intervals decreased.(ABSTRACT TRUNCATED AT 400 WORDS)

Gating mechanism of BK (Slo1) channels: so near, yet so far.

Large conductance calcium- and voltage-activated K+ channels (Slo1), also referred to as “BK” or “maxi K” channels because of their high single channel conductance (250–300 pS in symmetrical 150 mM KCl), are widely distributed in many different tissues ([Kaczorowski et al., 1996][1]). A

Sampling, log binning, fitting, and plotting durations of open and shut intervals from single channels and the effects of noise

Abstract(1) Analysis of the durations of open and shut intervals measured from single channel currents provides a means to investigate the mechanisms of channel gating. Durations of open and shut intervals are conveniently measured from single channel data by using a threshold level to indicate transitions between open and shut states. This paper presents a detailed characterization of sampling, binning, and noise errors associated with 50% threshold analysis, provides criteria to reduce these errors, methods to correct for them, and presents an efficient means of data handling for binning and plotting interval durations. (2) Measuring interval durations by sampling at a fixed rate introduces two types of errors, (a) the number of intervals of a given measured duration are increased (promoted) over that expected in the absence of sampling, producing a sampling promotion error, (b) sampling decreases the total fraction of true intervals that are detected, producing a sampling detection error. Sampling errors can be reduced to negligible levels if the actual or effective (after interpolation) sampling period is less than 10–20% of both the dead time and fastest time constant in the distribution of intervals. Dead time is given by the duration of a true interval that has a filtered amplitude equal to 50% of the true amplitude. (3) Methods are presented to correct for sampling promotion error during least squares and maximum likelihood fitting. Sampling detection error is more difficult to correct, but an empirical description of the sampling detection error can be used to calculate the effective fraction of detected events with sampling. (4) Noise in the single channel current record can produce two types of error. (a) If noise peaks in the absence of channel activity exceed the threshold for detection, then false channel events of brief duration are produced. Sufficient filtering will prevent this type of error. (b) Noise can also increase the total fraction of true intervals that are detected, producing a noise detection error. Increased filtering over that required to prevent false events is not necessarily the best method for reducing noise detection error, as increased filtering can prevent detection of the faster exponential components. (5) Noise detection error can be reduced in two ways: (a) an empirical description of the noise detection error can be used to calculate the effective fraction of detected events in the presence of noise. (b) The sampling period can be selected so that the sampling detection error cancels the noise detection error. (6) Combining (binning) intervals with a range of durations into single bins promotes the amplitudes of the bins, producing a binning promotion error similar to the sampling promotion error, but of smaller magnitude. Binning promotion error can be avoided if bin width is less than 20–30% of the fastest time constant. Methods are presented to correct for binning promotion error for interval durations measured with continuous time resolution or by sampling. (7) Storing and plotting intervals from single channels is often difficult because interval durations and frequency of occurrence can range over many orders of magnitude. Binning intervals based on the logarithms of their durations provides a convenient method to overcome these difficulties, as several hundred bins are sufficient to bin any number of intervals of any expected duration with essentially no errors associated with fitting and plotting the distributions of intervals. Log binning can reduce the time required to fit the data by orders of magnitude for large numbers of events, and log binning provides increasing bin widths as interval durations increase to combine the necessary number of intervals for plotting of data without excessive fluctuation. (8) Plotting distributions of intervals on log-log plots is an effective way to present distributions of intervals that span orders of magnitude in frequency of occurrence and duration. Each bump in the distributions on log-log plots indicates an exponential component. (9) Using the techniques described above for efficient data handling and for the prevention or reduction of errors associated with sampling, binning, and noise, true rate constants and expected distributions of intervals were determined from sampled, log binning, filtered, and noisy data with errors of typically less than 1–2% for two and four state models.

A study of desensitization of acetylcholine receptors using nerve‐released transmitter in the frog

1. Desensitization of acetylcholine (ACh) receptors was studied at the frog neuromuscular junction under voltage clamp.

Accounting for the Ca(2+)-dependent kinetics of single large-conductance Ca(2+)-activated K+ channels in rat skeletal muscle.

1. The Ca(2+)‐dependent kinetics of large‐conductance Ca(2+)‐activated K+ channels from cultured rat skeletal muscle were studied with the patch clamp technique. Data were collected in the absence of Na+ and Mg2+, which can alter the kinetics. About 2 x 10(5) open and shut intervals were analysed from each of five different excised membrane patches containing a single active channel. Analysis was restricted to activity in the normal mode, which includes 96% of the intervals. 2. The open probability (Popen) and dwell‐time distributions of open and shut intervals were obtained at three to four different [Ca2+]i for each of the channels. Popen data were also obtained from some multichannel patches. 3. Increasing [Ca2+]i increased Popen. At a pH of 7.0 the Hill coefficient was 3.7 +/‐ 0.8 (range of 3.0‐5.0) and a Popen of 0.5 occurred at 14 +/‐ 7 microM [Ca2+]i (K0.5) for data obtained at +30 mV (n = 6). At a pH of 7.2 the Hill coefficient was 3.0 +/‐ 0.5 (range of 2.2‐3.7) and K0.5 was 9 +/‐ 6 microM‐Ca2+ (n = 7). The large standard deviations for K0.5 reflect the observation that fourfold differences in K0.5 could be observed for different channels studied under the same experimental conditions. 4. Hill coefficients that can be greater than 3 suggest that the channel may bind four or more Ca2+ to become fully activated. The binding of four Ca2+ before opening would require a minimum of five shut states. This estimate of the minimum number of shut states is in general agreement with that obtained from the number of exponential components in the dwell‐time distributions of shut intervals. Thus, two different methods give similar estimates of the minimum number of shut states. If the channel can open with different numbers of bound Ca2+, then this could give rise to the three to four open states suggested by the three to four exponential components in the open dwell‐time distributions. 5. Kinetic schemes consistent with the Ca(2+)‐dependent kinetics were developed by simultaneously fitting open and shut dwell‐time distributions obtained at three to four different [Ca2+]i, using maximum likelihood techniques and corrections for missed events. Such simultaneous fitting can provide an increased ability to define models and rate constants.(ABSTRACT TRUNCATED AT 400 WORDS)

Quantitative description of three modes of activity of fast chloride channels from rat skeletal muscle.

The steady‐state kinetic properties of single Cl‐ channels with fast kinetics active at resting membrane potentials in cultured rat skeletal muscle were studied using the patch‐clamp technique. Membrane patches containing single active Cl‐ channels were often observed, and binomial analysis of the percentage open time in membrane patches containing several Cl‐ channels indicated that the channels did not occur as obligatory dimers and that they gated independently of one another. Channel activity could be divided into three categories: normal, which included about 99% of the openings and closings; buzz mode, which included about 1% and consisted of bursts of about 50 brief open and shut intervals; and inactivated shut states which included about 0.01% of the shut intervals and lasted for seconds, and occasionally minutes. The method of maximum likelihood was used to determine the number of significant exponential components required to fit the distributions of open and shut intervals during normal activity. Open interval distributions required at least two components, with time constants of 0.52 and 1.5 ms at ‐40 mV and 7.6 degrees C. Shut interval distributions required at least five exponential components, with time constants of 0.064, 0.72, 1.9, 12.3 and 350 ms. Kinetic reaction schemes were developed for the normal and buzz mode using maximum likelihood techniques to determine the most likely models and rate constants. In developing these models the effects of limited time resolution and missed events were taken into account. Each model tested typically had two or more sets of equally likely rate constants. Incorrect sets of rate constants resulting from the effect of missed events could be eliminated by analysis of the data with different time resolutions. Normal activity could be accounted for by several different seven‐state models with two open and five shut states. As different models could be found that gave identical descriptions of the data, the distributions of open and shut intervals were not sufficient to define a unique model. It was established that no other seven‐state models would be found that describe the distributions of open and shut intervals during normal activity better than the most likely presented models.(ABSTRACT TRUNCATED AT 400 WORDS)

Correcting single channel data for missed events

Interpretation of currents recorded from single ion channels in cellular membranes or lipid bilayers is complicated by the necessarily limited time resolution of the recording and detection systems. All intervals less than a certain duration, depending on the frequency response of the system, are not detected. Such missed events produce increases in the durations of observed open and shut intervals. In order to obtain the true kinetic scheme and rate constants underlying the observed activity, it is necessary to take into account missed events. We develop methods to correct for missed events for models with two or more states, including models with multiple open and shut states, compound states, and loops. Our methods can be used in a forward direction to predict observed distributions of open and shut intervals for a given kinetic scheme and time resolution. They can also be used in a backwards direction with iterative methods to determine rate constants consistent with the observed distributions. While a given kinetic scheme with rate constants predicts unique observed distributions of open and shut intervals, rate constants determined from observed distributions are not necessarily unique. Using these correction methods, we examine the effects of missed events for a five-state model consistent with some properties of large conductance Ca-activated K channels.