A method based upon an extension of Campbell's theorem is used to measure the amplitude, waveform, and frequency of occurrence of miniature endplate potentials (mepps) at rapidly secreting neuromuscular junctions of frog cutaneous pectoris muscles. Measurements of the variance, skew, and power spectrum of the fluctuations in membrane potential are used to deduce the mepp parameters. These estimates of mepp amplitude and frequency are insensitive to slow drifts in membrane potential that preclude the conventional application of Campbell's theorem, which uses the mean and variance. The new method becomes unreliable at high mepp frequencies because the distribution of the values of membrane potential approaches a Gaussian thereby reducing the accuracy of skew measurements. Frequencies approaching 10(4) s-1 can be measured, however, if the data are high-pass filtered. The method has been tested with computer simulated data and applied to junctions exposed to La3+; the effects of Ca2+ on the La3+-induced secretion have been explored. Some muscles were fixed after treatment with La3+, and changes in nerve terminal ultrastructure were assessed by morphometric analysis of electron micrographs. Horseradish peroxidase was used to obtain information about vesicle recycling.

A modification of the classical procedure of fluctuation analysis is used to measure the waveform, w(t), mean amplitude, (h), and mean rate of occurrence, (r), of miniature endplate potentials (MEPPs) at frog cutaneous pectoris neuromuscular junctions treated with black widow spider venom (BWSV) . MEPP parameters are determined from the power spectrum of the fluctuating potential and the second (variance), third (skew), and fourth semiinvariants (cumulants) of high-pass-filtered records of the potential . The method gives valid results even when the mean potential undergoes slow changes unrelated to MEPPs and when the MEPP rate is not stationary ; it detects changes in the distribution of MEPP amplitudes and corrects for the nonlinear summation of MEPPs . The effects of Ca" on -BWSV-induced secretion are studied in detail . When Ca" is absent, the power spectrum of the fluctuations is shaped like the spectrum of w(t) and secretion is quasi-stationary ; (r) rises smoothly to peak values of -1,500/s and then quickly subsides to levels near 10/s . Many relatively small and some "giant" MEPPs occur at the ends of the experiments, and the distribution of MEPP amplitudes broadens . When the effects of this broadening are corrected for, we find that^-0 .7 X 10 6 MEPPs occurred during the 30 min of intense secretion . Since BWSV depletes nerve terminals of their quanta of transmitter and their synaptic vesicles, this figure is an upper limit for the quantal store in a resting terminal . When Ca" is present, the noise spectrum deviates from the spectrum of w(t) and secretion is nonstationary ; (r) rises to similar peak values but is sustained at levels near 400/s for up to an hour and at least 1 .5 X 10 6 quanta are secreted within this period . Thus, the quantal store must have turned over at least twice under this condition . Data previously obtained at junctions treated with La" are corrected for nonlinear summation and for the distribution of MEPP amplitudes . The two corrections roughly compensate each other, and the corrected results confirm the previous conclusion that the number of quanta secreted from La"-treated terminals during 1 h is not strongly dependent upon the extracellular concentration of Ca z+ ;^-2 X 10 6 quanta are released even when Ca 2+ is absent .

Procedures are described for analyzing shot noise and determining the waveform, w(t), mean amplitude, (h), and mean rate of occurrence, (r), of the shots under a variety of nonideal conditions that include : (a) slow, spurious changes in the mean, (b) nonstationary shot rates, (c) nonuniform distribution of shot amplitudes, and (d) nonlinear summation of the shots . The procedures are based upon Rice's (1944 . Bell Telephone System journal. 23 : 282-332) extension of Campbell's theorem to the second (variance), X2, third (skew), X3, and fourth, X4, semi-invariants (cumulants) of the noise . It is shown that the spectra of X2 and X3 of nonstationary shot noise contain a set of components that are proportional to (r) and arise from w(t), and a set of components that are independent of (r) and arise from the temporal variations in r(t) . Since the latter components are additive and are limited by the bandwidth of r(t), they can be removed by appropriate filters ; then (r) and (h) can be determined from the X2 and X3 of the filtered noise . We also show that a factor related to the ratio (X3)2/(\2)(X4) monitors the spread in the distribution of shot amplitudes and can be used to correct the estimates of (r) and (h) for the effects of that spread, if the shape of the distribution is known and if r(t) is stationary . The accuracy of the measurements of X4 is assessed and corrections for the effects of nonlinear summation of A2, X3, and X4 are derived . The procedures give valid results when they are used to analyze shot noise produced by the (linear) summation of simulated miniature endplate potentials, which are generated either at nonstationary rates or with a distribution of amplitudes .

Summary. The effects of hydrostatic pressures up to 62 MPa upon the voltage-clamp currents of intact squid giant axons were measured using mineral oil as the pressure transmitting medium. The membrane resistance and capacitance were not appreciably affected over the whole range of pressures explored. The predominant effect of pressure is to slow the overall kinetics of the voltage-clamp currents 9 Both the early (Na) currents and the delayed (K) ones were slowed down by approximately the same time scale factor, which was in the range of 2 to 3 when pressure was increased from atmospheric to 62 MPa.Finer details of the effects, most evident at moderate depolarizations, are: the apparent initial delay in the turn-on of Na currents is increased by pressure less than is the phase of steepest time variation, and the later decay is slowed more than is the rising phase. The initial time course of the currents at high pressures can be made to overlap with that at normal pressure by a constant time compression factor, Ore, together with a small, voltage-dependent delay 9In a given axon, Om was fairly independent of voltage, and it increased exponentially with pressure according to an apparent activation volume, A V • ranging between 32 and 40 cmJ/mole. A V • tended to decrease with increasing temperature. Contrary to what is observed for moderate or large depolarizations, the kinetics of Na inactivation produced by conditioning prepulses of -50 or -60 mV was little affected over the whole range of pressures explored.Inferences about the pressure dependence of the steady-state Na activation were made from the comparison of the plots of early peak currents, Ip, versus membrane potential, E. The Na reversal potential, ENd, and the slope of the plots near EN, did not change significantly with pressure, but the peak Na conductance vs. E relationship was shifted by about + 9 mV upon increasing pressure to 62 MPa. Steady-state Na inactivation, h| was slightly affected by pressure. At 62 MPa the midpoint potential of the h~(E) curve, Eh, was shifted negatively by about 4 mV, while the slope at Eh decreased by about 38%.Under the tentative assumption that pressure directly affects the gating of Na channels, the Na activation data follows a simple Hodgkin-Huxley scheme if the opening of an m gate involves an activation volume of about 58 A_ 3 and a net volume increase of about 26 A 3. However, a self-consistent description of the totality of the effects of pressure on Na inactivation cannot be obtained within a similar simple context.

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