Power spectra of pulse sequences and implications for membrane fluctuations

Measurement of quantal secretion induced by ouabain and its correlation with depletion of synaptic vesicles

Ouabain (0.1 and 0.05 mM) was applied to frog cutaneous pectoris nerve-muscle preparations bathed in modified Ringer's solution containing either 1.8 mM Ca2+ (and 4 mM Mg2+) or no added Ca2+ (4 mM Mg2+ and 1 mM EGTA). During the intense quantal release of acetylcholine (ACh) induced by ouabain, the parameters of the miniature endplate potentials (mepps) were deduced from the variance, skew, and power spectra of the endplate recordings by applying a recently described modification of classical fluctuation analysis. Often the high frequency of mepps is not stationary; therefore, the signal was high-pass filtered (time constant of the resistance-capacitance filter of 2 ms) to remove the errors introduced by nonstationarity. When ouabain was applied in the presence of Ca2+, mepp frequency started to rise exponentially after a lag of 1.5-2 h, reached an average peak frequency of 1,300/s in approximately 30 min, and then suddenly subsided to low level (10/s). In Ca2+-free solution, after a shorter lag (1-1.5 h), mepp frequency rose to peak rate of 700/s in approximately 20 min and then gradually subsided. In spite of the different time course of secretion in the two experimental conditions, the cumulative quantal release was not significantly different (7.4 +/- 1.3 X 10(5) in Ca2+-containing and 8.8 +/- 2.7 X 10(5) in Ca2+-free solutions). 60 min after the peak secretion, the muscles were fixed for observation in the electron microscope. Morphometric analysis on micrographs of neuromuscular junctions revealed in both cases a profound depletion of synaptic vesicles and deep infoldings of presynaptic membrane. This rapid depletion and the lack of uptake of horseradish peroxidase suggest that ouabain impairs the recycling process that tends to conserve the vesicle population during intense secretion of neurotransmitter. The good correlation observed between the reduction in the store of synaptic vesicles and the total number of quanta of ACh secreted in the absence of a vigorous membrane recycling strongly supports the view that the secretion of a quantum of ACh requires the fusion of a synaptic vesicle with the axolemma.

Miniature endplate potential frequency and amplitude determined by an extension of Campbell's theorem

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.

1/f noise in membranes

The present situation of 1/f noise in the passage of ions across membranes is examined. A survey of biological and synthetic membranes is given at which a 1/f frequency dependence has been observed in the spectrum of voltage or current fluctuations. Empirical relations and theories of 1/f noise in membranes are critically discussed.

1/f Membrane noise generated by diffusion processes in unstirred solution layers

A mathematical treatment is given for 1/f noise observed in the ion transport through membranes. It is shown that this noise can be generated by current or voltage fluctuations which occur after step changes of the membrane permeability. Due to diffusion polarization in the unstirred solution layers near the membrane these fluctuations exhibit a 1 square root of t time course which produces noise with a 1/f frequency dependence. The spectral density of 1/f noise is calculated for porous membranes with random switches between a finite and zero pore permeability. A wide frequency range and a magnitude of 1/f noise are obtained which are compatible with experimental data of 1/f noise reported for nerve membranes.

Shot noise in ion channels

A theoretical treatment of electrical noise originating from the discontinuous movement of ions through pore-like channels in a membrane is given. Two simple models are considered, a port with a single energy barrier and a pore with a single binding site separated from the aqueous solutions by energy barriers on either side. The single-barrier pore acts as a white-noise source with a spectral density SJ of the current that is proportional to the total rate of jumps over the barrier. At voltages near the equilibrium potential of the permeable ion, SJ becomes equal to the spectral density of thermal (or Johnson) noise. On the other hand, in the limit of high voltages, SJ approaches the spectral density of a Schottky noise source. A similar behaviour is found for channels with a double barrier in the limit of low frequencies omega. At higher frequencies a dispersion of the spectral density near omega = 1/tau1 occurs, where tau1 is the average lifetime of the occupied state of the channel.