Integral correction of end-plate potentials: A useful alternative to peak amplitude correction

Validity of correction of peak amplitudes of end-plate potentials for non-linear summation of unit potentials may be affected by membrane capacitance and asynchrony of action of unit potentials. Compensatory adjustment for the opposing and interacting effects of these factors on the correction is difficult to calculate but may be circumvented by use of an integral correction procedure described here. This procedure involves correction of the voltage of the potential over its entire time course rather than at the peak only.     

Evidence for different nonlinear summation schemes for lines and gratings at threshold

Within a wide class of multichannel models of the visual system it is suggested that spatial distributions of luminance are processed by the independent activation of grating detectors, or spatial frequency channels. Probability summation is often described in terms of Quick's nonlinear pooling model [Quick RF (1974) Kybernetik 16:65–67]. Using this model, we find evidence for the existence of different kinds of nonlinear summation at threshold; for compound gratings with well-separated spatial frequency components, the threshold functions indicate nonlinear summation which is not compatible with probability summation, while for line patterns well separated in the spatial domain the probability summation rule proves compatible with the data. Received: 24 June 1998 / Accepted in revised form: 16 March 1999     

Evidence for nonlinear capacitance in biomembrane channel system.

The electrophysiological properties of voltage-dependent anion channels from mitochondrial membrane have been studied in a bilayer membrane system. It was observed that the probability of opening of the membrane channel depends on externally applied voltage and the plot is a bell-shaped curve symmetric around probability axis. A scheme of conformational energy levels under varying externally applied voltage was formulated. Assuming that the probability follows Boltzmann distribution, we arrive at an expression of change in energy containing a separate term identical to the energy of a capacitor. This fact indicates the possibility of existence of an added capacitance due to the channel protein. Further it was shown that the aforesaid channel capacitor could be a function of voltage leading to nonlinearity. We have offered a general method of calculating nonlinear capacitance from the experimental data on opening probability of a membrane channel. In case of voltage-dependent anion channel the voltage dependence of the capacitor has a power 0.786. The results have been interpreted in view of the structural organization of the channel protein in the membrane. Our hypothesis is that the phenomenon of capacitor behaviour is a general one for membrane channels.     

Upper and lower bounds on the non-linearity of sommation of end-plate potentials

The amplitudes of end-plate potentials are non-linearly related to the number of transmitter packets eliciting the potentials. The form of the non-linearity depends on the time-course of the change in membrane conductance as compared with the membrane time-constant. Approximate solutions for very short and very long time-constants provide upper and lower bounds on the relationship between the peak amplitude of the end-plate potential and the relative number of transmitter packets.     

Effect of carbachol on miniature end-plate potentials and currents of rat skeletal muscle

Experiments on rats showed that carbachol (10 µM) appreciably quickens miniature end-plate potentials in the soleus muscle kept in medium with potassium chloride concentration increased to 13 mM. Potentiation of spontaneous mediator release also took place when the membrane potential of the muscle fibers was clamped at the level of the potassium equilibrium potential. It is concluded that the presynaptic action of carbachol on synaptic liberation of acetylcholine from motor nerve endings is unconnected with depolarization of the postsynaptic membrane but takes place as a result of the direct effect of the mimetic on motor nerve endings.S. V. Kurashov Medical Institute, Ministry of Health of the RSFSR, Kazan'. Translated from Neirofiziologiya, Vol. 14, No. 2, pp. 185–189, March–April, 1982.     

Membrane potentials of differentiating enterocytes

A positional analysis of enterocyte membrane potential has been carried out using in vitro preparations of rabbit distal ileum. Young enterocytes were found to possess a microvillar membrane potential significantly less than that seen in older enterocytes. The length of enterocyte microvilli was also found to be significantly less in younger enterocytes. It is suggested that developmental changes in membrane potential, occurring during the early stages of enterocyte differentiation, probably reflect a changed permeability to ions associated with the establishment of a fully developed microvillar membrane. Other explanations for the observed findings are also considered.     

Loss of information on central summation of local postsynaptic potentials

The spatio-temporal pattern of spikes converging on a neuron and variations in the combined depolarizing potential in the trigger zone are regarded as information carriers. In both cases the quantity of information is calculated; it is assumed that the depolarizing potential is formed as the weighted sum of the local PSPs. It is concluded from a comparison of the results that "algebraic" summation of PSPs is accompained by loss of essential information, and information carried by variation in the combined PSP is generated only by unessential input information. The investigation confirms the important role of a high spatial damping constant of electrotonic potentials in the dendrites. The damping prevents annihilation of much of the information. Electrical action of "effective" synapses on the trigger zone must evidently be regarded as sensitivity control, with no effect on the information content of the process but capable of weakening or interrupting the transmission of information from dendrites to the trigger zone. It is concluded that the combined PSP cannot serve as an information carrier and that this function may perhaps be performed by signals of a different physical nature which do not undergo damping in the dendrites.M. I. Kalinin Leningrad Polytechnical Institute. Translated from Neirofiziologiya, Vol. 5, No. 2, pp. 186–192, March–April, 1973.     

The quantal nature of transmission and spontaneous potentials at the Torpedo electromotor junction

Miniature and stimulus evoked electroplaque potentials (mEpPs and EpPs) were recorded in Torpedo electrocytes intracellularly and extracellularly. The quantal release parameters of EpPs and the time course of quantal EpCs were estimated in normal and low Ca2+-high Mg2+ solutions. Amplitude-frequency distribution of mEpPs showed Gaussian or uneven character with an average mean value of 0.3 +/- 0.08 mV (S.D.). The mean coefficient of variation of mEpPs was 26.8 +/- 7.2% (n = 6). Tetrodotoxin reversibly blocked the stimulus evoked EpP but hardly influenced the amplitude-frequency histogram of spontaneous EpPs in 10(-8)-10(-6) M concentration. The quantum content of stimulus evoked EpPs varied between 100-400 in normal solution which decreased in low Ca2+-high Mg2+ solution and the quantal release conformed to binomial statistics and allowed determination of the parameters p and n. Frequency of the spontaneous discharges varied highly from electrocyte to electrocyte but an analysis of the time intervals showed randomness for the events. The decay phase of quantal current composed of non-exponential and exponential sections which was characteristic with 0.75 +/- 0.16 msec (mean, S.D., at 20 degrees C) time constant of exponential decay. Although, two types of mEpCs could be differentiated having significantly slower and faster time courses. Neostigmine prolonged the time constant of decay of mEpCs in dose-dependent manner with a factor of 2 in 10(-6) M and of 4 in 10(-5) M concentrations (at about 20 degrees C).     

Slow changes and wiener analysis of nonlinear summation in contractions of cat muscles

With regular trains of stimuli at a high frequency, the contribution of each stimulus to the force generated over time declines from the second to about the tenth stimulus, but then begins to increase again. This late increase is referred to as tetanic potentiation in analogy with the post-tetanic potentiation of the twitch after such a period of stimulation. With regular trains of stimuli at a low frequency, a progressive decrease in the essentially unfused twitches (negative staircase) is observed in the slow soleus muscle of the cat, while a progressive increase (positive staircase) is observed for the fast plantaris muscle. The time constant for the approximately exponential changes observed is on the order of 10 s. Random trains of stimuli were applied at intermediate frequencies and analyzed in terms of general methods of analysis for nonlinear systems. Systematic decreases in the magnitude and increases in the time course of the average tension per stimulus were observed with increasing mean rates of stimulation. Similar changes were observed for short intervals between stimuli within a given random train at a constant mean rate. These changes can be described in terms of an early depression and a later facilitation described in the previous papers in this series.     

Modeling of summation of individual twitches into unfused tetanus for various types of rat motor units.

Repeated stimulation of motor units (MUs) causes an increase of the force output that cannot be explained by linear summation of equal twitches evoked by the same stimulation pattern. To explain this phenomenon, an algorithm for reconstructing the individual twitches, that summate into an unfused tetanus is described in the paper. The algorithm is based on an analytical function for the twitch course modeling. The input parameters of this twitch model are lead time, contraction and half-relaxation times and maximal force. The measured individual twitches and unfused tetani at 10, 20, 30 and 40 Hz stimulation frequency of three rat motor units (slow, fast resistant to fatigue and fast fatigable) are processed. It is concluded that: (1) the analytical function describes precisely the course of individual twitches; (2) the summation of equal twitches does not follow the results from the experimentally measured unfused tetani, the differences depend on the type of the MU and are bigger for higher values of stimulation frequency and fusion index; (3) the reconstruction of individual twitches from experimental tetanic records can be successful if the tetanus is feebly fused (fusion index up to 0.7); (4) both the maximal forces and time parameters of individual twitches subtracted from unfused tetani change and influence the course of each tetanus. A discrepancy with respect to the relaxation phase was observed between experimental results and model prediction for tetani with fusion index exceeding 0.7. This phase was predicted longer than the experimental one for better fused tetani. Therefore, a separate series of physiological experiments and then, more complex model are necessary for explanation of this distinction.     

Membrane potentials of human fibroblast strains in culture

With a simple technique, the membrane electro-physiology of mammalian fibroblasts in tissue culture can be explored with micro-electrodes. Measured in complete, serum-containing medium, the mean membrane potential for human diploid cell strains in between 70 and 75 millivolts.     

Membrane chloride conductance and capacitance in Jurkat T lymphocytes during osmotic swelling.

Video microscopy and whole-cell patch-clamp recording were used to monitor changes in relative cell volume (V/Vo), chloride conductance (gCl), and membrane capacitance (Cm) during osmotically induced swelling in Jurkat T lymphocytes. Cellular swelling was initiated with hyperosmotic pipette solutions. Simultaneous evaluation of V/Vo and gCl revealed a 59-s delay between the inception of swelling and the activation of outwardly rectifying, ATP-dependent Cl- channels. Following the delay, increases in V/Vo and gCl progressed in parallel. In contrast, Cm, a measure of cell surface area, fell gradually at a rate of approximately 150 fF/min after whole-cell access was achieved. The decline in Cm lasted 200 s and was followed by a rapid rise (approximately 750 fF/min). The rise in Cm coincided with a variable increase in "leak" current, gCl increased at a slower rate and reached lower peak values in experiments performed without ATP; ATP had no effect on the biphasic Cm time course. The temporal separation of conductance and capacitance during swelling suggests that gCl and Cm vary independently, supporting the hypothesis that a large portion, if not all, of the whole-cell Cl- conductance activated during swelling is provided by volume-sensitive Cl- channels preexisting in the plasma membrane.     

Postactivation potentiation influences differently the nonlinear summation of contractions in young and elderly adults.

The force enhancement of a twitch after a maximal conditioning muscle contraction [i.e., postactivation potentiation (PAP)] is reduced with aging, but its influence on the summation of force in response to repetitive stimulation at different frequencies is not known. The purpose of this work was to compare the electrically evoked mechanical responses of the tibialis anterior muscle between young and elderly adults after a 6-s maximal voluntary contraction (MVC). The results showed that, immediately after the conditioning MVC, twitch torque and its maximal rate of development and relaxation were significantly enhanced in both groups, but the magnitude of potentiation was greater in young (148.0 +/- 14.2, 123.7 +/- 16.5, and 185.4 +/- 36.5%, respectively) compared with elderly adults (87.4 +/- 15.2, 63.8 +/- 9.9, and 62.9 +/- 11.0%, respectively). This age-related difference in potentiation of the twitch disappeared completely 1 min after the conditioning MVC. The potentiation of torque and speed-related parameters in response to two- and three-pulse trains, delivered at a constant interval of 10 ms (100 Hz), was less than for a single pulse for both groups. In young adults, the magnitude of PAP on the successive individual mechanical contributions within a train of stimuli declined progressively such that the third contribution did not differ significantly from the same contribution before the conditioning MVC. In contrast, the second and third contributions did not potentiate (P > 0.05) in elderly adults. Although these contributions did potentiate significantly at a lower frequency of stimulation (20 Hz) in the two groups, the difference in PAP between young and elderly adults still persisted. This overall attenuation of potentiation with aging, however, appears to have a moderate influence on the decrement of the muscular performance.     

Effects of quantal content,membrane potential,and cholinoceptor density on the time course of end-plate currents in the rat under during acetylcholinesterase inhibition

The time-course of multiquantal end-plate currents (EPCs) was compared with monoquantal synaptic responses, i.e., miniature end-plate currents (MEPCs), in voltage-clamped rat diaphragm muscle fibers. In the presence of active acetylcholinesterase (AChE), the time constant of the decay of EPCs, that were composed of 25–140 quanta, was 1.2 times greater than that of MEPCs. After inhibition of AChE with armine or proserine the decay of the EPC was longer than the decay of the MEPC by 10–100 times, and unlike the MEPC, in the majority of synapses it could be described by the sum of two (n=34) or three (n=9) exponentials: monoexponential EPCs were noted in only three cases. The nature and duration of the EPC decay depended on its quantal content. After a reduction in the quantal content a three-exponential EPC decay could be successively reduced to a two- and a mono-exponential decay. A ,slow, component of the EPC decay, unlike the MEPC decay, was extremely sensitive to changes in the membrane potential, and extracellular magnesium ion concentration. When the cholinoceptors were irreversibly blocked by -bungarotoxin the MEPC decay accelerated, and the monoexponential EPC decay initially slowed down before accelerating, but even during a profound blockade the open-times of the ion channels were not affected. It therefore appears that during the generation of multiquantal EPCs when AChE is inhibited, not only does the synchronicity of the ion channel opening change, but so do their kinetics, possibly because of ion channel blockade by endogenous acetylcholine.S. V. Kurashov Institute of Medicine, Russian Ministry of Public Health, Kazan. Translated from Neirofiziologiya, Vol. 24, No. 3, pp. 269–279, May–June, 1992.