Maximum likelihood estimation of non-uniform transmitter release probabilities at the crayfish neuromuscular junction

The classical model of quantal release of neurotransmitter assumes that a fixed number of quantal units are available for release in the presynaptic terminal, and that each unit has the same probability of being released. This model also assumes that different units are released independently of one another. We consider two variations of the classical model. In the first case we assume that release is independent, but with potentially different release probabilities at different sites. In the second case we allow for dependence among the release units. A maximum likelihood procedure for the estimation of model parameters is developed, and an estimator of the number of quantal units is proposed. The performance of the method is assessed through a simulation study, and the procedures are applied to the analysis of a sequence of post-synaptic potentials recorded intracellularly at the crayfish neuromuscular junction. Goodness of fit and hypothesis test procedures reject the classical model in favor of an independent release mechanism with differing release probabilities. A more general release mechanism, allowing for dependence in the release process, also provides a good fit to the data analyzed.     

Probabilistic secretion of quanta from nerve terminals at synaptic sites on muscle cells: non-uniformity, autoinhibition and the binomial hypothesis

A model of the secretion of a quantum at a release site is proposed in which, following the influx of calcium ions, synaptic vesicles are made available for release by the activation of kappa phosphorylation steps with rate alpha. At any time during this process the vesicles may become unavailable for secretion at rate gamma. On completion of the kappa phosphorylation steps the vesicles participate in the formation of a fusion pore with the terminal membrane to give exocytosis at rate delta. Changes in alpha, delta and kappa are shown to produce characteristic changes in the number and timecourse of quantal secretions following a nerve impulse, which are similar to those observed following drug treatments that are thought to act selectively on each of these processes. The number of quanta secreted from nerve terminals that consist of many release sites does not fluctuate much during a low frequency train of impulses: the variance is small compared with the mean level, so secretion follows binomial rather than Poisson statistics. A theory is derived that shows that variations in the probability of secretion amongst these release sites of any particular kind fails to reduce the variance of the total secretion from the terminal; Poisson rather than binomial statistics then still apply. The theory shows that an interaction between release sites is required to reduce this variance and such an effect is provided if secretion at a site inhibits secretion at nearby sites. Simulations show that incorporating this process of autoinhibition into the model reproduces the experimental observations on the effects of calcium ions on the binomial parameters p and n as well as on the relative constancy of p during facilitation and depression of quantal secretion. Methods for estimating the timecourse of changes in the probability of secretion at release sites following an impulse, by using either the time of occurrence of first, second, third or later quantal latencies, are given. These procedures show that current methods for estimating the time-dependent probability changes are inadequate for detecting interaction between release sites, such as autoinhibition, unless this is relatively large. Therefore, estimates from third quantal latencies are used.     

The role of calcium in modulation of the kinetics of synchronous and asynchronous quantal release at the neuromuscular junction

To elucidate the mechanisms of calcium regulation of the kinetics of the evoked neurotransmitter quantal release, we have investigated the temporal parameters of acetylcholine secretion in the mouse neuro-muscular junction at varying extracellular calcium concentration, in the presence of calcium channel blockers or intracellular calcium buffers. Acetylcholine secretion was induced by the motor nerve stimulation at a low frequency, which did not produce facilitation of the neurotransmitter release. The analysis of histograms of synaptic delays of uniquantal endplate currents recorded during 50 ms after the presynaptic action potential revealed three components of the secretion process: early and late periods of synchronous release and a delayed asynchronous release. At reduced extracellular calcium level, the relative number of quanta released during the asynchronous phase of secretion increased, while the rate of quantal release during the early synchronous period decreased. The findings support the hypothesis of participation of low- and high-affinity calcium sensors with different calcium binding kinetics in regulation of, respectively, synchronous and asynchronous release of neurotransmitter quanta.     

On the quantal hypothesis of neurotransmitter release: an explanation for the calcium dependence of the binomial parameters

Results for quantal neurotransmitter release can be explained by assuming a binomial distribution with a population of N elements each with a probability p to release a quantum in a given trial. The binomial parameter N was unexpectedly observed to depend on external calcium concentration and (to a lesser extent) on the frequency of stimulation. This observation is explained here by the hypothesis that the release population is not homogeneous. It is shown that the same hypothesis can also account for other experimental findings. A possible cause for this inhomogeneity is suggested.     

Short-term facilitation as a tool to know neuromodulator-induced change in Ca2+ movement in the nerve terminal.

A theory was developed to show how we can predict the actions of neuromodulators on Ca2+ movement (yo: impulse-induced increase in Ca2+ concentration; c: basal Ca2+ level) in the nerve terminal from their effects on an impulse-evoked transmitter release (m: quantal content) and short-term facilitation (F) elicited by paired impulses, based on the simplest version of the residual Ca2+ hypothesis of facilitation. It was demonstrated from this theory that yo should be increased (decreased) when both m and F were increased (decreased) and that c should be increased (decreased) when m and F were increased (decreased) and decreased (increased), respectively. These ideas could interpret some published experimental results well.     

Testing the fit of a quantal model of neurotransmission

Many studies of synaptic transmission have assumed a parametric model to estimate the mean quantal content and size or the effect upon them of manipulations such as the induction of long-term potentiation. Classical tests of fit usually assume that model parameters have been selected independently of the data. Therefore, their use is problematic after parameters have been estimated. We hypothesized that Monte Carlo (MC) simulations of a quantal model could provide a table of parameter-independent critical values with which to test the fit after parameter estimation, emulating Lilliefors's tests. However, when we tested this hypothesis within a conventional quantal model, the empirical distributions of two conventional goodness-of-fit statistics were affected by the values of the quantal parameters, falsifying the hypothesis. Notably, the tests' critical values increased when the combined variances of the noise and quantal-size distributions were reduced, increasing the distinctness of quantal peaks. Our results support two conclusions. First, tests that use a predetermined critical value to assess the fit of a quantal model after parameter estimation may operate at a differing unknown level of significance for each experiment. Second, a MC test enables a valid assessment of the fit of a quantal model after parameter estimation.     

Probability of quantal transmitter release from nerve terminals: theoretical considerations in the determination of spatial variation

The release of transmitter occurs in discrete quantal units, such that the number released (m) is equal to the number available (n) times the average probability of release (p). Although a common method of estimating these parameters is to use simple binomial statistics, results may be biased if there is spatial or temporal variation in n and p (vars p, vart n, vart p). The problem arises in the simultaneous analysis of five variables, which is impractical due to the complexity and margin of error involved. The proposed solution is to eliminate two variables (vart n, vart p) by assuming stationarity and to obtain the required information from the first three moments of m. The resulting quadratic equation gives two solutions, p1 and p2. Computer simulation of quantal output as a function of vars p indicates that p1 is the better estimator of p when vars p is small, but that p2 is better when vars p is large. This changeover or "inflection" occurs at points which correspond to the maximum vars p obtainable by unimodal distributions of p (larger vars p being obtained by bimodal distributions). Comparison of the simulated histogram of m with those predicted by p1 and p2 shows that p1 provides the better fit, whether vars p is large or small. This discrepancy indicates that histogram analysis is unable to distinguish the appropriate estimate. The major limitations in the procedure can be met by assuming (1) stationarity (which can be attained and tested experimentally), and (2) normal distribution of p (since vars p is then less than "inflection" point, p1 will always be the correct estimate). The overall findings demonstrate that vars p and unbiased estimates of n and p may be calculated, provided reasonable assumptions are made. This in turn should allow the continued use of quantal parameters for describing transmitter release.     

Fluctuation Analysis of Tetanic Rundown (Short-Term Depression) at a Corticothalamic Synapse

Hypothetical scenarios for “tetanic rundown” (“short-term depression”) of synaptic signals evoked by stimulus trains differ in evolution of quantal amplitude (Q) and covariances between signals. With corticothalamic excitatory postsynaptic currents (EPSCs) evoked by 2.5- to 20-Hz trains, we found Q (estimated using various corrections of variance/mean ratios) to be unchanged during rundown and close to the size of stimulus-evoked “miniatures”. Except for covariances, results were compatible with a depletion model, according to which incomplete “refill” after probabilistic quantal release entails release-site “emptying”. For five neurons with 20 train repetitions at each frequency, there was little between-neuron variation of rundown; pool-refill rate increased with stimulus frequency and evolved during rundown. Covariances did not fit the depletion model or theoretical alternatives, being excessively negative for adjacent EPSCs early in trains, absent at equilibrium, and anomalously positive for some nonadjacent EPSCs. The anomalous covariances were unaltered during pharmacological blockade of receptor desensitization and saturation. These findings suggest that pool-refill rate and release probability at each release site are continually modulated by antecedent outputs in its neighborhood, possibly via feedback mechanisms. In all data sets, sampling errors for between-train variances were much less than theoretical, warranting reconsideration of the probabilistic nature of quantal transmitter release.     

Functional heterogeneity at the frog sensory-motor synapse

This article compares four models of amplitude fluctuations in postsynaptic potentials. The convolution of two binomial distributions and the beta model proved the best fit with experimentally obtained data (as compared with the binomial model). The beta model is based on the assumption that the probability of quantal transmitter release is a random variable with a beta distribution. Numbers of quantal generators as estimated by the beta model were found to resemble numbers of morphological identifiable synaptic boutons. Findings from research using this model showed that the binomial parameter n may be interpreted as the number of transmitter release sites functioning with a probability in excess of 0.2. The findings obtained confirm the postulated functional diversity of release sites at interneuronal synapses.I. M. Sechenov Institute of Evolutionary Physiology and Biochemistry, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 21, No. 6, pp. 780–788, November–December, 1989.     

PKC theta activity maintains normal quantal size in chromaffin cells

Protein kinase C (PKC) activity mediates multiple neurosecretory processes, but these are poorly understood due in part to the existence of at least 12 PKC isoforms. Using amperometry to record quantal catecholamine release from chromaffin cells, we found that both broad spectrum PKC antagonists and rottlerin, a selective inhibitor of the novel isoforms PKC θ and PKC δ, decreased quantal size and the number of secretory events recorded per stimulus. In contrast, drugs that selectively inhibit the atypical and conventional PKC isoforms had no effect on these parameters. While both PKC θ and δ were expressed in chromaffin cells, mice deficient for PKC θ, but not for PKC δ, exhibited lower quantal size than wild-type and were insensitive to rottlerin. Finally, an inhibitory PKC θ pseudosubstrate produced rottlerin-like responses in wild-type mice, indicating that the lack of rottlerin response in the PKC θ mutants was not the result of a form of compensation. These findings demonstrate neurosecretory regulation by a novel PKC isoform, PKC θ, and should contribute to defining mechanisms of activity-dependent regulation of neurosecretion.     

The facilitated probability of quantal secretion within an array of calcium channels of an active zone at the amphibian neuromuscular junction

A Monte Carlo analysis has been made of the phenomenon of facilitation, whereby a conditioning impulse leaves nerve terminals in a state of heightened release of quanta by a subsequent test impulse, this state persisting for periods of hundreds of milliseconds. It is shown that a quantitative account of facilitation at the amphibian neuromuscular junction can be given if the exocytosis is triggered by the combined action of a low-affinity calcium-binding molecule at the site of exocytosis and a high-affinity calcium-binding molecule some distance away. The kinetic properties and spatial distribution of these molecules at the amphibian neuromuscular junction are arrived at by considering the appropriate values that the relevant parameters must take to successfully account for the experimentally observed amplitude and time course of decline of F1 and F2 facilitation after a conditioning impulse, as well as the growth of facilitation during short trains of impulses. This model of facilitation correctly predicts the effects on facilitation of exogenous buffers such as BAPTA during short trains of impulses. In addition, it accounts for the relative invariance of the kinetics of quantal release due to test-conditioning sequences of impulses as well as due to change in the extent of calcium influx during an impulse.     

Discrepancies between spontaneous and evoked synaptic potentials at normal, regenerating and botulinum toxin poisoned mammalian neuromuscular junctions

Amplitudes and times to peak of spontaneous miniature endplate potentials (m.e.p.ps) and evoked quantal endplate potentials (e.p.ps) were compared at normal, regenerating and botulinum toxin poisoned neuromuscular junctions of the extensor digitorum longus muscle of the rat. At normal junctions the mean time to peak of m.e.p.ps was longer and more variable than that of similar-sized e.p.ps. At endplates where nerve regeneration was induced by mechanical crushing of the motor nerve the frequency of m.e.p.ps was reduced and their amplitude distribution was broader than normal. The distribution of times to peak of m.e.p.ps was considerably broader than that of quantal e.p.ps recorded at the same endplates. At neuromuscular junctions poisoned with botulinum toxin type A, spontaneous and evoked transmitter release were greatly reduced. The amplitude distribution of m.e.p.ps was wider than that of e.p.ps and the time to peak of e.p.ps was about twice as fast as and less variable than that of m.e.p.ps. To explain the observed differences in time to peak among m.e.p.ps and between m.e.p.ps and quantal e.p.ps we suggest that some m.e.p.ps, but not e.p.ps, originate from transmitter quanta released from sites at a greater distance from postsynaptic receptors or that the release or diffusion process for acetylcholine is more prolonged when producing some of the m.e.p.ps. Such mechanisms produce at normal junctions a small population of m.e.p.ps with prolonged times to peak, at regenerating junctions a greater proportion of such m.e.p.ps and in botulinum toxin poisoning a majority.     

Sorting of calcium signals at the junctions of endoplasmic reticulum and mitochondria

Calcium signal transmission between endoplasmic reticulum (ER) and mitochondria is supported by a local [Ca(2+)] control that operates between IP(3)receptor Ca(2+)release channels (IP(3)R) and mitochondrial Ca(2+)uptake sites, and displays functional similarities to synaptic transmission. Activation of IP(3)R by IP(3)is known to evoke quantal Ca(2+)mobilization that is associated with incremental elevations of mitochondrial matrix [Ca(2+)] ([Ca(2+)](m)). Here we report that activation of IP(3)R by adenophostin-A (AP) yields non-quantal Ca(2+)mobilization in mast cells. We also show that the AP-induced continuous Ca(2+)release causes relatively small [Ca(2+)](m)responses, in particular, the sustained phase of Ca(2+)release is not sensed by the mitochondria. Inhibition of ER Ca(2+)pumps by thapsigargin slightly increases IP(3)-induced [Ca(2+)](m)responses, but augments AP-induced [Ca(2+)](m)responses in a large extent. In adherent permeabilized cells exposed to elevated [Ca(2+)], ER Ca(2+)uptake fails to affect global cytosolic [Ca(2+)], but attenuates [Ca(2+)](m)responses. Moreover, almost every mitochondrion exhibits a region very close to ER Ca(2+)pumps visualized by BODIPY-FL-thapsigargin or SERCA antibody. Thus, at the ER-mitochondrial junctions, localized ER Ca(2+)uptake provides a mechanism to attenuate the mitochondrial response during continuous Ca(2+)release through the IP(3)R or during gradual Ca(2+)influx to the junction between ER and mitochondria.     

Some effects of mating in female tsetse, Glossina austeni Newst

Virgin females of G. austeni were mated at carefully chosen physiological states to determine the effect of mating on ovulation, neurosecretion and blood meal size. The results suggest that ovulation and larviposition are controlled by neurosecretion, and that the release of neurosecretion requires both a mating stimulus and the presence of a mature egg in one of the ovarioles. The mating stimulus was also found to lead to an increase in blood meal size. Unmated female flies do not ovulate and their mature eggs eventually disintegrate. Virgin blood meal sizes remain relatively low.     

Short-term forms of presynaptic plasticity

Synapses exhibit several forms of short-term plasticity that play a multitude of computational roles. Short-term depression suppresses neurotransmitter release for hundreds of milliseconds to tens of seconds; facilitation and post-tetanic potentiation lead to synaptic enhancement lasting hundreds of milliseconds to minutes. Recent advances have provided insight into the mechanisms underlying these forms of plasticity. Vesicle depletion, as well as inactivation of both release sites and calcium channels, contribute to synaptic depression. Mechanisms of short-term enhancement include calcium channel facilitation, local depletion of calcium buffers, increases in the probability of release downstream of calcium influx, altered vesicle pool properties, and increases in quantal size. Moreover, there is a growing appreciation of the heterogeneity of vesicles and release sites and how they can contribute to use-dependent plasticity.     

5-HT offsets homeostasis of synaptic transmission during short-term facilitation.

In this study, we approach the topic of vesicle recruitment and recycling by perturbing neurotransmission at the crayfish neuromuscular junction with altered electrical activity and the presence of the neuromodulator serotonin (5-HT). After induction of short-term facilitation (STF) with stimulus pulse trains (40 Hz, 20 pulses), the amount of synaptic transmission can be maintained at a relatively constant level, producing a plateau in the amplitude of the excitatory postsynaptic potentials (EPSPs) throughout the remaining stimuli within a train of a few hundred milliseconds. With an increase in the frequency of the stimuli within a train (60 Hz, 20 pulses), an altered plateau of larger EPSP amplitudes occurs. This suggests that differential rates of vesicle recruitment can be rapidly reached and maintained. Exposure of nerve terminals to 5-HT further enhances the EPSP amplitudes to yet a higher plateau level. The effect of 5-HT is more pronounced for 40-Hz pulse trains than for 60-Hz trains. This suggests that 5-HT can recruit vesicles into the readily releasable pool (RRP) and that the recruitment is limited at higher stimulation frequencies. The attainment of a larger amplitude in the plateaus of the EPSPs at 60 Hz compared with 40 Hz also suggests that the rapid induction of STF enhances the entry of vesicles into the RRP. By direct quantal counts, mean quantal content increases linearly during STF, and 5-HT offsets the linear release. We propose that 5-HT and electrically induced recruitment of vesicles from a reserve pool to the RRP may share similar recruitment mechanisms.     

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).     

Activation of protein kinase C by presynaptic FLRFamide receptors facilitates transmitter release at an aplysia cholinergic synapse

Modulation of evoked quantal transmitter release by protein kinase C (PKC) was investigated at an identified cholinergic neuro-neuronal synapse of the Aplysia buccal ganglion. Evoked acetylcholine release was increased by a diacylglycerol analog that activates PKC and was decreased by H-7, a blocker of PKC. FLRFamide facilitated evoked quantal release by increasing presynaptic Ca2+ influx. The inhibition of PKC by H-7 prevented both the increase of presynaptic Ca2+ influx and the facilitation of evoked acetylcholine release induced by the activation of presynaptic FLRFamide receptors. These results provide evidence that the activation of PKC could be a step in the intracellular pathway by which FLRFamide receptors increase evoked quantal acetylcholine release.