Are transmitter release statistics meaningful?

Ca2+ dependence of the binomial parameters p and n at the mouse neuromuscular junction

The Ca(2+) dependence of synaptic quantal release is generally thought to be restricted to probability of vesicular release. However, some studies have suggested that the number of release sites (n) at the neuromuscular junction (NMJ) is also Ca(2+) dependent. In this study, we recorded endplate currents over a wide range of extracellular Ca(2+) concentrations and found the expected Ca(2+) dependency of release. A graphical technique was used to estimate p (probability of release) and n using standard binomial assumptions. The results suggested n was Ca(2+) dependent. The data were simulated using compound binomial statistics with variable n (Ca(2+) dependent) or fixed n (Ca(2+) independent). With fixed n, successful simulation of increasing Ca(2+) required that p increase abruptly at some sites from very low to high values. Successful simulation with variable n required the introduction of previously silent release sites (p = 0) with high values of p. Thus the success of both simulations required abrupt, large increases of p at a subset of release sites with initially low or zero p. Estimates of the time course of release obtained by deconvolving evoked endplate currents with average miniature endplate currents decreased slightly as Ca(2+) increased, thus arguing against sequential release of multiple quanta at higher Ca(2+) levels. Our results suggest that the apparent Ca(2+) dependence of n at the NMJ can be explained by an underlying Ca(2+) dependence of a spatially variable p such that p increases abruptly at a subset of sites as Ca(2+) is increased.

Variance-mean analysis: a simple and reliable approach for investigating synaptic transmission and modulation

The mechanisms underlying synaptic plasticity can be investigated by analyzing synaptic amplitude fluctuations before and after a synaptic modulation. However, many older fluctuation analysis techniques rely on models of synaptic transmission that incorporate unrealistic simplifying assumptions or have too many free parameters. As a result, these techniques have sometimes produced counterintuitive or contradictory results. In contrast, the variance-mean (V-M) technique requires fewer assumptions and is more robust than previous approaches. It achieves these improvements by focusing on two key parameters of synaptic transmission, the average probability that a vesicle is released from a synaptic terminal following a presynaptic stimulus (Pav), and the average amplitude of the postsynaptic response to a vesicle of transmitter (Qav). To apply V-M analysis, a fluctuating postsynaptic current (PSC) is recorded at several different extracellular Ca2+ or Cd2+ concentrations. The variance of the PSC amplitude is plotted against the mean amplitude at each concentration, forming a parabola. The degree of parabolic curvature estimates Pav, and the limiting slope under low release conditions estimates Qav. The shape of the V-M parabola changes in characteristic ways following each of the three standard forms of synaptic modulation: a change in Qav (postsynaptic), a change in Pav (presynaptic), or a change in the number of terminals (N). The approach does not require specialized software, and can even be implemented as a purely graphical technique. V-M analysis has been used to investigate the site of expression of long-term potentiation and the mechanisms underlying paired-pulse depression. This report presents a detailed mathematical development of the technique, and explores the limiting conditions under which it can confidently be applied. V-M analysis requires fewer than 100 PSC amplitude measurements to accurately estimate Pav and Qav, and it can reliably identify whether a synaptic modulation occurs at a pre- or postsynaptic site. In contrast to other techniques, V-M analysis is largely insensitive to recording noise, nonuniform modulation and intrinsic variability of the unitary synaptic amplitude.

Unveiling synaptic plasticity: a new graphical and analytical approach

Short-term synaptic plasticity has a key role in information processing in the CNS, whereas memories can be formed through long-lasting changes in synaptic strength. Despite the importance of these phenomena, it remains difficult to determine whether a synaptic modulation is expressed at a presynaptic or postsynaptic site. This article describes a new approach that, in its simplest form, can identify the site of expression by direct graphical means. A more-sophisticated form of the technique can quantify functional synaptic properties and determine which of these properties is altered following a modulation of synaptic strength.

Synaptic current at the rat ganglionic synapse and its interactions with the neuronal voltage-dependent currents

The membrane current activated by fast nicotinic excitation of intact and mature rat sympathetic neurons was studied at 37 degrees C, by using the two-microelectrode voltage-clamp technique. The excitatory postsynaptic current (EPSC) was modeled as the difference between two exponentials. A fast time constant (tau2; mean value 0.57 ms), which proves to be virtually voltage-independent, governs the current rise phase and a longer time constant (tau1; range 5.2-6.8 ms in 2 mM Ca2+) describes the current decay and shows a small negative voltage dependence. A mean peak synaptic conductance of 0.58 muS per neuron is measured after activation of the whole presynaptic input in 5 mM Ca2+ external solution (0.40 muS in 2 mM Ca2+). The miniature EPSCs also rise and decay with exponential time constants very similar to those of the compound EPSC recorded at the same voltage. A mean peak conductance of 4.04 nS is estimated for the unitary event. Deconvolution procedures were employed to decompose evoked macrocurrents. It is shown that under appropriate conditions the duration of the driving function describing quantal secretion can be reduced to <1 ms. The shape of the EPSC is accurately mimicked by a complete mathematical model of the sympathetic neuron incorporating the kinetic properties of five different voltage-dependent current types, which were characterized in a previous work. We show that IA channels are opened by depolarizing voltage steps or by synaptic potentials in the subthreshold voltage range, provided that the starting holding voltage is sufficiently negative to remove IA steady-state inactivation (less than -50 mV) and the voltage trajectories are sufficiently large to enter the IA activation range (greater than -65 mV). Under current-clamp conditions, this gives rise to an additional fast component in the early phase of membrane repolarization-in response to voltage pulses-and to a consistent distortion of the excitatory postsynaptic potential (EPSP) time course around its peak-in response to the synaptic signal. When the stimulation initiates an action potential, IA is shown to significantly increase the synaptic threshold conductance (up to a factor of 2 when IA is fully deinactivated), compared with that required when IA is omitted. The voltage dependence of this effect is consistent with the IA steady-state inactivation curve. It is concluded that IA, in addition to speeding up the spike repolarization process, also shunts the excitatory drive and delays or prevents the firing of the neuron action potential.

Analysis of fluctuations of "minimal" excitatory postsynaptic potentials during long-term potentiation in guinea pig hippocampal slices

In previous studies, quantal analysis assuming a simple binomial model has shown that long-term potentiation (LTP) is accompanied by an increase in both mean quantal content (m) and quantal size (v), whereby the increase in m predominates. In the present study, "compound" binomial distributions with variable probabilities were convolved with Gaussian distributions in computer experiments to simulate amplitude histograms of intracellular excitatory postsynaptic potentials (EPSPs). A deconvolution procedure assuming equal "quantal" separation (v) between discrete components, but without assuming binomial statistics, was applied to the simulated distributions to determine v. It was found that with a small ratio of standard deviation of noise to v (Sn/v less than 0.4), a reliable estimate of v can be obtained even for small samples (N = 100). When Sn/v was larger (0.4-0.6), approximate v estimates (within +/- 10-20% of the simulated v) could be obtained by averaging estimates from about 10 small samples (N = 100). "Minimal" EPSPs were recorded in area CA1 of guinea pig hippocampal slices. 37 EPSP amplitude samples of 9 neurones were measured before and up to 55 min after 10 tetanizations of stratum radiatum. In accordance with the previous data, the increase in v accounted for only about 10% of the average post-tetanic increase in EPSP amplitude and was not correlated with the latter. However, for an EPSP subset with small LTP magnitude, the increase in v accounted for an essential part of the LTP magnitude while the increase in m did not correlate with it. The results are in agreement with previous data obtained in the context of the simple binomial model and are interpreted as indicating primarily a presynaptic mechanism of LTP maintenance. The results suggest two types of synaptic mechanism of LTP maintenance related to the increases in m and v, respectively. The latter mechanism is saturated at about 10 to 30% increase in post-tetanic amplitude above the pre-tetanic EPSP amplitude.

Statistical analysis of long-term potentiation of large excitatory postsynaptic potentials recorded in guinea pig hippocampal slices: binomial model

Excitatory postsynaptic potentials (EPSPs) were recorded in guinea pig hippocampal slices (area CA1) from 15 neurons after stimulation of stratum radiatum (str. rad.) and stratum oriens. EPSP amplitudes increased in 8 neurones (10 post-tetanic regions) recorded 15 to 45 min after tetanic stimulation of str. rad. The increase was considered to represent long-term potentiation (LTP). Quantal analysis was performed by two methods assuming binomial statistics: the histogram method using deconvolution of noise and the variance method. According to both methods, LTP was associated with an increase in mean quantal content (m) which correlated with LTP magnitude. A statistically significant increase in quantal size (v) was found only by the histogram method and the increase was not correlated with LTP magnitude. A separate analysis of EPSPs with small LTP magnitude demonstrated that with the histogram method only v was increased but not m. A smaller increase in m for the pooled data of both methods did not correlate with LTP magnitude for this EPSP subset. The increase in m for the whole EPSP set corresponds to previous results on the quantal analysis of LTP in in vivo preparations and favours a presynaptic location of major mechanisms underlying LTP maintenance. The increase in v indicates the existence of another mechanism responsible for the maintenance of a small part of LTP. This mechanism might involve either pre- or postsynaptic changes or both.

Quantal parameters of "minimal" excitatory postsynaptic potentials in guinea pig hippocampal slices: binomial approach

Binomial distributions of amplitudes of excitatory postsynaptic potentials (EPSPs) mixed with Gaussian noise were simulated. The objective of Monte Carlo simulations was, firstly, to study influences of sampling size (N) and noise standard deviation (Sn) on estimates of mean quantal content (m), quantal size (v) and binomial parameters (n and p) by four methods of quantal analysis (histogram, variance, failures and combined method) based on the binomial model and, secondly, to modify these methods on the basis of comparison of estimated with simulated parameters. Reliable estimates (within +/- 10% of the simulated values) were obtained for large sample sizes (N = 500-1000) with Sn less than or equal to v by the histogram (deconvolution) method and with Sn less than or equal to 2v by the other three methods. Similar results were obtained by averages from about 10 simulations if smaller samples were used (N = 50-200). In electrophysiological experiments on slices, "minimal" EPSPs were recorded from CA1 pyramidal cells after low-intensity stimuli to stratum radiatum or stratum oriens. Amplitudes of minimal EPSPs fluctuated in a manner predicted by the quantum hypothesis. Amplitude distributions of EPSPs in the non-facilitated state were adequately described either by binomial statistics with an average p equal to about 0.4 (a range of 0.3-0.7) and an average n of about 3 (range 2-6) or by Poisson statistics with m of about 1. The quantal analysis suggests that typical values of m and v for a single activated fibre in stratum radiatum might be about 0.5-1 and 300-400 microV, respectively, with low p (0.1-0.3) and n (2-4). However, the estimates of binomial parameters should be considered as coarse approximations in view of the simulation results and a possible nonuniformity of parameter p. The comparison of results of various methods based on the binomial model, in both simulation and physiological experiments, indicates the reliability of estimates of basic quantal parameters (m and v) under realistic conditions of physiological experiments. The methods are considered to be sufficiently sensitive to make use of them for studies on mechanisms of long-term synaptic plasticity.

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.

Applicability of Pascal distribution to quantal analysis for non-stationary release of neurotransmitter

In order to assess the applicability of theoretical distributions to statistical analysis of neurotransmitter release, we made mathematical approaches such as derivation of frequency-generating function of the distributions, and obtained a result that a frequency distribution of the number of quanta released by the consecutive stimulations is described by a Pascal distribution when the Poisson parameter m varies temporally according to a gamma (gamma) distribution. Therefore, if the experimentally obtained distribution fits with a Pascal distribution, this suggests that non-stationary nature of the release mechanism.

Transmitter release: prepackaging and random mechanism or dynamic and deterministic process

Stepwise variations in end-plate potential amplitudes that are also multiples of spontaneous miniature end-plate potentials (MEPPs) demonstrate a quantal nature of evoked transmitter release at the vertebrate neuromuscular junction. Both the number of quanta which form relatively small end-plate potentials (EPPs) and the time intervals between MEPPs were found to fit Poisson statistics. These observations suggested that the release process randomly liberates uniform quantities of transmitter. Initial studies showed that quantal size remained stable after seemingly high rates of release which was interpreted to indicate that a large store of equally sized, equally available, and independently releasable quanta are present in the nerve terminals. The observation of numerous presynaptic vesicles that contain transmitter provided a morphological basis for prepacked transmitter (i.e., quanta). However, physiological studies over the last 15 years have yielded data that are difficult to incorporate into the quantum-vesicle hypothesis. With normal conditions and during most treatments which increase the rate of release, two classes of MEPPs have been found and both show a substructure. The bell-MEPP class was characterized by Fatt and Katz and the smaller skew-MEPP class has been studied by Kriebel. The ratio of the two classes and substructure compositions of both classes are variable. Short series of MEPPs and unitary EPPs (U-EPPs) show preferred amplitudes and longer series of MEPPs and U-EPPs show stepwise variations in amplitude. Slow-MEPPs and giant MEPPs belong to the skew class and represent nearly synchronous bursts of smaller MEPPs. Transmitter packet formation, preferred amplitudes, stepwise variations in amplitudes, random-like distributions and organized bursts can be simulated by a simple deterministic system, the drop formation process, that is known for its periodic and chaotic behaviors which are determined by the single parameter of flow rate. MEPP intervals, sizes and classes, are also dependent on rates of release which demonstrate that the release process(es) is highly organized and sensitive to different conditions. We demonstrate that the processes of drop formation and release of a packet of transmitter have similar properties and that deterministic characteristics describe MEPP and U-EPP time dependencies and amplitude substructures. The data and model presented here suggest that packet size of acetylcholine may be determined at the moment of release.

Cellular mechanisms controlling the strength of synapses

The mechanisms suspected as contributors to the regulation of synaptic strength act at a variety of sites along the causal chain that links activity in a presynaptic neuron to activity in a postsynaptic one. At several places in this chain, morphological factors are expected to have a powerful influence, and at several others, key insights into the mechanisms controlling synaptic action have been achieved using morphological techniques. A variety of presynaptic mechanisms controlling the release of neurotransmitter have been most directly shown to regulate the potency of synaptic connections. Traditional interpretations of the effect of postsynaptic geometry on synaptic strength need to be reevaluated in light of new views of the functional properties of dendritic membrane, and the new neurophysiological data must be incorporated into a more comprehensive view of the behavior of spatially distributed excitable membrane with specific patterns of distributed synaptic inputs.

Changes in binomial parameters of quantal release at crustacean motor axon terminals during presynaptic inhibition

1. The effects of presynaptic inhibition on quantal release of transmitter were investigated at neuromuscular junctions of the motor axon supplying one of the limb muscles of a crab (Pachygrapsus crassipes). 2. Binomial analysis of transmitter release recorded at selected neuromuscular junctions with an extracellular 'macro-patch' electrode indicated high probability of release (p) from a limited number of available sites (n). During presynaptic inhibition, both n and p were reduced. 3. The binomial model provided a good description of results from non-inhibited junctions. During presynaptic inhibition, results from some junctions could be described by the binomial model, while those from other junctions could not. An interpretation of this finding is that presynaptic inhibition differentially affects the probability of release at various release sites of the neuromuscular junctional complex. 4. A morphological study of the region of transmitter release under the macropatch electrode was made. Release-dependent uptake of horseradish peroxidase (HRP) into presynaptic terminals was restricted to the region under the recording electrode, by perfusing the preparation with calcium-free solution containing HRP. Transmitter release, and HRP uptake, occurred only at the site of the electrode, which was filled with a calcium-containing solution. Subsequently, serial sections were prepared for electron microscopy and the region of transmitter release was reconstructed. 5. Numerous axo-axonal synapses were found in the HRP-labelled region. Thus, the morphological prerequisite for presynaptic inhibition exists at the site of transmitter release, and not exclusively at a more remote region. 6. The number of morphologically identified excitatory neuromuscular synapses exceeded the 'release sites' estimated from the binomial model (n) by a wide margin. Morphological differences among synapses were observed. It is proposed that not all morphologically identified synapses participated in transmitter release under the experimental conditions employed. Thus, morphologically defined synapses are likely to be non-uniform in their response properties, including probability of transmitter release (p).

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.

Transformation of binomial input by the postsynaptic membrane at a central synapse

Although a binomial model gives an adequate description of the release properties of central afferent synapses, slight differences between experimental and predicted probability density functions are observed, with an excess number of responses recorded around the means. These discrepancies can be quantified by comparing experimental and theoretical entropies, which could relate to information transfer at these junctions. A model, based on the experimentally supported assumption that the postsynaptic membrane functions as a nonlinear processor, minimizes the differences between the distributions of the recorded and predicted potentials. According to this model, the nonlinearity is due to a localized interaction between the effects of simultaneously activated adjacent synapses.

Age-associated changes in neuromuscular transmission in the rat

The physiological changes in neuromuscular transmission associated with age were examined in rats between the ages of 1 mo (28 days) and 1 yr (364 days). Intracellular recording techniques were used to monitor end-plate potentials and miniature end-plate potentials at the rat diaphragm neuromuscular junction. Muscle action potentials were blocked by cutting the muscle fibers. Neuromuscular transmission was significantly different in 28-day-old rats compared with the older rats (42-364 days). The 28-day-old rats released fewer quanta. The statistical store in the immature rats was also significantly smaller than in the older age groups. The statistical probability of release, however, was not significantly different from the older animals. Examination of the presynaptic parameters in rats between the ages of 42 and 364 days revealed no significant increases in quantal release. It is concluded that the neuromuscular junction matures physiologically by 6 wk of age in rats and remains stable through the 1st yr of life.

The components of synaptic potentials evoked in cat spinal motoneurones by impulses in single group Ia afferents

1. Excitatory post-synaptic potentials (e.p.s.p.s) were evoked in cat spinal motoneurones by impulses in single group Ia afferent fibres. The probability density of the fluctuations in peak amplitude of each e.p.s.p. was calculated from the recorded peak amplitude and the probability density of the recording noise. 2. Most e.p.s.p.s fluctuated between different components (i.e. individual e.p.s.p.s of a particular discrete amplitude) with peak amplitudes which were integer multiples of the increment between successive components. The average peak amplitude of this incremental e.p.s.p. was about 90 microV for e.p.s.p.s generated at or near the soma. 3. In general, the probability density of the peak amplitude could not be described using Poisson or binomial distributions. 4. For many e.p.s.p.s the complete time course of each component could be calculated. There was no variability in the amplitude of these components nor in their latency of onset. For some e.p.s.p.s there were differences in the latency and time course of the components. 5. The increments between successive components of e.p.s.p. generated proximally were no larger (at the soma) than the corresponding increments for e.p.s.p.s generated at more distal dendritic sites. 6. These results and those from subsequent papers (Jack, Redman & Wong, 1981; Hirst, Redman & Wong, 1981) reinforce earlier suggestions that each bouton behaves in an all-or-nothing manner with respect to post-synaptic effect, and the probability of failure varies at different boutons arising from the same afferent.

Presynaptic effects of 4-aminopyridine and streptomycin on the neuromuscular junction

Studies were done to assess the effects of 4-aminopyridine (4AP) and streptomycin (SM) on transmitter release parameters and extracellularly recorded presynaptic action potential. The application of 5 micrometer 4AP resulted in a marked increase in the mean quantal content (m1) associated with an increase in the total number of the store of available quanta (n) but had no effect on the probability of release (p) and the fractional release (P). Focal recording showed that 50 micrometer 4AP modified the shape of the presynaptic action potential from a triphasic configuration to a diphasic one. In contrast, prolongation of the muscle action potential was found only at higher concentrations (greater than 1 mM) of of 4AP. Thus, the increase in n with 4 AP was associated with prolongation of the presynaptic action potential evoked by blocking the K current. SM (172 micrometer mM) had no effect on p and P. Reduction of n by SM was completely reversed by 4AP. As the presynaptic action potential change induced by 4AP was not antagonised by SM, it may be that the decrease of n by SM followed a modification of the voltage-dependent Ca channel.

Effects of 4-aminopyridine on statistical parameters of transmitter release at the neuromuscular junction

4-Aminopyridine (4-AP) potentiates transmitter release from motor nerve terminals by increasing the quantum content (m) of endplate potentials. Estimates of the binomial parameters of transmitter release shows that 4-AP enhances m by increasing n and not p.

Neurotransmitter release statistics: moment estimates for inhomogeneous Bernoulli trials

Evoked release of quanta of neurotransmitter is generally treated as a set of homogeneous, stationary Bernoulli trials, hence governed by the binomial distribution. Relaxing the assumptions of uniformity and stationarity leads to a more realistic physiological model of transmitter release but also introduces systematic biases in the moment estimates of the binomial parameters. We derive probability generating functions for quantal release and expressions for the moment estimates of n and p for a generalized model that incorporates temporal variation and nonuniformity in individual release probabilities and in numbers of release sites.