Quantal analysis using maximum entropy noise deconvolution

Late postnatal maturation of excitatory synaptic transmission permits adult-like expression of hippocampal-dependent behaviors

Sensorimotor systems in altricial animals mature incrementally during early postnatal development, with complex cognitive abilities developing late. Of prominence are cognitive processes that depend on an intact hippocampus, such as contextual-configural learning, allocentric and idiocentric navigation, and certain forms of trace conditioning. The mechanisms that regulate the delayed maturation of the hippocampus are not well understood. However, there is support for the idea that these behaviors come "on line" with the final maturation of excitatory synaptic transmission. First, by providing a timeline for the first behavioral expression of various forms of learning and memory, this study illustrates the late maturation of hippocampal-dependent cognitive abilities. Then, functional development of the hippocampus is reviewed to establish the temporal relationship between maturation of excitatory synaptic transmission and the behavioral evidence of adult-like hippocampal processing. These data suggest that, in rats, mechanisms necessary for the expression of adult-like synaptic plasticity become available at around 2 postnatal weeks of age. However, presynaptic plasticity mechanisms, likely necessary for refinement of the hippocampal network, predominate and impede information processing until the third postnatal week.

Mechanism for increased hippocampal synaptic strength following differential experience

Exposure to novel environments or behavioral training is associated with increased strength at hippocampal synapses. The present study employed quantal analysis techniques to examine the mechanism supporting changes in synaptic transmission that occur following differential behavioral experience. Measures of CA1 synaptic strength were obtained from hippocampal slices of rats exposed to novel environments or maintained in individual cages. The input/output (I/O) curve of extracellularly recorded population excitatory postsynaptic potentials (EPSPs) increased for animals exposed to enrichment. The amplitude of the synaptic response of the field potential was related to the fiber potential amplitude and the paired-pulse ratio, however, these measures were not altered by differential experience. Estimates of biophysical parameters of transmission were determined for intracellularly recorded unitary responses of CA1 pyramidal cells. Enrichment was associated with an increase in the mean unitary synaptic response, an increase in quantal size, and a trend for decreased input resistance and reduction in the stimulation threshold to elicit a unitary response. Paired-pulse facilitation, the percent of response failures, coefficient of variance, and estimates of quantal content were not altered by experience but correlated well with the mean unitary response amplitude. The results suggest that baseline synaptic strength is determined, to a large extent, by presynaptic release mechanisms. However, increased synaptic transmission following environmental enrichment is likely due to an increase in the number or efficacy of receptors at some synapses and the emergence of functional synaptic contacts between previously unconnected CA3 and CA1 cells.

Analysis and implications of equivalent uniform approximations of nonuniform unitary synaptic systems

Real synaptic systems consist of a nonuniform population of synapses with a broad spectrum of probability and response distributions varying between synapses, and broad amplitude distributions of postsynaptic unitary responses within a given synapse. A common approach to such systems has been to assume identical synapses and recover apparent quantal parameters by deconvolution procedures from measured evoked (ePSC) and unitary evoked postsynaptic current (uePSC) distributions. Here we explicitly consider nonuniform synaptic systems with both intra (type I) and intersynaptic (type II) response variability and formally define an equivalent system of uniform synapses in which both uePSC and ePSC amplitude distributions best approximate those of the actual nonuniform synaptic system. This equivalent system has the advantage of being fully defined by just four quantal parameters: ñ, the number of equivalent synapses;p, the mean probability of quantal release; mu, mean; and sigma(2), variance of the uePSC distribution. We show that these equivalent parameters are weighted averages of intrinsic parameters and can be approximated by apparent quantal parameters, therefore establishing a useful analytical link between the apparent and intrinsic parameters. The present study extends previous work on compound binomial analysis of synaptic transmission by highlighting the importance of the product of p and mu, and the variance of that product. Conditions for a unique deconvolution of apparent uniform synaptic parameters have been derived and justified. Our approach does not require independence of synaptic parameters, such as p and mu from each other, therefore the approach will hold even if feedback (i.e., via retrograde transmission) exists between pre and postsynaptic signals. Using numerical simulations we demonstrate how equivalent parameters are meaningful even when there is considerable variation in intrinsic parameters, including systems where subpopulations of high- and low-release probability synapses are present, therefore even under such conditions the apparent parameters estimated from experiments would be informative.

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.

Optical detection of a quantal presynaptic membrane turnover

Exploration of the mechanisms and plasticity of synaptic transmission has been hindered by the lack of a method to measure single vesicle turnover directly in individual presynaptic boutons at isolated nerve terminals. Although postsynaptic electrical recordings have provided a wealth of invaluable basic information about quantal presynaptic processes, this approach has often proved difficult to apply at most central nervous system synapses. Here we describe the direct optical detection of single quantal events in individual presynaptic boutons of cultured hippocampal neurons. Using the fluorescent dye FM 1-43 as a tracer for presynaptic endocytosis, we have characterized both evoked and spontaneous components of presynaptic function at the level of individual quanta. Our results are consistent with quantal interpretations of previous electrophysiological analyses and provide new information about the unitary membrane recycling event and its coupling to individual action potential stimuli, about spontaneous vesicle turnover at individual boutons, and about the numbers of vesicles recycling at individual boutons.

The effects of synaptic noise on measurements of evoked excitatory postsynaptic response amplitudes

Spontaneously occurring synaptic events (synaptic noise) recorded intracellularly are usually assumed to be independent of evoked postsynaptic responses and to contaminate measures of postsynaptic response amplitude in a roughly Gaussian manner. Here we derive analytically the expected noise distribution for excitatory synaptic noise and investigate its effects on amplitude histograms. We propose that some fraction of this excitatory noise is initiated at the same release sites that contribute to the evoked synaptic event and develop an analytical model of the interaction between this fraction of the noise and the evoked postsynaptic response amplitude. Recording intracellularly with sharp microelectrodes in the in vitro hippocampal slice preparation, we find that excitatory synaptic noise accounts for up to 70% of the intracellular recording noise, when inhibition is blocked pharmacologically. Up to 20% of this noise shows a significant correlation with the evoked event amplitude, and the behavior of this component of the noise is consistent with a model which assumes that each release site experiences a refractory period of approximately 60 ms after release. In contrast with classical models of quantal variance, our models predict that excitatory synaptic noise can cause the apparent variance of successive peaks in an excitatory synaptic amplitude histogram to decrease from left to right, and in some cases to be less than the variance of the measured noise.

Effects of variance in mini amplitude on stimulus-evoked release: a comparison of two models

The strength of synaptic connections between two neurons is characterized by the number of release sites (N) on the presynaptic cell, the probability (p) of transmitter release at those sites in response to a stimulus, and the average size (A) of the postsynaptic response from each site. Quantal analysis can determine N, p, and A, but the large variance in the amplitudes of minis at central synapses is predicted to obscure quantal peaks and render quantal analysis unusable. Recently it has been suggested that the variance in mini amplitude is generated by differences between release sites, rather than by quantum-to-quantum fluctuations at identical sites, and that this form of variance in mini amplitude reduces the amount of variance expected in quantal peaks. Using simulations, we examine the possibility of resolving quantal peaks assuming either form of variance in mini amplitude. We find that individual quantal peaks are resolvable in neither case, provided that the uniquantal distribution is similar to the mini distribution. Because this lack of resolution compromises the utility of quantal analysis, we develop a general description that can solve N and p, given the statistical parameters of the mini distribution and the evoked distribution. We find that this description is relatively insensitive to the source of variance in mini amplitude.

Quantal behaviour of synaptic transmission can be statistically examined using the Fourier line spectrum of the histogram of synaptic potentials

A statistical approach to reveal the quantal behaviour of postsynaptic potentials (PSPs) is described. This includes: (1) obtaining the Fourier line spectrum (decomposition into harmonics) of the PSP histogram; and (2) testing the null hypothesis, 'the spectrum is that of white noise', using an ANOVA. The harmonic that rejects the hypothesis will indicate the regular peaks in the histogram, i.e., the quantal size of PSPs. The method was tested using published results of three experimental studies in central synapses and yielded the quantal sizes close to those derived from other methods. However, using three examples of published simulation studies (where the quantal model of synaptic transmission was known a priori), it was shown that the approach can estimate quantal sizes of PSPs more reliably than other methods.

Limits of quantal analysis reliability: quantal and unimodal constraints and setting of confidence intervals for quantal size

An accurate objective method for determining the reliability of estimates of quantal size (Q) at central synapses was developed. To do this, distributions of amplitudes of postsynaptic responses were simulated by convolving a number of discrete amplitudes separated by equal increments Q with gaussian noise, after which the value of Q was estimated by the maximum likelihood method under different constraints on the discrete distribution. It was shown that the likelihood function (LF) had several local maxima under the quantal constraint, and, if the value of the ratio between Q and the standard deviation of the noise (sigma) was less than 3, the global maximum of the LF corresponded to a biased estimate of Q lying in a range of values less than 1.5 sigma. The best estimates of Q were obtained when unimodal discrete distributions of amplitudes resulting from the maximum likelihood method were selected. However, this method also gave biased estimates when Q/sigma was less than 1.5-2.3. The limit of reliability depended on the number of discrete components and the sample size. To calculate confidence intervals for the quantal size, different numbers and weights of components were used to simulate amplitude histograms with different values of Q/sigma. Three data sets were used to illustrate the procedure.

Quantal variability of excitatory transmission in the hippocampus: implications for the opening probability of fast glutamate-gated channels

The quantal description of synaptic transmission, first formulated at the neuromuscular junction, has recently been extended to the Schaffer collateral-CA1 synapse of the mammalian hippocampus. In a subset of connections, an upper limit can be placed on the coefficient of variation of the quantal amplitude, on occasion lower than 0.2. In the same connections, the average quantal amplitude implies that fewer than 20 fast glutamate-gated ion channels open to carry the quantal current. With so few channels opening, their stochastic behaviour imposes a minimal trial-to-trial variability on the quantal current. These observations can be reconciled by postulating that most of the available receptors in the synaptic cleft are bound by released transmitter and that ionophores open with a high probability.

Bayesian analysis of mixtures applied to post-synaptic potential fluctuations

Bayesian inference techniques have been applied to the analysis of fluctuation of post-synaptic potentials in the hippocampus. The underlying statistical model assumes that the varying synaptic signals are characterized by mixtures of (unknown) numbers of individual gaussian, or normal, component distributions. Each solution consists of a group of individual components with unique mean values and relative probabilities of occurrence and a predictive probability density. The advantages of bayesian inference techniques over the alternative method of maximum likelihood estimation (MLE) of the parameters of an unknown mixture distribution include the following: (1) prior information may be incorporated in the estimation of model parameters; (2) conditional probability estimates of the number of individual components in the mixture are calculated; (3) flexibility exists in the extent to which the estimated noise standard deviation indicates the width of each component; (4) posterior distributions for component means are calculated, including measures of uncertainty about the means; and (5) probability density functions of the component distributions and the overall mixture distribution are estimated in relation to the raw grouped data, together with measures of uncertainty about these estimates. This expository report describes this novel approach to the unconstrained identification of components within a mixture, and provides demonstration of the usefulness of the technique in the context of both simulations and the analysis of distributions of synaptic potential signals.