Recovering the parameters of finite mixtures of normal distributions from a noisy record: an empirical comparison of different estimating procedures

Temporal integration in sensorimotor synchronization

Abstract The concept of a temporal integration process in the timing mechanisms in the brain, postulated on the basis of experimental observations from various paradigms (for a review see P$oUppel, 1978), has been explored in a sensorimotor synchronization task. Subjects synchronized their finger taps to sequences of auditory stimuli with interstimulus-onset intervals (ISIs) between 300 and 4800 msec in different trials. Each tonal sequence consisted of 110 stimuli; the tones had a frequency of 500 Hz and a duration of 100 msec. As observed previously, response onsets preceded onsets of the stimuli by some tens of milliseconcls for ISIs in the range from about 600 to 1800 msec. For ISIs longer than or equal to 2400 msec, the ability to time the response sequence in such a way that the response 5 were placed right ahead of the stimuli started to break clown, i.e., the task was fulfilled by reactions to the stimuli rather than by advanced responses. This observation can he understood within the general framework of a temporal integration puce 55 that is supposed to have a maximal capacity (integration interval) of approximately 3 sec. Only if successive stimuli fall within one integration period, can motor programs be initiated properly by a prior stimulus and thus lead to an appropriate synchronization between the stimulus sequence and corresponding motor acts.

Evaluation of cerebral acetate transport and metabolic rates in the rat brain in vivo using 1H-[13C]-NMR

Acetate is a well-known astrocyte-specific substrate that has been used extensively to probe astrocytic function in vitro and in vivo. Analysis of amino acid turnover curves from (13)C-acetate has been limited mainly for estimation of first-order rate constants from exponential fitting or calculation of relative rates from steady-state (13)C enrichments. In this study, we used (1)H-[(13)C]-Nuclear Magnetic Resonance spectroscopy with intravenous infusion of [2-(13)C]acetate-Na(+) in vivo to measure the cerebral kinetics of acetate transport and utilization in anesthetized rats. Kinetics were assessed using a two-compartment (neuron/astrocyte) analysis of the (13)C turnover curves of glutamate-C4 and glutamine-C4 from [2-(13)C]acetate-Na(+), brain acetate levels, and the dependence of steady-state glutamine-C4 enrichment on blood acetate levels. The steady-state enrichment of glutamine-C4 increased with blood acetate concentration until 90% of plateau for plasma acetate of 4 to 5 mmol/L. Analysis assuming reversible, symmetric Michaelis-Menten kinetics for transport yielded 27+/-2 mmol/L and 1.3+/-0.3 micromol/g/min for K(t) and T(max), respectively, and for utilization, 0.17+/-0.24 mmol/L and 0.14+/-0.02 micromol/g/min for K(M_util) and V(max_util), respectively. The distribution space for acetate was only 0.32+/-0.12 mL/g, indicative of a large excluded volume. The astrocytic and neuronal tricarboxylic acid cycle fluxes were 0.37+/-0.03 micromol/g/min and 1.41+/-0.11 micromol/g/min, respectively; astrocytes thus comprised approximately 21%+/-3% of total oxidative metabolism.

Quantal analysis based on density estimation

When direct measurements of the quantal parameters for a synapse cannot be made, these parameters can be extracted from an analysis of the fluctuations in the evoked response at that synapse. In this article, a decision tree is described in which the ability of the data to match simple models of quantal transmission is rigorously compared with its ability to fit progressively more complex models. The Wilks statistic is the basis for this comparison. The procedure commences with optimal transformation of peak amplitude measurements into a probability density function (PDF). It then examines this PDF against various models of transmission, commencing with a multi-modal but non-quantal distribution, then to a multi-modal distribution with quantal peak separation with and without quantal variability, and, finally, the constraints of uniform and non-uniform release probabilities are imposed. These procedures are illustrated by example. A comparison is made between the relative sensitivities of the Wilks statistic and the chi2 goodness-of-fit criteria in rejecting inappropriate models at all stages in these procedures.

Using noise signature to optimize spike-sorting and to assess neuronal classification quality

We have developed a simple and expandable procedure for classification and validation of extracellular data based on a probabilistic model of data generation. This approach relies on an empirical characterization of the recording noise. We first use this noise characterization to optimize the clustering of recorded events into putative neurons. As a second step, we use the noise model again to assess the quality of each cluster by comparing the within-cluster variability to that of the noise. This second step can be performed independently of the clustering algorithm used, and it provides the user with quantitative as well as visual tests of the quality of the classification.

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.

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.

Noise deconvolution based on the L1-metric and decomposition of discrete distributions of postsynaptic responses

A statistical approach to analysis of amplitude fluctuations of postsynaptic responses is described. This includes (1) using a L1-metric in the space of distribution functions for minimisation with application of linear programming methods to decompose amplitude distributions into a convolution of Gaussian and discrete distributions; (2) deconvolution of the resulting discrete distribution with determination of the release probabilities and the quantal amplitude for cases with a small number (< 5) of discrete components. The methods were tested against simulated data over a range of sample sizes and signal-to-noise ratios which mimicked those observed in physiological experiments. In computer simulation experiments, comparisons were made with other methods of 'unconstrained' (generalized) and constrained reconstruction of discrete components from convolutions. The simulation results provided additional criteria for improving the solutions to overcome 'over-fitting phenomena' and to constrain the number of components with small probabilities. Application of the programme to recordings from hippocampal neurones demonstrated its usefulness for the analysis of amplitude distributions of postsynaptic responses.

Practical guidance for testing the accuracy of deconvolution results from quantal analysis

A Monte Carlo study was carried out to test the reliability of the Maximum Likelihood Estimator (MLE) approach for quantal analysis. This widely used statistical method was applied to extract a finite mixture of Gaussian distributions from simulated data. The data were generated by convolving a distribution of discrete amplitude steps (multiples of a unitary step Q) with Gaussian noise of various standard deviations (sigma n). Our results offer practical guidance on when to use the MLE, taking into account the determining parameters: signal to noise ratio (Q/sigma n, the most important parameter), number of samples collected and the number of components (k). For a given set of parameters the algorithm always converged to the "true" values, never converged to the "true" values or converged in only a fraction of cases to the "true" values. The behavior of the fitting routine in the parameter space is displayed in contour plots. These contour plots can be used as a guide to test the accuracy of deconvolution results.

NGF increases neuritic complexity of cholinergic interneurons in organotypic cultures of neonatal rat striatum

The influence of NGF on cholinergic interneurons in organotypic roller tube cultures of 4 day postnatal rat striatum was examined after 13 to 16 days in vitro. Cultures were divided into four groups. The medium of the NGF treated group was supplemented with 5 ng/ml NGF, whereas control groups were cultured either without NGF, by adding 20 ng/ml neutralising anti-NGF antibody, or by adding both NGF and anti-NGF antibody to the medium. Two different cell populations were identified by an image analysis system which measured acetylcholinesterase staining intensity. It was demonstrated that NGF promotes survival of the large, intensely stained population. Eighty computer-assisted reconstructions of intensely stained cells, 20 for each treatment group, were performed in a random order by means of a neuron tracing system. Axons and dendrites were analysed separately. NGF enhanced complexity of neuritic, predominantly axonal trees by increasing the number of axonal segments by 91% to 100% (P < 0.01), the number of dendritic segments by 33% to 63% (P = 0.09 to P < 0.01), maximal axonal branch order by 37% to 50% (P < 0.05), and maximal dendritic branch order by 22% to 37% (P < 0.05). Further evidence of more complex neuritic trees was given by Sholl concentric sphere analysis. Anti-NGF antibody could block all these effects. General rules of branching architecture were not affected by NGF treatment as shown by analysing mean segment length in relation to the branch order, branch point exit angles, total tortuosity, Rall's ratio, and tapering of neuritic trees.

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.

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.

Quantal analysis using maximum entropy noise deconvolution

When applying quantal analysis to synaptic transmission it is often unclear how much of the measured postsynaptic signal fluctuation arises from random sampling and noise rather than from the probabilistic transmitter release process. Unconstrained noise deconvolution methods do not overcome this because they tend to overfit the data, often giving a misleading picture of the underlying process. Instead, maximum entropy deconvolution provides a solution which is the smoothest, or most featureless, distribution that is still compatible with the data, taking noise and sample size into account. A simple way of achieving this is described, together with results of Monte Carlo simulations which show that the features present in the maximum entropy solution usually reflect the process underlying the data and not random sampling or noise.

Mathematical resolution of mixed in vivo voltammetry signals. Models, equipment, assessment by simultaneous microdialysis sampling

A microcomputer-assisted curve-fitting procedure was developed for the quantitative estimation of the components of the mixed "catechol peak" recorded with differential normal pulse voltammetry (DNPV) at electrochemically pretreated carbon fiber microelectrodes in the living brain. The contribution of each of the relevant electroactive species is fitted by a normal probability function, the parameters of which are previously determined in vitro for each electrode and substance. The voltammogram is thus modeled as a mixture of normal curves corresponding to the individual oxidizable substances plus a low order polynomial approximating the baseline. In a former approach the function was solved by linear least squares techniques. As a further improvement, we now propose a non-linear model of the voltammogram and a Gauss-Newton iterative algorithm with stepwise regression for parameter estimation. This report shows the application of the method for the resolution of the dopamine (DA) and dihydroxyphenylacetic acid (DOPAC) components of the DNPV signal recorded from the striatum of freely moving animals in response to amphetamine and pargyline. The method was validated by the chemical assay of contralateral microdialysates collected simultaneously. The changes detected by both methodologies were closely parallel, with highly significant correlation coefficients (0.87 and 0.99 for DA and DOPAC, respectively, P less than 0.001). This study further illustrates that the in vivo voltammetry methodology can be improved substantially by incorporating a suitable mathematical treatment of the electrochemical signals.

Presynaptic glutamate receptors depress excitatory monosynaptic transmission between mouse hippocampal neurones

1. Whole-cell patch-clamp techniques were used to record the excitatory postsynaptic current (EPSC) in a cultured mouse hippocampal neurone that resulted from electrical stimulation of another neurone in the cell culture. 2. L-Glutamate (less than 1 microM) reversibly depressed the EPSC amplitude in 67% of the synapses tested. The average amplitude reduction was 40%. The depression by glutamate was not blocked by extracellular magnesium (0.8 mM) or 2-amino-5-phosphonovaleric acid (AP5, 100 microM), indicating that N-methyl-D-aspartate (NMDA) receptors were not involved. 3. The phosphonic derivative of glutamate, L-2-amino-4-phosphonobutyrate (L-AP4), also depressed the EPSC amplitude. Neither glutamate nor L-AP4 induced any detectable inward current at concentrations which produced a potent depression of the EPSC. Statistical analysis of the amplitude fluctuations of evoked synaptic currents showed that the depression induced by both glutamate and L-AP4 was due to a decrease in the probability of synaptic release, confirming a presynaptic site of action. 4. Kainate and quisqualate also depressed excitatory synaptic transmission, but this action was related to the postsynaptic inward current that they induced. Statistical analysis showed that this action was consistent with a purely postsynaptic site of action. 5. Paired EPSCs separated by 20 ms showed either depression or potentiation of the second synaptic response. There was a strong correlation between those EPSCs which exhibited paired pulse depression and those depressed by glutamate application. 6. gamma-Aminobutyric acid (GABA) and baclofen also depressed excitatory synaptic transmission. This depression was not blocked by picrotoxin (100 microM). GABA (10 microM) was effective in 85% of cell pairs tested, while baclofen (5 microM) depressed every EPSC tested. A presynaptic site of action for both substances was indicated by the statistical analysis. 7. The results indicate that both glutamate and GABA suppress excitatory synaptic transmission by an action at presynaptic sites. The glutamate-induced depression may result from activation of a distinct excitatory amino acid receptor for which L-AP4 is a specific agonist.

A statistical test for demonstrating a presynaptic site of action for a modulator of synaptic amplitude

A statistical technique for demonstrating a presynaptic site of action for a modulator of synaptic amplitude was developed and tested. It requires that multiple measurements of peak synaptic amplitude be made under control and test conditions. The ratio of the coefficients of variation (CV) obtained under test and control conditions is calculated. A method was developed for determining the confidence interval for the CV ratio (CVR) statistic based on the null hypothesis that the synaptic modulation is purely postsynaptic. If the measured CVR falls outside the confidence interval, this implies that the modulator of synaptic amplitude is, at least in part, acting at a presynaptic site. The effectiveness of the technique and its limitations were investigated using Monte Carlo simulations. It was found to be sensitive and reliable under a variety of realistic recording conditions. The test was effective even in the presence of simulated presynaptic rundown of the synaptic response. Conventional deconvolution analysis was also applied to the Monte Carlo simulations and was found to be an inadequate indicator of the site of synaptic modulation when the discrete amplitude components were not well resolved. The CVR technique was applied to excitatory postsynaptic currents (epsc) recorded between pairs of cultured hippocampal neurones in control and test media containing 1 mM Ca2+ and 2 mM Ca2+, respectively. Test conditions increased the average synaptic amplitude, and the statistical analysis indicated that this modulation was produced by an action at a presynaptic site.

Applications of the expectation-maximization algorithm to quantal analysis of postsynaptic potentials

The expectation-maximization (EM) algorithm is a robust method for maximum likelihood estimation of the parameters of an incompletely sampled distribution. It has been used to resolve the trial-to-trial amplitude fluctuations of postsynaptic potentials, when these are recorded in the presence of noise. Its use has however been limited by the need for different recursion equations for each set of conditions defined by the signal and noise processes. These equations are derived for the following conditions which arise in studies of synaptic transmission: non-gaussian noise process; quantal fluctuation; quantal variability. In addition, a constraint can be incorporated to accommodate simple and compound binomial models of transmitter release. Some advantages of these methods are illustrated by Monte Carlo simulations.

Reduction by general anaesthetics of group Ia excitatory postsynaptic potentials and currents in the cat spinal cord

1. The effects of thiopentone and halothane on excitatory synaptic transmission at group Ia afferent synapses on lumbosacral motoneurones were studied in the anaesthetized or decerebrate cat. 2. Thiopentone (10 mg kg-1) infused on a background of light pentobarbitone anaesthesia caused a decrease in single-fibre monosynaptic group Ia excitatory postsynaptic potentials (EPSPs) of between 0 and 24%. A step increase in inspired halothane concentration in the range 0.7-0.9% produced a decrease in EPSP amplitude of between 0 and 31%. These effects were reversible when the anaesthetic level was reduced. 3. Fluctuation analysis of selected single-fibre group Ia EPSPs revealed that these effects could be accounted for by a decrease in the probability of occurrence of EPSPs of larger amplitude, and an increase in the probability of occurrence of EPSPs of smaller amplitude. The mean separation between discrete amplitudes was not altered by either anaesthetic agent. 4. EPSPs whose time course indicated a somatic site of origin were voltage clamped to study the effect of the anaesthetics on the time course of the synaptic currents. Neither thiopentone nor halothane produced a consistent effect on the time constant of decay of the current, although they both depressed its peak amplitude. 5. The results are interpreted as indicating a presynaptic site of action of both anaesthetics at the concentrations studied: the probability of release of neurotransmitter is reduced, without any detectable change in the mean duration of the postsynaptic conductance increase. These findings are discussed in relation to the mechanisms of action of anaesthetics on exocytosis and presynaptic inhibition.

Monosynaptic EPSPs in cat lumbosacral motoneurones from group Ia afferents and fibres descending in the spinal cord

1. Excitatory postsynaptic potentials (EPSPs) were elicited in lumbosacral motoneurones of pentobarbitone-anaesthetized cats by stimulating the ventral quadrants (VQ) of the thoracic spinal cord. These EPSPs were compared with monosynaptic EPSPs from small numbers of group Ia afferents, obtained by stimulating hindlimb muscle nerves with most of the dorsal roots severed. 2. EPSPs with average peak amplitude less than 1 mV were selected for fluctuation analysis. Three out of fourteen (21%) VQ EPSPs with peak voltage less than 150 mu V fluctuated in amplitude from trial to trial no more than could be accounted for by the background intracellular noise. Similarly, nine out of thirty-nine (23%) Ia EPSPs smaller than 150 mu V fluctuated to a comparable extent as the noise. These results are consistent with the view that there is little variation in the postsynaptic signal produced by an individual transmitter release event. 3. Of the EPSPs which did fluctuate more than the background noise, maximum likelihood estimates were obtained for the fluctuation patterns of ten VQ and fourteen Ia EPSPs. This was achieved by assuming that synaptic signals sum linearly with noise, but without constraining the results to conform to a statistical description of transmitter release. The fluctuation of both VQ and Ia EPSPs was made up of discrete amplitudes separated by roughly equal increments, in accordance with the quantal hypothesis of synaptic transmission. 4. Fluctuation patterns were obtained simultaneously for VQ and Ia EPSPs in seven motoneurones. The amplitudes of the quanta, defined as the mean increments between discrete amplitudes, were correlated (r = 0.90), suggesting common postsynaptic mechanisms. 5. For most EPSPs the time course of the voltage transient could be used to estimate the electrical distance from the soma at which the synaptic current was injected. There was a comparable distribution for VQ and Ia EPSPs. For those in which a quantal analysis was performed (nine VQ and eleven Ia), quantal size measured at the soma appeared to be independent of the deduced site of origin. 6. The results indicate no qualitative or quantitative differences in the behaviour of VQ and Ia EPSPs.

A cytophotometric analysis of the structure of hypothalamic cell populations in the frog, Rana temporaria (L.), with special reference to seasonal changes in chromatin status

We used cytophotometry after the Feulgen reaction and UV cytophotometry to measure the DNA content of quiescent cells of the hypothalamic preoptic region (HPR) of adult and juvenile frogs (Rana temporaria) that had been caught in their natural habitat in winter, spring and summer. The histone-to-DNA ratio in cell nuclei was cytophotometrically determined using a combined Feulgen, heparine and alcian-blue staining procedure. The vast majority of HPR cells studied had nuclei with a diploid DNA content. However, we observed great variability in the Feulgen-DNA content of the HPR cell population, which was not detected in the diploid standard (hepatocytes). This heterogeneity in the diploid sample of the HPR cell populations was always greater in prespawning frogs and may have been due to differences in the chromatin arrangement in nuclei. About 1% of cells had a DNA content either ranging between diploid and tetraploid levels (H2C cells) or at the tetraploid level (4C and 2C x 2 cells). The proportion of these cells was not affected by the age of the animals or the annual cycle, thus suggesting that there is no age-related increase in the mean DNA content in the frog HPR. The mean DNA contents of H2C and 4C cells were much higher than those in the standard (hepatocytes). This cannot be simply attributed to the presence of different amounts of nuclear proteins, but rather indicates that at least a certain proportion of the highest DNA contents may be due to a real extra-DNA synthesis.

A method for automatic classification of large and small myelinated fibre populations in peripheral nerves

The statistical analysis of morphometric data collected from biopsies of human superficial peroneal nerve is complicated by the heterogeneity of the population of myelinated fibres. In order to make separate statistical analyses of the subpopulations of large and small fibres we have developed a computer program (written in PASCAL) for their automatic separation. The method is based on a dynamic centres clustering algorithm and was applied to the multifactorial space defined by the principal component analysis of the morphometric variables: axonal diameter, myelin sheath thickness, circularity index and g-ratio. The classification technique was applied to measurements obtained from 5 control nerves, and to simulated data, and in each case it gave consistent Gaussian subpopulations with no need for the introduction of supplementary variables.

Presynaptic inhibition of synaptic potentials evoked in cat spinal motoneurones by impulses in single group Ia axons

1. Single-fibre group Ia excitatory post-synaptic potentials (e.p.s.p.s) were evoked in triceps surae motoneurones. These e.p.s.p.s were reduced by conditioning stimulation of group I axons in posterior biceps-semitendinosus nerves. 2. The investigation concentrated on e.p.s.p.s of somatic origin, because the amplitude of these e.p.s.p.s is not reduced by post-synaptic conductance increases. Any reduction in these e.p.s.p.s could therefore be attributed to presynaptic inhibition. 3. The reduction in somatic e.p.s.p. amplitude was greatest when the conditioning stimulus preceded the e.p.s.p. by 30 ms, and was negligible when the conditioning interval was extended to 200-300 ms. 4. The percentage reduction of somatic e.p.s.p.s was independent of their unconditioned peak amplitude. 5. E.p.s.p.s of somatic origin were reduced by the same amount, on average, as e.p.s.p.s of dendritic origin. 6. E.p.s.p.s evoked in the same motoneurone by impulses in different Ia axons were reduced by different amounts and e.p.s.p.s evoked in different motoneurones by impulses in the same Ia axon were also reduced by different amounts. 7. Analysis of fluctuations in e.p.s.p.s before and after conditioning indicated that after conditioning, larger discrete amplitudes became less probable, while smaller discrete amplitudes became more probable. The average increment between discrete amplitudes did not alter; nor were the discrete amplitudes reduced. 8. The probabilities of transmitter release at synaptic boutons were calculated before and during presynaptic inhibition. The maximum decrease in release probability was 0.64, suggesting a reduction in calcium influx of 10-15%.