Quantal analysis is a classical approach to the investigation of mechanisms underlying synaptic transmission, in which key parameters - the number of functional release sites (*N*), the quantal size (*q*) and the release probability - are extracted from fluctuations in synaptic responses using statistical models. Unlike the situation at the neuromuscular junction (NMJ), application of quantal analysis to central synapses has proved difficult because some of the necessary simplifying assumptions are often not valid. For example, at synapses where release probability is non-uniform, a compound binomial (Jack, Redman & Wong, 1981; Walmsley, Edwards & Tracey, 1988; Stricker, Field & Redman, 1996) rather than a simple binomial statistical model is required, increasing the number of parameters to be estimated from the data set. Variations in quantal size at individual release sites, and between release sites, makes it difficult to identify peaks in distributions of synaptic response amplitude and complicates their interpretation (Walmsley, 1995). Furthermore, the difficulty in testing the accuracy of these methods directly has led, for example, to controversy in attributing long-term changes in synaptic efficacy to a pre- or postsynaptic locus. Recently, several alternative strategies have been developed to examine the quantal properties of transmitter release. These include the use of a non-competitive antagonist to estimate release probability (Rosenmund, Clements & Westbrook, 1993), the use of capacitance measurement to monitor vesicle release (Heidelberger, Heinemann, Neher & Matthews, 1994), and the use of the fluorescent dye FM1-43 to examine vesicle cycling and transmitter release (Ryan, Reuter, Wendland, Schweizer, Tsien & Smith, 1993; Issacson & Hille, 1997; Murthy, Sejnowski & Stevens, 1997). However, these techniques provide only part of the quantal description of the synapse, and there are difficulties in applying them to slice preparations in which synaptic architecture is preserved.

In order to overcome these problems, we have developed a new approach which extends previous quantal analysis methods (del Castillo & Katz, 1954*a*; Miyamoto, 1975; Clamann, Mathis & Lüscher, 1989; Malinow & Tsien, 1990; Bekkers & Stevens, 1990). With this approach, which we term ‘multiple-probability fluctuation analysis’ (MPF analysis), quantal parameters are estimated from synaptic current fluctuations measured over a wide range of experimentally imposed release probabilities at the same input. This method, which is also related to non-stationary fluctuation analysis of ion channels (Sigworth, 1980; Traynelis, Silver & Cull-Candy, 1993; Silver, Cull-Candy & Takahashi, 1996) and to a method recently suggested by Frerking & Wilson (1996), provides estimates for the underlying quantal parameters with minimal assumptions. Furthermore, it can provide estimates of *N*, *q* and the mean release probability when both the quantal size and release probability are non-uniform.

At synaptic connections, the underlying quantal parameters are not static, but change with time as a result of short-term facilitation and depression (Zucker, 1989) or long-term changes in synaptic efficacy. Understanding this dynamic behaviour is central to understanding transmission, since synaptic efficacy, at any given time, is dependent on the recent history of the input. Furthermore, modelling studies have shown that the temporal behaviour of synaptic efficacy (the tendency to exhibit short-term facilitation or depression) is important in determining the pattern of frequency-coded information that is transmitted to the postsynaptic cell (Sen, Jorge-Rivera, Marder & Abbott, 1996; Tsodyks & Markram, 1997). Since the early work of del Castillo & Katz (1954*b*) at the NMJ, synaptic depression is generally assumed to have a presynaptic locus. However, at central glutamate synapses the situation appears less clear. While several studies have demonstrated presynaptic depression (Larkman, Stratford & Jack, 1991; Borst & Sakmann, 1996; von Gersdorff, Schneggenburger, Wies & Neher, 1997), non-NMDA receptors desensitize when exposed to low concentrations of glutamate, so postsynaptic desensitization may persist long after the synaptic current has decayed. Indeed, recent studies have shown that postsynaptic desensitization plays an important role in synaptic depression at some central excitatory synapses (Trussell, Zhang & Raman, 1993; Zhang & Trussell, 1994).

In this study, we have investigated transmission at the climbing fibre-Purkinje cell synaptic connection, which in paired-pulse experiments exhibits substantial EPSC depression (Konnerth, Llano & Armstrong, 1990; Perkel, Hestrin, Sah & Nicoll, 1990). This synaptic connection, as part of the olivocerebellar pathway, is thought to play an important role in the timing of motor tasks (Welsh, Lang, Sugihara & Llinas, 1995) and in motor learning (Ito, 1984). Each Purkinje cell is innervated by a single climbing fibre (CF) which forms a distributed synaptic connection with numerous contacts on the extensive dendritic tree. CF stimulation generates a large glutamate-mediated EPSC, which, under physiological conditions, causes Purkinje cells to fire complex spikes (Eccles, Llinas & Sasaki, 1966). We have investigated the locus of frequency-dependent depression by examining the underlying quantal parameters with MPF analysis. Our results show that this input has unusual quantal parameters for a central synaptic connection. Furthermore, we demonstrate with MPF analysis that the frequency-dependent depression at the CF synapse has a purely presynaptic origin over a physiological range of frequencies. Our results suggest that the temporal dynamics of release probability at this synapse are specialized to ensure highly reliable low-frequency transmission. Some of these findings have been published in this journal in a preliminary form (Silver, Momiyama & Cull-Candy, 1997).