Opinion TRENDS in Neurosciences Vol.30 No.12 What can we learn from synaptic weight distributions? Boris Barbour1, Nicolas Brunel2, Vincent Hakim3 and Jean-Pierre Nadal3 1 Laboratoire de Neurobiologie (CNRS UMR 8544), Ecole Normale Supe´ rieure, 46 rue d’Ulm, 75005 Paris, France 2 Laboratoire de Neurophysique et Physiologie (CNRS UMR 8990), Universite´ Rene´ Descartes, 45 rue des Saints Pe` res, 75006 Paris, France 3 Laboratoire de Physique Statistique (CNRS UMR 8550), Ecole Normale Supe´ rieure, 24 rue Lhomond, 75005 Paris, France Much research effort into synaptic plasticity has been specific synaptic plasticity rule, given some statistical motivated by the idea that modifications of synaptic assumptions about pre- and postsynaptic activity. A second weights (or strengths or efficacies) underlie learning approach is to link synaptic weights directly to the learning and memory. Here, we examine the possibility of exploit- task, bypassing the particular learning rule. Surprisingly, ing the statistics of experimentally measured synaptic this is, in some cases, possible, but a key condition is that weights to deduce information about the learning pro- the learning has been optimised in some way. This latter cess. Analysing distributions of synaptic weights requires approach appears to fit the data remarkably well and has a theoretical framework to interpret the experimental the ability to access high-level information (such as infor- measurements, but the results can be unexpectedly mation storage capacity) that is very difficult to obtain powerful, yielding strong constraints on possible learning experimentally. We end by highlighting several open theories as well as information that is difficult to obtain by issues and prospects for future progress. other means, such as the information storage capacity of a cell. We review the available experimental and theor- Experimental measurements of synaptic weight etical techniques as well as important open issues. distributions Available measurements of excitatory weights (see Box 1, Introduction Figure 1) have been obtained from somatic recordings. We Synaptic plasticity has been the subject of intense research shall therefore define synaptic weight as the peak depolar- since it was hypothesised to play a major role in learning isation a synapse produces at the soma. All of the distri- and memory [1] and was demonstrated by Bliss and Lomo butions of synaptic weights shown in Box 1 have very similar [2]. There have been significant efforts to link particular shapes — a monotonic decay from a peak very close to zero forms of synaptic plasticity to behavioural learning tasks weight. Another similarity between all of the synapse types [3–5]. Because synaptic plasticity alters synaptic weights is the apparent probability of connection of around 10%. For within the framework of particular learning tasks, we the remaining 90% of apparently unconnected cell pairs, it would expect the resulting weights to depend causally is, in general, unclear what fraction might be connected by upon both the learning rule and the task. Synaptic weights synapses with weights that fall below the detection should, therefore, be a source of information about threshold. Because the numbers of these synapses will be plasticity and learning. Ideally, one would be able to of particular theoretical interest, we shall review the evi- monitor the weights of multiple synapses before, during, dence quantifying these ‘‘silent’’ synapses, which we define and after learning, but such measurements are currently as lacking a detectable AMPA-receptor-mediated com- beyond the state of the art. However, some information ponent (NMDA or mGluR receptors might be present). about synaptic weights can be gathered using today’s In juvenile hippocampus, ‘‘silent’’ synapses have been methodology. In particular, statistical information about reported between Schaffer collaterals and CA1 pyramidal the distribution of synaptic weights is available for several cells. These synapses contain NMDA receptors, but few, if connection types. any, AMPA receptors [6,7]. The numbers of these synapses Here, we review what can be deduced from measure- are unknown; however, in immunochemical experiments, ments of synaptic weight distributions. First, we shall 20% of Schaffer collateral synapses in CA1 had no detect- describe measured distributions at different types of able AMPA receptors in the adult [8]. Moreover, a much synapses in various brain areas. We emphasise two strik- larger fraction of synapses displayed very weak labelling, ing observations: (i) the strong similarity of these distri- indicating that many synapses might have relatively weak butions, and (ii) the small fraction of detectable synapses, responses. As for all of the connections presented in Box 1, compared to the expectation from the geometry of axons the study of Sayer et al. [9] found that 10% of recordings of and dendritic arbors. We shall then examine two types of CA3-CA1 pyramidal cell pairs yielded detectable responses, theoretical framework. The first approach is to compare which would certainly leave room for many undetected the experimental data to the distribution produced by a synapses. Corresponding author: Barbour, B. ([email protected]). At the cerebellar granule cell-Purkinje cell synapse, a Available online 5 November 2007. large discrepancy between the connection rate predicted on www.sciencedirect.com 0166-2236/$ – see front matter ß 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.tins.2007.09.005 Opinion TRENDS in Neurosciences Vol.30 No.12 623 neurones. This is usually supplied in a statistical way, Box 1. Experimentally determined weight distributions and Poisson spike trains are a frequent simplifying The majority of published synaptic weight distributions concern assumption. Correlations between pre- and postsynaptic recurrent connections between pyramidal cells. One of the first such activity obviously play an important role. This correlation studies involved the recurrent connections between layer 2/3 pyramidal cells [56]. Typical pre- and postsynaptic responses from can result from the explicit dynamics of the chosen (model) that work are shown in the inset of Figure 1a. The distribution neurone subjected to presynaptic activity at its many obtained is shown in Figure 1a with those from two more recent synapses [24] or be imposed ad hoc to assess its effect on studies [57,58]. The overall shape is one of a monotonic decay from the weight distribution [25]. a peak (mode) near zero. Similar studies of the recurrent connec- Using a simple, additive rule, according to which the tions between layer 5 pyramidal cells [38,59–61] have revealed a remarkably similar distribution (Figure 1b). By far the largest data weight change is independent of the synapse strength, set is that of Sjo¨ stro¨ m et al., which contains 1004 connections. The STDP generally produces a bimodal distribution [24,26], mean response amplitude of these connections was 0.85 Æ 0.93 mV with synaptic strengths clustering both around zero and at (mean Æ SD), whereas the probability of connection was 11%. the maximum synaptic weight that must be imposed in Distributions obtained in other structures also have very similar this case to avoid unphysiologically strong synapses (see shapes, but different amplitude scales. In hippocampus, the connection between CA3 and CA1 pyramidal cells (Figure 1c) Figure 2). This can be understood rather simply: for uncor- displayed a mean of 131 mV and a connection probability of 6% related synaptic activity, the overall effect of the plasticity [9]. In cerebellum, the granule cell-Purkinje cell synapse [11,12] rule needs to be a weakening rather than a strengthening exhibited a mean amplitude of 72 Æ 63 mV and a connection of synaptic strength to avoid uncontrolled growth of synap- probability of 7% (Figure 1d). Weight distributions are also available for other synapse types, tic strength. This produces the mode at zero. However, including synapses involving neocortical interneurones [57], hippo- postsynaptic activity tends to be correlated with and to campal interneurones [62], and layer 4 spiny stellate cells in the follow presynaptic activity at stronger synapses. This neocortex [63]. Remarkably, these distributions all have similar positive feedback for sufficiently strong synapses leads shapes to those presented above, with one significant difference— to the other mode at the maximum synaptic strength. pyramidal cell-interneurone connections (in both directions) had much higher connection probabilities (>50%) [57]. The bimodal distribution resulting from an additive rule appears to be in conflict with existing data, in which no such bimodality can be detected. It could however poten- anatomical grounds [10] and that observed experimentally tially be reconciled with experimental data if maximum [11] strongly suggests the existence of a large majority of synaptic weights themselves have a wide distribution, as undetectable/silent synapses [11,12]. This notion is sup- can be expected for synapses distributed uniformly along ported by the very restricted simple-spike receptive fields the dendritic tree, because of electrotonic filtering effects. of Purkinje cells in vivo [13] and their huge expansion after The nature of the distribution is also sensitive to details of the induction of synaptic plasticity [14]. the rule. Multiplicative STDP rules, in which a synaptic Similar anatomical arguments for a high likelihood of a change depends on the strength of the synapse,