Learning from experience depends at least in part on changes in neuronal connections. We present the largest map of connectivity to date between cortical neurons of a defined type (L2/3 pyramidal cells), which was enabled by automated analysis of serial section electron microscopy images with improved handling of image defects. We used the map to identify constraints on the learning algorithms employed by the cortex. Previous cortical studies modeled a continuum of synapse sizes (Arellano et al. , 2007) by a log-normal distribution (Loewenstein, Kuras and Rumpel, 2011;de Vivo et al. , 2017;Santuy et al. , 2018) . A continuum is consistent with most neural network models of learning, in which synaptic strength is a continuously graded analog variable. Here we show that synapse size, when restricted to synapses between L2/3 pyramidal cells, is well-modeled by the sum of a binary variable and an analog variable drawn from a log-normal distribution. Two synapses sharing the same presynaptic and postsynaptic cells are known to be correlated in size (Sorra and Harris, 1993;Koester and Johnston, 2005;Bartol et al. , 2015;Kasthuri et al. , 2015;Dvorkin and Ziv, 2016;Bloss et al. , 2018;Motta et al. , 2019) . We show that the binary variables of the two synapses are highly correlated, while the analog variables are not. Binary variation could be the outcome of a Hebbian or other synaptic plasticity rule depending on activity signals that are relatively uniform across neuronal arbors, while analog variation may be dominated by other influences. We discuss the implications for the stability-plasticity dilemma. †Correspondence to svenmd@princeton.edu ,

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We present a semi-automated reconstruction of L2/3 mouse primary visual cortex from 3 million cubic microns of electron microscopic images, including pyramidal and inhibitory neurons, astrocytes, microglia, oligodendrocytes and precursors, pericytes, vasculature, mitochondria, and synapses. Visual responses of a subset of pyramidal cells are included. The data are being made publicly available, along with tools for programmatic and 3D interactive access. The density of synaptic inputs onto inhibitory neurons varies across cell classes and compartments. We uncover a compartment-specific correlation between mitochondrial coverage and synapse density. Frequencies of connectivity motifs in the graph of pyramidal cells are predicted quite accurately from node degrees using the configuration model of random graphs. Cells receiving more connections from nearby cells exhibit stronger and more reliable visual responses. These example findings illustrate the resource's utility for relating structure and function of cortical circuits as well as for neuronal cell biology.

Learning from experience depends at least in part on changes in neuronal connections. We present the largest map of connectivity to date between cortical neurons of a defined type (L2/3 pyramidal cells in mouse primary visual cortex), which was enabled by automated analysis of serial section electron microscopy images with improved handling of image defects (250×140×90 μm3 volume). We used the map to identify constraints on the learning algorithms employed by the cortex. Previous cortical studies modeled a continuum of synapse sizes by a log-normal distribution. A continuum is consistent with most neural network models of learning, in which synaptic strength is a continuously graded analog variable. Here we show that synapse size, when restricted to synapses between L2/3 pyramidal cells, is well-modeled by the sum of a binary variable and an analog variable drawn from a log-normal distribution. Two synapses sharing the same presynaptic and postsynaptic cells are known to be correlated in size . We show that the binary variables of the two synapses are highly correlated, while the analog variables are not. Binary variation could be the outcome of a Hebbian or other synaptic plasticity rule depending on activity signals that are relatively uniform across neuronal arbors, while analog variation may be dominated by other influences such as spontaneous dynamical fluctuations. We discuss the implications for the longstanding hypothesis that activity-dependent plasticity switches synapses between bistable states.