Complete reconstructions of vertebrate neuronal circuits on the synaptic level require new approaches. Here, serial section transmission electron microscopy was automated to densely reconstruct four volumes, totaling 670μm3, from the rat hippocampus as proving grounds to determine when axo-dendritic proximities predict synapses. First, in contrast with Peters’ rule, the density of axons within reach of dendritic spines did not predict synaptic density along dendrites because the fraction of axons making synapses was variable. Second, an axo-dendritic touch did not predict a synapse; nevertheless, the density of synapses along a hippocampal dendrite appeared to be a universal fraction, 0.2, of the density of touches. Finally, the largest touch between an axonal bouton and spine indicated the site of actual synapses with about 80% precision, but would miss about half of all synapses. Thus, it will be difficult to predict synaptic connectivity using data sets missing ultrastructural details that distinguish between axo-dendritic touches and bona fide synapses.

Wiring economy has successfully explained the individual placement of neurons in simple nervous systems like that of Caenorhabditis elegans [1-3] and the locations of coarser structures like cortical areas in complex vertebrate brains [4]. However, it remains unclear whether wiring economy can explain the placement of individual neurons in brains larger than that of C. elegans. Indeed, given the greater number of neuronal interconnections in larger brains, simply minimizing the length of connections results in unrealistic configurations, with multiple neurons occupying the same position in space. Avoiding such configurations, or volume exclusion, repels neurons from each other, thus counteracting wiring economy. Here we test whether wiring economy together with volume exclusion can explain the placement of neurons in a module of the Drosophila melanogaster brain known as lamina cartridge [5-13]. We used newly developed techniques for semiautomated reconstruction from serial electron microscopy (EM) [14] to obtain the shapes of neurons, the location of synapses, and the resultant synaptic connectivity. We show that wiring length minimization and volume exclusion together can explain the structure of the lamina microcircuit. Therefore, even in brains larger than that of C. elegans, at least for some circuits, optimization can play an important role in individual neuron placement.

Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation-Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L1 penalization methods.