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Models of cortical dynamics often assume a homogeneous connectivity structure. However, we show that heterogeneous input connectivity can prevent the dynamic balance between excitation and inhibition, a hallmark of cortical dynamics, and yield unrealistically sparse and temporally regular firing. Anatomically based estimates of the connectivity of layer 4 (L4) rat barrel cortex and numerical simulations of this circuit indicate that the local network possesses substantial heterogeneity in input connectivity, sufficient to disrupt excitation-inhibition balance. We show that homeostatic plasticity in inhibitory synapses can align the functional connectivity to compensate for structural heterogeneity. Alternatively, spike-frequency adaptation can give rise to a novel state in which local firing rates adjust dynamically so that adaptation currents and synaptic inputs are balanced. This theory is supported by simulations of L4 barrel cortex during spontaneous and stimulus-evoked conditions. Our study shows how synaptic and cellular mechanisms yield fluctuation-driven dynamics despite structural heterogeneity in cortical circuits.
The neurons in the cerebral cortex are not randomly interconnected. This specificity in wiring can result from synapse formation mechanisms that connect neurons depending on their electrical activity and genetically defined identity. Here, we report that the morphological properties of the neurons provide an additional prominent source by which wiring specificity emerges in cortical networks. This morphologically determined wiring specificity reflects similarities between the neurons’ axo-dendritic projections patterns, the packing density and cellular diversity of the neuropil. The higher these three factors are the more recurrent is the topology of the network. Conversely, the lower these factors are the more feedforward is the network’s topology. These principles predict the empirically observed occurrences of clusters of synapses, cell type-specific connectivity patterns, and nonrandom network motifs. Thus, we demonstrate that wiring specificity emerges in the cerebral cortex at subcellular, cellular and network scales from the specific morphological properties of its neuronal constituents.
Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neuronal networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters, and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a fixed wiring rule to fit the empirical data, SBI considers many parametrizations of a rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rule parameters and relies on machine learning methods to estimate a probability distribution (the 'posterior distribution over parameters conditioned on the data') that characterizes all data-compatible parameters. We demonstrate how to apply SBI in computational connectomics by inferring the parameters of wiring rules in an in silico model of the rat barrel cortex, given in vivo connectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.