Three-dimensional reverse engineering of neuronal microcircuits: The barrel cortex in silico

The mammalian neocortex is one of the most complex biological tissues and the center of higher brain functions. Currently, the specific distribution of neurons and neurites, as well as their intricate wiring within an entire neocortical area that emerge during development and are then refined throughout life, are not accessible. Here, I present a reverse engineered model of one neocortical area, the rat barrel cortex. First, I created a model of its structural composition constraint by measurements of cortex geometry, neuron distributions, and morphological reconstructions. This model provided anatomically realistic and robust estimates of the area's neuron and neurite distributions and captured the structural principles preserved across individuals. Second, I used the model's distribution of neurites to constrain synapse formation. Specifically, I introduced a stochastic synapse formation strategy that predicts the area's wiring diagrams if they were solely shaped by the area's structural composition in the absence of any learning or plasticity rules. I find that the predicted wiring diagrams are sparse, heterogeneous, correlated, and structured unlike random networks --- all of which are either observed or speculated properties of neocortical wiring. A systematic comparison between predicted and empirical wiring properties on the subcellular, cellular, and network level revealed a high degree of consistency. This demonstrates that the structural organization of the neuropil provides strong constraints for synapse formation. For the consistently predicted wiring properties, such as connection probabilities, it cannot be ruled out that they were shaped by the area's structural composition, i.e., implicitly by the developmental mechanisms that positioned neurons and neurites within the neuropil. A more sophisticated synapse formation strategy is not necessarily required. In contrast, such a sophisticated strategy might underlie the inconsistently predicted wiring properties, e.g., the frequency of certain circuit motifs. The herein presented approach can hence act as a starting point to identify wiring correlates of sensory experience or learning and provide a foundation to explore the relationship between synapse formation, an area's structural composition, and network architecture

Cell Type-Specific Structural Organization of the Six Layers in Rat Barrel Cortex

The cytoarchitectonic subdivision of the neocortex into six layers is often used to describe the organization of the cortical circuitry, sensory-evoked signal flow or cortical functions. However, each layer comprises neuronal cell types that have different genetic, functional and/or structural properties. Here, we reanalyze structural data from some of our recent work in the posterior-medial barrel-subfield of the vibrissal part of rat primary somatosensory cortex (vS1). We quantify the degree to which somata, dendrites and axons of the 10 major excitatory cell types of the cortex are distributed with respect to the cytoarchitectonic organization of vS1. We show that within each layer, somata of multiple cell types intermingle, but that each cell type displays dendrite and axon distributions that are aligned to specific cytoarchitectonic landmarks. The resultant quantification of the structural composition of each layer in terms of the cell type-specific number of somata, dendritic and axonal path lengths will aid future studies to bridge between layer- and cell type-specific analyses

The impact of neuron morphology on cortical network architecture

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 the 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

Prior predictive distribution for the DSO rule.

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.</div

Synapse-level wiring rule inferred with SBI differs from Peters’ rule.

We compared an SBI-inferred parametrized wiring rule predicting synapse counts on the subcellular level with a corresponding formulation of Peters’ rule. (A) SBI posterior for the wiring rule parameter θ (probability of forming a synapse if two neurons are close), compared to Peters’ rule assuming θ = 1 (gray). (B) Number of synapses predicted by the inferred posterior (blue) and Peters’ rule (gray) compared to the number of presynaptic boutons realistically available in the structural model (dashed black), plotted over the entire cortical depth of the barrel cortex column. (C) Connection probabilities simulated from the inferred synapse level posterior (blue) and Peters’ rule (gray) compared to the measured connection probabilities (black).</p

Conditional posterior distributions.

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.</div

Formulating wiring rules in the rat barrel cortex as simulation-based models.

(A) The structural model of the rat barrel cortex contains digital reconstructions of position, morphology, and subcellular features of several neuron types in the barrel cortex and the ventral posterior medial nucleus (VPM) of the thalamus. (B) We formulate a wiring rule that predicts the probability of a synapse between two neurons from their dense structural overlap (DSO), i.e., the product of the number of pre- and postsynaptic structural features, normalized by all postsynaptic features in a given subvolume (postAll). (C) By applying the wiring rule to every neuron-pair subvolume combination of the model to connection probabilities and then sampling corresponding synapse counts from a Poisson distribution (left), we can simulate a barrel cortex connectome. To compare the simulated data to measurements, we calculate population connection probabilities between VPM and barrel cortex cell types as they have been measured experimentally (right). (D) To obtain a simulation-based model, we introduce parameters to the rule and define a prior distribution (left) such that each parameter combination corresponds to a different rule configuration and leads to different simulated connection probabilities (right, grey; measured data in black, [34, 35]).</p

Validating SBI over wiring rule parameters with simulated data.

Validating SBI over wiring rule parameters with simulated data.</p