Fig 1.
Enhancing generative modeling in connectomics with simulation-based inference.
(A) Generative modeling is a common approach for testing hypotheses about the connectome: One implements a hypothesized wiring rule as a computational model that simulates connectivity data x (left) and then tests and manually refines the rule by comparing simulated with measured data xo (right). (B) Our goal is to make this approach more efficient using simulation-based Bayesian inference (SBI): By equipping the generative model with parameters θ, we define a space of multiple a-priori hypotheses (left) from which we can generate multiple simulated data x (middle). We then use the simulated data to perform density estimation with artificial neural networks to estimate the posterior distribution over model parameters conditioned on the measured data, i.e., p(θ|xo). The inferred posterior distribution characterizes all wiring rule parameters compatible with the measured data, replacing the manual refinement of single wiring rules in the conventional approach (bottom).
Fig 2.
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]).
Fig 3.
SBI posterior reveals parameter interactions and predicts unseen data.
(A) The posterior over the three wiring rule parameters scaling the DSO features (inset) inferred with SBI (blue) and the initial prior distribution over parameters (gray). The corner plot shows the one-dimensional marginal distribution of each parameter on the diagonal and the pairwise two-dimensional marginals on the off-diagonal (contour lines show the 34%, 68%, and 95% credible regions). (B) Comparison of measured connection probabilities (black, [34, 35]) with those simulated with parameter values sampled from the inferred posterior (blue), from the prior (gray) and the unparametrized a-priori DSO rule (orange). (C) Each panel shows the predictions for one held-out measurement generated from a posterior that was trained and conditioned only on the other six measurements, i.e., each panel refers to a different posterior.
Fig 4.
Neuron-level wiring rule inferred with SBI differs from Peters’ rule.
We used SBI to infer a proximity-based wiring rule at different spatial resolutions of the rat barrel cortex model and compared its predictions to that of Peters’ rule. (A) Distributions of the shared subvolumes v between neurons in the barrel cortex model for each spatial resolution (subvolume edge length, see legend in (b)). (B) SBI posteriors inferred over the connection threshold parameter of the wiring rule (θthres, number of shared subvolumes required to form a connection), shown for each spatial resolution (colors), and for Peters’ rule assuming θthres = 1 (gray). (C) Connection probabilities simulated from the inferred posterior (orange) and Peters’ rule (gray) compared to the measured connection probabilities (black).
Fig 5.
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).