Cellular connectomes as arbiters of local circuit models in the cerebral cortex

ARTICLE https://doi.org/10.1038/s41467-021-22856-z OPEN Cellular connectomes as arbiters of local circuit models in the cerebral cortex 1234567890():,; Emmanuel Klinger1,2,3, Alessandro Motta Moritz Helmstaedter 1 ✉ 1, Carsten Marr 2, Fabian J. Theis 2,3 ✉ & With the availability of cellular-resolution connectivity maps, connectomes, from the mammalian nervous system, it is in question how informative such massive connectomic data can be for the distinction of local circuit models in the mammalian cerebral cortex. Here, we investigated whether cellular-resolution connectomic data can in principle allow model discrimination for local circuit modules in layer 4 of mouse primary somatosensory cortex. We used approximate Bayesian model selection based on a set of simple connectome statistics to compute the posterior probability over proposed models given a to-be-measured connectome. We find that the distinction of the investigated local cortical models is faithfully possible based on purely structural connectomic data with an accuracy of more than 90%, and that such distinction is stable against substantial errors in the connectome measurement. Furthermore, mapping a fraction of only 10% of the local connectome is sufficient for connectome-based model distinction under realistic experimental constraints. Together, these results show for a concrete local circuit example that connectomic data allows model selection in the cerebral cortex and define the experimental strategy for obtaining such connectomic data. 1 Department of Connectomics, Max Planck Institute for Brain Research, Frankfurt, Germany. 2 Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Computational Biology, Neuherberg, Germany. 3 Technische Universität München, Center for Mathematics, Chair of Mathematical Modelling of Biological Systems, Garching, Germany. ✉email: ; NATURE COMMUNICATIONS | (2021)12:2785 | https://doi.org/10.1038/s41467-021-22856-z | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-22856-z I n molecular biology, the use of structural (x-ray crystallographic or single-particle electron microscopic) data for the distinction between kinetic models of protein function constitutes the gold standard (e.g.,1,2). In Neuroscience, however, the question whether structural data of neuronal circuits is informative for computational interpretations is still heavily disputed3–6, with the extreme positions that cellular connectomic measurements are likely uninterpretable6 or indispensable5. In fact, structural circuit data has been decisive in resolving competing models for the computation of directional selectivity in the mouse retina7. For the mammalian cerebral cortex, the situation can be considered more complicated: it can be argued that it is not even known which computation a given cortical area or local circuit module carries out. In this situation, hypotheses about the potentially relevant computations and about their concrete implementations are to be explored simultaneously. To complicate the investigation further, the relation between a given computation and its possible implementations is not unique. Take, for example pattern distinction (of tactile or visual inputs) as a possible computation in layer 4 of sensory cortex. This computation can be carried out by multi-layer perceptrons8, but also by random pools of connected neurons in an “echo state network”9 (Fig. 1a, Supplementary Fig. 1a–g) and similarly by networks configured as “synfire chains”10 (Fig. 1a). If one considers different computational tasks, however, such as the maintenance of sensory representations over time scales of seconds (short-term memory), or the stimulus tuning of sensory representations, then the relation between the computation and its implementation becomes more distinct (Fig. 1a). Specifically, a network implementation of antiphase b a Texture classification ER-ESN EXP-LSM Activity Propagation LAYERED Short-term memory using feature vector recombination SYNFIRE Model ER-ESN LAYERED SYNFIRE FEVER Contrastinvariant tuning API STDP-based self-organization STDP-SORN Fail FEVER API STDP-SORN Pass d Pia c Connectome C EXP-LSM Approximate Connectome Bayesian statistics Computation (ABC-SMC) Posterior p(m|C) Models m S1 Cortex r pee pei pie pii ree L1 L2 L3 L4 L5 L6 WM VPM [15%...25%] [15%...25%] [50%...60%] [50%...60%] [15%...35%] 2000 ~90% ~10% ExN IN L4 barrel 0 ExN Thalamus (VPM) # Neurons Computation inhibition for stimulus tuning11 is not capable of performing the short-term memory task (Supplementary Fig. 1k, l), and a network proposed for a short-term memory task (FEVER12), fails to perform stimulus tuning (Fig. 1a, Supplementary Figs. 1–3). Together, this illustrates that while it is impossible to uniquely equate computations with their possible circuit-level implementations, the ability to discriminate between proposed models would allow to narrow down the hypothesis space both about computations and their circuit-level implementations in the cortex. With this background, the question whether purely structural connectomic data is sufficiently informative to discriminate between several possible previously proposed models and thus a range of possible cortical computations is of interest. Here we asked whether for a concrete cortical circuit module, the “barrel” of a cortical column in mouse somatosensory cortex, the measurement of the local connectome can in principle serve as an arbiter for a set of possibly implemented local cortical models and their associated computations. We developed and tested a model selection approach (using Approximate Bayesian Computation with Sequential MonteCarlo Sampling, ABC-SMC13–15, Fig. 1c) on the main models proposed so far for local cortical circuits (Fig. 1b) ranging from pairwise random Erdős–Rényi (ER16) to highly structured “deep” layered networks used in machine learning17,18. We found that connectomic data alone is in principle sufficient for the discrimination between these investigated models, using a surprisingly simple set of connectome statistics. The model discrimination is stable against substantial measurement noise, and only partly mapped connectomes have already high discriminative power. Fig. 1 Relationship between models and possible computations in cortical circuits, and proposed strategy for connectomic model distinction in local circuit modules of the cerebral cortex. a Relationship between computations suggested for local cortical circuits (left) and possible circuit-level implementations (right). Colored lines indicate successful performance in the tested computation; gray lines indicate failure to perform the computation (see Supplementary Fig. 1 for details). b Enumeration of candidate models possibly implemented in a barrel-circuit module. See text for details. c Flowchart of connectomic model selection approac (...truncated)