The prix-fixe menu: a combinatorial code for neuronal function

The striking diversity of cells in the mammalian brain lies in stark contrast with the uniformity of cells in theoretical models and artificial networks. What computational advantage do these myriad cell types provide? Deciphering their roles first requires organizing cells in the appropriate manner. Typically, cells are organized into a hierarchical clustering of cells into cell types. This approach is based on a rich history of cell typing based on morphology and other accessible correlates. However, the very large-scale datasets enabled by advances in DNA sequencing potentially may reveal a finer-grained organization. Here, we propose instead a combinatorial model: we hypothesize that a cell’s transcriptome reflects the conjunction of multiple, potentially interchangeable genetic programs. This combinatorial approach would massively increase cellular diversity compared to a single hierarchy. An analogy is a prix-fixe menu: one dish is available from each meal course, and the potential number of meals grows combinatorially rather than linearly. To quantitatively group and classify cells in this manner, we apply an algorithm that discovers this combinatorial menu from data, known in the information theory literature as Residual Vector Quantization and here as Conjunctional k-Means (CkM). We apply CkM to two whole-brain, single-cell transcription datasets collected by the Allen Institute. We find that the combinatorial menus discovered with CkM explain more variance than standard clustering methods, challenging the standard hierarchical picture of cellular taxonomy. Additionally, we find clear layer- and area-specific patterns of the conjunctional subspace clusters. If the way the genome encodes function is combinatorial, we suggest that a cell's ‘menu selections’ may be more closely related to function than its location in a hierarchical tree. Our results suggest a path forward to exploiting the diversity of neuronal types in models of brain computation.