Signature of random connectivity in the distributionof neuronal tuning curves.

Understanding the relationship between circuit properties and the organization of neuronal population activity is a fundamental question in neuroscience. The fine tuning of neuronal activity to specific values of environmental or internal features are canonical examples of how information is encoded in the brain, possibly resulting from precisely organized inputs. Yet, in the cortex, finely tuned neurons are often recorded together with neurons whose tuning is much less specific, for example those of inhibitory neurons, and the connectivity statistics accounting for the overall distribution of tuning curves is unclear. Here, using recordings in the mouse head-direction system, we first show both in simulation and analytically that random linear combinations of ideal finely tuned inputs reproduce the distribution of fast-spiking neuron tuning curves, a class of neurons believed to operate in the linear regime. This transformation preserves, on the population level, the singular spectrum of the input tuning curves but the relative power of each singular component is independently distributed in each output cell, leading to a distribution ranging from uni-modal to symmetrically tuned cells. We then generalize the model to a non-linear transformation of the inputs, combined with background inhibition. Using recordings from input neurons in the thalamus, where tuning curves are near-ideal, the model reproduces for various levels of inhibition the entire range of observed neuronal responses in the cortex, from precisely and narrowly tuned neurons to multipeak excitatory cells, as well as symmetrical tuning curves of inhibitory neurons. We replicate these findings in a dataset of hippocampal recordings. In conclusion, the full distribution of tuning curves is a signature of input connectivity statistics, which, for fast-spiking neurons and thalamocortical circuits, is likely to be random rather than specifically organized.