RG-inspired analyses of activity in networks of real neurons*

The renormalization group (RG) allows us to understand how theories of macroscopic dynamics can be simpler and more universal than the underlying microscopic mechanisms. Inspired by these ideas, we develop an approach to coarse-graining complex biological systems in which highly correlated groups of variables play the role of spatial neighborhoods or block spins. We apply this to experiments on the activity of 1000+ neurons in mouse hippocampus, recorded as the animal navigates a virtual environment. We find power-law dependences of several static and dynamic quantities on the coarse-graining scale, over two decades, with exponents that are strikingly reproducible across experiments. In addition, the probability distribution of coarse-grained variables seems to converge on a non-trivial fixed form. We explore how different coarse-graining schemes affect the scaling behaviors, and construct minimal models for the coarse-grained variables. Finally, we investigate how the coding properties of the neurons change as we move along the RG flow.