Brain-wide representational drift: memory consolidation and entropic force

Memory engrams change on the microscopic level with time and experience as the neurons that compose them switch in a process termed representational drift. On the macroscopic level the engrams are not static either: numbers of engram neurons in different brain regions change over time, which is considered to reflect the process of memory consolidation. Here we predict a link between these two levels, using a novel statistical physics approach to engram modeling. Importantly, it is general as it makes only minimal assumptions on the engram's nature, does not rely on a specific architecture, and its fundamental implications hold for any representational drift with random component. Our first, analytically well tractable model shows that an entropic force emerges at the region level from random representational drift at the neuronal level. We refine the model by incorporating the interaction of the entropic force with biological processes that shape neuronal engrams. Here, the connectivity between the brain regions strongly influences the (quasi-)equilibrium engram distribution. The obtained distributions are in qualitative agreement with the ones of a biologically detailed drifting assembly model. Our engram description allows to predict the engram evolution in large neuronal systems such as the mouse brain. We find several predictions that are consistent across the valid tested parameter ranges, such as a strong tendency of the engram to leave the hippocampus. The results suggest that the brain operates in a regime where engrams drift, both deterministically and randomly, to allow for memory consolidation.