Optimal synaptic dynamics for memory maintenance in the presence of noise

Synaptic connections in many brain areas have been found to fluctuate significantly, with substantial turnover and remodelling occurring over hours to days. Remarkably, this flux in connectivity persists in the absence of overt learning or behavioural change. What proportion of these ongoing fluctuations can be attributed to systematic plasticity processes that maintain memories and neural circuit function? We show under general conditions that the optimal magnitude of systematic plasticity is typically less than the magnitude of perturbations due to internal biological noise. Thus, for any given amount of unavoidable noise, 50% or more of total synaptic turnover should be effectively random for optimal memory maintenance. Our analysis does not depend on specific neural circuit architectures or plasticity mechanisms and predicts previously unexplained experimental measurements of the activity-dependent component of ongoing plasticity.