When can neuronal activity-dependent homeostatic plasticity maintain circuit-level properties?

Neural circuits are remarkably robust to perturbations that threaten their function. Activity-dependent homeostatic plasticity (ADHP) is a stabilizing mechanism that supports robustness by tuning neuronal ion conductances to combat chronic over- or under-activity. Its restorative capacity has been demonstrated in the pyloric circuit of the crustacean stomatogastric ganglion, whose neurons must burst in a specific order to coordinate digestive muscles. After disruption by physical and pharmacological manipulations, this circuit reliably recovers not only the activity levels of constituent neurons, but also the proper burst order. But how could ADHP, operating only on local information about each neuron's average activity, maintain higher-order circuit properties? We explored this question in a computational model of the pyloric pattern generator. We first optimized a set of pyloric-like networks, then optimized ADHP mechanisms for each network to restore its pyloric character after parametric perturbations. This was possible for some networks and impossible for others, so we aimed to explain this disparity. We found that successful homeostatic regulators target average neural activity levels which happen to occur only among pyloric circuits and not among non-pyloric ones, within the set of reachable circuit configurations. Therefore, in subsets of parameter space where such dissociation is possible, activity carries indirect information about burst order, which ADHP can exploit to maintain pyloricness. Other subsets, whose pyloric averages are inseparable from non-pyloric ones, cannot be perfectly regulated. This separability property may explain differences in recovery capacity across perturbations and across individuals.