Stability of Neuronal Networks with Homeostatic Regulation

International audienceNeurons are equipped with homeostatic mechanisms that counteract long-term pertur-bations of their average activity and thereby keep neurons in a healthy and information-rich operating regime. Yet, systematic analysis of homeostatic control has been lacking. The analysis presented here reveals two important aspects of homeostatic control. First, we consider networks of neurons with homeostasis and show that homeostatic control that is stable for single neurons, can destabilize activity in otherwise stable recurrent networks leading to strong non-abating oscillations in the activity. This instability can be prevented by dramatically slowing down the homeostatic control. Next, we consider the case that homeostatic feedback is mediated via a cascade of multiple intermediate stages. Counter-intuitively, the addition of extra stages in the homeostatic control loop further destabilizes activity in single neurons and networks. Our theoretical framework for homeostasis thus reveals previously unconsidered constraints on homeostasis in biological networks, and provides a possible explanation for the slow time-constants of homeostatic regulation observed experimentally. Author summary Despite their apparent robustness many biological system work best in controlled environ-ments, the tightly regulated mammalian body temperature being a good example. Homeo-static control systems, not unlike those used in engineering, ensure that the right operating 1 conditions are met. Similarly, neurons appear to adjust the amount of activity they produce to be neither too high nor too low by, among other ways, regulating their excitability. How-ever, for no apparent reason the neural homeostatic processes are very slow, taking hours or even days to regulate the neuron. Here we use methods from mathematical control theory to show that if this weren't the case, in particular in networks of neurons the control system might otherwise become unstable and wild oscillations in the activity result. Our results lead to a deeper understanding of neural homeostasis and can help the design of artificial neural systems