Combined mechanisms of neural firing rate homeostasis

Spikes in the membrane potential of neurons comprise the currency of information processing in the brain. The ability of neurons to convert any information present across their multiple inputs into a significant modification to the pattern of their emitted spikes depends on the rate at which they emit spikes. If the mean rate is near the neuron's maximum, or if the rate is near zero, then changes in the inputs have minimal impact on the neuron's firing rate. Therefore, a neuron needs to control its mean rate. Protocols that either dramatically increase or decrease a neuron's firing rate lead to multiple compensatory changes that return the neuron's mean rate toward its prior value. In this primer, first as a summary of our previous work (Cannon and Miller in J Neurophysiol 116(5):2004-2022, 2016; Cannon and Miller in J Math Neurosci 7(1):1, 2017), we describe the advantages and disadvantages of having more than one such control mechanism responding to the neuron's firing rate. We suggest how problems of two, coexisting, potentially competing mechanisms can be overcome. Key requirements are: (1) the control be of a distribution of values, which the controlled variable achieves over a fast timescale compared to the timescale of the control system; (2) at least one of the control mechanisms be nonlinear; and (3) the two control systems are satisfied by a stable distribution or range of values that can be achieved by the variable. We show examples of functional control systems, including the previously studied integral feedback controller and new simulations of a "bang-bang" controller, that allow for compensation when inputs to the system change. Finally, we present new results describing how the underlying signal processing pathways would produce mechanisms of dual control, as opposed to a single mechanism with two outputs, and compare the responses of these systems to changes of input statistics.