Synaptic and intrinsic homeostasis cooperate to optimize single neuron response properties and tune integrator circuits

Abstract

Homeostatic processes that provide negative feedback to regulate neuronal firing rate are essential for normal brain function, and observations suggest that multiple such processes may operate simultaneously in the same network. We pose two questions: why might a diversity of homeostatic pathways be necessary, and how can they operate in concert without opposing and undermining each other? To address these questions, we perform a computational and analytical study of cell-intrinsic homeostasis and synaptic homeostasis in single-neuron and recurrent circuit models. We demonstrate analytically and in simulation that when two such mechanisms are controlled on a long time scale by firing rate via simple and general feedback rules, they can robustly operate in tandem to tune the mean and variance of single neuron's firing rate to desired goals. This property allows the system to recover desired behavior after chronic changes in input statistics. We illustrate the power of this homeostatic tuning scheme by using it to regain high mutual information between neuronal input and output after major changes in input statistics. We then show that such dual homeostasis can be applied to tune the behavior of a neural integrator, a system that is notoriously sensitive to variation in parameters. These results are robust to variation in goals and model parameters. We argue that a set of homeostatic processes that appear to redundantly regulate mean firing rate may work together to control firing rate mean and variance and thus maintain performance in a parameter-sensitive task such as integration.

Stable Control of Firing Rate Mean and Variance by Dual Homeostatic Mechanisms

“…In [8], we show the same result empirically for biophysically detailed model neurons. What all these models have in common is that changes in g significantly affect the firing rate variance in the same direction, whereas x controls mainly the firing rate mean and has little or no effect on the variance.…”

“…In a previous work [8], we showed in numerical simulations that a pair of homeostatic mechanisms regulating a single biophysically detailed neuron can stably maintain a characteristic firing rate mean and variance for that neuron. Here, we have analytically derived mathematical conditions sufficient for any model neuron exhibiting such dual homeostasis to exhibit this behavior.…”

“…In particular, if the firing rate is a sigmoidal function of input and the eigenvalue of firing rate dynamics near a fixed point is near zero, the upper and lower rate limits act to control runaway firing rates while the system acts as an integrator in the neighborhood of the fixed point. In [8], we show that a recurrent network of biophysically detailed neurons with sigmoidal activation curves can be robustly tuned by dual homeostasis to act as an integrator.…”

“…In a recent publication [8], we perform numerical simulations of dual homeostasis (intrinsic and synaptic) in biophysically detailed neurons. We show empirically that this dual homeostasis is stable across a broad swath of parameter space and that it serves to restore not only a characteristic mean firing rate but also a characteristic firing rate variance after perturbations.…”

“…This task is generally considered one that requires biologically implausible precise calibration of multiple parameters [9, 10] and is not well understood (though various solutions to the fine tuning problem have been proposed in [11–14]). In [8], we show empirically that a heterogeneous network of dually homeostatic neurons can tune itself to serve as an integrator. Here, we demonstrate analytically in a simple model of a recurrent excitatory network that integrating behavior can be stabilized by single-cell dual homeostasis and that this stability is robust to the homeostatic parameters of the neurons in the network.…”