A Theory of Rate Coding Control by Intrinsic Plasticity Effects

Abstract

Intrinsic plasticity (IP) is a ubiquitous activity-dependent process regulating neuronal excitability and a cellular correlate of behavioral learning and neuronal homeostasis. Because IP is induced rapidly and maintained long-term, it likely represents a major determinant of adaptive collective neuronal dynamics. However, assessing the exact impact of IP has remained elusive. Indeed, it is extremely difficult disentangling the complex non-linear interaction between IP effects, by which conductance changes alter neuronal activity, and IP rules, whereby activity modifies conductance via signaling pathways. Moreover, the two major IP effects on firing rate, threshold and gain modulation, remain unknown in their very mechanisms. Here, using extensive simulations and sensitivity analysis of Hodgkin-Huxley models, we show that threshold and gain modulation are accounted for by maximal conductance plasticity of conductance that situate in two separate domains of the parameter space corresponding to sub- and supra-threshold conductance (i.e. activating below or above the spike onset threshold potential). Analyzing equivalent integrate-and-fire models, we provide formal expressions of sensitivities relating to conductance parameters, unraveling unprecedented mechanisms governing IP effects. Our results generalize to the IP of other conductance parameters and allow strong inference for calcium-gated conductance, yielding a general picture that accounts for a large repertoire of experimental observations. The expressions we provide can be combined with IP rules in rate or spiking models, offering a general framework to systematically assess the computational consequences of IP of pharmacologically identified conductance with both fine grain description and mathematical tractability. We provide an example of such IP loop model addressing the important issue of the homeostatic regulation of spontaneous discharge. Because we do not formulate any assumptions on modification rules, the present theory is also relevant to other neural processes involving excitability changes, such as neuromodulation, development, aging and neural disorders.

Author Summary

Over the past decades, experimental and theoretical studies of the cellular basis of learning and memory have mainly focused on synaptic plasticity, the experience-dependent modification of synapses. However, behavioral learning has also been correlated with experience-dependent changes of non-synaptic voltage-dependent ion channels. This intrinsic plasticity changes the neuron's propensity to fire action potentials in response to synaptic inputs. Thus a fundamental problem is to relate changes of the neuron input-output function with voltage-gated conductance modifications. Using a sensitivity analysis in biophysically realistic models, we depict a generic dichotomy between two classes of voltage-dependent ion channels. These two classes modify the threshold and the slope of the neuron input-output relation, allowing neurons to regulate the range of inputs they respond to and the gain of that response, respectively. We further provide analytical descriptions that enlighten the dynamical mechanisms underlying these effects and propose a concise and realistic framework for assessing the computational impact of intrinsic plasticity in neuron network models. Our results account for a large repertoire of empirical observations and may enlighten functional changes that characterize development, aging and several neural diseases, which also involve changes in voltage-dependent ion channels.