Gain control with A-type potassium current: I _A as a switch between divisive and subtractive inhibition

Abstract

Neurons process and convey information by transforming barrages of synaptic inputs into spiking activity. Synaptic inhibition typically suppresses the output firing activity of a neuron, and is commonly classified as having a subtractive or divisive effect on a neuron’s output firing activity. Subtractive inhibition can narrow the range of inputs that evoke spiking activity by eliminating responses to non-preferred inputs. Divisive inhibition is a form of gain control: it modifies firing rates while preserving the range of inputs that evoke firing activity. Since these two “modes” of inhibition have distinct impacts on neural coding, it is important to understand the biophysical mechanisms that distinguish these response profiles. In this study, we use simulations and mathematical analysis of a neuron model to find the specific conditions (parameter sets) for which inhibitory inputs have subtractive or divisive effects. Significantly, we identify a novel role for the A-type Potassium current ( I _A ). In our model, this fast-activating, slowly-inactivating outward current acts as a switch between subtractive and divisive inhibition. In particular, if I _A is strong (large maximal conductance) and fast (activates on a time-scale similar to spike initiation), then inhibition has a subtractive effect on neural firing. In contrast, if I _A is weak or insufficiently fast-activating, then inhibition has a divisive effect on neural firing. We explain these findings using dynamical systems methods (plane analysis and fast-slow dissection) to define how a spike threshold condition depends on synaptic inputs and I _A . Our findings suggest that neurons can “self-regulate” the gain control effects of inhibition via combinations of synaptic plasticity and/or modulation of the conductance and kinetics of A-type Potassium channels. This novel role for I _A would add flexibility to neurons and networks, and may relate to recent observations of divisive inhibitory effects on neurons in the nucleus of the solitary tract.

Author summary

Neurons process information by generating spikes in response to two types of synaptic inputs. Excitatory inputs increase spike rates and inhibitory inputs decrease spike rates (typically). The interaction between these two input types and the transformation of these inputs into spike outputs is not, however, a simple matter of addition and subtraction. Inhibitory inputs can suppress outputs in a variety of ways. For instance, in some cases, inhibition adjusts the rate of spiking activity while preserving the range of inputs that evoke spiking activity; an important computational principle known as gain control. We use simulations and mathematical analysis of a neuron model to identify properties of a neuron that determine how inhibitory inputs affect spiking activity. Specifically, we demonstrate how the gain control effects of inhibition depend on the A-type Potassium current. This novel role for the A-type Potassium current provides a way for neurons to flexibly regulate how they process synaptic inputs and transmit signals to other areas of the brain.