# Computing the effects of excitatory-inhibitory balance on neuronal input-output properties

## TL;DR

This paper explores how the balance between excitatory and inhibitory neurons shapes how neurons respond to sensory stimuli.

## Contribution

A probabilistic framework is introduced to describe how excitatory and inhibitory inputs interact in feedforward inhibitory circuits.

## Key findings

- The model explains multiplicative and additive gain modulation in sensory systems.
- It accounts for non-monotonic input-output curves and diverse temporal firing patterns.
- The framework unifies various phenomena under a single, analytically tractable description.

## Abstract

In sensory systems, stimuli are represented through the diverse firing responses and receptive fields of neurons. These features emerge from the interaction between excitatory (E) and inhibitory (I) neuron populations within the network. Changes in sensory inputs alter this balance, leading to shifts in firing patterns and the input-output properties of individual neurons and the network. Although these phenomena have been extensively investigated experimentally and theoretically, the principles governing how E and I inputs are integrated remain unclear. Here, probabilistic rules are derived to describe how neurons in feedforward inhibitory circuits combine these inputs to generate stimulus-evoked responses. This simple model is broadly applicable, capturing a wide range of response features that would otherwise require multiple separate models, and offers insights into the cellular and network mechanisms influencing the input-output properties of neurons, gain modulation, and the emergence of diverse temporal firing patterns.

Sensory stimuli activate networks of excitatory and inhibitory neurons whose interactions shape how the brain represents information. An individual neuron’s response therefore depends not only on the strength of excitatory input, but also on how inhibition is recruited as stimulus conditions change. These interactions alter firing thresholds, response gain, and temporal firing patterns, yet the principles governing how excitatory and inhibitory inputs combine remain unclear. In this study, I develop a simple probabilistic framework to describe how excitatory and inhibitory synaptic inputs interact in feedforward inhibitory circuits. I express neuronal input–output relationships in terms of the probability that excitation survives coincident inhibition, thereby linking firing responses directly to identifiable synaptic and network parameters. Using this framework, I show that the model accounts for key features observed in sensory systems, including multiplicative and additive gain modulation, non-monotonic input–output curves, and diverse temporal firing patterns evoked by brief or sustained stimuli. By unifying these phenomena within a single, analytically tractable description, I provide insight into how changes in excitatory–inhibitory balance flexibly regulate neuronal responses across sensory conditions and behavioral states.