Imbalanced amplification: A mechanism of amplification and suppression from local imbalance of excitation and inhibition in cortical circuits

Understanding the relationship between external stimuli and the spiking activity of cortical populations is a central problem in neuroscience. Dense recurrent connectivity in local cortical circuits can lead to counterintuitive response properties, raising the question of whether there are simple arithmetical rules for relating circuits’ connectivity structure to their response properties. One such arithmetic is provided by the mean field theory of balanced networks, which is derived in a limit where excitatory and inhibitory synaptic currents precisely balance on average. However, balanced network theory is not applicable to some biologically relevant connectivity structures. We show that cortical circuits with such structure are susceptible to an amplification mechanism arising when excitatory-inhibitory balance is broken at the level of local subpopulations, but maintained at a global level. This amplification, which can be quantified by a linear correction to the classical mean field theory of balanced networks, explains several response properties observed in cortical recordings and provides fundamental insights into the relationship between connectivity structure and neural responses in cortical circuits.Author summary: Understanding how the brain represents and processes stimuli requires a quantitative understanding of how signals propagate through networks of neurons. Developing such an understanding is made difficult by the dense interconnectivity of neurons, especially in the cerebral cortex. One approach to quantifying neural processing in the cortex is derived from observations that excitatory (positive) and inhibitory (negative) interactions between neurons tend to balance each other in many brain areas. This balance is achieved under a class of computational models called “balanced networks.” However, previous approaches to the mathematical analysis of balanced network models is not possible under some biologically relevant connectivity structures. We show that, under these structures, balance between excitation and inhibition is necessarily broken and the resulting imbalance causes some stimulus features to be amplified. This “imbalanced amplification” of stimuli can explain several observations from recordings in mouse somatosensory and visual cortical circuits and provides fundamental insights into the relationship between connectivity structure and neural responses in cortical circuits.