Abstract
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.
Highlights
Information about a sensory stimulus is passed along a hierarchy of neural populations, from subcortical areas to the cerebral cortex where it propagates through multiple cortical areas and layers
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
To understand how the amplification and suppression mechanisms discussed above extend to such connectivity structures, we considered a model of a visual cortical circuit
Summary
Information about a sensory stimulus is passed along a hierarchy of neural populations, from subcortical areas to the cerebral cortex where it propagates through multiple cortical areas and layers. The densely recurrent structure of local cortical circuits can lead to counter-intuitive response properties [1,2,3,4,5], making it difficult to predict or interpret a population’s response to natural or artificial stimuli. This raises the question of whether there are underlying arithmetical principles through which one can understand the relationship between a local circuit’s connectivity structure and its response properties. Relevant questions are often more macroscopic in nature, e.g. “How does increased excitation to population A affect the average firing rate of neurons in population B?” For such questions, it is sufficient to establish a relationship between macroscopic connectivity structure and macroscopic response properties
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