Parametric computation predicts a multiplicative interaction between synaptic strength parameters that control gamma oscillations

Gamma oscillations are thought to be critical for a number of behavioral functions, they occur in many regions of the brain and through a variety of mechanisms. Fast repetitive bursting (FRB) neurons in layer 2 of the cortex are able to drive gamma oscillations over long periods of time. Even though the oscillation is driven by FRB neurons, strong feedback within the rest of the cortex must modulate properties of the oscillation such as frequency and power. We used a highly detailed model of the cortex to determine how a cohort of 33 parameters controlling synaptic drive might modulate gamma oscillation properties. We were interested in determining not just the effects of parameters individually, but we also wanted to reveal interactions between parameters beyond additive effects. To prevent a combinatorial explosion in parameter combinations that might need to be simulated, we used a fractional factorial design (FFD) that estimated the effects of individual parameters and two parameter interactions. This experiment required only 4096 model runs. We found that the largest effects on both gamma power and frequency came from a complex interaction between efficacy of synaptic connections from layer 2 inhibitory neurons to layer 2 excitatory neurons and the parameter for the reciprocal connection. As well as the effect of the individual parameters determining synaptic efficacy, there was an interaction between these parameters beyond the additive effects of the parameters alone. The magnitude of this effect was similar to that of the individual parameters, predicting that it is physiologically important in setting gamma oscillation properties.