Reduction of a biophysical neuronal decision-making model. The original model (top) is endowed with strong recurrent excitation between neurons with similar stimulus selectivity, and effective inhibition between them via shared inhibition. NS and I denote the nonselective excitatory (black) and inhibitory (green) pools of cells, respectively. Arrows, Excitatory connections; circles, inhibitory connections. I1 and I2 are inputs from external stimulus to selective neural populations 1 (blue) and 2 (red). Brown arrows, Background noisy inputs. w+ denotes enhanced excitatory connections within each selective neural pool. The numbers on the right displays the total number of dynamical equations involved in the model. First step, Mean-field approach reduces 2000 spiking neurons into four neural units (with a total of 11 dynamical variables). Second step, Simplify the linear input–output relation (F–I curves) of the cells: (1) fit the input–output relation (F–I curve) of the spiking neuronal model with a simple function (Abbott and Chance, 2005); (2) linearize F–I curve for I cells; and (3) assume constant activity of NS cells. The final step involves the assumption that all fast variables of the system reach steady states earlier than that of NMDAR. The final reduced two-variable model (bottom) consists of two neural units, endowed with self-excitation and effective mutual inhibition.
