Effective mean-field variables explain how biophysical parameters control firing rate and regularity in a spiking network

Abstract

Parameter sweeps of recurrent spiking networks are often interpreted as evidence that each nominal parameter controls activity through a distinct mechanism. We tested this interpretation in a 10,000 neuron Brunel type network using eight one factor sweeps, local sensitivity analysis, and a global Sobol design with 51,200 simulations. Under the standard calibration, seven of eight nominal parameters influenced the stationary state through effective quantities describing drive and recurrent coupling relative to threshold, input noise, and temporal scale ratios. Without fitting to simulation output, stationary Siegert theory predicted firing rates across the sweeps with a median error of 1%, while a renewal based approximation reproduced spike train regularity with R2 = 0.99 for the log coefficient of variation of interspike intervals. Applied without refitting to 10,240 parameter combinations, the theory explained 95% of firing rate variance and 90% of log regularity variance and reproduced the global sensitivity structure. Most apparent effects on rate and regularity therefore reflected the calibration. Synaptic delay contributed little to firing rate variance but was the leading total order factor for synchrony and bursting. Linear stability analysis predicted synchrony onset at 6.0 ms, within the observed transition from 5 to 9 ms, and reproduced oscillation frequencies. In a pre specified generality test, the theory also predicted firing rates in a fluctuation driven regime and reversals of threshold and synaptic time constant effects under alternative calibrations. These results support interpreting parameter dependence through effective drive, coupling, noise, and collective timing rather than nominal parameters alone.