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

Parameter sweeps of recurrent spiking networks have traditionally been viewed as evidence that each nominal parameter influences activity through a unique mechanism. To challenge this interpretation, researchers conducted an analysis on 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 standard calibration, seven of the eight nominal parameters were found to affect the stationary state through effective quantities that describe drive and recurrent coupling in relation to threshold, input noise, and temporal scale ratios.

The researchers discovered that stationary Siegert theory accurately predicted firing rates across the sweeps with a median error of just 1%. Similarly, a renewal-based approximation successfully reproduced spike train regularity, achieving an R2 value of 0.99 for the log coefficient of variation of interspike intervals. When applied to 10,240 parameter combinations without any refitting, the theory explained 95% of the variance in firing rates and 90% of the variance in log regularity, while also reproducing the global sensitivity structure.

It was observed that most apparent effects on rate and regularity were actually reflections of the calibration used. Synaptic delay had little impact on firing rate variance but emerged as the leading total order factor for synchrony and bursting. Linear stability analysis was able to predict the onset of synchrony at 6.0 ms, which closely matched the observed transition from 5 to 9 ms and also reproduced oscillation frequencies.

Additionally, the theory provided predictions for firing rates in a fluctuation-driven regime and changes in threshold and synaptic time constant effects under alternative calibrations. These findings support the idea that interpreting parameter dependence should focus on effective drive, coupling, noise, and collective timing rather than relying solely on nominal parameters.