Conductance-based refractory density approach: comparison with experimental data and generalization to lognormal distribution of input current.

The conductance-based refractory density (CBRD) approach is an efficient tool for modeling interacting neuronal populations. The model describes the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons, each receiving individual Gaussian noise and a common time-varying deterministic input. However, the approach requires experimental validation and extension to cases of distributed input signals (or input weights) among different neurons of such an ensemble. Here the CBRD model is verified by comparing with experimental data and then generalized for a lognormal (LN) distribution of the input weights. The model with equal weights is shown to reproduce efficiently the post-spike time histograms and the membrane voltage of experimental multiple trial response of single neurons to a step-wise current injection. The responses reveal a more rapid reaction of the firing-rate than voltage. Slow adaptive potassium channels strongly affected the shape of the responses. Next, a computationally efficient CBRD model is derived for a population with the LN input weight distribution and is compared with the original model with equal input weights. The analysis shows that the LN distribution: (1) provides a faster response, (2) eliminates oscillations, (3) leads to higher sensitivity to weak stimuli, and (4) increases the coefficient of variation of interspike intervals. In addition, a simplified firing-rate type model is tested, showing improved precision in the case of a LN distribution of weights. The CBRD approach is recommended for complex, biophysically detailed simulations of interacting neuronal populations, while the modified firing-rate type model is recommended for computationally reduced simulations.