Spiking network model

Questions to investigate

1. Weaken inhibition step by step. At what strength does activity change from rhythmic firing to large, seizure-like population bursts in the model?
2. Run the same settings with five different seeds. How much do the firing rates, the synchrony index and the peak frequency vary between networks built by the same rules?
3. Test the hypothesis that reducing inhibition increases synchrony with one seed per value and then with five. Do both designs reach the same conclusion?
4. Change the synaptic current from instantaneous to decaying over 5 ms. How do the synchrony and the power spectrum change?
5. Deliver a brief pulse to 20% of the excitatory cells. Does the activity spread to the cells that were not stimulated, and how does that depend on inhibition?
6. Raise the background input. Does the network move towards a more asynchronous or a more synchronous state?

In a real laboratory

Network models are built and analysed like experiments. The model, its parameters, the hypothesis, the values to be compared and the measures to be reported are written down before the simulations. Each condition is repeated on several independently generated networks (random seeds), because one random network is one sample. Robustness is checked with a smaller integration step, other network sizes and other plausible parameter values. Predictions are compared with recordings, such as firing rates, the irregularity of spike trains, correlations between cells and the spectrum of the local field potential, and parameters fitted to one data set are tested on another. Code, parameters and seeds are shared so that every figure can be reproduced. Models can reduce the number of animals by focusing experiments on the most informative conditions, but they do not replace the data against which they are validated.

How the simulation works

Each cell follows the equations of Izhikevich (2003): v′ = 0.04v² + 5v + 140 − u + I and u′ = a(bv − u), with v reset to c and u increased by d when v reaches 30 mV. Excitatory cells are regular spiking (a = 0.02, b = 0.2, c = −65 + 15r², d = 8 − 6r²) and inhibitory cells range from low-threshold to fast spiking (a = 0.02 + 0.08r, b = 0.25 − 0.05r, c = −65, d = 2), with r drawn at random for each cell. As in that paper, v is advanced in two half-steps of 0.5 ms per 1-ms step. With a much finer step, firing rates and synchrony can differ by tens of per cent, so all values are approximate. Cells are connected at random with a chosen probability, and weights are scaled so that the summed input stays comparable when network size or connection probability changes. Every cell receives Gaussian background input each millisecond. The LFP-like signal is the mean summed magnitude of the excitatory and inhibitory synaptic input to excitatory cells; its power spectrum is computed by fast Fourier transform with Welch averaging. In a parameter sweep, a slope is fitted for each seed and the slopes are summarised across seeds. Network states are labelled by simple thresholds on the synchrony index, the coefficient of variation and the spectral peak. The model has no dendrites, synaptic depression or facilitation, plasticity, neuromodulation, conductance-based synapses or spatial structure, and its seizure-like activity does not reproduce any specific disease.