Supplementary Figure 4: Modulating correlations of light pulse trains delivered to ChR2-expressing neurons.
From: Synaptic scaling rule preserves excitatory–inhibitory balance and salient neuronal network dynamics
For reasons given in Methods, the sequences of light pulses delivered to ChR2 neurons were generated using leaky-integrate-and-fire (LIF) units. Each unit was driven with noisy inputs and the resultant spikes were used to time the light pulses. (a) To introduce correlation in the light pulses, the current input Ik(t) to the LIF unit k (here k = [1, 2], Eq. 4 of the Methods) was a sum of an independent (Icom(t)) and a common (Icom(t) contribution that were weighted by 
and 
respectively (Eq. 5 of the Methods, see also ref. 31). By construction, the correlation between two input currents I1(t) and I2(t) was equal to Cstim, which varied from 0 (no correlation) to 1 (perfect correlation). (b) In the main text (Fig. 5), correlations were presented as Cstim rather than by the calculated spike count correlation for the following reason. Unlike Cstim, which is calculated from the continuous current, the correlations in the spikes (and hence light pulses) depend on the time window (Δt) used for counting spikes (see Methods). Plotting spike correlation vs Cstim shows different relations for Δt = 50 ms (red) and Δt = 10 ms (black). Therefore, to avoid potential confusion, it was more convenient to use Cstim.
