In my scenario, the input spike train ISI statistics to the cell type that I am modelling are not characterized and so, it is not clear whether modelling them using random sampling from a negexp distribution is appropriate in the first place (since there are other potential ISI distributions - see references at end). Then again, I see now that trying to force all the spikes to occur within the time window would negate the use of sampling ISIs from any type of distribution. By this logic, it seems that I am (reasonably) stuck with synapses that occasionally spike less than I want them to.

This has me wondering about another potential option, however. Would it be possible to randomly sample spike times (instead of ISIs) from a uniform distribution that has the same length of the time window? When computing the intervals between sorted random values sampled from a uniform distribution of a finite length, the histogram distribution of the intervals looks similar to a negative exponential distribution (see quick Matlab code example below). However in this approach, the spike times would be independent of each other, which I'm thinking would also be incorrect to assume.

Code: Select all

```
x = rand(10000,1)*100000; % i.e. 10000 spike times in 100 seconds
figure(1); histogram(x)
figure(2); histogram(diff(sort(x)))
figure(3); histfit(diff(sort(x)),54,'exponential')
```

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Taken from Ostojic, 2011:

"Irregular firing in vivo is often thought of as a Poisson process, but a close examination of experimental recordings reveals a large variety of interspike interval (ISI) statistics. Here we focus on the shapes of ISI distributions, which have been found to range from narrow to bursting (Bair et al. 1994; Compte et al. 2003; Maimon and Assad 2009)."

References:

Bair W, Koch C, Newsome W, Britten K. (1994). Power spectrum analysis of bursting cells in area MT in the behaving monkey. J Neurosci. 14(5 Pt 1):2870-92.

Compte A, Constantinidis C, Tegner J, Raghavachari S, Chafee MV, Goldman-Rakic PS, Wang XJ. (2003). Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. J Neurophysiol. 90(5):3441-54.

Maimon G, Assad JA. (2009). Beyond Poisson: increased spike-time regularity across primate parietal cortex. Neuron. 62(3):426-40.

Ostojic S. (2011). Interspike interval distributions of spiking neurons driven by fluctuating inputs. J Neurophysiol. 106(1):361-73.