Generating Quantitatively Accurate, but Computationally Concise, Models of Single Neurons - Computational Neuroscience: A Comprehensive Approach - page 205

(0.06 to 1s), a negative autocorrelation was found for most oxytocin cells, but for
larger window sizes, this negative autocorrelation disappears. Thus, at small time
scales (0.06 s to 1s), periods of relatively high activity are likely to be followed by
periods with relatively low average activity, and vice versa. Thus the average firing
rate over long periods of time is much more regular than would be expected from the
local variability in firing rate.
This type of analysis can be logically extended to serial dependence of interval
length. The simplest approach is to consider how the length of a given interval d t

depends upon the history of previous spike activity the preceding intervals t 2 , t 3 , t 4 ,

t 5 , ··· When oxytocin cell recordings are analysed in this way, there is a negative

relationship between t 1 and t 2 + ··· + t n , the slope of which is typically maximal for

n between 5 and 10, and which approaches 0 as n exceeds about 20. This indicates
that for oxytocin cells firing at typical background rates, there is a negative effect
of discharge rate upon spike activity through mechanisms slow enough to summate
over 5 to 10 spikes in 1 to 2s ( Figure 7.7) .
It should be remembered that the biological message encoded by a single oxytocin
cell is only the contribution that that cell makes to the secretion from the oxytocin
population as a whole. The overall secretion rate has considerable biological signif-
icance, and the rate must be maintained at an appropriate and steady average level
for prolonged periods when necessary for regulating sodium excretion (natriuresis),
but local second-by-second variability in the secretory rate of individual neurons is
of no biological significance unless such changes occur synchronously throughout
the population (as during reflex milk ejection). For oxytocin cells therefore, what
is important for natriuresis is only that they accurately maintain an average steady
state activity when measured over long periods. Oxytocin cells clearly have activity-
dependent negative-feedback mechanisms that ensure long term stability of average
firing rate.

7.4 Summary and conclusions

Although the interspike interval distributions of oxytocin cells seem to suggest that
spike arrival times (during spontaneous activity) are largely independent of previous
firing activity (except for the refractory period), closer analysis shows otherwise.
Firing rate analysis demonstrated that the index of dispersion did not equal 1 and was
not independent of bin width. Further, while the activity appears to be nearly random
at a small time scale, over a scale of several seconds it appears much more ordered.
The analysis of serial dependence showed that on a small time scale the activity is
clustered, but on a larger time scale the activity is more homogenous. Thus on a
short and medium time scale the cell possesses a memory and balances the activity,
whereby periods of short intervals tend to be followed by periods with longer ones,
and vice versa. However, on a long time scale the activity is rather homogenous.