Pacemaker synaptic interactions: Modelled locking and paradoxical features
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This communication describes a model for two “pacemaker” (i.e., regularly firing) nerve cells, such that one elicits IPSP's in the other. The assumptions involve essentially a linear dependence (“delay function”) of the postsynaptic interval lengthening (or “delay”) produced by the IPSP's on the position (or “phase”) with respect to the preceding spike of the latter's arrival. When the number of IPSP's in an interval increases, both the slope and intercept of the delay function increase, the former remaining under 2 and the latter unboundedly. Assumptions are more or less close to the actual biological reality, or are made for convenience. A recurrence equation for the phase can be calculated, as well as an expression for the “locking phase” (see below). Plots of postsynaptic vs presynaptic firing intensity averaged over steady conditions, e.g. of mean rates or intervals, are formed by a sequence of relatively broad“paradoxical” segments exhibiting positive slopes 1, 2, 1/2, 3, 1/3, ..., indicating that “inhibited” discharges are made more intense by those increases in “inhibitory” arrivals. These segments are separated by narrower “intercalated” segments where behavior is unclear except for a large overall negative slope, indicating that “inhibited” discharges are weakened markedly by other increases in inhibitory arrivals. Across the successive paradoxical segments that correspond to more and more intense presynaptic discharges (i.e., to higher rates or shorter intervals), postsynaptic intensities, though overlapping in part, become weaker and weaker. At the extremes, when the presynaptic discharge is very weak, or very intense, the postsynaptic cell tends to its natural undisturbed firing, or to not firing at all, respectively. The pre- and postsynaptic discharges inevitably achieve eventually an invariant relation, i.e., will “lock” at a constant phase, regardless of the phase of the first IPSP arrival. The characteristics of this behavior (e.g., the rate bounds of the paradoxical segments, or the magnitude of the locked phase) depend on such givens as presynaptic and postsynaptic pacemaker rates or intervals, and as the slope or intercept of the delay function.
KeywordsRecurrence Equation Positive Slope Rate Bound Invariant Relation Firing Intensity
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