Testing a model of excitatory interactions between oscillators

The experimentally observed influence of regularly arriving tugs upon the AP discharge of the slowly-adapting stretch receptor organ (SAO) of crayfish was compared to a model of pacemaker excitatory synaptic interactions (Segundo and Kohn 1981). Criteria for compliance referred to facets as A) the excitation, B) the postulates, and C) the behavior. A) Excitation was implied primarily by the tug initially increasing the AP rate (it subsequently decreased it). B) The pacemaker AP discharges, and with more reason the electronically driven tugs, were considered acceptably regular sequence (postulate i). Tugs advanced the next AP (postulate ii); the "delay function" plots of delays vs. phases, i.e. interval shortenings vs. the time from the last AP to the tug, were close to the V of postulate iii, even though the shortest phases tended to postpone the next AP and the longest ones did not trigger immediately but with an around 5 ms latency. These effects were displayed also as "old phase vs. new phase" plots. The interval following that with the tug tended to be lengthened, but the pre-tug timing was not recovered. C) Behavior during a train of excitatory events, both in model and experiments, went through very similar initial settlings and eventual steady-states. The latter were characterized in the model by 1. an average excitatory vs. excited rate display formed by an endless number of segments with all positive rational slopes separated by negative-going discontinuities, 2. locking in the sense of preferential phases, and 3. periodic repetition of the same phases and inter-AP intervals. Experimental results were compatible with this. Such behavior was absent when the tug sequence was highly irregular. The initial settling, in the SAO as in the model, depended jointly on the first phase phi 1 and the intertug interval E. If the former was under lambda, it went through one or two monotonic phase-decreasing stages (one smaller, the other larger, than lambda), or through a single increasing one, depending on E being smaller or greater than, respectively, an estimated but never actually observed E leading to unstable lockings. If the initial phase was greater than lambda, settling with E's under rN + lambda involved jumps between larger than and smaller than lambda phases; with E's over rn + lambda, it involved an intermediate stable locking with phi = E-rN.(ABSTRACT TRUNCATED AT 400 WORDS)