A model of excitatory synaptic interactions between pacemakers. Its reality, its generality, and the principles involved

This is a model of the steady-state influence of one pacemaker neuron upon another across a synapse with EPSP's. Its postulates require firstly the spontaneous regularity of both cells, whose intervals are E and N, respectively. In addition, they require a special shortening or negative "delay" of the interspike interval by one or more EPSP's, with a V-shaped dependence of the delay on the position or "phase" of the EPSP's in the interval; the minimum of the delay function corresponds to the earliest EPSP arrival phase (?) that triggers a spike immediately. Finally, they impose on the variables certain bounds. The model's behavior has two main features. The first is a zig-zag relationship with an overall increasing trend between the steady-state pre- and post-synaptic discharge intensities (Fig. 7). The zig-zag is formed predominantly, if not exclusively, by segments with positive slopes that are rational fractions. Passage from one such segment to others is negatively-sloped ("paradoxical"), involving staggered positively-sloped segments whose details are unclear for weak presynaptic discharges and discontinuities for intense discharges. The same postsynaptic intensity may result from several presynaptic ones; the maximum postsynaptic intensity may reflect refractoriness, or the earliest instants of immediate triggering. The second main feature is the "locking" of the discharges in an invariant forward and backward temporal relation. With at most one EPSP per postsynaptic spike, locking is always present. If the presynaptic interval E is in the closed {rN+?,(r+1)N} range, locking is 1:r+1, either stable at a greater-than-? phase or unstable at a smaller one; arrivals at integral multiples of N do not affect the postsynaptic intensity. If E is in {rN, rN+?} (r>0), locking is at other ratios (e.g., 2:3) and less apparent. With more than one EPSP per spike, when E is below bounds that depend on the interspike interval and the point of earliest triggering, locking happens in the simple s?:1 ratio (s?=2,3, ...) and is stable; when E is above those bounds, there are E ranges where locking is in other ratios (e.g., 3:2) and ranges where behavior is unclear. The validity of any model is based jointly upon an a priori judgment as to whether postulates depart reasonably little from nature, and upon an a posteriori experimental comparison of modelled and real behaviors. The model's domain of applicability depends on the specific embodiment, each of the latter tolerating characteristically each departure. The present model will be evaluated in the crayfish stretch-receptor neuron (Diez-Martinez et al., in preparation). The model is applicable to any physical system that complies with its postulates, and evidence compatible with this notion is available in many disparate fields. It illustrates the modelling path to a scientific proposition, other paths being inference from experimentation, or deduction from premises acceptable at other approach levels (in this case, for example, from that of synaptic mechanisms). The periodicity postulates set this model within the category of those for oscillators. The notion of an oscillator has a far broader applicability than appears at first sight, since all physically realizable systems have some predominant output frequency, i.e., to a certain extent are oscillators.