Periodically-modulated inhibition of living pacemaker neurons—III. The heterogeneity of the postsynaptic spike trains, and how control parameters affect it 1 Supported by funds from Trent H. Wells, Jr Inc. 1

Codings involving spike trains at synapses with inhibitory postsynaptic potentials on pacemakers were examined in crayfish stretch receptor organs by modulating presynaptic instantaneous rates periodically (triangles or sines; frequencies, slopes and depths under, respectively, 5.0 Hz, 40.0/s/s and 25.0/s). Timings were described by interspike and cross-intervals ("phases"); patterns (dispersions, sequences) and forms (timing classes) were identified using pooled graphs (instant along the cycle when a spike occurs vs preceding interval) and return maps (plots of successive intervals). A remarkable heterogeneity of postsynaptic intervals and phases characterizes each modulation. All cycles separate into the same portions: each contains a particular form and switches abruptly to the next. Forms differ in irregularity and predictability: they are (see text) "p:q alternations", "intermittent", "phase walk-throughs", "messy erratic" and "messy stammering". Postsynaptic cycles are asymmetric (hysteresis). This contrasts with the presynaptic homogeneity, smoothness and symmetry. All control parameters are, individually and jointly, strongly influential. Presynaptic slopes, say, act through a postsynaptic sensitivity to their magnitude and sign; when increasing, hysteresis augments and forms change or disappear. Appropriate noise attenuates between-train contrasts, providing modulations are under 0.5 Hz. Postsynaptic natural intervals impose critical time bases, separating presynaptic intervals (around, above or below them) with dissimilar consequences. Coding rules are numerous and have restricted domains; generalizations are misleading. Modulation-driven forms are trendy pacemaker-driven forms. However, dissimilarities, slight when patterns are almost pacemaker, increase as inhibition departs from pacemaker and incorporate unpredictable features. Physiological significance-(1) Pacemaker-driven forms, simple and ubiquitous, appear to be elementary building blocks of synaptic codings, present always but in each case distorted typically. (2) Synapses are prototype: similar behaviours should be widespread, and networks simulations benefit by nonlinear units generating all forms. (3) Relevant to periodic functions are that few variables need be involved in form selection, that distortions are susceptible to noise levels and, if periods are heterogeneous, that simple input cycles impose heterogeneous outputs. (4) Slow Na inactivations are necessary for obtaining complex forms and hysteresis. Formal significance--(1) Pacemaker-driven forms and presumably their modulation-driven counterparts, pertain to universal periodic, intermittent, quasiperiodic and chaotic categories whose formal properties carry physiological connotations. (2) Only relatively elaborate, nonlinear geometric models show all forms; simpler ones, show only alternations and walk-throughs. (3) Bifurcations resemble those of simple maps that can provide useful guidelines. (4) Heterogeneity poses the unanswered question of whether or not the entire cycle and all portions have the same behaviours: therefore, whether trajectories are continuous or have discontinuities and/or singular points.