PERIODICALLY MODULATED INHIBITION AND ITS POSTSYNAPTIC CONSEQUENCES .2. INFLUENCE OF MODULATION SLOPE, DEPTH, RANGE, NOISE AND OF POSTSYNAPTIC NATURAL DISCHARGES

This paper examines the relation, or ''synaptic coding'', between the discharges of inhibitory fibres whose instantaneous firing rate is mod ulated periodically and pacemaker postsynaptic neurons using crayfish synapses and point process statistics. Several control parameters were varied individually, and the other maintained constant as far as poss ible: it extends the preceding publication that described the general features and varied only the modulation frequency [Segundo et al. (199 5) Neuroscience 68, 657-692]. Statistics were mainly cycle histograms and Lissajous diagrams (with presynaptic and postsynaptic histograms o n the abscissae and ordinate, respectively), complemented occasionally by displays of intervals along time and of interval differences along order (''basic graphs'' and ''recurrence plots'', respectively). The postsynaptic influence of modulated inhibitory discharges is character istically sensitive to all control parameters examined. (1) The freque ncy was reported in the companion paper [Segundo et al. (1995) Neurosc ience 68, 657-692]. (2) The average slope per half-cycle, controlled v ia either frequency or depth, acts by way of its magnitude and sign in ways revealed by hysteretic loops. Hysteresis increases and varies as the modulation's steepness increases: it is minor and with a single c lockwise loop at small slopes, but major and multi-looped at the large r ones. Slopes, because of their different postsynaptic consequences, were separated into the categories of ''steep'', ''gentle'' and ''abru pt'' if around, respectively, 1.0, 30.0 and 150.0 s(-2). The influence of slopes in restricted portions of the cycle depends on their positi on in the inhibitory rate scale. (3) The modulation's range acts by wa y of its depth and of its position on the inhibitory rate scale. Deepe r ranges, when compared with the shallower ones they contain, induce e ffects similar to those of shallower modulations with their central po rtion, plus effects peculiar to them at extreme rates. Changes in rang e position from the centre to the extremes of the inhibitory rate scal e are influential (e.g., saturations appear). Changes within the centr e can be highly influential, particularly when ranges are narrow and c lose to the postsynaptic natural rate, and modulation frequencies are low: relations between corresponding rates can be linear increasing, l inear decreasing or piecewise linear. Changes around extreme rates are negligible, however, and saturations are present. (4) The usual modul ations whose individual cycles did not differ from the cycle histogram were compared to others with the same cycle histograms but whose indi vidual cycles had an unpredictable fast variability referred to as ''n oise''. Noise increases the resemblance between presynaptic and postsy naptic cycle histograms (as well as between individual cycles) when mo dulations are low frequency (e.g., 0.030 Hz), but not when modulations are high frequency (e.g., 2.000 Hz). Such simplifications are well kn own in sensory and synaptic operation. Effects are due to frequency in teractions between noise and signals. (5) When natural postsynaptic ra tes are very high or very low, the coding between pre- and postsynapti c trains differs from the modes encountered when natural rates are in the intermediate domain examined predominantly. Responsibility lies pr esumably in long-term changes that happen at the synapse and the posts ynaptic encoder. A recommended expression of driver rates and frequenc ies is as the ratio of their Values to those of the natural postsynapt ic rate: such normalizations, though useful, should be interpreted cau tiously. Observations are pertinent to synaptic coding generally and t o the set of rules that summarize it, or ''code''. A restricted set of rules that often appear together is a ''coding mode''. Modes may be g eneral and present in broad domains, or special and present in narrow domains. Synaptic coding is a complex non-linear mapping with a large number of rules and many modes. Each synaptic type is characterized by several modes, each reflecting a combination of control parameters. T his is true generally, and holds for modulated drivings. Synapses are the operational units of neural networks. The function (e.g., sensory) of the latter provides specific functional meaning to the former. The response of single neurons to slow modulations imposed by single mode rately powerful terminals or by sets of correlated weak ones are disto rted. Distortions are compensated for by sets of numerous weak termina ls converging on the same neuron because, when firing independently, t hey have noise-like consequences. Such sets are ubiquitous and, in thi s and other respects, are essential for neural network operation. The modulation parameter values explored here correspond to those in natur al functions. The central mechanisms underlying mammalian respiration are used as an example of networks with both powerful slow modulations and high frequency weak arrivals. Arriving discharges are analysed di fferently by investigators who observe them over long stationary epoch s, and by postsynaptic neurons that judge them over short periods, mak ing a joint weighted evaluation of pre- and postsynaptic averages and patterns. The postsynaptic neuron performs as an analyser of arriving trains, ''reading'' or ''not reading'' presynaptic changes that, respe ctively, modify or do not modify its discharge. Presynaptic trains pro vide general information about the discharge averages and patterns of the corresponding postsynaptic trains, and vice versa; the specific fu nctional meaning of this information depends on the function of the ne twork. Our strategy for developing dynamic models of synaptic driving involves (i) data generation in living and simulated preparations, (ii ) full description involving averages and patterns, (iii) diagnosis of deterministic and noisy issues in different discharge forms, and fina lly (iv) model enunciation. It is more advanced (and summarized here) for pacemaker drivings than for modulations and transients, but still incomplete. Modulated presynaptic driving is a relatively neglected su bject. These two papers confirm features reported earlier (e.g., frequ ency transfers, opposing trends, congruent segments, simplification by noise). They also refine and extend those reports by providing more d etails of the same features and by adding novel ones (e.g., different parameter domains, an overall variety of coding modes, disch