ALBERT

Notes: Abstract The correspondence between pre- and postsynaptic fluctuations in generation of action potentials was studied using the inhibitory synapse on the crayfish stretch receptor neuron. The presynaptic discharges were imposed by an appropriately controlled stimulator modulated with triangular or sine waves at 1/60 to 10 cps by±1 to 10 ips and around an average rate of 5 to 10 ips. The rate of the regular postsynaptic discharge was set, in the absence of IPSPs, at 5 to 20 ips by the degree of constant stretch on the receptor organ. Cycle histograms were constructed, i.e. discharges were averaged across several cycles, presynaptically on the one hand and postsynaptically on the other. This exploration led to the recognition of some of the rules whereby the correspondence between spike trains is established across a synapse with IPSPs. The mapping or coding from the presynaptic to the postsynaptic cycle histogram was complex, and its main facets were: i) the possibility of the transfer of a broad spectrum of frequencies, at least from 1/60 to 10 cps; ii) a general tendency for faster presynaptic discharges to be associated with slower postsynaptic ones (i.e. a negative overall slope in the presynaptic rate-postsynaptic rate graph); iii) interspersed consistently located segments of appreciable size where inhibitory accelerations led to faster postsynaptic discharges (i.e. positively-sloped “paradoxical” segments); iv) a sensitivity to whether the presynaptic cell was accelerating or decelerating (hysteresis); and, finally, v) minimal consequences of changes around extremes where the receptor was either hardly affected or halted by very low or high rates, respectively (saturation). The type, magnitude and ubiquity of the deviations (iii, iv, v) from a simple and negatively-sloped linearity (suggested by ii) makes them integral and practically important facets of inhibitory transfer. The form of the correspondence depended on such issues as the overall pre- and postsynaptic rates (e.g. 5 versus 10 ips), the modulation frequency (e.g. 1/60 versus 2 cps) and depth (e.g.±1 versus 10 ips), etc. When restrictions were placed upon these variables, the correspondence adopted special forms whose particular descriptions (e.g. linear in- or out-of-phase, rectifier-like, etc.) were acceptable only if conditional to those restrictions. A rapid presynaptic irregularity which increased the varibility of individual cycles without altering the average cycle reduced, sometimes markedly, deviations from linearity. This demonstrates the applicability to the living synapse, represented here by a system whose input and output spike trains are assimilated to point processes, of a concept developed for system whose input or output are continuous: namely, that the addition at the input of a high frequency “dither” reduces the complexities of the element. This effect has interesting physiological possibilities and explains apparent discrepancies between earlier publications.

Notes: Abstract 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.

Notes: Abstract It is known (e.g., Perkel et al., 1964) that when a pacemaker neuron elicits IPSP's in another, there are domains called “paradoxical segments” where in the steady-state i) faster inhibitory discharges determine faster inhibited ones, and ii) pre- and postsynaptic spikes are “locked” in an invariant forward-and-backward positioning in time, spikes alternating in the ratios 1:1 (1 pere for 1 postsynaptic), 1:2, 2:1..., that are also the slopes of the synaptic rate-transformation. The present project examined the matter further in the inhibitory synapse upon the crayfish tonic stretch receptor neuron, confirming the above. In addition it showed that locking and alternation existed also in the segments interposed between the 1:2, 1:1 and 2:1 paradoxical segments, even though they were not as marked and apparent, and that when tests were close to each other their order became influential and hysteresis-like phenomena appeared. The main finding was that paradoxical rate-relations, locking and alternation persisted when the presynaptic train was irregularized up to interval coefficients of variation of around 0.20 (Figs. 2–5). Therefore, both phenomena may not simply be laboratory curiosities, but also have a role in natural operation where probably a substantial population of neurons exhibits that kind of irregularity. As presynaptic irregularity increased, the paradoxical segment slopes and widths decreased and locking and alternation became less clear-cut. With CV's of about 0.20, only a relatively narrow 1:1 paradoxical segment with about O slope and little locking and alternation remained (Figs. 2b, 3g, 4right, 5third row). With larger CV's, the rate relation decreased monotonically and there was no locking nor alternation (Figs. 2e, 3h, 5bottom row). The postsynaptic discharge was more regular and had fewer changes in the number of presynaptic spikes per post-synaptic interval within paradoxical segments (particularly in their centers) than in segments interposed between them (left vs. right-hand columns in Figs. 5, 6; Fig. 7): the contrast, remarkable for regular stimuli, attenuated as variability increased. The following conclusions are relevant to coding of spike trains across a synapse with IPSP's. i) With fairly regular discharges, the same postsynaptic rate may result from several presynaptic ones (e.g., may result from rates in the 1:1 and 2:1 paradoxical segments and in the interposed one, Fig.2): in some cases but not others, the precise presynaptic rate can be identified on the basis of postsynaptic CV's, interval histograms and cycle slips. ii) A small rate change in a regular presynaptic discharge will have very different postsynaptic consequences depending on where it happens: if across a paradoxical-interposed boundary, for instance, it will cause remarkable rate, pattern and correlation changes. iii) The trans-synaptic mapping of variability involves an increase for the more regular presynaptic discharges and a decrease for the more irregular ones. iv) The postsynaptic discharge was slower with IPSP's than without in most cases; however, when the control discharge was weak or absent, IPSP's accelerated it. Results are relevant also to the operation of periodically performing systems that involve neuronal correlates, indicating that it is necessary in every case to ask whether zigzag relations and locking occur. The “delay function” plots the arrival time of an IPSP (or IPSP burst) relative to the last postsynaptic spike, i.e., the “phase” (Φ in Fig. 1b), against the interval lengthening produced, i.e., the “delay” (δ). In all cases, most points clustered around a straight line (Fig. 8), whose slope and ordinate intercept were in the 0.43–0.87 and the 0.02–0.52 ranges, respectively, for single IPSP's. The slope reflects how the IPSP effectiveness depends on when it arrives in the cycle; the intercept reflects the IPSP effectiveness. Large phases often showed “aberrant” points whose ordinates were either large (and having special formal implications), or very small (perhaps reflecting conduction and synaptic delays), or clustered around a second straight segment with a large negative slope (when spontaneous rates were low) (Fig. 8c). Delay functions for widely separated pairs of IPSP's could be multi-valued, points clustering around 2 or 3 parallel straight lines. A mathematical model of pacemaker inhibitory synaptic interactions (Segundo, 1979) agreed with this embodiment insofar as some postulated properties are concerned (e.g., regular discharge, interval lengthening by IPSP's, linear delay functions with slopes around 0.7) and as to the main aspects of the preparation's behavior (i.e., zigzag rate relations and locking), but not in terms of some aspects of the postulates (e.g., interval variability, rebound) or behavior (e.g., segment boundaries, jitter in the locking, and hysteresis). The model was judged to be on the balance satisfactorily realistic.

Notes: Abstract The correspondence between afferent discharges and sinusoidal length modulations (at 0.2–10 cps) was evaluated by average Lissajous displays of rate vs. length in isolated fast-adapting stretch receptor organs (FAO) of crayfish. Frequency effects (Diez Martínez et al., 1983) were compared using modulation depths and background lengths of, respectively, 1–10% of and 0.3–40% over resting length, well within physiological ranges. The receptor remained silent with shallow and slow stimuli. With greater depths, more frequencies became effective, discharges occupied more of each cycle, and peak and overall rates increased. At large depths, increases were smaller or were substituted by decreases (overstretch). With greater background lengths at 0.2 and 1 cps, individual and peak Lissajous rates increased, as did the overall value; eventually, the flat extension disappeared. At 0.2 cps, Lissajous plots became ellipses; at 1 cps, loops became counter-clockwise. At 3 and 10 cps, rates augmented only with small increases; beyond, peak rates remained unchanged or dropped. In short, each characteristic of the transduction is apparent only within a domain defined by the stimulus features as well as by the way stimuli and afferent discharges are evaluated. Each domain overlaps partially with others but falls short of that used in nature. For example: the stimulus-response relation was linear with low frequencies, large background lengths and moderate depths when observing average Lissajous plots; saturations were present with the low frequency, shallow modulations without discharges; clockwise loops occurred with particular frequencies, background lengths and depths, but not with others. Hence, any simple and succinct description is only a local rule that holds exclusively within restrictive constraints. Any generalization beyond this domain constitutes a misleading oversimplication.

Notes: Abstract The experimentally observed influence of regularly arriving tugs upon the AP discharge of the slowly-adapting stretch receptor organs (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” plost of delays vs. phases, i.e. interval shortenings vs. the time from the last AP to the tug, were close to theV of postulate iii (Fig. 2), even though the shortest phases tended to postopone 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 (Figs.2 and 3). The interval following that with the tug tended to be lengthened, but the pre-tug timing was not recovered (Fig. 4). 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 (Figs. 5 and 7–9). Such behavior was absent when the tug sequence was highly irregular (Fig. 9). The initial settling, in the SAO as in the model, depended jointly on the first phaseΦ 1 and the intertug intervalE. If the former was under λ, it went through one or two monotonic phase-decreasing stages (one smaller, the other larger, than λ), or through a single increasing one, depending onE being smaller or greater than, respectively, an estimated but never actually observedE * leading to unstable lockings. If the initial phase was greater than λ, settling withE's underrN+λ involved jumps between larger than and smaller than λ phases; withE's overrn+λ, it involved an intermediate stable locking with Φ=E-rN. The model-embodiment correspondence in terms of postulates was judged acceptable in spite of discrepancies like the imperfect regularities, the dispersion and extra segment in the delay function (Fig. 2), and the post-tug interval lengthening (Fig. 4). The correspondence in terms of behavior turned out to be quite precise (see above) and at times surprising because of its counterintuitiveness. This reiterates the epistemologically interesting issue of why the generality of model applicability.

Notes: Abstract This report calls attention to the magnitude and pervasiveness of hysteresis in the coding from length to afferent discharges in crayfish stretch receptor organs (SRO's). The influence of previous lengths on the rate that corresponded to a particular length L was manifest by a substantial excess of that encountered when L was arrived at from a shorter value over that when arrived at from a longer one. Hysteretic loops were present under dynamic conditions when length was modulated quasi-sinusoidally in the length vs. rate Lissajous plots of both the slowly and the fast-adapting organs (SAO, FAO), either not perturbed or perturbed. Loops became narrower with increasing frequency (except for when 1 to 1 locking appeared, Diez Martínez and Segundo, 1983). Hysteretic loops were present under static conditions when length changes were step-like, and fully adapted rates were noted in the SAO and in the perturbed FAO. Earlier reports suggest that hysteresis reflects jointly at least mechanical and electrogenic factors in the “length-to-local dendritic effects” and in the “generator potential to discharge” stages. Several models, either mechanical or mathematical, reveal hysteretic behavior. Detailed analysis has not been performed except for one instance (Chua and Bass, 1972) where, for example, loop-narrowing at higher frequencies occurs only with certain weighting functions whose physiological significance is as yet obscure. Hysteresis may be more widespread than suspected in sensory (and perhaps other) systems: it involves a multi-valuedness that raises the issue of how central mechanisms infer stimulus magnitude retrospectively from the discharge.

Notes: Abstract A mathematical model designed originally for pacemaker neurons and post synaptic potentials represents acceptably respiratory driving by a pump through the Hering-Breuer reflex (Vibert et al. 1981). Discrepancies with the respiratory embodiment arose firstly in the zig-zag plots of average driving and driven intervals where the boundaries between positively and negatively-sloped segments differed, and where a hysteresis-like dependence on the order of the observations occurred. Secondly, they arose from the fact that estimates of the slope A and intercept B of the linear dependence of the delay on the arrival phase of the driver differed when based on the model's formulae but using different aspects of the same data. The question thus arose as to which model shortcomings cause discrepancies with this particular embodiment. This communication presents computer simulations that explore the consequences of modifying, or imposing variabilities, upon several parameters. A reflects how the driver's (i.e. the inflation's) consequences increase as it arrives later in the driven (i.e. phrenic) cycle: when it departs from around 0.7, (as required by the model) and approaches 1. The positively sloped segments broaden at the expense of the negatively-sloped ones which disappear when A reaches 1. The intercept B reflects the effect of the driver when it arrives just after the driven event: its increases shift a relatively unchanged plot up and to the right. When the driving period I exhibits variability or the driver one N exhibits variability or trends, as happens often with the respiratory embodiment, the model-predicted behavior remains acceptably natural-like: in particular, that with a jittery driven period mimics well observations on cats with high CO2 or superficially anesthetized. For each driving period, the driven intervals pertained to a limited number of classes (e.g. to one, two or three) which occurred in an invariant sequence.

Notes: Abstract The relation between a maintained spatial orientation and the corresponding fully adapted discharge rate was multivalued in all the afferents tonically sensitive to maintained spatial orientation observed in isolated utricles of Rhinobates productus. The spread of rate values was of the order of changes produced by natural tilts. The occurrence of multivaluedness in isolated receptors indicated that peripheral issues are sufficient. Two factors contributed: firstly, the side from which the orientation had been reached (i.e. “hysteresis”): higher adapted rates occurred when the preceding orientation was characterized by lower rates and when the corresponding transition caused acceleration; secondly, “spontaneous” rate variations, some of which resembled markedly, and interacted with, the effects of tilts. It was not possible to identify the basic mechanisms underlying these factors. The multivaluedness in the coding of maintained position, because of its constancy and magnitude, cannot be ignored. It, as well as the sensitivity to fast transients, must be taken into account in utricular models, in evaluations of information transmission, and in psychophysical explorations.