Integrative Synaptic Mechanisms in the Caudal Ganglion of the Crayfish

A study of activity recorded with intracellular micropipettes was undertaken in the caudal abdominal ganglion of the crayfish in order to gain information about central fiber to fiber synaptic mechanisms. This synaptic system has well developed integrative properties. Excitatory post-synaptic potentials can be graded, and synaptic potentials from different inputs can sum to initiate spike discharge. In most impaled units, the spike discharge fails to destroy the synaptic potential, thereby allowing sustained depolarization and multiple spike discharge following single pulse stimulation to an afferent input. Some units had characteristics which suggest a graded threshold for spike generation along the post-synaptic fiber membrane. Other impaled units responded to afferent stimulation with spike discharges of two distinct amplitudes. The smaller or "abortive" spikes in such units may represent non-invading activity in branches of the post-synaptic axon. On a few occasions one afferent input was shown to inhibit the spike discharge initiated by another presynaptic input.     

Modes of Initiation and Propagation of Spikes in the Branching Axons of Molluscan Central Neurons

A study has been made of Aplysia nerve cells, mainly in the pleural ganglia, in which the main axon divides into at least two branches in the neighbourhood of the soma. Conduction between these branches was investigated by intracellular recordings from the soma following antidromic stimulation via the nerves containing the axonal branches. It has been shown that transmission between separate branches need not involve discharge of the soma but only of the axonal region between the soma and the origin of the branches. In some cells, the spike may fail to invade the other axonal branch, whereas transmission in the opposite direction is readily achieved. Often spikes in none of the branches are transmitted to the others, unless facilitated. Indications about the geometry of the neuron in the vicinity of the soma may be obtained from the study of the relative size of the A spikes originated in different branches. These observations, together with the presence of different sizes of A spikes, produced by orthodromic stimulation, provide evidence that spikes initiated at separate axonal "trigger zones" of Aplysia neurons may be conducted selectively to the effectors or other neurons innervated by the particular branch.     

Oscillation and Repetitive Firing in Squid Axons : Comparison of experiments with computations

Space-clamped squid axons treated with low calcium and computed Hodgkin-Huxley (HH) axons were stimulated by steps of superthreshold current from 101 to 400% of the rheobasic value over a temperature range of 5–27°C. The natural frequency of sustained repetitive firing of real and computed axons depended weakly upon stimulus intensity and strongly upon temperature, with a Q₁₀ of 2.7 (experimental) and 2.6 (computed). For real axons, but not the computed axon, the intervals between the first two spikes were shorter than between subsequent spikes. Constant spike frequencies from 75 Hz at low intensities and temperatures to 330 Hz at high intensities and temperatures were soon achieved. Subthreshold and superthreshold responses were sometimes intermixed in a train of responses from a real axon responding to a constant step of current, but not predicted by HH. The time interval following a spike was always longer than that following a subthreshold oscillation in slightly decalcified real axons, as Huxley and FitzHugh also found for computed axons. There was a bias toward spikes at the beginning of the train and toward subthreshold responses later on. Some repeated patterns were found, every second, third, or fourth response being a spike. Neither the HH equations nor the computed or experimental threshold behaviors show a critical temperature to support a membrane phase transition.     

Axonal contribution to subthreshold currents inaplysia bursting pacemaker neurons

The contribution of axonal activity to the ionic currents which generate bursting pacemaker activity was studied by using the two-electrode voltage-clamp technique in Aplysia bursting neuron somata in conjunction with intraaxonal voltage recordings. Depolarizing voltage-clamp pulses applied to bursting cell somata triggered axonal action potentials. The voltage-clamp current recording exhibited transient inward current "notches" corresponding to each of the axonal spikes. The addition of 50 microM tetrodotoxin (TTX) to the bathing medium blocked the fast axonal spikes and current notches, revealing a slower axonal spike which was blocked by the replacement of external Ca2+ with Co2+. The inward current evoked by applying a depolarizing voltage-clamp pulse in the soma is distorted by the occurrence of the axonal Ca2+ spike. Elimination of the axonal spike, by injecting hyperpolarizing current into the axon, changes both the time course and the magnitude of the inward current. The axonal Ca2+ spikes are followed by a series of Ca2+-dependent afterpotentials: a rapid postspike hyperpolarization, a depolarizing afterpotential (DAP) and, finally, a long-lasting postburst hyperpolarization. The long-lasting hyperpolarization is not blocked by 50 mM external tetraethyl ammonium, an effective blocker of Ca2+-activated K+ current [IK(Ca)], and does not appear to reverse at EK. Hence, the axonal long-lasting hyperpolarization may not be due to IK(Ca). Somatic voltage-clamp pulses in bursting neurons are followed by a slow inward tail current, which is sometimes coincident with a DAP in the axon. In some cells, the amplitude of the slow inward tail current is greatly reduced if axonal spikes and DAPs are prevented by hyperpolarization of the axon, while, in other cells, elimination of axonal activity has little effect. Therefore, the slow inward tail current is not necessarily an artifact of poor voltage-clamp control over the axonal membrane potential but probably results from the activation of an ionic conductance mechanism located partly in the axon and partly in the soma.     

Simulation study on effects of channel noise on differential conduction at an axon branch.

Effects of membrane channel noise (random opening and closing of ion channels) are studied on spike conduction at a branching point on an axon. Computer simulation is done on the basis of a stochastic version of the Hodgkin-Huxley cable model, into which the channel noise is incorporated. It is shown that the channel noise makes conduction of spikes into daughter branches random; spikes randomly succeed or fail in conduction into daughter branches. The conduction is then randomly differential even though the forms and properties of daughter branches are the same. The randomness is considerable when the radius of an axon is small (approximately 1 microns).     

Repetitive activity of a branched Hodgkin-Huxley axon with multiple encoding sites

Afferent activity in a receptor afferent fiber with several encoding sites is generally believed to represent the activity of the fastest pacemaker that resets all more slowly encoding sites. Alternatively, some impulse mixing as well as some nonlinear summation of receptor current to a single encoder have been considered. In this article the repetitive firing activity of a Hodgkin-Huxley axon consisting of two branches that join into a single stem axon was investigated. The model axon was stimulated by constant-current injection into either the right or the left or both branches. It was found that the model axon generated an (infinite) train of action potentials if the input current was large enough. The discharge frequency found was constant, and on combined stimulation of both branches with different current, the site of impulse initiation was always in the branch receiving the higher input current, excluding a simple impulse mixing. On the other hand, the combined stimulation of both branches evoked repetitive firing with a higher frequency than expected by the pacemaker-resetting hypothesis. Moreover, a stimulus that is subthreshold for repetitive firing if injected into one branch yields repetitive firing when it is injected into both branches, a behavior inconsistent with impulse mixing and pacemaker resetting. On the other hand, current injection into one branch allowed repetitive activity only within a rather limited range of firing frequencies. Using distributed current injection into both branches, however, allowed many more different firing frequencies. Such behavior is inconsistent with both pacemaker resetting and (nonlinear) input current summation. Consequently, the repetitive firing behavior of a branched Hodgkin-Huxley axon with multiple encoding sites appears to be more complex than postulated in the simple hypotheses.     

Extra spike formation in sensory neurons and the disruption of afferent spike patterning

The peculiar pseudounipolar geometry of primary sensory neurons can lead to ectopic generation of "extra spikes" in the region of the dorsal root ganglion potentially disrupting the fidelity of afferent signaling. We have used an explicit model of myelinated vertebrate sensory neurons to investigate the location and mechanism of extra spike formation, and its consequences for distortion of afferent impulse patterning. Extra spikes originate in the initial segment axon under conditions in which the soma spike becomes delayed and broadened. The broadened soma spike then re-excites membrane it has just passed over, initiating an extra spike which propagates outwards into the main conducting axon. Extra spike formation depends on cell geometry, electrical excitability, and the recent history of impulse activity. Extra spikes add to the impulse barrage traveling toward the spinal cord, but they also travel antidromically in the peripheral nerve colliding with and occluding normal orthodromic spikes. As a result there is no net increase in afferent spike number. However, extra spikes render firing more staccato by increasing the number of short and long interspike intervals in the train at the expense of intermediate intervals. There may also be more complex changes in the pattern of afferent spike trains, and hence in afferent signaling.     

Steps in the production of motoneuron spikes

1. Spikes evoked in spinal motoneurons by antidromic stimulation normally present an inflection in their rising phase. A similar inflection is present in spikes evoked by direct stimulation with short pulses. 2. In either case the inflection becomes less prominent if the motoneuron membrane is depolarized and more prominent when it is hyperpolarized. Both antidromic and direct spikes may fall from the level of the inflection thus evoking a "small spike" only if sufficient hyperpolarization is applied. Similar events occur when antidromic or direct spikes are evoked in the aftermath of a preceding spike. 3. Spikes evoked by direct stimuli applied shortly after firing of a "small spike" may also become partially blocked at a critical stimulus interval. At shorter intervals, however, spike size again increases and no inflection can be detected in the rising phase. 4. When a weak direct stimulus evokes a small spike only, a stronger stimulus may evoke a full spike. Curves of the strength of the stimuli required for eliciting small or full spikes have been constructed in a number of conditions. 5. To explain the results it is assumed that threshold of the major portions of the soma membrane is higher than the threshold of the axon, the transition occurring over a finite area near the axon hillock. Following antidromic or direct stimulation, soma excitation is then initiated in the region of the axon hillock. Spread of activity towards the soma occurs at first slowly and with low safety factor. At this stage block may be easily evoked. Safety factor for propagation increases rapidly as the growing impulse involves larger and larger areas of the soma membrane so that, once the critical areas are excited, activation of the remaining portions of the soma membrane will suddenly occur.     

Propagation of action potentials in squid giant axons. Repetitive firing at regions of membrane inhomogeneities

Effects of reduction in potassium conductance on impulse conduction were studied in squid giant axons. Internal perfusion of axons with tetraethylammonium (TEA) ions reduces G K and causes the duration of action potential to be increased up to 300 ms. This prolongation of action potentials does not change their conduction velocity. The shape of these propagating action potentials is similar to membrane action potentials in TEA. Axons with regions of differing membrane potassium conductances are obtained by perfusing the axon trunk and one of its two main branches with TEA after the second branch has been filled with normal perfusing solution. Although the latter is initially free of TEA, this ion diffuses in slowly. Up until a large amount of TEA has diffused into the second branch, action potentials in the two branches have very different durations. During this period, membrane regions with prolonged action potentials are a source of depolarizing current for the other, and repetitive activity may be initiated at transitional regions. After a single stimulus in either axon region, interactions between action potentials of different durations usually led to rebound, or a short burst, of action potentials. Complex interactions between two axon regions whose action potentials have different durations resembles electric activity recorded during some cardiac arrhythmias.     

Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons.

The Hodgkin-Huxley equations for space-clamped squid axon (18 degrees C) have been modified to approximate voltage clamp data from repetitive-firing crustacean walking leg axons and activity in response to constant current stimulation has been computed. The m infinity and h infinity parameters of the sodium conductance system were shifted along the voltage axis in opposite directions so that their relative overlap was increased approximately 7 mV. Time constants tau m and tau h, were moved in a similar manner. Voltage-dependent parameters of delayed potassium conductance, n infinity and tau n, were shifted 4.3 mV in the positive direction and tau n was uniformly increased by a factor of 2. Leakage conductance and capacitance were unchanged. Repetitive activity of this modified circuit was qualitatively similar to that of the standard model. A fifth branch was added to the circuit representing a transient potassium conductance system present in the repetitive walking leg axons and in other repetitive neurons. This model, with various parameter choices, fired repetitively down to approximately 2 spikes/s and up to 350/s. The frequency vs. stimulus current plot could be fit well by a straight line over a decade of the low frequency range and the general appearance of the spike trains was similar to that of other repetitive neurons. Stimulus intensities were of the same order as those which produce repetitive activity in the standard Hodgkin-Huxley axon. The repetitive firing rate and first spike latency (utilization time) were found to be most strongly influenced by the inactivation time constant of the transient potassium conductance (tau b), the delayed potassium conductance (tau n), and the value of leakage conductance (gL). The model presents a mechanism by which stable low frequency discharge can be generated by millisecond-order membrane conductance changes.     

The influence of an unmyelinated terminal on repetitive firing of a mammalian receptor afferent fiber

The distal end of a myelinated receptor afferent fiber consists of an unmyelinated terminal membrane which is assumed to be the site of sensory transduction, whereas the action potential encoding appears at a distal node of Ranvier. In the present paper a model of a mammalian myelinated nerve fiber was augmented by an unmyelinated terminal segment into which stimulating current was injected thus modelling the situation at a myelinated receptor afferent fiber. It was found that the introduction of the unmyelinated terminal reduces the repetitive firing rate shown by the model. However, also the amplitude of the spikes at the site of action potential generation diminishes through the large electrical load which the unmyelinated terminal imposes onto the active parts of the nerve fiber model. This "loss" of spike amplitude can abolish the ability of the model to show repetitive activity, if the unmyelinated terminal increases in size. On the other hand, the incorporation of sodium channels into the terminal membrane compensates the spike amplitude reduction introduced by the electrical load of that membrane. This allows repetitive firing at a lower frequency than would be possible for a model with an equivalent sodium-channel-free terminal. The results show that the unmyelinated terminal present at the distal end of myelinated receptor afferent fibers has not only the ability to provide sensory transduction but evokes also a reduction in the discharge rate of the encoding membrane.     

An axonal spike in an identified fast crab motor neuron has sodium and calcium components

1. High intensity intracellular stimulation of the FBE axon produced a spike discharge. The spikes divided into two components, each with a different frequency. 2. Ion replacement and blocking specific ion channels revealed that the FBE spike has calcium and sodium components. 3. The pronounced depolarizing wave that follows the FBE spike is not produced by changes in calcium conductance.     

Differential time course of the response to axotomy induced by cut or crush in the leech AP cell

The time course of the reaction to axotomy in the leech AP cell was determined by measuring the duration of the spontaneous spikes at different times after the operation. The axotomy performed by section of the segmental roots containing the AP axon induced an increase of the spike duration, which persisted over 30 days. A different time course was found when the axotomy was performed by nerve crush: the changes in duration of the spontaneous spikes, which occurred during the early 2 weeks, were significantly reduced afterwards. Dye staining of some cells axotomized by crushing revealed that the reversion of the changes, which had been set up by axotomy, was in some cases concomitant with the reconnection between proximal and distal axon stumps. The section of a single axonal branch was never sufficient to affect the membrane properties of the AP cells. It is concluded that the changes observed in axotomized AP cells are not produced by simple axonal injury and that the maintainance of normal properties in the somatic membrane requires the presence of at least part of the distal axon arborization.     

Impulse Propagation at the Septal and Commissural Junctions of Crayfish Lateral Giant Axons

Transmission across the septal junctions of the segmented giant axons of crayfish is accounted for quantitatively by a simple equivalent circuit. The septal membranes are passive, resistive components and transmission is ephaptic, by the electrotonic spread of the action current of the pre-septal spike. The electrotonic spread appears as a septal potential, considerably smaller than the pre-septal spike, but usually still large enough to initiate a new spike in the post-septal segments. The septal membranes do not exhibit rectification, at least over a range of ± 25 mv polarization and this accounts for their capacity for bidirectional transmission. The commissural branches, which are put forth by each lateral axon, make functional connections between the two axons. Transmission across these junctions can also be bidirectional and is probably also ephaptic. Under various conditions, the ladder-like network of cross-connections formed by the commissural junctions can give rise to circus propagation of impulses from one axon to the other. This can give rise to reverberatory activity of both axons at frequencies as high as 400/sec.     

Transient Responses to Sudden Illumination in Cells of the Eye of Limulus

Responses recorded from visual cells of Limulus (presumably eccentric cells) following abrupt and maintained illumination consist of depolarization with superimposed spikes. Both the depolarization and the frequency of firing are greater at the beginning of the response than later on. Frequency of firing decreases with time also during stimulation with constant currents, but the decay is then less than it is during constant illumination. Early and steady-state responses do not increase in the same proportion following illumination at different intensities. Membrane conductance is higher during the early peak of the response than in steady state. Early and late potential changes appear to tend to the same equilibrium value. The results support the assumptions that: (a) discharge of impulses is the consequence of depolarization of a specialized "pacemaker region" in the axon; (b) depolarization induced by light is the consequence of increase of membrane conductance. The major conductance changes occurring during constant illumination may be due to corresponding changes of the "stimulus" supplied by the photoreceptor or to changes of sensitivity of the eccentric cell's membrane to this stimulus. Some accessory phenomena may be the consequence of regenerative properties of the nerve cell itself.     

Electrophysiology of Supramedullary Neurons in Spheroides maculatus : I. Orthodromic and antidromic responses

This series of three papers presents data on a system of neurons, the large supramedullary cells (SMC) of the puffer, Spheroides maculatus, in terms of the physiological properties of the individual cells, of their afferent and efferent connections, and of their interconnections. Some of these findings are verified by available anatomical data, but others suggest structures that must be sought for in the light of the demonstration that these cells are not sensory neurons. Analysis on so broad a scale was made possible by the accessibility of the cells in a compact cluster on the dorsal surface of the spinal cord. Simultaneous recordings were made intracellularly and extracellularly from individual cells or from several, frequently with registration of the afferent or efferent activity as well. The passive and active electrical properties of the SMC are essentially similar to those of other neurons, but various response characteristics have been observed which are related to different excitabilities of different parts of the neuron, and to specific anatomical features. The SMC produce spikes to direct stimuli by intracellular depolarization, or by indirect synaptic excitation from many afferent paths, including tactile stimulation of the skin. Responses that were evoked by intracellular stimulation of a single cell cause an efferent discharge bilaterally in many dorsal roots, but not in the ventral. Sometimes several distinct spikes occurred in the same root, and behaved independently. Thus, a number of axons are efferent from each neuron. They are large unmyelinated fibers which give rise to the elevation of slowest conduction in the compound action potential of the dorsal root. A similar component is absent in the ventral root action potential. Antidromic stimulation of the axons causes small potentials in the cell body, indicating that the antidromic spikes are blocked distantly to the soma, probably in the axon branches. The failure of antidromic invasion is correlated with differences in excitability of the axons and the neurite from which they arise. As recorded in the cell body, the postsynaptic potentials associated with stimulation of afferent fibers in the dorsal roots or cranial nerves are too small to discharge the soma spike. The indirect spike has two components, the first of which is due to the synaptically initiated activity of the neurite and which invades the cell body. The second component is then produced when the soma is fired. The neurite impulse arises at some distance from the cell body and propagates centrifugally as well as centripetally. An indirect stimulus frequently produces repetitive spikes which are observed to occur synchronously in all the cells examined at one time. Each discharge gives rise to a large efferent volley in each of the dorsal roots and cranial nerves examined. The synchronized responses of all the SMC to indirect stimulation occur with slightly different latencies. They are due to a combination of excitation by synaptic bombardment from the afferent pathways and by excitatory interconnections among the SMC. Direct stimulation of a cell may also excite all the others. This spread of activity is facilitated by repetitive direct excitation of the cell as well as by indirect stimulation.     

Discharges of tectal neurons evoked by electrical stimulation of single retinal ganglion cells in frogs

"EEG quanta" — extracellular monosynaptic PSPs evoked by action potentials of a single axon — were recorded in the frog thalamus at a depth of 200–700 µ during electrical stimulation of the retina by single, double, or triple pulses of current of threshold strength. With an interval of 5–25 msec between consecutive stimuli, a negative spike, increasing as the microelectrode was inserted deeper, was observed at the peak of the testing EEG quanta, which were enlarged 1.5–2.5 times. It is postulated that this spike is the synchronous discharge of neuron bodies (population spike), evoked by an action potential of a single retinotectal axon. This axon branches in layers F or G. Discharges appear in neurons of layers 6–8. The possibility that the volley discharge of one class 3–5 detector excites tectal ganglion cells, whose axons mainly form the tecto-bulbospinal tract, is discussed.Research Institute of Cardiology and Laboratories of Electroencephalography and Neurocybernetics, Medical Institute, Kaunas, Lithuania. Translated from Neirofiziologiya, Vol. 16, No. 6, pp. 829–835, November–December, 1984.     

Sharpness of Spike Initiation in Neurons Explained by Compartmentalization

In cortical neurons, spikes are initiated in the axon initial segment. Seen at the soma, they appear surprisingly sharp. A standard explanation is that the current coming from the axon becomes sharp as the spike is actively backpropagated to the soma. However, sharp initiation of spikes is also seen in the input–output properties of neurons, and not only in the somatic shape of spikes; for example, cortical neurons can transmit high frequency signals. An alternative hypothesis is that Na channels cooperate, but it is not currently supported by direct experimental evidence. I propose a simple explanation based on the compartmentalization of spike initiation. When Na channels are placed in the axon, the soma acts as a current sink for the Na current. I show that there is a critical distance to the soma above which an instability occurs, so that Na channels open abruptly rather than gradually as a function of somatic voltage.     

Peripheral generation and modulation of crustacean motor axon activity at high temperatures

Summary We have examined the effects of temperature changes on the stretcher muscle and its motor supply in a crab (Pachygrapsus crassipes). An increase in temperature caused a decrease in the amplitude of evoked excitatory junctional potentials (ejp's). Above a critical threshold a single action potential in the excitor (E) or specific inhibitor (SI) axon provoked multiple spikes in the appropriate axon and concomitant ejp's or inhibitory junctional potentials (ijp's) in the stretcher muscle fibers. The critical temperature for generation of peripheral spikes was dependent upon the crab's thermal history.In preparations in which a shock to the E axon evoked repetitive firing, stimulation of the SI axon at about the same time as the E axon abolished or curtailed the peripherally generated E axon responses. No reciprocal modulation of SI activity by the E axon was observed. GABA abolished the peripheral generation of E spikes and picrotoxin prevented SI modulation of E activity. We suggest that the site of SI modulation is at the axo-axonal synapses, possibly at the fine E axon branches and the bottlenecks along the E axon where inhibitory synapses have been observed.Abbreviations CI common inhibitor (axon) - E excitor (axon) - ejp excitatory junctional potential - ijp inhibitory junctional potential - SI specific inhibitor axon This work was supported by grants awarded to Dr. Atwood from the National Research Council of Canada and the Muscular Dystrophy Association of Canada.     

Presynaptic irregularity and pacemaker inhibition

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 ( in Fig. 1b), against the interval lengthening produced, i.e., the delay (). 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.Supported by funds from the Brain Research Institute, UclaSupported by FAPESP (Sao Paulo, Brazil)