ALBERT

Notes: Abstract An elementary model of neuronal activity involves temporal and spatial summation of postsynaptic currents that are elicited by presynaptic spikes and that, in turn, elicit postsynaptic potentials at a trigger zone; when the potential at the trigger zone exceeds a “threshold” level, a postsynaptic spike is generated. This paper describes three methods of estimating the “summation function”, that is, the function of time that converts the synaptic current into potential at the trigger zone: namely, maximum likelihood, cross-correlation analysis and cross-spectral analysis. All three methods, when applied to input-output data collected on various neurons of Aplysia californica, give comparable results. As estimated, the summation function involved in the explored cells has an early positive-going swing that is large and brief. In the cell L5, but not in R2, there was also a late negative-going swing of longer duration.

Notes: Abstract A recent investigation of the influence of periodic inhibitory trains on a crayfish pacemaker neuron showed not only well-known locked periodic responses but also intermittent, messy, and hopping responses. This communication studies the responses of the Bonhoeffer-van der Pol (BVP) model with self-sustained oscillation when exposed to periodic pulse trains inputs. The analysis is similar to that used in crayfish and reveals interesting features, both comparable and complementary to those seen in the living preparation.

Notes: Abstract This paper studies the influence exerted by the presynaptic spike train on the postsynaptic one. It applies to synaptic exploration a novel method for characterization of point-process systems (Brillinger, 1974, 1975a), and draws from it physiologically meaningful conclusions. The departure point was a large data set of action potential trains from an Aplysia network whose neurons are connected by monosynaptic inhibitory or excitatory PSP's, and either discharged spontaneously or were driven by intracellular pulses. First, a sequence of “kernels” is estimated, each with a physiological connotation relevant to synaptic transmission. The kernel independent of time — of zero-order — measures the postsynaptic rate with no presynaptic discharge. That of a single time argument — of first-order — relates to the rate effect of the average PSP. Those of two, three, or more time arguments — of second, third or higher-order — relate to interactions between two, three, or more postsynaptic potentials (e.g. to facilitation) and/or spikes (e.g. to refractoriness). Then successive models are constructed recursively and based on the kernel of zero-order, on the kernels of zero and first order, on those of zero, first and second order, and so forth, until a desired approximation is achieved. The plausibilities of each kernel estimate and of each model are evaluated separately by way of spectra and coherences. The “linear” model based upon the zero and first-order kernel was tested (after that based exclusively on the zero-order one was proven inadequate). When presynaptic discharges are very irregular and at intermediate or low rates, it provides satisfactory description and prediction, and the first-order kernel is an uncontaminated display of the rate effects of the average presynaptic spike: this constitutes the “linear” domain. When presynaptic discharges are bursty, regular or very fast, the linear model is unsatisfyctory: this is referred to as “non-linear” domain. Reasons for non-linearity lie in PSP facilitation and anti-facilitation, conversion of membrane current into firing rate, after-spike excitability oscillations, and special pacemaker interactions. The model can be extended to three-neuron networks where partial coherences exract interactions between followers, even while submitted to a common driver. The basic and ubiquitous issues of spike train description and stability were discussed. The counting and the interval statistic of spike trains provide equivalent descriptions and their current opposition is conceptually meaningless. Concomitant short-term fluctuations in spike generation intensity at preand postsynaptic levels have funciional significance beyond changes in the overall average rate or interval: they are made precise by parameters whose definition, estimation and physiological interpretation are presented here. Some stability of the experimental preparation is presupposed by investigators, but variations (e.g. from cycles or deterioration) always exist. Hence, decisions as to the preparation's evolution and as to tolerable changes must be made, and based upon pre-existing knowledge, educated guesses and practical considerations. This study provided basic knowledge of the individual synapse considered the elementary building block of the nervous system when viewed as a network of interacting nerve cells. It also contributed generally applicable mathematical techniques which were illustrated by application to relatively well studied and simple networks.

Notes: Zusammenfassung 1. Bestimmte Input-Output Beziehungen wurden untersucht durch intraneurale Registrierungen von isolierten visceralen Ganglien von Aplysia californica. Alle Zellen wiesen eine verlängerte Folge von einem einzigen Typ von EPSPs auf, und lösten infolgedessen aufeinanderfolgende Spikes aus. EPSPs traten entweder (i) spontan auf, oder wurden (ii) ausgelöst durch Erregung eines Konnektifs mittels elektrischer Impulse eines Erregers, der durch einen Geigerzähler betrieben wurde. Die präspike Epoche wurde untersucht, und die Vorgänge, welche den postsynaptischen Spike auslösen, wurden probabilistisch identifiziert. Versuche mit durch digitalen Rechner simulierte Neuronen reproduzierten und erweiterten die Ergebnisse von Tierexperimenten. 2. Die Spike-Wahrscheinlichkeit spiegelt das Verhalten von EPSPs wieder, welche innerhalb eines begrenzten Zeitraumes (als Integrationsperiode bezeichnet) vorkommen und erfaßt daher nur eine begrenzte Anzahl dieser Potentiale (als beeinflussende EPSPs bezeichnet). Die Wahrscheinlichkeit, daß ein gegebenes EPSP einen Spike auslöst, ist im allgemeinen eine abnehmende Funktion des mittleren zeitlichen Abstands (eine zunehmende Funktion der Durchschnittsrate) einer bestimmten Anzahl von kurz zuvor erfolgten EPSPs. Bei gegebener mittlerer Zeitspanne (Durchschnittsrate) wird sie im allgemeinen größer bei Mustern, in denen sukzessive Intervalle immer kürzer werden. Darüber hinaus wird die Spike-Wahrscheinlichkeit beeinflußt durch kurz zuvor erfolgte postsynaptische Spikes; die Wirksamkeit irgendeiner EPSP-Konfiguration kann durch geeignete Anordnung in bezug auf die vorangegangenen Spikes verbessert werden. Es wird daraus gefolgert, daß eine postsynaptische Zelle die Entscheidung, einen Spike zu erzeugen, unter dem Einfluß einer großen Zahl von EPSPs durch laufende Auswertung der genauen Zeitfolge kurz zuvor erfolgter Input-Ereignisse fällt. Deshalb hängt die Bildung der postsynaptischen Spike-Kette von verschiedenen statistischen Besonderheiten der präsynaptischen Entladungen ab. Die Begrenzung dieser Begriffsbestimmung und ihre Anwendbarkeit auf verschiedene, z.T. komplexere Fälle wird diskutiert. 3. Die Arbeitsweise einer synaptischen Verbindung dieses Typs wird gemessen und diskutiert unter besonderer Berücksichtigung der folgenden drei Wahrscheinlichkeitswerte und deren Beziehungen untereinander: (i) die generative Wahrscheinlichkeit, daß eine bestimmte Input-Zeitfolge von präsynaptischen Spikes (oder EPSPs) erfolgt; (ii) die prospektive Wahrscheinlichkeit, daß ein Output-postsynaptischer Spike durch die vorhergehende Input-Zeitfolge ausgelöst wird; (iii) die retrospektive Wahrscheinlichkeit, daß eine bestimmte Input-Zeitfolge erfolgt ist, wenn ein Output-Spike ausgelöst wurde. Jeder dieser Wahrscheinlichkeitswerte (s. Appendix) kann direkt aus den Versuchsergebnissen abgeschätzt werden (a) und hat eine bestimmte physiologische Bedeutung in bezug auf die Eigenschaften der präsynaptischen Neurone, der synaptischen Verbindung, und/oder der postsynaptischen Neurone (b). Die in den prospektiven und retrospektiven Schemata bestehenden Unbestimmtheiten werden gemessen (s. Appendix). Die gefundenen Werte zeigten in welchem Ausmaß die Unbestimmtheit bezüglich Input (Output) reduziert werden kann durch das Bekanntsein von Output (Input) und wie sie verringert werden kann indem die betreffenden Wahrscheinlichkeiten als Funktion der Zeitfolge ausgedrückt werden.

Notes: Abstract A recent investigation of the influence of periodic inhibitory trains on a crayfish pacemaker neuron showed not only well-known locked periodic responses but also intermittent, messy, and hopping responses. This communication studies the responses of the Bonhoeffer-van der Pol (BVP) model with self-sustained oscillation when exposed to periodic pulse trains inputs. The analysis is similar to that used in crayfish and reveals interesting features, both comparable and complementary to those seen in the living preparation.

Notes: Abstract The Bonhoeffer-van der Pol (BVP) oscillator is a valuable dynamical system model of pacemaker neurons. Isochrons, phase transition curves (PTC), and two dimensional bifurcation diagrams served to analyze the neuron's response to periodic pulse stimuli. Responses are described and explained in terms of the nonlinear dynamical system theory. An important issue in the generation of spikes by pacemaker neurons is the existence of both slow and fast dynamics in the state point's trajectory in the phase plane. It is this feature in particular that makes the BVP oscillator a faithful model of living pacemaker neurons. Comparison of the model's responses with those of a living pacemaker was based also on return maps of interspike intervals. Analyzed in detail were the complex discharges called ‘stammering’ which involve interspike intervals that arise unpredictably and exhibit histograms with several modes separated by the equal intervals.

Notes: Summary Different synaptic terminals of the single excitor axon to the opener muscle of crayfish (Procambarus clarkii) often release transmitter in a very different manner when stimulated with the same equal-interval, doublet, or triplet patterns. Compared to synapses that show little facilitation (low Fe synapses), highly facilitating (high Fe) synapses show greater percentage increases in several measures of synaptic efficacy when stimulated with any of these patterns. Low Fe synapses usually show the greater absolute changes in these measures of synaptic efficacy. Changes in the span and pattern of doublets and triplets can independently affect both pre- and postsynaptic measures of synaptic efficacy at either low Fe or high Fe synapses.