In vitro study of phase resetting and phase locking in a time-comparison circuit in the electric fish, Eigenmannia

Monostable multivibrators as novel artificial neurons

Retriggerable and non-retriggerable monostable multivibrators are simple timers with a single characteristic, their period. Motivated by the fact that monostable multivibrators are implementable in large quantities as counters in digital programmable hardware, we set out to investigate their applicability as building blocks of artificial neural networks. We derive the nonlinear input-output firing rate relations for single multivibrator neurons as well as the equilibrium firing rate of large recurrent networks. We show that in rate-encoded monostable multivibrators networks the synaptic weights are tunable as the period ratio of connected units, and thus reconfigurable at run time in a counter-based digital implementation. This is illustrated with the task of handwritten digit recognition. Furthermore, we show in a task-independent manner that networks of monostable multivibrators are capable of nonlinear separation, when operating directly on pulse streams. Our research implies that pulse-coupled neural networks with excitable neurons showing a delayed response can perform computations even when working solely with suprathreshold pulses.

Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments

Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.

Phase-locked signals elucidate circuit architecture of an oscillatory pathway

This paper introduces the concept of phase-locking analysis of oscillatory cellular signaling systems to elucidate biochemical circuit architecture. Phase-locking is a physical phenomenon that refers to a response mode in which system output is synchronized to a periodic stimulus; in some instances, the number of responses can be fewer than the number of inputs, indicative of skipped beats. While the observation of phase-locking alone is largely independent of detailed mechanism, we find that the properties of phase-locking are useful for discriminating circuit architectures because they reflect not only the activation but also the recovery characteristics of biochemical circuits. Here, this principle is demonstrated for analysis of a G-protein coupled receptor system, the M3 muscarinic receptor-calcium signaling pathway, using microfluidic-mediated periodic chemical stimulation of the M3 receptor with carbachol and real-time imaging of resulting calcium transients. Using this approach we uncovered the potential importance of basal IP3 production, a finding that has important implications on calcium response fidelity to periodic stimulation. Based upon our analysis, we also negated the notion that the Gq-PLC interaction is switch-like, which has a strong influence upon how extracellular signals are filtered and interpreted downstream. Phase-locking analysis is a new and useful tool for model revision and mechanism elucidation; the method complements conventional genetic and chemical tools for analysis of cellular signaling circuitry and should be broadly applicable to other oscillatory pathways.

Key to robust discernment of cell circuit architecture is to have as many distinct response features as possible for comparison and evaluation. One under-appreciated characteristic of oscillatory circuits is that under periodic stimulation, these systems will exhibit responses synchronized to this stimulatory input, a phenomenon termed phase-locking. We demonstrate that phase-locked response characteristics vary noticeably depending on circuit activation and recovery properties; these response characteristics thereby provide a unique set of criteria for oscillatory circuit architecture analysis. The concept is validated through experiments on an oscillatory calcium pathway in mammalian cells; the experimental setup allowed us to explore, for the first time, the properties of chemically induced phase-locking of intracellular signals. Observations of this phenomenon were then used to test the predictions of several existing mathematical models of calcium signaling. Most of the models we evaluated were unable to match all our experimental observations, suggesting that current models are missing mechanistic elements in the context of calcium signaling for the cell type and receptor/stimulant tested. The observations of phase-locking further led us to identify one simple mechanistic modification that would account for all the experimental observations. The techniques and methodology presented should be broadly applicable to a variety of biological oscillators.

Walter Heiligenberg: the jamming avoidance response and beyond

Walter Heiligenberg (1938-1994) was an exceptionally gifted behavioral physiologist who made enormous contributions to the analysis of behavior and to our understanding of how the brain initiates and controls species-typical behavioral patterns. He was distinguished by his rigorous analytical approach used in both behavioral studies and neuroethological investigations. Among his most significant contributions to neuroethology are a detailed analysis of the computational rules governing the jamming avoidance response in weakly electric fish and the elucidation of the principal neural pathway involved in neural control of this behavior. Based on his work, the jamming avoidance response is perhaps the best-understood vertebrate behavior pattern in terms of the underlying neural substrate. In addition to this pioneering work, Heiligenberg stimulated research in a significant number of other areas of ethology and neuroethology, including: the quantitative assessment of aggressivity in cichlid fish; the ethological analysis of the stimulus-response relationship in the chirping behavior of crickets; the exploration of the neural and endocrine basis of communicatory behavior in weakly electric fish; the study of cellular mechanisms of neuronal plasticity in the adult fish brain; and the phylogenetic analysis of electric fishes using a combination of morphology, electrophysiology, and mitochondrial sequence data.

In vitro long-term potentiation of electrotonic responses of goldfish mauthner cells is accompanied by ultrastructural changes at afferent mixed synapses

The potentiated afferent mixed synapses of the Mauthner cells of fry and adult goldfish in stumps of the medulla oblongata incubated long-term in vitro were studied by electrophysiological and electron microscopic methods. It was shown that brief high-frequency stimulation of posterior branches of the eighth nerve induced a long-term potentiation of electrotonic transmission at large and small mixed club endings. It was about 135% upon subthreshold stimulation and about 200% upon suprathreshold stimulation. The ultrastructural analysis of ultrathin sections of potentiated mixed synaptic endings revealed an increase in the dimensions of desmosome-like contacts which was proportional to the degree of potentiation, about 135% or 200%, depending on the type of stimulation. The dimensions of gap junctions remained unchanged. The dimensions of active zones at potentiated synapses were reduced two-fold as compared with their unpotentiated counterparts, irrespective of the type of stimulation. Considering that desmosome-like contacts consist predominantly of F-actin, a molecule which possesses electroconductivity, it can be assumed that this cytoskeletal protein is involved in the process of potentiation. The increase in the synapse electrical conductivity can be mediated either directly, by shunting the synaptic junction with polymer actin filaments in the region of desmosome-like contacts, or indirectly, via the interaction of actin with gap junction connections situated nearby.

Phase sensitivity and entrainment in a modeled bursting neuron

A model of neuron R15 in Aplysia was used to study the mechanisms determining the phase-response curve (PRC) of the cell in response to both extrinsic current pulses and modeled synaptic input and to compare entrainment predictions from PRCs with those from actual simulations. Over the range of stimulus parameters studied, the PRCs of the model exhibited minimal dependence upon stimulus amplitude, and a strong dependence upon stimulus duration. State-space analysis of the effect of transient current pulses provided several important insights into the relationship between the PRC and the underlying dynamics of the model, such as a correlation between the prestimulus concentration of Ca2+ and the poststimulus phase of the oscillation. The system nullclines were also found to provide well-defined limits upon the perturbatory extent of a hyperpolarizing input. These results demonstrated that experimentally applied current pulses are sufficient to determine the shape of the PRC in response to a synaptic input, provided that the duration of the current pulse is of a duration similar to that of the evoked synaptic current. Furthermore, we found that predictions of phase-locked 1:m entrainment from PRCs were valid, even when the duration of the periodically applied pulses were a significant portion of the control limit cycle.