The Mauthner (M) cell is a critical element in a vital escape "reflex" triggered by abrupt or threatening events. Its properties at the molecular and synaptic levels, their various forms of plasticity, and the design of its networks, are all well adapted for this survival function. They guarantee that this behavior is appropriately unilateral, variable, and unpredictable. The M cell sets the behavioral threshold, and, acting in concert with other elements of the brainstem escape network, determines when, where, and how the escape is executed.

The search for chaotic patterns has occupied numerous investigators in neuroscience, as in many other fields of science. Their results and main conclusions are reviewed in the light of the most recent criteria that need to be satisfied since the first descriptions of the surrogate strategy. The methods used in each of these studies have almost invariably combined the analysis of experimental data with simulations using formal models, often based on modified Huxley and Hodgkin equations and/or of the Hindmarsh and Rose models of bursting neurons. Due to technical limitations, the results of these simulations have prevailed over experimental ones in studies on the nonlinear properties of large cortical networks and higher brain functions. Yet, and although a convincing proof of chaos (as defined mathematically) has only been obtained at the level of axons, of single and coupled cells, convergent results can be interpreted as compatible with the notion that signals in the brain are distributed according to chaotic patterns at all levels of its various forms of hierarchy.This chronological account of the main landmarks of nonlinear neurosciences follows an earlier publication [Faure, Korn, C. R. Acad. Sci. Paris, Ser. III 324 (2001) 773-793] that was focused on the basic concepts of nonlinear dynamics and methods of investigations which allow chaotic processes to be distinguished from stochastic ones and on the rationale for envisioning their control using external perturbations. Here we present the data and main arguments that support the existence of chaos at all levels from the simplest to the most complex forms of organization of the nervous system.We first provide a short mathematical description of the models of excitable cells and of the different modes of firing of bursting neurons (Section 1). The deterministic behavior reported in giant axons (principally squid), in pacemaker cells, in isolated or in paired neurons of Invertebrates acting as coupled oscillators is then described (Section 2). We also consider chaotic processes exhibited by coupled Vertebrate neurons and of several components of Central Pattern Generators (Section 3). It is then shown that as indicated by studies of synaptic noise, deterministic patterns of firing in presynaptic interneurons are reliably transmitted, to their postsynaptic targets, via probabilistic synapses (Section 4). This raises the more general issue of chaos as a possible neuronal code and of the emerging concept of stochastic resonance Considerations on cortical dynamics and of EEGs are divided in two parts. The first concerns the early attempts by several pioneer authors to demonstrate chaos in experimental material such as the olfactory system or in human recordings during various forms of epilepsies, and the belief in 'dynamical diseases' (Section 5). The second part explores the more recent period during which surrogate-testing, definition of unstable periodic orbits and period-doubling bifurcations have been used to establish more firmly the nonlinear features of r...

The classical coefficient of variation method for "quantal" analysis of synaptic responses allows unambiguous identification of pre- and postsynaptic loci underlying synaptic plasticity only when extensive simplifying restrictions are made. They include invariance of quantal parameters and the assumption that a single afferent produces the evoked potentials or currents. More general theoretical formulations and simulations demonstrate that the standard criteria do not always provide useful guidelines because when the other sources of physiological variance are included, putative pre- and postsynaptic domains may overlap. For example, data typically interpreted as indicating modifications at both sites can be due to a mechanism localized to only one of the two, if parameter variances are taken into consideration in the case of a single input cell, or if there are multiple inputs and the stimulus does not activate all of them reliably. With this perspective, other physiologically realistic hypotheses relevant to the expression of synaptic plasticity, such as that during long-term potentiation, can be envisioned.