Bonhoeffer Model

Physicochemical approaches to the excitation problem were developed alongside the pure biological investigations. A lot of trigger systems are known at present which can be regarded as some kind of excitation models. Two of them, currently known as the Lillie-Bonhoeffer model and Teorell s membrane system, have been found to be particularly suitable. Experimentation with these models has been particularly useful the behavioral features common to all excitable objects have been established and the concrete electrochemical mechanisms responsible for the activity of these systems have been well-investigated. Here we will review only the major characteristics of these models. 

The following processes take place on the iron surface  

The film decomposition begins after the iron potential rises above a certain threshold value. This is accompanied by a gradual extension of the film-free surface. This process is accelerated as iron dissolution progresses. Subsequently the accumulated nitrous acid promotes the regeneration of the passivating oxide film and then the system returns to its original state. 

In the case of excitation propagation, the potential is described by Eq. (9) in which C stands for the double layer capacitance per unit wire length, R for the resistance per unit length of solution, i for the current through unit surface length equal to lirrio (r is wire radius, / o is current density). As noted above. 

and I3 are the respective current densities of the above processes. The currents themselves are expressed as follows  

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Blier P, de Montigny C (1998) Possible serotonergic mechanisms underlying the antidepressant and anti-obsessive-compulsive disorder responses. Biol Psychiatry 44 313-323 Bonasera SJ, Tecott LH (2000) Mouse models of serotonin receptor function toward agenetic dissection of serotonin systems. Pharmacol Ther 88 133-142 Bonhoeffer T (1996) Neurotrophins and activity-dependent development of the neocortex. Curr Opin Nemobiol 6 119-126... 

In an attempt to elucidate the mechanism of these peroxide-carbohydrate reactions, a carefril study of products, particularly of gaseous ones, from various model compoimds has been undertaken. - Thus, formaldehyde gives hydrogen, carbon dioxide, and formic acid by the steps shown in equations (5) to (8). Using deuterated hydrogen peroxide, Bonhoeffer... 

One may wonder if there exist any specific reaction-diffusion models giving rise to negative a. Such a model in fact exists, for which one may even prove analytically the possibility of arbitrarily small a. This is a piecewise linear version of the Bonhoeffer - van der Pol model including diffusion, and is given by... 

Fig. 7.4. Nullclines of the piecewise-linear Bonhoeffer - van der Pol model. For larger b/c, the system becomes monostable as indicated by the broken line... 

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