Numerous animal behaviors, such as locomotion in vertebrates, are produced by rhythmic contractions that alternate between two muscle groups. The neuronal networks generating such alternate rhythmic activity are generally thought to rely on pacemaker cells or well-designed circuits consisting of inhibitory and excitatory neurons. However, experiments in organotypic cultures of embryonic rat spinal cord have shown that neuronal networks with purely excitatory and random connections may oscillate due to their synaptic depression, even without pacemaker cells. In this theoretical study, we investigate what happens if two such networks are symmetrically coupled by a small number of excitatory connections. We discuss a time-discrete mean-field model describing the average activity and the average synaptic depression of the two networks. Depending on the parameter values of the depression, the oscillations will be in phase, antiphase, quasiperiodic, or phase trapped. We put forward the hypothesis that pattern generators may rely on activity-dependent tuning of synaptic depression.

A three-dimensional model for release and di usion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a di usion function describing the spread of transmitter in the cleft. Concentration pro les of transmitter at the postsynaptic side were calculated for di erent transmitter concentrations in a vesicle, release scenarios and di usion coe cients. From the concentration pro les the receptor occupancy could be determined using AMPA receptor kinetics. It turned out that saturation of receptors and su ciently fast currents could only be obtained if the di usion coe cient was one order of magnitude lower than generally assumed, and if the postsynaptic receptors formed clusters with a diameter of roughly 100 nm directly opposite the release sites. Under these circumstances the gradient of the transmitter concentration at the postsynaptic membrane outside the receptor clusters was steep with minimal crosstalk among neighboring receptor clusters. These ndings suggest, that to each release site a corresponding receptor aggregate exists, subdividing an individual synapse into independent functional subunits without the need for speci c lateral di usion barriers.

The motor units of a skeletal muscle may be recruited according to different strategies. From all possible recruitment strategies nature selected the simplest one: in most actions of vertebrate skeletal muscles the recruitment of its motor units is by increasing size. This so-called size principle permits a high precision in muscle force generation since small muscle forces are produced exclusively by small motor units. Larger motor units are activated only if the total muscle force has already reached certain critical levels. We show that this recruitment by size is not only optimal in precision but also optimal in an information theoretical sense. We consider the motoneuron pool as an encoder generating a parallel binary code from a common input to that pool. The generated motoneuron code is sent down through the motoneuron axons to the muscle. We establish that an optimization of this motoneuron code with respect to its information content is equivalent to the recruitment of motor units by size. Moreover, maximal information content of the motoneuron code is equivalent to a minimal expected error in muscle force generation.

We consider a randomly connected neural network with linear threshold elements which update in discrete time steps. The two main features of the network are: (1) equally distributed and purely excitatory connections and (2) synaptic depression after repetitive firing. We focus on the time evolution of the expected network activity. The four types of qualitative behavior are investigated: singular excitation, convergence to a constant activity, oscillation, and chaos. Their occurrence is discussed as a function of the average number of connections and the synaptic depression time. Our model relies on experiments with a slice culture of disinhibited embryonic rat spinal cord. The dynamics of these networks essentially depends on the following characteristics: the low non-structured connectivity, the high synaptic depression time and the large EPSP with respect to the threshold value.

Fuzzy methods are commonly used to produce a desired output of a complex system which can be steered by known expert rules. But fuzzy methods can also be applied to the reversed problem: if the input-output behavior of a system is given one wishes to nd the rules by which this behavior is evoked. We introduce this reversed method to neuronal modeling and, as an example, apply it to a biological neuron of the HodgkinHuxley type. Going out from measured data of the membran potential, the sodiumand potassium-current, we rebuild the membran behavior by fuzzy rules and show how these rules can lead to a better understanding of the underlying mechanisms. The appeal of the approach is that once the system variables are identi ed, the analysis runs comletely automatically. De ning in advance the width of the membership functions the number and speci ty of the outcoming rules can be tuned.

A three-dimensional model for release and diffusion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a diffusion function describing the spread of transmitter in the cleft. Concentration profiles of transmitter at the postsynaptic side were calculated for different transmitter concentrations in a vesicle, release scenarios, and diffusion coefficients. From the concentration profiles the receptor occupancy could be determined using alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor kinetics. It turned out that saturation of receptors and sufficiently fast currents could only be obtained if the diffusion coefficient was one order of magnitude lower than generally assumed, and if the postsynaptic receptors formed clusters with a diameter of roughly 100 nm directly opposite the release sites. Under these circumstances the gradient of the transmitter concentration at the postsynaptic membrane outside the receptor clusters was steep, with minimal cross-talk among neighboring receptor clusters. These findings suggest that for each release site a corresponding receptor aggregate exists, subdividing an individual synapse into independent functional subunits without the need for specific lateral diffusion barriers.

The size principle implies that the motoneurons of a muscle pool are activated in ascending order of their sizes when that pool of motoneurons receives a common, increasing input. We suggest a simple discrete Lagrangian for an isometrically contracting skeletal muscle. Minimizing the time integral of this Lagrangian leads to recruitment of motor units according to increasing size.

The size principle consists in the activation of motoneurons of a muscle pool in ascending order of their sizes when that pool of motoneurons receives a common, increasing input. This technical report is a survey of possible explanations of the size principle for recruitment of motor units. As a pre-study for further works, we collected existing explanations, suggested some new ones and collected them. According to the constitution of our own group, the report is divided into 2 parts: a collection from a physiological point of view and a collection from a more theoretical point of view. 2 Part II: The view of theoreticians 6 2.1 Explanations emerging from an optimization task or what recruitment by size is good

The size principle consists in the activation of motoneurons of a muscle pool in ascending order of their sizes when that pool of motoneurons receives a common, increasing input. This technical report is a survey of possible explanations of the size principle for recruitment of motor units. As a pre-study for further works, we collected existing explanations, suggested some new ones and collected them. According to the constitution of our own group, the report is divided into 2 parts: a collection from a physiological point of view and a collection from a more theoretical point of view. 2 Part II: The view of theoreticians 6 2.1 Explanations emerging from an optimization task or what recruitment by size is good

In this report we describe a self-organizing map to solve the mapping problem in a multiprocessor system with a distributed memory architecture. Experimental results for 2-dim lattice based processor networks are presented and the generalization of this approach to arbitrary processor topologies is discussed.