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  • 1
    Electronic Resource
    Electronic Resource
    Selective stabilization of muscle innervation during development: A mathematical model (1983)
    Springer
    Biological cybernetics 46 (1983), S. 207-215 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract The biochemical model presented concerns a critical step of the development of skeletal muscle innervation. After invasion of the muscle by exploratory motor axons, several nerve terminals converge from different motoneurons onto each muscle fibre at a single endplate. During the folloing weeks the redundant innervation disappears: a single nerve ending per muscle fibre becomes stabilized. The model is based on the assumption that the numbers of motoneurons and of muscle fibres remain constant during this evolution and that the selective stabilization of the adult connectivity results from the competition of the active nerve terminals for a postsynaptic retrograde factor μ. At the peak of the multiple innervation, the synthesis of μ by the muscle fiber stops, possibly as a consequence of muscle electrical and/or mechanical activity. The stock of μ becomes limited; a retrograde trans-synaptic diffusion of μ from the muscle to the nerve endings takes place. Within each nerve ending, μ enters into a chemical autocatalytic reaction which results in the production of a presynaptic stabilization factor s. The nerve impulses reaching the nerve terminal initiate this reaction. Any given nerve terminal become stabilized when the concentration of s reaches a threshold value. The mathematical analysis of the model shows that there exists a unique solution which is physically acceptable. Its application and computer simulation predict that only one nerve terminal becomes stabilized per muscle fibre. The model accounts for the experimental observations that the reduction in size of the motor units is not necessarily accompanied by a reduction in the variability of their size. The model also accounts for the acceleration or delay in regression which follows modifications of the chronic activity of the nerve endings and for the variability of the pattern of innervation observed in isogenic organisms. Plausible biochemical hypotheses concerning the factors engaged in the “selective stabilization” of the nerve-endings are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00336802
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the stock–recruitment relationships in fish population models (1998)
    Springer
    Environmental modeling and assessment 3 (1998), S. 87-93 
    Details
    ISSN: 1573-2967
    Keywords: population dynamics ; fishery ; stage-structured model ; stock–recruitment relationship
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract The framework of this article is modeling applied to fisheries. It aims at relating some classical stock–recruitment curves to a dynamic structured model, consisting of the adults stages of the stock and a pre-recruits stage (i.e., eggs, larvae, juveniles). The main result is that no functional stock–recruitment relationship can be found, unless further restrictive assumptions are added to the model (slow–fast dynamics and uniformity). Among the curves thus obtained is the Beverton–Holt curve, but not Ricker's.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019098319460
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    Paper (German National Licenses)
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