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  • 1
    Title: Mathematics applied to deterministic problems in the natural sciences; 1
    Author: Lin, C. C.
    Contributer: Segel, L. A.
    Publisher: Philadelphia, PA :SIAM,
    Year of publication: 1988
    Pages: 609 S.
    Series Statement: Classics in applied mathematics 1
    Type of Medium: Book
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 65 (1991), S. 487-500 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Presented here is a minimal biophysical cell model, based on work by Hodgkin and Huxley and by Rinzel, that can exhibit both excitable and oscillatory behavior. Two versions of the model are studied, which conform to data for squid and lobster giant axons.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 19 (1984), S. 125-132 
    ISSN: 1432-1416
    Keywords: Chemotaxis ; travelling bands
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for describing the motion of chemotactic bacteria in a capillary tube containing substrate is treated. Chemotactic substrate threshold effects are included in the chemotactic response coefficient. The ratio of the substrate threshold, s T, to the substrate level far ahead of the travelling band, s ∞, is used as a small parameter in developing an asymptotic solution of “near travelling wave” form.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 62 (2000), S. 717-757 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Autoinhibition of neurotransmitter release occurs via binding of transmitter to appropriate receptors. Experiments have provided evidence suggesting that the control of neurotransmitter release in fast systems is mediated by these inhibitory autoreceptors. Earlier, the authors formulated and analysed a mathematical model for a theory of release control in which these autoreceptors played a key role. The key experimental findings on which the release-control theory is based are: (i) the inhibitory autoreceptor has high affinity for transmitter under rest potential and shifts to low affinity upon depolarization; (ii) the bound (with transmitter) autoreceptor associates with exocytotic machinery Ex and thereby blocks it, preventing release of neurotransmitter. Release commences when depolarization shifts the autoreceptor to a low-affinity state and thereby frees Ex from its association with the autoreceptors. Here we extend the model that describes control of release so that it also accounts for release autoinhibition. We propose that inhibition is achieved because addition of transmitter, above its rest level, causes transition of the complex of autoreceptor and Ex to a state of stronger association. Relief of Ex from this state requires higher depolarization than from the weakly associated complex. In contrast to the weakly associated complex that only requires binding of transmitter to the autoreceptor to be formed, the transition to the strongly associated complex is induced by a second messenger, which is produced as a result of the receptor binding to transmitter. The theory explains the following experimental results (among others): for inhibition via transmitter or its agonists, the magnitude of inhibition decreases with depolarization; a plot of inhibition as a function of the concentration of muscarine (an acetylcholine agonist) yields an S-shaped curve that shifts to the right for higher depolarizations; the time course of release does not change when transmitter is added; the time course of release also does not change when transmitter antagonists are added, although quantal content increases; however, addition of acetylcholine esterase (an enzyme that hydrolyses acetylcholine) prolongs release.
    Type of Medium: Electronic Resource
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