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  • 1
    Digitale Medien
    Digitale Medien
    Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells—I. Reduced systems (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 665-686 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This study is related to a model describing the behavior of barium-treatedAplysia neurons generating regular burst-plateau patterns. The model is represented by an autonomous dynamical system, defined inR 4 and depending on a small parameter. This paper is restricted to the qualitative study of three “reduced systems” deduced from the “complete system”. Part of the study is performed with the use of the qualitative theory of singular perturbations. The predicted behaviors are compared with experimental results.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462421
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells. II. Complete system (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 221-238 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper deals with a model describing the behavior of barium-treatedApalysia neurons. The model is represented by a dynamical system, so-called “complete system”, defined in R4 and depending on a small parameter. The study of this system under zero membrane current conditions was performed with the use of the qualitative theory of singular perturbations. We show that this system has a stable periodic solution of the discontinuous type when the small parameter tends to 0+. A reduced system defined in R3, associated to the complete system was also studied: it corresponds to a constant activation of the inward current. We demonstrate that the corresponding hypothetical cell remains silent under zero current conditions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02464639
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Qualitative study of a dynamical system for metrazol-induced paroxysmal depolarization shifts (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 903-922 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The convulsant pentylenetetrazol (PTZ) was used to trigger spike bursts and paroxysmal discharges inAplysia neurons. Voltage clamp experiments showed that PTZ induced a slow voltage-dependent potassium current and a persistent inward current. These currents are incorporated into a membrane model together with modified spike-generating Hodgkin-Huxley equations. From these data a metaphoric model is constructed and represented by a slow-fast dynamical system defined inR 4. With some values of the main physiological parameters, the system might have limit cycles for the fast dynamic. A qualitative study of the system shows that it satisfactorily reproduces the various observed patterns produced by PTZ.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02462078
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    An asymmetrical kinetic model for veratridine interactions with sodium channels in molluscan neurons (1982)
    Springer
    Bulletin of mathematical biology 44 (1982), S. 231-258 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Veratridine alkaloid induces bi-stability or saw-tooth-shaped long potential waves in molluscan neurons. Voltage clamp experiments reveal the production of a slow sodium current whose changes are described by an asymmetric kinetic diagram relating the states of the sodium channels. Methods of the qualitative theory of differential equations were used to determine the condition necessary for such a model to have either an oscillatory solution or a bi-stable behavior. The kinetic diagram was modified to account for the frequency dependence of the slow sodium current production upon repeated short depolarizations. The modified kinetic diagram suggests that open and inactivated sodium channels are turned into channels with slow kinetic parameters; the transition from open channels would be fast, irreversible and restricted to part of the open channels, whereas that from inactivated channels would be slow and fully reversible upon repolarization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02463249
    Standort Signatur Erwartet Verfügbarkeit
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