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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 41 (1979), S. 257-282 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Adaptation of repetitively firing sensory neurons and nerve models is correlated with specific inhibitory feedback phenomena—an electrogenic sodium pump, and post synaptic self inhibition. The quality of the adaptive responses depends on the excitation properties of the neuron in the interspike interval, or the description of these properties by the underlying impulse encoder model. THis model dependence is demonstrated by comparisons of the behavior of two classes of models; the “leaky integrator models” which assume a passive neural membrane, and the “variable-γ models”, for which the neural state of excitation varies according to first order differential equations. The complexity inherent in the variable-γ models is effectively boiled down to mathematically simple relationships which are derived from studies of the neural- and model frequency responses to small amplitude sinusoidal stimuli. It is argued, and supported with examples, that these relationships hold for impulse frequency transients resulting from more general stimulus conditions. Expressions are then derived which permit feedback parameters to be determined from impulse frequency data. In this connection, recent studies of neural dynamics are brought to bear to resolve ambiguities in data interpretation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 13 (1973), S. 104-112 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract A model for neuronal encoders is presented. Its mathematical description consists of two coupled first order, non-linear differential equations giving the time course of the membrane potential and of a leak function under conditions of continuous drive. The leak function is given by the ratio of the transmembrane conductance to the effective encoder capacitance and is closely tied to the Hodgkin-Huxley results on the behavior of g K and g Na. Since neuronal impulse encoding does not in general proceed in a space clamped region, the values of membrane potential and “leak” entering the differential equations are those at the trigger zone. The effects of electrotonic spread are then incorporated in the leak function. A particularly simple two parameter form of the model is explicitly written. By changing the value of one of the parameters the properties of the model change from that of exhibiting all features of rapid adaptation to those of tonic repetitive firing. Predictions of the model are discussed, as is the relationship between properties of the model and features of voltage clamp data.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    The journal of membrane biology 70 (1982), S. 115-123 
    ISSN: 1432-1424
    Keywords: surface charge ; calcium binding ; potassium channel ; axon membrane ; surface potential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Summary The calcium binding constant associated with external surface charge in a position to influence the voltage sensing charges for potassium channel gating appears to be ∼30 molar−1, a value much larger than previously thought and in approximate agreement with that found for artificial membranes composed of the lipid brain phosphatidylserene. Fixed charge on the periaxonal membrane surface is distributed in such a way that much larger charges occur at a distance of at least 8 angstroms from the channel pore openings. The separation between the ion pathway and the channel gating charge appears to be greater than or equal to 8 angstroms. Periaxonal surface charge which is in a position to determine the surface potential for gating has a magnitude greater than or equal to one (negative) electronic charge per 182 square angstrom before calcium binding, which is reduced to −e/625 Å in a normal divalent ionic environment. With the normal divalent ionic composition of seawater the surface potential at a position to influence the gating voltage sensor is ∼−15 millivolts relative to the bulk external potential. The external surface potential is ∼−3 mV at the pore mouth. There appears to be a negligible amount of fixed charge on the axoplasmic surface in the vicinity of the ion channel opening. Further, our results confirm earlier measurements that have given a negligible amount of axoplasmic surface fixed charge whose field components would be in a position to influence the channel gating charges.
    Type of Medium: Electronic Resource
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  • 4
    Publication Date: 1973-09-01
    Print ISSN: 0340-1200
    Electronic ISSN: 1432-0770
    Topics: Biology , Computer Science , Physics
    Published by Springer
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