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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 86 (1982), S. 2954-2958 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 440 (2006), S. 999-1000 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Neurons encode and transmit information by generating action potentials, or ‘spikes’ of voltage that sweep along their membranes (Box 1). It has been 50 years since Hodgkin and Huxley proposed a mechanistic model by which such spikes are generated in an electrically excitable membrane. The ...
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 60 (1998), S. 449-475 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We studied mathematical models for the length distributions of actin filaments under the effects of polymerization/depolymerization, and fragmentation. In this paper, we emphasize the effects of these two processes acting alone. In this case, simple discrete and continuous models can be derived and solved explicitly (in several special cases), making the problem interesting from a modeling and pedagogical point of view. In a companion paper (Ermentrout and Edelstein-Keshet, 1998, Bull. Math. Biol. 60, 477–503) we investigate what happens when the processes act together, with particular attention to fragmentation by gelsolin, and with a greater level of biological detail.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 60 (1998), S. 477-503 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a previous paper, we studied elementary models for polymerization, depolymerization, and fragmentation of actin filaments (Edelstein-Keshet and Ermentrout, 1998, Bull. Math. Biol. 60, 449–475). When these processes act together, more complicated dynamics occur. We concentrate on a particular case study, using the actin-fragmenting protein gelsolin. A set of biological parameter values (drawn from the experimental literature) is used in computer simulations of the kinetics of gelsolin-mediated actin filament fragmentation.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 353 (1991), S. 220-220 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] SIR - lan Stewart in News and Views1 claims that Mirollo and Strogatz2 have developed a theory that can explain the synchronization of huge congregations of South East Asian fireflies (Pteroptyx malaccae) as well as hippocampal neurons, menstrual cycles and the insulin-secreting cells of the ...
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 12 (1981), S. 327-342 
    ISSN: 1432-1416
    Keywords: Integrate and fire ; Oscillations ; Phase-locking ; Perturbation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two weakly coupled oscillators are studied and the existence of n:m phase-locked solutions is shown. With the use of a slow time scale, the problem is reduced to a two-dimensional system on an invariant attracting torus. This system is further reduced to a one-dimensional dynamical system. Fixed points of this system correspond to n:m phase-locked solutions. The method is applied to a forced oscillator, linearly coupled λ-ω systems, and a pair of integrate and fire neuron models.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 40 (2000), S. 64-96 
    ISSN: 1432-1416
    Keywords: Key words: Actin polymerization – Treadmilling – Spatial distribution of actin – Polymerization kinetics – Mathematical models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  We investigate the polymerization kinetics of rod-like polymer filaments interacting with a distribution of monomer in one spatial dimension (e.g. along a narrow tube). We consider a variety of possible cases, including competition by the filament tips for the available monomer, and behaviour analogous to “treadmilling” in which the polymer adds subunits to one end and loses them at the other end so as to maintain a constant length. Applications to biological polymers such as actin filaments and microtubules are discussed.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 22 (1985), S. 1-9 
    ISSN: 1432-1416
    Keywords: Oscillations ; phaselocking ; phase models ; all-to-all coupling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An exact solution to a model of mutually interacting sinusoidal oscillators is found. Limits on the variation of the native frequencies are determined in order for synchronization to occur. These limits are computed for different distributions of native frequencies.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 29 (1990), S. 33-58 
    ISSN: 1432-1416
    Keywords: Cell motion ; Contact response ; Pattern formation ; Cell alignment ; Parallel arrays ; Biological cellular automata ; Integro-partial differential equation models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Kinetic continuum models are derived for cells that crawl over a 2D substrate, undergo random reorientation, and turn in response to contact with a neighbor. The integro-partial differential equations account for changes in the distribution of orientations in the population. It is found that behavior depends on parameters such as total mass, random motility, adherence, and sloughing rates, as well as on broad aspects of the contact response. Linear stability analysis, and numerical, and cellular automata simulations reveal that as parameters are varied, a bifurcation leads to loss of stability of a uniform (isotropic) steady state, in favor of an (anisotropic) patterned state in which cells are aligned in parallel arrays.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 10 (1980), S. 97-100 
    ISSN: 1432-1416
    Keywords: Reaction diffusion equations ; Wave-trains ; Stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Summary Stability of a class of solutions to reaction-diffusion equations is studied numerically. It is found that the solutions do not persist under a variety of boundary conditions.
    Type of Medium: Electronic Resource
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