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  • 1
    Electronic Resource
    Electronic Resource
    On growth and form (1995)
    [s.l.] : Nature Publishing Group
    Nature 375 (1995), S. 745-746 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] HANS Meinhardt has achieved the remarkable feat of producing a book worthy of the coffee-table yet replete with partial differential equations. His topic is the diversity of pigment patterns on tropical sea shells. A mollusc enlarges its shell only at the edge; ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/375745a0
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  • 2
    Electronic Resource
    Electronic Resource
    Models for embryonic periodicity (1995)
    Springer
    Bulletin of mathematical biology 57 (1995), S. 947-948 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458305
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  • 3
    Electronic Resource
    Electronic Resource
    CaEGTA uncompetitively inhibits calcium activation of whorl morphogenesis inAcetabularia (1997)
    Springer
    Protoplasma 196 (1997), S. 190-196 
    Details
    ISSN: 1615-6102
    Keywords: Acetabularia acetabulum ; Whorl morphogenesis ; Reaction-diffusion ; EGTA ; Calcium receptors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary The spacing between adjacent hairs in vegetative whorls ofAcetabularia acetabulum (formerlyA. mediterranea) was earlier reported as being quantitatively responsive to calcium ion concentration in the culture medium. We here report a quantitative response to the concentration of the calcium-chelator EGTA, in the opposite sense to the effect of calcium. (Increasing [Ca2+] diminishes the spacing; increasing [EGTA] increases it.) The earlier work was interpreted in terms of control of the spacing by a putative reaction-diffusion mechanism in the cell membrane, in which a receptor R was activated by calcium-binding to initiate the process. We extend this interpretation by treating CaEGTA as an uncompetitive inhibitor of the effect of calcium on R. This leads to thermodynamic constants for CaEGTA binding to the CaR complex: ΔH 298 0 =−250 ± 60 kJ/mol; ΔS 298 0 =−820 ± 200 J/mol · K. Consistency of the concentration and temperature dependences reported here with the postulated dynamic mechanism increases the probability that this mechanism is correct.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01279567
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  • 4
    Electronic Resource
    Electronic Resource
    Computations of post-inductive dynamics in axolotl heart formation (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Developmental Dynamics 200 (1994), S. 242-256 
    Details
    ISSN: 1058-8388
    Keywords: Axolotl ; Heart localization ; Reaction-diffusion ; Heart induction ; Ambystoma ; Cardiac lethal ; Gierer-Meinhardt ; Organogenesis ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: This paper reports modelling of heart localization in the axolotl (Ambystoma mexicanum). The region of heart specification in the mesoderm defined by classical induction from the endoderm is larger than the area of final myocardial differentiation. For localizing the area of differentiation within the area of specification, we postulate a mesoderm in response to induction from the endoderm. This mechanism generates a spatial pattern for two chemicals, an activator and an inhibitor, corresponding to the area of myocardial differentiation. We postulate a diffusible chemical rescuer, which is absent in the cardiac lethal mutant, and which is a precursor to the reaction-diffusion mechanism. The activator, inhibitor, rescuer, and product of endodermal induction are presented in an enzyme mechanism with rate equations similar to the Gierer-Meinhardt equations. These equations were solved numerically in both one and two spatial dimensions. We have attained quantitative agreement with the experimental data for sizes of tissue regions and for times to heartbeat. Experiments modelled include wild-type heart localization as well as both in vitro and in vivo rescue of cardiac lethal mesoderm with wild-type mesoderm. Based upon the parameters necessary to model heart localization, we make a series of predictions. We predict: a specific profile for the endodermal inducer gradient; the possibility of producing multiple hearts in vivo; and a greater contribution to the heart from the wild-type mesoderm for in vivo transplants with cardiac lethal mesoderm. We make some suggestions as to the possible chemical nature of the substances in the model. We indicate that the inhibitory field and mechanochemical theories are probably not as promising as reaction-diffusion for the mechanism of heart localization. © 1994 Wiley-Liss, Inc.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aja.1002000306
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  • 5
    Electronic Resource
    Electronic Resource
    Hair morphogenesis inAcetabularia mediterranea: Temperature-dependent spacing and models of morphogen waves (1981)
    Springer
    Protoplasma 106 (1981), S. 211-221 
    Details
    ISSN: 1615-6102
    Keywords: Morphogenesis ; Acetabularia ; Morphogenetic models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary Whorls of sterile hairs inA. mediterranea show, at the moment of first appearance of hair initials, a spacing independent of number of hairs in the whorl but dependent on temperature. By changing the temperature at various times before appearance of hair initials, the pattern-forming event can be located at about 3–4 hours before initials become visible. The temperature dependence of spacing is like that of a chemical rate parameter: In (spacing)versus 1/T is linear. This suggests that the spacing is controlled by kinetic rather than structural factors, and correlates well with reaction-diffusion theory. Mathematical analysis and computer simulation have been used to show that the observed sequence of tip-flattening followed by whorl initiation can be interpreted in terms of published models for generation of “dissipative structures” by reaction and diffusion, and that at least two sequential processes must occur, the first of which shifts growth activity from extremity to circumference of the growing tip, permitting the second to operate around the circumference.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01275553
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  • 6
    Electronic Resource
    Electronic Resource
    Stripe selection: An intrinsic property of some pattern-forming models with nonlinear dynamics (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    American Journal of Anatomy 195 (1992), S. 201-215 
    Details
    ISSN: 0002-9106
    Keywords: Striped patterns ; Nonlinear dynamics ; Reaction-diffusion ; Ocular dominance ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Medicine
    Notes: In two-dimensional pattern formation, the genesis of striped rather than spotted patterns may involve preexisting spatial asymmetries, such as unidirectional gradients or asymmetric shape of the pattern-forming domain. In the absence of such asymmetries, some kinds of nonlinear dynamics still lead to striped rather than spotted patterns. We have studied the latter effect both by extensive computer experiments on a range of nonlinear models and by mathematical analysis. We conclude that, when the dynamic equations are written in terms of departure from the unpatterned state, the presence of nonlinearities which are odd functions of these departures (e.g., cubic terms) together with absence of even nonlinearities (e.g., quadratic terms) ensures stripe formation. In computer experiments, we have studied the dynamics of two-morphogen reaction-diffusion models. The mathematical analysis presented in the Appendix shows that the same property exists in more generalized models for pattern formation in the primary visual cortex. © 1993 Wiley-Liss, Inc.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aja.1001950306
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  • 7
    Electronic Resource
    Electronic Resource
    Where may reaction-diffusion mechanisms be operating in metameric patterning of Drosophila embryos? (1988)
    New York, NY : Wiley-Blackwell
    BioEssays 8 (1988), S. 118-124 
    Details
    ISSN: 0265-9247
    Keywords: Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Medicine
    Notes: Two general features of metameric patterning in Drosophilaare considered: (1) maintenance of a constant number of metameres (segments or parasegments) in the face of variation in length of the embryo; (2) expression of pattern by on-off switchings of particular genes, with only three or four rows of cells to each element of pattern. For each of these features, the general strategic question is raised: could reaction-diffusion theory account for this? In both cases, it is answered affirmatively. For the second feature, this review contains some hitherto unpublished computer simulations by one of us (K. Y. T.), illustrating that a reaction-diffusion mechanism can be transformed into a patterned switching mechanism by nothing more than compartmenting of the diffusion region. For the scale of three compartments to one pattern repeat unit (representing three rows of cells to a segment) the switching pattern predicted by computation is two-off to one-on. This resembles the pattern of expression of the engrailed gene, posteriorly localized in each segment.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bies.950080407
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  • 8
    Electronic Resource
    Electronic Resource
    Bioaccumulation and excretion of arsenic compounds by a marine unicellular alga, polyphysa peniculus (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Applied Organometallic Chemistry 8 (1994), S. 313-324 
    Details
    ISSN: 0268-2605
    Keywords: Arsenic species ; arsenic uptake ; arsenic methylation ; Polyphysa peniculus ; arsenic bioaccumulation ; non-reducible arsenicals ; Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Polyphysa peniculus was grown in artificial seawater in the presence of arsenate, arsenite, monomethylarsonate and dimethylarsinic acid. The separation and identification of some of the arsenic species produced in the cells as well as in the growth medium were achieved by using hydride generation-gas chromatography-atomic absorption spectrometry methodology. Arsenite and dimethylarsinate were detected following incubation with arsenate. When the alga was treated with arsenite, dimethylarsinate was the major metabolite in the cells and in the growth medium; trace amounts of monomethylarsonate were also detected in the cells. With monomethylarsonate as a substrate, the metabolite is dimethylarsinate. Polyphysa peniculus did not metabolize dimethylarsinic acid when it was used as a substrate. Significant amounts of more complex arsenic species, such as arsenosungars, were not observed in the cells or medium on the evidence of flow injection-microwave digestion-hydride generation-atomic absorption spectrometry methodology. Transfer of the exposed cells to fresh medium caused release of most cell-associated arsenicals to the surrounding environment.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aoc.590080406
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