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  • 1
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    Self-organizing and stochastic behaviors during the regeneration of hair stem cells (2011)
    American Association for the Advancement of Science (AAAS)
    Details
    Publication Date: 2011-04-30
    Description: Stem cells cycle through active and quiescent states. Large populations of stem cells in an organ may cycle randomly or in a coordinated manner. Although stem cell cycling within single hair follicles has been studied, less is known about regenerative behavior in a hair follicle population. By combining predictive mathematical modeling with in vivo studies in mice and rabbits, we show that a follicle progresses through cycling stages by continuous integration of inputs from intrinsic follicular and extrinsic environmental signals based on universal patterning principles. Signaling from the WNT/bone morphogenetic protein activator/inhibitor pair is coopted to mediate interactions among follicles in the population. This regenerative strategy is robust and versatile because relative activator/inhibitor strengths can be modulated easily, adapting the organism to different physiological and evolutionary needs.〈br /〉〈br /〉〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3321266/" target="_blank"〉〈img src="https://static.pubmed.gov/portal/portal3rc.fcgi/4089621/img/3977009" border="0"〉〈/a〉   〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3321266/" target="_blank"〉This paper as free author manuscript - peer-reviewed and accepted for publication〈/a〉〈br /〉〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Plikus, Maksim V -- Baker, Ruth E -- Chen, Chih-Chiang -- Fare, Clyde -- de la Cruz, Damon -- Andl, Thomas -- Maini, Philip K -- Millar, Sarah E -- Widelitz, Randall -- Chuong, Cheng-Ming -- AR47364/AR/NIAMS NIH HHS/ -- AR60306/AR/NIAMS NIH HHS/ -- R01 AR042177/AR/NIAMS NIH HHS/ -- R01 AR042177-17/AR/NIAMS NIH HHS/ -- R01 AR042177-18/AR/NIAMS NIH HHS/ -- R01 AR060306/AR/NIAMS NIH HHS/ -- R01 AR060306-02/AR/NIAMS NIH HHS/ -- R01 AR060306-03/AR/NIAMS NIH HHS/ -- R01-AR42177/AR/NIAMS NIH HHS/ -- R01-AR47709/AR/NIAMS NIH HHS/ -- New York, N.Y. -- Science. 2011 Apr 29;332(6029):586-9. doi: 10.1126/science.1201647.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉Department of Pathology, University of Southern California (USC), Los Angeles, CA 90033, USA.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/21527712" target="_blank"〉PubMed〈/a〉
    Keywords: Animals ; Bone Morphogenetic Proteins/*metabolism ; Computer Simulation ; Hair Follicle/*cytology/*growth & development/metabolism ; Mice ; Mice, Inbred C57BL ; Mice, Transgenic ; Models, Biological ; Rabbits ; *Regeneration ; *Signal Transduction ; Stem Cells/*physiology ; Stochastic Processes ; Wnt Proteins/*metabolism
    Print ISSN: 0036-8075
    Electronic ISSN: 1095-9203
    Topics: Biology , Chemistry and Pharmacology , Computer Science , Medicine , Natural Sciences in General , Physics
    Published by American Association for the Advancement of Science (AAAS)
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  • 2
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    Nonlinear effects on Turing patterns: Time oscillations and chaos (2012)
    American Physical Society (APS)
    Details
    Publication Date: 2012-08-09
    Description: Author(s): J. L. Aragón, R. A. Barrio, T. E. Woolley, R. E. Baker, and P. K. Maini We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying ... [Phys. Rev. E 86, 026201] Published Wed Aug 08, 2012
    Keywords: Chaos and pattern formation
    Print ISSN: 1539-3755
    Electronic ISSN: 1550-2376
    Topics: Physics
    Published by American Physical Society (APS)
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  • 3
    Electronic Resource
    Electronic Resource
    Pattern formation in a generalized chemotactic model (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 1-26 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1997.0010
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  • 4
    Electronic Resource
    Electronic Resource
    Enzyme kinetics at high enzyme concentration (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 483-499 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt ≈ 0 for the basic enzyme reaction at high enzyme concentration. For the first time, an approximate solution for the concentrations of the reactants uniformly valid in time is reported. Numerical simulations are presented to verify this solution. We show that an analytical approximation can be found for the reactants for each initial condition using the appropriate quasi-steady-state assumption. An advantage of the present formalism is that it provides a new procedure for fitting experimental data to determine reaction constants. Finally, a new necessary criterion is found that ensures the validity of the reverse quasi-steady-state assumption. This is verified numerically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0163
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  • 5
    Electronic Resource
    Electronic Resource
    A chemotactic model for the advance and retreat of the primitive streak in avian development (2000)
    Springer
    Bulletin of mathematical biology 62 (2000), S. 501-525 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The formation of the primitive streak in early avian development marks the onset of gastrulation, during which large scale cell movement leads to a trilaminar blastoderm comprising prospective endodermal, mesodermal and ectodermal tissue. During streak formation a specialized group of cells first moves anteriorly as a coherent column, beginning from the posterior end of the prospective anterior-posterior axis (a process called progression), and then reverses course and returns to the most posterior point on the axis (a process called regression). To date little is known concerning the mechanisms controlling either progression or regression. Here we develop a model in which chemotaxis directs the cell movement and which is capable of reproducing the principal features connected with progression and regression of the primitive streak. We show that this model exhibits a number of experimentally-observed features of normal and abnormal streak development, and we propose a number of experimental tests which may serve to illuminate the mechanisms. This paper represents the first attempt to model the global features of primitive streak formation, and provides an initial stage in the development of a more biologically-realistic discrete cell model that will allow for variation of properties between cells and control over movement of individual cells.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1999.0166
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  • 6
    Electronic Resource
    Electronic Resource
    Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation (1991)
    Springer
    Bulletin of mathematical biology 53 (1991), S. 701-719 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989,J. exp. Zool. 251, 186–202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461550
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  • 7
    Electronic Resource
    Electronic Resource
    A two-dimensional numerical study of spatial pattern formation in interacting Turing systems (1999)
    Springer
    Bulletin of mathematical biology 61 (1999), S. 483-505 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract For many years Turing systems have been proposed to account for spatial and spatiotemporal pattern formation in chemistry and biology. We extend the study of Turing systems to investigate the rôle of boundary conditions, domain shape, non-linearities, and coupling of such systems. We show that such modifications lead to a wide variety of patterns that bear a striking resemblance to pigmentation patterns in fish, particularly those involving stripes, spots and transitions between them. Using the Turing system as a metaphor for activator—inhibitor models we conclude that such a mechanism, with the aforementioned modifications, may play a rôle in fish patterning.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/bulm.1998.0093
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  • 8
    Electronic Resource
    Electronic Resource
    Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios (1988)
    Springer
    Journal of mathematical biology 26 (1988), S. 689-703 
    Details
    ISSN: 1432-1416
    Keywords: Michaelis Menten approximation ; Quasi-steady state assumption ; Scaling ; Singular perturbations ; Fast and slow timescales
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276148
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  • 9
    Electronic Resource
    Electronic Resource
    Spatial and spatio-temporal patterns in a cell-haptotaxis model (1989)
    Springer
    Journal of mathematical biology 27 (1989), S. 507-522 
    Details
    ISSN: 1432-1416
    Keywords: Morphogenesis ; Spatio-temporal pattern ; Mechanochemical ; Haptotaxis ; Singular dispersion relation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00288431
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  • 10
    Electronic Resource
    Electronic Resource
    Nonlinear pattern selection in a mechanical model for morphogenesis (1986)
    Springer
    Journal of mathematical biology 24 (1986), S. 525-541 
    Details
    ISSN: 1432-1416
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a technique for mode selection based on linear analysis and show that, in many cases, it is a reliable predictor for nonlinear mode selection. In order to determine the set of model parameters that can generate a particular pattern we develop a technique based on nonlinear least square fitting to a dispersion relation. As an application we present a scenario for sequential pattern formation of dermal aggregations in chick embryos which leads to the hexagonal array of cell aggregations observed in feather germ formation in vivo.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275682
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