Spatial and spatiotemporal pattern formation in generalised turing systems

Computers and Mathematics with Applications

Volumn 32, Issue 11, 1996, Pages 71-77

  Maini, P K ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Boundary conditions; Limb development; Robustness; Spatially varying parameters; Tooth morphogenesis

Indexed keywords

BIOLOGICAL MATERIALS; BOUNDARY CONDITIONS; COMPUTER SIMULATION; ROBUSTNESS (CONTROL SYSTEMS); TURING MACHINES;

LIMB DEVELOPMENT; SPATIALLY VARYING PARAMETERS; TOOTH MORPHOGENESIS;

BIOLOGY;

EID: 0030394666     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(96)00198-8     Document Type: Article

References (31)

1. L. Wolpert, Positional information and the spatial pattern of cellular differentiation, J. Theor. Biol. 25, 1-47 (1969).
2. A.M. Turing, The chemical basis of morphogenesis, Phil. Trans. R. Soc. Lond. B237, 37-72 (1952).
3. G.F. Oster, J.D. Murray and A.K. Harris, Mechanical aspects of mesenchymal morphogenesis, J. Embryol. Exp. Morphol. 78, 83-125 (1983).
4. G.F. Oster, J.D. Murray and P.K. Maini, A model for chondrogenic condensations in the developing limb: The role of extracellular matrix and cell tractions, J. Embryol. Exp. Morphol. 89 (1985 93-112).
5. J.D. Murray, Mathematical Biology, Springer-Verlag, (1989).
6. R. Dillon, P.K. Maini and H.G. Othmer, Pattern formation in generalized Turing systems. I. Steady-state patterns in systems with mixed boundary conditions, J. Math. Biol. 32, 345-393 (1994).
7. J. Bard and I. Lauder, How well does Turing's theory of morphogenesis work?, J. Theor. Biol. 45, 501-521 (1974).
8. E. Doedel, AUTO: Software for continuation and bifurcation problems in ordinary differential equations, Technical Report, California Institute of Technology, (1986).
9. G.A. Ngwa, The analysis of spatial and spatio-temporal patterns in models for morphogenesis, D.Phil. Thesis, Oxford, (1993).
10. A. Gierer and H. Meinhardt, A theory of biological pattern formation, Kybernetika 12 (30-39).
11. M. Herschkowitz-Kaufman, Bifurcation analysis of nonlinear reaction diffusion equations - II. Steady state solutions and comparison with numerical simulations, Bull. Math. Biol. 37, 589-636 (1975).
12. A. Hunding, Bifurcations in Turing systems of the second kind may explain blastula cleavage plane orientation, J. Math. Biol. 25, 109-121 (1987).
13. A. Hunding, S.A. Kauffman and B.C. Goodwin, Drosphila segmentation: Supercomputer simulation of prepattern hierarchy, J. Theor. Biol. 145, 369-384 (1990).
14. TC Lacalli, Modeling the Drosphila pair-rule pattern by reaction-diffusion: Gap input and pattern control in a 4-morphogen system, J. Theor. Biol. 144, 171-194 (1990).
15. A. Hunding, and M. Brøns, Bifurcation in a spherical reaction-diffusion system with imposed gradient, Physica D 44, 285-302 (1990).
16. D.L. Benson, J.A. Sherratt and P.K. Maini, Diffusion driven instability in an inhomogeneous domain, Bull. Math. Biol. 55, 365-384 (1993).
17. D.L. Benson, P.K. Maini and J.A. Sherratt, Analysis of pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients, Mathl. Comput. Modelling 17 (12), 29-34 (1993).
18. P.K. Maini and M. Solursh, Cellular mechanisms of pattern formation in the developing limb, Int. Rev. Cytology 129, 91-133 (1991).
19. S.A. Newman, H.L. Frisch and J.K. Percus, On the stationary state analysis of reaction-diffusion mechanisms for biological pattern formation, J. Theor. Biol. 134, 183-197 (1988).
20. D.L. Benson, Reaction-diffusion models with spatially inhomogeneous diffusion coefficients, Ph.D. Thesis, Oxford, (1994).
21. L. Wolpert and A. Hornbruch, Double anterior chick limb buds and models for cartilage rudiment specification, Development 109, 961-966 (1990).
22. P.K. Maini, D.L. Benson and J.A. Sherratt, Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients, IMA J. Math. Appl. Med. & Biol. 9, 197-213 (1992).
23. P.K. Maini, Coupled models for spatial organization in development, Ber. Bunsenges. Phys. Chem. 98 (9), 1172-1175 (1994).
24. B. Westergaard and M.W.J. Ferguson, Development of the dentition in Alligator mississippiensis. Early embryonic development in the lower jaw, J. Zool. Lond. 210, 575-597 (1986).
25. B. Westergaard and M.W.J. Ferguson, Development of the dentition in Alligator mississippiensis. Later development in the lower jaws of embryos, hatchlings and young juveniles, J. Zool. Lond. 212, 191-222 (1987).
26. B. Westergaard and M.W.J. Ferguson, Development of the dentition in Alligator mississippiensis. Upper jaw dental and craniofacial development in embryos, hatchlings and young juveniles, Am. J. Anatomy 187, 393-421 (1990).
27. P.M. Kulesa, G.C. Cruywagen, S.R. Lubkin, P.K. Maini, M.W.J. Ferguson and J.D. Murray, On a model mechanism for the spatial patterning of tooth primordia in the Alligator, J. Theor. Biol. (to appear).
28. J. Schnakenberg, Simple chemical reaction systems with limit cycle behaviour, J. Theor. Biol. 81, 389-400 (1979).
29. B.C. Goodwin, S. Kauffman and J.D. Murray, Is morphogenesis an intrinsically robust process?, J. Theor. Biol 163, 135-144 (1993).
30. F. Brümmer, G. Zempel, P. Buhle, J.-C. Stein and D.F. Hulser, Retinoic acid modulates gap junction permeability: A comparative study of dye spreading and ionic coupling in cultured cells, Exp. Cell Res. 196, 158-163 (1991).
31. C.N.D. Coelho and R.A. Kosher, A gradient in gap junction communication along the anterior-posterior axis of the developing chick limb bud, Dev. Biol. 148, 529-535 (1991).