Homogeneous auxin steady states and spontaneous oscillations in flux-based auxin transport models

SIAM Journal on Applied Dynamical Systems

Volumn 12, Issue 3, 2013, Pages 1330-1353

  Farcot, Etienne ^a,b   Yuan, Yuan ^c  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b Virtual Plants Inria Team   (France)

^c MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Active transport; Auxin; Bifurcations

Indexed keywords

ACTIVE TRANSPORT; ASYMPTOTICALLY STABLE; AUXIN; AUXIN TRANSPORT; SPONTANEOUS OSCILLATIONS; STABLE OSCILLATIONS; STEADY STATE; ZERO FLUX;

BIFURCATION (MATHEMATICS); HOPF BIFURCATION;

TISSUE;

EID: 84884940801     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/120891538     Document Type: Article

References (29)

1. J. Bang-Jensen and G. Gutin, Digraphs. Theory, Algorithms and Applications, 2nd ed., Springer-Verlag, New York, 2009.
2. E. M. Bayer, R. S. Smith, T. Mandel, N. Nakayama, M. Sauer, P. Prusinkiewicz, and C. Kuhlemeier, Integration of transport-based models for phyllotaxis and midvein formation, Genes Development, 23 (2009), pp. 373-384.
3. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, 2nd ed., SIAM, Philadelphia, 1994.
4. K. B. Blyuss, The effects of symmetry on the dynamics of antigenic variation, J. Math. Biol., 66 (2013), pp. 115-137.
5. C. O. Buckee and S. Gupta, A Network Approach to Understanding Pathogen Population Structure, Infectious Disease Informatics, Springer, New York, 2010.
6. P.-L. Buono and V. G. LeBlanc, Realization of critical eigenvalues for scalar and symmetric linear delay-differential equations, SIAM J. Appl. Dyn. Syst., 7 (2008), pp. 1323-1354.
7. I. De Smet, T. Tetsumura, B. De Rybel, N. F. Frey, L. Laplaze, I. Casimiro, R. Swarup, M. Naudts, S. Vanneste, D. Audenaert, D. Inze, M. J. Bennett, and T. Beeckman, Auxindependent regulation of lateral root positioning in the basal meristem of Arabidopsis, Development, 134 (2007), pp. 681-690.
8. D. Draelants, J. Broeckhove, G. T. S. Beemster, and W. Vanroose, Numerical bifurcation analysis of the pattern formation in a cell based auxin transport model, J. Math. Biol., 2012, DOI 10.1007/S00285-012-0588-8.
9. C. Feller, J. P. Gabriel, C. Mazza, and F. Yerly, Pattern formation in auxin flux, J. Math. Biol., 2013, DOI 10.1007/S00285-013-0655-9.
10. F. G. Feugier, A. Mochizuki, and Y. Iwasa, Self-organization of the vascular system in plant leaves: Inter-dependent dynamics of auxin flux and carrier proteins, J. Theoret. Biol., 236 (2005), pp. 366-375.
11. N. Geldner, J. Friml, Y.-D. Stierhof, G. Jurgens, and K. Palme, Auxin transport inhibitors block PIN1 cycling and vesicle trafficking, Nature, 413 (2001), pp. 425-428.
12. S. Guo and Y. Yuan, Pattern formation in a ring network with delay, Math. Models Methods Appl. Sci., 10 (2009), pp. 1797-1852.
13. H. Jonsson, M. Heisler, B. E. Shapiro, E. M. Meyerowitz, and E. Mjolsness, An auxin-driven polarized transport model for phyllotaxis, Proc. Natl. Acad. Sci. USA, 103 (2006), pp. 1633-1638.
14. P. Krupinski and H. Jonsson Modeling auxin-regulated development, Cold Spring Harb. Perspect. Biol., 2 (2010), a001560.
15. R. M. H. Merks, Y. Van de Peer, D. Inze, and G. T. S. Beemster, Canalization without flux sensors: A traveling-wave hypothesis, TRENDS Plant Sci., 12 (2007), pp. 384-390.
16. M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks, Princeton University Press, Princeton, NJ, 2010.
17. A. M. Middleton, J. R. King, M. J. Bennett, and M. R. Owen, Mathematical modelling of the Aux/IAA negative feedback loop, Bull. Math. Biol., 72 (2010), pp. 1383-1407.
18. V. V. Mironova, N. A. Omelyanchuk, G. Yosiphon, S. I. Fadeev, N. A. Kolchanov, E. Mjolsness, and V. A. Likhoshvai, A plausible mechanism for auxin patterning along the developing root, BMC Systems Biol., 4 (2010), p. 98.
19. G. J. Mitchison, A model for vein formation in higher plants, Proc. R. Soc. Lond. B, 207 (1980), pp. 79-109.
20. G. J. Mitchison, The dynamics of auxin transport, Proc. R. Soc. Lond. B, 209 (1980), pp. 489-511.
21. G. J. Mitchison, The polar transport of auxin and vein patterns in plants, Philos. Trans. R. Soc. Lond. B, 295 (1981), pp. 461-471.
22. M. A. Moreno-Risueno, J. M. Van Norman, A. Moreno, J. Zhang, S. E. Ahnert, and P. N. Benfey, Oscillating gene expression determines competence for periodic Arabidopsis root branching, Science, 329 (2010), pp. 1306-1311.
23. P. Prusinkiewicz, S. Crawford, R. S. Smith, K. Ljung, T. Bennett, V. Ongaro, and O. Leyser, Control of bud activation by an auxin transport switch, Proc. Natl. Acad. Sci. USA, 106 (2009), pp. 17431-17436.
24. A. G. Rolland-Lagan and P. Prusinkiewicz, Reviewing models of auxin canalization in the context of leaf vein pattern formation in arabidopsis, Plant J., 44 (2005), pp. 854-865.
25. P. Sahlin, B. Soderberg, and H. Jonsson, Regulated transport as a mechanism for pattern generation: Capabilities for phyllotaxis and beyond, J. Theoret. Biol., 258 (2009), pp. 60-70.
26. R. S. Smith, S. Guyomarc'h, T. Mandel, D. Reinhardt, C. Kuhlemeier, and P. Prusinkiewicz, A plausible model of phyllotaxis, Proc. Natl. Acad. Sci. USA, 103 (2005), pp. 1301-1306.
27. S. Stoma, M. Lucas, J. Chopard, M. Schaedel, J. Traas, and C. Godin, Flux-based transport enhancement as a plausible unifying mechanism for auxin transport in meristem development, PLoS Comput. Biol., 4 (2008), e1000207.
28. A. M. Turing, The chemical basis of morphogenesis, Philos. Trans. R. Soc. London, 237 (1952), pp. 37-72.
29. T. Vernoux, F. Besnard, and J. Traas, Auxin at the shoot apical meristem, Cold Spring Harb. Perspect. Biol., 2 (2010), a001487.