Reaction-subdiffusion model of morphogen gradient formation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 6, 2010, Pages

  Yuste, S B ^a   Abad, E ^a   Lindenberg, Katja ^b  

^a UNIVERSITY OF EXTREMADURA   (Spain)

^b UNIVERSITY OF CALIFORNIA SAN DIEGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANOMALOUS DIFFUSION; CONCENTRATION PROFILES; CONSTANT RATE; CONTINUOUS TIME; GRADIENT FORMATION; LOCATION DEPENDENTS; MORPHOGEN; MORPHOGEN GRADIENTS; MORPHOGENS; RANDOM WALK MODELS; SOURCE POINTS; SPATIAL DEPENDENCE; STATIONARY CONCENTRATIONS; SUBDIFFUSION; WAITING TIME DISTRIBUTIONS;

DIFFUSION;

DEGRADATION;

EID: 78651468385     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.061123     Document Type: Article

References (44)

1. F. Crick, Nature (London) 225, 420 (1970). 10.1038/225420a0
2. J. B. Gurdon and P.-Y. Bourillot, Nature (London) 413, 797 (2001). 10.1038/35101500
3. O. Wartlick, A. Kicheva, and M. González-Gaitán, Cold Spring Harb. Perspect. Biol. 1, a001255 (2009) 10.1101/cshperspect.a001255
4. A. Kicheva, P. Pantazis, T. Bollenbach, Y. Kalaidzidis, T. Bittig, F. Jülicher, and M. González-Gaitán, Science 315, 521 (2007) 10.1126/science.1135774
5. S. R. Yu, M. Burkhardt, M. Nowak, J. Ries, Z. Petrek, S. Scholpp, P. Schwille, and M. Brand, Nature (London) 461, 533 (2009). 10.1038/nature08391
6. A. Eldar, D. Rosin, B.-Z. Shilo, and N. Barkai, Dev. Cell 5, 635 (2003). 10.1016/S1534-5807(03)00292-2
7. M. Ibañes and J. C. Izpisúa Belmonte, Mol. Syst. Biol. 4, 176 (2008). 10.1038/msb.2008.14
8. I. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen Phys. Rev. Lett. 93, 078102 (2004) 10.1103/PhysRevLett.93.078102
9. I. Golding and E. C. Cox, Phys. Rev. Lett. 96, 098102 (2006) 10.1103/PhysRevLett.96.098102
10. J. A. Dix and A. S. Verkman, Annu. Rev. Biophys. 37, 247 (2008) 10.1146/annurev.biophys.37.032807.125824
11. M. R. Horton, F. Höfling, J. O. Rädler, and T. Franosch, Soft Matter 6, 2648 (2010). 10.1039/b924149c
12. G. Hornung, B. Berkowitz, and N. Barkai, Phys. Rev. E 72, 041916 (2005). 10.1103/PhysRevE.72.041916
13. T. Bollenbach, K. Kruse, P. Pantazis, M. González-Gaitán, and F. Jülicher, Phys. Rev. Lett. 94, 018103 (2005). 10.1103/PhysRevLett. 94.018103
14. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000). 10.1016/S0370- 1573(00)00070-3
15. W. M. Saltzman and W. L. Olbricht, Nat. Rev. Drug Discovery 1, 177 (2002). 10.1038/nrd744
16. R. Metzler and J. Klafter, J. Phys. A 37, R161 (2004). 10.1088/0305-4470/37/31/R01
17. A. Yadav and W. Horsthemke, Phys. Rev. E 74, 066118 (2006). 10.1103/PhysRevE.74.066118
18. Y. Nec and A. A. Nepomnyashchy, J. Phys. A: Math. Theor. 40, 14687 (2007). 10.1088/1751-8113/40/49/005
19. S. Eule, R. Friedrich, F. Jenko, and I. M. Sokolov, Phys. Rev. E 78, 060102 (R) (2008). 10.1103/PhysRevE.78.060102
20. S. Fedotov, Phys. Rev. E 81, 011117 (2010). 10.1103/PhysRevE.81.011117
21. V. Mendez, S. Fedotov, and W. Horsthemke, Reaction-Transport Systems: Mesoscopic Foundation, Fronts, and Spatial Instabilities (Springer-Verlag, Berlin, 2010), p 82.
22. A. Yadav, S. M. Milu, and W. Horsthemke, Phys. Rev. E 78, 026116 (2008); 10.1103/PhysRevE.78.026116
23. M. O. Vlad and J. Ross, Phys. Rev. E 66, 061908 (2002). 10.1103/PhysRevE.66.061908
24. K. Seki, A. I. Shushin, M. Wojcik, and M. Tachiya, J. Phys.: Condens. Matter 19, 065117 (2007). 10.1088/0953-8984/19/6/065117
25. I. M. Sokolov, M. G. W. Schmidt, and F. Sagués, Phys. Rev. E 73, 031102 (2006). 10.1103/PhysRevE.73.031102
26. E. Abad, S. B. Yuste, and K. Lindenberg, Phys. Rev. E 81, 031115 (2010). 10.1103/PhysRevE.81.031115
27. S. B. Yuste and K. Lindenberg, Phys. Rev. E 76, 051114 (2007) 10.1103/PhysRevE.76.051114
28. R. Borrego, S. B. Yuste, and E. Abad, Phys. Rev. E 80, 061121 (2009) 10.1103/PhysRevE.80.061121
29. I. M. Zaid, M. A. Lomholt, and R. Metzler, Biophys. J. 97, 710 (2009). 10.1016/j.bpj.2009.05.022
30. B. I. Henry, T. A. M. Langlands, and S. L. Wearne, Phys. Rev. E 74, 031116 (2006). 10.1103/PhysRevE.74.031116
31. D. Froemberg and I. M. Sokolov, Phys. Rev. Lett. 100, 108304 (2008) 10.1103/PhysRevLett.100.108304
32. D. Froemberg and I. M. Sokolov, Acta Phys. Pol. B 41, 989 (2010).
33. R. Gorenflo and F. Mainardi, in Anomalous Transport, edited by, R. Klages,, G. Radons, and, I. M. Sokolov, (Wiley-VCH, Weinheim, 2008).
34. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).
35. D. Ben-Zvi and N. Barkai, Proc. Natl. Acad. Sci. U.S.A. 107, 6924 (2010). 10.1073/pnas.0912734107
36. T. Gregor, W. Bialek, R. R. de Ruyter van Steveninck, D. W. Tank, and E. F. Wieschaus, Proc. Natl. Acad. Sci. U.S.A. 102, 18403 (2005). 10.1073/pnas.0509483102
37. O. Grimm, M. Coppey, and E. Wieschaus, Development 137, 2253 (2010). 10.1242/dev.032409
38. F. Tostevin, P. R. ten Wolde, and M. Howard, PLOS Comput. Biol. 3, e78 (2007). 10.1371/journal.pcbi.0030078
39. T. E. Saunders and M. Howard, Phys. Rev. E 80, 041902 (2009). 10.1103/PhysRevE.80.041902
40. Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008) 10.1103/PhysRevLett.101.058101
41. M. Magdziarz, A. Weron, and K. Burnecki, Phys. Rev. Lett. 103, 180602 (2009) 10.1103/PhysRevLett.103.180602
42. J. Szymanski and M. Weiss, Phys. Rev. Lett. 103, 038102 (2009) 10.1103/PhysRevLett.103.038102
43. S. C. Weber, A. J. Spakowitz, and J. A. Theriot, Phys. Rev. Lett. 104, 238102 (2010). 10.1103/PhysRevLett.104.238102
44. A. Lubelski and J. Klafter, Biophys. J. 94, 4646 (2008). 10.1529/biophysj.107.119081