A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line

Journal of Mathematical Biology

Volumn 71, Issue 1, 2015, Pages 171-214

  Di Costanzo, E ^a   Natalini, R ^b   Preziosi, L ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b CNR   (Italy)

^c POLITECNICO DI TORINO   (Italy)

Author keywords

Cell migration; Cellular signaling; Embryogenesis; Neuromast formation; Self organization; Zebrafish

Indexed keywords

FIBROBLAST GROWTH FACTOR; FIBROBLAST GROWTH FACTOR RECEPTOR; ZEBRAFISH PROTEIN;

ANIMAL; BIOLOGICAL MODEL; BIOLOGY; CELL AGGREGATION; CELL MOTION; COMPUTER SIMULATION; CYTOLOGY; EMBRYOLOGY; LATERAL LINE SYSTEM; MATHEMATICAL PHENOMENA; MORPHOGENESIS; PHYSIOLOGY; ZEBRA FISH;

ANIMALS; CELL AGGREGATION; CELL MOVEMENT; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; FIBROBLAST GROWTH FACTORS; LATERAL LINE SYSTEM; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; MORPHOGENESIS; RECEPTORS, FIBROBLAST GROWTH FACTOR; ZEBRAFISH; ZEBRAFISH PROTEINS;

EID: 84939883612     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-014-0812-9     Document Type: Article

References (49)

1. Albi G, Pareschi L (2013) Modeling self-organized systems interacting with few individuals: from microscopic to macroscopic dynamics. Appl Math Lett 26(4):397–401
2. Arboleda-Estudillo Y, Krieg M, Stühmer J, Licata NA, Muller DJ, Heisenberg CP (2010) Movement directionality in collective migration of germ layer progenitors. Curr Biol 20:161–169
3. Bayly PV, Taber LA, Carlsson AE (2012) Damped and persistent oscillations in a simple model of cell crawling. J R Soc Interface 9(71):1241–1253
4. Beenken A, Mohammadi M (2009) The fgf family: biology, pathophysiology and therapy. Nat Rev Drug Discov 8(3):235–253
5. Bell GI, Dembo M, Bongrand P (1984) Cell adhesion. Competition between nonspecific repulsion and specific bonding. Biophys J 45(6):1051–1064
6. Böttcher RT, Niehrs C (2005) Fibroblast growth factor signaling during early vertebrate development. Endocr Rev 26(1):63–77
7. Chitnis AB, Nogare DD, Matsuda M (2012) Building the posterior lateral line system in zebrafish. Dev Neurobiol 72(3):234–255
8. Colombi A, Scianna M, Tosin A (2011) Differentiated cell behavior: a multiscale approach using measure theory. submitted, arXiv:1108.1212v2
9. Coombs S, Netten SV (2005) The hydrodynamics and structural mechanics of the lateral line system. Fish Physiol 23:103–139
10. Cristiani E, Piccoli B, Tosin A (2011) Multiscale modeling of granular flows with application to crowd dynamics. Multiscale Model Sim 9(1):155–182
11. Cucker F, Smale S (2007) Emergent behavior in flocks. IEEE T Automat Contr 52(5):852–862
12. Donà E, Barry JD, Valentin G, Quirin C, Khmelinskii A, Kunze A, Durdu S, Newton LR, Fernandez-Minan A, Huber W, Knop M, Gilmour D (2013) Directional tissue migration through a self-generated chemokine gradient. Nature 503:285–289
13. D’Orsogna MR, Chuang YL, Bertozzi AL, Chayes LS (2006) Self-propelled particles with soft–core interactions: patterns, stability, and collapse. Phys Rev Lett 96(10):104302
14. Draper BW, Morcos PA, Kimmel CB (2001) Inhibition of zebrafish fgf8 Pre-mRNA splicing with morpholino oligos: a quantifiable method for gene knockdown. Genesis 30:154–156
15. Eisenbach M, Lengeler JW (2004) Chemotaxis. Imperial College Press, London
16. Filion RJ, Popel AS (2005) Intracoronary administration of FGF-2: a computational model of myocardial deposition and retention. Am J Physiol Heart Circ Physiol 288(1):H263–H279
17. Fournier MF, Sauser R, Ambrosi D, Meister JJ, Verkhovsky AB (2010) Force transmission in migrating cells. J Cell Biol 188(2):287–297
18. Ghysen A, Chaudière CD (2004) Development of the zebrafish lateral line. Curr Opin Neurobiol 14:67–73
19. Ha SY, Liu JG (2009) A simple proof of the Cucker–Smale flocking dynamics and mean-field limit. Commun Math Sci 7(2):297–325
20. Haas P, Gilmour D (2006) Chemokine signaling mediates self-organizing tissue migration in the zebrafish lateral line. Dev Cell 10:673–680
21. Haddon C, Smithers L, Schneider-Maunoury S, Coche T, Henrique D, Lewis J (1998) Multiple delta genes and lateral inhibition in zebrafish primary neurogenesis. Development 125:359–370
22. Hart A, Papadopoulou S, Edlund H (2003) Fgf10 Maintains notch activation, stimulates proliferation, and blocks differentiation of pancreatic epithelial cells. Dev Dynam 228:185–193
23. He L, Niemeyer B (2003) A novel correlation for protein diffusion coefficients based on molecular weight and radius of gyration. Biotechnol Prog 19:544–548
24. Hundsdorfer W, Verwer JG (2003) Numerical solution of time-dependent advection–diffusion–reaction equations. Computational mathematics. Springer, Berlin
25. Itoh M, Chitnis AB (2001) Expression of proneural and neurogenic genes in the zebrafish lateral line primordium correlates with selection of hair cell fate in neuromasts. Mech Dev 102:263–266
26. Joie J, Lei Y, Colin T, Durrieu MC, Poignard C, Saut O (2013) Modelling of migration and orientation of endothelial cells on micropatterned polymers, http://hal.inria.fr/docs/00/99/07/77/PDF/RR-discret2.pdf. Research Report INRIA RR-8252, p 20
27. Kerstetter A, Azodi E, Marrs JA, Liu Q (2004) Cadherin-2 function in the cranial ganglia and lateral line system of developing zebrafish. Dev Dynam 230:137–143
28. Kirkpatrick B, Nguyen L, Kondrikova G, Herberg S, Hill WD (2010) Brief technical note: stability of human stromal-derived factor-1$$\alpha $$α (CXCL12$$\alpha $$α) after blood sampling. Ann Clin Lab Sci 40(3):257–260
29. Lecaudey V, Akdogan GC, Norton WHJ, Gilmour D (2008) Dynamic fgf signaling couples morphogenesis and migration in the zebrafish lateral line primordium. Development 135:2695–2705. doi:10.1242/dev.025981
30. Lee J, Blaber M (2010) Increased functional half-life of fibroblast growth factor-1 by recovering a vestigial disulfide bond. J Prot Proteom 1(2):37–42
31. Li Q, Shirabe K, Kuwada JY (2004) Chemokine signaling regulates sensory cell migration in zebrafish. Dev Biol 269:123–136
32. Liu Q, Ensign RD, Azodi E (2003) Cadherin-1, -2 and -4 expression in the cranial ganglia and lateral line system of developing zebrafish. Gene Expr Patterns 3:653–658
33. Liu Q, Dalman MR, Sarmah S, Chen S, Chen Y, Hurlbut AK, Spencer MA, Marrs JA (2011) Cell adhesion molecule cadherin-6 function in zebrafish cranial and lateral line ganglia development. Dev Dynam 240:1716–1726
34. Matsuda M, Chitnis AB (2010) Atoh1a expression must be restricted by Notch signaling for effective morphogenesis of the posterior lateral line primordium in zebrafish. Development 137:3477–3487
35. Mertz AF, Che Y, Banerjee S, Goldstein J, Rosowski KR, Revilla SF, Niessen CM, Marchetti MC, Dufresne ER, Horsley V (2013) Cadherin-based intercellular adhesions organize epithelial cell-matrix traction forces. Proc Natl Acad Sci USA 103(3):842–847
36. Mizoguchi T, Togawa S, Kawakami K, Itoh M (2011) Neuron and sensory epithelial cell fate is sequentially determined by Notch signaling in zebrafish lateral line development. J Neurosci 31(43):15,522–15,530
37. Murray JD (2003) Mathematical biology II: spatial models and biomedical applications, 3rd edn. Springer, Berlin
38. Nechiporuk A, Raible D (2008) FGF-dependent mechanosensory organ patterning in zebrafish. Science 320:1774–1777
39. Papusheva E, Heisenberg CP (2010) Spatial organization of adhesion: force-dependent regulation and function in tissue morphogenesis. EMBO J 29:2753–2768
40. Perthame B (2007) Transport equations in biology. Birkhäuser, Boston
41. Rubinstein B, Fournier MF, Jacobson K, Verkhovsky AB, Mogilner A (2009) Actin–myosin viscoelastic flow in the keratocyte lamellipod. Biophys J 97:1853–1863
42. Sarrazin AF, Nuñez VA, Sapède D, Tassin V, Chaudière CD (2010) Origin and early development of the posterior lateral line system of zebrafish. J Neurosci 30(24):8234–8244
43. Sepúlveda N, Petitjean L, Cochet O, Grasland-Mongrain E, Silberzan P, Hakim V (2013) Collective cell motion in an epithelial sheet can be quantitatively described by a stochastic interacting particle model. PLOS Comput Biol 9(3):e1002944
44. Streichan SJ, Velentin G, Gilmour D, Hufnagel L (2011) Collective cell migration guided by dynamically maintained gradients. Phys Biol 8:045004
45. Sweet EM, Vemaraju S, Riley BB (2011) Sox2 and Fgf interact with atoh1 to promote sensory competence throughout the zebrafish inner ear. Dev Biol 358:113–121
46. Szabò B, Szöllösi GJ, Gönci B, Jurànyi Z, Selmeczi D, Vicsek T (2006) Phase transition in the collective migration of tissue cells: experiment and model. Phys Rev E 74(6):061908
47. Vicsek T, Cziròk A, Ben-Jacob E, Cohen I, Shochet O (1995) Novel type of phase transition in a system of self-driven particles. Phys Rev Lett 75(6):1226–1229
48. Walshe J, Mason I (2003) Fgf signalling is required for formation of cartilage in the head. Dev Biol 264:522–536
49. Yeh BK, Igarashi M, Eliseenkova AV, Plotnikov AN, Sher I, Ron D, Aaronson SA, Mohammadi M (2003) Structural basis by which alternative splicing confers specificity in fibroblast growth factor receptors. Proc Natl Acad Sci USA 100(5):2266–2271