Autocatalytic loop, amplification and diffusion: A mathematical and computational model of cell polarization in neural chemotaxis

PLoS Computational Biology

Volumn 5, Issue 8, 2009, Pages

  Causin, Paola ^a   Facchetti, Giuseppe ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CELLS; COMPUTATION THEORY; COMPUTATIONAL METHODS; COORDINATION REACTIONS; CROSSLINKING; CYTOLOGY; MOLECULES; POLARIZATION;

AUTOCATALYTIC; CELL POLARIZATION; CELL-BE; CELL/B.E; CHEMOTACTIC RESPONSE; CHEMOTAXI; COMPLEX PROCESSES; COMPUTATIONAL MODELLING; CYTOSKELETONS; GROWTH CONES;

AMPLIFICATION;

ARTICLE; CATALYSIS; CELL DIFFERENTIATION; CHEMOTAXIS; CYTOPLASM; CYTOSKELETON; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NERVE CELL; NERVE FIBER; NERVE MEMBRANE; POLARIZATION; QUANTITATIVE ANALYSIS; SIGNAL TRANSDUCTION; ANIMAL; BIOLOGICAL MODEL; BIOLOGY; CELL POLARITY; COMPUTER PROGRAM; DIFFUSION; FEEDBACK SYSTEM; HUMAN; METABOLISM; METHODOLOGY; PATHOLOGY; PHYSIOLOGY; THEORETICAL MODEL;

ANIMALS; CATALYSIS; CELL POLARITY; CHEMOTAXIS; COMPUTATIONAL BIOLOGY; CYTOSKELETON; DIFFUSION; FEEDBACK; HUMANS; MODELS, BIOLOGICAL; MODELS, THEORETICAL; NEURONS; SIGNAL TRANSDUCTION; SOFTWARE;

EID: 70149103973     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1000479     Document Type: Article

References (49)

1. Bourne H, Weiner O (2002) Cell polarity: a chemical compass. Nature 419: 21.
2. van Haastert P, Devreotes P (2004) Chemotaxis: signalling the way forward. Nat Rev Mol Cell Biol 5: 626-634.
3. Li S, Guan J, Chein S (2005) Biochemistry and biomechanics of cell motility. Annu Rev Biomed Eng 7: 105-150.
4. Rappel W, Thomas P, Levine H, Loomis W (1998) Establishing direction during chemotaxis in eukaryotic cells. Biophys J 83: 1361-1367. (Pubitemid 34977709)
5. Meinhardt H (1999) Orientation of chemotactic cells and growth cones: models and mechanisms. J Cell Sci 112: 2867-2874.
6. Levchenko A, Iglesias P (2002) Models of eukaryotic gradient sensing: application to chemotaxis of amoebae and neutrophils. Biophys J 82: 50-63. (Pubitemid 34289781)
7. Narang A, Subramanian KK, Lauffenburger DA (2001) A mathematical model for chemoattractant gradient sensing based on receptor-regulated membrane phospholipid signalling dynamics. Ann Rev Biomed Eng 29: 677-769
8. Gamba A, de Candia A, Di Talia S, Coniglio A, Bussolino F, et al. (2005) Diffusion-limited phase separation in eukaryotic chemotaxis. PNAS 102(47). (Pubitemid 41692660)
9. Onsum M, Rao C (2007) A mathematical model for neutrophil gradient sensing and polarization. PLoS Comput Biol 3: e36. (Pubitemid 46535736)
10. Mori Y, Jilkine A, Edelstein-Keshet L (2008) Wave-pinning and cell polarity from a bistable reaction-diffusion system. Biophys J 94: 3684-3697
11. Mortimer D, Fothergill T, Pujic Z, Richards L, Goodhill G (2007) Growth cone chemotaxis. Trends Neurosci 31: 90-98.
12. Buettner HM, Pittman RN, Ivins J (1994) A model of neurite extension across regions of nonpermissive substrate: simulations based on experimental measurements of growth cone motility and filopodial dynamics. Dev Biol 163: 407-422.
13. Maskery SM, Shinbrot T (2005) Deterministic and stochastic elements of axonal guidance. Annu Rev Biomed Eng 7: 187-221.
14. Hentschel HGE, van Ooyen A (2000) Dynamic mechanisms for bundling and guidance during neural network formation. Physica A 288: 369-379.
15. Aletti G, Causin P (2008) Mathematical characterization of the transduction chain in growth cone pathfinding. IET Sys Biol 2: 150-161. (Pubitemid 351803035)
16. Aeschlimann M, Tettoni L (2001) Biophysical model of axonal pathfinding. Neurocomputing 38-40: 87-92.
17. Goodhill GJ, Gu M, Urbach JS (2004) Predicting axonal response to molecular gradients with a computational model of filopodial dynamics. Neural Comp 16: 2221-2243. (Pubitemid 39392552)
18. Xu J, Rosoff W, Urbach J, Goodhill G (2005) Adaptation is not required to explain the long-term response of axons to molecular gradients. Development 132: 4545-4562. (Pubitemid 41632232)
19. Bouzigues C, Morel M, Triller A, Dahan M (2007) Asymmetric redistribution of GABA receptors during GABA gradient sensing by nerve growth cones analyzed by single quantum dot imaging. PNAS 104: 251-256. (Pubitemid 47175127)
20. Ueda M, Sako Y, Tanaka T, Devreotes P, Yanagida T (2001) Single-molecule analysis of chemotactic signaling in Dictyostelium cells. Science 294: 864-867. (Pubitemid 33032106)
21. SaxtonM(1994) Single{particle tracking: models of directed transport. Biophys J 67: 2110-2119.
22. Song H, Poo MM (1999) Signal transduction underlying growth cone guidance by diffusible factors. Curr Opin Neurobiol 9: 355-363. (Pubitemid 29267608)
23. 2+ channels by cyclic nucleotide cross activation of opposing protein kinases in rabbit portal vein. Circ Res 82: 557-565.
24. Hong K, Hinck L, Nishiyama M, Poo M, Tessier-Lavigne M, et al. (1999) A ligand-gated association between cytoplasmatic domains of UNC5 and DCC family receptors converts Netrin-induced growth cone attraction to repulsion. Cell 97: 927-941. (Pubitemid 29375051)
25. Ming Gl, Song Hj, Berninger B, Holt C, Tessier-Lavigne M, et al. (1997) cAMP-dependent growth cone guidance by netrin-1. Neuron 19: 1225-1235. (Pubitemid 28030542)
26. Keino-Masu K, Masu M, Hinck L, Leonardo ED, Chan SSY, et al. (1996) Deleted in Colorectal Cancer (DCC) encodes a netrin receptor. Cell 87: 175-185. (Pubitemid 26358997)
27. Tessier-Lavigne M, Goodman C (1996) The molecular biology of axon guidance. Science 274: 1123-1133.
28. 2+ channels sets the polarity of nerve growth-cone turning. Letters to Nature 423: 990-995.
29. Clément F, Monniaux D, Stark J, Hardy K, Thallabrd J, et al. (2001) Mathematical model of FSH-induced cAMP production in ovarian follicles. Am J Physiol Endocrinol Metab 281: E35-E53. (Pubitemid 32911751)
30. Song H, Poo MM (2001) The cell biology of neuronal navigation. Nat Cell Biol 3: E81-E88.
31. Hamelin M, Zhou Y, Su M, Scott I, Culotti J (1993) Expression of the UNC-5 guidance receptor in the touch neurons of C. elegans steers their axons dorsally. Nature 364: 327-330. (Pubitemid 23969260)
32. Hong K, Nishiyama M, Henley J, Tessier-Lavigne M, Poo M (2003) Calcium signalling in the guidance of nerve growth by netrin-1. Nature 403: 93-98. (Pubitemid 30038528)
33. Goodhill GJ (1997) Diffusion in axon guidance. Eur J Neur 9: 1414-1421.
34. Goodhill GJ, Urbach JS (1999) Theoretical analysis of gradient detection by growth cones. J Neurobiol 41: 230-241. (Pubitemid 29494149)
35. Zheng JQ, Felder M, Connor JA, Poo M (1994) Turning of nerve growth cone induced by neuro-transmitters. Nature 368: 140-144. (Pubitemid 24101523)
36. Tessier-Lavigne M, Placzek M, Lumsden AG, Dodd J, Jessell TM (1988) Chemotropic guidance of developing axons in the mammalian central nervous system. Nature 336: 775-778. (Pubitemid 19014437)
37. Cirulli V, Yebra M (2007) Netrins: beyond the brain. Nature Reviews 8: 296-306.
38. Murray JD (2004) Mathematical Biology. Vol I,II. New York: Springer.
39. Brune B, Ulrich V (1991) 12-Hydroperoxyeicosatetraenoic acid inhibits main platelet functions by activation of soluble guanylate cyclase. Mol Pharmacol 39: 671-678.
40. v1 L-channel gating via cGMP-dependent protein kinase in cell-attached patches of bovine chromaffn cells. J Physiol 541: 351-366.
41. Courant R, Hilbert D (1989) Methods of mathematical physics. John Wiley and Sons.
42. Bouzigues C, Dahan M (2007) Transient directed motions of GABAA receptors in growth cones detected by a speed correlation index. Biophys J 92: 654-660. (Pubitemid 46145797)
43. Jékely G, Song HH, Luque C, Rorth P (2005) Regulators of endocytosis maintain localized receptor tyrosine kinase signaling in guided migration. Dev Cell 9: 197-207. (Pubitemid 41051739)
44. Bell J, Biltonen R, Brunton L (1989) Non-steady state kinetic analysis of the regulation of Adeny-late Cyclase by GTP-binding proteins. Mol Pharmacol 37: 535-545. (Pubitemid 20130797)
45. Quarteroni A, Valli A (1997) Numerical Approximation of Partial Differential Equations. Springer-Verlag.
46. Brinkerhoff C, Sun Choi J, Linderman J (2008) Diffusion-limited reactions in G-protein activation: unexpected consequences of antagonist and agonist competition. J Theor Biol 251: 561-569.
47. L M, Linderman J (1997) Mechanism model of G-protein signal transduction. Bioch Pharm 53: 518-530.
48. Modchang C, Triampo W, Lenbury Y (2008) Mathematical modeling and application of genetic algorithm to parameter estimation in signal transduction: Trafficking and promiscuous coupling of G-protein coupled receptors. Comput Biol Med 38: 574-582.
49. Chau V, Huang L, Romero G, Biltonen R, Huang C (1980) Kinetic studies on the dissociation of adenosine cyclic 3′-5′-monophosphate from the regulatory subunit of protein kinase from rabbit skeletal muscle. Biochemistry 19: 924-928.