Multiscale Modeling of Diffusion in the Early Drosophila Embryo

Overview

Journal Proc Natl Acad Sci U S A

Specialty Science

Date 2010 May 19

PMID 20479267

Citations 20

Authors

Christine Sample

Stanislav Y Shvartsman

Affiliations

Soon will be listed here.

Abstract

We developed a multiscale approach for the computationally efficient modeling of morphogen gradients in the syncytial Drosophila embryo, a single cell with multiple dividing nuclei. By using a homogenization technique, we derived a coarse-grained model with parameters that are explicitly related to the geometry of the syncytium and kinetics of nucleocytoplasmic shuttling. One of our main results is an accurate analytical approximation for the effective diffusivity of a morphogen molecule as a function of the nuclear density. We used this expression to explore the dynamics of the Bicoid morphogen gradient, a signal that patterns the anterior-posterior axis of the embryo. A similar approach can be used to analyze the dynamics of all three maternal morphogen gradients in Drosophila.

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References

Saunders T, Howard M . Morphogen profiles can be optimized to buffer against noise. Phys Rev E Stat Nonlin Soft Matter Phys. 2009; 80(4 Pt 1):041902. DOI: 10.1103/PhysRevE.80.041902. View

Bergmann S, Sandler O, Sberro H, Shnider S, Schejter E, Shilo B . Pre-steady-state decoding of the Bicoid morphogen gradient. PLoS Biol. 2007; 5(2):e46. PMC: 1790957. DOI: 10.1371/journal.pbio.0050046. View

Coppey M, Berezhkovskii A, Kim Y, Boettiger A, Shvartsman S . Modeling the bicoid gradient: diffusion and reversible nuclear trapping of a stable protein. Dev Biol. 2007; 312(2):623-30. PMC: 2789574. DOI: 10.1016/j.ydbio.2007.09.058. View

Othmer H . A continuum model for coupled cells. J Math Biol. 1983; 17(3):351-69. DOI: 10.1007/BF00276521. View

Kanodia J, Rikhy R, Kim Y, Lund V, Delotto R, Lippincott-Schwartz J . Dynamics of the Dorsal morphogen gradient. Proc Natl Acad Sci U S A. 2009; 106(51):21707-12. PMC: 2799810. DOI: 10.1073/pnas.0912395106. View

Wolpert L . Positional information and the spatial pattern of cellular differentiation. J Theor Biol. 1969; 25(1):1-47. DOI: 10.1016/s0022-5193(69)80016-0. View

Gregor T, Bialek W, de Ruyter van Steveninck R, Tank D, Wieschaus E . Diffusion and scaling during early embryonic pattern formation. Proc Natl Acad Sci U S A. 2005; 102(51):18403-7. PMC: 1311912. DOI: 10.1073/pnas.0509483102. View

Braunstein S, Secomb T . Effect of cell arrangement and interstitial volume fraction on the diffusivity of monoclonal antibodies in tissue. Biophys J. 1993; 64(5):1638-46. PMC: 1262492. DOI: 10.1016/S0006-3495(93)81532-7. View

Spirov A, Fahmy K, Schneider M, Frei E, Noll M, Baumgartner S . Formation of the bicoid morphogen gradient: an mRNA gradient dictates the protein gradient. Development. 2009; 136(4):605-14. PMC: 2685955. DOI: 10.1242/dev.031195. View

10.

Crick F . Diffusion in embryogenesis. Nature. 1970; 225(5231):420-2. DOI: 10.1038/225420a0. View

11.

Surkova S, Kosman D, Kozlov K, Manu , Myasnikova E, Samsonova A . Characterization of the Drosophila segment determination morphome. Dev Biol. 2007; 313(2):844-62. PMC: 2254320. DOI: 10.1016/j.ydbio.2007.10.037. View

12.

Kopito R, Elbaum M . Reversibility in nucleocytoplasmic transport. Proc Natl Acad Sci U S A. 2007; 104(31):12743-8. PMC: 1937537. DOI: 10.1073/pnas.0702690104. View

13.

Kim Y, Coppey M, Grossman R, Ajuria L, Jimenez G, Paroush Z . MAPK substrate competition integrates patterning signals in the Drosophila embryo. Curr Biol. 2010; 20(5):446-51. PMC: 2846708. DOI: 10.1016/j.cub.2010.01.019. View

14.

Niessing D, Dostatni N, Jackle H, Rivera-Pomar R . Sequence interval within the PEST motif of Bicoid is important for translational repression of caudal mRNA in the anterior region of the Drosophila embryo. EMBO J. 1999; 18(7):1966-73. PMC: 1171281. DOI: 10.1093/emboj/18.7.1966. View

15.

Hecht I, Rappel W, Levine H . Determining the scale of the Bicoid morphogen gradient. Proc Natl Acad Sci U S A. 2009; 106(6):1710-5. PMC: 2644102. DOI: 10.1073/pnas.0807655106. View

16.

Jaeger J . Modelling the Drosophila embryo. Mol Biosyst. 2009; 5(12):1549-68. DOI: 10.1039/b904722k. View

17.

Gregor T, Wieschaus E, McGregor A, Bialek W, Tank D . Stability and nuclear dynamics of the bicoid morphogen gradient. Cell. 2007; 130(1):141-52. PMC: 2253672. DOI: 10.1016/j.cell.2007.05.026. View

18.

Coppey M, Boettiger A, Berezhkovskii A, Shvartsman S . Nuclear trapping shapes the terminal gradient in the Drosophila embryo. Curr Biol. 2008; 18(12):915-9. PMC: 2500156. DOI: 10.1016/j.cub.2008.05.034. View

19.

St Johnston D, Nusslein-Volhard C . The origin of pattern and polarity in the Drosophila embryo. Cell. 1992; 68(2):201-19. DOI: 10.1016/0092-8674(92)90466-p. View

20.

Tao L, Nicholson C . Maximum geometrical hindrance to diffusion in brain extracellular space surrounding uniformly spaced convex cells. J Theor Biol. 2004; 229(1):59-68. DOI: 10.1016/j.jtbi.2004.03.003. View