Abstract
Bone Morphogenetic Proteins (BMPs) play an important role in dorsal–ventral (DV) patterning of the early zebrafish embryo. BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands. Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however it is not clear how the source-sink mechanism shapes patterns in 3D, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo. We propose a new three-dimensional growing Partial Differential Equation (PDE)-based model to simulate the BMP patterning process during the blastula stage. This model provides a starting point to elucidate how different mechanisms and components work together in 3D to create and maintain the BMP gradient in the embryo. We also show how the 3D model fits the BMP signaling gradient data at multiple time points along both axes. Furthermore, sensitivity analysis of the model suggests that the spatiotemporal patterns of Chordin and BMP ligand gene expression are dominant drivers of shape in 3D and more work is needed to quantify the spatiotemporal profiles of gene and protein expression to further refine the models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bhat N, Kwon H-J, Riley BB (2013) A gene network that coordinates preplacodal competence and neural crest specification in zebrafish. Dev Biol 373:107–117. https://doi.org/10.1016/J.YDBIO.2012.10.012
Bird RB, Stewart WE, Lightfoot EN (2006) Transport phenomena, Revised 2 edn. Wiley, Hoboken
Blader P, Rastegar S, Fischer N, Strähle U (1997) Cleavage of the BMP-4 antagonist chordin by zebrafish tolloid. Science (80-) 278:1937–1940. https://doi.org/10.1126/science.278.5345.1937
Bökel C, Brand M (2013) Generation and interpretation of FGF morphogen gradients in vertebrates. Curr Opin Genet Dev 23:415–422. https://doi.org/10.1016/J.GDE.2013.03.002
Crampin E, Gaffney EA, Maini PK (1999) Reaction and diffusion on growing domains: scenarios for robust pattern formation. Bull Math Biol 61:1093–1120. https://doi.org/10.1006/bulm.1999.0131
Dal-Pra S, Fürthauer M, Van-Celst J et al (2006) Noggin1 and Follistatin-like2 function redundantly to Chordin to antagonize BMP activity. Dev Biol 298:514–526. https://doi.org/10.1016/j.ydbio.2006.07.002
De Robertis EM, Sasai Y (1996) A common plan for dorsoventral patterning in Bilateria. Nature 380:37–40. https://doi.org/10.1038/380037a0
Dutko JA, Mullins MC (2011) SnapShot: BMP signaling in development. Cell 145:636-636.e2. https://doi.org/10.1016/j.cell.2011.05.001
Fried P, Iber D (2014) Dynamic scaling of morphogen gradients on growing domains. Nat Commun 5:5077. https://doi.org/10.1038/ncomms6077
Hashiguchi M, Mullins MC (2013) Anteroposterior and dorsoventral patterning are coordinated by an identical patterning clock. Development 140:1970–1980. https://doi.org/10.1242/dev.088104
Hengenius JB, Gribskov M, Rundell AE et al (2011) Analysis of gap gene regulation in a 3D organism-scale model of the Drosophila melanogaster embryo. PLoS ONE 6:e26797. https://doi.org/10.1371/journal.pone.0026797
Holley SA, Ferguson EL (1997) Fish are like flies are like frogs: conservation of dorsal–ventral patterning mechanisms. BioEssays 19:281–284. https://doi.org/10.1002/bies.950190404
Keller PJ, Schmidt AD, Wittbrodt J, Stelzer EHK (2008) Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy. Science 322:1065–1069. https://doi.org/10.1126/science.1162493
Khokha MK, Yeh J, Grammer TC, Harland RM (2005) Depletion of three BMP antagonists from spemann’s organizer leads to a catastrophic loss of dorsal structures. Dev Cell 8:401–411. https://doi.org/10.1016/j.devcel.2005.01.013
Klika V, Gaffney EA (2017) History dependence and the continuum approximation breakdown: the impact of domain growth on Turing’s instability. Proc R Soc A Math Phys Eng Sci 473:20160744. https://doi.org/10.1098/rspa.2016.0744
Lecuit T, Cohen SM (1998) Dpp receptor levels contribute to shaping the Dpp morphogen gradient in the Drosophila wing imaginal disc. Development 125:4901–4907
Lepage SE, Bruce AEE (2010) Zebrafish epiboly: mechanics and mechanisms. Int J Dev Biol 54:1213–1228. https://doi.org/10.1387/ijdb.093028sl
Little SC, Mullins MC (2006) Extracellular modulation of BMP activity in patterning the dorsoventral axis. Birth Defects Res Part C Embryo Today Rev 78:224–242. https://doi.org/10.1002/bdrc.20079
Luo J-Y, Zhang Y, Wang L, Huang Y (2015) Regulators and effectors of bone morphogenetic protein signalling in the cardiovascular system. J Physiol 593:2995–3011. https://doi.org/10.1113/JP270207
Madzvamuse A, Maini PK, Wathen AJ (2005) A moving grid finite element method for the simulation of pattern generation by turing models on growing domains. J Sci Comput 24:247–262. https://doi.org/10.1007/s10915-004-4617-7
Maini PK, Solursh M (1991) Cellular mechanisms of pattern formation in the developing limb. Int Rev Cytol 129:91–133
Piccolo S, Agius E, Lu B et al (1997) Cleavage of chordin by xolloid metalloprotease suggests a role for proteolytic processing in the regulation of spemann organizer activity. Cell 91:407–416. https://doi.org/10.1016/S0092-8674(00)80424-9
Pomreinke AP, Soh GH, Rogers KW et al (2017) Dynamics of BMP signaling and distribution during zebrafish dorsal-ventral patterning. Elife 6:e25861. https://doi.org/10.7554/eLife.25861
Rogers KW, Schier AF (2011) Morphogen gradients: from generation to interpretation. Annu Rev Cell Dev Biol 27:377–407. https://doi.org/10.1146/annurev-cellbio-092910-154148
Rushlow CA, Shvartsman SY (2012) Temporal dynamics, spatial range, and transcriptional interpretation of the dorsal morphogen gradient. Curr Opin Genet Dev 22:542–546. https://doi.org/10.1016/J.GDE.2012.08.005
Sansom SN, Livesey FJ (2009) Gradients in the brain: the control of the development of form and function in the cerebral cortex. Cold Spring Harb Perspect Biol 1:a002519. https://doi.org/10.1101/cshperspect.a002519
Thibault J, Bergeron S, Bonin HW (1987) On finite-difference solutions of the heat equation in spherical coordinates. Numer Heat Transf 12:457–474. https://doi.org/10.1080/10407788708913597
Tuazon FB, Mullins MC (2015) Temporally coordinated signals progressively pattern the anteroposterior and dorsoventral body axes. Semin Cell Dev Biol 42:118–133. https://doi.org/10.1016/j.semcdb.2015.06.003
Tucker JA, Mintzer KA, Mullins MC (2008) The BMP signaling gradient patterns dorsoventral tissues in a temporally progressive manner along the anteroposterior axis. Dev Cell 14:108–119. https://doi.org/10.1016/j.devcel.2007.11.004
Umulis DM, Othmer HG (2015) The role of mathematical models in understanding pattern formation in developmental biology. Bull Math Biol 77:817–845. https://doi.org/10.1007/s11538-014-0019-7
Umulis D, O’Connor MB, Blair SS (2009) The extracellular regulation of bone morphogenetic protein signaling. Development 136:3715–3728. https://doi.org/10.1242/dev.031534
Umulis DM, Shimmi O, O’Connor MB, Othmer HG (2010) Organism-scale modeling of early drosophila patterning via bone morphogenetic proteins. Dev Cell 18:260–274. https://doi.org/10.1016/j.devcel.2010.01.006
von Bubnoff A, Cho KWY (2001) Intracellular BMP signaling regulation in vertebrates: pathway or network? Dev Biol 239:1–14. https://doi.org/10.1006/dbio.2001.0388
Wagner DO, Sieber C, Bhushan R et al (2010) BMPs: from bone to body morphogenetic proteins. Sci Signal 3:mr1. https://doi.org/10.1126/scisignal.3107mr1
Wang RN, Green J, Wang Z et al (2014) Bone morphogenetic protein (BMP) signaling in development and human diseases. Genes Dis 1:87–105. https://doi.org/10.1016/j.gendis.2014.07.005
Warga RM, Kimmel CB (1990) Cell movements during epiboly and gastrulation in zebrafish. Development 108:569–580
Zhang YT, Lander AD, Nie Q (2007) Computational analysis of BMP gradients in dorsal-ventral patterning of the zebrafish embryo. J Theor Biol 248:579–589. https://doi.org/10.1016/j.jtbi.2007.05.026
Zinski J, Bu Y, Wang X et al (2017) Systems biology derived source-sink mechanism of bmp gradient formation. Elife 6:1–32. https://doi.org/10.7554/eLife.22199
Acknowledgements
We would like to acknowledge funding from NIH Grants R01GM132501 to DMU, and NIH R01GM056326 and R35GM131908 to MCM, and editing help from Matt Thompson.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Li, L., Wang, X., Mullins, M.C. et al. Evaluation of BMP-mediated patterning in a 3D mathematical model of the zebrafish blastula embryo. J. Math. Biol. 80, 505–520 (2020). https://doi.org/10.1007/s00285-019-01449-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-019-01449-x