Evaluation of BMP-mediated patterning in a 3D mathematical model of the zebrafish blastula embryo

  • Linlin Li
  • Xu Wang
  • Mary C. Mullins
  • David M. UmulisEmail author


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.


Pattern formation Morphogen gradient Zebrafish PDE BMP 

Mathematics Subject Classification

35Q92 92C42 92C15 



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.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Linlin Li
    • 1
  • Xu Wang
    • 2
  • Mary C. Mullins
    • 3
  • David M. Umulis
    • 1
    • 2
    Email author
  1. 1.Weldon School of Biomedical EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Department of Agricultural and Biological EngineeringPurdue UniversityWest LafayetteUSA
  3. 3.Department of Cell and Developmental Biology, Perelman School of MedicineUniversity of PennsylvaniaPhiladelphiaUSA

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