Revealing the role of SGK1 in the dynamics of medulloblastoma using a mathematical model

J Theor Biol. 2014 Aug 7:354:105-12. doi: 10.1016/j.jtbi.2014.03.028. Epub 2014 Mar 28.


Deregulation of signaling pathways and subsequent abnormal interactions of downstream genes very often results in carcinogenesis. In this paper, we propose a two-compartment model describing intricate dynamics of the target genes of the Wnt signaling pathway in medulloblastoma. The system of nine nonlinear ordinary differential equations accounts for the formation and dissociation of complexes as well as for the transcription, translation and transport between the cytoplasm and the nucleus. We focus on the interplay between MYC and SGK1 (serum and glucocorticoid-inducible kinase 1), which are the products of Wnt/β-catenin signaling pathway, and GSK3β (glycogen synthase kinase). Numerical simulations of the model solutions yield a better understanding of the process and indicate the importance of the SGK1 gene in the development of medulloblastoma, which has been confirmed in our recent experiments. The model is calibrated based on the gene expression microarray data for two types of medulloblastoma, characterized by monosomy and trisomy of chromosome 6q to highlight the difference between diagnoses.

Keywords: Differential equations; GSK3β; MYC; Wnt signaling pathway.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Humans
  • Immediate-Early Proteins / genetics
  • Immediate-Early Proteins / metabolism*
  • Medulloblastoma / enzymology*
  • Medulloblastoma / genetics
  • Medulloblastoma / pathology
  • Models, Biological*
  • Protein Serine-Threonine Kinases / genetics
  • Protein Serine-Threonine Kinases / metabolism*
  • Proto-Oncogene Proteins c-myc / genetics
  • Proto-Oncogene Proteins c-myc / metabolism
  • Wnt Signaling Pathway*


  • Immediate-Early Proteins
  • MYC protein, human
  • Proto-Oncogene Proteins c-myc
  • Protein Serine-Threonine Kinases
  • serum-glucocorticoid regulated kinase