A Mathematical Model of Granule Cell Generation During Mouse Cerebellum Development

Shoshana R. Leffler, Emilie Legué, Orlando Aristizábal, Alexandra L. Joyner, Charles S. Peskin, Daniel H. Turnbull

Research output: Contribution to journalArticlepeer-review


Determining the cellular basis of brain growth is an important problem in developmental neurobiology. In the mammalian brain, the cerebellum is particularly amenable to studies of growth because it contains only a few cell types, including the granule cells, which are the most numerous neuronal subtype. Furthermore, in the mouse cerebellum granule cells are generated from granule cell precursors (gcps) in the external granule layer (EGL), from 1 day before birth until about 2 weeks of age. The complexity of the underlying cellular processes (multiple cell behaviors, three spatial dimensions, time-dependent changes) requires a quantitative framework to be fully understood. In this paper, a differential equation-based model is presented, which can be used to estimate temporal changes in granule cell numbers in the EGL. The model includes the proliferation of gcps and their differentiation into granule cells, as well as the process by which granule cells leave the EGL. Parameters describing these biological processes were derived from fitting the model to histological data. This mathematical model should be useful for understanding altered gcp and granule cell behaviors in mouse mutants with abnormal cerebellar development and cerebellar cancers.

Original languageEnglish (US)
Pages (from-to)859-878
Number of pages20
JournalBulletin of Mathematical Biology
Issue number5
StatePublished - May 1 2016


  • Differential equations
  • EGL
  • External granule layer
  • Granule cell precursor cells

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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