title: A Mathematical Model of Granule Cell Generation During Mouse Cerebellum Development.
abstract: 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.
authors.affiliation: Skirball Institute of Biomolecular Medicine, New York University School of Medicine, 540 First Avenue, New York, NY, 10016, USA.|Developmental Genetics Graduate Program, NYU School of Medicine, New York, NY, USA.
authors.forename: Shoshana R
authors.initials: SR
authors.lastname: Leffler
authors.affiliation: Developmental Biology Program, Sloan Kettering Institute, New York, NY, USA.
authors.forename: Emilie
authors.initials: E
authors.lastname: Legué
authors.affiliation: Skirball Institute of Biomolecular Medicine, New York University School of Medicine, 540 First Avenue, New York, NY, 10016, USA.
authors.forename: Orlando
authors.initials: O
authors.lastname: Aristizábal
authors.affiliation: Developmental Biology Program, Sloan Kettering Institute, New York, NY, USA.
authors.forename: Alexandra L
authors.initials: AL
authors.lastname: Joyner
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA. peskin@cims.nyu.edu.
authors.forename: Charles S
authors.initials: CS
authors.lastname: Peskin
authors.affiliation: Skirball Institute of Biomolecular Medicine, New York University School of Medicine, 540 First Avenue, New York, NY, 10016, USA. daniel.turnbull@med.nyu.edu.|Developmental Genetics Graduate Program, NYU School of Medicine, New York, NY, USA. daniel.turnbull@med.nyu.edu.|Departments of Radiology and Pathology, NYU School of Medicine, New York, NY, USA. daniel.turnbull@med.nyu.edu.
authors.forename: Daniel H
authors.initials: DH
authors.lastname: Turnbull
mesh_terms: D000465:Algorithms; D000818:Animals; D000831:Animals, Newborn; D002454:Cell Differentiation; D002531:Cerebellum / Q000166:cytology* / Q000196:embryology / Q000254:growth & development*; D003198:Computer Simulation; D055641:Mathematical Concepts; D051379:Mice; D008818:Mice, Neurologic Mutants; D008959:Models, Neurological; D058953:Neural Stem Cells / Q000166:cytology; D009474:Neurons / Q000145:classification / Q000166:cytology*
keywords: Differential equations; EGL; External granule layer; Granule cell precursor cells