TY - JOUR
T1 - A Mathematical Model of Granule Cell Generation During Mouse Cerebellum Development
AU - Leffler, Shoshana R.
AU - Legué, Emilie
AU - Aristizábal, Orlando
AU - Joyner, Alexandra L.
AU - Peskin, Charles S.
AU - Turnbull, Daniel H.
N1 - Funding Information:
This research was supported by Grants from the National Institutes of Health (NIH): R01NS038461 (to DHT) and R37MH085726 (to ALJ). Partial support was also provided by the NIH Cancer Center Support Grants at New York University Langone Medical Center (P30CA016087) and Memorial Sloan-Kettering Cancer Center (P30CA008748). SRL was partially supported by the NYU Developmental Genetics Graduate Program NIH Training Grant (T32HD007520), and CSP was partially supported by the Systems Biology Center New York under NIH grant P50GM071558. We thank Dr. Kamila Szulc for analyzing MRI data related to the vermis width and Jae Han (Andy) Lee for assistance with some of the analysis of histological data. We also thank the Histopathology Core at NYU School of Medicine for help with scanning the histological sections at high resolution.
Publisher Copyright:
© 2016, Society for Mathematical Biology.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - 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.
AB - 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.
KW - Differential equations
KW - EGL
KW - External granule layer
KW - Granule cell precursor cells
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U2 - 10.1007/s11538-016-0163-3
DO - 10.1007/s11538-016-0163-3
M3 - Article
C2 - 27125657
AN - SCOPUS:84964483847
SN - 0092-8240
VL - 78
SP - 859
EP - 878
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
IS - 5
ER -