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Table 1 Notations used for variables and parameters in the model formulation

From: A multiscale mathematical model of cell dynamics during neurogenesis in the mouse cerebral cortex

Notation Unit Definition Description
AP   Apical progenitor  
IP   Intermediate progenitor  
N   Neuron  
IPN   Neurogenic IP IP that divides symmetrically to give two Ns
IPP   Proliferative / IPgenic IP IP that divides symmetrically to give rise to two IPNs
FAP(t) cell nb/hour AP inflow into neurogenesis Instantaneous AP Number fuelling neurogenesis
K AP cell nb/hour Parameters of FAP(t) formulated in (Eq. (16)) Scaling factor
t + day   Location of the rise inflexion point
s + day −1   The slope of FAP(t) at t+ is approximately 4s+KAP
t day   Location of the decay inflexion point
s day −1   The slope of FAP(t) at t is approximately −4sKAP
β(t)   Ratio of IP-genic divisions of APs Proportion of fated AP subject to direct neurogenesis
γ(t)   Ratio of IPP-genic AP divisions Proportion of fated AP subject to an IPgenic division entering an IPP cell cycle
γ 0   Parameters of γ(t) formulated in a sigmoid (Eq. (15)) Limit value of γ(t) for t→−
γ 1    Limit value of γ(t) for t→+
t γ day   Location of inflexion point of γ(t)
s γ day −1   4sγ/(γ1γ0) is the slope of γ(t) at tγ
IPP(t,a) cell nb/hour Density of cells at time t and age a Density of cells of type IPP, solution of PDE (Eq. (1))
IPN(t,a) cell nb/hour Density of cells at time t and age a Density of cells of type IPN, solution of PDE (Eq. (2))
\(\overline {IPP} (t)\) cell nb Number of cells of type IPP Number of cells IPP at time t.
\(\overline {IPN} (t)\) cell nb Number of cells of type IPN Number of cells IPN at time t.
a hour age Location within the cell cycle
\(\overline {X}_{P} (t)\) cell number X in the P phase X{IPP,IPN,IP}; P{G1,S,G2,M}
LI(t)   Labeling index (Eq. (13)) Proportion of cells in S phase over the total number of cycling cells (defined for a specific progenitor type)
MI(t)   Mitotic index (Eq. (14)) Proportion of cells in M phase over the total number of cycling cells (defined for a specific progenitor type)
ψ(t)   IP neurogenic fraction (Eq. 12) Proportion of IP mitoses fated to neurogenic divisions
ρ(t,Δt)   Proportion of IP cells in S phase at t and t+Δt detected by double labeling (Eq. (25)) Efficiency of detection of cells undergoing a second S phase by double-labeling techniques based on a large delay Δt
\(r^{N}_{AP}\)   Neuronal yield (Eq. (19)) Ratio of the final number of produced neurons over the cumulated number of AP that have entered neurogenesis