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 −4s−KAP | |
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/(γ1−γ0) 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 |