In meyer-lab/cell-cycle-growth: Analysis of Cell Cycle Reporter Data

Our model is has cells existing in the G1 or G2 state, then transition from G2 to G1 doubles that cell.

$\frac{dG1}{dt} = -\beta [G1] + 2\alpha [G2] - \gamma_1 [G1]$

$\frac{dG2}{dt} = \beta [G1] + \alpha [G2] - \gamma_2 [G2]$

Based on this, the S.S.S. growth rate is:

$\frac{\alpha - \gamma_2 - \gamma_1 R}{1 + R}$

where R is $[G1]/[G2]$ at S.S.S.

Ratio of [G1] to [G2]

By differentiating ratio:

$\delta \left( \frac{[G1]}{[G2]} \right)$

we get:

$R = \frac{b + \sqrt{b^2 + 8\alpha \beta}}{2 \beta}$

$b = \gamma_2 + \alpha - \gamma_1 - \beta$

for the ratio acheived in steady-state.

meyer-lab/cell-cycle-growth documentation built on May 13, 2019, 6:09 p.m.