CellCycle

Systems · Continuous · Chem bio systems

Dimension: 6

Equations

\[ \begin{aligned} \dot{y_{0}} &= \frac{Kim vi}{Kim + y_{4}} - kd_{1} y_{0} - \frac{vd y_{0} y_{2}}{Kd_{1} + y_{0}} \\ \dot{y_{1}} &= - \frac{V_{2} y_{1}}{K + y_{1}} + \frac{Vm_{1} y_{0} \left(1 - y_{1}\right)}{\left(Kc + y_{0}\right) \left(K - y_{1} + 1\right)} \\ \dot{y_{2}} &= - \frac{V_{4} y_{2}}{K + y_{2}} + \frac{Vm_{3} y_{1} \left(1 - y_{2}\right)}{K - y_{2} + 1} \\ \dot{y_{3}} &= \frac{Kim vi}{Kim + y_{1}} - kd_{1} y_{3} - \frac{vd y_{3} y_{5}}{Kd_{1} + y_{3}} \\ \dot{y_{4}} &= - \frac{V_{2} y_{4}}{K + y_{4}} + \frac{Vm_{1} y_{3} \left(1 - y_{4}\right)}{\left(Kc + y_{3}\right) \left(K - y_{4} + 1\right)} \\ \dot{y_{5}} &= - \frac{V_{4} y_{5}}{K + y_{5}} + \frac{Vm_{3} y_{4} \left(1 - y_{5}\right)}{K - y_{5} + 1} \end{aligned} \]

Parameters

parameter	default
K	0.01
Kc	0.5
Kd1	0.02
Kim	0.65
V2	0.15
V4	0.05
Vm1	0.3
Vm3	0.1
kd1	0.001
vd	0.025
vi	0.05

Usage

import tsdynamics as ts

sys = ts.CellCycle()
traj = sys.integrate(final_time=100.0, dt=0.01)

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