HES1 Michaelis-Menten Model¶
- class pints.toy.Hes1Model(m0=None, fixed_parameters=None)[source]¶
HES1 Michaelis-Menten model of regulatory dynamics [1].
This model describes the expression level of the transcription factor Hes1.
\[\begin{split}\frac{dm}{dt} &= -k_{deg}m + \frac{1}{1 + (p_2/P_0)^h} \\ \frac{dp_1}{dt} &= -k_{deg} p_1 + \nu m - k_1 p_1 \\ \frac{dp_2}{dt} &= -k_{deg} p_2 + k_1 p_1\end{split}\]The system is determined by 3 state variables \(m\), \(p_1\), and \(p_2\). It is assumed that only \(m\) can be observed, that is only \(m\) is an observable. The initial condition of the other two state variables and \(k_{deg}\) are treated as implicit parameters of the system. The input order of parameters of interest is \(\{ P_0, \nu, k_1, h \}\).
Extends
pints.ForwardModel
,pints.toy.ToyModel
.- Parameters:
m0 (float) – The initial condition of the observable
m
. Requiresm0 >= 0
.fixed_parameters – The fixed parameters of the model which are not inferred, given as a vector
[p1_0, p2_0, k_deg]
withp1_0, p2_0, k_deg >= 0
.
References
- fixed_parameters()[source]¶
Returns the fixed parameters of the model which are not inferred, given as a vector
[p1_0, p2_0, k_deg]
.
- initial_conditions()¶
Returns the initial conditions of the model.
- set_initial_conditions(y0)¶
Sets the initial conditions of the model.
- simulate(parameters, times)¶
- simulateS1(parameters, times)¶
- simulate_all_states(parameters, times)[source]¶
Returns all state variables that
simulate()
does not return.
- suggested_values()[source]¶
Returns a suggested set of values that matches
suggested_times()
.