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. Requires m0 >= 0.
  • fixed_parameters – The fixed parameters of the model which are not inferred, given as a vector [p1_0, p2_0, k_deg] with p1_0, p2_0, k_deg >= 0.

References

[1]Silk, D., el al. 2011. Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes. Nature communications, 2, p.489. https://doi.org/10.1038/ncomms1496
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.

jacobian(state, time, parameters)[source]

See pints.ToyModel.jacobian().

m0()[source]

Returns the initial conditions of the m variable.

n_outputs()[source]

See pints.ForwardModel.n_outputs().

n_parameters()[source]

See pints.ForwardModel.n_parameters().

n_states()[source]

See pints.ToyODEModel.n_states().

set_fixed_parameters(k)[source]

Changes the implicit parameters for this model.

set_initial_conditions(y0)

Sets the initial conditions of the model.

set_m0(m0)[source]

Sets the initial conditions of the m variable.

simulate(parameters, times)

See pints.ForwardModel.simulate().

simulateS1(parameters, times)

See pints.ForwardModelS1.simulateS1().

simulate_all_states(parameters, times)[source]

Returns all state variables that simulate() does not return.

suggested_parameters()[source]

See pints.toy.ToyModel.suggested_parameters().

suggested_times()[source]

See pints.toy.ToyModel.suggested_times().

suggested_values()[source]

Returns a suggested set of values that matches suggested_times().