Goodwin oscillator model

class pints.toy.GoodwinOscillatorModel[source]

Three-state Goodwin oscillator toy model introduced in [1], [2], but best described in [3]. The model considers level of mRNA, \(x\), which is translated into protein \(y\), which, in turn, stimulated production of protein \(z\) that inhibits production of mRNA. The ODE system is described by the following equations,

\[ \begin{align}\begin{aligned}\dot{x} = 1 / (1 + z^{10}) - m_1 x\\\dot{y} = k_2 x - m_2 y\\\dot{z} = k_3 y - m_3 z\end{aligned}\end{align} \]

Parameters are \([k_2, k_3, m_1, m_2, m_3]\). The initial conditions are hard-coded at [0.0054, 0.053, 1.93].

Extends pints.ForwardModelS1, pints.toy.ToyODEModel.

References

[1]Oscillatory behavior in enzymatic control processes. Goodwin (1965) Advances in enzyme regulation. https://doi.org/10.1016/0065-2571(65)90067-1
[2]Mathematics of cellular control processes I. Negative feedback to one gene. Griffith (1968) Journal of theoretical biology. https://doi.org/10.1016/0022-5193(68)90189-6
[3]Estimating Bayes factors via thermodynamic integration and population MCMC. Ben Calderhead and Mark Girolami, 2009, Computational Statistics and Data Analysis.
initial_conditions()

Returns the initial conditions of the model.

jacobian(state, time, parameters)[source]

See pints.ToyODEModel.jacobian().

n_outputs()[source]

See pints.ForwardModel.n_outputs().

n_parameters()[source]

See pints.ForwardModel.n_parameters().

n_states()

Returns number of states in underlying ODE. Note: will not be same as n_outputs() for models where only a subset of states are observed.

set_initial_conditions(y0)

Sets the initial conditions of the model.

simulate(parameters, times)

See pints.ForwardModel.simulate().

simulateS1(parameters, times)

See pints.ForwardModelS1.simulateS1().

suggested_parameters()[source]

See pints.toy.ToyModel.suggested_parameters().

suggested_times()[source]

See pints.toy.ToyModel.suggested_times().