Repressilator model

class pints.toy.RepressilatorModel(y0=None)

The “Repressilator” model describes oscillations in a network of proteins that suppress their own creation [1], [2].

The formulation used here is taken from [3] and analysed in [4]. It has three protein states (\(p_i\)), each encoded by mRNA (\(m_i\)). Once expressed, they suppress each other:

\[ \begin{align}\begin{aligned}\dot{m_0} = -m_0 + \frac{\alpha}{1 + p_2^n} + \alpha_0\\\dot{m_1} = -m_1 + \frac{\alpha}{1 + p_0^n} + \alpha_0\\\dot{m_2} = -m_2 + \frac{\alpha}{1 + p_1^n} + \alpha_0\\\dot{p_0} = -\beta (p_0 - m_0)\\\dot{p_1} = -\beta (p_1 - m_1)\\\dot{p_2} = -\beta (p_2 - m_2)\end{aligned}\end{align} \]

With parameters alpha_0, alpha, beta, and n.

Only the mRNA states are visible as output.

Extends pints.ForwardModel, pints.toy.ToyModel.

Parameters:

y0 – The system’s initial state, must have 6 entries all >=0.

References

[1]

A Synthetic Oscillatory Network of Transcriptional Regulators. Elowitz, Leibler (2000) Nature. https://doi.org/10.1038/35002125

[2]

https://en.wikipedia.org/wiki/Repressilator

[3]

Dynamic models in biology. Ellner, Guckenheimer (2006) Princeton University Press

[4]

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Toni, Welch, Strelkowa, Ipsen, Stumpf (2009) J. R. Soc. Interface. https://doi.org/10.1098/rsif.2008.0172

n_outputs()

See pints.ForwardModel.n_outputs().

n_parameters()

See pints.ForwardModel.n_parameters().

simulate(parameters, times)

See pints.ForwardModel.simulate().

suggested_parameters()

See pints.toy.ToyModel.suggested_parameters().

suggested_times()

See pints.toy.ToyModel.suggested_times().