8. Blinking bacteria: The repressilator enables self-sustaining oscillations

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Design principle

• Delayed, ultrasensitive, negative feedback can generate self-sustaining oscillations in cells.

Techniques

• Composition of functions

• Linear stability analysis

• Linear stability diagrams

• Numerical calculation of a scalar fixed point

• Synthetic biology

References

• Elowitz & Leibler, A synthetic oscillatory network of transcriptional regulators, Nature, 2000

• Synchronous long-term oscillations in a synthetic gene circuit, Nature, 2016

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import numpy as np
import scipy.integrate
import scipy.optimize

import bokeh.plotting
import bokeh.io

# We will use Matplotlib to make a 3D plot
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
%matplotlib inline
%config InlineBackend.figure_format = 'retina'

import panel as pn
pn.extension()

bokeh.io.output_notebook()