Control-Based Continuation
(CBC) is a general and systematic method
to carry out the bifurcation analysis of physical experiments. CBC
does not rely on a mathematical model and thus overcomes the uncertainty
introduced when identifying bifurcation curves indirectly through
modeling and parameter estimation. We demonstrate,
in silico
, CBC applicability to biochemical processes by tracking the equilibrium
curve of a toggle switch, which includes additive process noise and
exhibits bistability. We compare the results obtained when CBC uses
a model-free and model-based control strategy and show that both can
track stable and unstable solutions, revealing bistability. We then
demonstrate CBC in conditions more representative of an
in
vivo
experiment using an agent-based simulator describing
cell growth and division, cell-to-cell variability, spatial distribution,
and diffusion of chemicals. We further show how the identified curves
can be used for parameter estimation and discuss how CBC can significantly
accelerate the prototyping of synthetic gene regulatory networks.