Improved parameter estimation for systems with an experimentally determined Hopf bifurcation
When performing system identification, we have two sources of
information: experimental data and prior knowledge. Many
cell-biological systems are oscillating, and sometimes we know an
input where the system reaches a Hopf bifurcation. This is the case,
for example, for glycolysis in yeast cells and for the
Belousov\u2013Zhabotinsky reaction, and for both of these systems
there exist significant numbers of quenching data, ideal for system
identification. We present a method that includes prior knowledge of
the location of a Hopf bifurcation in estimation based on
time-series. The main contribution is a reformulation of the prior
knowledge into the standard formulation of a constrained optimisation
problem. This formulation allows for any of the standard methods to be
applied, including all the theories regarding the method's
properties. The reformulation is carried out through an
over-parametrisation of the original problem. The over-parametrisation
allows for extra constraints to be formed, and the net effect is a
reduction of the search space. A method that can solve the new
formulation of the problem is presented, and the advantage of adding
the prior knowledge is demonstrated on the Brusselator.
G. Cedersund and C. Knudsen
IEE Proceedings - Systems Biology,
2005
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