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Towards Biological System Identification: Fast and Accurate Estimates of Parameters in Genetic Regulatory Networks

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Mary J. Dunlop and Richard M. Murray

Submitted, 2006 Conference on Decision and Control

System identification tools are useful for developing mathematical models of dynamical systems based on
experimental observations, but many standard techniques are
not applicable to biological problems where nonlinear effects
are the norm and output measurements are limited. We focus
on parameter identification in genetic regulatory networks as an
example of a class of interesting biological system identification
problems. We compare the performance of two methods, the
extended Kalman filter and a nonlinear least squares fit, as
they estimate the parameters in a model of a bistable genetic
circuit. The extended Kalman filter does dramatically better
than the nonlinear fit in predicting parameters when sensor
noise is high. The settling time of the parameter estimate is also
measured and it is shown that by choosing inputs appropriately,
the convergence time of the parameter estimates can be reduced.
We present a method for choosing an approximation of the
optimal input for parameter estimation. Some challenges that
are unique to biological system identification problems are
discussed.

Conference Paper

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Richard Murray
(murray@cds. caltech.edu)