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

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.

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Richard Murray (murray@cds.