Transtrum, Mark K and Peng Qiu. 2012. Optimal experiment selection for parameter estimation in biological differential equation models. Bioinformatics. 13(181): 1-12.
Background: Parameter estimation in biological models is a common yet challenging problem. In this work we
explore the problem for gene regulatory networks modeled by differential equations with unknown parameters, such
as decay rates, reaction rates, Michaelis-Menten constants, and Hill coefficients. We explore the question to what
extent parameters can be efficiently estimated by appropriate experimental selection.
Results: A minimization formulation is used to find the parameter values that best fit the experiment data. When the
data is insufficient, the minimization problem often has many local minima that fit the data reasonably well. We show
that selecting a new experiment based on the local Fisher Information of one local minimum generates additional
data that allows one to successfully discriminate among the many local minima. The parameters can be estimated to
high accuracy by iteratively performing minimization and experiment selection. We show that the experiment choices
are roughly independent of which local minima is used to calculate the local Fisher Information.
Conclusions: We show that by an appropriate choice of experiments, one can, in principle, efficiently and accurately
estimate all the parameters of gene regulatory network. In addition, we demonstrate that appropriate experiment
selection can also allow one to restrict model predictions without constraining the parameters using many fewer
experiments. We suggest that predicting model behaviors and inferring parameters represent two different
approaches to model calibration with different requirements on data and experimental cost.
Keywords: systems biology, differential equation models, experimental design, parameter estimation, data fitting
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