Abstract
Dynamic behavior of biological systems is commonly represented by non-linear models such as ordinary differential equations. A frequently encountered task in such systems is the estimation of model parameters based on measurement of biochemical compounds. Non-linear models require special techniques to estimate the uncertainty of the obtained model parameters and predictions, e.g. by exploiting the concept of the profile likelihood. Model parameters with significant uncertainty associated with their estimates hinder the interpretation of model results. Informing these model parameters by optimal experimental design minimizes the additional amount of data and therefore resources required in experiments. However, existing techniques of experimental design either require prior parameter distributions in Bayesian approaches or do not adequately deal with the non-linearity of the system in frequentist approaches. For identification of optimal experimental designs, we propose a two-dimensional profile likelihood approach, providing a design criterion which meaningfully represents the expected parameter uncertainty after measuring data for a specified experimental condition. The described approach is implemented into the open source toolbox Data2Dynamics in Matlab. The applicability of the method is demonstrated on an established systems biology model. For this demonstration, available data has been censored to simulate a setting in which parameters are not yet well determined. After determining the optimal experimental condition from the censored ones, a realistic evaluation was possible by re-introducing the censored data point corresponding to the optimal experimental condition. This provided a validation that our method is feasible in real-world applications. The approach applies to, but is not limited to, models in systems biology.
Highlights
With Fisher’s pioneering work on optimizing the design of agricultural experiments lying a century in the past, the design of informative experiments has long since become a foundation for most quantitative sciences
We propose a frequentist approach for optimal experimental design which realizes the full potential of the profile likelihood approach by extending the previously best-performing method (Steiert et al, 2012)
The second example is based on the published experimental data for a model of erythropoietin (EPO) degradation (Becker et al, 2010) for which data has been censored in order to mimic a setting in which experimental design can be applied
Summary
With Fisher’s pioneering work on optimizing the design of agricultural experiments lying a century in the past, the design of informative experiments has long since become a foundation for most quantitative sciences. The underlying models used for analyses become increasingly complex. This is due to the fields aspiration to provide holistic descriptions of biological systems which are able to capture static properties of a system but the dynamic interactions of the system’s components (Kitano, 2002; Nurse and Hayles, 2011). For these systems, mathematical models are established to reduce the complexity of the biological components to their relevant features. Close cooperation of experimenters and theoreticians throughout the process increases the chance of generating data that is suitable for this task
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