Model Selection in Systems Biology Depends on Experimental Design

Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a model's predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis.Author Summary: Different models of the same process represent distinct hypotheses about reality. These can be decided between within the framework of model selection, where the evidence for each is given by their ability to reproduce a set of experimental data. Even if one of the models is correct, the chances of identifying it can be hindered by the quality of the data, both in terms of its signal to measurement error ratio and the intrinsic discriminatory potential of the experiment undertaken. This potential can be predicted in various ways, and maximising it is one aim of experimental design. In this work we present a computationally efficient method of experimental design for model selection. We exploit the efficiency to consider the implications of the realistic case where all models are more or less incorrect, showing that experiments can be chosen that, considered individually, lead to unequivocal support for opposed hypotheses.