Stimulus Design for Model Selection and Validation in Cell Signaling

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Abstract
Mechanism-based chemical kinetic models are increasingly being used to describe biological signaling. Such models serve to encapsulate current understanding of pathways and to enable insight into complex biological processes. One challenge in model development is that, with limited experimental data, multiple models can be consistent with known mechanisms and existing data. Here, we address the problem of model ambiguity by providing a method for designing dynamic stimuli that, in stimulus–response experiments, distinguish among parameterized models with different topologies, i.e., reaction mechanisms, in which only some of the species can be measured. We develop the approach by presenting two formulations of a model-based controller that is used to design the dynamic stimulus. In both formulations, an input signal is designed for each candidate model and parameterization so as to drive the model outputs through a target trajectory. The quality of a model is then assessed by the ability of the corresponding controller, informed by that model, to drive the experimental system. We evaluated our method on models of antibody–ligand binding, mitogen-activated protein kinase (MAPK) phosphorylation and de-phosphorylation, and larger models of the epidermal growth factor receptor (EGFR) pathway. For each of these systems, the controller informed by the correct model is the most successful at designing a stimulus to produce the desired behavior. Using these stimuli we were able to distinguish between models with subtle mechanistic differences or where input and outputs were multiple reactions removed from the model differences. An advantage of this method of model discrimination is that it does not require novel reagents, or altered measurement techniques; the only change to the experiment is the time course of stimulation. Taken together, these results provide a strong basis for using designed input stimuli as a tool for the development of cell signaling models. A major focus of systems biology is the development of mechanism-based models of cell signaling pathways. These models hold the promise of encapsulating our understanding of complex biological processes while also predicting new behavior. However, as these models become more complex, it can be difficult to distinguish between model alternatives. One means of improved model discrimination involves making measurements of additional components in the biological system to provide more detailed data. Here we present an alternative, which is to apply a time-varying input while monitoring the same network components. This new method was able to discriminate among models with subtle mechanistic differences. A particular advantage is that for many cases, time-varying input stimulation is fairly easy to apply experimentally, whereas measuring additional network components can involve the creation of new reagents or measurement assays. Thus, we believe that the application of time-varying input stimulation will become a powerful tool in the field of systems biology as the community places increased emphasis on the development of quantitative, mechanistic, and predictive models of biological network behavior.