MIDOE: Maximally-informed Design of Experiment to infer experimentally inaccessible transcription factors dynamics

1The TGF-{beta}/Smad signaling pathway regulates growth, development, and homeostasis of tissues across the animal kingdom. The pathway is activated when transforming growth factor -{beta} (TGF-{beta}) binds to its cognate transmembrane receptors to activate Smad2 by phosphorylation. The activated phosphor-Smad2 (PSmad2) undergoes a series of biochemical interactions with transcriptional activator Smad4 to form several oligomers, including the transcription factor (PSmad2)2/Smad4, which regulates target gene expression. Quantitative live cell imaging and mathematical modeling have been used to estimate the dynamics of (PSmad2)2/Smad4. However, due to the emergent nature of Smad2-Smad4 interactions, deconvolving the dynamics of the (PSmad2)2/Smad4 is challenging. We show that the Smad model is sloppy, has large parameter uncertainties (O[~]1015), and the eigenvalues of the Fisher Information Matrix span over several decades. As such, well-fit parameter sets generate highly under-constrained predictions. To overcome this, we employ Profile Log-Likelihood to guide maximally informed design of experiments (MIDOE) and infer the dynamics of (PSmad2)2/Smad4. We generate these experiments computationally and validate that MIDOE can optimally constrain model predictions. We demonstrate that such careful analysis would not only improve the predictive power of models in systems biology but also reduce the time and expense of performing non-optimal experiments.