Two major methodological challenges in modeling biological systems are model (in)validation and parameter estimation. The traditional approach is to fit the model parameters to data. An alternative approach pioneered by Packard, Frenklach, Seiler and colleagues (Frenklach et al., 2002) defines the range of parameter values that is consistent with the data while taking into account parametric and data uncertainty. If an invalidation certificate is found, the feasible parameter space is proved empty; otherwise, attempts to describe the feasible parameter space are carried out. We refer to this methodology as Robust Model Validation (RMV). Here we perform RMV using sum of squares (SOS) programs implemented by the MATLAB toolbox SOSTOOLS (Prajna et al., 2002). The principal advantage of SOS over conventional semidefinite programming (SDP) techniques such as the Sprocedure is the possibility of using higher-order multipliers to obtain tighter parameter bounds. We applied SOSTOOLS to a simple model of the yeast heterotrimeric G-protein cycle. We were able to invalidate the model based on real experimental data. Furthermore, using synthetic data that did not invalidate the model, we explored different techniques for representing the feasible parameter space
