We introduce a procedure for deciding when a mass-action model is incompatible with observed steady-state data that does not require any parameter estimation. Thus, we avoid the difficulties of nonlinear optimization typically associated with methods based on parameter fitting. Instead, we borrow ideas from algebraic geometry to construct a transformation of the model variables such that any set of steady states of the model under that transformation lies on a common plane, irrespective of the values of the model parameters. Model rejection can then be performed by assessing the degree to which the transformed data deviate from coplanarity. We demonstrate our method by applying it to models of multisite phosphorylation and cell death signaling. Our framework offers a parameter-free perspective on the statistical model selection problem, which can complement conventional statistical methods in certain classes of problems where inference has to be based on steady-state data and the model structures allow for suitable algebraic relationships among the steady-state solutions.
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