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COMBOS: A Web Application for Finding Identifiable Parameter Combinations of Nonlinear Ordinary Differential Equation Models


Parameter identifiability problems can plague biomodelers when they reach the quantification stage of development, even for relatively simple models. Novice modelers often may not even recognize that identifiability properties of the model are the problem. This highly technical subject is also difficult to teach.

COMBOS is a user-friendly web app that addresses and solves key aspects of the structural identifiability (SI) problem for a practical class of nonlinear (and linear) ordinary differential equation (ODE) systems biology and other models. Given the ODE and measurement models (user input) of the form dx/dt = f(x,p,u) and y = g(x,p), it provides not only a list of uniquely (globally) and non-uniquely (locally) SI model parameters, but also the combinations of parameters that are not individually SI. If locally SI, it also provides the number of solutions. The behind-the-scenes symbolic differential algebra algorithm is based on computing Gröbner bases of model attributes established after some algebraic transformations and is currently run in the computer algebra system Maxima.

COMBOS was developed for facile instructional as well as research use. It has been validated for models of moderate dimensions with and without initial conditions. COMBOS includes several built-in examples, including linear 2 to 4-compartment models and a 4th-order nonlinear unidentifiable HIV dynamics model.

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