On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation

Abstract

Parameter identifiability problems can plague biomodelers when they reach the quantification stage of development, even for relatively simple models. Structural identifiability (SI) is the primary question, usually understood as knowing which of P unknown biomodel parameters p 1,…, pi,…, pP are-and which are not-quantifiable in principle from particular input-output (I-O) biodata. It is not widely appreciated that the same database also can provide quantitative information about the structurally unidentifiable (not quantifiable) subset, in the form of explicit algebraic relationships among unidentifiable pi. Importantly, this is a first step toward finding what else is needed to quantify particular unidentifiable parameters of interest from new I–O experiments. We further develop, implement and exemplify novel algorithms that address and solve the SI problem for a practical class of ordinary differential equation (ODE) systems biology models, as a user-friendly and universally-accessible web application (app)–COMBOS. Users provide the structural ODE and output measurement models in one of two standard forms to a remote server via their web browser. COMBOS provides a list of uniquely and non-uniquely SI model parameters, and–importantly-the combinations of parameters not individually SI. If non-uniquely SI, it also provides the maximum number of different solutions, with important practical implications. The behind-the-scenes symbolic differential algebra algorithms are based on computing Gröbner bases of model attributes established after some algebraic transformations, using the computer-algebra system Maxima. COMBOS was developed for facile instructional and research use as well as modeling. We use it in the classroom to illustrate SI analysis; and have simplified complex models of tumor suppressor p53 and hormone regulation, based on explicit computation of parameter combinations. It’s illustrated and validated here for models of moderate complexity, with and without initial conditions. Built-in examples include unidentifiable 2 to 4-compartment and HIV dynamics models.

The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study

“…Equations (17) indicate the number of degrees of freedom and provide the exact constraints to include into the model equations in order to reach global identifiability. In this case, it is easy to see from (17) that there are only two free parameters ( 1 , ). By including (17) in the model equations (16), the four redundant parameters { 1 , 2 , , } are constrained as functions of the two free parameters.…”

“…In this case, it is easy to see from (17) that there are only two free parameters ( 1 , ). By including (17) in the model equations (16), the four redundant parameters { 1 , 2 , , } are constrained as functions of the two free parameters. Now we want to show that this result could be qualitatively determined by a sensitivity-based identifiability approach, possibly arriving to discover a correlation between the above six unidentifiable parameters.…”

“…However, if the postulated model has an infinite number (unidentifiable) of parameter solutions, the parameter estimates that could still be obtained by some numerical optimization algorithms would be unreliable and vary randomly depending, for instance, on the initialization of the algorithm [15]. Vice versa, in case of nonidentifiability, the outcome of structural identifiability, that is, the Gröbner bases of the exhaustive summary, provides algebraic nonlinear equations which define the relations between unidentifiable parameters [16,17]. These equations describe the equivalence class of parameters with respect to their ability to describe the output function.…”

Combined Estimation and Optimal Control of Batch Membrane Processes

“…There are few frameworks and software tools available that assist in identifiability analysis [29,30]. To the authors knowledge, there are three common software tools that use one of the above-mentioned methods for testing global identifiability of non-linear systems.…”

“…To the authors knowledge, there are three common software tools that use one of the above-mentioned methods for testing global identifiability of non-linear systems. These are DAISY [31], COMBOS [30] and GenSSI. The open-source tool GenSSI implements the generating series approach and is chosen here for the identifiability analysis of the parameters.…”