**Date:**April 30, 2015**People:**Nikki Meshkat (nicolette.meshkat[at]gmail.com), Christine Kuo (ckuo24[at]gmail.com)**Primary Citations:**Meshkat et al.*Math Biosci*233:19-31 (2011)

http://www.ncbi.nlm.nih.gov/pubmed/21763702

Meshkat et al. PLOS ONE 9:1-14 (2014) journals.plos.org/plosone/article?id=10.1371/journal.pone.0110261

The Biocybernetics laboratory has been making seminal contributions to the theory and practice of structural identifiability analysis since the early 1980s. Structural identifiability (SI) is the primary question, usually understood as knowing which unknown biomodel parameters are – and which are not – quantifiable in principle from particular input-output (I-O) biodata. Importantly, parameter identifiability problems can plague modelers during model quantification, even for relatively simple models. Often, too many parameters of interest are unidentifiable. The lab director and his students have been focusing on this *unidentifiability problem* since the outset. There’s useful quantitative information about unidentifiable parameters in all I-O data, such as finite parameter *ranges* and structurally identifiable parameter *combinations*. Solution algorithms, based in ordinary and differential algebra, have been developed and published in more than a dozen articles (see the **Publications **section). Many of these are embedded in our new web application (app) COMBOS, described in greater detail and illustrated at the URL above.

*Structural identifiability* (*SI*) is the primary question, usually understood as knowing which of *P* unknown biomodel parameters *p*_{1},…, *p _{i}*,…,

The behind-the-scenes symbolic differential algebra algorithm is based on computing Gröbner bases of model attributes established after some algebraic transformations, all using the computer algebra system Maxima. Built-in examples include unidentifiable 2 to 4-compartment models and an HIV dynamics model.

COMBOS was developed for facile instructional and research use. We use it in the classroom to illustrate *SI* analysis; and also have simplified complex models of tumor suppressor p53 and hormone regulation – based on explicit computation of parameter combinations. The code is open-source and freely available to others intent on enhancing it or using its facile user interface for other purposes.** **

We are currently working on rendering COMBOS computational algorithms more efficient, so they can handle a wider variety of models of greater complexity, and analyze them for structural identifiability more quickly.

**The COMBOS web app user interface.** (a) Header, user instructions and placeholder for user model – if already available in a file.

**(b)** Interactive model entry illustrating a 4-compartment nonlinear HIV model example with one experimental input and 2 output measurements. Equations are entered using familiar math programming language and translated on the right into natural math (“pretty”). Six additional example models are selectable on the interface, to familiarize users with the app and its features.

**(c)** Structural identifiability (*SI*) analysis results provided in ~32 secs; 2 individual and one product of 9 *SI* combos are shown uniquely *SI*; 4 remaining product or sum combos of other 7 parameters are shown to have three feasible solutions each. The** Model in Copy/Paste Format** can be readily used to run variations of this model, using the copy/paste input window shown in (a).

**Flow chart of information flow in COMBOS.** HTML and ASCIIMathML are utilized in the user section; the web interface is written in PHP and MathJax 2.0; and the symbolic algebra is done in Maxima, ported via PHP.