{"id":686,"date":"2015-05-11T22:30:28","date_gmt":"2015-05-11T22:30:28","guid":{"rendered":"http:\/\/biocyb0.cs.ucla.edu\/wp\/?page_id=686"},"modified":"2020-10-28T22:19:34","modified_gmt":"2020-10-28T22:19:34","slug":"structural-identifiability-algorithms-software","status":"publish","type":"page","link":"http:\/\/biocyb0.cs.ucla.edu\/wp\/?page_id=686","title":{"rendered":"Structural identifiability algorithms &#038; software"},"content":{"rendered":"\t<div class=\"vc_row wpb_row vc_row-fluid\"  >\n\t<div class=\"vc_col-sm-12 wpb_column vc_column_container \">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t\n\t<div class=\"wpb_text_column wpb_content_element \">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h3 style=\"text-align: center;\">Structural identifiability algorithms &amp; software<\/h3>\n\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_text_column wpb_content_element  vc_custom_1431383457784\">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<ul>\n<li><strong>Date:<\/strong> April 30, 2015<\/li>\n<li><strong>People:<\/strong> Nikki Meshkat (nicolette.meshkat[at]gmail.com), Christine Kuo (ckuo24[at]gmail.com)<\/li>\n<li><strong>Primary Citations:<\/strong> Meshkat et al. <em>Math Biosci <\/em>233:19-31 (2011)<br \/>\n<a href=\"http:\/\/www.ncbi.nlm.nih.gov\/pubmed\/21763702\">http:\/\/www.ncbi.nlm.nih.gov\/pubmed\/21763702<\/a><\/li>\n<\/ul>\n<p style=\"padding-left: 30px;\">Meshkat et al. PLOS ONE 9:1-14 (2014) <a href=\"http:\/\/journals.plos.org\/plosone\/article?id=10.1371\/journal.pone.0110261\">journals.plos.org\/plosone\/article?id=10.1371\/journal.pone.0110261<\/a><\/p>\n<ul>\n<li><strong><a href=\"http:\/\/biocyb1.cs.ucla.edu\/combos\/\">Website<\/a><\/strong><\/li>\n<\/ul>\n\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_text_column wpb_content_element \">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p>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 \u2013 and which are not \u2013 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 <em>unidentifiability problem<\/em> since the outset. There\u2019s useful quantitative information about unidentifiable parameters in all I-O data, such as finite parameter <em>ranges<\/em> and structurally identifiable parameter <em>combinations<\/em>. Solution algorithms, based in ordinary and differential algebra, have been developed and published in more than a dozen articles (see the <strong>Publications <\/strong>section). Many of these are embedded in our new web application (app) COMBOS, described in greater detail and illustrated at the URL above.<\/p>\n\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_text_column wpb_content_element \">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<h3 style=\"text-align: center;\"><strong>The COMBOS Web App<\/strong><\/h3>\n<p><em>Structural identifiability<\/em> (<em>SI<\/em>) is the primary question, usually understood as knowing which of <em>P<\/em> unknown biomodel parameters <em>p<\/em><sub>1<\/sub>,\u2026, <em>p<sub>i<\/sub><\/em>,\u2026, <em>p<sub>P<\/sub><\/em> are \u2013 and which are not \u2013 quantifiable in principle from particular input-output (I-O) biodata. It is not widely appreciated, however, that the same data-base also can provide quantitative information about the structurally <u>un<\/u>identifiable (<u>not<\/u> quantifiable) subset, in the form of algebraic relationships among (combinations of) unidentifiable <em>p<sub>i<\/sub><\/em>. Importantly, this is a first step toward finding what else is needed to quantify particular <u>un<\/u>identifiable parameters of interest \u2013 possibly even all parameters \u2013 e.g. from new I-O experiments. We\u2019ve developed novel algorithms that address and solve the<em> SI <\/em>problem for a practical class of nonlinear (and linear) ordinary differential equation (ODE) systems biology models, and implemented them as a user-friendly web application (app) \u2013 COMBOS. Users provide the structural ODE and output measurement models in one of two standard forms. COMBOS provides a list of uniquely (globally) and non-uniquely (locally) <em>SI<\/em> model parameters, and \u2013 importantly \u2013 the <u>combinations<\/u> of parameters not individually <em>SI<\/em>. If locally <em>SI<\/em>, it also provides the number of different solutions \u2013 also with important implications in practice.<\/p>\n<p>The behind-the-scenes symbolic differential algebra algorithm is based on computing Gr\u00f6bner 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.<\/p>\n<p>COMBOS was developed for facile instructional and research use. We use it in the classroom to illustrate <em>SI<\/em> analysis; and also have simplified complex models of tumor suppressor p53 and hormone regulation \u2013 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.<strong>\u00a0 <\/strong><\/p>\n<p>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.<\/p>\n<p><strong>The COMBOS web app user interface.<\/strong> <a href=\"http:\/\/biocyb1.cs.ucla.edu\/combos\">http:\/\/biocyb1.cs.ucla.edu\/combos<\/a><\/p>\n\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_single_image wpb_content_element vc_align_center\">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t\n\t\t\t<div class=\"vc_single_image-wrapper   vc_box_border_grey\"><img loading=\"lazy\" decoding=\"async\" width=\"794\" height=\"629\" src=\"http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos3.jpg\" class=\"vc_single_image-img attachment-full\" alt=\"\" srcset=\"http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos3.jpg 794w, http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos3-300x238.jpg 300w\" sizes=\"(max-width: 794px) 100vw, 794px\" \/><\/div>\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_text_column wpb_content_element \">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><strong>(b)<\/strong>\u00a0Interactive 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 (\u201cpretty\u201d). Six additional example models are selectable on the interface, to familiarize users with the app and its features.<\/p>\n\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_single_image wpb_content_element vc_align_center\">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t\n\t\t\t<div class=\"vc_single_image-wrapper   vc_box_border_grey\"><img loading=\"lazy\" decoding=\"async\" width=\"804\" height=\"867\" src=\"http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos2b.jpg\" class=\"vc_single_image-img attachment-full\" alt=\"\" srcset=\"http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos2b.jpg 804w, http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos2b-278x300.jpg 278w\" sizes=\"(max-width: 804px) 100vw, 804px\" \/><\/div>\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_text_column wpb_content_element \">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><strong>(c)<\/strong> Structural identifiability (<em>SI<\/em>) analysis results provided in ~32 secs; 2 individual and one product of 9 <em>SI<\/em> combos are shown uniquely <em>SI<\/em>; 4 remaining product or sum combos of other 7 parameters are shown to have three feasible solutions each. The<strong> Model in Copy\/Paste Format<\/strong> can be readily used to run variations of this model, using the copy\/paste input window shown in (a).<\/p>\n\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_single_image wpb_content_element vc_align_center\">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t\n\t\t\t<div class=\"vc_single_image-wrapper   vc_box_border_grey\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"480\" src=\"http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos3-copy.jpg\" class=\"vc_single_image-img attachment-full\" alt=\"\" srcset=\"http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos3-copy.jpg 750w, http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/combos3-copy-300x192.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/div>\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_text_column wpb_content_element \">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><strong>Flow chart of information flow in COMBOS.<\/strong> 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.<\/p>\n\n\t\t<\/div> \n\t<\/div> \n\t<div class=\"wpb_single_image wpb_content_element vc_align_center\">\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t\n\t\t\t<div class=\"vc_single_image-wrapper   vc_box_border_grey\"><img loading=\"lazy\" decoding=\"async\" width=\"1990\" height=\"890\" src=\"http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/Screenshot-2015-05-01-14.49.26.png\" class=\"vc_single_image-img attachment-full\" alt=\"\" srcset=\"http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/Screenshot-2015-05-01-14.49.26.png 1990w, http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/Screenshot-2015-05-01-14.49.26-300x134.png 300w, http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/Screenshot-2015-05-01-14.49.26-1024x458.png 1024w, http:\/\/biocyb0.cs.ucla.edu\/wp\/wp-content\/uploads\/2015\/04\/Screenshot-2015-05-01-14.49.26-940x420.png 940w\" sizes=\"(max-width: 1990px) 100vw, 1990px\" \/><\/div>\n\t\t<\/div> \n\t<\/div> \n\t\t<\/div> \n\t<\/div> \n<\/div><div class=\"vc_row-full-width\"><\/div>\n","protected":false},"excerpt":{"rendered":"Structural identifiability algorithms &amp; software 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 Website The Biocybernetics laboratory has been making seminal contributions to the theory and practice of structural identifiability analysis since the early","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"template-full.php","meta":{"footnotes":""},"_links":{"self":[{"href":"http:\/\/biocyb0.cs.ucla.edu\/wp\/index.php?rest_route=\/wp\/v2\/pages\/686"}],"collection":[{"href":"http:\/\/biocyb0.cs.ucla.edu\/wp\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/biocyb0.cs.ucla.edu\/wp\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/biocyb0.cs.ucla.edu\/wp\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/biocyb0.cs.ucla.edu\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=686"}],"version-history":[{"count":9,"href":"http:\/\/biocyb0.cs.ucla.edu\/wp\/index.php?rest_route=\/wp\/v2\/pages\/686\/revisions"}],"predecessor-version":[{"id":1023,"href":"http:\/\/biocyb0.cs.ucla.edu\/wp\/index.php?rest_route=\/wp\/v2\/pages\/686\/revisions\/1023"}],"wp:attachment":[{"href":"http:\/\/biocyb0.cs.ucla.edu\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}