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Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009598","type":"journal-article","created":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T13:47:03Z","timestamp":1655128023000},"page":"e1009598","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["Differential methods for assessing sensitivity in biological models"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6498-7727","authenticated-orcid":true,"given":"Rachel","family":"Mester","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8091-7294","authenticated-orcid":true,"given":"Alfonso","family":"Landeros","sequence":"additional","affiliation":[]},{"given":"Chris","family":"Rackauckas","sequence":"additional","affiliation":[]},{"given":"Kenneth","family":"Lange","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,6,13]]},"reference":[{"issue":"2","key":"pcbi.1009598.ref001","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1038\/nprot.2014.025","article-title":"A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation","volume":"9","author":"J Liepe","year":"2014","journal-title":"Nature protocols"},{"issue":"11","key":"pcbi.1009598.ref002","first-page":"2","article-title":"MCMC using Hamiltonian dynamics.","volume":"2","author":"RM Neal","year":"2011","journal-title":"Handbook of markov chain monte carlo."},{"issue":"4","key":"pcbi.1009598.ref003","doi-asserted-by":"crossref","first-page":"2530","DOI":"10.1529\/biophysj.104.053405","article-title":"Sensitivity analysis of discrete stochastic systems","volume":"88","author":"R Gunawan","year":"2005","journal-title":"Biophysical journal"},{"issue":"1","key":"pcbi.1009598.ref004","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2105-6-155","article-title":"Iterative approach to model identification of biological networks","volume":"6","author":"KG Gadkar","year":"2005","journal-title":"BMC bioinformatics"},{"issue":"3","key":"pcbi.1009598.ref005","doi-asserted-by":"crossref","first-page":"e1000696","DOI":"10.1371\/journal.pcbi.1000696","article-title":"Parameter estimation and model selection in computational biology","volume":"6","author":"G Lillacci","year":"2010","journal-title":"PLoS computational biology"},{"issue":"16","key":"pcbi.1009598.ref006","doi-asserted-by":"crossref","first-page":"2311","DOI":"10.1093\/bioinformatics\/btr370","article-title":"AMIGO, a toolbox for advanced model identification in systems biology using global optimization","volume":"27","author":"E Balsa-Canto","year":"2011","journal-title":"Bioinformatics"},{"issue":"1","key":"pcbi.1009598.ref007","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.jtbi.2008.04.011","article-title":"A methodology for performing global uncertainty and sensitivity analysis in systems biology","volume":"254","author":"S Marino","year":"2008","journal-title":"Journal of theoretical biology"},{"issue":"3","key":"pcbi.1009598.ref008","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.1137\/S1064827501380630","article-title":"Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution","volume":"24","author":"Y Cao","year":"2003","journal-title":"SIAM journal on scientific computing"},{"key":"pcbi.1009598.ref009","author":"G. 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