{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T16:59:38Z","timestamp":1790701178466,"version":"4.1.0"},"reference-count":53,"publisher":"American Chemical Society (ACS)","issue":"38","license":[{"start":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T00:00:00Z","timestamp":1789430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,29]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We present EMBED, an ensemble-based extension of MATCONT that addresses the persistent design\u2013build\u2013test\u2013learn (DBTL) gap in synthetic biology from a mechanistic, dynamical systems perspective. While the DBTL gap is widely attributed to biological complexity, context dependence, and incomplete models, here we show that it also arises fundamentally from the geometry of high-dimensional parameter spaces, where desired dynamical regimes occupy narrow and fragile regions. Conventional use of MATCONT is limited to single-parameter or single-trajectory bifurcation analysis, restricting its ability to capture this global organization. To overcome this, we integrate MATCONT with large-scale parameter sampling and automated continuation, enabling high-throughput and reproducible ensemble bifurcation analysis. Using dual phosphorylation\u2013dephosphorylation (PdP) systems as a model, we demonstrate that although saddle-node, pitchfork, and saddle-node\u2013transcritical bifurcations are theoretically possible, they are confined to finely tuned parameter regions and are therefore difficult to realize experimentally. In contrast, robust nonsingular dynamics such as ultrasensitive and biphasic responses dominate under biologically relevant conditions. We further show that the choice of control parameter fundamentally constrains accessible dynamics, establishing a key design axis for biochemical systems. By quantifying the prevalence, robustness, and accessibility of dynamical regimes, EMBED enables the identification of parameter regions that are not only functionally desirable but also experimentally realizable. Thus, EMBED complements existing DBTL approaches by providing a global, structure-based framework that links kinetic parameters to dynamical behavior. In doing so, it transforms MATCONT from a local analysis tool into a scalable platform for global dynamical mapping and offers a principled strategy for the rational design of robust biological circuits across signaling and gene regulatory networks.<\/jats:p>","DOI":"10.1021\/acsomega.6c05467","type":"journal-article","created":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T09:02:04Z","timestamp":1789462924000},"page":"57307-57331","source":"Crossref","is-referenced-by-count":0,"title":["EMBED: Ensemble MATCONT-Based Detection and Classification\nof Bifurcations in Dual Phosphorylation\u2013Dephosphorylation Reaction\nNetworks"],"prefix":"10.1021","volume":"11","author":[{"given":"Guturu L.","family":"Harika","sequence":"first","affiliation":[{"name":"IIIT-Delhi , , ,","place":["New Delhi, INDIA, 110020"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0362-0956","authenticated-orcid":true,"given":"Krishnamachari","family":"Sriram","sequence":"additional","affiliation":[{"name":"IIIT-Delhi , , ,","place":["New Delhi, India, 110020"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,15]]},"reference":[{"key":"2026092911122441900_cit1","doi-asserted-by":"publisher","first-page":"2844","DOI":"10.1021\/acssynbio.4c00272","article-title":"Pattern formation and bistability\nin a synthetic intercellular genetic toggle","volume":"13","author":"de Freitas Magalha\u0303es","year":"2024","journal-title":"ACS Synth. Biol."},{"key":"2026092911122441900_cit2","doi-asserted-by":"publisher","first-page":"3163","DOI":"10.1021\/acssynbio.5c00299","article-title":"Engineering\ncell fate with adaptive feedback control","volume":"14","author":"Britto Bisso","year":"2025","journal-title":"ACS\nSynth. Biol."},{"key":"2026092911122441900_cit3","doi-asserted-by":"publisher","first-page":"106379","DOI":"10.1016\/j.isci.2023.106379","article-title":"Origin, heterogeneity,\nand interconversion of noncanonical bistable\nswitches from the positive feedback loops under dual signaling","volume":"26","author":"Das","year":"2023","journal-title":"iScience"},{"key":"2026092911122441900_cit4","doi-asserted-by":"publisher","first-page":"2865","DOI":"10.1021\/acssynbio.3c00033","article-title":"Automated\ndesign of synthetic gene circuits in the presence of molecular noise","volume":"12","author":"Sequeiros","year":"2023","journal-title":"ACS Synth. Biol."},{"key":"2026092911122441900_cit5","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1021\/sb300027y","article-title":"Automated design of\ngenetic toggle switches with predetermined bistability","volume":"1","author":"Chen","year":"2012","journal-title":"ACS Synth. Biol."},{"key":"2026092911122441900_cit6","doi-asserted-by":"publisher","first-page":"103143","DOI":"10.1016\/j.copbio.2024.103143","article-title":"Synthetic\nbiology advances towards\na bio-based society in the era of artificial intelligence","volume":"87","author":"Iram","year":"2024","journal-title":"Curr. Opin. Biotechnol."},{"key":"2026092911122441900_cit7","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pbio.3002116","article-title":"Synthetic biology: Learning the way\ntoward high-precision biological design","volume":"21","author":"Kitano","year":"2023","journal-title":"PLoS\nBiol."},{"key":"2026092911122441900_cit8","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1038\/nchembio.1519","article-title":"Engineering synergy in biotechnology","volume":"10","author":"Nielsen","year":"2014","journal-title":"Nat. Chem. Biol."},{"key":"2026092911122441900_cit9","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.0030189","article-title":"Universally\nsloppy parameter sensitivities in systems\nbiology models","volume":"3","author":"Gutenkunst","year":"2007","journal-title":"PLoS Comput. Biol."},{"key":"2026092911122441900_cit10","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005227","article-title":"The limitations of model-based experimental\ndesign\nand parameter estimation in sloppy systems","volume":"12","author":"White","year":"2016","journal-title":"PLoS Comput. Biol."},{"key":"2026092911122441900_cit11","doi-asserted-by":"publisher","first-page":"2742","DOI":"10.1021\/acssynbio.3c00708","article-title":"Evaluating the contribution of model\ncomplexity in predicting genetic circuit","volume":"13","author":"Buecherl","year":"2024","journal-title":"ACS\nSynth. Biol."},{"key":"2026092911122441900_cit12","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1145\/779359.779362","article-title":"MATCONT","volume":"29","author":"Dhooge","year":"2003","journal-title":"ACM\nTrans. Math. Softw."},{"key":"2026092911122441900_cit13","unstructured":"The MathWorks, Inc.\n          \n          MATLAB and Statistics and Machine\nLearning Toolbox; Version R2024b; MathWorks,\nInc. 2024."},{"key":"2026092911122441900_cit14","doi-asserted-by":"crossref","unstructured":"Ermentrout, B.\n          \n          Simulating,\nAnalyzing, and Animating Dynamical Systems: A Guide to XPPAUT for\nResearchers and Students; Society for Industrial\nand Applied Mathematics, 2002.","DOI":"10.1137\/1.9780898718195"},{"key":"2026092911122441900_cit15","doi-asserted-by":"publisher","first-page":"1950104","DOI":"10.1142\/S0218127419501049","article-title":"Automatic detection of saddle-node-transcritical interactions","volume":"29","author":"van Veen","year":"2019","journal-title":"Int. J. Bifurc. Chaos"},{"key":"2026092911122441900_cit16","volume-title":"Nonlinear Dynamics\nand Chaos: With Applications to Physics, Biology, Chemistry","author":"Strogatz","year":"2015"},{"key":"2026092911122441900_cit17","article-title":"Mathematical\nBiology","volume-title":"Interdisciplinary\nApplied Mathematics","author":"Murray","year":"2002","edition":"3"},{"key":"2026092911122441900_cit18","doi-asserted-by":"publisher","first-page":"1020","DOI":"10.1016\/j.physd.2011.02.012","article-title":"A mathematical\nframework for critical transitions: Bifurcations, fast-slow systems\nand stochastic dynamics","volume":"240","author":"Kuehn","year":"2011","journal-title":"Physica D"},{"key":"2026092911122441900_cit19","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1016\/j.tibs.2014.08.003","article-title":"Ultrasensitivity\npart I: Michaelian responses and zero-order ultrasensitivity","volume":"39","author":"Ferrell","year":"2014","journal-title":"Trends Biochem. Sci."},{"key":"2026092911122441900_cit20","doi-asserted-by":"publisher","first-page":"1961","DOI":"10.1529\/biophysj.105.073874","article-title":"Bistability, stochasticity, and oscillations\nin the mitogen-activated protein kinase cascade","volume":"90","author":"Wang","year":"2006","journal-title":"Biophys. J."},{"key":"2026092911122441900_cit21","doi-asserted-by":"publisher","DOI":"10.7554\/elife.65358","article-title":"Symmetry breaking meets\nmultisite modification","volume":"10","author":"Ramesh","year":"2021","journal-title":"eLife"},{"key":"2026092911122441900_cit22","doi-asserted-by":"publisher","first-page":"2846","DOI":"10.1038\/sj.onc.1202462","article-title":"Instabilities\nin phosphorylation-dephosphorylation cascades and cell cycle checkpoints","volume":"18","author":"Aguda","year":"1999","journal-title":"Oncogene"},{"key":"2026092911122441900_cit23","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.pbiomolbio.2009.06.004","article-title":"Bistability\nby multiple phosphorylation of regulatory proteins","volume":"100","author":"Kapuy","year":"2009","journal-title":"Prog. Biophys. Mol. Biol."},{"key":"2026092911122441900_cit24","doi-asserted-by":"publisher","first-page":"1506","DOI":"10.1093\/bioinformatics\/bth110","article-title":"Bifurcation\nanalysis of the regulatory modules of the\nmammalian G1\/S transition","volume":"20","author":"Swat","year":"2004","journal-title":"Bioinformatics"},{"key":"2026092911122441900_cit25","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1083\/jcb.200308060","article-title":"Signaling\nswitches and bistability\narising from multisite phosphorylation in protein kinase cascades","volume":"164","author":"Markevich","year":"2004","journal-title":"J. Cell Biol."},{"key":"2026092911122441900_cit26","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1063\/1.1349894","article-title":"Bistability in cell\nsignaling: How to make continuous processes discontinuous,\nand reversible processes irreversible","volume":"11","author":"Ferrell","year":"2001","journal-title":"Chaos:\nAn Interdisciplinary Journal of Nonlinear Science"},{"key":"2026092911122441900_cit27","doi-asserted-by":"publisher","first-page":"R458","DOI":"10.1016\/j.cub.2012.03.045","article-title":"Bistability,\nbifurcations, and Waddington\u2019s epigenetic landscape","volume":"22","author":"Ferrell","year":"2012","journal-title":"Curr. Biol."},{"key":"2026092911122441900_cit28","doi-asserted-by":"publisher","first-page":"556","DOI":"10.1016\/j.tibs.2014.09.003","article-title":"Ultrasensitivity\npart II: Multisite phosphorylation, stoichiometric\ninhibitors, and positive feedback","volume":"39","author":"Ferrell","year":"2014","journal-title":"Trends Biochem.\nSci."},{"key":"2026092911122441900_cit29","doi-asserted-by":"publisher","first-page":"612","DOI":"10.1016\/j.tibs.2014.10.002","article-title":"Ultrasensitivity\npart III: Cascades, bistable switches, and oscillators","volume":"39","author":"Ferrell","year":"2014","journal-title":"Trends Biochem. Sci."},{"key":"2026092911122441900_cit30","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011432","volume-title":"An Introduction to Systems\nBiology: Design Principles of Biological Circuits","author":"Alon","year":"2006"},{"key":"2026092911122441900_cit31","doi-asserted-by":"publisher","first-page":"10078","DOI":"10.1073\/pnas.93.19.10078","article-title":"Ultrasensitivity in the mitogen-activated\nprotein kinase\ncascade","volume":"93","author":"Huang","year":"1996","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026092911122441900_cit32","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1016\/S0968-0004(96)20026-X","article-title":"Tripping\nthe switch fantastic: How a protein kinase cascade can convert graded\ninputs into switch-like outputs","volume":"21","author":"Ferrell","year":"1996","journal-title":"Trends Biochem.\nSci."},{"key":"2026092911122441900_cit33","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/j.copbio.2008.06.009","article-title":"Uncovering\nmechanisms of bistability in biological systems","volume":"19","author":"Pomerening","year":"2008","journal-title":"Curr. Opin. Biotechnol."},{"key":"2026092911122441900_cit34","article-title":"Lectures on chemical\nreaction networks","volume-title":"Mathematics Research\nCenter","author":"Feinberg","year":"1979"},{"key":"2026092911122441900_cit35","doi-asserted-by":"publisher","first-page":"19008","DOI":"10.1074\/jbc.272.30.19008","article-title":"Mechanistic\nStudies of the Dual Phosphorylation of\nMitogen-activated Protein Kinase","volume":"272","author":"Ferrell","year":"1997","journal-title":"J. Biol. Chem."},{"key":"2026092911122441900_cit36","doi-asserted-by":"publisher","first-page":"1383","DOI":"10.1016\/j.bpj.2018.08.019","article-title":"When More Is Less: Dual Phosphorylation\nProtects Signaling\nOff State against Overexpression","volume":"115","author":"Witzel","year":"2018","journal-title":"Biophys. J."},{"key":"2026092911122441900_cit37","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0003-8","volume-title":"Differential Equations\nand Dynamical Systems","author":"Perko","year":"2001","edition":"3"},{"key":"2026092911122441900_cit38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.5642\/codee.NZHZ5522","article-title":"Differential equations for modeling\npathways leading\nto diabetes onset","volume":"18","author":"Savatorova","year":"2024","journal-title":"CODEE Journal"},{"key":"2026092911122441900_cit39","doi-asserted-by":"publisher","first-page":"arXiv:1002.4150","DOI":"10.48550\/arXiv.1002.4150","article-title":"The saddle-node-transcritical bifurcation\nin a population model with constant rate harvesting","author":"Saputra","year":"2010","journal-title":"arXiv"},{"key":"2026092911122441900_cit40","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1038\/35002131","article-title":"Construction of\na genetic toggle\nswitch in Escherichia coli","volume":"403","author":"Gardner","year":"2000","journal-title":"Nature"},{"key":"2026092911122441900_cit41","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/S0955-0674(02)00314-9","article-title":"Self-perpetuating\nstates in signal transduction: Positive\nfeedback, double-negative feedback and bistability","volume":"14","author":"Ferrell","year":"2002","journal-title":"Curr. Opin. Cell Biol."},{"key":"2026092911122441900_cit42","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/S0955-0674(03)00017-6","article-title":"Sniffers,\nbuzzers, toggles and blinkers:\nDynamics of regulatory and signaling pathways in the cell","volume":"15","author":"Tyson","year":"2003","journal-title":"Curr. Opin. Cell Biol."},{"key":"2026092911122441900_cit43","doi-asserted-by":"publisher","first-page":"010901","DOI":"10.1063\/1.4923066","article-title":"Perspective: Sloppiness\nand emergent theories in physics,\nbiology, and beyond","volume":"143","author":"Transtrum","year":"2015","journal-title":"J. Chem. Phys."},{"key":"2026092911122441900_cit44","doi-asserted-by":"publisher","first-page":"856","DOI":"10.1002\/biot.201200085","article-title":"Contextualizing context for synthetic biology - Identifying\ncauses of failure of synthetic biological systems","volume":"7","author":"Cardinale","year":"2012","journal-title":"Biotechnol. J."},{"key":"2026092911122441900_cit45","doi-asserted-by":"publisher","first-page":"20160380","DOI":"10.1098\/rsif.2016.0380","article-title":"Control theory meets\nsynthetic biology","volume":"13","author":"Del Vecchio","year":"2016","journal-title":"J. R. Soc. Interface"},{"key":"2026092911122441900_cit46","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1038\/nbt1330","article-title":"Ensemble modeling for\nanalysis of cell signaling dynamics","volume":"25","author":"Kuepfer","year":"2007","journal-title":"Nat. Biotechnol."},{"key":"2026092911122441900_cit47","doi-asserted-by":"publisher","first-page":"20110544","DOI":"10.1098\/rsta.2011.0544","article-title":"Joining forces of Bayesian\nand frequentist methodology: A study for inference in the presence\nof non-identifiability","volume":"371","author":"Raue","year":"2013","journal-title":"Phil. Trans. R. Soc.\nA"},{"key":"2026092911122441900_cit48","doi-asserted-by":"publisher","first-page":"R244","DOI":"10.1016\/j.cub.2008.02.035","article-title":"Feedback\nregulation of opposing enzymes generates robust, all-or-none bistable\nresponses","volume":"18","author":"Ferrell","year":"2008","journal-title":"Curr. Biol."},{"key":"2026092911122441900_cit49","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1038\/nrm2203","article-title":"Mechanisms of Specificity in Protein\nPhosphorylation","volume":"8","author":"Ubersax","year":"2007","journal-title":"Nat. Rev. Mol. Cell Biol."},{"key":"2026092911122441900_cit50","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1126\/science.1198701","article-title":"Scaffold Proteins: Hubs for Controlling\nthe Flow of Cellular Information","volume":"332","author":"Good","year":"2011","journal-title":"Science"},{"key":"2026092911122441900_cit51","doi-asserted-by":"publisher","first-page":"aac7341","DOI":"10.1126\/science.aac7341","article-title":"Genetic Circuit Design Automation","volume":"352","author":"Nielsen","year":"2016","journal-title":"Science"},{"key":"2026092911122441900_cit52","volume-title":"Biomolecular\nFeedback Systems","author":"Del Vecchio","year":"2018"},{"key":"2026092911122441900_cit53","doi-asserted-by":"publisher","first-page":"arXiv:2606.01444","DOI":"10.48550\/arXiv.2606.01444","article-title":"Self-Revising Discovery\nSystems for Science: A Categorical\nFramework for Agentic Artificial Intelligence","author":"Wang","year":"2026","journal-title":"arXiv"}],"container-title":["ACS Omega"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acsomega.6c05467","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/acsodf\/article-pdf\/11\/38\/57307\/68507466\/acsomega.6c05467.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/acsodf\/article-pdf\/11\/38\/57307\/68507466\/acsomega.6c05467.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T16:14:21Z","timestamp":1790698461000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/acsodf\/article\/11\/38\/57307\/5429775\/EMBED-Ensemble-MATCONT-Based-Detection-and"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,15]]},"references-count":53,"journal-issue":{"issue":"38","published-online":{"date-parts":[[2026,9,15]]},"published-print":{"date-parts":[[2026,9,29]]}},"URL":"https:\/\/doi.org\/10.1021\/acsomega.6c05467","relation":{},"ISSN":["2470-1343"],"issn-type":[{"value":"2470-1343","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,15]]}}}