{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T04:43:34Z","timestamp":1768797814290,"version":"3.49.0"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T00:00:00Z","timestamp":1731974400000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Innovation, Science and Research of the German","award":["313\/323-400-00213"],"award-info":[{"award-number":["313\/323-400-00213"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,11,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>Expanding on constraint-based metabolic models, protein allocation models (PAMs) enhance flux predictions by accounting for protein resource allocation in cellular metabolism. Yet, to this date, there are no dedicated methods for analyzing and understanding the growth-limiting factors in simulated phenotypes in PAMs.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>Here, we introduce a systematic framework for identifying the most sensitive enzyme concentrations (sEnz) in PAMs. The framework exploits the primal and dual formulations of these models to derive sensitivity coefficients based on relations between variables, constraints, and the objective function. This approach enhances our understanding of the growth-limiting factors of metabolic phenotypes under specific environmental or genetic conditions. Compared to other traditional methods for calculating sensitivities, sEnz requires substantially less computation time and facilitates more intuitive comparison and analysis of sensitivities. The sensitivities calculated by sEnz cover enzymes, reactions and protein sectors, enabling a holistic overview of the factors influencing metabolism. When applied to an Escherichia coli PAM, sEnz revealed major pathways and enzymes driving overflow metabolism. Overall, sEnz offers a computational efficient framework for understanding PAM predictions and unraveling the factors governing a particular metabolic phenotype.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>sEnz is implemented in the modular toolbox for the generation and analysis of PAMs in Python (PAModelpy; v.0.0.3.3), available on Pypi (https:\/\/pypi.org\/project\/PAModelpy\/). The source code together with all other python scripts and notebooks are available on GitHub (https:\/\/github.com\/iAMB-RWTH-Aachen\/PAModelpy).<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btae691","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T06:38:13Z","timestamp":1731998293000},"source":"Crossref","is-referenced-by-count":5,"title":["Sensitivities in protein allocation models reveal distribution of metabolic capacity and flux control"],"prefix":"10.1093","volume":"40","author":[{"given":"Samira","family":"van den Bogaard","sequence":"first","affiliation":[{"name":"Institute of Applied Microbiology, Aachen Biology and Biotechnology, RWTH Aachen University , Aachen 52074,","place":["Germany"]}]},{"given":"Pedro A","family":"Saa","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Qu\u00edmica y Bioprocesos, Escuela de Ingenier\u00eda, Pontificia Universidad Cat\u00f3lica de Chile , Santiago 7820436,","place":["Chile"]},{"name":"Instituto de Ingenier\u00eda Matem\u00e1tica y Computacional, Pontificia Universidad Cat\u00f3lica de Chile , Santiago 7820436,","place":["Chile"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9593-4388","authenticated-orcid":false,"given":"Tobias B","family":"Alter","sequence":"additional","affiliation":[{"name":"Institute of Applied Microbiology, Aachen Biology and Biotechnology, RWTH Aachen University , Aachen 52074,","place":["Germany"]}]}],"member":"286","published-online":{"date-parts":[[2024,11,18]]},"reference":[{"key":"2024121102400463500_btae691-B1","doi-asserted-by":"crossref","first-page":"e00625-20","DOI":"10.1128\/msystems.00625-20","article-title":"Proteome regulation patterns determine Escherichia coli wild-type and mutant phenotypes","volume":"6","author":"Alter","year":"2021","journal-title":"mSystems"},{"key":"2024121102400463500_btae691-B2","doi-asserted-by":"crossref","first-page":"4402","DOI":"10.1021\/bi2002289","article-title":"The moderately efficient enzyme: evolutionary and physicochemical trends shaping enzyme parameters","volume":"50","author":"Bar-Even","year":"2011","journal-title":"Biochemistry"},{"key":"2024121102400463500_btae691-B3","doi-asserted-by":"crossref","first-page":"12663","DOI":"10.1073\/pnas.0609845104","article-title":"Intracellular crowding defines the mode and sequence of substrate uptake by Escherichia coli and constrains its metabolic activity","volume":"104","author":"Beg","year":"2007","journal-title":"Proc Natl Acad Sci USA"},{"key":"2024121102400463500_btae691-B4","doi-asserted-by":"crossref","first-page":"e109105","DOI":"10.1371\/journal.pone.0109105","article-title":"The interrelationship between promoter strength, gene expression, and growth rate","volume":"9","author":"Bienick","year":"2014","journal-title":"PLoS One"},{"key":"2024121102400463500_btae691-B5","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1126\/science.275.5304.1305","article-title":"Crystal structure of formate dehydrogenase H: catalysis involving Mo, molybdopterin, selenocysteine, and an Fe4S4 cluster","volume":"275","author":"Boyington","year":"1997","journal-title":"Science (New York, N.Y.)"},{"key":"2024121102400463500_btae691-B6","doi-asserted-by":"crossref","first-page":"17592","DOI":"10.1073\/pnas.1906569116","article-title":"Energy metabolism controls phenotypes by protein efficiency and allocation","volume":"116","author":"Chen","year":"2019","journal-title":"Proc Natl Acad Sci USA"},{"key":"2024121102400463500_btae691-B7","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s00018-019-03380-2","article-title":"The common message of constraint-based optimization approaches: overflow metabolism is caused by two growth-limiting constraints","volume":"77","author":"de Groot","year":"2020","journal-title":"Cell Mol Life Sci"},{"key":"2024121102400463500_btae691-B8","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1186\/1752-0509-7-74","article-title":"COBRApy: constraints-based reconstruction and analysis for python","volume":"7","author":"Ebrahim","year":"2013","journal-title":"BMC Syst Biol"},{"key":"2024121102400463500_btae691-B9","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1002\/bit.28493","article-title":"Sensitivity analysis and adaptive mutation strategy differential evolution algorithm for optimizing enzymes\u2019 turnover numbers in metabolic models","volume":"120","author":"Fan","year":"2023","journal-title":"Biotechnol Bioeng"},{"key":"2024121102400463500_btae691-B10","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1042\/bj2380781","article-title":"Fat synthesis in adipose tissue. 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