{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T20:24:01Z","timestamp":1776716641436,"version":"3.51.2"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1008208","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T00:00:00Z","timestamp":1612828800000}}],"reference-count":83,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Mathematical models of metabolic networks utilize simulation to study system-level mechanisms and functions. Various approaches have been used to model the steady state behavior of metabolic networks using genome-scale reconstructions, but formulating dynamic models from such reconstructions continues to be a key challenge. Here, we present the Mass Action Stoichiometric Simulation Python (MASSpy) package, an open-source computational framework for dynamic modeling of metabolism. MASSpy utilizes mass action kinetics and detailed chemical mechanisms to build dynamic models of complex biological processes. MASSpy adds dynamic modeling tools to the COnstraint-Based Reconstruction and Analysis Python (COBRApy) package to provide an unified framework for constraint-based and kinetic modeling of metabolic networks. MASSpy supports high-performance dynamic simulation through its implementation of libRoadRunner: the Systems Biology Markup Language (SBML) simulation engine. Three examples are provided to demonstrate how to use MASSpy: (1) a validation of the MASSpy modeling tool through dynamic simulation of detailed mechanisms of enzyme regulation; (2) a feature demonstration using a workflow for generating ensemble of kinetic models using Monte Carlo sampling to approximate missing numerical values of parameters and to quantify biological uncertainty, and (3) a case study in which MASSpy is utilized to overcome issues that arise when integrating experimental data with the computation of functional states of detailed biological mechanisms. MASSpy represents a powerful tool to address challenges that arise in dynamic modeling of metabolic networks, both at small and large scales.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008208","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T14:49:24Z","timestamp":1611845364000},"page":"e1008208","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":43,"title":["MASSpy: Building, simulating, and visualizing dynamic biological models in Python using mass action kinetics"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6175-5050","authenticated-orcid":true,"given":"Zachary B.","family":"Haiman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel C.","family":"Zielinski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuko","family":"Koike","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9403-509X","authenticated-orcid":true,"given":"James T.","family":"Yurkovich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2357-6785","authenticated-orcid":true,"given":"Bernhard O.","family":"Palsson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2021,1,28]]},"reference":[{"key":"pcbi.1008208.ref001","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1038\/msb.2008.8","article-title":"Formulating genome-scale kinetic models in the post-genome era","volume":"4","author":"N Jamshidi","year":"2008","journal-title":"Mol Syst Biol"},{"key":"pcbi.1008208.ref002","doi-asserted-by":"crossref","first-page":"907","DOI":"10.3389\/fmicb.2016.00907","article-title":"From DNA to FBA: How to Build Your Own Genome-Scale Metabolic Model","volume":"7","author":"DA Cuevas","year":"2016","journal-title":"Frontiers in Microbiology"},{"issue":"3","key":"pcbi.1008208.ref003","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1093\/bioinformatics\/btq679","article-title":"SurreyFBA: a command line tool and graphics user interface for constraint-based modeling of genome-scale metabolic reaction networks","volume":"27","author":"A Gevorgyan","year":"2011","journal-title":"Bioinformatics"},{"issue":"1","key":"pcbi.1008208.ref004","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1186\/s12918-015-0238-z","article-title":"FlexFlux: combining metabolic flux and regulatory network analyses","volume":"9","author":"L Marmiesse","year":"2015","journal-title":"BMC Systems Biology"},{"issue":"8","key":"pcbi.1008208.ref005","doi-asserted-by":"crossref","first-page":"e9235","DOI":"10.15252\/msb.20199235","article-title":"Community standards to facilitate development and address challenges in metabolic modeling","volume":"16","author":"MA Carey","year":"2020","journal-title":"Molecular Systems Biology"},{"issue":"10","key":"pcbi.1008208.ref006","doi-asserted-by":"crossref","first-page":"5528","DOI":"10.1073\/pnas.97.10.5528","article-title":"The Escherichia coli MG1655 in silico metabolic genotype: its definition, characteristics, and capabilities","volume":"97","author":"JS Edwards","year":"2000","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"4","key":"pcbi.1008208.ref007","doi-asserted-by":"crossref","first-page":"1506","DOI":"10.1016\/j.juro.2011.12.029","article-title":"Re: Haem oxygenase is synthetically lethal with the tumour suppressor fumarate hydratase","volume":"187","author":"A Atala","year":"2012","journal-title":"J Urol"},{"issue":"7","key":"pcbi.1008208.ref008","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1038\/nchembio.580","article-title":"Metabolic engineering of Escherichia coli for direct production of 1,4-butanediol","volume":"7","author":"H Yim","year":"2011","journal-title":"Nat Chem Biol"},{"issue":"6098","key":"pcbi.1008208.ref009","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1126\/science.1216861","article-title":"Network context and selection in the evolution to enzyme specificity","volume":"337","author":"H Nam","year":"2012","journal-title":"Science"},{"issue":"2","key":"pcbi.1008208.ref010","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1111\/j.1365-2796.2011.02494.x","article-title":"Using the reconstructed genome-scale human metabolic network to study physiology and pathology","volume":"271","author":"A Bordbar","year":"2012","journal-title":"J Intern Med"},{"key":"pcbi.1008208.ref011","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1186\/1752-0509-6-41","article-title":"A network perspective on metabolic inconsistency","volume":"6","author":"N Sonnenschein","year":"2012","journal-title":"BMC Syst Biol"},{"key":"pcbi.1008208.ref012","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1038\/msb.2013.18","article-title":"Basic and applied uses of genome-scale metabolic network reconstructions of Escherichia coli","volume":"9","author":"D McCloskey","year":"2013","journal-title":"Mol Syst Biol"},{"issue":"6137","key":"pcbi.1008208.ref013","doi-asserted-by":"crossref","first-page":"1220","DOI":"10.1126\/science.1234012","article-title":"Structural systems biology evaluation of metabolic thermotolerance in Escherichia coli","volume":"340","author":"RL Chang","year":"2013","journal-title":"Science"},{"issue":"2","key":"pcbi.1008208.ref014","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1038\/nbt.2458","article-title":"Potentiating antibacterial activity by predictably enhancing endogenous microbial ROS production","volume":"31","author":"MP Brynildsen","year":"2013","journal-title":"Nat Biotechnol"},{"issue":"4","key":"pcbi.1008208.ref015","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1038\/nrmicro2737","article-title":"Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods","volume":"10","author":"NE Lewis","year":"2012","journal-title":"Nat Rev Microbiol"},{"issue":"3","key":"pcbi.1008208.ref016","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1038\/s41596-018-0098-2","article-title":"Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0","volume":"14","author":"L Heirendt","year":"2019","journal-title":"Nat Protoc"},{"issue":"10","key":"pcbi.1008208.ref017","doi-asserted-by":"crossref","first-page":"3724","DOI":"10.1128\/AEM.60.10.3724-3731.1994","article-title":"Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110","volume":"60","author":"A Varma","year":"1994","journal-title":"Appl Environ Microbiol"},{"key":"pcbi.1008208.ref018","doi-asserted-by":"crossref","first-page":"46249","DOI":"10.1038\/srep46249","article-title":"Elucidating dynamic metabolic physiology through network integration of quantitative time-course metabolomics","volume":"7","author":"A Bordbar","year":"2017","journal-title":"Sci Rep"},{"issue":"5","key":"pcbi.1008208.ref019","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1111\/tpj.12763","article-title":"Integration of transcriptomics and metabolomics data specifies the metabolic response of Chlamydomonas to rapamycin treatment","volume":"81","author":"S Kleessen","year":"2015","journal-title":"Plant J"},{"issue":"2","key":"pcbi.1008208.ref020","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.ymben.2012.01.003","article-title":"Exploring the gap between dynamic and constraint-based models of metabolism","volume":"14","author":"D Machado","year":"2012","journal-title":"Metab Eng"},{"issue":"11","key":"pcbi.1008208.ref021","doi-asserted-by":"crossref","first-page":"e79195","DOI":"10.1371\/journal.pone.0079195","article-title":"Systematic construction of kinetic models from genome-scale metabolic networks","volume":"8","author":"NJ Stanford","year":"2013","journal-title":"PLoS One"},{"issue":"12","key":"pcbi.1008208.ref022","doi-asserted-by":"crossref","first-page":"5606","DOI":"10.1529\/biophysj.108.135442","article-title":"Ensemble Modeling of Metabolic Networks","volume":"95","author":"LM Tran","year":"2008","journal-title":"Biophysical Journal"},{"issue":"14","key":"pcbi.1008208.ref023","doi-asserted-by":"crossref","first-page":"1797","DOI":"10.1093\/bioinformatics\/btq278","article-title":"ABC-SysBio\u2013approximate Bayesian computation in Python with GPU support","volume":"26","author":"J Liepe","year":"2010","journal-title":"Bioinformatics"},{"issue":"8","key":"pcbi.1008208.ref024","doi-asserted-by":"crossref","first-page":"e1006356","DOI":"10.1371\/journal.pcbi.1006356","article-title":"Network-level allosteric effects are elucidated by detailing how ligand-binding events modulate utilization of catalytic potentials","volume":"14","author":"JT Yurkovich","year":"2018","journal-title":"PLoS Comput Biol"},{"issue":"8","key":"pcbi.1008208.ref025","doi-asserted-by":"crossref","first-page":"2426","DOI":"10.1016\/S0021-9258(18)64638-1","article-title":"Metabolic Control Mechanisms: V. A SOLUTION FOR THE EQUATIONS REPRESENTING INTERACTION BETWEEN GLYCOLYSIS AND RESPIRATION IN ASCITES TUMOR CELLS","volume":"235","author":"the technical assistance of E M Chance II W","year":"1960","journal-title":"Journal of Biological Chemistry"},{"issue":"2","key":"pcbi.1008208.ref026","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.bpj.2009.09.064","article-title":"Mass Action Stoichiometric Simulation Models: Incorporating Kinetics and Regulation into Stoichiometric Models","volume":"98","author":"N Jamshidi","year":"2010","journal-title":"Biophysical Journal"},{"issue":"1","key":"pcbi.1008208.ref027","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1186\/s12918-016-0283-2","article-title":"Evaluation of rate law approximations in bottom-up kinetic models of metabolism","volume":"10","author":"B Du","year":"2016","journal-title":"BMC Syst Biol"},{"issue":"4","key":"pcbi.1008208.ref028","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.cels.2015.10.003","article-title":"Personalized Whole-Cell Kinetic Models of Metabolism for Discovery in Genomics and Pharmacodynamics","volume":"1","author":"A Bordbar","year":"2015","journal-title":"Cell Syst"},{"key":"pcbi.1008208.ref029","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511736179","volume-title":"Systems Biology: Simulation of Dynamic Network States","author":"B\u00d8 Palsson","year":"2011"},{"issue":"4","key":"pcbi.1008208.ref030","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/0010-4809(88)90052-3","article-title":"Theory formation in postulating enzyme kinetic mechanisms: reasoning with constraints","volume":"21","author":"V Soo","year":"1988","journal-title":"Computers and biomedical research, an international journal"},{"key":"pcbi.1008208.ref031","unstructured":"Anand, Sonnenschein N. opencobra\/MASS-Toolbox: Updated Documentation; 2017. Available from: https:\/\/doi.org\/10.5281\/zenodo.803492."},{"key":"pcbi.1008208.ref032","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":"A Ebrahim","year":"2013","journal-title":"BMC Syst Biol"},{"issue":"6","key":"pcbi.1008208.ref033","doi-asserted-by":"crossref","first-page":"e1004867","DOI":"10.1371\/journal.pcbi.1004867","article-title":"An Introduction to Programming for Bioscientists: A Python-Based Primer","volume":"12","author":"B Ekmekci","year":"2016","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1008208.ref034","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1007\/3-540-47789-6_72","volume-title":"Computational Science\u2014ICCS 2002","author":"K Hinsen","year":"2002"},{"issue":"5","key":"pcbi.1008208.ref035","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1016\/j.cels.2017.08.003","article-title":"A Padawan Programmer\u2019s Guide to Developing Software Libraries","volume":"5","author":"JT Yurkovich","year":"2017","journal-title":"Cell Syst"},{"issue":"3","key":"pcbi.1008208.ref036","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: fundamental algorithms for scientific computing in Python","volume":"17","author":"P Virtanen","year":"2020","journal-title":"Nat Methods"},{"issue":"2","key":"pcbi.1008208.ref037","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/MCSE.2011.37","article-title":"The NumPy Array: A Structure for Efficient Numerical Computation","volume":"13","author":"S van der Walt","year":"2011","journal-title":"Comput Sci Eng"},{"key":"pcbi.1008208.ref038","doi-asserted-by":"crossref","first-page":"e103","DOI":"10.7717\/peerj-cs.103","article-title":"SymPy: symbolic computing in Python","volume":"3","author":"A Meurer","year":"2017","journal-title":"PeerJ Computer Science"},{"key":"pcbi.1008208.ref039","unstructured":"Reback J, McKinney W, jbrockmendel, den Bossche JV, Augspurger T, Cloud P, et al.. pandas-dev\/pandas: Pandas 1.1.3; 2020. Available from: https:\/\/doi.org\/10.5281\/zenodo.4067057."},{"issue":"3","key":"pcbi.1008208.ref040","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MCSE.2007.55","article-title":"Matplotlib: A 2D Graphics Environment","volume":"9","author":"JD Hunter","year":"2007","journal-title":"Comput Sci Eng"},{"key":"pcbi.1008208.ref041","unstructured":"Kluyver T, Ragan-Kelley B, P\u00e9rez F, Granger BE, Bussonnier M, Frederic J, et al. Jupyter Notebooks\u2014a publishing format for reproducible computational workflows. In: ELPUB; 2016. p. 87\u201390."},{"issue":"3","key":"pcbi.1008208.ref042","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/MCSE.2007.53","article-title":"IPython: A System for Interactive Scientific Computing","volume":"9","author":"F Perez","year":"2007","journal-title":"Computing in Science & Engineering"},{"issue":"239","key":"pcbi.1008208.ref043","article-title":"Docker: Lightweight Linux Containers for Consistent Development and Deployment","volume":"2014","author":"D Merkel","year":"2014","journal-title":"Linux J"},{"issue":"8","key":"pcbi.1008208.ref044","first-page":"1","article-title":"Escher: A Web Application for Building, Sharing, and Embedding Data-Rich Visualizations of Biological Pathways","volume":"11","author":"ZA King","year":"2015","journal-title":"PLOS Computational Biology"},{"issue":"20","key":"pcbi.1008208.ref045","doi-asserted-by":"crossref","first-page":"3315","DOI":"10.1093\/bioinformatics\/btv363","article-title":"libRoadRunner: a high performance SBML simulation and analysis library","volume":"31","author":"ET Somogyi","year":"2015","journal-title":"Bioinformatics"},{"issue":"6","key":"pcbi.1008208.ref046","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1093\/bioinformatics\/btn051","article-title":"LibSBML: an API library for SBML","volume":"24","author":"BJ Bornstein","year":"2008","journal-title":"Bioinformatics"},{"issue":"9","key":"pcbi.1008208.ref047","doi-asserted-by":"crossref","first-page":"139","DOI":"10.21105\/joss.00139","article-title":"Optlang: An algebraic modeling language for mathematical optimization","volume":"2","author":"K Jensen","year":"2017","journal-title":"JOSS"},{"key":"pcbi.1008208.ref048","unstructured":"Makhorin AO. GNU Linear Programming Kit; 2018."},{"issue":"9","key":"pcbi.1008208.ref049","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1038\/nprot.2011.308","article-title":"Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0","volume":"6","author":"J Schellenberger","year":"2011","journal-title":"Nature Protocols"},{"issue":"4","key":"pcbi.1008208.ref050","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1093\/bioinformatics\/btg015","article-title":"The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models","volume":"19","author":"M Hucka","year":"2003","journal-title":"Bioinformatics"},{"key":"pcbi.1008208.ref051","unstructured":"Nowak U, Weimann L. A Family of Newton Codes for Systems of Highly Nonlinear Equations. Konrad-Zuse-Zentrum f\u00fcr Informationstechnik Berlin, 1991; 1991."},{"issue":"3","key":"pcbi.1008208.ref052","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1145\/1089014.1089020","article-title":"SUNDIALS: Suite of nonlinear and differential\/algebraic equation solvers","volume":"31","author":"AC Hindmarsh","year":"2005","journal-title":"ACM Trans Math Softw"},{"issue":"2","key":"pcbi.1008208.ref053","first-page":"266","article-title":"The Systems Biology Markup Language (SBML): Language Specification for Level 3 Version 1 Core","volume":"12","author":"M Hucka","year":"2015","journal-title":"J Integr Bioinform"},{"issue":"1","key":"pcbi.1008208.ref054","article-title":"SBML Level 3 Package: Flux Balance Constraints version 2","volume":"15","author":"G Brett","year":"2018","journal-title":"J Integr Bioinform"},{"issue":"3","key":"pcbi.1008208.ref055","first-page":"290","article-title":"SBML Level 3 package: Groups, Version 1 Release 1","volume":"13","author":"LPS Michael Hucka","year":"2016","journal-title":"J Integr Bioinform"},{"key":"pcbi.1008208.ref056","unstructured":"EMCA International. Standard ECMA-404; 2017."},{"issue":"5","key":"pcbi.1008208.ref057","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s00239-015-9681-0","article-title":"Evolution of Enzyme Kinetic Mechanisms","volume":"80","author":"NN Ulusu","year":"2015","journal-title":"Journal of Molecular Evolution"},{"issue":"9","key":"pcbi.1008208.ref058","doi-asserted-by":"crossref","first-page":"5457","DOI":"10.1074\/jbc.R800048200","article-title":"Use of randomized sampling for analysis of metabolic networks","volume":"284","author":"J Schellenberger","year":"2009","journal-title":"J Biol Chem"},{"key":"pcbi.1008208.ref059","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.ymben.2014.05.014","article-title":"A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data","volume":"25","author":"A Khodayari","year":"2014","journal-title":"Metab Eng"},{"issue":"1","key":"pcbi.1008208.ref060","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1287\/opre.46.1.84","article-title":"Direction Choice for Accelerated Convergence in Hit-and-Run Sampling","volume":"46","author":"DE Kaufman","year":"1998","journal-title":"Operations Research"},{"issue":"2","key":"pcbi.1008208.ref061","doi-asserted-by":"crossref","first-page":"e86587","DOI":"10.1371\/journal.pone.0086587","article-title":"optGpSampler: an improved tool for uniformly sampling the solution-space of genome-scale metabolic networks","volume":"9","author":"W Megchelenbrink","year":"2014","journal-title":"PLoS One"},{"key":"pcbi.1008208.ref062","doi-asserted-by":"crossref","DOI":"10.1038\/msb4100074","article-title":"Putative regulatory sites unraveled by network-embedded thermodynamic analysis of metabolome data","volume":"2","author":"A K\u00fcmmel","year":"2006","journal-title":"Mol Syst Biol"},{"issue":"2","key":"pcbi.1008208.ref063","doi-asserted-by":"crossref","first-page":"e1003483","DOI":"10.1371\/journal.pcbi.1003483","article-title":"Pathway Thermodynamics Highlights Kinetic Obstacles in Central Metabolism","volume":"10","author":"E Noor","year":"2014","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"pcbi.1008208.ref064","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1002\/biot.201100186","article-title":"Metabolic ensemble modeling for strain engineers","volume":"7","author":"Y Tan","year":"2012","journal-title":"Biotechnol J"},{"issue":"1","key":"pcbi.1008208.ref065","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1038\/msb.2010.68","article-title":"Insight into human alveolar macrophage and M. tuberculosis interactions via metabolic reconstructions","volume":"6","author":"A Bordbar","year":"2010","journal-title":"Molecular Systems Biology"},{"issue":"43","key":"pcbi.1008208.ref066","doi-asserted-by":"crossref","first-page":"16432","DOI":"10.1073\/pnas.0805779105","article-title":"Dynamics of shear-induced ATP release from red blood cells","volume":"105","author":"J Wan","year":"2008","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1008208.ref067","doi-asserted-by":"crossref","unstructured":"Conn AR, Gould NIM, Toint PL. Trust Region Methods. Society for Industrial and Applied Mathematics; 2000. Available from: https:\/\/epubs.siam.org\/doi\/abs\/10.1137\/1.9780898719857.","DOI":"10.1137\/1.9780898719857"},{"issue":"4","key":"pcbi.1008208.ref068","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.cels.2015.09.008","article-title":"Pseudo-transition Analysis Identifies the Key Regulators of Dynamic Metabolic Adaptations from Steady-State Data","volume":"1","author":"L Gerosa","year":"2015","journal-title":"Cell Syst"},{"issue":"10","key":"pcbi.1008208.ref069","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1038\/nbt.3956","article-title":"i ML1515, a knowledgebase that computes Escherichia coli traits","volume":"35","author":"JM Monk","year":"2017","journal-title":"Nat Biotechnol"},{"issue":"1","key":"pcbi.1008208.ref070","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1038\/nbt.3418","article-title":"The quantitative and condition-dependent Escherichia coli proteome","volume":"34","author":"A Schmidt","year":"2016","journal-title":"Nat Biotechnol"},{"issue":"7","key":"pcbi.1008208.ref071","doi-asserted-by":"crossref","first-page":"e23126","DOI":"10.1371\/journal.pone.0023126","article-title":"Condition-dependent cell volume and concentration of Escherichia coli to facilitate data conversion for systems biology modeling","volume":"6","author":"B Volkmer","year":"2011","journal-title":"PLoS One"},{"issue":"D1","key":"pcbi.1008208.ref072","doi-asserted-by":"crossref","first-page":"D770","DOI":"10.1093\/nar\/gkr874","article-title":"eQuilibrator\u2014the biochemical thermodynamics calculator","volume":"40","author":"A Flamholz","year":"2012","journal-title":"Nucleic Acids Research"},{"issue":"7","key":"pcbi.1008208.ref073","doi-asserted-by":"crossref","first-page":"e1003098","DOI":"10.1371\/journal.pcbi.1003098","article-title":"Consistent estimation of Gibbs energy using component contributions","volume":"9","author":"E Noor","year":"2013","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1008208.ref074","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1016\/j.isci.2019.08.045","article-title":"PyBioNetFit and the Biological Property Specification Language","volume":"19","author":"ED Mitra","year":"2019","journal-title":"iScience"},{"issue":"4","key":"pcbi.1008208.ref075","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1093\/bioinformatics\/btx626","article-title":"PyDREAM: high-dimensional parameter inference for biological models in python","volume":"34","author":"EM Shockley","year":"2018","journal-title":"Bioinformatics (Oxford, England)"},{"key":"pcbi.1008208.ref076","doi-asserted-by":"crossref","first-page":"e55","DOI":"10.7717\/peerj-cs.55","article-title":"Probabilistic programming in Python using PyMC3","volume":"2","author":"J Salvatier","year":"2016","journal-title":"PeerJ Computer Science"},{"issue":"32","key":"pcbi.1008208.ref077","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.21105\/joss.01057","article-title":"Altair: Interactive Statistical Visualizations for Python","volume":"3","author":"J VanderPlas","year":"2018","journal-title":"Journal of Open Source Software"},{"issue":"1","key":"pcbi.1008208.ref078","doi-asserted-by":"crossref","DOI":"10.1016\/j.isci.2019.100748","article-title":"Interactive Multiresolution Visualization of Cellular Network Processes","volume":"23","author":"OO Ortega","year":"2020","journal-title":"iScience"},{"issue":"4","key":"pcbi.1008208.ref079","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1093\/bioinformatics\/bti046","article-title":"Modelling cellular systems with PySCeS","volume":"21","author":"BG Olivier","year":"2005","journal-title":"Bioinformatics"},{"key":"pcbi.1008208.ref080","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.biosystems.2018.07.006","article-title":"Tellurium: An extensible python-based modeling environment for systems and synthetic biology","volume":"171","author":"K Choi","year":"2018","journal-title":"Biosystems"},{"issue":"24","key":"pcbi.1008208.ref081","doi-asserted-by":"crossref","first-page":"3067","DOI":"10.1093\/bioinformatics\/btl485","article-title":"COPASI\u2014a COmplex PAthway SImulator","volume":"22","author":"S Hoops","year":"2006","journal-title":"Bioinformatics"},{"key":"pcbi.1008208.ref082","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1038\/msb.2013.1","article-title":"Programming biological models in Python using PySB","volume":"9","author":"CF Lopez","year":"2013","journal-title":"Mol Syst Biol"},{"issue":"12","key":"pcbi.1008208.ref083","doi-asserted-by":"crossref","first-page":"e1002802","DOI":"10.1371\/journal.pcbi.1002802","article-title":"Ten simple rules for the open development of scientific software","volume":"8","author":"A Prli\u0107","year":"2012","journal-title":"PLoS Comput Biol"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1008208","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T00:00:00Z","timestamp":1612828800000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008208","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T22:49:30Z","timestamp":1612910970000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008208"}},"subtitle":[],"editor":[{"given":"Pedro","family":"Mendes","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,1,28]]},"references-count":83,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1,28]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1008208","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2020.07.31.230334","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,28]]}}}