{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T02:55:57Z","timestamp":1787021757092,"version":"build-2736575974"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009410","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T00:00:00Z","timestamp":1632700800000}}],"reference-count":74,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T00:00:00Z","timestamp":1631145600000},"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 biochemical networks can largely facilitate the comprehension of the mechanisms at the basis of cellular processes, as well as the formulation of hypotheses that can be tested by means of targeted laboratory experiments. However, two issues might hamper the achievement of fruitful outcomes. On the one hand, detailed mechanistic models can involve hundreds or thousands of molecular species and their intermediate complexes, as well as hundreds or thousands of chemical reactions, a situation generally occurring in rule-based modeling. On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration, or to test the effect of perturbations. As a consequence, the computational capabilities of modern Central Processing Units can be easily overtaken, possibly making the modeling of biochemical networks a worthless or ineffective effort. To the aim of overcoming the limitations of the current state-of-the-art simulation approaches, we present in this paper FiCoS, a novel \u201cblack-box\u201d deterministic simulator that effectively realizes both a fine-grained and a coarse-grained parallelization on Graphics Processing Units. In particular, FiCoS exploits two different integration methods, namely, the Dormand\u2013Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations. We tested the performance of FiCoS against different deterministic simulators, by considering models of increasing size and by running analyses with increasing computational demands. FiCoS was able to dramatically speedup the computations up to 855\u00d7, showing to be a promising solution for the simulation and analysis of large-scale models of complex biological processes.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009410","type":"journal-article","created":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T14:15:44Z","timestamp":1631196944000},"page":"e1009410","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":2,"title":["FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5856-4453","authenticated-orcid":true,"given":"Andrea","family":"Tangherloni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7692-7203","authenticated-orcid":true,"given":"Marco S.","family":"Nobile","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7780-0434","authenticated-orcid":true,"given":"Paolo","family":"Cazzaniga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giulia","family":"Capitoli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3383-367X","authenticated-orcid":true,"given":"Simone","family":"Spolaor","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3341-5483","authenticated-orcid":true,"given":"Leonardo","family":"Rundo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3520-4022","authenticated-orcid":true,"given":"Giancarlo","family":"Mauri","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5532-3059","authenticated-orcid":true,"given":"Daniela","family":"Besozzi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2021,9,9]]},"reference":[{"key":"pcbi.1009410.ref001","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/9780262195485.001.0001","volume-title":"System Modeling in Cellular Biology: From Concepts to Nuts and Bolts","author":"Z Szallasi","year":"2006"},{"key":"pcbi.1009410.ref002","unstructured":"Besozzi D. Reaction-Based Models of Biochemical Networks. In: Beckmann A, Bienvenu L, Jonoska N, editors. Proc. of Pursuit of the Universal, 12th Conference on Computability in Europe. vol. 9709 of LNCS. Switzerland: Springer International Publishing; 2016. p. 24\u201334."},{"key":"pcbi.1009410.ref003","doi-asserted-by":"crossref","unstructured":"Cazzaniga P, Nobile MS, Besozzi D. The impact of particles initialization in PSO: parameter estimation as a case in point. In: Proc. of Computational Intelligence in Bioinformatics and Computational Biology. IEEE; 2015. p. 1\u20138.","DOI":"10.1109\/CIBCB.2015.7300288"},{"key":"pcbi.1009410.ref004","volume-title":"Quantitative biology: theory, computational methods, and models","author":"B Munsky","year":"2018"},{"issue":"11","key":"pcbi.1009410.ref005","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1038\/ncb1497","article-title":"Physicochemical modelling of cell signalling pathways","volume":"8","author":"BB Aldridge","year":"2006","journal-title":"Nat Cell Biol"},{"issue":"2","key":"pcbi.1009410.ref006","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.mbs.2009.03.002","article-title":"Recent developments in parameter estimation and structure identification of biochemical and genomic systems","volume":"219","author":"IC Chou","year":"2009","journal-title":"Math Biosci"},{"key":"pcbi.1009410.ref007","doi-asserted-by":"crossref","first-page":"105494","DOI":"10.1016\/j.asoc.2019.105494","article-title":"Biochemical parameter estimation vs. benchmark functions: a comparative study of optimization performance and representation design","volume":"81","author":"A Tangherloni","year":"2019","journal-title":"Appl Soft Comput"},{"issue":"5","key":"pcbi.1009410.ref008","first-page":"870","article-title":"Graphics processing units in bioinformatics, computational biology and systems biology","volume":"18","author":"MS Nobile","year":"2017","journal-title":"Brief Bioinform"},{"issue":"2","key":"pcbi.1009410.ref009","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1038\/nrg2509","article-title":"Stochastic modelling for quantitative description of heterogeneous biological systems","volume":"10","author":"D Wilkinson","year":"2009","journal-title":"Nat Rev Genet"},{"issue":"20\u201321","key":"pcbi.1009410.ref010","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.csbj.2014.10.003","article-title":"Stochastic simulation in systems biology","volume":"12","author":"TJ Sz\u00e9kely","year":"2014","journal-title":"Comput Struct Biotechnol J"},{"issue":"14","key":"pcbi.1009410.ref011","doi-asserted-by":"crossref","first-page":"144107","DOI":"10.1063\/1.2354085","article-title":"A \u201cpartitioned leaping\u201d approach for multiscale modeling of chemical reaction dynamics","volume":"125","author":"LA Harris","year":"2006","journal-title":"J Chem Phys"},{"issue":"2","key":"pcbi.1009410.ref012","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1177\/1094342009106066","article-title":"Efficient parallelization of the stochastic simulation algorithm for chemically reacting systems on the graphics processing unit","volume":"24","author":"H Li","year":"2010","journal-title":"Int J High Perform Comput Appl"},{"issue":"4","key":"pcbi.1009410.ref013","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/0021-9991(76)90041-3","article-title":"A general method for numerically simulating the stochastic time evolution of coupled chemical reactions","volume":"22","author":"DT Gillespie","year":"1976","journal-title":"J Comput Phys"},{"issue":"6","key":"pcbi.1009410.ref014","doi-asserted-by":"crossref","first-page":"874","DOI":"10.1093\/bioinformatics\/btr015","article-title":"GPU accelerated biochemical network simulation","volume":"27","author":"Y Zhou","year":"2011","journal-title":"Bioinformatics"},{"issue":"1","key":"pcbi.1009410.ref015","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s11227-014-1208-8","article-title":"GPU-accelerated simulations of mass-action kinetics models with cupSODA","volume":"69","author":"MS Nobile","year":"2014","journal-title":"J Supercomput"},{"issue":"1","key":"pcbi.1009410.ref016","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1137\/0904010","article-title":"Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations","volume":"4","author":"L Petzold","year":"1983","journal-title":"SIAM J Sci Stat Comp"},{"issue":"3","key":"pcbi.1009410.ref017","doi-asserted-by":"crossref","first-page":"e91963","DOI":"10.1371\/journal.pone.0091963","article-title":"cuTauLeaping: a GPU-powered tau-leaping stochastic simulator for massive parallel analyses of biological systems","volume":"9","author":"MS Nobile","year":"2014","journal-title":"PLoS One"},{"issue":"4","key":"pcbi.1009410.ref018","doi-asserted-by":"crossref","first-page":"044109","DOI":"10.1063\/1.2159468","article-title":"Efficient step size selection for the tau-leaping simulation method","volume":"124","author":"Y Cao","year":"2006","journal-title":"J Chem Phys"},{"issue":"21","key":"pcbi.1009410.ref019","doi-asserted-by":"crossref","first-page":"3492","DOI":"10.1093\/bioinformatics\/btx420","article-title":"GPU-powered model analysis with PySB\/cupSODA","volume":"33","author":"LA Harris","year":"2017","journal-title":"Bioinformatics"},{"issue":"1","key":"pcbi.1009410.ref020","doi-asserted-by":"crossref","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":"1","key":"pcbi.1009410.ref021","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1186\/s12859-017-1666-0","article-title":"LASSIE: simulating large-scale models of biochemical systems on GPUs","volume":"18","author":"A Tangherloni","year":"2017","journal-title":"BMC Bioinform"},{"issue":"6","key":"pcbi.1009410.ref022","doi-asserted-by":"crossref","first-page":"e37370","DOI":"10.1371\/journal.pone.0037370","article-title":"Accelerating the Gillespie \u03c4-leaping method using graphics processing units","volume":"7","author":"I Komarov","year":"2012","journal-title":"PLoS One"},{"issue":"11","key":"pcbi.1009410.ref023","doi-asserted-by":"crossref","first-page":"e46693","DOI":"10.1371\/journal.pone.0046693","article-title":"Accelerating the Gillespie exact stochastic simulation algorithm using hybrid parallel execution on graphics processing units","volume":"7","author":"I Komarov","year":"2012","journal-title":"PLoS One"},{"key":"pcbi.1009410.ref024","doi-asserted-by":"crossref","first-page":"42","DOI":"10.3389\/fphys.2015.00042","article-title":"Acceleration of discrete stochastic biochemical simulation using GPGPU","volume":"6","author":"K Sumiyoshi","year":"2015","journal-title":"Front Physiol"},{"issue":"12","key":"pcbi.1009410.ref025","doi-asserted-by":"crossref","first-page":"e1005220","DOI":"10.1371\/journal.pcbi.1005220","article-title":"Stochastic simulation service: bridging the gap between the computational expert and the biologist","volume":"12","author":"B Drawert","year":"2016","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1009410.ref026","doi-asserted-by":"crossref","unstructured":"Panchiwala H, Shah S, Planatscher H, Zakharchuk M, K\u00f6nig M, Dr\u00e4ger A. The Systems Biology Simulation Core Library. Preprints. 2020.","DOI":"10.20944\/preprints202012.0296.v1"},{"issue":"8","key":"pcbi.1009410.ref027","doi-asserted-by":"crossref","first-page":"e9110","DOI":"10.15252\/msb.20199110","article-title":"SBML Level 3: an extensible format for the exchange and reuse of biological models","volume":"16","author":"SM Keating","year":"2020","journal-title":"Mol Syst Biol"},{"issue":"1","key":"pcbi.1009410.ref028","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/0771-050X(80)90013-3","article-title":"A family of embedded Runge-Kutta formulae","volume":"6","author":"JR Dormand","year":"1980","journal-title":"J Comput Appl Math"},{"key":"pcbi.1009410.ref029","volume-title":"Numerical methods for differential equations: a computational approach","author":"JR Dormand","year":"1996"},{"key":"pcbi.1009410.ref030","volume-title":"Solving ordinary differential equations I","author":"E Hairer","year":"2008"},{"key":"pcbi.1009410.ref031","volume-title":"Solving ordinary differential equations II","author":"E Hairer","year":"2002"},{"issue":"1-2","key":"pcbi.1009410.ref032","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0377-0427(99)00134-X","article-title":"Stiff differential equations solved by Radau methods","volume":"111","author":"E Hairer","year":"1999","journal-title":"J Comput Appl Math"},{"key":"pcbi.1009410.ref033","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1146\/annurev.physchem.58.032806.104637","article-title":"Stochastic simulation of chemical kinetics","volume":"58","author":"DT Gillespie","year":"2007","journal-title":"Annu Rev Phys Chem"},{"issue":"24","key":"pcbi.1009410.ref034","doi-asserted-by":"crossref","first-page":"12784","DOI":"10.1063\/1.1627296","article-title":"Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method","volume":"119","author":"M Rathinam","year":"2003","journal-title":"J Chem Phys"},{"issue":"2","key":"pcbi.1009410.ref035","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BF01989751","article-title":"Stiffness of ODEs","volume":"33","author":"DJ Higham","year":"1993","journal-title":"BIT Numer Math"},{"issue":"3","key":"pcbi.1009410.ref036","doi-asserted-by":"crossref","first-page":"e0116550","DOI":"10.1371\/journal.pone.0116550","article-title":"Computational analysis of an Autophagy\/Translation switch based on mutual inhibition of MTORC1 and ULK1","volume":"10","author":"P Szyma\u0144ska","year":"2015","journal-title":"PLoS One"},{"key":"pcbi.1009410.ref037","doi-asserted-by":"crossref","unstructured":"Totis N, Tangherloni A, Beccuti M, Cazzaniga P, Nobile MS, Besozzi D, et al. Efficient and settings-free calibration of detailed kinetic metabolic models with enzyme isoforms characterization. In: Proc. of International Meeting on Computational Intelligence Methods for Bioinformatics and Biostatistics. Springer; 2018. p. 187\u2013202.","DOI":"10.1007\/978-3-030-34585-3_17"},{"issue":"5","key":"pcbi.1009410.ref038","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1137\/0910062","article-title":"VODE: A variable-coefficient ODE solver","volume":"10","author":"PN Brown","year":"1989","journal-title":"SIAM J Sci Stat Comp"},{"issue":"20","key":"pcbi.1009410.ref039","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":"2","key":"pcbi.1009410.ref040","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1063\/1.4822377","article-title":"CVODE, a stiff\/nonstiff ODE solver in C","volume":"10","author":"SD Cohen","year":"1996","journal-title":"Comput Phys"},{"issue":"24","key":"pcbi.1009410.ref041","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"},{"issue":"5","key":"pcbi.1009410.ref042","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1049\/iet-syb:20080102","article-title":"Virtual Cell modelling and simulation software environment","volume":"2","author":"II Moraru","year":"2008","journal-title":"IET Syst Biol"},{"key":"pcbi.1009410.ref043","unstructured":"Nvidia. CUDA C Programming Guide, version 8.0; 2016."},{"key":"pcbi.1009410.ref044","doi-asserted-by":"crossref","DOI":"10.1002\/9780470753767","volume-title":"Numerical methods for ordinary differential equations","author":"JC Butcher","year":"2008"},{"key":"pcbi.1009410.ref045","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/978-3-540-70529-1_94","volume-title":"Encyclopedia of Applied and Computational Mathematics","author":"JR Cash","year":"2015"},{"key":"pcbi.1009410.ref046","unstructured":"Jones E, Oliphant T, Peterson P, et al. SciPy: Open source scientific tools for Python; 2001. Available from: http:\/\/www.scipy.org\/."},{"issue":"21","key":"pcbi.1009410.ref047","doi-asserted-by":"crossref","first-page":"3366","DOI":"10.1093\/bioinformatics\/btw469","article-title":"BioNetGen 2.2: advances in rule-based modeling","volume":"32","author":"LA Harris","year":"2016","journal-title":"Bioinformatics"},{"issue":"2","key":"pcbi.1009410.ref048","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":"Biophys J"},{"issue":"7208","key":"pcbi.1009410.ref049","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1038\/nature07211","article-title":"Metabolic gene regulation in a dynamically changing environment","volume":"454","author":"MR Bennett","year":"2008","journal-title":"Nature"},{"issue":"3","key":"pcbi.1009410.ref050","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.molcel.2013.01.018","article-title":"Understanding metabolic regulation and its influence on cell physiology","volume":"49","author":"CM Metallo","year":"2013","journal-title":"Mol Cell"},{"issue":"17","key":"pcbi.1009410.ref051","doi-asserted-by":"crossref","first-page":"2832","DOI":"10.1016\/j.febslet.2013.06.043","article-title":"A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes","volume":"587","author":"K Smallbone","year":"2013","journal-title":"FEBS Lett"},{"issue":"4-5","key":"pcbi.1009410.ref052","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s11064-006-9132-9","article-title":"Kinetic parameters and lactate dehydrogenase isozyme activities support possible lactate utilization by neurons","volume":"32","author":"J O\u2019Brien","year":"2007","journal-title":"Neurochem Res"},{"issue":"3914","key":"pcbi.1009410.ref053","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1126\/science.167.3914.63","article-title":"Lactate dehydrogenase isozymes: kinetic properties at high enzyme concentrations","volume":"167","author":"T Wuntch","year":"1970","journal-title":"Science"},{"issue":"1-3","key":"pcbi.1009410.ref054","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0378-4754(00)00270-6","article-title":"Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates","volume":"55","author":"IM Sobol","year":"2001","journal-title":"Math Comput Simul"},{"issue":"2","key":"pcbi.1009410.ref055","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.cpc.2009.09.018","article-title":"Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index","volume":"181","author":"A Saltelli","year":"2010","journal-title":"Comput Phys Commun"},{"issue":"2","key":"pcbi.1009410.ref056","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/S0010-4655(02)00280-1","article-title":"Making best use of model evaluations to compute sensitivity indices","volume":"145","author":"A Saltelli","year":"2002","journal-title":"Comput Phys Commun"},{"key":"pcbi.1009410.ref057","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.swevo.2017.09.001","article-title":"Fuzzy Self-Tuning PSO: A settings-free algorithm for global optimization","volume":"39","author":"MS Nobile","year":"2018","journal-title":"Swarm Evol Comput"},{"issue":"1","key":"pcbi.1009410.ref058","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s11721-007-0002-0","article-title":"Particle swarm optimization","volume":"1","author":"R Poli","year":"2007","journal-title":"Swarm intelligence"},{"key":"pcbi.1009410.ref059","doi-asserted-by":"crossref","unstructured":"Nobile MS, Tangherloni A, Rundo L, Spolaor S, Besozzi D, Mauri G, et al. Computational Intelligence for Parameter Estimation of Biochemical Systems. In: Proc. Congress on Evolutionary Computation (CEC). IEEE; 2018. p. 1\u20138.","DOI":"10.1109\/CEC.2018.8477873"},{"issue":"1","key":"pcbi.1009410.ref060","doi-asserted-by":"crossref","first-page":"15722","DOI":"10.1038\/s41598-017-15313-9","article-title":"Gpufit: An open-source toolkit for GPU-accelerated curve fitting","volume":"7","author":"A Przybylski","year":"2017","journal-title":"Sci Rep"},{"key":"pcbi.1009410.ref061","unstructured":"Jones S. Introduction to dynamic parallelism. In: GPU Technology Conference Presentation S. vol. 338; 2012. p. 2012."},{"key":"pcbi.1009410.ref062","doi-asserted-by":"crossref","unstructured":"Wang J, Yalamanchili S. Characterization and analysis of dynamic parallelism in unstructured GPU applications. In: Proc. of International Symposium on Workload Characterization. IEEE; 2014. p. 51\u201360.","DOI":"10.1109\/IISWC.2014.6983039"},{"key":"pcbi.1009410.ref063","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.pisc.2014.12.002","article-title":"One hundred years of Michaelis\u2013Menten kinetics","volume":"4","author":"A Cornish-Bowden","year":"2015","journal-title":"Perspect Sci"},{"key":"pcbi.1009410.ref064","first-page":"4","article-title":"The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves","volume":"40","author":"AV Hill","year":"1910","journal-title":"J Physiol"},{"issue":"12","key":"pcbi.1009410.ref065","doi-asserted-by":"crossref","first-page":"7844","DOI":"10.1007\/s11227-018-2549-5","article-title":"ginSODA: massive parallel integration of stiff ODE systems on GPUs","volume":"75","author":"MS Nobile","year":"2019","journal-title":"J Supercomput"},{"key":"pcbi.1009410.ref066","doi-asserted-by":"crossref","unstructured":"Besozzi D, Cazzaniga P, Mauri G, Pescini D. BioSimWare: a software for the modeling, simulation and analysis of biological systems. In: proc. of International Conference on Membrane Computing. Springer; 2010. p. 119\u2013143.","DOI":"10.1007\/978-3-642-18123-8_12"},{"issue":"4","key":"pcbi.1009410.ref067","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1109\/MCS.2009.932926","article-title":"Modeling and analysis of mass-action kinetics","volume":"29","author":"V Chellaboina","year":"2009","journal-title":"IEEE Control Syst"},{"issue":"1","key":"pcbi.1009410.ref068","doi-asserted-by":"crossref","first-page":"e1004012","DOI":"10.1371\/journal.pcbi.1004012","article-title":"150 years of the mass action law","volume":"11","author":"EO Voit","year":"2015","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1009410.ref069","article-title":"SMGen: A generator of synthetic models of biochemical reaction networks","author":"SG Riva","year":"2021","journal-title":"bioRxiv"},{"issue":"11","key":"pcbi.1009410.ref070","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1002\/kin.20369","article-title":"Sensitivity analysis and robust experimental design of a signal transduction pathway system","volume":"40","author":"H Yue","year":"2008","journal-title":"Int J Chem Kinet"},{"issue":"8","key":"pcbi.1009410.ref071","doi-asserted-by":"crossref","first-page":"2464","DOI":"10.1016\/j.camwa.2009.12.025","article-title":"A 17th-order Radau IIA method for package RADAU. Applications in mechanical systems","volume":"59","author":"J Mart\u00edn-Vaquero","year":"2010","journal-title":"Comput Math Appl"},{"issue":"125","key":"pcbi.1009410.ref072","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1090\/S0025-5718-1974-0331793-2","article-title":"On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations","volume":"28","author":"A Prothero","year":"1974","journal-title":"Math Comp"},{"key":"pcbi.1009410.ref073","doi-asserted-by":"crossref","first-page":"105355","DOI":"10.1016\/j.ast.2019.105355","article-title":"A strongly S-stable low-dissipation and low-dispersion Runge-Kutta scheme for convection diffusion systems","volume":"93","author":"Y Du","year":"2019","journal-title":"Aerosp Sci Technol"},{"key":"pcbi.1009410.ref074","unstructured":"Nvidia. cuBLAS library 8.0; 2015."}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1009410","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T00:00:00Z","timestamp":1632700800000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009410","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T16:10:44Z","timestamp":1632759044000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1009410"}},"subtitle":[],"editor":[{"given":"Dina","family":"Schneidman-Duhovny","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2021,9,9]]},"references-count":74,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9,9]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1009410","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2021.01.15.426855","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,9]]}}}