References¶

sbmlsim builds on the standards of the COMBINE community and on the simulation and analysis libraries of the scientific python ecosystem. These are the publications behind them; cite them when you describe a simulation experiment, and cite sbmlsim itself as described in Home.

Simulation¶

libRoadRunner. The SBML simulation engine all simulations run on.

Welsh C, Xu J, Smith L, König M, Choi K, Sauro HM. libRoadRunner 2.0: a high performance SBML simulation and analysis library. Bioinformatics. 2023;39(1):btac770. doi:10.1093/bioinformatics/btac770

Somogyi ET, Bouteiller JM, Glazier JA, König M, Medley JK, Swat MH, Sauro HM. libRoadRunner: a high performance SBML simulation and analysis library. Bioinformatics. 2015;31(20):3315-3321. doi:10.1093/bioinformatics/btv363

Standards¶

SBML Level 3. The format of the models.

Keating SM, Waltemath D, König M, Zhang F, Dräger A, Chaouiya C, Bergmann FT, Finney A, Gillespie CS, Helikar T, Hoops S, Malik-Sheriff RS, Moodie SL, Moraru II, Myers CJ, Naldi A, Olivier BG, Sahle S, Schaff JC, Smith LP, Swat MJ, Thieffry D, Watanabe L, Wilkinson DJ, Blinov ML, Begley K, Faeder JR, Gómez HF, Hamm TM, Inagaki Y, Liebermeister W, Lister AL, Lucio D, Mjolsness E, Proctor CJ, Raman K, Rodriguez N, Shaffer CA, Shapiro BE, Stelling J, Swainston N, Tanimura N, Wagner J, Meier-Schellersheim M, Sauro HM, Palsson B, Bolouri H, Kitano H, Funahashi A, Hermjakob H, Doyle JC, Hucka M; SBML Level 3 Community members. SBML Level 3: an extensible format for the exchange and reuse of biological models. Molecular Systems Biology. 2020;16(8):e9110. doi:10.15252/msb.20199110

SED-ML. The description of simulation experiments. sbmlsim no longer reads or writes SED-ML; a fit is exchanged as a PEtab problem instead, see PEtab.

Smith LP, Bergmann FT, Garny A, Helikar T, Karr J, Nickerson D, Sauro H, Waltemath D, König M. The simulation experiment description markup language (SED-ML): language specification for level 1 version 4. Journal of Integrative Bioinformatics. 2021;18(3):20210021. doi:10.1515/jib-2021-0021

Waltemath D, Adams R, Bergmann FT, Hucka M, Kolpakov F, Miller AK, Moraru II, Nickerson D, Sahle S, Snoep JL, Le Novère N. Reproducible computational biology experiments with SED-ML — the Simulation Experiment Description Markup Language. BMC Systems Biology. 2011;5:198. doi:10.1186/1752-0509-5-198

Parameter fitting¶

Identifiability. What it means for the data to determine a parameter, and the difference between the structural identifiability of a model and the practical identifiability of a model and its data, see Parameter fitting.

Bellman R, Åström KJ. On structural identifiability. Mathematical Biosciences. 1970;7(3-4):329-339. doi:10.1016/0025-5564(70)90132-X

Raue A, Karlsson J, Saccomani MP, Jirstrand M, Timmer J. Comparison of approaches for parameter identifiability analysis of biological systems. Bioinformatics. 2014;30(10):1440-1448. doi:10.1093/bioinformatics/btu006

Structural identifiability. Whether the observables of a model determine its parameters at all, which is a property of the model and not of the data. sbmlsim does not analyse it; these are the methods and the tools which do.

Chis O-T, Banga JR, Balsa-Canto E. Structural identifiability of systems biology models: a critical comparison of methods. PLoS ONE. 2011;6(11):e27755. doi:10.1371/journal.pone.0027755

Villaverde AF, Barreiro A, Papachristodoulou A. Structural identifiability of dynamic systems biology models. PLoS Computational Biology. 2016;12(10):e1005153. doi:10.1371/journal.pcbi.1005153

Sloppiness and the Fisher information. The eigenvalues of the Fisher information of sbmlsim.fit.fisher, which are spread over orders of magnitude in most models of systems biology, see Parameter fitting.

Gutenkunst RN, Waterfall JJ, Casey FP, Brown KS, Myers CR, Sethna JP. Universally sloppy parameter sensitivities in systems biology models. PLoS Computational Biology. 2007;3(10):e189. doi:10.1371/journal.pcbi.0030189

Transtrum MK, Machta BB, Brown KS, Daniels BC, Myers CR, Sethna JP. Perspective: Sloppiness and emergent theories in physics, biology, and beyond. The Journal of Chemical Physics. 2015;143(1):010901. doi:10.1063/1.4923066

Profile likelihood. The identifiability analysis of sbmlsim.fit.identifiability, see Parameter fitting: the profile likelihood, its threshold and the classification of the parameters.

Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmüller U, Timmer J. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics. 2009;25(15):1923-1929. doi:10.1093/bioinformatics/btp358

Kreutz C, Raue A, Kaschek D, Timmer J. Profile likelihood in systems biology. The FEBS Journal. 2013;280(11):2564-2571. doi:10.1111/febs.12276

Wieland FG, Hauber AL, Rosenblatt M, Tönsing C, Timmer J. On structural and practical identifiability. Current Opinion in Systems Biology. 2021;25:60-69. doi:10.1016/j.coisb.2021.03.005

Coupled parameters and model reduction. The paths of the other parameters along a profile, which the figures of a profile show.

Maiwald T, Hass H, Steiert B, Vanlier J, Engesser R, Raue A, Kipkeew F, Bock HH, Kaschek D, Kreutz C, Timmer J. Driving the model to its limit: profile likelihood based model reduction. PLoS ONE. 2016;11(9):e0162366. doi:10.1371/journal.pone.0162366

Algorithms. The adaptive steps along a profile, the confidence intervals from constrained optimization and the profile-wise workflow, which the implementation follows.

Schälte Y, Fröhlich F, Jost PJ, Vanhoefer J, Pathirana D, Stapor P, Lakrisenko P, Wang D, Raimúndez E, Merkt S, Schmiester L, Städter P, Grein S, Dudkin E, Doresic D, Weindl D, Hasenauer J. pyPESTO: a modular and scalable tool for parameter estimation for dynamic models. Bioinformatics. 2023;39(11):btad711. doi:10.1093/bioinformatics/btad711

Borisov I, Metelkin E. Confidence intervals by constrained optimization—An algorithm and software package for practical identifiability analysis in systems biology. PLoS Computational Biology. 2020;16(12):e1008495. doi:10.1371/journal.pcbi.1008495

Simpson MJ, Maclaren OJ. Profile-wise analysis: a profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. PLoS Computational Biology. 2023;19(9):e1011515. doi:10.1371/journal.pcbi.1011515

COMBINE archive. The container for models, simulation experiments and data.

Bergmann FT, Adams R, Moodie S, Cooper J, Glont M, Golebiewski M, Hucka M, Laibe C, Miller AK, Nickerson DP, Olivier BG, Rodriguez N, Sauro HM, Scharm M, Soiland-Reyes S, Waltemath D, Yvon F, Le Novère N. COMBINE archive and OMEX format: one file to share all information to reproduce a modeling project. BMC Bioinformatics. 2014;15:369. doi:10.1186/s12859-014-0369-z

KISAO. The ontology of simulation algorithms and their parameters, see sbmlsim.simulation.algorithm.

Courtot M, Juty N, Knüpfer C, Waltemath D, Zhukova A, Dräger A, Dumontier M, Finney A, Golebiewski M, Hastings J, Hoops S, Keating S, Kell DB, Kerrien S, Lawson J, Lister A, Lu J, Machne R, Mendes P, Pocock M, Rodriguez N, Villeger A, Wilkinson DJ, Wimalaratne S, Laibe C, Hucka M, Le Novère N. Controlled vocabularies and semantics in systems biology. Molecular Systems Biology. 2011;7:543. doi:10.1038/msb.2011.77

PEtab. The specification of parameter estimation problems which sbmlsim.fit.petab_omex packages, see Parameter fitting.

Schmiester L, Schälte Y, Bergmann FT, Camba T, Dudkin E, Egert J, Fröhlich F, Fuhrmann L, Hauber AL, Kemmer S, Lakrisenko P, Loos C, Merkt S, Müller W, Pathirana D, Raimúndez E, Refisch L, Rosenblatt M, Stapor PL, Städter P, Wang D, Wieland FG, Banga JR, Timmer J, Villaverde AF, Sahle S, Kreutz C, Hasenauer J, Weindl D. PEtab — Interoperable specification of parameter estimation problems in systems biology. PLoS Computational Biology. 2021;17(1):e1008646. doi:10.1371/journal.pcbi.1008646

Sensitivity analysis¶

The global methods of sbmlsim.sensitivity are the implementations of SALib, see Sensitivity analysis.

Herman J, Usher W. SALib: An open-source Python library for Sensitivity Analysis. Journal of Open Source Software. 2017;2(9):97. doi:10.21105/joss.00097

Iwanaga T, Usher W, Herman J. Toward SALib 2.0: Advancing the accessibility and interpretability of global sensitivity analyses. Socio-Environmental Systems Modelling. 2022;4:18155. doi:10.18174/sesmo.18155

Sobol indices. Variance based first order and total effect indices.

Sobol' IM. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation. 2001;55(1-3):271-280. doi:10.1016/S0378-4754(00)00270-6

Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications. 2010;181(2):259-270. doi:10.1016/j.cpc.2009.09.018

Morris method. Elementary effects screening.

Morris MD. Factorial sampling plans for preliminary computational experiments. Technometrics. 1991;33(2):161-174. doi:10.1080/00401706.1991.10484804

Campolongo F, Cariboni J, Saltelli A. An effective screening design for sensitivity analysis of large models. Environmental Modelling & Software. 2007;22(10):1509-1518. doi:10.1016/j.envsoft.2006.10.004

FAST. The Fourier amplitude sensitivity test and its extended form.

Cukier RI, Fortuin CM, Shuler KE, Petschek AG, Schaibly JH. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory. The Journal of Chemical Physics. 1973;59(8):3873-3878. doi:10.1063/1.1680571

Saltelli A, Tarantola S, Chan KPS. A quantitative model-independent method for global sensitivity analysis of model output. Technometrics. 1999;41(1):39-56. doi:10.1080/00401706.1999.10485594

Data structures¶

xarray. Simulation results are stored as labeled N-dimensional arrays, see sbmlsim.result.xresult.

Hoyer S, Hamman J. xarray: N-D labeled arrays and datasets in Python. Journal of Open Research Software. 2017;5(1):10. doi:10.5334/jors.148