×

Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach. (English) Zbl 1471.65085

Summary: Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding. Here, we consider the optimal scaling method which has been developed in statistics for categorical data and has been applied to dynamical systems. This approach turns qualitative variables into quantitative ones, accounting for constraints on their relation. We derive a reduced formulation for the optimization problem defining the optimal scaling. The reduced formulation possesses the same optimal points as the established formulation but requires less degrees of freedom. Parameter estimation for dynamical models of cellular pathways revealed that the reduced formulation improves the robustness and convergence of optimizers. This resulted in substantially reduced computation times. We implemented the proposed approach in the open-source Python Parameter EStimation TOolbox (pyPESTO) to facilitate reuse and extension. The proposed approach enables efficient parameterization of quantitative dynamical models using qualitative data.

MSC:

65L09 Numerical solution of inverse problems involving ordinary differential equations
37N25 Dynamical systems in biology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aldridge, BB; Burke, JM; Lauffenburger, DA; Sorger, PK, Physicochemical modelling of cell signalling pathways, Nat Cell Biol, 8, 11, 1195-1203 (2006)
[2] Bachmann, J.; Raue, A.; Schilling, M.; Böhm, ME; Kreutz, C.; Kaschek, D.; Busch, H.; Gretz, N.; Lehmann, WD; Timmer, J.; Klingmüller, U., Division of labor by dual feedback regulators controls JAK2/STAT5 signaling over broad ligand range, Mol Syst Biol, 7, 1, 516 (2011)
[3] Balsa-Canto, E.; Banga, JR, AMIGO, a toolbox for advanced model identification in systems biology using global optimization, Bioinformatics, 27, 16, 2311-2313 (2011)
[4] Banga, JR, Optimization in computational systems biology, BMC Syst Biol, 2, 47, 1-7 (2008)
[5] Birtwistle, MR; von Kriegsheim, A.; Kida, K.; Schwarz, JP; Anderson, KI; Kolch, W., Linear approaches to intramolecular förster resonance energy transfer probe measurements for quantitative modeling, PloS one, 6, 11, e27823 (2011)
[6] Boehm, ME; Adlung, L.; Schilling, M.; Roth, S.; Klingmüller, U.; Lehmann, WD, Identification of isoform-specific dynamics in phosphorylation-dependent STAT5 dimerization by quantitative mass spectrometry and mathematical modeling, J Proteome Res, 13, 12, 5685-5694 (2014)
[7] Boyd, S.; Vandenberghe, L., Convex Optimisation (2004), Cambridge: Cambridge University Press, Cambridge · Zbl 1058.90049
[8] Butler TA, Paul JW, Chan E-C, Smith R, Tolosa JM (2019) Misleading westerns: Common quantification mistakes in western blot densitometry and proposed corrective measures. BioMed research international, 2019
[9] Chis, O-T; Banga, JR; Balsa-Canto, E., Structural identifiability of systems biology models: A critical comparison of methods, PLoS ONE, 6, 11, e27755 (2011)
[10] Fiedler, A.; Raeth, S.; Theis, FJ; Hausser, A.; Hasenauer, J., Tailored parameter optimization methods for ordinary differential equation models with steady-state constraints, BMC Syst Biol, 10, 1, 80 (2016)
[11] Fröhlich, F.; Kaltenbacher, B.; Theis, FJ; Hasenauer, J., Scalable parameter estimation for genome-scale biochemical reaction networks, PLoS Comput Biol, 13, 1, e1005331 (2017)
[12] Hass, H.; Loos, C.; Raimúndez-Álvarez, E.; Timmer, J.; Hasenauer, J.; Kreutz, C., Benchmark problems for dynamic modeling of intracellular processes, Bioinformatics, 35, 17, 3073-3082 (2019)
[13] Hindmarsh, AC; Brown, PN; Grant, KE; Lee, SL; Serban, R.; Shumaker, DE; Woodward, CS, SUNDIALS: suite of nonlinear and differential/algebraic equation solvers, ACM T Math Software, 31, 3, 363-396 (2005) · Zbl 1136.65329
[14] Hoops, S.; Sahle, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.; Singhal, M.; Xu, L.; Mendes, P.; Kummer, U., COPASI - a COmplex PAthway SImulator, Bioinformatics, 22, 24, 3067-3074 (2006)
[15] Jones E, Oliphant T, Peterson P, et al. (2001) SciPy: Open source scientific tools for Python. http://www.scipy.org/
[16] Klipp, E.; Nordlander, B.; Krüger, R.; Gennemark, P.; Hohmann, S., Integrative model of the response of yeast to osmotic shock, Nat Biotechnol, 23, 8, 975-982 (2005)
[17] Ligon, TS; Fröhlich, F.; Chi, OT; Banga, JR; Balsa-Canto, E.; Hasenauer, J., GenSSI 2.0: Multi-experiment structural identifiability analysis of SBML models, Bioinformatics, 34, 8, 1421-1423 (2018)
[18] Loos, C.; Krause, S.; Hasenauer, J., Hierarchical optimization for the efficient parametrization of ODE models, Bioinformatics, 34, 24, 4266-4273 (2018)
[19] Maier, C.; Loos, C.; Hasenauer, J., Robust parameter estimation for dynamical systems from outlier-corrupted data, Bioinformatics, 33, 5, 718-725 (2017)
[20] Mitra, ED; Hlavacek, WS, Bayesian inference using qualitative observations of underlying continuous variables, Bioinformatics, 36, 10, 3177-3184 (2020)
[21] Mitra, ED; Dias, R.; Posner, RG; Hlavacek, WS, Using both qualitative and quantitative data in parameter identification for systems biology models, Nat commun, 9, 1, 3901 (2018)
[22] Mitra, ED; Suderman, R.; Colvin, J.; Ionkov, A.; Hu, A.; Sauro, HM; Posner, RG; Hlavacek, WS, PyBioNetFit and the biological property specification language, iScience, 19, 1012-1036 (2019)
[23] Pargett, M.; Umulis, DM, Quantitative model analysis with diverse biological data: applications in developmental pattern formation, Methods, 62, 1, 56-67 (2013)
[24] Pargett, M.; Rundell, AE; Buzzard, GT; Umulis, DM, Model-based analysis for qualitative data: an application in drosophila germline stem cell regulation, PLoS Comput Biol, 10, 3, e1003498 (2014)
[25] Raia, V.; Schilling, M.; Böhm, M.; Hahn, B.; Kowarsch, A.; Raue, A.; Sticht, C.; Bohl, S.; Saile, M.; Möller, P., Dynamic mathematical modeling of il13-induced signaling in hodgkin and primary mediastinal b-cell lymphoma allows prediction of therapeutic targets, Cancer Res, 71, 3, 693-704 (2011)
[26] 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, 25, 25, 1923-1929 (2009)
[27] Raue, A.; Schilling, M.; Bachmann, J.; Matteson, A.; Schelke, M.; Kaschek, D.; Hug, S.; Kreutz, C.; Harms, BD; Theis, FJ; Klingmüller, U.; Timmer, J., Lessons learned from quantitative dynamical modeling in systems biology, PLoS ONE, 8, 9, e74335 (2013)
[28] Raue, A.; Kreutz, C.; Theis, FJ; Timmer, J., Joining forces of Bayesian and frequentist methodology: A study for inference in the presence of non-identifiability, Philos T Roy Soc A, 371, 1984, 20110544 (2013) · Zbl 1353.62013
[29] Raue, A.; Steiert, B.; Schelker, M.; Kreutz, C.; Maiwald, T.; Hass, H.; Vanlier, J.; Tönsing, C.; Adlung, L.; Engesser, R.; Mader, W.; Heinemann, T.; Hasenauer, J.; Schilling, M.; Höfer, T.; Klipp, E.; Theis, FJ; Klingmüller, U.; Schöberl, B.; Timmer, J., Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems, Bioinformatics, 31, 21, 3558-3560 (2015)
[30] Rosenblatt, M.; Timmer, J.; Kaschek, D., Customized steady-state constraints for parameter estimation in non-linear ordinary differential equation models, Front Cell Dev Biol, 4, 41 (2016)
[31] Schälte, Y.; Stapor, P.; Hasenauer, J., Evaluation of derivative-free optimizers for parameter estimation in systems biology, IFAC-PapersOnLine, 51, 19, 98-101 (2018)
[32] Schälte Y, Fröhlich F, Stapor P, Wang D, Weindl D (2019) pyPESTO v0.0.7. 10.5281/zenodo.2600850
[33] Schmiester, L.; Schälte, Y.; Fröhlich, F.; Hasenauer, J.; Weindl, D., Efficient parameterization of large-scale dynamic models based on relative measurements, Bioinformatics, 36, 2, 594-602 (2019)
[34] 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, Pathirana D, Raimúndez E, Refisch L, Rosenblatt M, Stapor PL, Städter P, Wang D, Wieland F-G, Banga JR, Timmer J, Villaverde AF, Sahle S, Kreutz C, Hasenauer J, Weindl D (2020) PEtab – interoperable specification of parameter estimation problems in systems biology. arXiv preprint arXiv:2004.01154
[35] Schöberl, B.; Pace, EA; Fitzgerald, JB; Harms, BD; Xu, L.; Nie, L.; Linggi, B.; Kalra, A.; Paragas, V.; Bukhalid, R.; Grantcharova, V.; Kohli, N.; West, KA; Leszczyniecka, M.; Feldhaus, MJ; Kudla, AJ; Nielsen, UB, Therapeutically targeting ErbB3: A key node in ligand-induced activation of the ErbB receptor-PI3K axis, Sci Signal, 2, 77, ra31 (2009)
[36] Shepard, RN, The analysis of proximities: multidimensional scaling with an unknown distance function. I., Psychometrika, 27, 2, 125-140 (1962) · Zbl 0129.12103
[37] Stapor, P.; Weindl, D.; Ballnus, B.; Hug, S.; Loos, C.; Fiedler, A.; Krause, S.; Hross, S.; Fröhlich, F.; Hasenauer, J., PESTO: Parameter EStimation TOolbox, Bioinformatics, 34, 4, 705-707 (2018)
[38] Villaverde, AF; Froehlich, F.; Weindl, D.; Hasenauer, J.; Banga, JR, Benchmarking optimization methods for parameter estimation in large kinetic models, Bioinformatics, 35, 5, 830-838 (2018)
[39] Weber P, Hasenauer J, Allgöwer F, Radde N (2011) Parameter estimation and identifiability of biological networks using relative data. In Proc. of the 18th IFAC World Congress. Milano, 18, pp. 11648-11653
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.