Data-based identifiability analysis of non-linear dynamical models
Open accessAbstract
Motivation: Mathematical modelling of biological systems is becoming a standard approach to investigate complex dynamic, non-linear interaction mechanisms in cellular processes. However, models may comprise non-identifiable parameters which cannot be unambiguously determined. Non-identifiability manifests itself in functionally related parameters, which are difficult to detect. Results: We present the method of mean optimal transformations, a non-parametric bootstrap-based algorithm for identifiability testing, capable of identifying linear and non-linear relations of arbitrarily many parameters, regardless of model size or complexity. This is performed with use of optimal transformations, estimated using the alternating conditional expectation algorithm (ACE). An initial guess or prior knowledge concerning the underlying relation of the parameters is not required. Independent, and hence identifiable parameters are determined as well. The quality of data at disposal is included in our approach, i.e. the non-linear model is fitted to data and estimated parameter values are investigated with respect to functional relations. We exemplify our approach on a realistic dynamical model and demonstrate that the variability of estimated parameter values decreases from 81 to 1% after detection and fixation of structural non-identifiabilities. Availability: Our algorithm is written in Matlab and R. It is available from the authors on request. An implementation of ACE, written in Matlab as well as in C, is available online at www.stefanhengl.de Contact: hengl@fdm.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The Hengl et al. (2007) approach detects structural non-identifiability via functional relations for arbitrary models but is not intended to detect practical non-identifiability.
“An approach to detect structural non-identifiability by the corresponding functional relations was introduced by Hengl et al. (2007).It is able to detect flatness of likelihood for arbitrary models, but it is not intended to detect practical non-identifiability.”
From Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood (2009) · cites this paper as Hengl et al., 2007
The Approach and Conclusion describe detecting structural non-identifiability through functionally related parameters in nonlinear models. But the Introduction explicitly lists practical identifiability analysis, accounting for data quality, as an aim of the method, contrary to the claim that it is not intended for that purpose. The passages do not specifically describe the method as detecting likelihood flatness. (LLM, conf=0.90)
Experimental — accuracy not yet measuredNon-identifiability of our model arises in part because the quantity, quality and type of data are inadequate and relationships among parameters and experimental observables are inherently non-unique.
“Non-identifiability of our model arises in part because the quantity, quality and type of data are inadequate and relationships among parameters and experimental observables are inherently non-unique (Hengl et al, 2007).”
From Input–output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data (2009) · cites this paper as Hengl et al, 2007
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Experimental Design and Data Analysis for Biologists
Quinn, G. P., & Keough, M. J. (2002) · doi:10.1017/cbo9780511806384 · Cited by 10,674 · cited 1× · see citing works
“However, available data-based approaches for a posteriori identifiability analysis of non-linear models, like multivariate regression, require prior knowledge concerning explicit linear or nonlinear functional relations (Quinn and Keough, 2002; Seber and Wild, 1988).”
Estimating Optimal Transformations for Multiple Regression and Correlation
Breiman, L., & Friedman, J. H. (1985) · Journal of the American Statistical Association · doi:10.1080/01621459.1985.10478157 · Cited by 1,713 · see citing works
On global identifiability for arbitrary model parametrizations
Lennart Ljung, A., & Glad, T. (1994) · Automatica · doi:10.1016/0005-1098(94)90029-9 · Cited by 644 · see citing works
System identifiability based on the power series expansion of the solution
Pohjanpalo, H. (1978) · Mathematical Biosciences · doi:10.1016/0025-5564(78)90063-9 · Cited by 440 · see citing works
Global identifiability of nonlinear models of biological systems
Audoly, S., Bellu, G., D’Angiò, L., Saccomani, M. P., & Cobelli, C. (2001) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.900248 · Cited by 324 · see citing works
Parameter identifiability of nonlinear systems: the role of initial conditions
Saccomani, M. P., Audoly, S., & D’Angiò, L. (2003) · Automatica · doi:10.1016/s0005-1098(02)00302-3 · Cited by 233 · see citing works
Similarity transformation approach to identifiability analysis of nonlinear compartmental models
Vajda, S., Godfrey, K. R., & RABITZ, H. A. (1989) · Mathematical Biosciences · doi:10.1016/0025-5564(89)90024-2 · Cited by 227 · see citing works
Jacquez, J. A., & Greif, P. (1985) · Mathematical Biosciences · doi:10.1016/0025-5564(85)90098-7 · Cited by 205 · see citing works
Reconstruction of non-linear time delay models from data by the use of optimal transformations
Voss, H. U., & Kurths, J. (1997) · Physics Letters A · doi:10.1016/s0375-9601(97)00598-7 · Cited by 137 · see citing works
Simulation methods for optimal experimental design in systems biology
Faller, D., Klingmüller, U., & Timmer, J. (2003) · SIMULATION · doi:10.1177/0037549703040937 · Cited by 137 · see citing works
Self-citationRemarks on Functional Canonical Variates, Alternating Least Squares Methods and Ace
Buja, A. (1990) · The Annals of Statistics · doi:10.1214/aos/1176347739 · Cited by 109 · see citing works
Parametric, nonparametric and parametric modelling of a chaotic circuit time series
Timmer, J., Rust, H. W., Horbelt, W., & Voss, H. U. (2000) · Physics Letters A · doi:10.1016/s0375-9601(00)00548-x · Cited by 60 · see citing works
Self-citationIdentifying Nonlinear Relationships in Regression using the ACE Algorithm
Wang, D., & Murphy, M. (2005) · Journal of Applied Statistics · doi:10.1080/02664760500054517 · Cited by 17 · see citing works
Flagged first, then by citations
Research works printed but not linked: 3
- [5]5. Godfrey,K.R. and DiStefano, J.J. (1987) Identifiabiliy of Model Parameters in Identifiability of Parametric Models, Chapter 1. Pergamon Press, Oxford, pp. 1-20.
- [7]7. Lecourtier,Y. et al. (1987) Volterra and Generating Power Series Approach to Identifiability Testing in Identifiability of Parametric Models, Chapter 5. Pergamon Press, Oxford, pp. 50-66.
- [12]12. Seber,G. and Wild,C. (1988) Nonlinear Regression. Wiley, New York.
Cited by
Sorted by citations
Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmüller, U., & Timmer, J. (2009) · Bioinformatics · doi:10.1093/bioinformatics/btp358 · Cited by 1,442 · see citing works
Self-citationStructural identifiability of systems biology models: a critical comparison of methods
Chis, O.-T., Banga, J. R., & Balsa-Canto, E. (2011) · PLoS ONE · doi:10.1371/journal.pone.0027755 · Cited by 448 · see citing works
Chen, W. W., Schoeberl, B., Jasper, P. J., Niepel, M., Nielsen, U. B., Lauffenburger, D. A., & Sorger, P. K. (2009) · Molecular Systems Biology · doi:10.1038/msb.2008.74 · Cited by 391 · see citing works
Systems biology: parameter estimation for biochemical models
Ashyraliyev, M., Fomekong‐Nanfack, Y., Kaandorp, J. A., & Blom, J. G. (2009) · The FEBS Journal · doi:10.1111/j.1742-4658.2008.06844.x · Cited by 323 · see citing works
Systems biology: experimental design
Kreutz, C., & Timmer, J. (2009) · The FEBS Journal · doi:10.1111/j.1742-4658.2008.06843.x · Cited by 257 · see citing works
Self-citationDynamical modeling and multi-experiment fitting with PottersWheel
Maiwald, T., & Timmer, J. (2008) · Bioinformatics · doi:10.1093/bioinformatics/btn350 · Cited by 231 · see citing works
Self-citationMaximizing the information content of experiments in systems biology
Liepe, J., Filippi, S., Komorowski, M., & Stumpf, M. P. H. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002888 · Cited by 170 · see citing works
Addressing parameter identifiability by model-based experimentation
Raue, A., Kreutz, C., Maiwald, T., Klingmüller, U., & Timmer, J. (2011) · IET Systems Biology · doi:10.1049/iet-syb.2010.0061 · Cited by 145 · see citing works
Self-citationQuaiser, T., & Mönnigmann, M. (2009) · BMC Systems Biology · doi:10.1186/1752-0509-3-50 · Cited by 114 · see citing works
Theoretical and experimental analysis links isoform-specific ERK signalling to cell fate decisions
Schilling, M., Maiwald, T., Hengl, S., Winter, D., Kreutz, C., Kolch, W., Lehmann, W. D., Timmer, J., & Klingmüller, U. (2009) · Molecular Systems Biology · doi:10.1038/msb.2009.91 · Cited by 79 · see citing works
Self-citationParameter identifiability of power-law biochemical system models
Srinath, S., & Gunawan, R. (2010) · Journal of Biotechnology · doi:10.1016/j.jbiotec.2010.02.019 · Cited by 68 · see citing works
‘Glocal’ Robustness Analysis and Model Discrimination for Circadian Oscillators
Hafner, M., Koeppl, H., Hasler, M., & Wagner, A. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000534 · Cited by 63 · see citing works
Workflow for generating competing hypothesis from models with parameter uncertainty
Gomez-Cabrero, D., Compte, A., & Tegner, J. (2011) · Interface Focus · doi:10.1098/rsfs.2011.0015 · Cited by 33 · see citing works
Identifiability and experimental design in perturbation studies
Gross, T., & Blüthgen, N. (2020) · Bioinformatics · doi:10.1093/bioinformatics/btaa404 · Cited by 11 · see citing works
- Authors
- Hengl, S., Kreutz, C., Timmer, J., & Maiwald, T.
- Affiliations
- University of Freiburg (DE)
- Corresponding author
- Hengl, S.
- Venue
- Bioinformatics
- Publisher
- Oxford University Press (OUP)
- Published
- 2007-07-28
- Volume
- 23
- Issue
- 19
- Pages
- 2612-2618
- ISSN
- 1367-4803 (ISSN-L)
- 1367-4811
- OpenAlex
- W2130191588
- Cited by
- 166
- References
- 13
- Citations by year
- 2026: 4 · 2025: 1 · 2024: 7 · 2023: 5 · 2022: 4 · 2021: 10 · 2020: 7 · 2019: 5 · 2018: 6 · 2017: 3 · 2016: 13 · 2015: 14 · 2014: 12 · 2013: 14 · 2012: 12
- FWCI
- 4.24
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Bioinformatics (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Deutsches Krebsforschungszentrum
- Bundesministerium für Bildung und Forschung (0313074D)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Keywords
- parameter identifiability, alternating conditional expectation, biological systems modelling, data quality assessment
- MeSH terms
- Algorithms, Artificial Intelligence, Computer Simulation, Models, Biological, Pattern Recognition, Automated, Signal Transduction, Databases, Factual, Information Storage and Retrieval, Nonlinear Dynamics, Proteome
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
