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Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood
Open accessAbstract
MOTIVATION: Mathematical description of biological reaction networks by differential equations leads to large models whose parameters are calibrated in order to optimally explain experimental data. Often only parts of the model can be observed directly. Given a model that sufficiently describes the measured data, it is important to infer how well model parameters are determined by the amount and quality of experimental data. This knowledge is essential for further investigation of model predictions. For this reason a major topic in modeling is identifiability analysis. RESULTS: We suggest an approach that exploits the profile likelihood. It enables to detect structural non-identifiabilities, which manifest in functionally related model parameters. Furthermore, practical non-identifiabilities are detected, that might arise due to limited amount and quality of experimental data. Last but not least confidence intervals can be derived. The results are easy to interpret and can be used for experimental planning and for model reduction. AVAILABILITY: An implementation is freely available for MATLAB and the PottersWheel modeling toolbox at http://web.me.com/andreas.raue/profile/software.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
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TL;DR
The paper presents a profile-likelihood method for assessing structural and practical identifiability in partially observed dynamical models and for deriving likelihood-based confidence intervals. Applied to a JAK-STAT signaling model, it identifies four structurally non-identifiable parameters and one practically non-identifiable parameter, and shows how additional measurements can resolve these ambiguities.
Key findings
- Profile likelihood distinguishes structural non-identifiability, seen as a flat profile, from practical non-identifiability, seen as a profile with a minimum that fails to cross the confidence threshold in one or both directions; identifiable parameters cross the threshold on both sides.
- In the JAK-STAT application, parameters p2, x1(0), s1, and s2 were structurally non-identifiable, with functional relations p2·x1(0)=const, s1·x1(0)=const, and s2·x1(0)=const; p3 was practically non-identifiable for increasing values.
- Table 1 reports infinite likelihood-based intervals for the structurally non-identifiable parameters, whereas Hessian-based asymptotic intervals were finite but misleadingly narrow, e.g. p2: −33 to +31, x1(0): −31 to +32, s1: −32 to +31, s2: −32 to +31; for p3, the profile-likelihood interval was −1.14 to +∞ versus −1.14 to +0.15 from the Hessian.
- Adding hypothetical measurements of x1(0)=200±20 nM and x3/(x2+x3)=0.90±0.05 at t=20 min made p2, x1(0), s1, and s2 structurally identifiable and p3 practically identifiable, while p2 remained practically non-identifiable. Profile-likelihood computation took 54±18 s per parameter on a 1 GHz CPU with 2 GB RAM.
Methods
- The approach uses an ODE model with weighted least-squares objective χ², computes the profile likelihood for each parameter by re-optimizing all other parameters at fixed values of the target parameter, and derives likelihood-based confidence intervals from χ² thresholds.
- The application is a JAK-STAT signaling model inspired by Swameye et al., calibrated to experimental data; observables are phosphorylated STAT in cytoplasm (y1) and total STAT in cytoplasm (y2) measured by quantitative western blotting, with cytoplasm and nucleus volumes of 1400 µm³ and 450 µm³.
- Parameters calibrated include p1–p4, s1, s2, and x1(0), with x2(0)–x4(0) set to zero; the model was implemented and fitted with PottersWheel, and experimental planning and model reduction were explored via profile-likelihood trajectories, Monte Carlo simulations, and likelihood-ratio thresholds.
Limitations
- The authors state that structural non-identifiability cannot be resolved by refining existing measurements or reducing noise; it requires a qualitatively new measurement that changes the observation mapping, such as observing additional species. Practical non-identifiability can be resolved by increasing the amount or quality of data and/or selecting better measurement time points.
- The authors note that recovering functional relations unambiguously from parameter changes along the profile likelihood is only possible when the corresponding manifold is one-dimensional; higher-dimensional manifolds require further analysis, such as the approach of Hengl et al.
- Evident from the text: the method is demonstrated on a single JAK-STAT model and dataset, with no broad empirical comparison across many model classes; the approach also assumes a sufficiently adequate model and normally distributed measurement noise.
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In the paper
“The largest discrepancy occurs for practically non-identifiable parameters, where asymptotic confidence intervals are significantly smaller than likelihood-based confidence intervals.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“The variability of the predicted model observables y along the profile likelihood of p 3 remains consistent with the measurement errors, as shown in Figure 6.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“The resulting plots of profile likelihood versus parameter reveal four structurally non-identifiable parameters p 2 , x 1 (0), s 1 , s 2 by their flat profile likelihood, see Figure 3, upper panel.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 5 APPLICATION
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In the paper
“For identifiable parameters the discrepancies are small.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“The functional relations h connecting these structurally non-identifiable parameters can be recovered from the changes of the remaining parameters, while calculating the profile likelihood of the structurally non-identifiable parameters, as shown in Figure 4.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“The recalculated profile likelihood reveals, that parameters p 2 , x 1 (0), s 1 , s 2 become structurally identifiable (Fig. 3, lower panel), by measuring only one of them.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“The profile likelihood reveals that parameter p 3 is practically non-identifiable for increasing parameter values.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- The authors state this as an assumption: An appropriate model M that sufficiently describes the available experimental data is assumed.
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In the paper
“Nevertheless, a lower confidence bound can be derived.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“In this case, asymptotic approximation leads to large but nevertheless finite confidence intervals for the structurally non-identifiable parameters.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“All internal model states can only be identified up to a common factor.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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In the paper
“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.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
- Partly supportedcites Hengl et al., 2007 sourceExperimental — accuracy not yet measured
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)
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In the paper
“Spots of largest variability suggest where and when a measurement of a species most efficiently determines theses parameters: x 1 at times t = 0 or t > 50; x 2 to x 4 at times 5 < t < 30.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“Calculating the profile likelihood takes 54 ± 18 s per parameter, using an implementation of the approach embedded in the Potters-Wheel fitting toolbox (1 GHz CPU, 2 GB RAM), which is described in the Supplementary Material.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 5 APPLICATION
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In the paper
“Parameter p 3 becomes practically identifiable, only previously structurally non-identifiable parameter p 2 remains practically non-identifiable.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“The trajectories of the internal model states x along the profile likelihood of the practically non-identifiable parameter p 3 shown in Figure 6 comprises large antipodal variability of species x 2 and x 3 , revealing that the experimental setup is inappropriate to estimate this parameter with confidence.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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In the paper
“h 1 (θ sub ) = p 2 •x 1 (0)-const = 0 h 2 (θ sub ) = s 1 •x 1 (0)-const = 0 ( 1 1 ) h 3 (θ sub ) = s 2 •x 1 (0)-const = 0”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The approach was applied to a model of the JAK-STAT signaling pathway.Non-identifiable parameters were detected, revealing limitations in the experimental setup.Additional measurements that efficiently improve parameter identification were suggested and validated.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“They are exact if the observables y depend linearly on θ.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.1 Asymptotic confidence intervals
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In the paper
“Unfortunately, these methods become rapidly infeasible with increasing model size (Margaria et al., 2001;White et al., 2001).Practical non-identifiability cannot be detected, since experimental data are disregarded.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
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In the paper
“Even identifiable parameters can only be determined within confidence intervals, which contain the true value of the parameter with a desired probability (Lehmann and Leo, 1983).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 1 INTRODUCTION
What the sources say
- Not matchedcites Lehmann and Leo, 1983
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In the paper
“These methods are appropriate if functional relations h between the parameters emerging from structural non-identifiability are linear.This is often not the case for reaction networks modeled by ODE, because observables depend non-linearly on the parameters.Practical non-identifiability cannot be detected, because a quadratic approximation is not able to explain increasing but limited behavior of”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 3 EXISTING METHODS
What the sources say
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In the paper
“However, even for the simplest reaction network the observables y depend nonlinearly on θ and the amount and quality of experimental data is often insufficient.Therefore, asymptotic confidence intervals might not be appropriate (Joshi et al., 2006).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.1 Asymptotic confidence intervals
What the sources say
- Not checked — no full text of the sourcecites Joshi et al., 2006 source
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In the paper
“Likelihood-based confidence intervals are considered superior to asymptotic confidence intervals for finite samples (Neale and Miller, 1997).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.2.2 Finite sample confidence intervals
What the sources say
- Not checked — no full text of the sourcecites Neale and Miller, 1997 source
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In the paper
“Along a practical non-identifiability, the observable y change only negligibly remaining compliant with the given measurement accuracy.Nevertheless, model behavior in terms of internal states x might vary strongly.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > )]:
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In the paper
“This arises frequently if amount and quality of experimental data is insufficient and manifests in a confidence interval that is infinite.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 2.3.2 Practical non-identifiability
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In the paper
“The points of passover represent likelihoodbased confidence intervals as defined in Equation ( 8) (Royston, 2007).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 4 APPROACH
What the sources say
- Not checked — no full text of the sourcecites Royston, 2007 source
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In the paper
“The results are easy to interpret”
- Also stated in: § 6 DISCUSSION · plain
“The approach results in easily interpretable plots of profile likelihood versus parameter.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Abstract
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- Also stated in: § 6 DISCUSSION · plain
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In the paper
“The profile likelihood of a practically non-identifiable parameter has a minimum, but is not excessing a threshold α for increasing and/or decreasing values of θ i (see Definition 1).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 4 APPROACH
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In the paper
“This gives insight into a complex and high-dimensional parameter space.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“It can be automated, but an explicit advantage is that the output might be evaluated visually.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“The approach can be applied to any parameter estimation problem, where a likelihood or a similar objective criterion is available, e.g.partial differential equations (PDE) or stochastic differential equations (SDE).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“The profile likelihood can be calculated for each parameter separately.Thereby it is possible to restrict the analysis to the parameters relevant for the biological question.Moreover, this allows to perfectly parallelize the approach, which is a major benefit for its scalability.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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In the paper
“Working in logarithmic parameter space linearizes the functional relations given in Equation (11).”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Structural non-identifiability
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The impact of new measurements can be evaluated by Monte Carlo simulations.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > Experimental planning
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus, identifiability analysis ensures that the model complexity is tailored to the information content given by the experimental data.”
§ Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood > 6 DISCUSSION
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The authors state this as an assumption.
The measurement noise is normally distributed.
“The measurement noise (t) is assumed to be normally distributed.”
The authors state this as an assumption.
An appropriate model M that sufficiently describes the available experimental data is assumed.
“Furthermore, an appropriate model M that sufficiently describes the available experimental data is assumed.”
The paper relies on this without support.
No approach for explicit testing of practical non-identifiability is available.
“Similar to a clear formal definition, an approach for explicit testing of practical non-identifiability is not available to our knowledge.”
The authors state this as an assumption.
The initial values of species x2 to x4 are equal to zero.
“The initial values of species x 2 to x 4 are assumed to be equal to zero.”
The authors state this as an assumption.
For the model-reduction argument, a parameter θi is practically non-identifiable for decreasing parameter value.
“Assume that a parameter θ i is practically non-indentifiable for decreasing parameter value.”
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The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Such parameter estimations usually yield statistical information related to parameter precision (importantly, not accuracy) such as standard errors or correlation matrices, and sometimes information derived from more sophisticated approaches such as profile likelihood.39”
From Best Practices to Maximize the Use and Reuse of Quantitative and Systems Pharmacology Models: Recommendations From the United Kingdom Quantitative and Systems Pharmacology Network (2019) · cites this paper as [39]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Raue et al. (2009) referred to likelihood ratio C.I.s as finite sample C.I.s, to underscore the superiority of likelihood ratio C.I.s over Wald-type C.I.s.”
From rSalvador: An R Package for the Fluctuation Experiment (2017) · cites this paper as Raue et al. 2009
In the citing paper
“When two models are nested (Mð hPL Þ and Mð hopt Þ) their likelihood ratio is approximately distributed according to a v 2 p distribution.Here p refers to the number of degrees of freedom which is defined as the difference in the number of parameters (which in this case is 1).”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“In such cases, more reliable confidence intervals can be obtained using the Profile Likelihood method [36].”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“Techniques for this exist in both a frequentist [13,36,91] as well as a Bayesian setting [87,90].”
From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [36]
In the citing paper
“Fortunately, recent literature is correcting this (e.g. [129–140]).”
From Reverse engineering and identification in systems biology: strategies, perspectives and challenges (2014) · cites this paper as [133]
In the citing paper
“Given the data, not all parameters are identifiable (Raue et al., 2009).”
From A bayesian approach to targeted experiment design (2012) · cites this paper as Raue et al., 2009
In the citing paper
“Methods for an approximate sampling of the parameter space, e.g. the Markov Chain Monte Carlo (MCMC) methods [11,12], and bootstrap based approaches [4,13] are numerically demanding and provide only rough approximations for ODE models. Therefore, it is difficult to control the coverage of the prediction confidence intervals for such approaches.”
From Likelihood based observability analysis and confidence intervals for predictions of dynamic models (2012) · cites this paper as [4]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Concentration unit conflicts with figure labels
MinorThe text says concentrations are modeled in nanometers, a unit of length, while the figure labels use nM, a unit of concentration.
“Species concentrations are modeled in nanometer.”
“time / min x 1 / nM”
Citations
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Roda, W. C., Varughese, M., Han, D., & Li, M. Y. (2020) · Infectious Disease Modelling · doi:10.1016/j.idm.2020.03.001 · Cited by 636
A systems study reveals concurrent activation of AMPK and mTOR by amino acids
Dalle Pezze, P., Ruf, S., Sonntag, A. G., Langelaar-Makkinje, M., Hall, P., Heberle, A. M., Razquin Navas, P., van Eunen, K., Tölle, R. C., Schwarz, J. J., et al. (2016) · Nature Communications · doi:10.1038/ncomms13254 · Cited by 148
Effective connectivity: Influence, causality and biophysical modeling
Valdes-Sosa, P. A., Roebroeck, A. F., Jean Daunizeau, A., & Friston, K. J. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2011.03.058 · Cited by 399
“This is the basic idea behind the profile likelihood approach (Raue et al., 2009), which is based on the profile of the evidence for models with different parameter values.”
Chowell, G. (2017) · Infectious Disease Modelling · doi:10.1016/j.idm.2017.08.001 · Cited by 361
“As a general rule, a parameter is identifiable when its confidence interval lies in a finite range of values (Cobelli & Romanin-Jacur, 1976; Jacquez, 1996; Raue et al., 2009) .”
BackgroundInfluentialSystems biology informed deep learning for inferring parameters and hidden dynamics
Yazdani, A. Z. K., Lu, L., Raissi, M., & Karniadakis, G. E. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007575 · Cited by 350
“Usually, experimental data are insufficient considering the size of the model, which results in parameters that are non-identifiable [15] or only identifiable within confidence intervals (see more details in [16]).”
BackgroundMethodInfluentialOn structural and practical identifiability
Wieland, F.-G., Hauber, A. L., Rosenblatt, M., Tönsing, C., & Timmer, J. (2021) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2021.03.005 · Cited by 402
Self-citationLessons Learned from Quantitative Dynamical Modeling in Systems Biology
Raue, A., Schilling, M., Bachmann, J., Matteson, A., Schelke, M., Kaschek, D., Hug, S., Kreutz, C., Harms, B. D., Theis, F. J., et al. (2013) · PLoS ONE · doi:10.1371/journal.pone.0074335 · Cited by 316
Self-citationKinetic models in industrial biotechnology – Improving cell factory performance
Almquist, J. O., Cvijović, M., Vassily Hatzimanikatis, A., Nielsen, J., & Jirstrand, M. (2014) · Metabolic Engineering · doi:10.1016/j.ymben.2014.03.007 · Cited by 303
“Consider N measured data points, DN ¼ d1; ;dN , taken at time points t1; ; tN , which are described by a scalar-valued model output, y(t) (at the expense of a little more notation the line of though easily extends to the case with vector-valued outputs, see for instance Raue et al., 2009).”
BackgroundMethodInfluentialStructural Identifiability of Dynamic Systems Biology Models
Villaverde, A. F., Barreiro, A., & Papachristodoulou, A. (2016) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005153 · Cited by 279
In-host Mathematical Modelling of COVID-19 in Humans
Hernandez-Vargas, E. A., & Velasco‐Hernández, J. X. (2020) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2020.09.006 · Cited by 245
Reverse engineering and identification in systems biology: strategies, perspectives and challenges
Villaverde, A. F., & Banga, J. R. (2014) · Journal of The Royal Society Interface · doi:10.1098/rsif.2013.0505 · Cited by 229
Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems
Raue, A., Steiert, B., Schelker, M., Kreutz, C., Maiwald, T., Hass, H., Vanlier, J., Tönsing, C., Adlung, L., Engesser, R., et al. (2015) · Bioinformatics · doi:10.1093/bioinformatics/btv405 · Cited by 227
Self-citationNakagawa, S., Yang, Y., Macartney, E. L., Spake, R., & Lagisz, M. (2023) · Environmental Evidence · doi:10.1186/s13750-023-00301-6 · Cited by 242
“Of relevance, when running complex models, some model parameters cannot be estimated well, or they are not ‘identifiable’ [88].”
BackgroundCazzaniga, P., Nobile, M. S., Besozzi, D., Bellini, M., & Mauri, G. (2014) · BioMed Research International · doi:10.1155/2014/863298 · Cited by 203
“Indeed, standard investigations of biological systems usually rely on computational methods that require the execution of a large number of simulations, such as parameter sweep analysis [3], sensitivity analysis [4], structure and parameter identifiability [5], parameter estimation [6–8], and reverse engineering of mo…”
BackgroundKalra, A. V., Kim, J., Klinz, S. G., Paz, N., Cain, J. E., Drummond, D. C., Nielsen, U. B., & Fitzgerald, J. B. (2014) · Cancer Research · doi:10.1158/0008-5472.can-14-0572 · Cited by 199
Guillaume, J. H. A., Jakeman, J. D., Marsili-Libelli, S., et al. (2019) · Environmental Modelling & Software · doi:10.1016/j.envsoft.2019.07.007 · Cited by 196
The Novel Coronavirus, 2019-nCoV, is Highly Contagious and More Infectious Than Initially EstimatedPreprint
Sanche, S., Lin, Y. T., Xu, C., et al. (2020) · medRxiv · doi:10.1101/2020.02.07.20021154 · Cited by 189
“To translate this into meaningful predictions, we use the framework proposed by Lipsitch et al (16) with the parameters we estimated for 2019-nCoV.”
MethodComparison of approaches for parameter identifiability analysis of biological systems
Raue, A., Karlsson, J., Saccomani, M. P., Jirstrand, M., & Timmer, J. (2014) · Bioinformatics · doi:10.1093/bioinformatics/btu006 · Cited by 188
Self-citationFrom word models to executable models of signaling networks using automated assembly
Gyori, B. M., Bachman, J. A., Subramanian, K., Muhlich, J. L., Galescu, L., & Sorger, P. K. (2017) · Molecular Systems Biology · doi:10.15252/msb.20177651 · Cited by 188
“…Dynamical models and systems theory have proven extremely effective in elucidating mechanisms of all-or-none response to apoptosis-inducing ligands (Rehm et al , 2002; Albeck et al , 2008), sequential execution of cell cycle phases (Chen et al , 2004), the interplay between stochastic and…”
Profile likelihood in systems biology
Kreutz, C., Raue, A., Kaschek, D., & Timmer, J. (2013) · FEBS Journal · doi:10.1111/febs.12276 · Cited by 190
“In the Systems Biology setting, the parameter profile likelihood has been proposed for the calculation of confidence intervals and in addition for the investigation of parameter identifiability [19, 20].”
InfluentialSelf-citationRobust and efficient parameter estimation in dynamic models of biological systems
Gábor, A., & Banga, J. R. (2015) · BMC Systems Biology · doi:10.1186/s12918-015-0219-2 · Cited by 182
“Similarly, the computation of the covariance and correlation of the parameters ([59, 60]) and the computation of confidence regions of the model predictions [48] are usually performed based on the Fisher information matrix (FIM).”
MethodDetermination of parameter identifiability in nonlinear biophysical models: A Bayesian approach
Hines, K., Middendorf, T. R., & Aldrich, R. W. (2014) · The Journal of General Physiology · doi:10.1085/jgp.201311116 · Cited by 171
“Demonstrating that a system’s design matrix is full-rank is a necessary, but not sufficient, condition for ensuring that the model’s parameters can be uniquely estimated from experimental data (Jacquez and Greif, 1985; Faller et al., 2003; Raue et al., 2009).”
BackgroundMethodInfluentialSaa, P. A., & Nielsen, L. K. (2017) · Biotechnology Advances · doi:10.1016/j.biotechadv.2017.09.005 · Cited by 166
“In reveal non-intuitive structural and practical identifiability issues in biochemical kinetic models (Raue et al., 2009).”
BackgroundMcLean, K. A. P., & McAuley, K. B. (2011) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.20660 · Cited by 167
Musuamba, F. T., Rusten, I. S., Lesage, R., Russo, G. L., Bursi, R., Emili, L., Wangorsch, G., Manolis, E., Karlsson, K. E., Kulesza, A. J., et al. (2021) · CPT Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.12669 · Cited by 175
Network quantification of EGFR signaling unveils potential for targeted combination therapy
Klinger, B., Sieber, A., Fritsche‐Guenther, R., Witzel, F., Berry, L., Schumacher, D., Yan, Y., Durek, P., Merchant, M. A., Schäfer, R., et al. (2013) · Molecular Systems Biology · doi:10.1038/msb.2013.29 · Cited by 155
Covering a Broad Dynamic Range: Information Processing at the Erythropoietin Receptor
Becker, V., Schilling, M., Bachmann, J., Baumann, U., Raue, A., Maiwald, T., Timmer, J., & Klingmüller, U. (2010) · Science · doi:10.1126/science.1184913 · Cited by 159
Self-citationModeling Influenza Virus Infection: A Roadmap for Influenza Research
Boianelli, A., Nguyễn, V. K., Ebensen, T., Schulze, K., Wilk, E., Sharma, N., Stegemann‐Koniszewski, S., Bruder, D., Toapanta, F. R., Guzmán, C. A., et al. (2015) · Viruses · doi:10.3390/v7102875 · Cited by 158
“The aim of this approach is to detect directions where the likelihood flattens out [72].”
BackgroundTime-domain fitting of battery electrochemical impedance models
Alavi, S. M. M., Birkl, C. R., & Howey, D. A. (2015) · Journal of Power Sources · doi:10.1016/j.jpowsour.2015.04.099 · Cited by 155
“Practical identifiability analysis [40] is an approach to assess the data.”
MethodBrouwer, A. F., Eisenberg, J. N. S., Pomeroy, C. D., Shulman, L. M., Hindiyeh, M. Y., Manor, Y., Grotto, I., Koopman, J. S., & Eisenberg, M. C. (2018) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1808798115 · Cited by 151
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
“Therefore, [6] utilizes likelihood-based confidence intervals.”
BackgroundMethodInfluentialSelf-citationMulti-chromatic control of mammalian gene expression and signaling
Müller, K., Engesser, R., Schulz, S., Steinberg, T., Tomakidi, P., Weber, C. C., Ulm, R., Timmer, J., Zurbriggen, M. D., & Weber, W. (2013) · Nucleic Acids Research · doi:10.1093/nar/gkt340 · Cited by 151
Self-citationEffects of Aging on Influenza Virus Infection Dynamics
Hernandez-Vargas, E. A., Wilk, E., Canini, L., Toapanta, F. R., Binder, S. C., Uvarovskii, A., Ross, T. M., Guzmán, C. A., Perelson, A. S., & Meyer‐Hermann, M. (2014) · Journal of Virology · doi:10.1128/jvi.03644-13 · Cited by 141
Fröhlich, F., Kessler, T., Weindl, D., Shadrin, A., Schmiester, L., Hache, H., Muradyan, A., Schütte, M., Lim, J.-H., Heinig, M., et al. (2018) · Cell Systems · doi:10.1016/j.cels.2018.10.013 · Cited by 143
Pervolaraki, K., Talemi, S. R., Albrecht, D., Bormann, F., Bamford, C., Mendoza, J. L., García, K. C., McLauchlan, J., Höfer, T., Stanifer, M. L., et al. (2018) · PLoS Pathogens · doi:10.1371/journal.ppat.1007420 · Cited by 145
Bayesian Solution Uncertainty Quantification for Differential Equations
Chkrebtii, O., Campbell, D. A., Calderhead, B., & Girolami, M. (2016) · Bayesian Analysis · doi:10.1214/16-ba1017 · Cited by 143
“Analysis is based on experimental data (Swameye et al., 2003; Raue et al., 2009).”
Roosa, K. M., & Chowell, G. (2019) · Theoretical Biology and Medical Modelling · doi:10.1186/s12976-018-0097-6 · Cited by 137
A protocol for dynamic model calibration
Villaverde, A. F., Pathirana, D., Fröhlich, F., Hasenauer, J., & Banga, J. R. (2021) · Briefings in Bioinformatics · doi:10.1093/bib/bbab387 · Cited by 147
Daily precipitation concentration around the world according to several indices
Monjo, R., & Vide, J. M. (2016) · International Journal of Climatology · doi:10.1002/joc.4596 · Cited by 136
“Statistical analysis The nor index was obtained using the profile log-likelihood (PLL) approach (Raue et al., 2009).”
MethodIdentifiability and observability analysis for experimental design in nonlinear dynamical models
Raue, A., Becker, V., Klingmüller, U., & Timmer, J. (2010) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3528102 · Cited by 137
Self-citationLikelihood based observability analysis and confidence intervals for predictions of dynamic models
Kreutz, C., Raue, A., & Timmer, J. (2012) · BMC Systems Biology · doi:10.1186/1752-0509-6-120 · Cited by 134
Self-citationObservability and Structural Identifiability of Nonlinear Biological Systems
Villaverde, A. F. (2019) · Complexity · doi:10.1155/2019/8497093 · Cited by 149
“These properties may also be analysed with other symbolic approaches, such as power series [11, 48, 76], differential algebra [4, 16, 26, 38, 43], or others [15, 66, 78], to name just a few, as well as with semi-numerical [33, 56] or numerical approaches [53, 60].”
BackgroundGenSSI: a software toolbox for structural identifiability analysis of biological models
Chis, O., Banga, J. R., & Balsa‐Canto, E. (2011) · Bioinformatics · doi:10.1093/bioinformatics/btr431 · Cited by 126
Model selection in systems and synthetic biology
Kirk, P., Thorne, T., & Stumpf, M. P. (2013) · Current Opinion in Biotechnology · doi:10.1016/j.copbio.2013.03.012 · Cited by 118
Schneider, N., Wieland, F.-G., Kong, D., Fischer, A., Hörner, M., Timmer, J., Ye, H., & Weber, W. (2021) · Science Advances · doi:10.1126/sciadv.abd3568 · Cited by 122
Self-citationParameter uncertainty in biochemical models described by ordinary differential equations
Vanlier, J., Tiemann, C. A., Hilbers, P. A. J., & van Riel, N. A. W. (2013) · Mathematical Biosciences · doi:10.1016/j.mbs.2013.03.006 · Cited by 116
“Techniques for this exist in both a frequentist [13,36,91] as well as a Bayesian setting [87,90].”
BackgroundMethodResultInfluentialInsulin Signaling in Type 2 Diabetes
Brännmark, C., Nyman, E., Fagerholm, S., Bergenholm, L., Ekstrand, E.-M., Cedersund, G., & Strålfors, P. (2013) · Journal of Biological Chemistry · doi:10.1074/jbc.m112.432062 · Cited by 122
rSalvador: An R Package for the Fluctuation Experiment
Zheng, Q. (2017) · G3 Genes|Genomes|Genetics · doi:10.1534/g3.117.300120 · Cited by 98
“Efron and Hinkley (1978) were among the fi rst to observe that likelihood ratio C.I.s are preferable to the commonly used Wald-type C.I.s. Raue et al. (2009) referred to likelihood ratio C.I.s as fi nite sample C.I.s, to underscore the superiority of likelihood ratio C.I.s over Wald-type C.I.s.…”
BackgroundMethodInfluentialRational evaluation of various epidemic models based on the COVID-19 data of China
Yang, W., Zhang, D., Peng, L., Zhuge, C., & Hong, L. (2021) · Epidemics · doi:10.1016/j.epidem.2021.100501 · Cited by 126
Raue, A., Kreutz, C., Theis, F. J., & Timmer, J. (2013) · Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences · doi:10.1098/rsta.2011.0544 · Cited by 119
“(a) Identifiability analysis using posterior profiles The profile likelihood approach for identifiability analysis [7] can be translated to a profile posterior approach.”
InfluentialSelf-citationWang, Z., Chen, Y., & Li, Y. (2019) · Energy and Buildings · doi:10.1016/j.enbuild.2019.04.042 · Cited by 114
Kalisch, R., Köber, G., Binder, H., Ahrens, K. F., Basten, U., Chmitorz, A., Choi, K. W., Fiebach, C. J., Goldbach, N., Neumann, R. J., et al. (2021) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.710493 · Cited by 122
Docherty, P., Chase, J., Lotz, T., & Desaive, T. (2011) · BioMedical Engineering OnLine · doi:10.1186/1475-925x-10-39 · Cited by 113
“Recent dissatisfaction with the classical algorithms has resulted in the development of new methods that recognise assay error and discrete measurements as critical to identifiability [4,5].”
BackgroundJohnson, K. E., Howard, G. R., Mo, W., Strasser, M. K., Lima, E. A. B. F., Huang, S., & Brock, A. (2019) · PLoS Biology · doi:10.1371/journal.pbio.3000399 · Cited by 106
“To evaluate whether these model parameters were practically identifiable and quantify the corresponding uncertainty on these model parameters, the profile likelihood method was used as described in [51].”
MethodA practical approach to parameter estimation applied to model predicting heart rate regulation
Olufsen, M. S., & Ottesen, J. T. (2013) · Journal of Mathematical Biology · doi:10.1007/s00285-012-0535-8 · Cited by 106
Division of labor by dual feedback regulators controls JAK2/STAT5 signaling over broad ligand range
Bachmann, J., Raue, A., Schilling, M., Böhm, M. E., Kreutz, C., Kaschek, D., Busch, H. S., Gretz, N., Lehmann, W. D., Timmer, J., et al. (2011) · Molecular Systems Biology · doi:10.1038/msb.2011.50 · Cited by 107
“To allow for global parameter estimates, we scanned the parameter space, beginning from reasonable initial guesses by taking into account the time scale of the measurements, over orders of magnitude along the profile likelihood (Raue et al, 2009).”
InfluentialSelf-citationCand1-Mediated Adaptive Exchange Mechanism Enables Variation in F-Box Protein Expression
Liu, X., Reitsma, J. M., Mamrosh, J. L., Zhang, Y., Straube, R., & Deshaies, R. J. (2018) · Molecular Cell · doi:10.1016/j.molcel.2018.01.038 · Cited by 108
A guide to equivalent circuit fitting for impedance analysis and battery state estimation
Santoni, F., Angelis, A. D., Moschitta, A., Carbone, P., Galeotti, M., Cinà, L., Giammanco, C., & Carlo, A. D. (2024) · Journal of Energy Storage · doi:10.1016/j.est.2023.110389 · Cited by 108
Identifiability analysis for stochastic differential equation models in systems biology
Browning, A. P., Warne, D. J., Burrage, K., Baker, R. E., & Simpson, M. J. (2020) · Journal of The Royal Society Interface · doi:10.1098/rsif.2020.0652 · Cited by 103
“By formulating a system of moment equations, we show how existing techniques for structural identifiability analysis of ODE models can be applied directly to SDE models [27,30,31,134].”
BackgroundMethodInfluentialKinetic Modeling of Mammalian Cell Culture Bioprocessing: The Quest to Advance Biomanufacturing
Kyriakopoulos, S., Ang, K. S., Lakshmanan, M., Huang, Z., Yoon, S., Gunawan, R., & Lee, D. (2017) · Biotechnology Journal · doi:10.1002/biot.201700229 · Cited by 106
A bayesian approach to targeted experiment design
Vanlier, J., Tiemann, C. A., Hilbers, P. A. J., & van Riel, N. A. W. (2012) · Bioinformatics · doi:10.1093/bioinformatics/bts092 · Cited by 98
Identification of models of heterogeneous cell populations from population snapshot data
Hasenauer, J., Waldherr, S., Doszczak, M., Radde, N. E., Scheurich, P., & Allgöwer, F. (2011) · BMC Bioinformatics · doi:10.1186/1471-2105-12-125 · Cited by 102
“Furthermore, one may directly access the remaining uncertainty of the estimation result and the prediction uncertainties via the calculation of Bayesian confidence intervals [17,18].”
MethodSelenium Uptake and Methylation by the Microalga Chlamydomonas reinhardtii
Vriens, B., Behra, R., Voegelin, A., Županič, A., & Winkel, L. H. E. (2015) · Environmental Science & Technology · doi:10.1021/acs.est.5b04169 · Cited by 103
Kim, O. D., Rocha, M., & Maia, P. (2018) · Frontiers in Microbiology · doi:10.3389/fmicb.2018.01690 · Cited by 107
Lee, D., Jayaraman, A., & Kwon, J. S. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1008472 · Cited by 105
“Also, available measurements of an intracellular signaling pathway are often limited both in quantity and quality, which may further limit the direct application of a data-driven approach [20, 21].”
BackgroundDriving the Model to Its Limit: Profile Likelihood Based Model Reduction
Maiwald, T., Hass, H., Steiert, B., et al. (2016) · PLoS ONE · doi:10.1371/journal.pone.0162366 · Cited by 98
“In [10], the authors provide a more detailed description on parameter identifiability.”
BackgroundInfluentialSelf-citationRaue, A., Kreutz, C., Theis, F. J., & Timmer, J. (2016) · Cited by 101
Self-citationSelection of model discrepancy priors in Bayesian calibration
Ling, Y., Mullins, J., & Mahadevan, S. (2014) · Journal of Computational Physics · doi:10.1016/j.jcp.2014.08.005 · Cited by 100
Fischer, M., Belanger, S. E., Berckmans, P., et al. (2019) · Toxicological Sciences · doi:10.1093/toxsci/kfz057 · Cited by 98
“(Raue et al., 2009), using an in-house R script (https://github.”
MethodDetermining identifiable parameter combinations using subset profiling
Eisenberg, M. C., & Hayashi, M. A. L. (2014) · Mathematical Biosciences · doi:10.1016/j.mbs.2014.08.008 · Cited by 95
“pi, we can trace out the form of the identifiable combinations (as developed in [18]).”
BackgroundMethodInfluentialEstimation of Breast Cancer Overdiagnosis in a U.S. Breast Screening Cohort
Ryser, M. D., Lange, J., Inoue, L. Y. T., O’Meara, E. S., Gard, C. C., Miglioretti, D. L., Bulliard, J., Brouwer, A. F., Hwang, E. S., & Etzioni, R. B. (2022) · Annals of Internal Medicine · doi:10.7326/m21-3577 · Cited by 104
“Accounting for a mixture of progressive and nonprogressive cancer complicates modeling and may lead to nonidentifiability, which occurs when multiple model solutions explain the observed data equally well (16, 17).”
BackgroundOn the relationship between sloppiness and identifiability
Chis, O.-T., Villaverde, A. F., Banga, J. R., & Balsa-Canto, E. (2016) · Mathematical Biosciences · doi:10.1016/j.mbs.2016.10.009 · Cited by 84
A Green-Light-Responsive System for the Control of Transgene Expression in Mammalian and Plant Cells
Chatelle, C. V., Ochoa‐Fernandez, R., Engesser, R., Schneider, N., Beyer, H. M., Jones, A. R., Timmer, J., Zurbriggen, M. D., & Weber, W. (2018) · ACS Synthetic Biology · doi:10.1021/acssynbio.7b00450 · Cited by 95
Self-citationCedersund, G. (2012) · The FEBS Journal · doi:10.1111/j.1742-4658.2012.08725.x · Cited by 81
Environmental drivers of increased ecosystem respiration in a warming tundra
Maes, S. L., Dietrich, J., Midolo, G., Schwieger, S., Kummu, M., Vandvik, V., Aerts, R., Althuizen, I., Biasi, C., Björk, R. G., et al. (2024) · Nature · doi:10.1038/s41586-024-07274-7 · Cited by 97
“Models were validated by evaluating funnel and profile plots and testing the residuals for the assumption of normality and variance homogeneity 73,82 .”
MethodAkt phosphorylates insulin receptor substrate to limit PI3K-mediated PIP3 synthesis
Kearney, A. L., Norris, D. M., Ghomlaghi, M., Wong, M. K. L., Humphrey, S. J., Carroll, L., Yang, G., Cooke, K. C., Yang, P., Geddes, T. A., et al. (2021) · eLife · doi:10.7554/elife.66942 · Cited by 94
Defective homologous recombination DNA repair as therapeutic target in advanced chordoma
Gröschel, S., Hübschmann, D., Raimondi, F., Horak, P., Warsow, G., Fröhlich, M., Klink, B., Gieldon, L., Hutter, B., Kleinheinz, K., et al. (2019) · Nature Communications · doi:10.1038/s41467-019-09633-9 · Cited by 92
Decomposition trajectories of diverse litter types: a model selection analysis
Cornwell, W. K., & Weedon, J. T. (2013) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12138 · Cited by 93
“This is again a consequence of the formulation and parameterization of these models: in the case of the discrete parallel, discrete series and continuous exponential models, the parameters to be fitted are practically (if not structurally) non-identifiable (sensu Raue et al. 2009).”
MethodDose-response relationships for environmentally mediated infectious disease transmission models
Brouwer, A. F., Weir, M. H., Eisenberg, M. C., et al. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005481 · Cited by 91
Jackson‐Blake, L., Sample, J. E., Wade, A. J., et al. (2017) · Water Resources Research · doi:10.1002/2016wr020132 · Cited by 91
Bayesian parameter estimation for dynamical models in systems biology
Linden-Santangeli, N. J., Krämer, B., & Rangamani, P. (2022) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1010651 · Cited by 103
“Structural parameter identifiability analysis reveals which of the parameters can be estimated given a specific dynamical systems model and a set of measurable outputs [28, 29, 35, 36].”
BackgroundPractical parameter identifiability for spatio-temporal models of cell invasion
Simpson, M. J., Baker, R. E., Vittadello, S. T., & Maclaren, O. J. (2020) · Journal of The Royal Society Interface · doi:10.1098/rsif.2020.0055 · Cited by 85
“As such, a flat profile is indicative of non-identifiability, therefore a lack of information in the data about a parameter [15].”
BackgroundMethodInfluentialEnzymatic study on AtCCD4 and AtCCD7 and their potential to form acyclic regulatory metabolites
Bruno, M., Koschmieder, J., Wüst, F., Schaub, P., Fehling-Kaschek, M., Timmer, J., Beyer, P., & Al‐Babili, S. (2016) · Journal of Experimental Botany · doi:10.1093/jxb/erw356 · Cited by 85
“confidence intervals are computed by the profile likelihood method (Raue et al., 2009).”
MethodSelf-citationConstructing kinetic models of metabolism at genome‐scales: A review
Srinivasan, S., Cluett, W. R., & Mahadevan, R. (2015) · Biotechnology Journal · doi:10.1002/biot.201400522 · Cited by 88
“Conceiving experiments on the basis of proven experimental design techniques [66, 91] that inform on the quality and quantity of data required for efficient identification and estimation of parameters in kinetic models followed up by a large scale data collection endeavor is necessary to address…”
BackgroundLinking Models and Experiments
Bonvin, D., Georgakis, C., Pantelides, C. C., Barolo, M., Grover, M. A., Rodrigues, D., Schneider, R., & Dochain, D. (2016) · Industrial & Engineering Chemistry Research · doi:10.1021/acs.iecr.5b04801 · Cited by 88
Computational systems biology in disease modeling and control, review and perspectives
Yue, R., & Dutta, A. (2022) · npj Systems Biology and Applications · doi:10.1038/s41540-022-00247-4 · Cited by 103
Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling
Schartau, M., Wallhead, P., Hemmings, J. C. P., Löptien, U., Kriest, I., Krishna, S., Ward, B. A., Slawig, T., & Oschlies, A. (2017) · Biogeosciences · doi:10.5194/bg-14-1647-2017 · Cited by 85
How to deal with parameters for whole-cell modelling
Babtie, A. C., & Stumpf, M. P. H. (2017) · Journal of The Royal Society Interface · doi:10.1098/rsif.2017.0237 · Cited by 88
Influence of circadian clocks on adaptive immunity and vaccination responses
Ince, L. M., Barnoud, C., Lutes, L. K., Pick, R., Wang, C., Sinturel, F., Chen, C.-S., de Juan, A., Weber, J., Holtkamp, S., et al. (2023) · Nature Communications · doi:10.1038/s41467-023-35979-2 · Cited by 93
Sutandy, F. X. R., Ebersberger, S., Huang, L., Busch, A., Bach, M., Kang, H.-S., Fallmann, J., Maticzka, D., Backofen, R., Stadler, P. F., et al. (2018) · Genome Research · doi:10.1101/gr.229757.117 · Cited by 83
“Determining parameter confidence intervals using a profile likelihood approach (Raue et al. 2009) confirmed that the Kd values of the high-affinity sites (Kd < 1 μM) can be inferred with good accuracy (on average, fivefold difference between 5% and 95% confidence levels) (Fig.”
MethodInfluentialBenchmark problems for dynamic modeling of intracellular processes
Hass, H., Loos, C., Raimúndez, E., Timmer, J., Hasenauer, J., & Kreutz, C. (2019) · Bioinformatics · doi:10.1093/bioinformatics/btz020 · Cited by 80
Self-citationInference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion
Fröhlich, F., Thomas, P., Kazeroonian, A., Theis, F. J., Grima, R., & Hasenauer, J. (2016) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005030 · Cited by 74
“The 2MA and EMRE models are studied along with the well-known RRE model by Raue et al. [53].”
InfluentialParameter estimation in systems biology models using spline approximation
Zhan, C., & Yeung, L. F. (2011) · BMC Systems Biology · doi:10.1186/1752-0509-5-14 · Cited by 77
“Perform a sensitivity analysis and identifiability analysis before the identification phase [36-38].”
BackgroundMethodRyl, T., Kuchen, E. E., Bell, E., Shao, C., Flórez, A. F., Mönke, G., Gogolin, S., Friedrich, M., Lamprecht, F., Westermann, F., et al. (2017) · Cell Systems · doi:10.1016/j.cels.2017.07.005 · Cited by 79
Parameter estimation and uncertainty quantification for systems biology models
Mitra, E. D., & Hlavacek, W. S. (2019) · Current Opinion in Systems Biology · doi:10.1016/j.coisb.2019.10.006 · Cited by 90
The PI3K and MAPK/p38 pathways control stress granule assembly in a hierarchical manner
Heberle, A. M., Navas, P. R., Langelaar‐Makkinje, M., Kasack, K., Sadik, A., Faessler, E., Hahn, U., Marx‐Stoelting, P., Opitz, C. A., Sers, C., et al. (2019) · Life Science Alliance · doi:10.26508/lsa.201800257 · Cited by 80
“…model (Fig S11 and Tables S2 and S3), an additional parameter estimation was performed by an iterative approach of profile likelihood estimation (Raue et al, 2009) (PLE) and LHS500 (500 different starting points for LHS) runs, starting with the parameters associated with the initial…”
MethodCompeting G protein‐coupled receptor kinases balance G protein and β‐arrestin signaling
Heitzler, D., Durand, G., Gallay, N., Rizk, A., Ahn, S., Kim, J., Violin, J. D., Dupuy, L., Gauthier, C., Piketty, V., et al. (2012) · Molecular Systems Biology · doi:10.1038/msb.2012.22 · Cited by 83
“This raises problems of identifiability since many of the parameters have to be determined through an optimization process dependent on the available experimental data (Raue et al, 2009).”
BackgroundA time- and single-cell-resolved model of murine bone marrow hematopoiesis
Kuciński, I., Campos, J., Barile, M., Severi, F., Bohin, N., Moreira, P. N., Allen, L., Lawson, H., Haltalli, M. L. R., Kinston, S., et al. (2024) · Cell stem cell · doi:10.1016/j.stem.2023.12.001 · Cited by 87
Identifiability of Generalized Randles Circuit Models
Alavi, S. M. M., Mahdi, A., Payne, S. J., et al. (2016) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2016.2635582 · Cited by 77
“Parameter estimation accuracy considers the practical aspects of the problem that come with real data, such as noise and bias [21].”
Parameter identifiability and model selection for sigmoid population growth models
Simpson, M. J., Browning, A. P., Warne, D. J., Maclaren, O. J., & Baker, R. E. (2021) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2021.110998 · Cited by 76
Metadata
- Authors
- Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmüller, U., & Timmer, J.
- Affiliations
- University of Freiburg (DE)
- Corresponding author
- Raue, A.
- Venue
- Bioinformatics
- Publisher
- Oxford University Press (OUP)
- Published
- 2009-06-08
- Volume
- 25
- Issue
- 15
- Pages
- 1923-1929
- ISSN
- 1367-4803 (ISSN-L)
- 1367-4811
- OpenAlex
- W2168648059
- Cited by
- 1,442
- References
- 29
- Citations by year
- 2026: 209 · 2025: 107 · 2024: 103 · 2023: 82 · 2022: 98 · 2021: 118 · 2020: 97 · 2019: 116 · 2018: 94 · 2017: 78 · 2016: 87 · 2015: 64 · 2014: 52 · 2013: 54 · 2012: 39
- FWCI
- 10.99
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Bioinformatics (publishedVersion)
- PubMed (publishedVersion)
- OPUS (Augsburg University) (submittedVersion)
- Funders
- Deutsches Krebsforschungszentrum
- European Commission (223188, EU-FP7, FP7 HEALTH)
- Bundesministerium für Bildung und Forschung (FRISYS 0313921, 0313074D, 0313921)
- FP7 Health
- 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
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Microbial Metabolic Engineering and Bioproduction
- Keywords
- identifiability analysis, profile likelihood, parameter estimation, confidence intervals, experimental design, model reduction
- MeSH terms
- Algorithms, Models, Biological, Probability, Computational Biology
About these checks
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