The DOI matches its Crossref record; 28 of the 29 references it cites were found in a registry or an index; 1 of the 12 sources its claims cite were checked for support.
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.
Overview
AI snapshot
Written from the paper’s full text.
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.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
1 of 12 cited sources checked · 0 supported · 0 flagged · accuracy not yet measured
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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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
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.
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
“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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesA 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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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.
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
“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
Strength:plain· 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
“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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes
- It may state two separate claims as one. 14
- Probably not a substantial claim. 13
The cited sources support only part of this claim — read each source’s verdict below.
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)
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Partly supported
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
The 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
“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
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
A claim is checked only against the cited paper’s full text, never its abstract, and none is available for its sources.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
- Not matched
None of the sources cited for this claim have been checked yet.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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
“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 > )]:
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
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 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
Strength:plain· not yet calibratedTests✓ Asserted: passes✗ Checkable: fails✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
- Also stated in: § 6 DISCUSSION · plain
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 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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may state two separate claims as one.
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
“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
Tests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence.
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
“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
Strength:hedged· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
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 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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
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 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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
“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
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✗ Based: failsProbably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
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.”
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 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
Cites
Press, W. H., Teukolsky, S. L. A., Flannery, B. P., & Vetterling, W. T. (1990) · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · Cited by 6,980
Ziegel, E. R., Lehmann, E. L., & Casella, G. (1999) · Technometrics · doi:10.2307/1270597 · Cited by 4,203
Lehmann, E. L. (1983) · Springer eBooks · doi:10.1007/978-1-4757-2769-2 · Cited by 1,357
Murphy, S. A., & Van Der Vaart, A. W. (2000) · Journal of the American Statistical Association · doi:10.1080/01621459.2000.10474219 · Cited by 712
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
A method for computing profile-likelihood-based confidence intervals
Venzon, D. J., & Moolgavkar, S. H. (1988) · Applied Statistics · doi:10.2307/2347496 · Cited by 565
Systems biology toolbox for matlab: a computational platform for research in systems biology
Schmidt, H., & Jirstrand, M. (2006) · Bioinformatics · doi:10.1093/bioinformatics/bti799 · Cited by 473
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
Parameter and structural identifiability concepts and ambiguities: a critical review and analysis
Cobelli, C., & DiStefano, J. J. (1980) · American Journal of Physiology-Regulatory, Integrative and Comparative Physiology · doi:10.1152/ajpregu.1980.239.1.r7 · Cited by 402
Swameye, I., Müller, T. G., Timmer, J., Sandra, O., & Klingmüller, U. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0237333100 · Cited by 316
Self-citation
Flagged first, then by citations
1 of the 29 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Items 201–300 of 1,414
Parameter estimation and identifiability in a neural population model for electro-cortical activity
Hartoyo, A., Cadusch, P. J., Liley, D. T. J., & Hicks, D. G. (2019) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1006694 · Cited by 44
Kazeroonian, A., Fröhlich, F., Raue, A., Theis, F. J., & Hasenauer, J. (2016) · PLoS ONE · doi:10.1371/journal.pone.0146732 · Cited by 42
“The second example studied using CERENA is a model of the JAK-STAT signaling pathway introduced by [35].”
MethodInfluentialSelf-citationDynamic Modeling, Parameter Estimation, and Uncertainty Analysis in R
Kaschek, D., Mader, W., Fehling-Kaschek, M., Rosenblatt, M., & Timmer, J. (2019) · Journal of Statistical Software · doi:10.18637/jss.v088.i10 · Cited by 40
Self-citationSokolov, V. V., Yakovleva, T. A., Chu, L., Tang, W., Greasley, P. J., Johansson, S. A., Peskov, K. V., Helmlinger, G., Boulton, D. W., & Penland, R. C. (2020) · CPT Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.12498 · Cited by 42
Fu, Q., Scheidegger, A., Laczkó, E., & Hollender, J. (2021) · Environmental Science & Technology · doi:10.1021/acs.est.0c07887 · Cited by 43
Systematic In Vivo Characterization of Fluorescent Protein Maturation in Budding Yeast
Guerra, P., Vuillemenot, L.-A., Rae, B., Ladyhina, V., & Milias‐Argeitis, A. (2022) · ACS Synthetic Biology · doi:10.1021/acssynbio.1c00387 · Cited by 40
Structural and Practical Identifiability Analysis of Zika Epidemiological Models
Tuncer, N., Marctheva, M., LaBarre, B., & Payoute, S. (2018) · Bulletin of Mathematical Biology · doi:10.1007/s11538-018-0453-z · Cited by 41
Identifying spatio-temporal seizure propagation patterns in epilepsy using Bayesian inference
Vattikonda, A. N., Hashemi, M., Sip, V., Woodman, M., Bartolomei, F., & Jirsa, V. (2021) · Communications Biology · doi:10.1038/s42003-021-02751-5 · Cited by 40
Forsgren, M. F., Leinhard, O. D., Dahlström, N., et al. (2014) · PLoS ONE · doi:10.1371/journal.pone.0095700 · Cited by 39
Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method
Jia, G., Stephanopoulos, G. N., & Gunawan, R. (2011) · Bioinformatics · doi:10.1093/bioinformatics/btr293 · Cited by 38
Jonak, K., Kurpas, M. K., Szołtysek, K., Janus, P., Abramowicz, A., & Puszyński, K. (2016) · BMC Systems Biology · doi:10.1186/s12918-016-0293-0 · Cited by 39
“The second common problem of the complex biological network models is a practical non-identifiability – the existence of various parameters sets that have more or less equivalent fitting capability [34].”
BackgroundHashemi, M., Hutt, A., Buhry, L., & SLEIGH, J. W. (2018) · Neuroinformatics · doi:10.1007/s12021-018-9369-x · Cited by 30
“Once the model parameters have been estimated, it is nec-276 essary to determine the identifiability of the estimates, i.e., whether the model parameters can be uniquely determined by the given experimental data (Raue et al. 2011, 2009; Quaiser and Monnigmann 2009).”
Estimation methods for heterogeneous cell population models in systems biology
Waldherr, S. (2018) · Journal of The Royal Society Interface · doi:10.1098/rsif.2018.0530 · Cited by 36
Modeling the Control of TGF-β/Smad Nuclear Accumulation by the Hippo Pathway Effectors, Taz/Yap
Labibi, B., Bashkurov, M., Wrana, J. L., & Attisano, L. (2020) · iScience · doi:10.1016/j.isci.2020.101416 · Cited by 39
Cause and cure of sloppiness in ordinary differential equation models
Tönsing, C., Timmer, J., & Kreutz, C. (2014) · Physical Review E · doi:10.1103/physreve.90.023303 · Cited by 33
Self-citationMethods of quantifying interactions among populations using Lotka-Volterra models
Davis, J. D., Olivença, D. V., Brown, S. P., & Voit, E. O. (2022) · Frontiers in Systems Biology · doi:10.3389/fsysb.2022.1021897 · Cited by 41
Practical identifiability analysis of a minimal cardiovascular system model
Pironet, A., Docherty, P. D., Dauby, P. C., Chase, J. G., & Desaive, T. (2017) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2017.01.005 · Cited by 38
“Methods to test for practical identifiability include Monte Carlo simulations [16, 7] and building the parameters’ profile likelihood curves [32, 2].”
BackgroundMethodAn easy and efficient approach for testing identifiability
Kreutz, C. (2018) · Bioinformatics · doi:10.1093/bioinformatics/bty035 · Cited by 39
“16 Profile likelihood of model parameters As a classical approach, identifiability of the model parameters was assessed using the profile likelihood [7].”
MethodInfluentialSelf-citationSigma Factor-Mediated Tuning of Bacterial Cell-Free Synthetic Genetic Oscillators
Yelleswarapu, M., van der Linden, A. J., van Sluijs, B., Pieters, P. A., Dubuc, E., de Greef, T. F. A., & Huck, W. T. S. (2018) · ACS Synthetic Biology · doi:10.1021/acssynbio.8b00300 · Cited by 37
ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative–quantitative modeling
Streif, S., Savchenko, A., Rumschinski, P., Borchers, S., & Findeisen, R. (2012) · Bioinformatics · doi:10.1093/bioinformatics/bts137 · Cited by 37
Merkle, R., Steiert, B., Salopiata, F., Depner, S., Raue, A., Iwamoto, N., Schelker, M., Hass, H., Wäsch, M., Böhm, M. E., et al. (2016) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005049 · Cited by 37
Self-citationKrausch, N., Barz, T., Sawatzki, A., Gruber, M., Kamel, S., Neubauer, P. B., & Bournazou, M. N. C. (2019) · Frontiers in Bioengineering and Biotechnology · doi:10.3389/fbioe.2019.00122 · Cited by 43
“, the variance exceeds some predefined threshold), which is known as parameter nonidentifiability and an issue that has been widely addressed in literature (Holmberg, 1982; Vanrolleghem, 1995; Raue et al., 2009; Muñoz-Tamayo et al., 2018).”
BackgroundMethodInfluentialAnane, E., C., D. C. L., Barz, T., Sin, G., Gernaey, K. V., Neubauer, P. B., & Bournazou, M. N. C. (2019) · Biochemical Engineering Journal · doi:10.1016/j.bej.2019.107247 · Cited by 37
“There are numerous papers and reviews on the topic for both biosystems [13] and general mechanistic models [14–16].”
BackgroundDissecting DISC regulation via pharmacological targeting of caspase-8/c-FLIPL heterodimer
Hillert-Richter, L. K., Ivanisenko, N. V., Busse, D., Espe, J., König, C., Peltek, S. E., Kolchanov, N. A., Иванисенко, В. А., & Lavrik, I. N. (2020) · Cell Death and Differentiation · doi:10.1038/s41418-020-0489-0 · Cited by 38
Evaluation framework for systems models
Braakman, S. T., Pathmanathan, P., & Moore, H. A. (2021) · CPT Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.12755 · Cited by 38
Kanodia, J., Chai, D. H., Vollmer, J., Kim, J., Raue, A., Finn, G., & Schoeberl, B. (2014) · Cell Communication and Signaling · doi:10.1186/1478-811x-12-34 · Cited by 39
“However, nonidentifiability of model parameters and uncertainty in parameter space in general can compromise the predictability of a mathematical model [36].”
Self-citationIterative integral parameter identification of a respiratory mechanics model
Schranz, C., Docherty, P. D., Chiew, Y. S., et al. (2012) · BioMedical Engineering OnLine · doi:10.1186/1475-925x-11-38 · Cited by 37
“The LMA is a popular parameter identification method for linear and non-linear problems [9,28,29].”
MethodTakhaveev, V., Özsezen, S., Smith, E. N., Zylstra, A., Chaillet, M. L., Chen, H., Papagiannakis, A., Milias-Argeitis, A., & Heinemann, M. (2023) · Nature Metabolism · doi:10.1038/s42255-023-00741-x · Cited by 36
On the identifiability of metabolic network models
Berthoumieux, S., Brilli, M., Kahn, D., de Jong, H., & Eugenio Cinquemani, B. (2012) · Journal of Mathematical Biology · doi:10.1007/s00285-012-0614-x · Cited by 36
“…topic of identifiability has gained considerable interest in the field of systems biology (Chen et al., 2010; Chis et al., 2011b; Nikerel et al., 2009; Raue et al., 2009, 2011; Gutenkunst et al., 2007; Nemcova, 2010; Srinath and Gunawan, 2010; Voit et al., 2006a) and several specialized software…”
BackgroundModel-Based Characterization of Inflammatory Gene Expression Patterns of Activated Macrophages
Rex, J., Albrecht, U., Ehlting, C., Thomas, M., Zanger, U. M., Sawodny, O., Häussinger, D., Ederer, M., Feuer, R., & Bode, J. G. (2016) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005018 · Cited by 33
“It was implemented using the MATLAB Toolbox PottersWheel [51] and comprises 23 species and 47 parameters.”
MethodInfluentialParameter estimation for dynamical systems with discrete events and logical operations
Fröhlich, F., Theis, F. J., Rädler, J. O., & Hasenauer, J. (2016) · Bioinformatics · doi:10.1093/bioinformatics/btw764 · Cited by 38
Yakovleva, T. A., Sokolov, V., Chu, L., Tang, W., Greasley, P. J., Sjögren, H. P., Johansson, S. A., Peskov, K. V., Helmlinger, G., Boulton, D. W., et al. (2019) · Diabetes Obesity and Metabolism · doi:10.1111/dom.13858 · Cited by 36
“The remaining 17 parameters were estimated using a gradient-driven maximum likelihood method and included parameter uncertainty using a combined (additive plus proportional) residual error structure.(21) Model quality was evaluated using multiple criteria: (a) change in the objective function value, (b) inspection of…”
MethodJohnson, K. E., Howard, G. R., Morgan, D., Brenner, E. A., Gardner, A. L., Durrett, R., Mo, W., Al’Khafaji, A. M., Sontag, E. D., Jarrett, A. M., et al. (2020) · Physical Biology · doi:10.1088/1478-3975/abb09c · Cited by 35
Designing and interpreting 4D tumour spheroid experiments
Murphy, R. J., Browning, A. P., Gunasingh, G., Haass, N. K., & Simpson, M. J. (2022) · Communications Biology · doi:10.1038/s42003-022-03018-3 · Cited by 37
“Specifically, we assume that experimental measurements are noisy observations of the deterministic mathematical model [63, 64].”
BackgroundThe impacts of linear infrastructure on terrestrial vertebrate populations: A trait‐based approach
de Jonge, M. M. J., Gallego‐Zamorano, J., Huijbregts, M. A. J., Schipper, A. M., & Benítez‐López, A. (2022) · Global Change Biology · doi:10.1111/gcb.16450 · Cited by 35
Liu, Y., Suh, K., Maini, P. K., Cohen, D. J., & Baker, R. E. (2024) · Journal of The Royal Society Interface · doi:10.1098/rsif.2023.0607 · Cited by 38
“Raue et al. [26] discussed the application of profile likelihoods to detect non-identifiable parameters, illustrated with an example in the context of ODE models.”
MethodRobust parameter estimation for dynamical systems from outlier-corrupted data
Maier, C., Loos, C., & Hasenauer, J. (2016) · Bioinformatics · doi:10.1093/bioinformatics/btw703 · Cited by 34
“The uncertainty of an individual estimate can be assessed by computing the confidence interval (CI) for a confidence level α using profile likelihoods (Raue et al., 2009).”
MethodWorkflow for Target‐Oriented Parametrization of an Enhanced Mechanistic Cell Culture Model
Ulonska, S., Kröll, P., Fricke, J., Clemens, C., Voges, R., Müller, M. M., & Herwig, C. (2017) · Biotechnology Journal · doi:10.1002/biot.201700395 · Cited by 34
Nonidentifiability in Model Calibration and Implications for Medical Decision Making
Alarid‐Escudero, F., MacLehose, R. F., Peralta, Y., Kuntz, K. M., & Enns, E. A. (2018) · Medical Decision Making · doi:10.1177/0272989x18792283 · Cited by 34
Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows
Eriksson, O., Bhalla, U. S., Blackwell, K. T., Crook, S. M., Keller, D. X., Kramer, A., Linne, M., Saudargienė, A., Wade, R. C., & Kotaleski, J. H. (2022) · eLife · doi:10.7554/elife.69013 · Cited by 36
Modeling Intracellular Signaling Underlying Striatal Function in Health and Disease
Nair, A. G., Gutierrez‐Arenas, O., Eriksson, O., Jauhiainen, A., Blackwell, K. T., & Kotaleski, J. H. (2014) · Progress in molecular biology and translational science · doi:10.1016/b978-0-12-397897-4.00013-9 · Cited by 32
“The relationship between the experimental data and the model can be such that the system is nonidentifiable.(35,37)”
BackgroundSignal integration by the CYP1A1 promoter -- a quantitative study
Schulthess, P., Loffler, A., Vetter, S., Kreft, L., Schwarz, M., Braeuning, A., & Blüthgen, N. (2015) · Nucleic Acids Research · doi:10.1093/nar/gkv423 · Cited by 35
“Only the cooperative binding energy between the D- and the E-DRE was practically non-identifiably (according to the terminology in (63)) and thus could not be reliably determined from the data (Supplementary Figures S10 and S11).”
BackgroundMethodInfluentialEriksson, O., Jauhiainen, A., Sasane, S. M., Kramer, A., Nair, A. G., Sartorius, C., & Kotaleski, J. H. (2018) · Bioinformatics · doi:10.1093/bioinformatics/bty607 · Cited by 32
Zitzmann, C., Schmid, B., Ruggieri, A., Perelson, A. S., Binder, M., Bartenschlager, R. F. W., & Kaderali, L. (2020) · Frontiers in Microbiology · doi:10.3389/fmicb.2020.00725 · Cited by 32
“The profile likelihood method evaluates the change in the likelihood function after modification of one individual model parameter by re-optimizing the remaining model parameters (Raue et al., 2009; Kreutz et al., 2013; Maiwald et al., 2016), thus assessing if changes in a given parameter can be compensated by modific…”
BackgroundMethodParameter Trajectory Analysis to Identify Treatment Effects of Pharmacological Interventions
Tiemann, C. A., Vanlier, J., Oosterveer, M. H., Groen, A. K., Hilbers, P. A. J., & van Riel, N. A. W. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1003166 · Cited by 32
“An additional analysis was performed to investigate the identifiability of parameters for the untreated phenotype, using ADAPT and the Profile Likelihood method [64] (see Supporting Information Text S9).”
Modelling signalling networks from perturbation data
Dorel, M., Klinger, B., Groß, T., Sieber, A., Prahallad, A., Bosdriesz, E., Wessels, L. F. A., & Blüthgen, N. (2018) · Bioinformatics · doi:10.1093/bioinformatics/bty473 · Cited by 31
“Our pipeline allows to calculate the profile likelihood for the model, which shows the change in maximum likelihood when one (primary) parameter is varied (Raue et al., 2009).”
MethodRodríguez, T. H., Posch, C., Schmutzhard, J., Stettner, J., Weihs, C., Pörtner, R., & Frahm, B. (2019) · Biotechnology and Bioengineering · doi:10.1002/bit.27125 · Cited by 33
Correction: Lessons Learned from Quantitative Dynamical Modeling in Systems Biology
Raue, A., Schilling, M., Bachmann, J., Matteson, A., Schelker, M., Kaschek, D., Hug, S., Kreutz, C., Harms, B. D., Theis, F. J., et al. (2013) · PLoS ONE · doi:10.1371/annotation/ea0193d8-1f7f-492a-b0b7-d877629fdcee · Cited by 37
Self-citationSchaber, J., & Klipp, E. (2011) · Current Opinion in Biotechnology · doi:10.1016/j.copbio.2010.09.014 · Cited by 33
Parameter subset selection techniques for problems in mathematical biology
Olsen, C. H., Ottesen, J. T., Smith, R. C., & Olufsen, M. S. (2018) · Biological Cybernetics · doi:10.1007/s00422-018-0784-8 · Cited by 31
Quaglio, M., Waldron, C. J., Pankajakshan, A., Cao, E., Gavriilidis, A., Fraga, E. S., & Galvanin, F. (2019) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2019.01.010 · Cited by 33
Mathematical modeling and numerical simulations of Zika in Colombia considering mutation
L., D. F. A., González‐Parra, G., & Benincasa, T. (2019) · Mathematics and Computers in Simulation · doi:10.1016/j.matcom.2019.02.009 · Cited by 33
Kursawe, J., Baker, R. E., & Fletcher, A. G. (2018) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2018.01.020 · Cited by 29
An artificial neural network approach to recognise kinetic models from experimental data
Quaglio, M., Roberts, L., Jaapar, M. S. B., Fraga, E. S., Dua, V., & Galvanin, F. (2020) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2020.106759 · Cited by 36
Bull, J. A., Macklin, P. S., Quaiser, T., Braun, F., Waters, S. L., Pugh, C. W., & Byrne, H. M. (2020) · Scientific Reports · doi:10.1038/s41598-020-75180-9 · Cited by 32
Ensemble Kinetic Modeling of Metabolic Networks from Dynamic Metabolic Profiles
Jia, G., Stephanopoulos, G. N., & Gunawan, R. (2012) · Metabolites · doi:10.3390/metabo2040891 · Cited by 33
“As we and many others have shown [8–11], the estimation of unknown parameters by fitting model simulations to biological measurements is typically ill-posed.”
ResultOptimal design of stimulus experiments for robust discrimination of biochemical reaction networks
Flassig, R. J., & Sundmacher, K. (2012) · Bioinformatics · doi:10.1093/bioinformatics/bts585 · Cited by 31
“Much work on optimal experimental stimulus design (OESD) for biological systems focuses on information maximization with respect to parameter identification (Balsa-Canto et al ., 2008; Bandara et al ., 2009; Heine et al ., 2008; Raue et al ., 2010; Schenkendorf et al ., 2009a).”
BackgroundMethodAnalysis of CFSE time-series data using division-, age- and label-structured population models
Hroß, S., & Hasenauer, J. (2016) · Bioinformatics · doi:10.1093/bioinformatics/btw131 · Cited by 32
Learning (from) the errors of a systems biology model
Engelhardt, B., Fröhlich, H., & Kschischo, M. (2016) · Scientific Reports · doi:10.1038/srep20772 · Cited by 31
“Parameter estimation algorithms 4,10,26 applied to the nominal model using the experimental data (Fig.”
MethodTo be certain about the uncertainty: Bayesian statistics for 13 C metabolic flux analysis
Theorell, A., Leweke, S., Wiechert, W., & Nöh, K. (2017) · Biotechnology and Bioengineering · doi:10.1002/bit.26379 · Cited by 29
“However, even if a flux has a uniqueMLE ν̂MLE , it can be considered practically non-identifiable if the log-likelihood is close to optimal for a large range of flux values (Raue et al., 2009).”
BackgroundScalable Inference of Ordinary Differential Equation Models of Biochemical Processes
Fröhlich, F., Loos, C., & Hasenauer, J. (2018) · Methods in molecular biology · doi:10.1007/978-1-4939-8882-2_16 · Cited by 32
“These techniques generalize to other model analysis techniques that require optimization or gradient computation, such as uncertainty analysis [154, 155], experimental design [156] and the inference of model structure.”
MethodAlmquist, J. O., Bendrioua, L., Adiels, C. B., Goksör, M., Hohmann, S., & Jirstrand, M. (2015) · PLoS ONE · doi:10.1371/journal.pone.0124050 · Cited by 32
Dynamic modeling of Nrf2 pathway activation in liver cells after toxicant exposure
Hiemstra, S. W., Fehling-Kaschek, M., Kuijper, I. A., Bischoff, L. J. M., Wijaya, L. S., Rosenblatt, M., Esselink, J. J., van Egmond, A., Mos, J., Beltman, J. B., et al. (2022) · Scientific Reports · doi:10.1038/s41598-022-10857-x · Cited by 31
Self-citationIncremental parameter estimation of kinetic metabolic network models
Jia, G., Stephanopoulos, G. N., & Gunawan, R. (2012) · BMC Systems Biology · doi:10.1186/1752-0509-6-142 · Cited by 30
“The positive DOF means that there exist infinitely many solutions to the dynamic flux estimation, which is one of the factors underlying the parameter identifiability issues plaguing many estimation problems in systems biology [23,24].”
BackgroundMethodOptimization and profile calculation of ODE models using second order adjoint sensitivity analysis
Stapor, P. L., Fröhlich, F., & Hasenauer, J. (2018) · Bioinformatics · doi:10.1093/bioinformatics/bty230 · Cited by 30
A Unified Model for Inclusive Inheritance in Livestock Species
David, I., & Ricard, A. (2019) · Genetics · doi:10.1534/genetics.119.302375 · Cited by 30
Fehling-Kaschek, M., Peckys, D. B., Kaschek, D., et al. (2019) · Scientific Reports · doi:10.1038/s41598-019-49019-x · Cited by 31
Self-citationStochastic modeling reveals kinetic heterogeneity in post-replication DNA methylation
Busto‐Moner, L., Morival, J. L. P., Ren, H., Fahim, A., Reitz, Z., Downing, T. L., & Read, E. L. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007195 · Cited by 31
Model-based data analysis of tissue growth in thin 3D printed scaffolds
Browning, A. P., Maclaren, O. J., Buenzli, P. R., Lanaro, M., Allenby, M. C., Woodruff, M. A., & Simpson, M. J. (2021) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2021.110852 · Cited by 30
A microfluidic optimal experimental design platform for forward design of cell-free genetic networks
van Sluijs, B., Maas, R. J. M., van der Linden, A. J., de Greef, T. F. A., & Huck, W. T. S. (2022) · Nature Communications · doi:10.1038/s41467-022-31306-3 · Cited by 32
Computational models of the JAK1/2-STAT1 signaling
Gambin, A., Charzyńska, A., Ellert‐Miklaszewska, A., & Rybiński, M. (2013) · JAK-STAT · doi:10.4161/jkst.24672 · Cited by 31
“Using GSA, complemented with the profile-likelihood based identifiability analysis, 35 we showed that the on-membrane pre-assembly of the dimers in the absence of ligand increases the overall environmental robustness of the pathway model.”
BackgroundMethodComprehensive estimation of input signals and dynamics in biochemical reaction networks
Schelker, M., Raue, A., Timmer, J., & Kreutz, C. (2012) · Bioinformatics · doi:10.1093/bioinformatics/bts393 · Cited by 30
Self-citationSaccomani, M. P., & Thomaseth, K. (2018) · Complexity · doi:10.1155/2018/2380650 · Cited by 31
Reconstructing Mammalian Sleep Dynamics with Data Assimilation
Sedigh-Sarvestani, M., Schiff, S. J., & Gluckman, B. J. (2012) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002788 · Cited by 30
“A comparable experimental or empirical version of identifiability has also been discussed by[62–65].”
BackgroundA Vine-copula Based Adaptive MCMC Sampler for Efficient Inference of Dynamical Systems
Schmidl, D., Czado, C., Hug, S., & Theis, F. J. (2013) · Bayesian Analysis · doi:10.1214/13-ba801 · Cited by 30
“A discussion on the structural parameter identifiability issues of the particular system can be found in Timmer et al. (2004) and Raue et al. (2009).”
BackgroundParameter identifiability in Bayesian inference for building energy models
Yi, D. H., Kim, D.-W., & Park, C. S. (2019) · Energy and Buildings · doi:10.1016/j.enbuild.2019.06.012 · Cited by 31
Mechanistically detailed systems biology modeling of the HGF/Met pathway in hepatocellular carcinoma
Jafarnejad, M., Sové, R. J., Danilova, L., Mirando, A. C., Zhang, Y., Yarchoan, M. M., Tran, P. T., Pandey, N. B., Fertig, E. J., & Popel, A. S. (2019) · npj Systems Biology and Applications · doi:10.1038/s41540-019-0107-2 · Cited by 28
“Implementation of the likelihood methods could be beneficial in the future iterations of the model to improve efficiency of the confidence interval calculations.(61,62) Additionally, we assumed that the tumor is homogenous, which is often not the case for tumors, especially for HCC tumors in advanced stages.”
MethodDrugs modulating stochastic gene expression affect the erythroid differentiation process
Guillemin, A., Duchesne, R., Crauste, F., Gonin-Giraud, S., & Gandrillon, O. (2019) · PLoS ONE · doi:10.1371/journal.pone.0225166 · Cited by 30
“We have already proven that our model identifiable, both theoretically and practically [39], using the profile likelihood approach [59].”
MethodPiazzola, C., Tamellini, L., & Tempone, R. F. (2020) · Mathematical Biosciences · doi:10.1016/j.mbs.2020.108514 · Cited by 30
“Such uniform estimate might be more robust for limited datasets [70].”
BackgroundJohnson, M. E., Chen, A., Faeder, J. R., Henning, P., Moraru, I. I., Meier‐Schellersheim, M., Murphy, R. F., Prüstel, T., Theriot, J. A., & Uhrmacher, A. M. (2020) · Molecular Biology of the Cell · doi:10.1091/mbc.e20-08-0530 · Cited by 32
“With decreasing complexity of a model, it also becomes easier to perform robust parameter estimations and to determine how well the model is justified based on the available data (Raue et al., 2009).”
BackgroundStructural identifiability analysis of age-structured PDE epidemic models
Renardy, M., Kirschner, D. E., & Eisenberg, M. C. (2022) · Journal of Mathematical Biology · doi:10.1007/s00285-021-01711-1 · Cited by 29
“For more details on profile likelihood approaches to identifiability, the reader is referred to (Raue et al. 2009; Venzon and Moolgavkar 1988).”
BackgroundMethodWithin-host influenza dynamics: A small-scale mathematical modeling approach
Manchanda, H., Seidel, N., Krumbholz, A., et al. (2014) · Biosystems · doi:10.1016/j.biosystems.2014.02.004 · Cited by 30
Oguz, C., Laomettachit, T., Chen, K. C., Watson, L. T., Baumann, W. T., & Tyson, J. J. (2013) · BMC Systems Biology · doi:10.1186/1752-0509-7-53 · Cited by 31
“Relevant recent work regarding identifiability and model reduction in systems biology includes implementations of singular value decomposition to reduce models where parameter estimation is posed as a linear regression problem [18,19], computation of confidence intervals by extensive parameter sampling to detect non–i…”
de Cellès, M. D., Zahar, J., Abadie, V., et al. (2013) · BMC Infectious Diseases · doi:10.1186/1471-2334-13-187 · Cited by 30
“Profile likelihoods were used to derive 95% confidence intervals (CI) [28].”
MethodRobustness of signal transduction pathways
Blüthgen, N., & Legewie, S. (2012) · Cellular and Molecular Life Sciences · doi:10.1007/s00018-012-1162-7 · Cited by 31
Villaverde, A. F., & Banga, J. R. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005878 · Cited by 27
Jacob, P. E., Alavi, S. M. M., Mahdi, A., Payne, S. J., & Howey, D. A. (2017) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2017.2672402 · Cited by 31
“The authors in [33] propose a method for the design of periodic excitation signals to identify the battery models given by ODEs.”
MethodDankwa, E. A., Brouwer, A. F., & Donnelly, C. A. (2022) · Epidemics · doi:10.1016/j.epidem.2022.100643 · Cited by 34
“on the other hand, is related to the adequacy of the available observed data for the estimation problem at hand (Balsa-Canto et al., 2010; Brouwer et al., 2017; Kao and Eisenberg, 2018; Miao et al., 2011; Raue et al., 2009; Tuncer et al., 2016; Tuncer and Le, 2018).”
BackgroundCampbell, D., & Lele, S. R. (2013) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2013.09.013 · Cited by 29
Rouchier, S., Busser, T., Pailha, M., Piot, A., & Woloszyn, M. (2016) · Building and Environment · doi:10.1016/j.buildenv.2016.12.012 · Cited by 29
Deconinck, A.-H., & Roels, S. (2017) · Journal of Building Physics · doi:10.1177/1744259116688384 · Cited by 29
“In the literature, the notion of identifiability is twofold (Raue et al., 2009).”
BackgroundMethodInfluentialQuantifying ventilator unloading in CPAP ventilation
Guy, E. F. S., Chase, J. G., Knopp, J. L., & Shaw, G. M. (2022) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2022.105225 · Cited by 28
A Model-Based Initial Guess for Estimating Parameters in Systems of Ordinary Differential Equations
Dattner, I. (2015) · Biometrics · doi:10.1111/biom.12348 · Cited by 29
“The problem of practical identifiability has received some attention recently and statistical methods for dealing with such situations are developed (e.g., Raue et al., 2009; Campbell and Lele, 2014).”
MethodFachet, M., Flassig, R., Rihko‐Struckmann, L., & Sundmacher, K. (2014) · Bioresource Technology · doi:10.1016/j.biortech.2014.08.124 · Cited by 31
Parameter estimation for externally simulated thermal network models
Brastein, O. M., Lie, B., Sharma, R. K., & Skeie, N. (2019) · Energy and Buildings · doi:10.1016/j.enbuild.2019.03.018 · Cited by 30
How robust are estimates of key parameters in standard viral dynamic models?
Zitzmann, C., Ke, R., Ribeiro, R. M., & Perelson, A. S. (2024) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1011437 · Cited by 30
Probabilistic correction of RCM precipitation in the Basque Country (Northern Spain)
Monjo, R., Chust, G., & Caselles, V. (2013) · Theoretical and Applied Climatology · doi:10.1007/s00704-013-1008-8 · Cited by 28
“…parameter, Po, which represents the most probable precipitation, and the other one is the scale parameter, P1: λ≡ P−Po P1 : ð3Þ The most likely value for each parameter was estimated by statistical inference, in particular with the profile log-likelihood (Akaike 1974; Raue et al. 2009).”
MethodLee, E. C., Kelly, M. R., Ochocki, B. M., et al. (2017) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2017.01.032 · Cited by 28
“We found a linear canyon which achieved the same minimum goodness-of-fit as the true parameters, corresponding to a structurally identifiable combination [58, 61].”
BackgroundPatient asynchrony modelling during controlled mechanical ventilation therapy
Arunachalam, G. R., Chiew, Y. S., Tan, C. P., et al. (2019) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2019.105103 · Cited by 28
Quantitative Nanoinfrared Spectroscopy of Anisotropic van der Waals Materials
Ruta, F. L., Sternbach, A. J., Dieng, A. B., et al. (2020) · Nano Letters · doi:10.1021/acs.nanolett.0c02671 · Cited by 28
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
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.
A language model drew the claims from the paper on 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
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
