Determining minimal output sets that ensure structural identifiability

Joubert, Dominique; Stigter, J.D.; Molenaar, Jaap

doi:10.1371/journal.pone.0207334

Cited by 12 publications

(7 citation statements)

References 30 publications

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“…To fix a model's lack of structural identifiability there are mainly two approaches, i.e., reparametrization [88,89] or to apply more model outputs/measurements [5,6], where both will reduce the parameter-to-output ratio. Regarding the latter approach, the specific choice of which measurement to include is of great importance with respect to structural identifiability [16,17]. In this context, we suggest to use flow measurements as alternative model outputs, and we have presented two different modeling approaches on how to incorporate flow measurements into a model.…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, given a set of available measurements, it is in general not straight forward to determine the smallest set of measurements that is sufficient to uniquely estimate a model's parameters. In this context, the concept of structural identifiability [10][11][12][13][14][15] is a helpful tool for determining this smallest set of measurements [16,17]. The core of the concept states that [10] "If a model is structurally identifiable, it is theoretically possible to uniquely determine the values of its parameters by observing its outputs."…”

Section: Introductionmentioning

confidence: 99%

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Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

Haus,

Drengstig,

Thorsen

2023

PLoS Comput Biol

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Controller motifs are simple biomolecular reaction networks with negative feedback. They can explain how regulatory function is achieved and are often used as building blocks in mathematical models of biological systems. In this paper we perform an extensive investigation into structural identifiability of controller motifs, specifically the so–called basic and antithetic controller motifs. Structural identifiability analysis is a useful tool in the creation and evaluation of mathematical models: it can be used to ensure that model parameters can be determined uniquely and to examine which measurements are necessary for this purpose. This is especially useful for biological models where parameter estimation can be difficult due to limited availability of measureable outputs. Our aim with this work is to investigate how structural identifiability is affected by controller motif complexity and choice of measurements. To increase the number of potential outputs we propose two methods for including flow measurements and show how this affects structural identifiability in combination with, or in the absence of, concentration measurements. In our investigation, we analyze 128 different controller motif structures using a combination of flow and/or concentration measurements, giving a total of 3648 instances. Among all instances, 34% of the measurement combinations provided structural identifiability. Our main findings for the controller motifs include: i) a single measurement is insufficient for structural identifiability, ii) measurements related to different chemical species are necessary for structural identifiability. Applying these findings result in a reduced subset of 1568 instances, where 80% are structurally identifiable, and more complex/interconnected motifs appear easier to structurally identify. The model structures we have investigated are commonly used in models of biological systems, and our results demonstrate how different model structures and measurement combinations affect structural identifiability of controller motifs.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

Haus,

Drengstig,

Thorsen

2023

PLoS Comput Biol

View full text Add to dashboard Cite

show abstract

“…The singular values are calculated by singular value decomposition (SVD) [2], [40]. The perpendicular parts of sensitivity vectors S j are calculated as .…”

Section: Methodsmentioning

confidence: 99%

“…The key and frequent drawback of mechanistic models of regulatory pathways is lack of identifiability meaning that model parameters may not be determined by existing data. Here, we focus on the NF- κ B regulatory pathway, as recent works point out that the known detailed models for this very important pathway are not identifiable [1], [2], [3]. In this study we reduce the original 15-variable NF- κ B model developed by Lipniacki et al [4] in a way that it preserves the dynamics of key variables (in contrast to ealier simplified models [5], [6], [7]), but makes the model structurally and practically identifiable.…”

Section: Introductionmentioning

confidence: 99%

A plausible identifiable model of the canonical NF-κB signaling pathway

Jaruszewicz-Błońska

Kosiuk

Prus

et al. 2022

Preprint

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An overwhelming majority of mathematical models of regulatory pathways, including intensively studied NF-kB pathway, remains non-identifiable meaning that their parameters may not be determined by existing data. The existing NF-kB models that are capable to reproduce experimental data, contain non-identifiable parameters, while simplified models with a smaller number of parameters exhibit dynamics that significantly differs from that observed in experiments. Here, we reduce an existing model of the canonical NF-kB pathway by decreasing the number of equations from 15 to 6 in a way that the resulting model exhibits dynamics closely following that of the original model, both for the nominal and the randomly selected parameters. We carried out the sensitivity-based linear analysis and Monte Carlo-based analysis to demonstrate that the resulting model is structurally and practically identifiable based on a simple TNF stimulation protocol in which 5 model variables are measured. The reduced model is capable to reproduce different types of responses characteristic to regulatory motives controlled by negative feedback loops: nearly perfect adaptation, damped and sustained oscillations. It can serve as a building block of more comprehensive models of immune responses and cancer, where NF-kB plays a decisive role. Our approach, although may not be automatically generalized, suggests that other regulatory pathways models can be transformed to identifiable, while retaining their dynamical features.

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“…An alternative way to reinstate the model's structural identifiability is the addition of one or more sensors to the model's measured output . Which sensors might be added can efficiently be solved by determining a model's minimal sensor set, the minimal set of sensors that needs to be measured to ensure model identifiability 13 . In this example, the identifiability can be reinstated by adding either state To understand the role this model's initial conditions play in its unidentifiability, we analyse the model for the conditions stipulated in (20), with both [E po](0), [E poR](0) assumed to be nonzero.…”

Section: /16mentioning

confidence: 99%

Assessing the Role of Initial Conditions in the Local Structural Identifiability of Large Dynamic Models

Joubert

Stigter

Molenaar

2021

Preprint

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Structural identifiability is a binary property that determines whether or not unique parameter values can, in principle, be estimated from error-free input-output data. The many papers that have been written on this topic collectively stress theimportance of this a priori analysis in the model development process. The story however, often ends with a structurallyunidentifiable model. This may leave a model developer with no plan of action on how to address this potential issue. We continue this model exploration journey by identifying one of the possible sources of a model’s unidentifiability: problematic initial conditions. It is well-known that certain initial values may result in the loss of local structural identifiability. Nevertheless, literature on this topic has been limited to the analysis of small toy models. Here, we present a systematic approach to detect problematic initial conditions of real-world systems biology models, that are usually not small. A model’s identifiability can often be reinstated by changing the value of such problematic initial conditions. This provides modellers an option to resolve the “unidentifiablemodel” problem. Additionally, a good understanding of which initial values should rather be avoided can be very useful during experimental design. We show how our approach works in practice by applying it to five models. First, two small benchmark models are studied toget the reader acquainted with the method. The first one shows the effect of a zero-valued problematic initial condition. The second one illustrates that the approach also yields correct results in the presence of input signals and that problematic initial conditions need not be zero-values. For the remaining three examples, we set out to identify key initial values which may result in the structural unidentifiability. The third and fourth examples involve a systems biology Epo receptor model and a JAK/STAT model, respectively. In the final Pharmacokinetics model, of which its global structural identifiability has only recently been confirmed, we indicate that there are still sets of initial values for which this property does not hold.

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Determining minimal output sets that ensure structural identifiability

Cited by 12 publications

References 30 publications

Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

Structural identifiability of biomolecular controller motifs with and without flow measurements as model output

A plausible identifiable model of the canonical NF-κB signaling pathway

Assessing the Role of Initial Conditions in the Local Structural Identifiability of Large Dynamic Models

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