Driving the Model to Its Limit: Profile Likelihood Based Model Reduction

Maiwald, Thomas; Hass, Helge; Steiert, Bernhard; Vanlier, J Joep; Engesser, Raphael; Raue, Andreas; Kipkeew, Friederike; Bock, Hans H.; Kaschek, Daniel; Kreutz, Clemens; Timmer, Jens

doi:10.1371/journal.pone.0162366

Cited by 95 publications

(117 citation statements)

References 38 publications

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“…Alone or in combination, such methods can be used to interrogate which parameters can be estimated, determine measurement scenarios to ensure identifiability (Anguelova et al, 2012; Cheung et al, 2013), improve predictions of different variables and dynamic patterns (Kreutz et al, 2012; Vanlier et al, 2012b), and evaluate the structure of dependencies between estimated parameters (Janzén et al, 2016; Raue et al, 2014). In the case of unidentifiability, such dependencies can often be used to reduce or reparameterize the model to ensure identifiability (Maiwald et al, 2016; Meshkat and Sullivant, 2014). Several studies have evaluated structural and/or practical identifiability for intracellular cancer regulatory network models (Bachmann et al, 2012; Raue et al, 2014), and the literature examining identifiability of compartmental models in pharmacokinetics and pharmacodynamics is quite extensive (e.g.…”

Section: Introductionmentioning

confidence: 99%

A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study

Eisenberg

Jain

2017

Journal of Theoretical Biology

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Mathematical modeling has a long history in the field of cancer therapeutics, and there is increasing recognition that it can help uncover the mechanisms that underlie tumor response to treatment. However, making quantitative predictions with such models often requires parameter estimation from data, raising questions of parameter identifiability and estimability. Even in the case of structural (theoretical) identifiability, imperfect data and the resulting practical unidentifiability of model parameters can make it difficult to infer the desired information, and in some cases, to yield biologically correct inferences and predictions. Here, we examine parameter identifiability and estimability using a case study of two compartmental, ordinary differential equation models of cancer treatment with drugs that are cell cycle-specific (taxol) as well as non-specific (oxaliplatin). We proceed through model building, structural identifiability analysis, parameter estimation, practical identifiability analysis and its biological implications, as well as alternative data collection protocols and experimental designs that render the model identifiable. We use the differential algebra/input-output relationship approach for structural identifiability, and primarily the profile likelihood approach for practical identifiability. Despite the models being structurally identifiable, we show that without consideration of practical identifiability, incorrect cell cycle distributions can be inferred, that would result in suboptimal therapeutic choices. We illustrate the usefulness of estimating practically identifiable combinations (in addition to the more typically considered structurally identifiable combinations) in generating biologically meaningful insights. We also use simulated data to evaluate how the practical identifiability of the model would change under alternative experimental designs. These results highlight the importance of understanding the underlying mechanisms rather than purely using parsimony or information criteria/goodness-of-fit to decide model selection questions. The overall roadmap for identifiability testing laid out here can be used to help provide mechanistic insight into complex biological phenomena, reduce experimental costs, and optimize model-driven experimentation.

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Section: Introductionmentioning

confidence: 99%

A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study

Eisenberg

Jain

2017

Journal of Theoretical Biology

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“…Additionally, we reduced the complexity of the model without substantially impairing the model agreement to the comprehensive data set. We applied an iterative method, which relies on profile likelihood calculation (Maiwald et al, 2016). The resulting population-average model (Figure 2A) differed from the previously published model in three aspects: (i) SHP1 activation was simplified by considering the total amount of SHP1 as not-limiting, (ii) SOCS3 transcription and translation process were summarized in a single reaction and (iii) the CIS transcriptional delay was shortened, which was modeled by the linear chain trick (MacDonald, 1976) (for details and biological interpretation, see STAR Methods section "Model reduction").…”

Section: Dynamical Modeling Of Epo-induced Jak2/stat5 Signal Transducmentioning

confidence: 99%

“…Based on the comprehensive experimental data set and the original population-average model topology, a systematic data-based model reduction was performed by iteratively analyzing the profile likelihood (Hass et al, 2017;Maiwald et al, 2016;Tönsing et al, 2018). By this, non-identifiabilities can be resolved without changing the dynamics of the observed model entities.…”

Section: Model Reductionmentioning

confidence: 99%

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Cell-to-cell variability in JAK2/STAT5 pathway components and cytoplasmic volumes define survival threshold in erythroid progenitor cells

Adlung

Stapor

Tönsing

et al. 2019

Preprint

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Highlights• Mathematical modeling enables integration of heterogeneous data • Single-cell modeling captures binary decision process • Multiple sources of cell-to-cell variability in erythroid progenitor cells • Minimal amount of active STAT5 sufficient for survival of erythroid progenitor cells Summary Survival or apoptosis is a binary decision in individual cells. Yet, at the cell population level, a graded increase in survival of CFU-E cells is observed upon stimulation with Erythropoietin (Epo). To identify components of JAK2/STAT5 signal transduction that contribute to the graded population response, a cell population-level model calibrated with experimental data was extended to study the behavior in single cells. The single-cell model showed that the high cell-to-cell variability in nuclear phosphorylated STAT5 is caused by variability in the amount of EpoR:JAK2 complexes and of SHP1 as well as the extent of nuclear import due to the large variance in the cytoplasmic volume of CFU-E cells. 24 to 118 pSTAT5 molecules in the nucleus for 120 min are sufficient to ensure cell survival. Thus, variability in membraneassociated processes are responsible to convert a switch-like behavior at the single-cell level to a graded population level response.

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“…The parameters of the biological process are often transformed to improve the convergence of optimization and to eliminate structural non-identifiabilities (Maiwald et al, 2016). A common practice is the transformation of the parameters from linear to logarithmic scale.…”

Section: Parametersmentioning

confidence: 99%

Benchmark Problems for Dynamic Modeling of Intracellular Processes

Hass

Loos

Alvarez

et al. 2018

Preprint

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Motivation: Dynamic models are used in systems biology to study and understand cellular processes like gene regulation or signal transduction. Frequently, ordinary differential equation (ODE) models are used to model the time and dose dependency of the abundances of molecular compounds as well as interactions and translocations. A multitude of computational approaches have been developed within recent years. However, many of these approaches lack proper testing in application settings because a comprehensive set of benchmark problems is yet missing. Results:We present a collection of 20 ODE models developed given experimental data as benchmark problems in order to evaluate new and existing methodologies, e.g. for parameter estimation or uncertainty analysis. In addition to the equations of the dynamical system, the benchmark collection provides experimental measurements as well as observation functions and assumptions about measurement noise distributions and parameters. The presented benchmark models comprise problems of different size, complexity and numerical demands. Important characteristics of the models and methodological requirements are summarized, estimated parameters are provided, and some example studies were performed for illustrating the capabilities of the presented benchmark collection.Availability: The models are provided in several standardized formats, including an easy-to-use human readable form and machine-readable SBML files. The data is provided as Excel sheets. All files are available at https://github.com/Benchmarking-Initiative/Benchmark-Models, with MATLAB code to process and simulate the models.

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Driving the Model to Its Limit: Profile Likelihood Based Model Reduction

Cited by 95 publications

References 38 publications

A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study

A confidence building exercise in data and identifiability: Modeling cancer chemotherapy as a case study

Cell-to-cell variability in JAK2/STAT5 pathway components and cytoplasmic volumes define survival threshold in erythroid progenitor cells

Benchmark Problems for Dynamic Modeling of Intracellular Processes

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