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Díaz-Seoane S, Rey Barreiro X, Villaverde AF. STRIKE-GOLDD 4.0: user-friendly, efficient analysis of structural identifiability and observability. Bioinformatics 2023; 39:6833126. [PMID: 36398887 PMCID: PMC9805590 DOI: 10.1093/bioinformatics/btac748] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 11/15/2022] [Accepted: 11/17/2022] [Indexed: 11/19/2022] Open
Abstract
MOTIVATION STRIKE-GOLDD is a toolbox that analyses the structural identifiability and observability of possibly non-linear, non-rational ODE models that may have known and unknown inputs. Its broad applicability comes at the expense of a lower computational efficiency than other tools. RESULTS STRIKE-GOLDD 4.0 includes a new algorithm, ProbObsTest, specifically designed for the analysis of rational models. ProbObsTest is significantly faster than the previously available FISPO algorithm when applied to computationally expensive models. Providing both algorithms in the same toolbox allows combining generality and computational efficiency. STRIKE-GOLDD 4.0 is implemented as a Matlab toolbox with a user-friendly graphical interface. AVAILABILITY AND IMPLEMENTATION STRIKE-GOLDD 4.0 is a free and open-source tool available under a GPLv3 license. It can be downloaded from GitHub at https://github.com/afvillaverde/strike-goldd. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Sandra Díaz-Seoane
- Department of Systems and Control Engineering, Universidade de Vigo, Galicia, 36310 Vigo, Spain
| | - Xabier Rey Barreiro
- Department of Systems and Control Engineering, Universidade de Vigo, Galicia, 36310 Vigo, Spain
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52
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Profile likelihood-based parameter and predictive interval analysis guides model choice for ecological population dynamics. Math Biosci 2023; 355:108950. [PMID: 36463960 DOI: 10.1016/j.mbs.2022.108950] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2022] [Revised: 11/01/2022] [Accepted: 11/26/2022] [Indexed: 12/03/2022]
Abstract
Calibrating mathematical models to describe ecological data provides important insight via parameter estimation that is not possible from analysing data alone. When we undertake a mathematical modelling study of ecological or biological data, we must deal with the trade-off between data availability and model complexity. Dealing with the nexus between data availability and model complexity is an ongoing challenge in mathematical modelling, particularly in mathematical biology and mathematical ecology where data collection is often not standardised, and more broad questions about model selection remain relatively open. Therefore, choosing an appropriate model almost always requires case-by-case consideration. In this work we present a straightforward approach to quantitatively explore this trade-off using a case study exploring mathematical models of coral reef regrowth after some ecological disturbance, such as damage caused by a tropical cyclone. In particular, we compare a simple single species ordinary differential equation (ODE) model approach with a more complicated two-species coupled ODE model. Univariate profile likelihood analysis suggests that the both models are practically identifiable. To provide additional insight we construct and compare approximate prediction intervals using a new parameter-wise prediction approximation, confirming both the simple and complex models perform similarly with regard to making predictions. Our approximate parameter-wise prediction interval analysis provides explicit information about how each parameter affects the predictions of each model. Comparing our approximate prediction intervals with a more rigorous and computationally expensive evaluation of the full likelihood shows that the new approximations are reasonable in this case. All algorithms and software to support this work are freely available as jupyter notebooks on GitHub so that they can be adapted to deal with any other ODE-based models.
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53
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Mowbray MR, Wu C, Rogers AW, Rio-Chanona EAD, Zhang D. A reinforcement learning-based hybrid modeling framework for bioprocess kinetics identification. Biotechnol Bioeng 2023; 120:154-168. [PMID: 36225098 PMCID: PMC10092184 DOI: 10.1002/bit.28262] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2022] [Revised: 07/18/2022] [Accepted: 10/09/2022] [Indexed: 11/09/2022]
Abstract
Constructing predictive models to simulate complex bioprocess dynamics, particularly time-varying (i.e., parameters varying over time) and history-dependent (i.e., current kinetics dependent on historical culture conditions) behavior, has been a longstanding research challenge. Current advances in hybrid modeling offer a solution to this by integrating kinetic models with data-driven techniques. This article proposes a novel two-step framework: first (i) speculate and combine several possible kinetic model structures sourced from process and phenomenological knowledge, then (ii) identify the most likely kinetic model structure and its parameter values using model-free Reinforcement Learning (RL). Specifically, Step 1 collates feasible history-dependent model structures, then Step 2 uses RL to simultaneously identify the correct model structure and the time-varying parameter trajectories. To demonstrate the performance of this framework, a range of in-silico case studies were carried out. The results show that the proposed framework can efficiently construct high-fidelity models to quantify both time-varying and history-dependent kinetic behaviors while minimizing the risks of over-parametrization and over-fitting. Finally, the primary advantages of the proposed framework and its limitation were thoroughly discussed in comparison to other existing hybrid modeling and model structure identification techniques, highlighting the potential of this framework for general bioprocess modeling.
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Affiliation(s)
- Max R Mowbray
- Department of Chemical Engineering, Centre for Process Integration, University of Manchester, Manchester, UK
| | - Chufan Wu
- Department of Chemical Engineering, Centre for Process Integration, University of Manchester, Manchester, UK
| | - Alexander W Rogers
- Department of Chemical Engineering, Centre for Process Integration, University of Manchester, Manchester, UK
| | | | - Dongda Zhang
- Department of Chemical Engineering, Centre for Process Integration, University of Manchester, Manchester, UK
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54
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The Structural Identifiability of a Humidity-Driven Epidemiological Model of Influenza Transmission. Viruses 2022; 14:v14122795. [PMID: 36560799 PMCID: PMC9780807 DOI: 10.3390/v14122795] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Revised: 12/08/2022] [Accepted: 12/10/2022] [Indexed: 12/23/2022] Open
Abstract
Influenza epidemics cause considerable morbidity and mortality every year worldwide. Climate-driven epidemiological models are mainstream tools to understand seasonal transmission dynamics and predict future trends of influenza activity, especially in temperate regions. Testing the structural identifiability of these models is a fundamental prerequisite for the model to be applied in practice, by assessing whether the unknown model parameters can be uniquely determined from epidemic data. In this study, we applied a scaling method to analyse the structural identifiability of four types of commonly used humidity-driven epidemiological models. Specifically, we investigated whether the key epidemiological parameters (i.e., infectious period, the average duration of immunity, the average latency period, and the maximum and minimum daily basic reproductive number) can be uniquely determined simultaneously when prevalence data is observable. We found that each model is identifiable when the prevalence of infection is observable. The structural identifiability of these models will lay the foundation for testing practical identifiability in the future using synthetic prevalence data when considering observation noise. In practice, epidemiological models should be examined with caution before using them to estimate model parameters from epidemic data.
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55
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Butner JD, Dogra P, Chung C, Pasqualini R, Arap W, Lowengrub J, Cristini V, Wang Z. Mathematical modeling of cancer immunotherapy for personalized clinical translation. NATURE COMPUTATIONAL SCIENCE 2022; 2:785-796. [PMID: 38126024 PMCID: PMC10732566 DOI: 10.1038/s43588-022-00377-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 11/14/2022] [Indexed: 12/23/2023]
Abstract
Encouraging advances are being made in cancer immunotherapy modeling, especially in the key areas of developing personalized treatment strategies based on individual patient parameters, predicting treatment outcomes and optimizing immunotherapy synergy when used in combination with other treatment approaches. Here we present a focused review of the most recent mathematical modeling work on cancer immunotherapy with a focus on clinical translatability. It can be seen that this field is transitioning from pure basic science to applications that can make impactful differences in patients' lives. We discuss how researchers are integrating experimental and clinical data to fully inform models so that they can be applied for clinical predictions, and present the challenges that remain to be overcome if widespread clinical adaptation is to be realized. Lastly, we discuss the most promising future applications and areas that are expected to be the focus of extensive upcoming modeling studies.
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Affiliation(s)
- Joseph D. Butner
- Mathematics in Medicine Program, Houston Methodist Research Institute, Houston, TX, USA
| | - Prashant Dogra
- Mathematics in Medicine Program, Houston Methodist Research Institute, Houston, TX, USA
| | - Caroline Chung
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, TX, USA
| | - Renata Pasqualini
- Rutgers Cancer Institute of New Jersey, Newark, NJ, USA
- Department of Radiation Oncology, Division of Cancer Biology, Rutgers New Jersey Medical School, Newark, NJ, USA
| | - Wadih Arap
- Rutgers Cancer Institute of New Jersey, Newark, NJ, USA
- Department of Medicine, Division of Hematology/Oncology, Rutgers New Jersey Medical School, Newark, NJ, USA
| | - John Lowengrub
- Department of Mathematics, University of California at Irvine, Irvine, CA, USA
| | - Vittorio Cristini
- Mathematics in Medicine Program, Houston Methodist Research Institute, Houston, TX, USA
- Neal Cancer Center, Houston Methodist Research Institute, Houston, TX, USA
- Department of Imaging Physics, University of Texas MD Anderson Cancer Center, Houston, TX, USA
- Physiology, Biophysics, and Systems Biology Program, Graduate School of Medical Sciences, Weill Cornell Medicine, New York, NY, USA
| | - Zhihui Wang
- Mathematics in Medicine Program, Houston Methodist Research Institute, Houston, TX, USA
- Neal Cancer Center, Houston Methodist Research Institute, Houston, TX, USA
- Department of Physiology and Biophysics, Weill Cornell Medicine, New York, NY, USA
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56
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Dankwa EA, Brouwer AF, Donnelly CA. Structural identifiability of compartmental models for infectious disease transmission is influenced by data type. Epidemics 2022; 41:100643. [PMID: 36308994 PMCID: PMC9772104 DOI: 10.1016/j.epidem.2022.100643] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Revised: 09/05/2022] [Accepted: 10/14/2022] [Indexed: 12/29/2022] Open
Abstract
If model identifiability is not confirmed, inferences from infectious disease transmission models may not be reliable, so they might result in misleading recommendations. Structural identifiability analysis characterises whether it is possible to obtain unique solutions for all unknown model parameters, given the model structure. In this work, we studied the structural identifiability of some typical deterministic compartmental models for infectious disease transmission, focusing on the influence of the data type considered as model output on the identifiability of unknown model parameters, including initial conditions. We defined 26 model versions, each having a unique combination of underlying compartmental structure and data type(s) considered as model output(s). Four compartmental model structures and three common data types in disease surveillance (incidence, prevalence and detected vector counts) were studied. The structural identifiability of some parameters varied depending on the type of model output. In general, models with multiple data types as outputs had more structurally identifiable parameters, than did models with a single data type as output. This study highlights the importance of a careful consideration of data types as an integral part of the inference process with compartmental infectious disease transmission models.
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Affiliation(s)
- Emmanuelle A Dankwa
- Department of Statistics, University of Oxford, 24-29 St Giles', Oxford, United Kingdom
| | - Andrew F Brouwer
- Department of Epidemiology, University of Michigan, 1415 Washington Heights, Ann Arbor, MI 48109-2029, USA
| | - Christl A Donnelly
- Department of Statistics, University of Oxford, 24-29 St Giles', Oxford, United Kingdom; Department of Infectious Disease Epidemiology, Faculty of Medicine, School of Public Health, Imperial College London, United Kingdom.
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57
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Murphy RJ, Maclaren OJ, Calabrese AR, Thomas PB, Warne DJ, Williams ED, Simpson MJ. Computationally efficient framework for diagnosing, understanding and predicting biphasic population growth. J R Soc Interface 2022; 19:20220560. [PMID: 36475389 PMCID: PMC9727659 DOI: 10.1098/rsif.2022.0560] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as biphasic growth for the commonly encountered situation involving two phases. Biphasic population growth occurs over a massive range of spatial and temporal scales, ranging from microscopic growth of tumours over several days, to decades-long regrowth of corals in coral reefs that can extend for hundreds of kilometres. Different mathematical models and statistical methods are used to diagnose, understand and predict biphasic growth. Common approaches can lead to inaccurate predictions of future growth that may result in inappropriate management and intervention strategies being implemented. Here, we develop a very general computationally efficient framework, based on profile likelihood analysis, for diagnosing, understanding and predicting biphasic population growth. The two key components of the framework are as follows: (i) an efficient method to form approximate confidence intervals for the change point of the growth dynamics and model parameters and (ii) parameter-wise profile predictions that systematically reveal the influence of individual model parameters on predictions. To illustrate our framework we explore real-world case studies across the life sciences.
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Affiliation(s)
- Ryan J. Murphy
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Oliver J. Maclaren
- Department of Engineering Science, University of Auckland, Auckland, New Zealand
| | - Alivia R. Calabrese
- Queensland Bladder Cancer Initiative and School of Biomedical Sciences, Faculty of Health, Queensland University of Technology at Translational Research Institute, Brisbane, Australia
| | - Patrick B. Thomas
- Queensland Bladder Cancer Initiative and School of Biomedical Sciences, Faculty of Health, Queensland University of Technology at Translational Research Institute, Brisbane, Australia
| | - David J. Warne
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Elizabeth D. Williams
- Queensland Bladder Cancer Initiative and School of Biomedical Sciences, Faculty of Health, Queensland University of Technology at Translational Research Institute, Brisbane, Australia
| | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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58
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Butner JD, Farhat M, Cristini V, Chung C, Wang Z. Protocol for mathematical prediction of patient response and survival to immune checkpoint inhibitor immunotherapy. STAR Protoc 2022; 3:101886. [PMID: 36595890 PMCID: PMC9719106 DOI: 10.1016/j.xpro.2022.101886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Revised: 10/03/2022] [Accepted: 11/03/2022] [Indexed: 12/03/2022] Open
Abstract
This protocol describes the application of a mechanistic mathematical model of immune checkpoint inhibitor (ICI) immunotherapy to patient tumor imaging data for predicting solid tumor response and patient survival under ICI intervention. We describe steps for data collection and processing, data pipelines, and approaches to increase precision. The protocol is highly predictive as early as the first restaging after treatment start and can be used with standard-of-care imaging measures. For complete details on the use and execution of this protocol, please refer to Butner et al. (2020)1 and Butner et al. (2021).2.
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Affiliation(s)
- Joseph D. Butner
- Mathematics in Medicine Program, Houston Methodist Research Institute, Houston, TX 77030, USA,Corresponding author
| | - Maguy Farhat
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA
| | - Vittorio Cristini
- Mathematics in Medicine Program, Houston Methodist Research Institute, Houston, TX 77030, USA,Neal Cancer Center, Houston Methodist Research Institute, Houston, TX 77030, USA,Department of Imaging Physics, University of Texas MD Anderson Cancer Center, Houston, TX 77230, USA,Physiology, Biophysics, and Systems Biology Program, Graduate School of Medical Sciences, Weill Cornell Medicine, New York, NY 10065, USA
| | - Caroline Chung
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, TX 77030, USA,Corresponding author
| | - Zhihui Wang
- Mathematics in Medicine Program, Houston Methodist Research Institute, Houston, TX 77030, USA,Neal Cancer Center, Houston Methodist Research Institute, Houston, TX 77030, USA,Department of Physiology and Biophysics, Weill Cornell Medicine, New York, NY 10065, USA,Department of Medical Education, Texas A&M University School of Medicine, Bryan, TX 77807, USA,Corresponding author
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59
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Massonis G, Villaverde AF, Banga JR. Improving dynamic predictions with ensembles of observable models. Bioinformatics 2022; 39:6842325. [PMID: 36416122 PMCID: PMC9805594 DOI: 10.1093/bioinformatics/btac755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Revised: 10/20/2022] [Accepted: 11/22/2022] [Indexed: 11/24/2022] Open
Abstract
MOTIVATION Dynamic mechanistic modelling in systems biology has been hampered by the complexity and variability associated with the underlying interactions, and by uncertain and sparse experimental measurements. Ensemble modelling, a concept initially developed in statistical mechanics, has been introduced in biological applications with the aim of mitigating those issues. Ensemble modelling uses a collection of different models compatible with the observed data to describe the phenomena of interest. However, since systems biology models often suffer from a lack of identifiability and observability, ensembles of models are particularly unreliable when predicting non-observable states. RESULTS We present a strategy to assess and improve the reliability of a class of model ensembles. In particular, we consider kinetic models described using ordinary differential equations with a fixed structure. Our approach builds an ensemble with a selection of the parameter vectors found when performing parameter estimation with a global optimization metaheuristic. This technique enforces diversity during the sampling of parameter space and it can quantify the uncertainty in the predictions of state trajectories. We couple this strategy with structural identifiability and observability analysis, and when these tests detect possible prediction issues we obtain model reparameterizations that surmount them. The end result is an ensemble of models with the ability to predict the internal dynamics of a biological process. We demonstrate our approach with models of glucose regulation, cell division, circadian oscillations and the JAK-STAT signalling pathway. AVAILABILITY AND IMPLEMENTATION The code that implements the methodology and reproduces the results is available at https://doi.org/10.5281/zenodo.6782638. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Gemma Massonis
- Computational Biology Lab, MBG-CSIC (Spanish National Research Council), Pontevedra, Galicia 36143, Spain
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60
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Zamudio Lara JM, Dewasme L, Hernández Escoto H, Vande Wouwer A. Parameter Estimation of Dynamic Beer Fermentation Models. Foods 2022; 11:foods11223602. [PMID: 36429194 PMCID: PMC9689312 DOI: 10.3390/foods11223602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 11/04/2022] [Accepted: 11/07/2022] [Indexed: 11/16/2022] Open
Abstract
In this study, two dynamic models of beer fermentation are proposed, and their parameters are estimated using experimental data collected during several batch experiments initiated with different sugar concentrations. Biomass, sugar, ethanol, and vicinal diketone concentrations are measured off-line with an analytical system while two on-line immersed probes deliver temperature, ethanol concentration, and carbon dioxide exhaust rate measurements. Before proceeding to the estimation of the unknown model parameters, a structural identifiability analysis is carried out to investigate the measurement configuration and the kinetic model structure. The model predictive capability is investigated in cross-validation, in view of opening up new perspectives for monitoring and control purposes. For instance, the dynamic model could be used as a predictor in receding-horizon observers and controllers.
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Affiliation(s)
- Jesús Miguel Zamudio Lara
- Systèmes, Estimation, Commande et Optimisation, Université de Mons, 7000 Mons, Belgium
- Departamento de Ingeniería Química, Universidad de Guanajuato, Guanajuato 36050, Mexico
| | - Laurent Dewasme
- Systèmes, Estimation, Commande et Optimisation, Université de Mons, 7000 Mons, Belgium
| | | | - Alain Vande Wouwer
- Systèmes, Estimation, Commande et Optimisation, Université de Mons, 7000 Mons, Belgium
- Correspondence:
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61
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Argus F, Zhao D, Babarenda Gamage TP, Nash MP, Maso Talou GD. Automated model calibration with parallel MCMC: Applications for a cardiovascular system model. Front Physiol 2022; 13:1018134. [PMID: 36439250 PMCID: PMC9683692 DOI: 10.3389/fphys.2022.1018134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Accepted: 10/24/2022] [Indexed: 11/10/2022] Open
Abstract
Computational physiological models continue to increase in complexity, however, the task of efficiently calibrating the model to available clinical data remains a significant challenge. One part of this challenge is associated with long calibration times, which present a barrier for the routine application of model-based prediction in clinical practice. Another aspect of this challenge is the limited available data for the unique calibration of complex models. Therefore, to calibrate a patient-specific model, it may be beneficial to verify that task-specific model predictions have acceptable uncertainty, rather than requiring all parameters to be uniquely identified. We have developed a pipeline that reduces the set of fitting parameters to make them structurally identifiable and to improve the efficiency of a subsequent Markov Chain Monte Carlo (MCMC) analysis. MCMC was used to find the optimal parameter values and to determine the confidence interval of a task-specific prediction. This approach was demonstrated on numerical experiments where a lumped parameter model of the cardiovascular system was calibrated to brachial artery cuff pressure, echocardiogram volume measurements, and synthetic cerebral blood flow data that approximates what can be obtained from 4D-flow MRI data. This pipeline provides a cerebral arterial pressure prediction that may be useful for determining the risk of hemorrhagic stroke. For a set of three patients, this pipeline successfully reduced the parameter set of a cardiovascular system model from 12 parameters to 8–10 structurally identifiable parameters. This enabled a significant (>4×) efficiency improvement in determining confidence intervals on predictions of pressure compared to performing a naive MCMC analysis with the full parameter set. This demonstrates the potential that the proposed pipeline has in helping address one of the key challenges preventing clinical application of such models. Additionally, for each patient, the MCMC approach yielded a 95% confidence interval on systolic blood pressure prediction in the middle cerebral artery smaller than ±10 mmHg (±1.3 kPa). The proposed pipeline exploits available high-performance computing parallelism to allow straightforward automation for general models and arbitrary data sets, enabling automated calibration of a parameter set that is specific to the available clinical data with minimal user interaction.
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Affiliation(s)
- Finbar Argus
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
- *Correspondence: Finbar Argus,
| | - Debbie Zhao
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | | | - Martyn P. Nash
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
- Department of Engineering Science, University of Auckland, Auckland, New Zealand
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62
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Linden NJ, Kramer B, Rangamani P. Bayesian parameter estimation for dynamical models in systems biology. PLoS Comput Biol 2022; 18:e1010651. [PMID: 36269772 PMCID: PMC9629650 DOI: 10.1371/journal.pcbi.1010651] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Revised: 11/02/2022] [Accepted: 10/12/2022] [Indexed: 11/07/2022] Open
Abstract
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent advances in experimental measurements, including sensor development and '-omics' studies that have helped populate protein-protein interaction networks in great detail, modeling in systems biology lacks systematic methods to estimate kinetic parameters and quantify associated uncertainties. This is because of multiple reasons, including sparse and noisy experimental measurements, lack of detailed molecular mechanisms underlying the reactions, and missing biochemical interactions. Additionally, the inherent nonlinearities with respect to the states and parameters associated with the system of differential equations further compound the challenges of parameter estimation. In this study, we propose a comprehensive framework for Bayesian parameter estimation and complete quantification of the effects of uncertainties in the data and models. We apply these methods to a series of signaling models of increasing mathematical complexity. Systematic analysis of these dynamical systems showed that parameter estimation depends on data sparsity, noise level, and model structure, including the existence of multiple steady states. These results highlight how focused uncertainty quantification can enrich systems biology modeling and enable additional quantitative analyses for parameter estimation.
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Affiliation(s)
- Nathaniel J. Linden
- Department of Mechanical and Aerospace Engineering, University of California San Diego, San Diego, California, United States of America
| | - Boris Kramer
- Department of Mechanical and Aerospace Engineering, University of California San Diego, San Diego, California, United States of America
- * E-mail: (BK); (PR)
| | - Padmini Rangamani
- Department of Mechanical and Aerospace Engineering, University of California San Diego, San Diego, California, United States of America
- * E-mail: (BK); (PR)
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63
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Monsalve-Bravo GM, Lawson BAJ, Drovandi C, Burrage K, Brown KS, Baker CM, Vollert SA, Mengersen K, McDonald-Madden E, Adams MP. Analysis of sloppiness in model simulations: Unveiling parameter uncertainty when mathematical models are fitted to data. SCIENCE ADVANCES 2022; 8:eabm5952. [PMID: 36129974 PMCID: PMC9491719 DOI: 10.1126/sciadv.abm5952] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Accepted: 08/10/2022] [Indexed: 06/15/2023]
Abstract
This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.
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Affiliation(s)
- Gloria M. Monsalve-Bravo
- School of Earth and Environmental Sciences, The University of Queensland, St Lucia, QLD 4072, Australia
- Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, QLD 4072, Australia
- School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
| | - Brodie A. J. Lawson
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Plant Success in Nature and Agriculture, Queensland University of Technology, Brisbane, QLD 4001, Australia
| | - Christopher Drovandi
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
| | - Kevin Burrage
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Plant Success in Nature and Agriculture, Queensland University of Technology, Brisbane, QLD 4001, Australia
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK
| | - Kevin S. Brown
- Department of Pharmaceutical Sciences, Oregon State University, Corvallis, OR 97331, USA
- Department of Chemical, Biological, & Environmental Engineering, Oregon State University, Corvallis, OR 97331, USA
| | - Christopher M. Baker
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia
- Melbourne Centre for Data Science, The University of Melbourne, Parkville, VIC 3010, Australia
- Centre of Excellence for Biosecurity Risk Analysis, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Sarah A. Vollert
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
| | - Kerrie Mengersen
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
| | - Eve McDonald-Madden
- School of Earth and Environmental Sciences, The University of Queensland, St Lucia, QLD 4072, Australia
- Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, QLD 4072, Australia
| | - Matthew P. Adams
- School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
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64
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Cárdenas SD, Reznik CJ, Ranaweera R, Song F, Chung CH, Fertig EJ, Gevertz JL. Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer. NPJ Syst Biol Appl 2022; 8:32. [PMID: 36075912 PMCID: PMC9458753 DOI: 10.1038/s41540-022-00244-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 08/05/2022] [Indexed: 11/09/2022] Open
Abstract
The promise of precision medicine has been limited by the pervasive resistance to many targeted therapies for cancer. Inferring the timing (i.e., pre-existing or acquired) and mechanism (i.e., drug-induced) of such resistance is crucial for designing effective new therapeutics. This paper studies cetuximab resistance in head and neck squamous cell carcinoma (HNSCC) using tumor volume data obtained from patient-derived tumor xenografts. We ask if resistance mechanisms can be determined from this data alone, and if not, what data would be needed to deduce the underlying mode(s) of resistance. To answer these questions, we propose a family of mathematical models, with each member of the family assuming a different timing and mechanism of resistance. We present a method for fitting these models to individual volumetric data, and utilize model selection and parameter sensitivity analyses to ask: which member(s) of the family of models best describes HNSCC response to cetuximab, and what does that tell us about the timing and mechanisms driving resistance? We find that along with time-course volumetric data to a single dose of cetuximab, the initial resistance fraction and, in some instances, dose escalation volumetric data are required to distinguish among the family of models and thereby infer the mechanisms of resistance. These findings can inform future experimental design so that we can best leverage the synergy of wet laboratory experimentation and mathematical modeling in the study of novel targeted cancer therapeutics.
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Affiliation(s)
- Santiago D Cárdenas
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, USA
| | - Constance J Reznik
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, USA.,Datacor, Inc., Florham Park, NJ, USA
| | - Ruchira Ranaweera
- Department of Head and Neck-Endocrine Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Feifei Song
- Department of Head and Neck-Endocrine Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Christine H Chung
- Department of Head and Neck-Endocrine Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Elana J Fertig
- Convergence Institute, Department of Oncology, Department of Biomedical Engineering, Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA.
| | - Jana L Gevertz
- Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, USA.
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65
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Process Model Inversion in the Data-Driven Engineering Context for Improved Parameter Sensitivities. Processes (Basel) 2022. [DOI: 10.3390/pr10091764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Industry 4.0 has embraced process models in recent years, and the use of model-based digital twins has become even more critical in process systems engineering, monitoring, and control. However, the reliability of these models depends on the model parameters available. The accuracy of the estimated parameters is, in turn, determined by the amount and quality of the measurement data and the algorithm used for parameter identification. For the definition of the parameter identification problem, the ordinary least squares framework is still state-of-the-art in the literature, and better parameter estimates are only possible with additional data. In this work, we present an alternative strategy to identify model parameters by incorporating differential flatness for model inversion and neural ordinary differential equations for surrogate modeling. The novel concept results in an input-least-squares-based parameter identification problem with significant parameter sensitivity changes. To study these sensitivity effects, we use a classic one-dimensional diffusion-type problem, i.e., an omnipresent equation in process systems engineering and transport phenomena. As shown, the proposed concept ensures higher parameter sensitivities for two relevant scenarios. Based on the results derived, we also discuss general implications for data-driven engineering concepts used to identify process model parameters in the recent literature.
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66
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Colebank MJ, Chesler NC. An in-silico analysis of experimental designs to study ventricular function: A focus on the right ventricle. PLoS Comput Biol 2022; 18:e1010017. [PMID: 36126091 PMCID: PMC9524687 DOI: 10.1371/journal.pcbi.1010017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Revised: 09/30/2022] [Accepted: 09/07/2022] [Indexed: 11/19/2022] Open
Abstract
In-vivo studies of pulmonary vascular disease and pulmonary hypertension (PH) have provided key insight into the progression of right ventricular (RV) dysfunction. Additional in-silico experiments using multiscale computational models have provided further details into biventricular mechanics and hemodynamic function in the presence of PH, yet few have assessed whether model parameters are practically identifiable prior to data collection. Moreover, none have used modeling to devise synergistic experimental designs. To address this knowledge gap, we conduct a practical identifiability analysis of a multiscale cardiovascular model across four simulated experimental designs. We determine a set of parameters using a combination of Morris screening and local sensitivity analysis, and test for practical identifiability using profile likelihood-based confidence intervals. We employ Markov chain Monte Carlo (MCMC) techniques to quantify parameter and model forecast uncertainty in the presence of noise corrupted data. Our results show that model calibration to only RV pressure suffers from practical identifiability issues and suffers from large forecast uncertainty in output space. In contrast, parameter and model forecast uncertainty is substantially reduced once additional left ventricular (LV) pressure and volume data is included. A comparison between single point systolic and diastolic LV data and continuous, time-dependent LV pressure-volume data reveals that at least some quantitative data from both ventricles should be included for future experimental studies.
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Affiliation(s)
- Mitchel J. Colebank
- University of California, Irvine–Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
| | - Naomi C. Chesler
- University of California, Irvine–Edwards Lifesciences Foundation Cardiovascular Innovation and Research Center, and Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
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67
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Identifiability of parameters in mathematical models of SARS-CoV-2 infections in humans. Sci Rep 2022; 12:14637. [PMID: 36030320 PMCID: PMC9418662 DOI: 10.1038/s41598-022-18683-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2022] [Accepted: 08/16/2022] [Indexed: 12/12/2022] Open
Abstract
Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of the parameter estimates to the noise in the data, we developed a novel two-patch within-host mathematical model that considered the infection of both respiratory tracts and assumed that the viral load in the lower respiratory tract decays in a density dependent manner and investigated its ability to match population level data. We proposed several approaches that can improve practical identifiability of parameters, including an optimal experimental approach, and found that availability of viral data early in the infection is of essence for improving the accuracy of the estimates. Our findings can be useful for designing interventions.
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68
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Gaudreault J, Durocher Y, Henry O, De Crescenzo G. Multi-temperature experiments to ease analysis of heterogeneous binder solutions by surface plasmon resonance biosensing. Sci Rep 2022; 12:14401. [PMID: 36002549 PMCID: PMC9402583 DOI: 10.1038/s41598-022-18450-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 08/11/2022] [Indexed: 11/09/2022] Open
Abstract
Surface Plasmon Resonance (SPR) biosensing is a well-established tool for the investigation of binding kinetics between a soluble species and an immobilized (bio)molecule. While robust and accurate data analysis techniques are readily available for single species, methods to exploit data collected with a solution containing multiple interactants are scarce. In a previous study, our group proposed two data analysis algorithms for (1) the precise and reliable identification of the kinetic parameters of N interactants present at different ratios in N mixtures and (2) the estimation of the composition of a given mixture, assuming that the kinetic parameters and the total concentration of all interactants are known. Here, we extend the first algorithm by reducing the number of necessary mixtures. This is achieved by conducting experiments at different temperatures. Through the Van't Hoff and Eyring equations, identifying the kinetic and thermodynamic parameters of N binders becomes possible with M mixtures with M comprised between 2 and N and at least N/M temperatures. The second algorithm is improved by adding the total analyte concentration as a supplementary variable to be identified in an optimization routine. We validated our analysis framework experimentally with a system consisting of mixtures of low molecular weight drugs, each competing to bind to an immobilized protein. We believe that the analysis of mixtures and composition estimation could pave the way for SPR biosensing to become a bioprocess monitoring tool, on top of expanding its already substantial role in drug discovery and development.
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Affiliation(s)
- Jimmy Gaudreault
- Department of Chemical Engineering, Polytechnique Montréal, Centre-Ville Station, P.O. Box 6079, Montreal, QC, H3C 3A7, Canada
| | - Yves Durocher
- Life Sciences, NRC Human Health Therapeutics Portfolio, Building Montreal-Royalmount, National Research Council Canada, Montreal, QC, H4P 2R2, Canada
| | - Olivier Henry
- Department of Chemical Engineering, Polytechnique Montréal, Centre-Ville Station, P.O. Box 6079, Montreal, QC, H3C 3A7, Canada.
| | - Gregory De Crescenzo
- Department of Chemical Engineering, Polytechnique Montréal, Centre-Ville Station, P.O. Box 6079, Montreal, QC, H3C 3A7, Canada.
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69
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Non-Linear Observer Design with Laguerre Polynomials. ENTROPY 2022; 24:e24070913. [PMID: 35885136 PMCID: PMC9316067 DOI: 10.3390/e24070913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Revised: 06/28/2022] [Accepted: 06/28/2022] [Indexed: 01/27/2023]
Abstract
In this paper, a methodology for a non-linear system state estimation is demonstrated, exploiting the input and parameter observability. For this purpose, the initial system is transformed into the canonical observability form, and the function that aggregates the non-linear dynamics of the system, which may be unknown or difficult to be computed, is approximated by a linear combination of Laguerre polynomials. Hence, the system identification translates into the estimation of the parameters involved in the linear combination in order for the system to be observable. For the validation of the elaborated observer, we consider a biological model from the literature, investigating whether it is practically possible to infer its states, taking into account the new coordinates to design the appropriate observer of the system states. Through simulations, we investigate the parameter settings under which the new observer can identify the state of the system. More specifically, as the parameter θ increases, the system converges more quickly to the steady-state, decreasing the respective distance from the system’s initial state. As for the first state, the estimation error is in the order of 10−2 for θ=15, and assuming c0={0,1},c1=1. Under the same conditions, the estimation error of the system’s second state is in the order of 10−1, setting a performance difference of 10−1 in relation to the first state. The outcomes show that the proposed observer’s performance can be further improved by selecting even higher values of θ. Hence, the system is observable through the measurement output.
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70
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Lazarus A, Dalton D, Husmeier D, Gao H. Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics. Biomech Model Mechanobiol 2022; 21:953-982. [PMID: 35377030 PMCID: PMC9132878 DOI: 10.1007/s10237-022-01571-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Accepted: 02/28/2022] [Indexed: 01/08/2023]
Abstract
Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.
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Affiliation(s)
- Alan Lazarus
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - David Dalton
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Dirk Husmeier
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
| | - Hao Gao
- School of Mathematics and Statistics, University of Glasgow, Glasgow, UK
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71
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Fábregas-Ibáñez L, Jeschke G, Stoll S. Compactness regularization in the analysis of dipolar EPR spectroscopy data. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2022; 339:107218. [PMID: 35439683 DOI: 10.1016/j.jmr.2022.107218] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Revised: 04/04/2022] [Accepted: 04/05/2022] [Indexed: 06/14/2023]
Abstract
Dipolar electron paramagnetic resonance (EPR) experiments, such as double electron-electron resonance (DEER), measure distributions of nanometer-scale distances between paramagnetic centers, which are valuable for structural characterization of proteins and other macromolecular systems. One challenge in the least-squares fitting analysis of dipolar EPR data is the separation of the inter-molecular contribution (background) and the intra-molecular contribution. For noisy experimental traces of insufficient length, this separation is not unique, leading to identifiability problems for the background model parameters and the long-distance region of the intra-molecular distance distribution. Here, we introduce a regularization approach that mitigates this by including an additional penalty term in the objective function that is proportional to the variance of the distance distribution and thereby penalizes non-compact distributions. We examine the reliability of this approach statistically on a large set of synthetic data and illustrate it with an experimental example. The results show that the introduction of compactness can improve identifiability.
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Affiliation(s)
- Luis Fábregas-Ibáñez
- ETH Zurich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, Zurich 8093, Switzerland.
| | - Gunnar Jeschke
- ETH Zurich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, Zurich 8093, Switzerland
| | - Stefan Stoll
- University of Washington, Department of Chemistry, Seattle, WA 98195, USA
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72
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Prybutok AN, Cain JY, Leonard JN, Bagheri N. Fighting fire with fire: deploying complexity in computational modeling to effectively characterize complex biological systems. Curr Opin Biotechnol 2022; 75:102704. [DOI: 10.1016/j.copbio.2022.102704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2021] [Revised: 01/27/2022] [Accepted: 02/06/2022] [Indexed: 11/03/2022]
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73
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Dynamic Modeling of Crop–Soil Systems to Design Monitoring and Automatic Irrigation Processes: A Review with Worked Examples. WATER 2022. [DOI: 10.3390/w14060889] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
The smart use of water is a key factor in increasing food production. Over the years, irrigation has relied on historical data and traditional management policies. Control techniques have been exploited to build automatic irrigation systems based on climatic records and weather forecasts. However, climate change and new sources of information motivate better irrigation strategies that might take advantage of the new sources of information in the spectrum of systems and control methodologies in a more systematic way. In this connection, two open questions deserve interest: (i) How can one deal with the space–time variability of soil conditions? (ii) How can one provide robustness to an irrigation system under unexpected environmental change? In this review, the different elements of an automatic control system are described, including the mathematical modeling of the crop–soil systems, instrumentation and actuation, model identification and validation from experimental data, estimation of non-measured variables and sensor fusion, and predictive control based on crop–soil and weather models. An overview of the literature is given, and several specific examples are worked out for illustration purposes.
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74
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Symmetries in Dynamic Models of Biological Systems: Mathematical Foundations and Implications. Symmetry (Basel) 2022. [DOI: 10.3390/sym14030467] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Symmetries are ubiquitous in nature. Almost all organisms have some kind of “symmetry”, meaning that their shape does not change under some geometric transformation. This geometrical concept of symmetry is intuitive and easy to recognize. On the other hand, the behavior of many biological systems over time can be described with ordinary differential equations. These dynamic models may also possess “symmetries”, meaning that the time courses of some variables remain invariant under certain transformations. Unlike the previously mentioned symmetries, the ones present in dynamic models are not geometric, but infinitesimal transformations. These mathematical symmetries can be related to certain features of the system’s dynamic behavior, such as robustness or adaptation capabilities. However, they can also arise from questionable modeling choices, which may lead to non-identifiability and non-observability. This paper provides an overview of the types of symmetries that appear in dynamic models, the mathematical tools available for their analyses, the ways in which they are related to system properties, and the implications for biological modeling.
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75
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Litwin T, Timmer J, Kreutz C. Optimal Experimental Design Based on Two-Dimensional Likelihood Profiles. Front Mol Biosci 2022; 9:800856. [PMID: 35281278 PMCID: PMC8906444 DOI: 10.3389/fmolb.2022.800856] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2021] [Accepted: 01/07/2022] [Indexed: 11/13/2022] Open
Abstract
Dynamic behavior of biological systems is commonly represented by non-linear models such as ordinary differential equations. A frequently encountered task in such systems is the estimation of model parameters based on measurement of biochemical compounds. Non-linear models require special techniques to estimate the uncertainty of the obtained model parameters and predictions, e.g. by exploiting the concept of the profile likelihood. Model parameters with significant uncertainty associated with their estimates hinder the interpretation of model results. Informing these model parameters by optimal experimental design minimizes the additional amount of data and therefore resources required in experiments. However, existing techniques of experimental design either require prior parameter distributions in Bayesian approaches or do not adequately deal with the non-linearity of the system in frequentist approaches. For identification of optimal experimental designs, we propose a two-dimensional profile likelihood approach, providing a design criterion which meaningfully represents the expected parameter uncertainty after measuring data for a specified experimental condition. The described approach is implemented into the open source toolbox Data2Dynamics in Matlab. The applicability of the method is demonstrated on an established systems biology model. For this demonstration, available data has been censored to simulate a setting in which parameters are not yet well determined. After determining the optimal experimental condition from the censored ones, a realistic evaluation was possible by re-introducing the censored data point corresponding to the optimal experimental condition. This provided a validation that our method is feasible in real-world applications. The approach applies to, but is not limited to, models in systems biology.
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Affiliation(s)
- Tim Litwin
- Institute of Medical Biometry and Statistics (IMBI), Faculty of Medicine and Medical Center, University of Freiburg, Freiburg, Germany
- Freiburg Center for Data Analysis and Modelling (FDM), University of Freiburg, Freiburg, Germany
- Institute of Physics, University of Freiburg, Freiburg, Germany
- *Correspondence: Tim Litwin,
| | - Jens Timmer
- Freiburg Center for Data Analysis and Modelling (FDM), University of Freiburg, Freiburg, Germany
- Institute of Physics, University of Freiburg, Freiburg, Germany
- Centre for Integrative Biological Signalling Studies (CIBSS), University of Freiburg, Freiburg, Germany
| | - Clemens Kreutz
- Institute of Medical Biometry and Statistics (IMBI), Faculty of Medicine and Medical Center, University of Freiburg, Freiburg, Germany
- Freiburg Center for Data Analysis and Modelling (FDM), University of Freiburg, Freiburg, Germany
- Centre for Integrative Biological Signalling Studies (CIBSS), University of Freiburg, Freiburg, Germany
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76
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Dray KE, Muldoon JJ, Mangan NM, Bagheri N, Leonard JN. GAMES: A Dynamic Model Development Workflow for Rigorous Characterization of Synthetic Genetic Systems. ACS Synth Biol 2022; 11:1009-1029. [PMID: 35023730 PMCID: PMC9097825 DOI: 10.1021/acssynbio.1c00528] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Mathematical modeling is invaluable for advancing understanding and design of synthetic biological systems. However, the model development process is complicated and often unintuitive, requiring iteration on various computational tasks and comparisons with experimental data. Ad hoc model development can pose a barrier to reproduction and critical analysis of the development process itself, reducing the potential impact and inhibiting further model development and collaboration. To help practitioners manage these challenges, we introduce the Generation and Analysis of Models for Exploring Synthetic Systems (GAMES) workflow, which includes both automated and human-in-the-loop processes. We systematically consider the process of developing dynamic models, including model formulation, parameter estimation, parameter identifiability, experimental design, model reduction, model refinement, and model selection. We demonstrate the workflow with a case study on a chemically responsive transcription factor. The generalizable workflow presented in this tutorial can enable biologists to more readily build and analyze models for various applications.
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Affiliation(s)
- Kate E. Dray
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA
| | - Joseph J. Muldoon
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA.,Interdisciplinary Biological Sciences Program, Northwestern University, Evanston, IL 60208, USA
| | - Niall M. Mangan
- Engineering Sciences and Applied Mathematics Program, Northwestern University, Evanston, IL 60208, USA.,Center for Synthetic Biology, Northwestern University, Evanston, IL 60208, USA
| | - Neda Bagheri
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA.,Interdisciplinary Biological Sciences Program, Northwestern University, Evanston, IL 60208, USA.,Center for Synthetic Biology, Northwestern University, Evanston, IL 60208, USA.,Departments of Biology and Chemical Engineering, University of Washington, Seattle, WA 98195, USA.,Co-corresponding authors: Joshua N. Leonard, , Neda Bagheri,
| | - Joshua N. Leonard
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA.,Interdisciplinary Biological Sciences Program, Northwestern University, Evanston, IL 60208, USA.,Center for Synthetic Biology, Northwestern University, Evanston, IL 60208, USA.,Chemistry of Life Processes Institute, and Robert H. Lurie Comprehensive Cancer Center, Northwestern University, Evanston, IL 60208, USA.,Co-corresponding authors: Joshua N. Leonard, , Neda Bagheri,
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77
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Abstract
AbstractTumour spheroid experiments are routinely used to study cancer progression and treatment. Various and inconsistent experimental designs are used, leading to challenges in interpretation and reproducibility. Using multiple experimental designs, live-dead cell staining, and real-time cell cycle imaging, we measure necrotic and proliferation-inhibited regions in over 1000 4D tumour spheroids (3D space plus cell cycle status). By intentionally varying the initial spheroid size and temporal sampling frequencies across multiple cell lines, we collect an abundance of measurements of internal spheroid structure. These data are difficult to compare and interpret. However, using an objective mathematical modelling framework and statistical identifiability analysis we quantitatively compare experimental designs and identify design choices that produce reliable biological insight. Measurements of internal spheroid structure provide the most insight, whereas varying initial spheroid size and temporal measurement frequency is less important. Our general framework applies to spheroids grown in different conditions and with different cell types.
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78
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Duchesne R, Guillemin A, Gandrillon O, Crauste F. Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis. BMC Bioinformatics 2021; 22:478. [PMID: 34607573 PMCID: PMC8489053 DOI: 10.1186/s12859-021-04373-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 08/28/2021] [Indexed: 12/02/2022] Open
Abstract
Background Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities. Results Herein we rather propose a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in the in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition. Conclusions We conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.
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Affiliation(s)
- Ronan Duchesne
- Laboratory of Biology and Modeling of the Cell, CNRS UMR 5239, INSERM U1210, Université de Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, 46 allée d'Italie, 69007, Lyon, France. .,Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, Lyon, France.
| | - Anissa Guillemin
- Laboratory of Biology and Modeling of the Cell, CNRS UMR 5239, INSERM U1210, Université de Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, 46 allée d'Italie, 69007, Lyon, France
| | - Olivier Gandrillon
- Laboratory of Biology and Modeling of the Cell, CNRS UMR 5239, INSERM U1210, Université de Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, 46 allée d'Italie, 69007, Lyon, France.,Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, Lyon, France
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79
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Browning AP, Maclaren OJ, Buenzli PR, Lanaro M, Allenby MC, Woodruff MA, Simpson MJ. Model-based data analysis of tissue growth in thin 3D printed scaffolds. J Theor Biol 2021; 528:110852. [PMID: 34358535 DOI: 10.1016/j.jtbi.2021.110852] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Revised: 07/08/2021] [Accepted: 07/26/2021] [Indexed: 10/24/2022]
Abstract
Tissue growth in three-dimensional (3D) printed scaffolds enables exploration and control of cell behaviour in more biologically realistic geometries than that allowed by traditional 2D cell culture. Cell proliferation and migration in these experiments have yet to be explicitly characterised, limiting the ability of experimentalists to determine the effects of various experimental conditions, such as scaffold geometry, on cell behaviour. We consider tissue growth by osteoblastic cells in melt electro-written scaffolds that comprise thin square pores with sizes that were deliberately increased between experiments. We collect highly detailed temporal measurements of the average cell density, tissue coverage, and tissue geometry. To quantify tissue growth in terms of the underlying cell proliferation and migration processes, we introduce and calibrate a mechanistic mathematical model based on the Porous-Fisher reaction-diffusion equation. Parameter estimates and uncertainty quantification through profile likelihood analysis reveal consistency in the rate of cell proliferation and steady-state cell density between pore sizes. This analysis also serves as an important model verification tool: while the use of reaction-diffusion models in biology is widespread, the appropriateness of these models to describe tissue growth in 3D scaffolds has yet to be explored. We find that the Porous-Fisher model is able to capture features relating to the cell density and tissue coverage, but is not able to capture geometric features relating to the circularity of the tissue interface. Our analysis identifies two distinct stages of tissue growth, suggests several areas for model refinement, and provides guidance for future experimental work that explores tissue growth in 3D printed scaffolds.
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Affiliation(s)
- Alexander P Browning
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia.
| | - Oliver J Maclaren
- Department of Engineering Science, University of Auckland, Auckland 1142, New Zealand
| | - Pascal R Buenzli
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Matthew Lanaro
- School of Mechanical, Medical & Process Engineering, Centre for Biomedical Technologies, Queensland University of Technology, Brisbane, Australia
| | - Mark C Allenby
- School of Mechanical, Medical & Process Engineering, Centre for Biomedical Technologies, Queensland University of Technology, Brisbane, Australia
| | - Maria A Woodruff
- School of Mechanical, Medical & Process Engineering, Centre for Biomedical Technologies, Queensland University of Technology, Brisbane, Australia
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia; ARC Centre of Excellence for Mathematical and Statistical Frontiers, QUT, Australia
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Burgos-Morales O, Gueye M, Lacombe L, Nowak C, Schmachtenberg R, Hörner M, Jerez-Longres C, Mohsenin H, Wagner H, Weber W. Synthetic biology as driver for the biologization of materials sciences. Mater Today Bio 2021; 11:100115. [PMID: 34195591 PMCID: PMC8237365 DOI: 10.1016/j.mtbio.2021.100115] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2021] [Revised: 05/16/2021] [Accepted: 05/18/2021] [Indexed: 01/16/2023] Open
Abstract
Materials in nature have fascinating properties that serve as a continuous source of inspiration for materials scientists. Accordingly, bio-mimetic and bio-inspired approaches have yielded remarkable structural and functional materials for a plethora of applications. Despite these advances, many properties of natural materials remain challenging or yet impossible to incorporate into synthetic materials. Natural materials are produced by living cells, which sense and process environmental cues and conditions by means of signaling and genetic programs, thereby controlling the biosynthesis, remodeling, functionalization, or degradation of the natural material. In this context, synthetic biology offers unique opportunities in materials sciences by providing direct access to the rational engineering of how a cell senses and processes environmental information and translates them into the properties and functions of materials. Here, we identify and review two main directions by which synthetic biology can be harnessed to provide new impulses for the biologization of the materials sciences: first, the engineering of cells to produce precursors for the subsequent synthesis of materials. This includes materials that are otherwise produced from petrochemical resources, but also materials where the bio-produced substances contribute unique properties and functions not existing in traditional materials. Second, engineered living materials that are formed or assembled by cells or in which cells contribute specific functions while remaining an integral part of the living composite material. We finally provide a perspective of future scientific directions of this promising area of research and discuss science policy that would be required to support research and development in this field.
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Affiliation(s)
- O. Burgos-Morales
- École Supérieure de Biotechnologie de Strasbourg - ESBS, University of Strasbourg, Illkirch, 67412, France
- Faculty of Biology, University of Freiburg, Freiburg, 79104, Germany
| | - M. Gueye
- École Supérieure de Biotechnologie de Strasbourg - ESBS, University of Strasbourg, Illkirch, 67412, France
| | - L. Lacombe
- École Supérieure de Biotechnologie de Strasbourg - ESBS, University of Strasbourg, Illkirch, 67412, France
| | - C. Nowak
- École Supérieure de Biotechnologie de Strasbourg - ESBS, University of Strasbourg, Illkirch, 67412, France
- Faculty of Biology, University of Freiburg, Freiburg, 79104, Germany
| | - R. Schmachtenberg
- École Supérieure de Biotechnologie de Strasbourg - ESBS, University of Strasbourg, Illkirch, 67412, France
- Faculty of Biology, University of Freiburg, Freiburg, 79104, Germany
| | - M. Hörner
- Faculty of Biology, University of Freiburg, Freiburg, 79104, Germany
- Signalling Research Centres BIOSS and CIBSS, University of Freiburg, Freiburg, 79104, Germany
| | - C. Jerez-Longres
- Faculty of Biology, University of Freiburg, Freiburg, 79104, Germany
- Signalling Research Centres BIOSS and CIBSS, University of Freiburg, Freiburg, 79104, Germany
- Spemann Graduate School of Biology and Medicine - SGBM, University of Freiburg, Freiburg, 79104, Germany
| | - H. Mohsenin
- Faculty of Biology, University of Freiburg, Freiburg, 79104, Germany
- Signalling Research Centres BIOSS and CIBSS, University of Freiburg, Freiburg, 79104, Germany
| | - H.J. Wagner
- Faculty of Biology, University of Freiburg, Freiburg, 79104, Germany
- Signalling Research Centres BIOSS and CIBSS, University of Freiburg, Freiburg, 79104, Germany
- Department of Biosystems Science and Engineering - D-BSSE, ETH Zurich, Basel, 4058, Switzerland
| | - W. Weber
- Faculty of Biology, University of Freiburg, Freiburg, 79104, Germany
- Signalling Research Centres BIOSS and CIBSS, University of Freiburg, Freiburg, 79104, Germany
- Spemann Graduate School of Biology and Medicine - SGBM, University of Freiburg, Freiburg, 79104, Germany
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