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Velleuer E, Domínguez-Hüttinger E, Rodríguez A, Harris LA, Carlberg C. Concepts of multi-level dynamical modelling: understanding mechanisms of squamous cell carcinoma development in Fanconi anemia. Front Genet 2023; 14:1254966. [PMID: 38028610 PMCID: PMC10652399 DOI: 10.3389/fgene.2023.1254966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 10/18/2023] [Indexed: 12/01/2023] Open
Abstract
Fanconi anemia (FA) is a rare disease (incidence of 1:300,000) primarily based on the inheritance of pathogenic variants in genes of the FA/BRCA (breast cancer) pathway. These variants ultimately reduce the functionality of different proteins involved in the repair of DNA interstrand crosslinks and DNA double-strand breaks. At birth, individuals with FA might present with typical malformations, particularly radial axis and renal malformations, as well as other physical abnormalities like skin pigmentation anomalies. During the first decade of life, FA mostly causes bone marrow failure due to reduced capacity and loss of the hematopoietic stem and progenitor cells. This often makes hematopoietic stem cell transplantation necessary, but this therapy increases the already intrinsic risk of developing squamous cell carcinoma (SCC) in early adult age. Due to the underlying genetic defect in FA, classical chemo-radiation-based treatment protocols cannot be applied. Therefore, detecting and treating the multi-step tumorigenesis process of SCC in an early stage, or even its progenitors, is the best option for prolonging the life of adult FA individuals. However, the small number of FA individuals makes classical evidence-based medicine approaches based on results from randomized clinical trials impossible. As an alternative, we introduce here the concept of multi-level dynamical modelling using large, longitudinally collected genome, proteome- and transcriptome-wide data sets from a small number of FA individuals. This mechanistic modelling approach is based on the "hallmarks of cancer in FA", which we derive from our unique database of the clinical history of over 750 FA individuals. Multi-omic data from healthy and diseased tissue samples of FA individuals are to be used for training constituent models of a multi-level tumorigenesis model, which will then be used to make experimentally testable predictions. In this way, mechanistic models facilitate not only a descriptive but also a functional understanding of SCC in FA. This approach will provide the basis for detecting signatures of SCCs at early stages and their precursors so they can be efficiently treated or even prevented, leading to a better prognosis and quality of life for the FA individual.
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Affiliation(s)
- Eunike Velleuer
- Department of Cytopathology, Heinrich Heine University, Düsseldorf, Germany
- Center for Child and Adolescent Health, Helios Klinikum, Krefeld, Germany
| | - Elisa Domínguez-Hüttinger
- Departamento Düsseldorf Biología Molecular y Biotecnología, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, Ciudad México, Mexico
| | - Alfredo Rodríguez
- Departamento de Medicina Genómica y Toxicología Ambiental, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, Ciudad México, Mexico
- Instituto Nacional de Pediatría, Ciudad México, Mexico
| | - Leonard A. Harris
- Department of Biomedical Engineering, University of Arkansas, Fayetteville, AR, United States
- Interdisciplinary Graduate Program in Cell and Molecular Biology, University of Arkansas, Fayetteville, AR, United States
- Cancer Biology Program, Winthrop P Rockefeller Cancer Institute, University of Arkansas for Medical Sciences, Little Rock, AR, United States
| | - Carsten Carlberg
- Institute of Animal Reproduction and Food Research, Polish Academy of Sciences, Olsztyn, Poland
- School of Medicine, Institute of Biomedicine, University of Eastern Finland, Kuopio, Finland
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2
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Nonlinear programming reformulation of dynamic flux balance analysis models. Comput Chem Eng 2022. [DOI: 10.1016/j.compchemeng.2022.108101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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3
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Thuillier K, Baroukh C, Bockmayr A, Cottret L, Paulevé L, Siegel A. MERRIN: MEtabolic regulation rule INference from time series data. Bioinformatics 2022; 38:ii127-ii133. [PMID: 36124795 DOI: 10.1093/bioinformatics/btac479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
MOTIVATION Many techniques have been developed to infer Boolean regulations from a prior knowledge network (PKN) and experimental data. Existing methods are able to reverse-engineer Boolean regulations for transcriptional and signaling networks, but they fail to infer regulations that control metabolic networks. RESULTS We present a novel approach to infer Boolean rules for metabolic regulation from time-series data and a PKN. Our method is based on a combination of answer set programming and linear programming. By solving both combinatorial and linear arithmetic constraints, we generate candidate Boolean regulations that can reproduce the given data when coupled to the metabolic network. We evaluate our approach on a core regulated metabolic network and show how the quality of the predictions depends on the available kinetic, fluxomics or transcriptomics time-series data. AVAILABILITY AND IMPLEMENTATION Software available at https://github.com/bioasp/merrin. SUPPLEMENTARY INFORMATION Supplementary data are available at https://doi.org/10.5281/zenodo.6670164.
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Affiliation(s)
- Kerian Thuillier
- INRIA, CNRS, IRISA, University of Rennes, Rennes F-35000, France
| | - Caroline Baroukh
- LIPME, INRAE, CNRS, Université de Toulouse, Castanet-Tolosan F-31326, France
| | - Alexander Bockmayr
- Institute of Mathematics, Freie Universität Berlin, Berlin D-14195, Germany
| | - Ludovic Cottret
- LIPME, INRAE, CNRS, Université de Toulouse, Castanet-Tolosan F-31326, France
| | - Loïc Paulevé
- Univ. Bordeaux, Bordeaux INP, CNRS, LaBRI, UMR5800, F-33400 Talence, France
| | - Anne Siegel
- INRIA, CNRS, IRISA, University of Rennes, Rennes F-35000, France
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Liu P, Hu Q, Li L, Liu M, Chen X, Piao C, Liu X. Fast control parameterization optimal control with improved Polak-Ribière-Polyak conjugate gradient implementation for industrial dynamic processes. ISA TRANSACTIONS 2022; 123:188-199. [PMID: 34020789 DOI: 10.1016/j.isatra.2021.05.020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2020] [Revised: 04/09/2021] [Accepted: 05/12/2021] [Indexed: 06/12/2023]
Abstract
This paper proposes a fast control parameterization optimal control algorithm for industrial dynamic process with constraints. Derived from the frame of control variable parameterization (CVP) technique, the proposed method combines an efficient gradient computation strategy with an improved nonlinear optimization computation approach to overcome the challenge of computation efficiency caused by gradients and bounds in optimal control problems. Firstly, a fast gradient computation method based on the costate system of Hamiltonian function is developed to decrease the computational expense of gradients by employing approximate treatments and numerical integration strategy. Then, a trigonometric function transformation scheme is presented to tackle the boundary constraints so that the original optimal control problem is further converted into an unconstrained one. On this basis, an improved restricted Polak-Ribière-Polyak (PRP) conjugate gradient approach is introduced to solve the nonlinear optimization problem by using conjugate gradient iterations and strong Wolfe line search. Meanwhile, to enhance the convergence, a restricting condition is imposed in strong Wolfe line search to create iteration step-length. Finally, the proposed algorithm is implemented on three dynamic processes. The detailed comparison among the classical CVP method, literature results and the proposed method are carried out. Simulation studies show that the proposed fast approach averagely saves more than 90% computation time in contrast to the classical CVP method, demonstrating the effectiveness of the proposed fast optimal control approach.
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Affiliation(s)
- Ping Liu
- College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; State Key Laboratory of Industry Control Technology, College of Control Science & Engineering, Zhejiang University, Hangzhou 310027, China.
| | - Qingquan Hu
- College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
| | - Lei Li
- College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
| | - Mingjie Liu
- College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
| | - Xiaolei Chen
- College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
| | - Changhao Piao
- College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China.
| | - Xinggao Liu
- State Key Laboratory of Industry Control Technology, College of Control Science & Engineering, Zhejiang University, Hangzhou 310027, China
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5
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Ewald J, Rivieccio F, Radosa L, Schuster S, Brakhage AA, Kaleta C. Dynamic optimization reveals alveolar epithelial cells as key mediators of host defense in invasive aspergillosis. PLoS Comput Biol 2021; 17:e1009645. [PMID: 34898608 PMCID: PMC8699926 DOI: 10.1371/journal.pcbi.1009645] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Revised: 12/23/2021] [Accepted: 11/15/2021] [Indexed: 11/18/2022] Open
Abstract
Aspergillus fumigatus is an important human fungal pathogen and its conidia are constantly inhaled by humans. In immunocompromised individuals, conidia can grow out as hyphae that damage lung epithelium. The resulting invasive aspergillosis is associated with devastating mortality rates. Since infection is a race between the innate immune system and the outgrowth of A. fumigatus conidia, we use dynamic optimization to obtain insight into the recruitment and depletion of alveolar macrophages and neutrophils. Using this model, we obtain key insights into major determinants of infection outcome on host and pathogen side. On the pathogen side, we predict in silico and confirm in vitro that germination speed is an important virulence trait of fungal pathogens due to the vulnerability of conidia against host defense. On the host side, we found that epithelial cells, which have been underappreciated, play a role in fungal clearance and are potent mediators of cytokine release. Both predictions were confirmed by in vitro experiments on established cell lines as well as primary lung cells. Further, our model affirms the importance of neutrophils in invasive aspergillosis and underlines that the role of macrophages remains elusive. We expect that our model will contribute to improvement of treatment protocols by focusing on the critical components of immune response to fungi but also fungal virulence traits.
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Affiliation(s)
- Jan Ewald
- Department of Bioinformatics, Friedrich Schiller University Jena, Jena, Germany.,Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), University of Leipzig, Leipzig, Germany
| | - Flora Rivieccio
- Department of Molecular and Applied Microbiology, Leibniz Institute for Natural Product Research and Infection Biology - Hans Knöll Institute (HKI), Jena, Germany.,Department of Microbiology and Molecular Biology, Institute of Microbiology, Friedrich Schiller University Jena, Jena, Germany
| | - Lukáš Radosa
- Department of Molecular and Applied Microbiology, Leibniz Institute for Natural Product Research and Infection Biology - Hans Knöll Institute (HKI), Jena, Germany
| | - Stefan Schuster
- Department of Bioinformatics, Friedrich Schiller University Jena, Jena, Germany
| | - Axel A Brakhage
- Department of Molecular and Applied Microbiology, Leibniz Institute for Natural Product Research and Infection Biology - Hans Knöll Institute (HKI), Jena, Germany.,Department of Microbiology and Molecular Biology, Institute of Microbiology, Friedrich Schiller University Jena, Jena, Germany
| | - Christoph Kaleta
- Research Group Medical Systems Biology, Institute of Experimental Medicine, Kiel University, Kiel, Germany
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Sharp JA, Burrage K, Simpson MJ. Implementation and acceleration of optimal control for systems biology. J R Soc Interface 2021; 18:20210241. [PMID: 34428951 PMCID: PMC8385371 DOI: 10.1098/rsif.2021.0241] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Abstract
Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.
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Affiliation(s)
- Jesse A Sharp
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia
| | - Kevin Burrage
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Australia.,Department of Computer Science, University of Oxford, Oxford OX2 6GG, UK
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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Newmiwaka T, Engelhardt B, Wendland P, Kahl D, Fröhlich H, Kschischo M. SEEDS: data driven inference of structural model errors and unknown inputs for dynamic systems biology. Bioinformatics 2021; 37:1330-1331. [PMID: 32931565 DOI: 10.1093/bioinformatics/btaa786] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Revised: 08/05/2020] [Accepted: 09/03/2020] [Indexed: 11/14/2022] Open
Abstract
SUMMARY Dynamic models formulated as ordinary differential equations can provide information about the mechanistic and causal interactions in biological systems to guide targeted interventions and to design further experiments. Inaccurate knowledge about the structure, functional form and parameters of interactions is a major obstacle to mechanistic modeling. A further challenge is the open nature of biological systems which receive unknown inputs from their environment. The R-package SEEDS implements two recently developed algorithms to infer structural model errors and unknown inputs from output measurements. This information can facilitate efficient model recalibration as well as experimental design in the case of misfits between the initial model and data. AVAILABILITY AND IMPLEMENTATION For the R-package seeds, see the CRAN server https://cran.r-project.org/package=seeds.
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Affiliation(s)
- Tobias Newmiwaka
- Department of Mathematics and Technology, University of Applied Sciences Koblenz, RheinAhrCampus, Remagen 53424, Germany
| | - Benjamin Engelhardt
- Department of Mathematics and Technology, University of Applied Sciences Koblenz, RheinAhrCampus, Remagen 53424, Germany.,Bonn-Aachen International Center for IT (b-it), Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn 53115, Germany.,AbbVie Deutschland GmbH & Co. KG, Clinical Pharmacology and Pharmacometrics, Knollstrasse, Ludwigshafen 67061, Germany
| | - Philipp Wendland
- Department of Mathematics and Technology, University of Applied Sciences Koblenz, RheinAhrCampus, Remagen 53424, Germany
| | - Dominik Kahl
- Department of Mathematics and Technology, University of Applied Sciences Koblenz, RheinAhrCampus, Remagen 53424, Germany
| | - Holger Fröhlich
- Bonn-Aachen International Center for IT (b-it), Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn 53115, Germany
| | - Maik Kschischo
- Department of Mathematics and Technology, University of Applied Sciences Koblenz, RheinAhrCampus, Remagen 53424, Germany
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Hemmerich J, Tenhaef N, Wiechert W, Noack S. pyFOOMB: Python framework for object oriented modeling of bioprocesses. Eng Life Sci 2021; 21:242-257. [PMID: 33716622 PMCID: PMC7923582 DOI: 10.1002/elsc.202000088] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Revised: 12/09/2020] [Accepted: 12/09/2020] [Indexed: 12/21/2022] Open
Abstract
Quantitative characterization of biotechnological production processes requires the determination of different key performance indicators (KPIs) such as titer, rate and yield. Classically, these KPIs can be derived by combining black-box bioprocess modeling with non-linear regression for model parameter estimation. The presented pyFOOMB package enables a guided and flexible implementation of bioprocess models in the form of ordinary differential equation systems (ODEs). By building on Python as powerful and multi-purpose programing language, ODEs can be formulated in an object-oriented manner, which facilitates their modular design, reusability, and extensibility. Once the model is implemented, seamless integration and analysis of the experimental data is supported by various Python packages that are already available. In particular, for the iterative workflow of experimental data generation and subsequent model parameter estimation we employed the concept of replicate model instances, which are linked by common sets of parameters with global or local properties. For the description of multi-stage processes, discontinuities in the right-hand sides of the differential equations are supported via event handling using the freely available assimulo package. Optimization problems can be solved by making use of a parallelized version of the generalized island approach provided by the pygmo package. Furthermore, pyFOOMB in combination with Jupyter notebooks also supports education in bioprocess engineering and the applied learning of Python as scientific programing language. Finally, the applicability and strengths of pyFOOMB will be demonstrated by a comprehensive collection of notebook examples.
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Affiliation(s)
- Johannes Hemmerich
- Institute of Bio‐ and Geosciences ‐ IBG‐1: BiotechnologyForschungszentrum Jülich GmbHJülichGermany
| | - Niklas Tenhaef
- Institute of Bio‐ and Geosciences ‐ IBG‐1: BiotechnologyForschungszentrum Jülich GmbHJülichGermany
| | - Wolfgang Wiechert
- Institute of Bio‐ and Geosciences ‐ IBG‐1: BiotechnologyForschungszentrum Jülich GmbHJülichGermany
- Computational Systems Biotechnology (AVT.CSB)RWTH Aachen UniversityAachenGermany
- Bioeconomy Science Center (BioSC)Forschungszentrum JülichJülichGermany
| | - Stephan Noack
- Institute of Bio‐ and Geosciences ‐ IBG‐1: BiotechnologyForschungszentrum Jülich GmbHJülichGermany
- Bioeconomy Science Center (BioSC)Forschungszentrum JülichJülichGermany
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9
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Mairet F, Bayen T. The promise of dawn: Microalgae photoacclimation as an optimal control problem of resource allocation. J Theor Biol 2021; 515:110597. [PMID: 33476606 DOI: 10.1016/j.jtbi.2021.110597] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Revised: 12/11/2020] [Accepted: 01/14/2021] [Indexed: 11/19/2022]
Abstract
Photosynthetic microorganisms are known to adjust their photosynthetic capacity according to light intensity. This so-called photoacclimation process is thought to maximize growth at equilibrium, but its dynamics under varying conditions remains less understood. To tackle this problem, microalgae growth and photoacclimation are represented by a (coarse-grained) resource allocation model. Using optimal control theory (the Pontryagin maximum principle) and numerical simulations, we determine the optimal strategy of resource allocation to maximize microalgal growth rate over a time horizon. We show that, after a transient, the optimal trajectory approaches the optimal steady state, a behavior known as the turnpike property. Then, a bi-level optimization problem is solved numerically to estimate model parameters from experimental data. The fitted trajectory represents well a Dunaliella tertiolecta culture facing a light down-shift. Finally, we study photoacclimation dynamics under day/night cycle. In the optimal trajectory, the synthesis of the photosynthetic apparatus surprisingly starts a few hours before dawn. This anticipatory behavior has actually been observed both in the laboratory and in the field. This shows the algal predictive capacity and the interest of our method which predicts this phenomenon.
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Affiliation(s)
- Francis Mairet
- Ifremer, Physiology and Biotechnology of Algae Laboratory, rue de l'Ile d'Yeu, 44311 Nantes, France.
| | - Térence Bayen
- Avignon Université, Laboratoire de Mathématiques d'Avignon (EA 2151), F-84018, France.
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10
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Tsiantis N, Banga JR. Using optimal control to understand complex metabolic pathways. BMC Bioinformatics 2020; 21:472. [PMID: 33087041 PMCID: PMC7579911 DOI: 10.1186/s12859-020-03808-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 10/13/2020] [Indexed: 12/16/2022] Open
Abstract
BACKGROUND Optimality principles have been used to explain the structure and behavior of living matter at different levels of organization, from basic phenomena at the molecular level, up to complex dynamics in whole populations. Most of these studies have assumed a single-criteria approach. Such optimality principles have been justified from an evolutionary perspective. In the context of the cell, previous studies have shown how dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point, and a single objective for the optimality criteria. RESULTS Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework which has been designed with scalability and efficiency in mind, including mechanisms to avoid the most common pitfalls. Third, we illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments. CONCLUSIONS We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we also show how to consider general cost/benefit trade-offs. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction or gene regulatory networks.
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Affiliation(s)
- Nikolaos Tsiantis
- Bioprocess Engineering Group, Spanish National Research Council, IIM-CSIC, C/Eduardo Cabello 6, 36208 Vigo, Spain
- Department of Chemical Engineering, University of Vigo, 36310 Vigo, Spain
| | - Julio R. Banga
- Bioprocess Engineering Group, Spanish National Research Council, IIM-CSIC, C/Eduardo Cabello 6, 36208 Vigo, Spain
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11
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Villaverde AF, Tsiantis N, Banga JR. Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models. J R Soc Interface 2019; 16:20190043. [PMID: 31266417 PMCID: PMC6685009 DOI: 10.1098/rsif.2019.0043] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.
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Affiliation(s)
| | - Nikolaos Tsiantis
- 1 Bioprocess Engineering Group , IIM-CSIC , Vigo , Galicia 36208 , Spain.,2 Department of Chemical Engineering , University of Vigo , Vigo , Galicia 36310 , Spain
| | - Julio R Banga
- 1 Bioprocess Engineering Group , IIM-CSIC , Vigo , Galicia 36208 , Spain
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