1
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Braniff N, Pearce T, Lu Z, Astwood M, Forrest WSR, Receno C, Ingalls B. NLoed: A Python Package for Nonlinear Optimal Experimental Design in Systems Biology. ACS Synth Biol 2022; 11:3921-3928. [PMID: 36473701 PMCID: PMC9765746 DOI: 10.1021/acssynbio.2c00131] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Indexed: 12/12/2022]
Abstract
Modeling in systems and synthetic biology relies on accurate parameter estimates and predictions. Accurate model calibration relies, in turn, on data and on how well suited the available data are to a particular modeling task. Optimal experimental design (OED) techniques can be used to identify experiments and data collection procedures that will most efficiently contribute to a given modeling objective. However, implementation of OED is limited by currently available software tools that are not well suited for the diversity of nonlinear models and non-normal data commonly encountered in biological research. Moreover, existing OED tools do not make use of the state-of-the-art numerical tools, resulting in inefficient computation. Here, we present the NLoed software package and demonstrate its use with in vivo data from an optogenetic system in Escherichia coli. NLoed is an open-source Python library providing convenient access to OED methods, with particular emphasis on experimental design for systems biology research. NLoed supports a wide variety of nonlinear, multi-input/output, and dynamic models and facilitates modeling and design of experiments over a wide variety of data types. To support OED investigations, the NLoed package implements maximum likelihood fitting and diagnostic tools, providing a comprehensive modeling workflow. NLoed offers an accessible, modular, and flexible OED tool set suited to the wide variety of experimental scenarios encountered in systems biology research. We demonstrate NLoed's capabilities by applying it to experimental design for characterization of a bacterial optogenetic system.
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Affiliation(s)
- Nathan Braniff
- Department of Applied Mathematics, University of Waterloo, Waterloo, OntarioN2L 3G1, Canada
| | - Taylor Pearce
- Department of Applied Mathematics, University of Waterloo, Waterloo, OntarioN2L 3G1, Canada
| | - Zixuan Lu
- Department of Applied Mathematics, University of Waterloo, Waterloo, OntarioN2L 3G1, Canada
| | - Michael Astwood
- Department of Applied Mathematics, University of Waterloo, Waterloo, OntarioN2L 3G1, Canada
| | - William S. R. Forrest
- Department of Applied Mathematics, University of Waterloo, Waterloo, OntarioN2L 3G1, Canada
| | - Cody Receno
- Department of Applied Mathematics, University of Waterloo, Waterloo, OntarioN2L 3G1, Canada
| | - Brian Ingalls
- Department of Applied Mathematics, University of Waterloo, Waterloo, OntarioN2L 3G1, Canada
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2
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Marsh L, Dufresne E, Byrne HM, Harrington HA. Algebra, Geometry and Topology of ERK Kinetics. Bull Math Biol 2022; 84:137. [PMID: 36273372 PMCID: PMC9588486 DOI: 10.1007/s11538-022-01088-2] [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: 02/27/2022] [Accepted: 09/16/2022] [Indexed: 12/01/2022]
Abstract
The MEK/ERK signalling pathway is involved in cell division, cell specialisation, survival and cell death (Shaul and Seger in Biochim Biophys Acta (BBA)-Mol Cell Res 1773(8):1213–1226, 2007). Here we study a polynomial dynamical system describing the dynamics of MEK/ERK proposed by Yeung et al. (Curr Biol 2019, 10.1016/j.cub.2019.12.052) with their experimental setup, data and known biological information. The experimental dataset is a time-course of ERK measurements in different phosphorylation states following activation of either wild-type MEK or MEK mutations associated with cancer or developmental defects. We demonstrate how methods from computational algebraic geometry, differential algebra, Bayesian statistics and computational algebraic topology can inform the model reduction, identification and parameter inference of MEK variants, respectively. Throughout, we show how this algebraic viewpoint offers a rigorous and systematic analysis of such models.
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Affiliation(s)
- Lewis Marsh
- Mathematical Institute, University of Oxford, Oxford, UK.
- Ludwig Institute for Cancer Research, University of Oxford, Oxford, UK.
| | | | - Helen M Byrne
- Mathematical Institute, University of Oxford, Oxford, UK
- Ludwig Institute for Cancer Research, University of Oxford, Oxford, UK
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3
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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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4
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Sharp JA, Browning AP, Burrage K, Simpson MJ. Parameter estimation and uncertainty quantification using information geometry. J R Soc Interface 2022; 19:20210940. [PMID: 35472269 PMCID: PMC9042578 DOI: 10.1098/rsif.2021.0940] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
In this work, we: (i) review likelihood-based inference for parameter estimation and the construction of confidence regions; and (ii) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar curvature, to supplement typical techniques for uncertainty quantification, such as Bayesian methods, profile likelihood, asymptotic analysis and bootstrapping. These techniques from information geometry provide data-independent insights into uncertainty and identifiability, and can be used to inform data collection decisions. All code used in this work to implement the inference and information geometry techniques is available on GitHub.
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Affiliation(s)
- Jesse A Sharp
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Alexander P Browning
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Kevin Burrage
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia.,ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, Queensland, Australia.,Department of Computer Science, University of Oxford, Oxford, UK
| | - Matthew J Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia.,Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
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5
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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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6
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Villaverde AF, Pathirana D, Fröhlich F, Hasenauer J, Banga JR. A protocol for dynamic model calibration. Brief Bioinform 2022; 23:bbab387. [PMID: 34619769 PMCID: PMC8769694 DOI: 10.1093/bib/bbab387] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2021] [Revised: 08/06/2021] [Accepted: 08/29/2021] [Indexed: 12/23/2022] Open
Abstract
Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.
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Affiliation(s)
- Alejandro F Villaverde
- Universidade de Vigo, Department of Systems Engineering & Control, Vigo 36310, Galicia, Spain
| | - Dilan Pathirana
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn 53115, Germany
| | - Fabian Fröhlich
- Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg 85764, Germany
| | - Jan Hasenauer
- Center for Mathematics, Technische Universität München, Garching 85748, Germany
- Harvard Medical School, Cambridge, MA 02115, USA
| | - Julio R Banga
- Bioprocess Engineering Group, IIM-CSIC, Vigo 36208, Galicia, Spain
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7
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Jashnsaz H, Fox ZR, Hughes JJ, Li G, Munsky B, Neuert G. Diverse Cell Stimulation Kinetics Identify Predictive Signal Transduction Models. iScience 2020; 23:101565. [PMID: 33083733 PMCID: PMC7549069 DOI: 10.1016/j.isci.2020.101565] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2019] [Revised: 08/18/2020] [Accepted: 09/11/2020] [Indexed: 11/28/2022] Open
Abstract
Computationally understanding the molecular mechanisms that give rise to cell signaling responses upon different environmental, chemical, and genetic perturbations is a long-standing challenge that requires models that fit and predict quantitative responses for new biological conditions. Overcoming this challenge depends not only on good models and detailed experimental data but also on the rigorous integration of both. We propose a quantitative framework to perturb and model generic signaling networks using multiple and diverse changing environments (hereafter "kinetic stimulations") resulting in distinct pathway activation dynamics. We demonstrate that utilizing multiple diverse kinetic stimulations better constrains model parameters and enables predictions of signaling dynamics that would be impossible using traditional dose-response or individual kinetic stimulations. To demonstrate our approach, we use experimentally identified models to predict signaling dynamics in normal, mutated, and drug-treated conditions upon multitudes of kinetic stimulations and quantify which proteins and reaction rates are most sensitive to which extracellular stimulations.
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Affiliation(s)
- Hossein Jashnsaz
- Department of Molecular Physiology and Biophysics, School of Medicine, Vanderbilt University, Nashville, TN 37232, USA
| | - Zachary R Fox
- Inria Saclay Ile-de-France, Palaiseau 91120, France.,Institut Pasteur, USR 3756 IP CNRS, Paris 75015, France.,Keck Scholars, School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, USA
| | - Jason J Hughes
- Department of Molecular Physiology and Biophysics, School of Medicine, Vanderbilt University, Nashville, TN 37232, USA
| | - Guoliang Li
- Department of Molecular Physiology and Biophysics, School of Medicine, Vanderbilt University, Nashville, TN 37232, USA
| | - Brian Munsky
- Keck Scholars, School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523, USA.,Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, CO 80523, USA
| | - Gregor Neuert
- Department of Molecular Physiology and Biophysics, School of Medicine, Vanderbilt University, Nashville, TN 37232, USA.,Department of Biomedical Engineering, School of Engineering, Vanderbilt University, Nashville, TN 37232, USA.,Department of Pharmacology, School of Medicine, Vanderbilt University, Nashville, TN 37232, USA
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8
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Loskot P, Atitey K, Mihaylova L. Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks. Front Genet 2019; 10:549. [PMID: 31258548 PMCID: PMC6588029 DOI: 10.3389/fgene.2019.00549] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2019] [Accepted: 05/24/2019] [Indexed: 01/30/2023] Open
Abstract
The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered-perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.
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Affiliation(s)
- Pavel Loskot
- College of Engineering, Swansea University, Swansea, United Kingdom
| | - Komlan Atitey
- College of Engineering, Swansea University, Swansea, United Kingdom
| | - Lyudmila Mihaylova
- Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, United Kingdom
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9
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Identifiability from a Few Species for a Class of Biochemical Reaction Networks. Bull Math Biol 2019; 81:2133-2175. [PMID: 30945101 DOI: 10.1007/s11538-019-00594-0] [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: 11/20/2018] [Accepted: 03/04/2019] [Indexed: 10/27/2022]
Abstract
Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of a class of biochemical networks which are abundant, such as multisite phosphorylation systems and phosphorylation cascades (for example, MAPK cascades). For any system of this class, we explicitly exhibit a single species for each connected component of the associated digraph such that the successive total derivatives of its concentration allow us to identify all the parameters occurring in the component. The number of derivatives needed is bounded essentially by the length of the corresponding connected component of the digraph. Moreover, in the particular case of the cascades, we show that the parameters can be identified from a bounded number of successive derivatives of the last product of the last layer. This theoretical result induces also a heuristic interpolation-based identifiability procedure to recover the values of the rate constants from exact measurements.
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10
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Prediction of Optimal Drug Schedules for Controlling Autophagy. Sci Rep 2019; 9:1428. [PMID: 30723233 PMCID: PMC6363771 DOI: 10.1038/s41598-019-38763-9] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Accepted: 12/27/2018] [Indexed: 12/19/2022] Open
Abstract
The effects of molecularly targeted drug perturbations on cellular activities and fates are difficult to predict using intuition alone because of the complex behaviors of cellular regulatory networks. An approach to overcoming this problem is to develop mathematical models for predicting drug effects. Such an approach beckons for co-development of computational methods for extracting insights useful for guiding therapy selection and optimizing drug scheduling. Here, we present and evaluate a generalizable strategy for identifying drug dosing schedules that minimize the amount of drug needed to achieve sustained suppression or elevation of an important cellular activity/process, the recycling of cytoplasmic contents through (macro)autophagy. Therapeutic targeting of autophagy is currently being evaluated in diverse clinical trials but without the benefit of a control engineering perspective. Using a nonlinear ordinary differential equation (ODE) model that accounts for activating and inhibiting influences among protein and lipid kinases that regulate autophagy (MTORC1, ULK1, AMPK and VPS34) and methods guaranteed to find locally optimal control strategies, we find optimal drug dosing schedules (open-loop controllers) for each of six classes of drugs and drug pairs. Our approach is generalizable to designing monotherapy and multi therapy drug schedules that affect different cell signaling networks of interest.
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11
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Lugagne JB, Dunlop MJ. Cell-machine interfaces for characterizing gene regulatory network dynamics. ACTA ACUST UNITED AC 2019; 14:1-8. [PMID: 31579842 DOI: 10.1016/j.coisb.2019.01.001] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Gene regulatory networks and the dynamic responses they produce offer a wealth of information about how biological systems process information about their environment. Recently, researchers interested in dissecting these networks have been outsourcing various parts of their experimental workflow to computers. Here we review how, using microfluidic or optogenetic tools coupled with fluorescence imaging, it is now possible to interface cells and computers. These platforms enable scientists to perform informative dynamic stimulations of genetic pathways and monitor their reaction. It is also possible to close the loop and regulate genes in real time, providing an unprecedented view of how signals propagate through the network. Finally, we outline new tools that can be used within the framework of cell-machine interfaces.
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Affiliation(s)
- Jean-Baptiste Lugagne
- Department of Biomedical Engineering, Boston University, Boston, MA, USA.,Biological Design Center, Boston University, Boston, MA, USA
| | - Mary J Dunlop
- Department of Biomedical Engineering, Boston University, Boston, MA, USA.,Biological Design Center, Boston University, Boston, MA, USA
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12
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Component Characterization in a Growth-Dependent Physiological Context: Optimal Experimental Design. Processes (Basel) 2019. [DOI: 10.3390/pr7010052] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Synthetic biology design challenges have driven the use of mathematical models to characterize genetic components and to explore complex design spaces. Traditional approaches to characterization have largely ignored the effect of strain and growth conditions on the dynamics of synthetic genetic circuits, and have thus confounded intrinsic features of the circuit components with cell-level context effects. We present a model that distinguishes an activated gene’s intrinsic kinetics from its physiological context. We then demonstrate an optimal experimental design approach to identify dynamic induction experiments for efficient estimation of the component’s intrinsic parameters. Maximally informative experiments are chosen by formulating the design as an optimal control problem; direct multiple-shooting is used to identify the optimum. Our numerical results suggest that the intrinsic parameters of a genetic component can be more accurately estimated using optimal experimental designs, and that the choice of growth rates, sampling schedule, and input profile each play an important role. The proposed approach to coupled component–host modelling can support gene circuit design across a range of physiological conditions.
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13
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Braniff N, Richards A, Ingalls B. Optimal Experimental Design for a Bistable Gene Regulatory Network. ACTA ACUST UNITED AC 2019. [DOI: 10.1016/j.ifacol.2019.12.267] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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14
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15
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New opportunities for optimal design of dynamic experiments in systems and synthetic biology. ACTA ACUST UNITED AC 2018. [DOI: 10.1016/j.coisb.2018.02.005] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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16
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17
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Nguyen VK, Klawonn F, Mikolajczyk R, Hernandez-Vargas EA. Analysis of Practical Identifiability of a Viral Infection Model. PLoS One 2016; 11:e0167568. [PMID: 28036339 PMCID: PMC5201286 DOI: 10.1371/journal.pone.0167568] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2016] [Accepted: 11/16/2016] [Indexed: 11/27/2022] Open
Abstract
Mathematical modelling approaches have granted a significant contribution to life sciences and beyond to understand experimental results. However, incomplete and inadequate assessments in parameter estimation practices hamper the parameter reliability, and consequently the insights that ultimately could arise from a mathematical model. To keep the diligent works in modelling biological systems from being mistrusted, potential sources of error must be acknowledged. Employing a popular mathematical model in viral infection research, existing means and practices in parameter estimation are exemplified. Numerical results show that poor experimental data is a main source that can lead to erroneous parameter estimates despite the use of innovative parameter estimation algorithms. Arbitrary choices of initial conditions as well as data asynchrony distort the parameter estimates but are often overlooked in modelling studies. This work stresses the existence of several sources of error buried in reports of modelling biological systems, voicing the need for assessing the sources of error, consolidating efforts in solving the immediate difficulties, and possibly reconsidering the use of mathematical modelling to quantify experimental data.
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Affiliation(s)
- Van Kinh Nguyen
- Systems Medicine of Infectious Diseases, Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig, Germany
- Epidemiology Department, Ho Chi Minh University of Medicine and Pharmacy, Ho Chi Minh, Vietnam
- PhD Programme “Epidemiology”, Braunschweig-Hannover, Germany
| | - Frank Klawonn
- Biostatistics, Helmholtz Centre for Infection Research, Braunschweig, Germany
- Department of Computer Science, Ostfalia University, Wolfenbüttel, Germany
| | - Rafael Mikolajczyk
- Epidemiological and Statistical Methods, Helmholtz Centre for Infection Research, Braunschweig, Germany
- German Centre for Infection Research, site Hannover-Braunschweig, Germany
- Hannover Medical School, Hannover, Germany
- [Institute of] Medical Epidemiology, Biometry and Informatics, Martin-Luther University Halle-Wittenberg, Germany
| | - Esteban A. Hernandez-Vargas
- Systems Medicine of Infectious Diseases, Department of Systems Immunology and Braunschweig Integrated Centre of Systems Biology, Helmholtz Centre for Infection Research, Braunschweig, Germany
- * E-mail:
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On the relationship between sloppiness and identifiability. Math Biosci 2016; 282:147-161. [DOI: 10.1016/j.mbs.2016.10.009] [Citation(s) in RCA: 50] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Revised: 10/21/2016] [Accepted: 10/23/2016] [Indexed: 01/15/2023]
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19
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Heinemann T, Raue A. Model calibration and uncertainty analysis in signaling networks. Curr Opin Biotechnol 2016; 39:143-149. [PMID: 27085224 DOI: 10.1016/j.copbio.2016.04.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2015] [Revised: 03/27/2016] [Accepted: 04/01/2016] [Indexed: 10/22/2022]
Abstract
For a long time the biggest challenges in modeling cellular signal transduction networks has been the inference of crucial pathway components and the qualitative description of their interactions. As a result of the emergence of powerful high-throughput experiments, it is now possible to measure data of high temporal and spatial resolution and to analyze signaling dynamics quantitatively. In addition, this increase of high-quality data is the basis for a better understanding of model limitations and their influence on the predictive power of models. We review established approaches in signal transduction network modeling with a focus on ordinary differential equation models as well as related developments in model calibration. As central aspects of the calibration process we discuss possibilities of model adaptation based on data-driven parameter optimization and the concomitant objective of reducing model uncertainties.
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Affiliation(s)
- Tim Heinemann
- Merrimack, One Kendall Sq., Suite B7201, Cambridge, MA 02139, USA
| | - Andreas Raue
- Merrimack, One Kendall Sq., Suite B7201, Cambridge, MA 02139, USA.
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20
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Landry BD, Clarke DC, Lee MJ. Studying Cellular Signal Transduction with OMIC Technologies. J Mol Biol 2015; 427:3416-40. [PMID: 26244521 PMCID: PMC4818567 DOI: 10.1016/j.jmb.2015.07.021] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2015] [Revised: 07/25/2015] [Accepted: 07/27/2015] [Indexed: 11/24/2022]
Abstract
In the gulf between genotype and phenotype exists proteins and, in particular, protein signal transduction systems. These systems use a relatively limited parts list to respond to a much longer list of extracellular, environmental, and/or mechanical cues with rapidity and specificity. Most signaling networks function in a highly non-linear and often contextual manner. Furthermore, these processes occur dynamically across space and time. Because of these complexities, systems and "OMIC" approaches are essential for the study of signal transduction. One challenge in using OMIC-scale approaches to study signaling is that the "signal" can take different forms in different situations. Signals are encoded in diverse ways such as protein-protein interactions, enzyme activities, localizations, or post-translational modifications to proteins. Furthermore, in some cases, signals may be encoded only in the dynamics, duration, or rates of change of these features. Accordingly, systems-level analyses of signaling may need to integrate multiple experimental and/or computational approaches. As the field has progressed, the non-triviality of integrating experimental and computational analyses has become apparent. Successful use of OMIC methods to study signaling will require the "right" experiments and the "right" modeling approaches, and it is critical to consider both in the design phase of the project. In this review, we discuss common OMIC and modeling approaches for studying signaling, emphasizing the philosophical and practical considerations for effectively merging these two types of approaches to maximize the probability of obtaining reliable and novel insights into signaling biology.
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Affiliation(s)
- Benjamin D Landry
- Program in Systems Biology, University of Massachusetts Medical School, Worcester, MA 01605, USA
| | - David C Clarke
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, V5A 1S6 Canada
| | - Michael J Lee
- Program in Systems Biology, University of Massachusetts Medical School, Worcester, MA 01605, USA; Program in Molecular Medicine, Department of Molecular, Cell, and Cancer Biology, University of Massachusetts Medical School, Worcester, MA 01605, USA.
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21
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Yu H, Yue H, Halling P. Optimal Experimental Design for an Enzymatic Biodiesel Production System. ACTA ACUST UNITED AC 2015. [DOI: 10.1016/j.ifacol.2015.09.141] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
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22
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Hagen DR, Tidor B. Efficient Bayesian estimates for discrimination among topologically different systems biology models. MOLECULAR BIOSYSTEMS 2014; 11:574-84. [PMID: 25460000 DOI: 10.1039/c4mb00276h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A major effort in systems biology is the development of mathematical models that describe complex biological systems at multiple scales and levels of abstraction. Determining the topology-the set of interactions-of a biological system from observations of the system's behavior is an important and difficult problem. Here we present and demonstrate new methodology for efficiently computing the probability distribution over a set of topologies based on consistency with existing measurements. Key features of the new approach include derivation in a Bayesian framework, incorporation of prior probability distributions of topologies and parameters, and use of an analytically integrable linearization based on the Fisher information matrix that is responsible for large gains in efficiency. The new method was demonstrated on a collection of four biological topologies representing a kinase and phosphatase that operate in opposition to each other with either processive or distributive kinetics, giving 8-12 parameters for each topology. The linearization produced an approximate result very rapidly (CPU minutes) that was highly accurate on its own, as compared to a Monte Carlo method guaranteed to converge to the correct answer but at greater cost (CPU weeks). The Monte Carlo method developed and applied here used the linearization method as a starting point and importance sampling to approach the Bayesian answer in acceptable time. Other inexpensive methods to estimate probabilities produced poor approximations for this system, with likelihood estimation showing its well-known bias toward topologies with more parameters and the Akaike and Schwarz Information Criteria showing a strong bias toward topologies with fewer parameters. These results suggest that this linear approximation may be an effective compromise, providing an answer whose accuracy is near the true Bayesian answer, but at a cost near the common heuristics.
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Affiliation(s)
- David R Hagen
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
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23
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Pauwels E, Lajaunie C, Vert JP. A Bayesian active learning strategy for sequential experimental design in systems biology. BMC SYSTEMS BIOLOGY 2014; 8:102. [PMID: 25256134 PMCID: PMC4181721 DOI: 10.1186/s12918-014-0102-6] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/10/2014] [Accepted: 08/14/2014] [Indexed: 11/23/2022]
Abstract
BackgroundDynamical models used in systems biology involve unknown kinetic parameters. Setting these parameters is a bottleneck in many modeling projects. This motivates the estimation of these parameters from empirical data. However, this estimation problem has its own difficulties, the most important one being strong ill-conditionedness. In this context, optimizing experiments to be conducted in order to better estimate a system¿s parameters provides a promising direction to alleviate the difficulty of the task.ResultsBorrowing ideas from Bayesian experimental design and active learning, we propose a new strategy for optimal experimental design in the context of kinetic parameter estimation in systems biology. We describe algorithmic choices that allow to implement this method in a computationally tractable way and make it fully automatic. Based on simulation, we show that it outperforms alternative baseline strategies, and demonstrate the benefit to consider multiple posterior modes of the likelihood landscape, as opposed to traditional schemes based on local and Gaussian approximations.ConclusionThis analysis demonstrates that our new, fully automatic Bayesian optimal experimental design strategy has the potential to support the design of experiments for kinetic parameter estimation in systems biology.
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Affiliation(s)
- Edouard Pauwels
- />CNRS, LAAS, 7 Avenue du Colonel Roche, Toulouse, F-31400 France
- />Université de Toulouse LAAS, Toulouse, F-31400 France
| | - Christian Lajaunie
- />MINES ParisTech, PSL-Research University, CBIO-Centre for Computational Biology, 35 rue Saint-Honoré, Fontainebleau, 77300 France
- />Institut Curie, 26 rue d’Ulm, F-75248, Paris, France
- />INSERM U900, Paris, F-75248 France
| | - Jean-Philippe Vert
- />MINES ParisTech, PSL-Research University, CBIO-Centre for Computational Biology, 35 rue Saint-Honoré, Fontainebleau, 77300 France
- />Institut Curie, 26 rue d’Ulm, F-75248, Paris, France
- />INSERM U900, Paris, F-75248 France
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24
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Villaverde AF, Banga JR. Reverse engineering and identification in systems biology: strategies, perspectives and challenges. J R Soc Interface 2014; 11:20130505. [PMID: 24307566 PMCID: PMC3869153 DOI: 10.1098/rsif.2013.0505] [Citation(s) in RCA: 163] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2013] [Accepted: 11/12/2013] [Indexed: 12/17/2022] Open
Abstract
The interplay of mathematical modelling with experiments is one of the central elements in systems biology. The aim of reverse engineering is to infer, analyse and understand, through this interplay, the functional and regulatory mechanisms of biological systems. Reverse engineering is not exclusive of systems biology and has been studied in different areas, such as inverse problem theory, machine learning, nonlinear physics, (bio)chemical kinetics, control theory and optimization, among others. However, it seems that many of these areas have been relatively closed to outsiders. In this contribution, we aim to compare and highlight the different perspectives and contributions from these fields, with emphasis on two key questions: (i) why are reverse engineering problems so hard to solve, and (ii) what methods are available for the particular problems arising from systems biology?
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Affiliation(s)
| | - Julio R. Banga
- BioProcess Engineering Group, IIM-CSIC, Spanish National Research Council, Vigo 36208, Spain
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Ruess J, Milias-Argeitis A, Lygeros J. Designing experiments to understand the variability in biochemical reaction networks. J R Soc Interface 2013; 10:20130588. [PMID: 23985733 DOI: 10.1098/rsif.2013.0588] [Citation(s) in RCA: 60] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Exploiting the information provided by the molecular noise of a biological process has proved to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single-cell measurements. However, quantifying this additional information a priori, to decide whether a single-cell experiment might be beneficial, is currently only possible in systems where either the chemical master equation is computationally tractable or a Gaussian approximation is appropriate. Here, we provide formulae for computing the information provided by measured means and variances from the first four moments and the parameter derivatives of the first two moments of the underlying process. For stochastic kinetic models for which these moments can be either computed exactly or approximated efficiently, the derived formulae can be used to approximate the information provided by single-cell distribution experiments. Based on this result, we propose an optimal experimental design framework which we employ to compare the utility of dual-reporter and perturbation experiments for quantifying the different noise sources in a simple model of gene expression. Subsequently, we compare the information content of a set of experiments which have been performed in an engineered light-switch gene expression system in yeast and show that well-chosen gene induction patterns may allow one to identify features of the system which remain hidden in unplanned experiments.
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Affiliation(s)
- Jakob Ruess
- Automatic Control Laboratory, ETH Zurich, 8092 Zurich, Switzerland
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26
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Anderson ARA, Tomlin CJ, Couch J, Gallahan D. Mathematics of the Integrative Cancer Biology Program. Interface Focus 2013. [DOI: 10.1098/rsfs.2013.0023] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Alexander R. A. Anderson
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL 33612, USA
| | - Claire J. Tomlin
- Department of Electrical Engineering and Computer Sciences, UC Berkeley, Berkeley, CA 94720, USA
| | - Jennifer Couch
- National Cancer Institute, Division of Cancer Biology, Rockville, MD 20850, USA
| | - Dan Gallahan
- National Cancer Institute, Division of Cancer Biology, Rockville, MD 20850, USA
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