1
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Oliveira RHDM, Annex BH, Popel AS. Endothelial cells signaling and patterning under hypoxia: a mechanistic integrative computational model including the Notch-Dll4 pathway. Front Physiol 2024; 15:1351753. [PMID: 38455844 PMCID: PMC10917925 DOI: 10.3389/fphys.2024.1351753] [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: 12/07/2023] [Accepted: 02/12/2024] [Indexed: 03/09/2024] Open
Abstract
Introduction: Several signaling pathways are activated during hypoxia to promote angiogenesis, leading to endothelial cell patterning, interaction, and downstream signaling. Understanding the mechanistic signaling differences between endothelial cells under normoxia and hypoxia and their response to different stimuli can guide therapies to modulate angiogenesis. We present a novel mechanistic model of interacting endothelial cells, including the main pathways involved in angiogenesis. Methods: We calibrate and fit the model parameters based on well-established modeling techniques that include structural and practical parameter identifiability, uncertainty quantification, and global sensitivity. Results: Our results indicate that the main pathways involved in patterning tip and stalk endothelial cells under hypoxia differ, and the time under hypoxia interferes with how different stimuli affect patterning. Additionally, our simulations indicate that Notch signaling might regulate vascular permeability and establish different Nitric Oxide release patterns for tip/stalk cells. Following simulations with various stimuli, our model suggests that factors such as time under hypoxia and oxygen availability must be considered for EC pattern control. Discussion: This project provides insights into the signaling and patterning of endothelial cells under various oxygen levels and stimulation by VEGFA and is our first integrative approach toward achieving EC control as a method for improving angiogenesis. Overall, our model provides a computational framework that can be built on to test angiogenesis-related therapies by modulation of different pathways, such as the Notch pathway.
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Affiliation(s)
| | - Brian H. Annex
- Medical College of Georgia, Augusta University, Augusta, GA, United States
| | - Aleksander S. Popel
- Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, Baltimore, MD, United States
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2
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Mohammad Mirzaei N, Shahriyari L. Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models. Phys Biol 2024; 21:022001. [PMID: 38330444 DOI: 10.1088/1478-3975/ad2777] [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: 10/07/2023] [Accepted: 02/08/2024] [Indexed: 02/10/2024]
Abstract
Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.
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Affiliation(s)
- Navid Mohammad Mirzaei
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, United States of America
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, United States of America
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3
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Connors BM, Thompson J, Ertmer S, Clark RL, Pfleger BF, Venturelli OS. Control points for design of taxonomic composition in synthetic human gut communities. Cell Syst 2023; 14:1044-1058.e13. [PMID: 38091992 PMCID: PMC10752370 DOI: 10.1016/j.cels.2023.11.007] [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: 08/03/2022] [Revised: 06/22/2023] [Accepted: 11/20/2023] [Indexed: 12/23/2023]
Abstract
Microbial communities offer vast potential across numerous sectors but remain challenging to systematically control. We develop a two-stage approach to guide the taxonomic composition of synthetic microbiomes by precisely manipulating media components and initial species abundances. By combining high-throughput experiments and computational modeling, we demonstrate the ability to predict and design the diversity of a 10-member synthetic human gut community. We reveal that critical environmental factors governing monoculture growth can be leveraged to steer microbial communities to desired states. Furthermore, systematically varied initial abundances drive variation in community assembly and enable inference of pairwise inter-species interactions via a dynamic ecological model. These interactions are overall consistent with conditioned media experiments, demonstrating that specific perturbations to a high-richness community can provide rich information for building dynamic ecological models. This model is subsequently used to design low-richness communities that display low or high temporal taxonomic variability over an extended period. A record of this paper's transparent peer review process is included in the supplemental information.
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Affiliation(s)
- Bryce M Connors
- Department of Biochemistry, University of Wisconsin-Madison, Madison, WI 53706, USA; Department of Chemical & Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Jaron Thompson
- Department of Biochemistry, University of Wisconsin-Madison, Madison, WI 53706, USA; Department of Chemical & Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Sarah Ertmer
- Department of Biochemistry, University of Wisconsin-Madison, Madison, WI 53706, USA; Department of Chemical & Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Ryan L Clark
- Department of Biochemistry, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Brian F Pfleger
- Department of Chemical & Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
| | - Ophelia S Venturelli
- Department of Biochemistry, University of Wisconsin-Madison, Madison, WI 53706, USA; Department of Chemical & Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA; Department of Bacteriology, University of Wisconsin-Madison, Madison, WI 53706, USA.
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4
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Policicchio BB, Cardozo-Ojeda EF, Xu C, Ma D, He T, Raehtz KD, Sivanandham R, Kleinman AJ, Perelson AS, Apetrei C, Pandrea I, Ribeiro RM. CD8 + T cells control SIV infection using both cytolytic effects and non-cytolytic suppression of virus production. Nat Commun 2023; 14:6657. [PMID: 37863982 PMCID: PMC10589330 DOI: 10.1038/s41467-023-42435-8] [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: 08/18/2022] [Accepted: 10/11/2023] [Indexed: 10/22/2023] Open
Abstract
Whether CD8+ T lymphocytes control human immunodeficiency virus infection by cytopathic or non-cytopathic mechanisms is not fully understood. Multiple studies highlighted non-cytopathic effects, but one hypothesis is that cytopathic effects of CD8+ T cells occur before viral production. Here, to examine the role of CD8+ T cells prior to virus production, we treated SIVmac251-infected macaques with an integrase inhibitor combined with a CD8-depleting antibody, or with either reagent alone. We analyzed the ensuing viral dynamics using a mathematical model that included infected cells pre- and post- viral DNA integration to compare different immune effector mechanisms. Macaques receiving the integrase inhibitor alone experienced greater viral load decays, reaching lower nadirs on treatment, than those treated also with the CD8-depleting antibody. Models including CD8+ cell-mediated reduction of viral production (non-cytolytic) were found to best explain the viral profiles across all macaques, in addition an effect in killing infected cells pre-integration (cytolytic) was supported in some of the best models. Our results suggest that CD8+ T cells have both a cytolytic effect on infected cells before viral integration, and a direct, non-cytolytic effect by suppressing viral production.
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Affiliation(s)
- Benjamin B Policicchio
- Department of Infectious Diseases and Microbiology, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | | | - Cuiling Xu
- Department of Pathology, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Dongzhu Ma
- Department of Pathology, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Tianyu He
- Department of Pathology, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Kevin D Raehtz
- Division of Infectious Diseases, Department of Medicine, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Ranjit Sivanandham
- Department of Pathology, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Adam J Kleinman
- Division of Infectious Diseases, Department of Medicine, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Alan S Perelson
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Cristian Apetrei
- Department of Infectious Diseases and Microbiology, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA, 15261, USA
- Division of Infectious Diseases, Department of Medicine, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Ivona Pandrea
- Department of Infectious Diseases and Microbiology, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA, 15261, USA
- Department of Pathology, School of Medicine, University of Pittsburgh, Pittsburgh, PA, 15261, USA
| | - Ruy M Ribeiro
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
- Laboratório de Biomatemática, Faculdade de Medicina da Universidade de Lisboa (previous address), Lisboa, Portugal.
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5
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Beik SP, Harris LA, Kochen MA, Sage J, Quaranta V, Lopez CF. Unified tumor growth mechanisms from multimodel inference and dataset integration. PLoS Comput Biol 2023; 19:e1011215. [PMID: 37406008 DOI: 10.1371/journal.pcbi.1011215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2022] [Accepted: 05/25/2023] [Indexed: 07/07/2023] Open
Abstract
Mechanistic models of biological processes can explain observed phenomena and predict responses to a perturbation. A mathematical model is typically constructed using expert knowledge and informal reasoning to generate a mechanistic explanation for a given observation. Although this approach works well for simple systems with abundant data and well-established principles, quantitative biology is often faced with a dearth of both data and knowledge about a process, thus making it challenging to identify and validate all possible mechanistic hypothesis underlying a system behavior. To overcome these limitations, we introduce a Bayesian multimodel inference (Bayes-MMI) methodology, which quantifies how mechanistic hypotheses can explain a given experimental datasets, and concurrently, how each dataset informs a given model hypothesis, thus enabling hypothesis space exploration in the context of available data. We demonstrate this approach to probe standing questions about heterogeneity, lineage plasticity, and cell-cell interactions in tumor growth mechanisms of small cell lung cancer (SCLC). We integrate three datasets that each formulated different explanations for tumor growth mechanisms in SCLC, apply Bayes-MMI and find that the data supports model predictions for tumor evolution promoted by high lineage plasticity, rather than through expanding rare stem-like populations. In addition, the models predict that in the presence of cells associated with the SCLC-N or SCLC-A2 subtypes, the transition from the SCLC-A subtype to the SCLC-Y subtype through an intermediate is decelerated. Together, these predictions provide a testable hypothesis for observed juxtaposed results in SCLC growth and a mechanistic interpretation for tumor treatment resistance.
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Affiliation(s)
- Samantha P Beik
- Medical Scientist Training Program, Vanderbilt University School of Medicine, Nashville, Tennessee, United States of America
| | - Leonard A Harris
- Department of Biomedical Engineering, University of Arkansas, Fayetteville, Arkansas, United States of America
- Interdisciplinary Graduate Program in Cell & Molecular Biology, University of Arkansas, Fayetteville, Arkansas, United States of America
- Cancer Biology Program, Winthrop P. Rockefeller Cancer Institute, University of Arkansas for Medical Sciences, Little Rock, Arkansas, United States of America
| | - Michael A Kochen
- Department of Bioengineering, University of Washington, Seattle, Washington, United States of America
| | - Julien Sage
- Departments of Pediatrics, Stanford University, Stanford, California, United States of America
- Departments of Genetics, Stanford University, Stanford, California, United States of America
| | - Vito Quaranta
- Program in Chemical and Physical Biology, Vanderbilt University, Nashville, Tennessee, United States of America
- Department of Biochemistry, Vanderbilt University, Nashville, Tennessee, United States of America
| | - Carlos F Lopez
- Department of Biochemistry, Vanderbilt University, Nashville, Tennessee, United States of America
- Altos Laboratories, Redwood City, California, United States of America
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6
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Brummer AB, Xella A, Woodall R, Adhikarla V, Cho H, Gutova M, Brown CE, Rockne RC. Data driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables. Front Immunol 2023; 14:1115536. [PMID: 37256133 PMCID: PMC10226275 DOI: 10.3389/fimmu.2023.1115536] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Accepted: 03/27/2023] [Indexed: 06/01/2023] Open
Abstract
In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.
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Affiliation(s)
- Alexander B. Brummer
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA, United States
- Department of Physics and Astronomy, College of Charleston, Charleston, SC, United States
| | - Agata Xella
- Department of Hemtaology and Hematopoietic Cell Translation and Immuno-Oncology, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA, United States
| | - Ryan Woodall
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA, United States
| | - Vikram Adhikarla
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA, United States
| | - Heyrim Cho
- Department of Mathematics, University of California, Riverside, Riverside, CA, United States
| | - Margarita Gutova
- Department of Stem Cell Biology and Regenerative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA, United States
| | - Christine E. Brown
- Department of Hemtaology and Hematopoietic Cell Translation and Immuno-Oncology, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA, United States
| | - Russell C. Rockne
- Division of Mathematical Oncology, Department of Computational and Quantitative Medicine, Beckman Research Institute, City of Hope National Medical Center, Duarte, CA, United States
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7
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Fajiculay E, Hsu CP. Localization of Noise in Biochemical Networks. ACS OMEGA 2023; 8:3043-3056. [PMID: 36713703 PMCID: PMC9878546 DOI: 10.1021/acsomega.2c06113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/22/2022] [Accepted: 12/27/2022] [Indexed: 06/18/2023]
Abstract
Noise, or uncertainty in biochemical networks, has become an important aspect of many biological problems. Noise can arise and propagate from external factors and probabilistic chemical reactions occurring in small cellular compartments. For species survival, it is important to regulate such uncertainties in executing vital cell functions. Regulated noise can improve adaptability, whereas uncontrolled noise can cause diseases. Simulation can provide a detailed analysis of uncertainties, but parameters such as rate constants and initial conditions are usually unknown. A general understanding of noise dynamics from the perspective of network structure is highly desirable. In this study, we extended the previously developed law of localization for characterizing noise in terms of (co)variances and developed noise localization theory. With linear noise approximation, we can expand a biochemical network into an extended set of differential equations representing a fictitious network for pseudo-components consisting of variances and covariances, together with chemical species. Through localization analysis, perturbation responses at the steady state of pseudo-components can be summarized into a sensitivity matrix that only requires knowledge of network topology. Our work allows identification of buffering structures at the level of species, variances, and covariances and can provide insights into noise flow under non-steady-state conditions in the form of a pseudo-chemical reaction. We tested noise localization in various systems, and here we discuss its implications and potential applications. Results show that this theory is potentially applicable in discriminating models, scanning network topologies with interesting noise behavior, and designing and perturbing networks with the desired response.
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Affiliation(s)
- Erickson Fajiculay
- Institute
of Chemistry, Academia Sinica, Taipei115201, Taiwan
- Bioinformatics
Program, Institute of Information Science, Taiwan International Graduate
Program, Academia Sinica, Taipei115201, Taiwan
- Institute
of Bioinformatics and Structural Biology, National Tsing Hua University, Hsinchu300044, Taiwan
| | - Chao-Ping Hsu
- Institute
of Chemistry, Academia Sinica, Taipei115201, Taiwan
- Bioinformatics
Program, Institute of Information Science, Taiwan International Graduate
Program, Academia Sinica, Taipei115201, Taiwan
- Physics
Division, National Center for Theoretical
Sciences, Taipei106319, Taiwan
- Genome
and Systems Biology Degree Program, National
Taiwan University, Taipei106319, Taiwan
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8
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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: 4] [Impact Index Per Article: 2.0] [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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9
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Eriksson O, Bhalla US, Blackwell KT, Crook SM, Keller D, Kramer A, Linne ML, Saudargienė A, Wade RC, Hellgren Kotaleski J. Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows. eLife 2022; 11:e69013. [PMID: 35792600 PMCID: PMC9259018 DOI: 10.7554/elife.69013] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 05/13/2022] [Indexed: 12/22/2022] Open
Abstract
Modeling in neuroscience occurs at the intersection of different points of view and approaches. Typically, hypothesis-driven modeling brings a question into focus so that a model is constructed to investigate a specific hypothesis about how the system works or why certain phenomena are observed. Data-driven modeling, on the other hand, follows a more unbiased approach, with model construction informed by the computationally intensive use of data. At the same time, researchers employ models at different biological scales and at different levels of abstraction. Combining these models while validating them against experimental data increases understanding of the multiscale brain. However, a lack of interoperability, transparency, and reusability of both models and the workflows used to construct them creates barriers for the integration of models representing different biological scales and built using different modeling philosophies. We argue that the same imperatives that drive resources and policy for data - such as the FAIR (Findable, Accessible, Interoperable, Reusable) principles - also support the integration of different modeling approaches. The FAIR principles require that data be shared in formats that are Findable, Accessible, Interoperable, and Reusable. Applying these principles to models and modeling workflows, as well as the data used to constrain and validate them, would allow researchers to find, reuse, question, validate, and extend published models, regardless of whether they are implemented phenomenologically or mechanistically, as a few equations or as a multiscale, hierarchical system. To illustrate these ideas, we use a classical synaptic plasticity model, the Bienenstock-Cooper-Munro rule, as an example due to its long history, different levels of abstraction, and implementation at many scales.
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Affiliation(s)
- Olivia Eriksson
- Science for Life Laboratory, School of Electrical Engineering and Computer Science, KTH Royal Institute of TechnologyStockholmSweden
| | - Upinder Singh Bhalla
- National Center for Biological Sciences, Tata Institute of Fundamental ResearchBangaloreIndia
| | - Kim T Blackwell
- Department of Bioengineering, Volgenau School of Engineering, George Mason UniversityFairfaxUnited States
| | - Sharon M Crook
- School of Mathematical and Statistical Sciences, Arizona State UniversityTempeUnited States
| | - Daniel Keller
- Blue Brain Project, École Polytechnique Fédérale de LausanneLausanneSwitzerland
| | - Andrei Kramer
- Science for Life Laboratory, School of Electrical Engineering and Computer Science, KTH Royal Institute of TechnologyStockholmSweden
- Department of Neuroscience, Karolinska InstituteStockholmSweden
| | - Marja-Leena Linne
- Faculty of Medicine and Health Technology, Tampere UniversityTampereFinland
| | - Ausra Saudargienė
- Neuroscience Institute, Lithuanian University of Health SciencesKaunasLithuania
- Department of Informatics, Vytautas Magnus UniversityKaunasLithuania
| | - Rebecca C Wade
- Molecular and Cellular Modeling Group, Heidelberg Institute for Theoretical Studies (HITS)HeidelbergGermany
- Center for Molecular Biology (ZMBH), ZMBH-DKFZ Alliance, University of HeidelbergHeidelbergGermany
- Interdisciplinary Center for Scientific Computing (IWR), Heidelberg UniversityHeidelbergGermany
| | - Jeanette Hellgren Kotaleski
- Science for Life Laboratory, School of Electrical Engineering and Computer Science, KTH Royal Institute of TechnologyStockholmSweden
- Department of Neuroscience, Karolinska InstituteStockholmSweden
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10
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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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11
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Weizbauer RA, Cook DD. Cell wall mechanics: Some new twists. Biophys J 2022; 121:865-868. [PMID: 35235769 PMCID: PMC8943809 DOI: 10.1016/j.bpj.2022.02.017] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Revised: 01/05/2022] [Accepted: 02/09/2022] [Indexed: 11/02/2022] Open
Affiliation(s)
- Renate A Weizbauer
- Department of Plant Biology, Carnegie Institution of Washington, Stanford, California.
| | - Douglas D Cook
- Department of Mechanical Engineering, Brigham Young University, Provo, Utah
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12
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Mertins SD. Capturing Biomarkers and Molecular Targets in Cellular Landscapes From Dynamic Reaction Network Models and Machine Learning. Front Oncol 2022; 11:805592. [PMID: 35127516 PMCID: PMC8813744 DOI: 10.3389/fonc.2021.805592] [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: 10/30/2021] [Accepted: 12/31/2021] [Indexed: 12/02/2022] Open
Abstract
Computational dynamic ODE models of cell function describing biochemical reactions have been created for decades, but on a small scale. Still, they have been highly effective in describing and predicting behaviors. For example, oscillatory phospho-ERK levels were predicted and confirmed in MAPK signaling encompassing both positive and negative feedback loops. These models typically were limited and not adapted to large datasets so commonly found today. But importantly, ODE models describe reaction networks in well-mixed systems representing the cell and can be simulated with ordinary differential equations that are solved deterministically. Stochastic solutions, which can account for noisy reaction networks, in some cases, also improve predictions. Today, dynamic ODE models rarely encompass an entire cell even though it might be expected that an upload of the large genomic, transcriptomic, and proteomic datasets may allow whole cell models. It is proposed here to combine output from simulated dynamic ODE models, completed with omics data, to discover both biomarkers in cancer a priori and molecular targets in the Machine Learning setting.
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Affiliation(s)
- Susan D. Mertins
- Department of Science, Mount St. Mary’s University, Emmitsburg, MD, United States
- Biomedical Informatics and Data Science Directorate, Frederick National Laboratory for Cancer Research, Leidos Biomedical Research, Limited Liability Company (LLC), Frederick, MD, United States
- BioSystems Strategies, Limited Liability Company (LLC), Frederick, MD, United States
- *Correspondence: Susan D. Mertins,
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13
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Deneer A, Fleck C. Mathematical Modelling in Plant Synthetic Biology. Methods Mol Biol 2022; 2379:209-251. [PMID: 35188665 DOI: 10.1007/978-1-0716-1791-5_13] [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] [Indexed: 06/14/2023]
Abstract
Mathematical modelling techniques are integral to current research in plant synthetic biology. Modelling approaches can provide mechanistic understanding of a system, allowing predictions of behaviour and thus providing a tool to help design and analyse biological circuits. In this chapter, we provide an overview of mathematical modelling methods and their significance for plant synthetic biology. Starting with the basics of dynamics, we describe the process of constructing a model over both temporal and spatial scales and highlight crucial approaches, such as stochastic modelling and model-based design. Next, we focus on the model parameters and the techniques required in parameter analysis. We then describe the process of selecting a model based on tests and criteria and proceed to methods that allow closer analysis of the system's behaviour. Finally, we highlight the importance of uncertainty in modelling approaches and how to deal with a lack of knowledge, noisy data, and biological variability; all aspects that play a crucial role in the cooperation between the experimental and modelling components. Overall, this chapter aims to illustrate the importance of mathematical modelling in plant synthetic biology, providing an introduction for those researchers who are working with or working on modelling techniques.
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Affiliation(s)
- Anna Deneer
- Biometris, Department of Mathematical and Statistical Methods, Wageningen University, Wageningen, The Netherlands
| | - Christian Fleck
- ETH Zurich, Department of Biosystems Science and Engineering, Basel, Switzerland.
- Freiburg Institute for Data Analysis and Mathematical Modelling, University of Freiburg, Freiburg im Breisgau, Germany.
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Estrada AC, Irons L, Rego BV, Li G, Tellides G, Humphrey JD. Roles of mTOR in thoracic aortopathy understood by complex intracellular signaling interactions. PLoS Comput Biol 2021; 17:e1009683. [PMID: 34898595 PMCID: PMC8700007 DOI: 10.1371/journal.pcbi.1009683] [Citation(s) in RCA: 10] [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: 09/27/2021] [Revised: 12/23/2021] [Accepted: 11/26/2021] [Indexed: 02/01/2023] Open
Abstract
Thoracic aortopathy–aneurysm, dissection, and rupture–is increasingly responsible for significant morbidity and mortality. Advances in medical genetics and imaging have improved diagnosis and thus enabled earlier prophylactic surgical intervention in many cases. There remains a pressing need, however, to understand better the underlying molecular and cellular mechanisms with the hope of finding robust pharmacotherapies. Diverse studies in patients and mouse models of aortopathy have revealed critical changes in multiple smooth muscle cell signaling pathways that associate with disease, yet integrating information across studies and models has remained challenging. We present a new quantitative network model that includes many of the key smooth muscle cell signaling pathways and validate the model using a detailed data set that focuses on hyperactivation of the mechanistic target of rapamycin (mTOR) pathway and its inhibition using rapamycin. We show that the model can be parameterized to capture the primary experimental findings both qualitatively and quantitatively. We further show that simulating a population of cells by varying receptor reaction weights leads to distinct proteomic clusters within the population, and that these clusters emerge due to a bistable switch driven by positive feedback in the PI3K/AKT/mTOR signaling pathway. Cell signaling drives changes across scales, from altered transcription at the single-cell level to tissue-level growth and remodeling. Studying complex interactions within cell signaling pathways can lead to a better understanding of the progression of disease. In particular, we are interested in how vascular cells can change their phenotype in a way that exacerbates aortopathy, namely, the development of aneurysms, dissections, and rupture. In this study we built a novel cell signaling network model of a vascular smooth muscle cell using archival data and used it to capture the effects of a genetic knock-out and subsequent pharmacologic rescue. We then used the model to simulate populations of smooth muscle cells and found that small perturbations to the strength of signaling can lead to distinct clusters of cells. With further analysis of the network substructures, we found that a positive feedback loop within the network was responsible for the distinct phenotypes we saw in our clusters of simulated cells. We believe that this work not only helps us to understand changes in smooth muscle cell phenotype but also opens the possibility to study other signaling perturbations associated with aortopathy.
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Affiliation(s)
- Ana C. Estrada
- Department of Biomedical Engineering, Yale University; New Haven, Connecticut, United States of America
| | - Linda Irons
- Department of Biomedical Engineering, Yale University; New Haven, Connecticut, United States of America
| | - Bruno V. Rego
- Department of Biomedical Engineering, Yale University; New Haven, Connecticut, United States of America
| | - Guangxin Li
- Department of Surgery, Yale School of Medicine; New Haven, Connecticut, United States of America
| | - George Tellides
- Department of Surgery, Yale School of Medicine; New Haven, Connecticut, United States of America
- Vascular Biology and Therapeutics Program, Yale School of Medicine; New Haven, Connecticut, United States of America
| | - Jay D. Humphrey
- Department of Biomedical Engineering, Yale University; New Haven, Connecticut, United States of America
- Vascular Biology and Therapeutics Program, Yale School of Medicine; New Haven, Connecticut, United States of America
- * E-mail:
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15
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Schmiester L, Weindl D, Hasenauer J. Efficient gradient-based parameter estimation for dynamic models using qualitative data. BIOINFORMATICS (OXFORD, ENGLAND) 2021. [PMID: 34260697 DOI: 10.1101/2021.02.06.430039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
MOTIVATION Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence. RESULTS Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data. AVAILABILITY AND IMPLEMENTATION The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Leonard Schmiester
- Institute of Computational Biology, Helmholtz Zentrum München - German Research Center for Environmental Health, Neuherberg 85764, Germany
- Center for Mathematics, Technische Universität München, Garching 85748, Germany
| | - Daniel Weindl
- Institute of Computational Biology, Helmholtz Zentrum München - German Research Center for Environmental Health, Neuherberg 85764, Germany
| | - Jan Hasenauer
- Institute of Computational Biology, Helmholtz Zentrum München - German Research Center for Environmental Health, Neuherberg 85764, Germany
- Center for Mathematics, Technische Universität München, Garching 85748, Germany
- Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn 53113, Germany
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16
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Lubbock AL, Lopez CF. Programmatic modeling for biological systems. CURRENT OPINION IN SYSTEMS BIOLOGY 2021; 27:100343. [PMID: 34485764 PMCID: PMC8411905 DOI: 10.1016/j.coisb.2021.05.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/30/2023]
Abstract
Computational modeling has become an established technique to encode mathematical representations of cellular processes and gain mechanistic insights that drive testable predictions. These models are often constructed using graphical user interfaces or domain-specific languages, with community standards used for interchange. Models undergo steady state or dynamic analysis, which can include simulation and calibration within a single application, or transfer across various tools. Here, we describe a novel programmatic modeling paradigm, whereby modeling is augmented with software engineering best practices. We focus on Python - a popular programming language with a large scientific package ecosystem. Models can be encoded as programs, adding benefits such as modularity, testing, and automated documentation generators, while still being extensible and exportable to standardized formats for use with external tools if desired. Programmatic modeling is a key technology to enable collaborative model development and enhance dissemination, transparency, and reproducibility.
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Affiliation(s)
- Alexander L.R. Lubbock
- Department of Biochemistry, Vanderbilt University, Nashville, Tennessee 37212, United States of America
- Vanderbilt-Ingram Cancer Center, Vanderbilt University, Nashville Tennessee 37212, United States of America
| | - Carlos F. Lopez
- Department of Biochemistry, Vanderbilt University, Nashville, Tennessee 37212, United States of America
- Vanderbilt-Ingram Cancer Center, Vanderbilt University, Nashville Tennessee 37212, United States of America
- Department of Biomedical Informatics, Vanderbilt University, Nashville, Tennessee 37212, United States of America
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Schmiester L, Weindl D, Hasenauer J. Efficient gradient-based parameter estimation for dynamic models using qualitative data. Bioinformatics 2021; 37:4493-4500. [PMID: 34260697 PMCID: PMC8652033 DOI: 10.1093/bioinformatics/btab512] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/2021] [Revised: 07/02/2021] [Accepted: 07/08/2021] [Indexed: 11/22/2022] Open
Abstract
Motivation Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence. Results Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data. Availability and implementation The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613. Supplementary information Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Leonard Schmiester
- Institute of Computational Biology, Helmholtz Zentrum München-German Research Center for Environmental Health, Neuherberg, 85764, Germany.,Center for Mathematics, Technische Universität München, Garching, 85748, Germany
| | - Daniel Weindl
- Institute of Computational Biology, Helmholtz Zentrum München-German Research Center for Environmental Health, Neuherberg, 85764, Germany
| | - Jan Hasenauer
- Institute of Computational Biology, Helmholtz Zentrum München-German Research Center for Environmental Health, Neuherberg, 85764, Germany.,Center for Mathematics, Technische Universität München, Garching, 85748, Germany.,Faculty of Mathematics and Natural Sciences, University of Bonn, Bonn, 53113, Germany
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18
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Makaryan SZ, Finley SD. An optimal control approach for enhancing natural killer cells' secretion of cytolytic molecules. APL Bioeng 2020; 4:046107. [PMID: 33376936 PMCID: PMC7758091 DOI: 10.1063/5.0024726] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 11/27/2020] [Indexed: 12/31/2022] Open
Abstract
Natural killer (NK) cells are immune effector cells that can detect and lyse cancer cells. However, NK cell exhaustion, a phenotype characterized by reduced secretion of cytolytic models upon serial stimulation, limits the NK cell's ability to lyse cells. In this work, we investigated in silico strategies that counteract the NK cell's reduced secretion of cytolytic molecules. To accomplish this goal, we constructed a mathematical model that describes the dynamics of the cytolytic molecules granzyme B (GZMB) and perforin-1 (PRF1) and calibrated the model predictions to published experimental data using a Bayesian parameter estimation approach. We applied an information-theoretic approach to perform a global sensitivity analysis, from which we found that the suppression of phosphatase activity maximizes the secretion of GZMB and PRF1. However, simply reducing the phosphatase activity is shown to deplete the cell's intracellular pools of GZMB and PRF1. Thus, we added a synthetic Notch (synNotch) signaling circuit to our baseline model as a method for controlling the secretion of GZMB and PRF1 by inhibiting phosphatase activity and increasing production of GZMB and PRF1. We found that the optimal synNotch system depends on the frequency of NK cell stimulation. For only a few rounds of stimulation, the model predicts that inhibition of phosphatase activity leads to more secreted GZMB and PRF1; however, for many rounds of stimulation, the model reveals that increasing production of the cytolytic molecules is the optimal strategy. In total, we developed a mathematical framework that provides actionable insight into engineering robust NK cells for clinical applications.
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Affiliation(s)
- Sahak Z Makaryan
- Department of Biomedical Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Stacey D Finley
- Department of Biomedical Engineering, Mork Family Department of Chemical Engineering and Materials Science, and Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, California 90089, USA
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Mitra ED, Hlavacek WS. Bayesian inference using qualitative observations of underlying continuous variables. Bioinformatics 2020; 36:3177-3184. [PMID: 32049328 PMCID: PMC7214020 DOI: 10.1093/bioinformatics/btaa084] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2019] [Revised: 01/08/2020] [Accepted: 02/03/2020] [Indexed: 01/28/2023] Open
Abstract
MOTIVATION Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of a lack of a statistical interpretation of the objective functions used in optimization. RESULTS We formulated likelihood functions suitable for performing Bayesian UQ using qualitative observations of underlying continuous variables or a combination of qualitative and quantitative data. To demonstrate the resulting UQ capabilities, we analyzed a published model for immunoglobulin E (IgE) receptor signaling using synthetic qualitative and quantitative datasets. Remarkably, estimates of parameter values derived from the qualitative data were nearly as consistent with the assumed ground-truth parameter values as estimates derived from the lower throughput quantitative data. These results provide further motivation for leveraging qualitative data in biological modeling. AVAILABILITY AND IMPLEMENTATION The likelihood functions presented here are implemented in a new release of PyBioNetFit, an open-source application for analyzing Systems Biology Markup Language- and BioNetGen Language-formatted models, available online at www.github.com/lanl/PyBNF. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Eshan D Mitra
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - William S Hlavacek
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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