1
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Cogno N, Axenie C, Bauer R, Vavourakis V. Agent-based modeling in cancer biomedicine: applications and tools for calibration and validation. Cancer Biol Ther 2024; 25:2344600. [PMID: 38678381 PMCID: PMC11057625 DOI: 10.1080/15384047.2024.2344600] [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: 10/30/2023] [Accepted: 04/15/2024] [Indexed: 04/29/2024] Open
Abstract
Computational models are not just appealing because they can simulate and predict the development of biological phenomena across multiple spatial and temporal scales, but also because they can integrate information from well-established in vitro and in vivo models and test new hypotheses in cancer biomedicine. Agent-based models and simulations are especially interesting candidates among computational modeling procedures in cancer research due to the capability to, for instance, recapitulate the dynamics of neoplasia and tumor - host interactions. Yet, the absence of methods to validate the consistency of the results across scales can hinder adoption by turning fine-tuned models into black boxes. This review compiles relevant literature that explores strategies to leverage high-fidelity simulations of multi-scale, or multi-level, cancer models with a focus on verification approached as simulation calibration. We consolidate our review with an outline of modern approaches for agent-based models' validation and provide an ambitious outlook toward rigorous and reliable calibration.
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Affiliation(s)
- Nicolò Cogno
- Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA
- Institute for Condensed Matter Physics, Technische Universit¨at Darmstadt, Darmstadt, Germany
| | - Cristian Axenie
- Computer Science Department and Center for Artificial Intelligence, Technische Hochschule Nürnberg Georg Simon Ohm, Nuremberg, Germany
| | - Roman Bauer
- Nature Inspired Computing and Engineering Research Group, Computer Science Research Centre, University of Surrey, Guildford, UK
| | - Vasileios Vavourakis
- Department of Medical Physics and Biomedical Engineering, University College London, London, UK
- Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus
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2
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Ma C, Gurkan-Cavusoglu E. A comprehensive review of computational cell cycle models in guiding cancer treatment strategies. NPJ Syst Biol Appl 2024; 10:71. [PMID: 38969664 PMCID: PMC11226463 DOI: 10.1038/s41540-024-00397-7] [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: 01/26/2024] [Accepted: 06/24/2024] [Indexed: 07/07/2024] Open
Abstract
This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.
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Affiliation(s)
- Chenhui Ma
- Department of Electrical, Computer and Systems Engineering, Case Western Reserve University, Cleveland, OH, USA.
| | - Evren Gurkan-Cavusoglu
- Department of Electrical, Computer and Systems Engineering, Case Western Reserve University, Cleveland, OH, USA
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3
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Marzban S, Srivastava S, Kartika S, Bravo R, Safriel R, Zarski A, Anderson A, Chung CH, Amelio AL, West J. Spatial interactions modulate tumor growth and immune infiltration. RESEARCH SQUARE 2024:rs.3.rs-3962451. [PMID: 38826398 PMCID: PMC11142313 DOI: 10.21203/rs.3.rs-3962451/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2024]
Abstract
Lenia, a cellular automata framework used in artificial life, provides a natural setting to implement mathematical models of cancer incorporating features such as morphogenesis, homeostasis, motility, reproduction, growth, stimuli response, evolvability, and adaptation. Historically, agent-based models of cancer progression have been constructed with rules that govern birth, death and migration, with attempts to map local rules to emergent global growth dynamics. In contrast, Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining an interaction kernel governing density-dependent growth dynamics. Lenia can recapitulate a range of cancer model classifications including local or global, deterministic or stochastic, non-spatial or spatial, single or multi-population, and off or on-lattice. Lenia is subsequently used to develop data-informed models of 1) single-population growth dynamics, 2) multi-population cell-cell competition models, and 3) cell migration or chemotaxis. Mathematical modeling provides important mechanistic insights. First, short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects. Next, we find that asymmetric interaction tumor-immune kernels lead to poor immune response. Finally, modeling recapitulates immune-ECM interactions where patterns of collagen formation provide immune protection, indicated by an emergent inverse relationship between disease stage and immune coverage.
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Affiliation(s)
- Sadegh Marzban
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Sonal Srivastava
- Dept. of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Sharon Kartika
- Dept. of Biological Sciences, Indian Institute of Science Education and Research Kolkata
| | - Rafael Bravo
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Rachel Safriel
- High School Internship Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Aidan Zarski
- High School Internship Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Alexander Anderson
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Christine H. Chung
- Dept. of Head and Neck-Endocrine Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Antonio L. Amelio
- Dept. of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
- Dept. of Head and Neck-Endocrine Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Jeffrey West
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
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4
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Marzban S, Srivastava S, Kartika S, Bravo R, Safriel R, Zarski A, Anderson A, Chung CH, Amelio AL, West J. Spatial interactions modulate tumor growth and immune infiltration. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.01.10.575036. [PMID: 38370722 PMCID: PMC10871273 DOI: 10.1101/2024.01.10.575036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/20/2024]
Abstract
Direct observation of immune cell trafficking patterns and tumor-immune interactions is unlikely in human tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen formation evolve as a mechanism of immune escape, but the exact nature of the interaction between immune cells and collagen is poorly understood. Spatial data quantifying the degree of collagen fiber alignment in squamous cell carcinomas indicates that late stage disease is associated with highly aligned fibers. Here, we introduce a computational modeling framework (called Lenia) to discriminate between two hypotheses: immune cell migration that moves 1) parallel or 2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-ECM interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. We also illustrate the capabilities of Lenia to model the evolution of tumor progression and immune predation. Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining a kernel cell-cell interaction function that governs tumor growth dynamics under immune predation with immune cell migration. Mathematical modeling provides important mechanistic insights into cell interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interactions drives tumor growth and infiltration.
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Affiliation(s)
- Sadegh Marzban
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Sonal Srivastava
- Dept. of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Sharon Kartika
- Dept. of Biological Sciences, Indian Institute of Science Education and Research Kolkata
| | - Rafael Bravo
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Rachel Safriel
- High School Internship Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Aidan Zarski
- High School Internship Program, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Alexander Anderson
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Christine H. Chung
- Dept. of Head and Neck-Endocrine Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Antonio L. Amelio
- Dept. of Tumor Microenvironment and Metastasis, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
- Dept. of Head and Neck-Endocrine Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
| | - Jeffrey West
- Integrated Mathematical Oncology Dept., H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL
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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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Cotner M, Meng S, Jost T, Gardner A, De Santiago C, Brock A. Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics. Am J Physiol Cell Physiol 2023; 324:C247-C262. [PMID: 36503241 PMCID: PMC9886359 DOI: 10.1152/ajpcell.00185.2022] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2022] [Revised: 11/21/2022] [Accepted: 11/21/2022] [Indexed: 12/15/2022]
Abstract
Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.
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Affiliation(s)
- Michael Cotner
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Sarah Meng
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Tyler Jost
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Andrea Gardner
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Carolina De Santiago
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
| | - Amy Brock
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas
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7
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Rechberger JS, Power BT, Power EA, Nesvick CL, Daniels DJ. H3K27-altered diffuse midline glioma: a paradigm shifting opportunity in direct delivery of targeted therapeutics. Expert Opin Ther Targets 2023; 27:9-17. [PMID: 36744399 PMCID: PMC10165636 DOI: 10.1080/14728222.2023.2177531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
INTRODUCTION Despite much progress, the prognosis for H3K27-altered diffuse midline glioma (DMG), previously known as diffuse intrinsic pontine glioma when located in the brainstem, remains dark and dismal. AREAS COVERED A wealth of research over the past decade has revolutionized our understanding of the molecular basis of DMG, revealing potential targetable vulnerabilities for treatment of this lethal childhood cancer. However, obstacles to successful clinical implementation of novel therapies remain, including effective delivery across the blood-brain barrier (BBB) to the tumor site. Here, we review relevant literature and clinical trials and discuss direct drug delivery via convection-enhanced delivery (CED) as a promising treatment modality for DMG. We outline a comprehensive molecular, pharmacological, and procedural approach that may offer hope for afflicted patients and their families. EXPERT OPINION Challenges remain in successful drug delivery to DMG. While CED and other techniques offer a chance to bypass the BBB, the variables influencing successful intratumoral targeting are numerous and complex. We discuss these variables and potential solutions that could lead to the successful clinical implementation of preclinically promising therapeutic agents.
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Affiliation(s)
- Julian S Rechberger
- Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, USA.,Department of Molecular Pharmacology and Experimental Therapeutics, Mayo Clinic Graduate School of Biomedical Sciences, Rochester, MN, USA
| | - Blake T Power
- Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, USA
| | - Erica A Power
- Loyola University Chicago Stritch School of Medicine, Maywood, IL, USA
| | - Cody L Nesvick
- Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, USA
| | - David J Daniels
- Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, USA.,Department of Molecular Pharmacology and Experimental Therapeutics, Mayo Clinic Graduate School of Biomedical Sciences, Rochester, MN, USA
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8
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Bergman DR, Karikomi MK, Yu M, Nie Q, MacLean AL. Modeling the effects of EMT-immune dynamics on carcinoma disease progression. Commun Biol 2021; 4:983. [PMID: 34408236 PMCID: PMC8373868 DOI: 10.1038/s42003-021-02499-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2020] [Accepted: 07/27/2021] [Indexed: 02/07/2023] Open
Abstract
During progression from carcinoma in situ to an invasive tumor, the immune system is engaged in complex sets of interactions with various tumor cells. Tumor cell plasticity alters disease trajectories via epithelial-to-mesenchymal transition (EMT). Several of the same pathways that regulate EMT are involved in tumor-immune interactions, yet little is known about the mechanisms and consequences of crosstalk between these regulatory processes. Here we introduce a multiscale evolutionary model to describe tumor-immune-EMT interactions and their impact on epithelial cancer progression from in situ to invasive disease. Through simulation of patient cohorts in silico, the model predicts that a controllable region maximizes invasion-free survival. This controllable region depends on properties of the mesenchymal tumor cell phenotype: its growth rate and its immune-evasiveness. In light of the model predictions, we analyze EMT-inflammation-associated data from The Cancer Genome Atlas, and find that association with EMT worsens invasion-free survival probabilities. This result supports the predictions of the model, and leads to the identification of genes that influence outcomes in bladder and uterine cancer, including FGF pathway members. These results suggest new means to delay disease progression, and demonstrate the importance of studying cancer-immune interactions in light of EMT.
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Affiliation(s)
- Daniel R. Bergman
- grid.266093.80000 0001 0668 7243Department of Mathematics, University of California, Irvine, CA USA
| | - Matthew K. Karikomi
- grid.266093.80000 0001 0668 7243Department of Mathematics, University of California, Irvine, CA USA
| | - Min Yu
- grid.42505.360000 0001 2156 6853USC Norris Comprehensive Cancer Center, Keck School of Medicine of the University of Southern California, Los Angeles, CA, USA ,grid.42505.360000 0001 2156 6853Department of Stem Cell Biology and Regenerative Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA USA
| | - Qing Nie
- grid.266093.80000 0001 0668 7243Department of Mathematics, University of California, Irvine, CA USA ,grid.266093.80000 0001 0668 7243Department of Cell and Developmental Biology, University of California, Irvine, CA USA
| | - Adam L. MacLean
- grid.266093.80000 0001 0668 7243Department of Mathematics, University of California, Irvine, CA USA ,grid.42505.360000 0001 2156 6853USC Norris Comprehensive Cancer Center, Keck School of Medicine of the University of Southern California, Los Angeles, CA, USA ,grid.42505.360000 0001 2156 6853Department of Quantitative and Computational Biology, University of Southern California, Los Angeles, CA, USA
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9
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A novel mathematical model of heterogeneous cell proliferation. J Math Biol 2021; 82:34. [PMID: 33712945 DOI: 10.1007/s00285-021-01580-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Revised: 10/21/2020] [Accepted: 02/14/2021] [Indexed: 12/22/2022]
Abstract
We present a novel mathematical model of heterogeneous cell proliferation where the total population consists of a subpopulation of slow-proliferating cells and a subpopulation of fast-proliferating cells. The model incorporates two cellular processes, asymmetric cell division and induced switching between proliferative states, which are important determinants for the heterogeneity of a cell population. As motivation for our model we provide experimental data that illustrate the induced-switching process. Our model consists of a system of two coupled delay differential equations with distributed time delays and the cell densities as functions of time. The distributed delays are bounded and allow for the choice of delay kernel. We analyse the model and prove the nonnegativity and boundedness of solutions, the existence and uniqueness of solutions, and the local stability characteristics of the equilibrium points. We find that the parameters for induced switching are bifurcation parameters and therefore determine the long-term behaviour of the model. Numerical simulations illustrate and support the theoretical findings, and demonstrate the primary importance of transient dynamics for understanding the evolution of many experimental cell populations.
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10
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Hari A, Lobo D. Fluxer: a web application to compute, analyze and visualize genome-scale metabolic flux networks. Nucleic Acids Res 2020; 48:W427-W435. [PMID: 32442279 PMCID: PMC7319574 DOI: 10.1093/nar/gkaa409] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2020] [Revised: 04/20/2020] [Accepted: 05/06/2020] [Indexed: 12/19/2022] Open
Abstract
Next-generation sequencing has paved the way for the reconstruction of genome-scale metabolic networks as a powerful tool for understanding metabolic circuits in any organism. However, the visualization and extraction of knowledge from these large networks comprising thousands of reactions and metabolites is a current challenge in need of user-friendly tools. Here we present Fluxer (https://fluxer.umbc.edu), a free and open-access novel web application for the computation and visualization of genome-scale metabolic flux networks. Any genome-scale model based on the Systems Biology Markup Language can be uploaded to the tool, which automatically performs Flux Balance Analysis and computes different flux graphs for visualization and analysis. The major metabolic pathways for biomass growth or for biosynthesis of any metabolite can be interactively knocked-out, analyzed and visualized as a spanning tree, dendrogram or complete graph using different layouts. In addition, Fluxer can compute and visualize the k-shortest metabolic paths between any two metabolites or reactions to identify the main metabolic routes between two compounds of interest. The web application includes >80 whole-genome metabolic reconstructions of diverse organisms from bacteria to human, readily available for exploration. Fluxer enables the efficient analysis and visualization of genome-scale metabolic models toward the discovery of key metabolic pathways.
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Affiliation(s)
- Archana Hari
- Department of Biological Sciences, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Daniel Lobo
- Department of Biological Sciences, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
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11
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Johnson KE, Howard GR, Morgan D, Brenner EA, Gardner AL, Durrett RE, Mo W, Al’Khafaji A, Sontag ED, Jarrett AM, Yankeelov TE, Brock A. Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer. Phys Biol 2020; 18:016001. [PMID: 33215611 PMCID: PMC8156495 DOI: 10.1088/1478-3975/abb09c] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.
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Affiliation(s)
- Kaitlyn E Johnson
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Grant R Howard
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Daylin Morgan
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Eric A Brenner
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Institute for Cellular and Molecular Biology, The
University of Texas at Austin, Austin, TX, 78712, United States of America
| | - Andrea L Gardner
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Russell E Durrett
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Institute for Cellular and Molecular Biology, The
University of Texas at Austin, Austin, TX, 78712, United States of America
| | - William Mo
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
| | - Aziz Al’Khafaji
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Institute for Cellular and Molecular Biology, The
University of Texas at Austin, Austin, TX, 78712, United States of America
| | - Eduardo D Sontag
- Department of Electrical and Computer Engineering,
Northeastern University, Boston, MA, 02115, United States of America
- Department of Bioengineering, Northeastern University,
Boston, MA, 02115, United States of America
- Laboratory of Systems Pharmacology, Program in Therapeutics
Science, Harvard Medical School, Boston, MA, 02115, United States of America
| | - Angela M Jarrett
- Livestrong Cancer Institutes, Dell Medical School, The
University of Texas at Austin, Austin, TX, 78712, United States of America
- Oden Institute for Computational Engineering and Sciences,
The University of Texas at Austin
| | - Thomas E Yankeelov
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Livestrong Cancer Institutes, Dell Medical School, The
University of Texas at Austin, Austin, TX, 78712, United States of America
- Oden Institute for Computational Engineering and Sciences,
The University of Texas at Austin
- Department of Diagnostic Medicine, The University of Texas
at Austin, Austin, TX, 78712, United States of America
- Department of Oncology, The University of Texas at Austin,
Austin, TX, 78712, United States of America
- Department of Imaging Physics, The MD Anderson Cancer
Center Houston, TX, 77030, United States of America
| | - Amy Brock
- Department of Biomedical Engineering, The University of
Texas at Austin, Austin, TX, 78712, United States of America
- Institute for Cellular and Molecular Biology, The
University of Texas at Austin, Austin, TX, 78712, United States of America
- Livestrong Cancer Institutes, Dell Medical School, The
University of Texas at Austin, Austin, TX, 78712, United States of America
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12
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Mofers A, Perego P, Selvaraju K, Gatti L, Gullbo J, Linder S, D'Arcy P. Analysis of determinants for in vitro resistance to the small molecule deubiquitinase inhibitor b-AP15. PLoS One 2019; 14:e0223807. [PMID: 31639138 PMCID: PMC6804958 DOI: 10.1371/journal.pone.0223807] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Accepted: 09/27/2019] [Indexed: 11/18/2022] Open
Abstract
BACKGROUND b-AP15/VLX1570 are small molecule inhibitors of the ubiquitin specific peptidase 14 (USP14) and ubiquitin carboxyl-terminal hydrolase 5 (UCHL5) deubiquitinases (DUBs) of the 19S proteasome. b-AP15/VLX1570 have been shown to be cytotoxic to cells resistant to bortezomib, raising the possibility that this class of drugs can be used as a second-line therapy for treatment-resistant multiple myeloma. Limited information is available with regard to potential resistance mechanisms to b-AP15/VLX1570. RESULTS We found that b-AP15-induced cell death is cell-cycle dependent and that non-cycling tumor cells may evade b-AP15-induced cell death. Such non-cycling cells may re-enter the proliferative state to form colonies of drug-sensitive cells. Long-term selection of cells with b-AP15 resulted in limited drug resistance (~2-fold) that could be reversed by buthionine sulphoximine, implying altered glutathione (GSH) metabolism as a resistance mechanism. In contrast, drug uptake and overexpression of drug efflux transporters were found not to be associated with b-AP15 resistance. CONCLUSIONS The proteasome DUB inhibitors b-AP15/VLX1570 are cell cycle-active. The slow and incomplete development of resistance towards these compounds is an attractive feature in view of future clinical use.
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Affiliation(s)
- Arjan Mofers
- Department of Medicine and Health, Linköping University, Linköping, Sweden
| | - Paola Perego
- Molecular Pharmacology Unit, Department of Applied Research and Technological Development, Fondazione IRCCS Istituto Nazionale dei Tumori, Milan, Italy
| | - Karthik Selvaraju
- Department of Medicine and Health, Linköping University, Linköping, Sweden
| | - Laura Gatti
- Cerebrovascular Unit, Department of Clinical Neurosciences, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan, Italy
| | - Joachim Gullbo
- Department of Radiology, Oncology and Radiation Science, Section of Oncology, Uppsala University, Uppsala, Sweden
| | - Stig Linder
- Department of Medicine and Health, Linköping University, Linköping, Sweden
- Department of Oncology-Pathology, Karolinska Institutet, Stockholm, Sweden
| | - Padraig D'Arcy
- Department of Medicine and Health, Linköping University, Linköping, Sweden
- * E-mail:
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13
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Harris LA, Beik S, Ozawa PMM, Jimenez L, Weaver AM. Modeling heterogeneous tumor growth dynamics and cell-cell interactions at single-cell and cell-population resolution. CURRENT OPINION IN SYSTEMS BIOLOGY 2019; 17:24-34. [PMID: 32642602 PMCID: PMC7343346 DOI: 10.1016/j.coisb.2019.09.005] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Cancer is a complex, dynamic disease that despite recent advances remains mostly incurable. Inter- and intratumoral heterogeneity are generally considered major drivers of therapy resistance, metastasis, and treatment failure. Recent advances in high-throughput experimentation have produced a wealth of data on tumor heterogeneity and researchers are increasingly turning to mathematical modeling to aid in the interpretation of these complex datasets. In this mini-review, we discuss three important classes of approaches for modeling cellular dynamics within heterogeneous tumors: agent-based models, population dynamics, and multiscale models. An important new focus, for which we provide an example, is the role of intratumoral cell-cell interactions.
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Affiliation(s)
- Leonard A. Harris
- Department of Biochemistry, Vanderbilt University School of Medicine, Nashville, TN, USA
| | - Samantha Beik
- Cancer Biology Graduate Program, Vanderbilt University School of Medicine, Nashville, TN, USA
| | - Patricia M. M. Ozawa
- Department of Cell and Developmental Biology, Vanderbilt University School of Medicine, Nashville, TN, USA
| | - Lizandra Jimenez
- Department of Cell and Developmental Biology, Vanderbilt University School of Medicine, Nashville, TN, USA
| | - Alissa M. Weaver
- Department of Cell and Developmental Biology, Vanderbilt University School of Medicine, Nashville, TN, USA
- Department of Pathology, Microbiology, and Immunology, Vanderbilt University School of Medicine, Nashville, TN, USA
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14
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Akbarpour Ghazani M, Nouri Z, Saghafian M, Soltani M. Mathematical modeling reveals how the density of initial tumor and its distance to parent vessels alter the growth trend of vascular tumors. Microcirculation 2019; 27:e12584. [DOI: 10.1111/micc.12584] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2019] [Revised: 06/10/2019] [Accepted: 08/05/2019] [Indexed: 12/21/2022]
Affiliation(s)
- Mehran Akbarpour Ghazani
- Department of Mechanical Engineering Isfahan University of Technology Isfahan Iran
- Faculty of Mechanical Engineering University of Tabriz Tabriz Iran
| | - Zahra Nouri
- Department of Mechanical Engineering Isfahan University of Technology Isfahan Iran
| | - Mohsen Saghafian
- Department of Mechanical Engineering Isfahan University of Technology Isfahan Iran
| | - Madjid Soltani
- Department of Mechanical Engineering K.N. Toosi University of Technology Tehran Iran
- Advanced Bioengineering Initiative Center Computational Medicine Center K. N. Toosi University of Technology Tehran Iran
- Cancer Biology Research Center Cancer Institute of Iran Tehran University of Medical Sciences Tehran Iran
- Centre for Biotechnology and Bioengineering (CBB) University of Waterloo Waterloo ON Canada
- Department of Electrical and Computer Engineering University of Waterloo Waterloo ON Canada
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15
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Turk M, Simončič U, Roth A, Valentinuzzi D, Jeraj R. Computational modelling of resistance and associated treatment response heterogeneity in metastatic cancers. Phys Med Biol 2019; 64:115001. [PMID: 30790781 DOI: 10.1088/1361-6560/ab0924] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Metastatic cancer patients invariably develop treatment resistance. Different levels of resistance lead to observed heterogeneity in treatment response. The main goal was to evaluate treatment response heterogeneity with a computation model simulating the dynamics of drug-sensitive and drug-resistant cells. Model parameters included proliferation, drug-induced death, transition and proportion of intrinsically resistant cells. The model was benchmarked with imaging metrics extracted from 39 metastatic prostate cancer patients who had 18F-NaF-PET/CT scans performed at baseline and at three cycles into chemotherapy or hormonal therapy. Two initial model assumptions were evaluated: considering only inter-patient heterogeneity and both inter-patient and intra-patient heterogeneity in the proportion of intrinsically resistant cells. The correlation between the median proportion of intrinsically resistant cells and baseline patient-level imaging metrics was assessed with Spearman's rank correlation coefficient. The impact of model parameters on simulated treatment response was evaluated with a sensitivity study. Treatment response after periods of six, nine, and 12 months was predicted with the model. The median predicted range of response for patients treated with both therapies was compared with a Wilcoxon rank sum test. For each patient, the time was calculated when the proportion of disease with a non-favourable response outperformed a favourable response. By taking into account inter-patient and intra-patient heterogeneity in the proportion of intrinsically resistant cells, the model performed significantly better ([Formula: see text]) than by taking into account only inter-patient heterogeneity ([Formula: see text]). The median proportion of intrinsically resistant cells showed a moderate correlation (ρ = 0.55) with mean patient-level uptake, and a low correlation (ρ = 0.36) with the dispersion of mean metastasis-level uptake in a patient. The sensitivity study showed a strong impact of the proportion of intrinsically resistant cells on model behaviour after three cycles of therapy. The difference in the median range of response (MRR) was not significant between cohorts at any time point (p > 0.15). The median time when the proportion of disease with a non-favourable response outperformed the favourable response was eight months, for both cohorts. The model provides an insight into inter-patient and intra-patient heterogeneity in the evolution of treatment resistance.
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Affiliation(s)
- Maruša Turk
- Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia. Author to whom any correspondence should be addressed
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16
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Pouchol C, Trélat E. Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations. JOURNAL OF BIOLOGICAL DYNAMICS 2018; 12:872-893. [PMID: 30353778 DOI: 10.1080/17513758.2018.1515994] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2017] [Accepted: 08/17/2018] [Indexed: 06/08/2023]
Abstract
We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer, and they generalize the usual Lotka-Volterra ordinary differential equations. Our aim is to give conditions under which there is persistence of all species. Through the analysis of a Lyapunov function, our first main result gives a simple and general condition on the matrix of interactions, together with a convergence rate. The second main result establishes another type of condition in the specific case of mutualistic interactions. When either of these conditions is met, we describe which traits are asymptotically selected.
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Affiliation(s)
- Camille Pouchol
- a Laboratoire Jacques-Louis Lions , Sorbonne Universités, Paris , France
- b INRIA Team Mamba , INRIA Paris , Paris , France
| | - Emmanuel Trélat
- a Laboratoire Jacques-Louis Lions , Sorbonne Universités, Paris , France
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17
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Jarrett AM, Lima EABF, Hormuth DA, McKenna MT, Feng X, Ekrut DA, Resende ACM, Brock A, Yankeelov TE. Mathematical models of tumor cell proliferation: A review of the literature. Expert Rev Anticancer Ther 2018; 18:1271-1286. [PMID: 30252552 PMCID: PMC6295418 DOI: 10.1080/14737140.2018.1527689] [Citation(s) in RCA: 51] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
INTRODUCTION A defining hallmark of cancer is aberrant cell proliferation. Efforts to understand the generative properties of cancer cells span all biological scales: from genetic deviations and alterations of metabolic pathways to physical stresses due to overcrowding, as well as the effects of therapeutics and the immune system. While these factors have long been studied in the laboratory, mathematical and computational techniques are being increasingly applied to help understand and forecast tumor growth and treatment response. Advantages of mathematical modeling of proliferation include the ability to simulate and predict the spatiotemporal development of tumors across multiple experimental scales. Central to proliferation modeling is the incorporation of available biological data and validation with experimental data. Areas covered: We present an overview of past and current mathematical strategies directed at understanding tumor cell proliferation. We identify areas for mathematical development as motivated by available experimental and clinical evidence, with a particular emphasis on emerging, non-invasive imaging technologies. Expert commentary: The data required to legitimize mathematical models are often difficult or (currently) impossible to obtain. We suggest areas for further investigation to establish mathematical models that more effectively utilize available data to make informed predictions on tumor cell proliferation.
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Affiliation(s)
- Angela M Jarrett
- a Institute for Computational Engineering and Sciences , The University of Texas at Austin , Austin , USA
- b Livestrong Cancer Institutes , The University of Texas at Austin , Austin , USA
| | - Ernesto A B F Lima
- a Institute for Computational Engineering and Sciences , The University of Texas at Austin , Austin , USA
| | - David A Hormuth
- a Institute for Computational Engineering and Sciences , The University of Texas at Austin , Austin , USA
- b Livestrong Cancer Institutes , The University of Texas at Austin , Austin , USA
| | - Matthew T McKenna
- c Department of Biomedical Engineering , Vanderbilt University , Nashville , USA
| | - Xinzeng Feng
- a Institute for Computational Engineering and Sciences , The University of Texas at Austin , Austin , USA
| | - David A Ekrut
- a Institute for Computational Engineering and Sciences , The University of Texas at Austin , Austin , USA
| | - Anna Claudia M Resende
- a Institute for Computational Engineering and Sciences , The University of Texas at Austin , Austin , USA
- d Department of Computational Modeling , National Laboratory for Scientific Computing , Petrópolis , Brazil
| | - Amy Brock
- b Livestrong Cancer Institutes , The University of Texas at Austin , Austin , USA
- e Department of Biomedical Engineering , The University of Texas at Austin , Austin , USA
| | - Thomas E Yankeelov
- a Institute for Computational Engineering and Sciences , The University of Texas at Austin , Austin , USA
- b Livestrong Cancer Institutes , The University of Texas at Austin , Austin , USA
- e Department of Biomedical Engineering , The University of Texas at Austin , Austin , USA
- f Department of Diagnostic Medicine , The University of Texas at Austin , Austin , USA
- g Department of Oncology , The University of Texas at Austin , Austin , USA
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18
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Howard GR, Johnson KE, Rodriguez Ayala A, Yankeelov TE, Brock A. A multi-state model of chemoresistance to characterize phenotypic dynamics in breast cancer. Sci Rep 2018; 8:12058. [PMID: 30104569 PMCID: PMC6089904 DOI: 10.1038/s41598-018-30467-w] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2018] [Accepted: 07/25/2018] [Indexed: 12/11/2022] Open
Abstract
The development of resistance to chemotherapy is a major cause of treatment failure in breast cancer. While mathematical models describing the dynamics of resistant cancer cell subpopulations have been proposed, experimental validation has been difficult due to the complex nature of resistance that limits the ability of a single phenotypic marker to sufficiently identify the drug resistant subpopulations. We address this problem with a coupled experimental/modeling approach to reveal the composition of drug resistant subpopulations changing in time following drug exposure. We calibrate time-resolved drug sensitivity assays to three mathematical models to interrogate the models' ability to capture drug response dynamics. The Akaike information criterion was employed to evaluate the three models, and it identified a multi-state model incorporating the role of population heterogeneity and cellular plasticity as the optimal model. To validate the model's ability to identify subpopulation composition, we mixed different proportions of wild-type MCF-7 and MCF-7/ADR resistant cells and evaluated the corresponding model output. Our blinded two-state model was able to estimate the proportions of cell types with an R-squared value of 0.857. To the best of our knowledge, this is the first work to combine experimental time-resolved drug sensitivity data with a mathematical model of resistance development.
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Affiliation(s)
- Grant R Howard
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, 78712, USA
- Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas, 78712, USA
| | - Kaitlyn E Johnson
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, 78712, USA
| | - Areli Rodriguez Ayala
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, 78712, USA
| | - Thomas E Yankeelov
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, 78712, USA
- Institute for Computational Engineering Sciences, The University of Texas at Austin, Austin, Texas, 78712, USA
- Livestrong Cancer Institutes, Dell Medical School, The University of Texas at Austin, Austin, Texas, USA
- Diagnostic Medicine, Dell Medical School, The University of Texas at Austin, Austin, Texas, USA
- Oncology, Dell Medical School, The University of Texas at Austin, Austin, Texas, USA
| | - Amy Brock
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas, 78712, USA.
- Institute for Computational Engineering Sciences, The University of Texas at Austin, Austin, Texas, 78712, USA.
- Livestrong Cancer Institutes, Dell Medical School, The University of Texas at Austin, Austin, Texas, USA.
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19
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Picco N, Sahai E, Maini PK, Anderson ARA. Integrating Models to Quantify Environment-Mediated Drug Resistance. Cancer Res 2017; 77:5409-5418. [PMID: 28754669 PMCID: PMC8455089 DOI: 10.1158/0008-5472.can-17-0835] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2017] [Revised: 07/19/2017] [Accepted: 07/19/2017] [Indexed: 11/16/2022]
Abstract
Drug resistance is the single most important driver of cancer treatment failure for modern targeted therapies, and the dialog between tumor and stroma has been shown to modulate the response to molecularly targeted therapies through proliferative and survival signaling. In this work, we investigate interactions between a growing tumor and its surrounding stroma and their role in facilitating the emergence of drug resistance. We used mathematical modeling as a theoretical framework to bridge between experimental models and scales, with the aim of separating intrinsic and extrinsic components of resistance in BRAF-mutated melanoma; the model describes tumor-stroma dynamics both with and without treatment. Integration of experimental data into our model revealed significant variation in either the intensity of stromal promotion or intrinsic tissue carrying capacity across animal replicates. Cancer Res; 77(19); 5409-18. ©2017 AACR.
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Affiliation(s)
- Noemi Picco
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center and Research Institute, Tampa, Florida.
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, United Kingdom
| | - Erik Sahai
- Tumour Cell Biology Laboratory, The Francis Crick Institute, London, United Kingdom
| | - Philip K Maini
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, United Kingdom
| | - Alexander R A Anderson
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center and Research Institute, Tampa, Florida
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20
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Tissot T, Thomas F, Roche B. Non-cell-autonomous effects yield lower clonal diversity in expanding tumors. Sci Rep 2017; 7:11157. [PMID: 28894191 PMCID: PMC5593982 DOI: 10.1038/s41598-017-11562-w] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2017] [Accepted: 08/21/2017] [Indexed: 01/07/2023] Open
Abstract
Recent cancer research has investigated the possibility that non-cell-autonomous (NCA) driving tumor growth can support clonal diversity (CD). Indeed, mutations can affect the phenotypes not only of their carriers (“cell-autonomous”, CA effects), but also sometimes of other cells (NCA effects). However, models that have investigated this phenomenon have only considered a restricted number of clones. Here, we designed an individual-based model of tumor evolution, where clones grow and mutate to yield new clones, among which a given frequency have NCA effects on other clones’ growth. Unlike previously observed for smaller assemblages, most of our simulations yield lower CD with high frequency of mutations with NCA effects. Owing to NCA effects increasing competition in the tumor, clones being already dominant are more likely to stay dominant, and emergent clones not to thrive. These results may help personalized medicine to predict intratumor heterogeneity across different cancer types for which frequency of NCA effects could be quantified.
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Affiliation(s)
- Tazzio Tissot
- CREEC/MIVEGEC, UMR IRD/CNRS/UM 5290, 911 Avenue Agropolis, BP 64501, 34394, Montpellier, Cedex 5, France.
| | - Frédéric Thomas
- CREEC/MIVEGEC, UMR IRD/CNRS/UM 5290, 911 Avenue Agropolis, BP 64501, 34394, Montpellier, Cedex 5, France
| | - Benjamin Roche
- CREEC/MIVEGEC, UMR IRD/CNRS/UM 5290, 911 Avenue Agropolis, BP 64501, 34394, Montpellier, Cedex 5, France.,Unité mixte internationale de Modélisation Mathématique et Informatique des Systèmes Complexes. (UMI IRD/UPMC UMMISCO), 32 Avenue Henri Varagnat, 93143, Bondy Cedex, France
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21
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Lorz A, Botesteanu DA, Levy D. Modeling Cancer Cell Growth Dynamics In vitro in Response to Antimitotic Drug Treatment. Front Oncol 2017; 7:189. [PMID: 28913178 PMCID: PMC5582072 DOI: 10.3389/fonc.2017.00189] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2017] [Accepted: 08/09/2017] [Indexed: 01/06/2023] Open
Abstract
Investigating the role of intrinsic cell heterogeneity emerging from variations in cell-cycle parameters and apoptosis is a crucial step toward better informing drug administration. Antimitotic agents, widely used in chemotherapy, target exclusively proliferative cells and commonly induce a prolonged mitotic arrest followed by cell death via apoptosis. In this paper, we developed a physiologically motivated mathematical framework for describing cancer cell growth dynamics that incorporates the intrinsic heterogeneity in the time individual cells spend in the cell-cycle and apoptosis process. More precisely, our model comprises two age-structured partial differential equations for the proliferative and apoptotic cell compartments and one ordinary differential equation for the quiescent compartment. To reflect the intrinsic cell heterogeneity that governs the growth dynamics, proliferative and apoptotic cells are structured in "age," i.e., the amount of time remaining to be spent in each respective compartment. In our model, we considered an antimitotic drug whose effect on the cellular dynamics is to induce mitotic arrest, extending the average cell-cycle length. The prolonged mitotic arrest induced by the drug can trigger apoptosis if the time a cell will spend in the cell cycle is greater than the mitotic arrest threshold. We studied the drug's effect on the long-term cancer cell growth dynamics using different durations of prolonged mitotic arrest induced by the drug. Our numerical simulations suggest that at confluence and in the absence of the drug, quiescence is the long-term asymptotic behavior emerging from the cancer cell growth dynamics. This pattern is maintained in the presence of small increases in the average cell-cycle length. However, intermediate increases in cell-cycle length markedly decrease the total number of cells and can drive the cancer population to extinction. Intriguingly, a large "switch-on/switch-off" increase in the average cell-cycle length maintains an active cell population in the long term, with oscillating numbers of proliferative cells and a relatively constant quiescent cell number.
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Affiliation(s)
- Alexander Lorz
- CEMSE Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France
| | - Dana-Adriana Botesteanu
- Women’s Malignancies Branch, Center for Cancer Research, National Cancer Institute, Bethesda, MD, United States
- Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, United States
| | - Doron Levy
- Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, United States
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22
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Becker M, Levy D. Modeling the Transfer of Drug Resistance in Solid Tumors. Bull Math Biol 2017; 79:2394-2412. [PMID: 28852953 DOI: 10.1007/s11538-017-0334-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2017] [Accepted: 08/08/2017] [Indexed: 11/30/2022]
Abstract
ABC efflux transporters are a key factor leading to multidrug resistance in cancer. Overexpression of these transporters significantly decreases the efficacy of anti-cancer drugs. Along with selection and induction, drug resistance may be transferred between cells, which is the focus of this paper. Specifically, we consider the intercellular transfer of P-glycoprotein (P-gp), a well-known ABC transporter that was shown to confer resistance to many common chemotherapeutic drugs. In a recent paper, Durán et al. (Bull Math Biol 78(6):1218-1237, 2016) studied the dynamics of mixed cultures of resistant and sensitive NCI-H460 (human non-small lung cancer) cell lines. As expected, the experimental data showed a gradual increase in the percentage of resistance cells and a decrease in the percentage of sensitive cells. The experimental work was accompanied with a mathematical model that assumed P-gp transfer from resistant cells to sensitive cells, rendering them temporarily resistant. The mathematical model provided a reasonable fit to the experimental data. In this paper, we develop a new mathematical model for the transfer of drug resistance between cancer cells. Our model is based on incorporating a resistance phenotype into a model of cancer growth (Greene et al. in J Theor Biol 367:262-277, 2015). The resulting model for P-gp transfer, written as a system of integro-differential equations, follows the dynamics of proliferating, quiescent, and apoptotic cells, with a varying resistance phenotype. We show that this model provides a good match to the dynamics of the experimental data of Durán et al. (2016). The mathematical model shows a better fit when resistant cancer cells have a slower division rate than the sensitive cells.
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Affiliation(s)
- Matthew Becker
- Department of Mathematics, University of Maryland, College Park, MD, 20742, USA
| | - Doron Levy
- Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, 20742, USA.
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23
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Greene JM, Levy D, Herrada SP, Gottesman MM, Lavi O. Mathematical Modeling Reveals That Changes to Local Cell Density Dynamically Modulate Baseline Variations in Cell Growth and Drug Response. Cancer Res 2016; 76:2882-90. [PMID: 26933088 DOI: 10.1158/0008-5472.can-15-3232] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2015] [Accepted: 02/17/2016] [Indexed: 11/16/2022]
Abstract
Cell-to-cell variations contribute to drug resistance with consequent therapy failure in cancer. Experimental techniques have been developed to monitor tumor heterogeneity, but estimates of cell-to-cell variation typically fail to account for the expected spatiotemporal variations during the cell growth process. To fully capture the extent of such dynamic variations, we developed a mechanistic mathematical model supported by in vitro experiments with an ovarian cancer cell line. We introduce the notion of dynamic baseline cell-to-cell variation, showing how the emerging spatiotemporal heterogeneity of one cell population can be attributed to differences in local cell density and cell cycle. Manipulation of the geometric arrangement and spatial density of cancer cells revealed that given a fixed global cell density, significant differences in growth, proliferation, and paclitaxel-induced apoptosis rates were observed based solely on cell movement and local conditions. We conclude that any statistical estimate of changes in the level of heterogeneity should be integrated with the dynamics and spatial effects of the baseline system. This approach incorporates experimental and theoretical methods to systematically analyze biologic phenomena and merits consideration as an underlying reference model for cell biology studies that investigate dynamic processes affecting cancer cell behavior. Cancer Res; 76(10); 2882-90. ©2016 AACR.
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Affiliation(s)
- James M Greene
- Department of Mathematics, Rutgers University, New Brunswick, New Jersey
| | - Doron Levy
- Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Maryland
| | - Sylvia P Herrada
- Laboratory of Cell Biology, Center for Cancer Research, NCI, NIH, Bethesda, Maryland
| | - Michael M Gottesman
- Laboratory of Cell Biology, Center for Cancer Research, NCI, NIH, Bethesda, Maryland
| | - Orit Lavi
- Laboratory of Cell Biology, Center for Cancer Research, NCI, NIH, Bethesda, Maryland.
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24
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Barbolosi D, Ciccolini J, Lacarelle B, Barlési F, André N. Computational oncology — mathematical modelling of drug regimens for precision medicine. Nat Rev Clin Oncol 2015; 13:242-54. [DOI: 10.1038/nrclinonc.2015.204] [Citation(s) in RCA: 144] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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