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Martínez-Calvo A, Trenado-Yuste C, Lee H, Gore J, Wingreen NS, Datta SS. Interfacial morphodynamics of proliferating microbial communities. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.10.23.563665. [PMID: 37961366 PMCID: PMC10634769 DOI: 10.1101/2023.10.23.563665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2023]
Abstract
In microbial communities, various cell types often coexist by occupying distinct spatial domains. What determines the shape of the interface between such domains-which in turn influences the interactions between cells and overall community function? Here, we address this question by developing a continuum model of a 2D spatially-structured microbial community with two distinct cell types. We find that, depending on the balance of the different cell proliferation rates and substrate friction coefficients, the interface between domains is either stable and smooth, or unstable and develops finger-like protrusions. We establish quantitative principles describing when these different interfacial behaviors arise, and find good agreement both with the results of previous experimental reports as well as new experiments performed here. Our work thus helps to provide a biophysical basis for understanding the interfacial morphodynamics of proliferating microbial communities, as well as a broader range of proliferating active systems.
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2
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Uhl P, Lowengrub J, Komarova N, Wodarz D. Spatial dynamics of feedback and feedforward regulation in cell lineages. PLoS Comput Biol 2022; 18:e1010039. [PMID: 35522694 PMCID: PMC9116666 DOI: 10.1371/journal.pcbi.1010039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Revised: 05/18/2022] [Accepted: 03/18/2022] [Indexed: 11/19/2022] Open
Abstract
Feedback mechanisms within cell lineages are thought to be important for maintaining tissue homeostasis. Mathematical models that assume well-mixed cell populations, together with experimental data, have suggested that negative feedback from differentiated cells on the stem cell self-renewal probability can maintain a stable equilibrium and hence homeostasis. Cell lineage dynamics, however, are characterized by spatial structure, which can lead to different properties. Here, we investigate these dynamics using spatially explicit computational models, including cell division, differentiation, death, and migration / diffusion processes. According to these models, the negative feedback loop on stem cell self-renewal fails to maintain homeostasis, both under the assumption of strong spatial restrictions and fast migration / diffusion. Although homeostasis cannot be maintained, this feedback can regulate cell density and promote the formation of spatial structures in the model. Tissue homeostasis, however, can be achieved if spatially restricted negative feedback on self-renewal is combined with an experimentally documented spatial feedforward loop, in which stem cells regulate the fate of transit amplifying cells. This indicates that the dynamics of feedback regulation in tissue cell lineages are more complex than previously thought, and that combinations of spatially explicit control mechanisms are likely instrumental.
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Affiliation(s)
- Peter Uhl
- Department of Mathematics and Statistics, San Diego State University, San Diego, California, United States of America
- Department of Population Health and Disease Prevention, Program in Public Health, University of California, Irvine, California, United States of America
| | - John Lowengrub
- Department of Mathematics, University of California, Irvine, California, United States of America
| | - Natalia Komarova
- Department of Mathematics, University of California, Irvine, California, United States of America
| | - Dominik Wodarz
- Department of Population Health and Disease Prevention, Program in Public Health, University of California, Irvine, California, United States of America
- Department of Mathematics, University of California, Irvine, California, United States of America
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3
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Mathematical Modeling of Tumor and Cancer Stem Cells Treated with CAR-T Therapy and Inhibition of TGF-$$\beta $$. Bull Math Biol 2022; 84:58. [DOI: 10.1007/s11538-022-01015-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Accepted: 03/22/2022] [Indexed: 11/26/2022]
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4
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Comparing the effects of linear and one-term Ogden elasticity in a model of glioblastoma invasion. BRAIN MULTIPHYSICS 2022. [DOI: 10.1016/j.brain.2022.100050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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5
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Vernerey FJ, Lalitha Sridhar S, Muralidharan A, Bryant SJ. Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms. Chem Rev 2021; 121:11085-11148. [PMID: 34473466 DOI: 10.1021/acs.chemrev.1c00046] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.
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Affiliation(s)
- Franck J Vernerey
- Department of Mechanical Engineering, University of Colorado at Boulder, 1111 Engineering Drive, Boulder, Colorado 80309-0428, United States.,Materials Science and Engineering Program, University of Colorado at Boulder, 4001 Discovery Drive, Boulder, Colorado 80309-613, United States
| | - Shankar Lalitha Sridhar
- Department of Mechanical Engineering, University of Colorado at Boulder, 1111 Engineering Drive, Boulder, Colorado 80309-0428, United States
| | - Archish Muralidharan
- Materials Science and Engineering Program, University of Colorado at Boulder, 4001 Discovery Drive, Boulder, Colorado 80309-613, United States
| | - Stephanie J Bryant
- Materials Science and Engineering Program, University of Colorado at Boulder, 4001 Discovery Drive, Boulder, Colorado 80309-613, United States.,Department of Chemical and Biological Engineering, University of Colorado at Boulder, 3415 Colorado Avenue, Boulder, Colorado 80309-0596, United States.,BioFrontiers Institute, University of Colorado at Boulder, 3415 Colorado Avenue, Boulder, Colorado 80309-0596, United States
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6
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NAZARI FERESHTEH, PEARSON ALEXANDERT, JACKSON TRACHETTEL. MATHEMATICAL CHARACTERIZATION OF HETEROGENEITY IN A CANCER STEM CELL DRIVEN TUMOR GROWTH MODEL WITH NONLINEAR SELF-RENEWAL. J BIOL SYST 2021. [DOI: 10.1142/s0218339021500029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The detection, in a wide variety of cancer types, of a population of highly tumorigenic cells that exhibit self-renewal and multipotency, which are hallmarks of stem cells, has transformed the current view of tumor initiation, progression, and treatment. Here, we develop and analyze a mathematical model for tumor growth that is based on the current biological understanding of the processes that underlie cellular expansion under the hierarchical guidelines of the cancer stem cell (CSC) hypothesis. Important features of the model include (i) a nonlinear probability of CSC self-renewal that reflects the fact that this key type of stem cell division can be regulated by extrinsic and intrinsic chemical signaling as well as environmental (niche) constraints and (ii) an amplification factor that captures the transient amplifying divisions that are a defining characteristic of progenitor cells. We present a thorough mathematical analysis of the model and highlight the conditions required for tumors to evolve toward either bounded or exponential growth. Numerical simulations further illustrate the impact of the various parameters on the tumor growth rate and on the heterogeneous cellular composition, which varies during progression.
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Affiliation(s)
- FERESHTEH NAZARI
- Applied BioMath, 210 Broadway, Suite 201, Cambridge, MA 02139, USA
| | - ALEXANDER T PEARSON
- Department of Medicine, Section of Hematology/Oncology, The University of Chicago, Chicago, IL 60637, USA
| | - TRACHETTE L JACKSON
- Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48108-1043, USA
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7
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Weiss LD, van den Driessche P, Lowengrub JS, Wodarz D, Komarova NL. Effect of feedback regulation on stem cell fractions in tissues and tumors: Understanding chemoresistance in cancer. J Theor Biol 2020; 509:110499. [PMID: 33130064 DOI: 10.1016/j.jtbi.2020.110499] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Revised: 07/16/2020] [Accepted: 09/15/2020] [Indexed: 11/18/2022]
Abstract
While resistance mutations are often implicated in the failure of cancer therapy, lack of response also occurs without such mutants. In bladder cancer mouse xenografts, repeated chemotherapy cycles have resulted in cancer stem cell (CSC) enrichment, and consequent loss of therapy response due to the reduced susceptibility of CSCs to drugs. A particular feedback loop present in the xenografts has been shown to promote CSC enrichment in this system. Yet, many other regulatory loops might also be operational and might promote CSC enrichment. Their identification is central to improving therapy response. Here, we perform a comprehensive mathematical analysis to define what types of regulatory feedback loops can and cannot contribute to CSC enrichment, providing guidance to the experimental identification of feedback molecules. We derive a formula that reveals whether or not the cell population experiences CSC enrichment over time, based on the properties of the feedback. We find that negative feedback on the CSC division rate or positive feedback on differentiated cell death rate can lead to CSC enrichment. Further, the feedback mediators that achieve CSC enrichment can be secreted by either CSCs or by more differentiated cells. The extent of enrichment is determined by the CSC death rate, the CSC self-renewal probability, and by feedback strength. Defining these general characteristics of feedback loops can guide the experimental screening for and identification of feedback mediators that can promote CSC enrichment in bladder cancer and potentially other tumors. This can help understand and overcome the phenomenon of CSC-based therapy resistance.
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Affiliation(s)
- Lora D Weiss
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States
| | - P van den Driessche
- Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada
| | - John S Lowengrub
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States
| | - Dominik Wodarz
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States; Department of Population Health and Disease Prevention, Program in Public Health, Susan and Henry Samueli College of Health Sciences, University of California, Irvine, CA 92697, United States
| | - Natalia L Komarova
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, United States.
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8
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Azimzade Y, Saberi AA, Sahimi M. Effect of heterogeneity and spatial correlations on the structure of a tumor invasion front in cellular environments. Phys Rev E 2019; 100:062409. [PMID: 31962455 DOI: 10.1103/physreve.100.062409] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2019] [Indexed: 06/10/2023]
Abstract
Analysis of invasion front has been widely used to decipher biological properties, as well as the growth dynamics of the corresponding populations. Likewise, the invasion front of tumors has been investigated, from which insights into the biological mechanisms of tumor growth have been gained. We develop a model to study how tumors' invasion front depends on the relevant properties of a cellular environment. To do so, we develop a model based on a nonlinear reaction-diffusion equation, the Fisher-Kolmogorov-Petrovsky-Piskunov equation, to model tumor growth. Our study aims to understand how heterogeneity in the cellular environment's stiffness, as well as spatial correlations in its morphology, the existence of both of which has been demonstrated by experiments, affects the properties of tumor invasion front. It is demonstrated that three important factors affect the properties of the front, namely the spatial distribution of the local diffusion coefficients, the spatial correlations between them, and the ratio of the cells' duplication rate and their average diffusion coefficient. Analyzing the scaling properties of tumor invasion front computed by solving the governing equation, we show that, contrary to several previous claims, the invasion front of tumors and cancerous cell colonies cannot be described by the well-known models of kinetic growth, such as the Kardar-Parisi-Zhang equation.
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Affiliation(s)
- Youness Azimzade
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
| | - Abbas Ali Saberi
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
- Institut für Theoretische Physik, Universitat zu Köln, 50937 Köln, Germany
| | - Muhammad Sahimi
- Mork Family Department of Chemical Engineering Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
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9
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Montes-Olivas S, Marucci L, Homer M. Mathematical Models of Organoid Cultures. Front Genet 2019; 10:873. [PMID: 31592020 PMCID: PMC6761251 DOI: 10.3389/fgene.2019.00873] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Accepted: 08/20/2019] [Indexed: 12/18/2022] Open
Abstract
Organoids are engineered three-dimensional tissue cultures derived from stem cells and capable of self-renewal and self-organization into a variety of progenitors and differentiated cell types. An organoid resembles the cellular structure of an organ and retains some of its functionality, while still being amenable to in vitro experimental study. Compared with two-dimensional cultures, the three-dimensional structure of organoids provides a more realistic environment and structural organization of in vivo organs. Similarly, organoids are better suited to reproduce signaling pathway dynamics in vitro, due to a more realistic physiological environment. As such, organoids are a valuable tool to explore the dynamics of organogenesis and offer routes to personalized preclinical trials of cancer progression, invasion, and drug response. Complementary to experiments, mathematical and computational models are valuable instruments in the description of spatiotemporal dynamics of organoids. Simulations of mathematical models allow the study of multiscale dynamics of organoids, at both the intracellular and intercellular levels. Mathematical models also enable us to understand the underlying mechanisms responsible for phenotypic variation and the response to external stimulation in a cost- and time-effective manner. Many recent studies have developed laboratory protocols to grow organoids resembling different organs such as the intestine, brain, liver, pancreas, and mammary glands. However, the development of mathematical models specific to organoids remains comparatively underdeveloped. Here, we review the mathematical and computational approaches proposed so far to describe and predict organoid dynamics, reporting the simulation frameworks used and the models’ strengths and limitations.
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Affiliation(s)
- Sandra Montes-Olivas
- Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom
| | - Lucia Marucci
- Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom.,School of Cellular and Molecular Medicine, University of Bristol, Bristol, United Kingdom.,Bristol Centre for Synthetic Biology, University of Bristol, Bristol, United Kingdom
| | - Martin Homer
- Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom
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10
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Jilkine A. Mathematical Models of Stem Cell Differentiation and Dedifferentiation. CURRENT STEM CELL REPORTS 2019. [DOI: 10.1007/s40778-019-00156-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
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11
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Koay EJ, Lee Y, Cristini V, Lowengrub JS, Kang Y, Lucas FAS, Hobbs BP, Ye R, Elganainy D, Almahariq M, Amer AM, Chatterjee D, Yan H, Park PC, Rios Perez MV, Li D, Garg N, Reiss KA, Yu S, Chauhan A, Zaid M, Nikzad N, Wolff RA, Javle M, Varadhachary GR, Shroff RT, Das P, Lee JE, Ferrari M, Maitra A, Taniguchi CM, Kim MP, Crane CH, Katz MH, Wang H, Bhosale P, Tamm EP, Fleming JB. A Visually Apparent and Quantifiable CT Imaging Feature Identifies Biophysical Subtypes of Pancreatic Ductal Adenocarcinoma. Clin Cancer Res 2018; 24:5883-5894. [PMID: 30082477 PMCID: PMC6279613 DOI: 10.1158/1078-0432.ccr-17-3668] [Citation(s) in RCA: 62] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2017] [Revised: 05/14/2018] [Accepted: 07/30/2018] [Indexed: 12/12/2022]
Abstract
PURPOSE Pancreatic ductal adenocarcinoma (PDAC) is a heterogeneous disease with variable presentations and natural histories of disease. We hypothesized that different morphologic characteristics of PDAC tumors on diagnostic computed tomography (CT) scans would reflect their underlying biology. EXPERIMENTAL DESIGN We developed a quantitative method to categorize the PDAC morphology on pretherapy CT scans from multiple datasets of patients with resectable and metastatic disease and correlated these patterns with clinical/pathologic measurements. We modeled macroscopic lesion growth computationally to test the effects of stroma on morphologic patterns, hypothesizing that the balance of proliferation and local migration rates of the cancer cells would determine tumor morphology. RESULTS In localized and metastatic PDAC, quantifying the change in enhancement on CT scans at the interface between tumor and parenchyma (delta) demonstrated that patients with conspicuous (high-delta) tumors had significantly less stroma, higher likelihood of multiple common pathway mutations, more mesenchymal features, higher likelihood of early distant metastasis, and shorter survival times compared with those with inconspicuous (low-delta) tumors. Pathologic measurements of stromal and mesenchymal features of the tumors supported the mathematical model's underlying theory for PDAC growth. CONCLUSIONS At baseline diagnosis, a visually striking and quantifiable CT imaging feature reflects the molecular and pathological heterogeneity of PDAC, and may be used to stratify patients into distinct subtypes. Moreover, growth patterns of PDAC may be described using physical principles, enabling new insights into diagnosis and treatment of this deadly disease.
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Affiliation(s)
- Eugene J Koay
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas.
| | - Yeonju Lee
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Vittorio Cristini
- Center for Precision Biomedicine, The University of Texas Health Science Center, Houston, Texas
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, Texas
- Department of Imaging Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - John S Lowengrub
- Department of Mathematics, University of California, Irvine, California
- Department of Biomedical Engineering, University of California, Irvine, California
- Chao Family Comprehensive Cancer Center, University of California, Irvine, California
- Center for Complex Biological Systems, University of California, Irvine, California
| | - Ya'an Kang
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - F Anthony San Lucas
- Sheikh Ahmed Center for Pancreatic Cancer Research, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Brian P Hobbs
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Rong Ye
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Dalia Elganainy
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Muayad Almahariq
- Deparment of Pharmacology and Toxicology, University of Texas Medical Branch, Galveston, Texas
| | - Ahmed M Amer
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Deyali Chatterjee
- Department of Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Huaming Yan
- Department of Mathematics, University of California, Irvine, California
| | - Peter C Park
- Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Mayrim V Rios Perez
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Dali Li
- Sheikh Ahmed Center for Pancreatic Cancer Research, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Naveen Garg
- Department of Diagnostic Radiology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Kim A Reiss
- Department of Medical Oncology, The University of Pennsylvania Abramson Cancer Center, Philadelphia, Pennsylvania
| | - Shun Yu
- Department of Internal Medicine, The University of Pennsylvania, Philadelphia, Pennsylvania
| | - Anil Chauhan
- Department of Radiology, The University of Pennsylvania, Philadelphia, Pennsylvania
| | - Mohamed Zaid
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Newsha Nikzad
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Robert A Wolff
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Milind Javle
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Gauri R Varadhachary
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Rachna T Shroff
- Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Prajnan Das
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Jeffrey E Lee
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Mauro Ferrari
- Department of Nanomedicine, Houston Methodist Research Institute, Houston, Texas
| | - Anirban Maitra
- Sheikh Ahmed Center for Pancreatic Cancer Research, The University of Texas MD Anderson Cancer Center, Houston, Texas
- Department of Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Cullen M Taniguchi
- Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Michael P Kim
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Christopher H Crane
- Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, New York
| | - Matthew H Katz
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Huamin Wang
- Department of Pathology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Priya Bhosale
- Department of Diagnostic Radiology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Eric P Tamm
- Department of Diagnostic Radiology, The University of Texas MD Anderson Cancer Center, Houston, Texas
| | - Jason B Fleming
- Department of Surgical Oncology, The University of Texas MD Anderson Cancer Center, Houston, Texas
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12
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Yan H, Konstorum A, Lowengrub JS. Three-Dimensional Spatiotemporal Modeling of Colon Cancer Organoids Reveals that Multimodal Control of Stem Cell Self-Renewal is a Critical Determinant of Size and Shape in Early Stages of Tumor Growth. Bull Math Biol 2018; 80:1404-1433. [PMID: 28681151 PMCID: PMC5756149 DOI: 10.1007/s11538-017-0294-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Accepted: 05/11/2017] [Indexed: 12/16/2022]
Abstract
We develop a three-dimensional multispecies mathematical model to simulate the growth of colon cancer organoids containing stem, progenitor and terminally differentiated cells, as a model of early (prevascular) tumor growth. Stem cells (SCs) secrete short-range self-renewal promoters (e.g., Wnt) and their long-range inhibitors (e.g., Dkk) and proliferate slowly. Committed progenitor (CP) cells proliferate more rapidly and differentiate to produce post-mitotic terminally differentiated cells that release differentiation promoters, forming negative feedback loops on SC and CP self-renewal. We demonstrate that SCs play a central role in normal and cancer colon organoids. Spatial patterning of the SC self-renewal promoter gives rise to SC clusters, which mimic stem cell niches, around the organoid surface, and drive the development of invasive fingers. We also study the effects of externally applied signaling factors. Applying bone morphogenic proteins, which inhibit SC and CP self-renewal, reduces invasiveness and organoid size. Applying hepatocyte growth factor, which enhances SC self-renewal, produces larger sizes and enhances finger development at low concentrations but suppresses fingers at high concentrations. These results are consistent with recent experiments on colon organoids. Because many cancers are hierarchically organized and are subject to feedback regulation similar to that in normal tissues, our results suggest that in cancer, control of cancer stem cell self-renewal should influence the size and shape in similar ways, thereby opening the door to novel therapies.
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Affiliation(s)
- Huaming Yan
- Department of Mathematics, University of California, Irvine, Irvine, CA, 92697, USA
| | - Anna Konstorum
- Center for Quantitative Medicine, University of Connecticut Health Center, Farmington, CT, 06030, USA
| | - John S Lowengrub
- Department of Mathematics, Department of Biomedical Engineering, Center for Complex Biological Systems, and Chao Comprehensive Cancer Center, University of California, Irvine, Irvine, CA, 92697, USA.
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13
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Dufour A, Gontran E, Deroulers C, Varlet P, Pallud J, Grammaticos B, Badoual M. Modeling the dynamics of oligodendrocyte precursor cells and the genesis of gliomas. PLoS Comput Biol 2018; 14:e1005977. [PMID: 29590097 PMCID: PMC5903643 DOI: 10.1371/journal.pcbi.1005977] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2017] [Revised: 04/17/2018] [Accepted: 01/10/2018] [Indexed: 11/24/2022] Open
Abstract
Oligodendrocyte precursor cells (OPCs) have remarkable properties: they represent the most abundant cycling cell population in the adult normal brain and they manage to achieve a uniform and constant density throughout the adult brain. This equilibrium is obtained by the interplay of four processes: division, differentiation or death, migration and active self-repulsion. They are also strongly suspected to be at the origin of gliomas, when their equilibrium is disrupted. In this article, we present a model of the dynamics of OPCs, first in a normal tissue. This model is based on a cellular automaton and its rules are mimicking the ones that regulate the dynamics of real OPCs. The model is able to reproduce the homeostasis of the cell population, with the maintenance of a constant and uniform cell density and the healing of a lesion. We show that there exists a fair quantitative agreement between the simulated and experimental parameters, such as the cell velocity, the time taken to close a lesion, and the duration of the cell cycle. We present three possible scenarios of disruption of the equilibrium: the appearance of an over-proliferating cell, of a deadless/non-differentiating cell, or of a cell that lost any contact-inhibition. We show that the appearance of an over-proliferating cell is sufficient to trigger the growth of a tumor that has low-grade glioma features: an invasive behaviour, a linear radial growth of the tumor with a corresponding growth velocity of less than 2 mm per year, as well a cell density at the center which exceeds the one in normal tissue by a factor of less than two. The loss of contact inhibition leads to a more high-grade-like glioma. The results of our model contribute to the body of evidence that identify OPCs as possible cells of origin of gliomas. Gliomas are the most common brain tumors and result in more years of life lost than any other tumor. Standard treatments only confer a limited improvement in overall survival, underscoring the need for new therapies. Finding the type of cells at the origin of these tumors could lead to the development of new drugs, specifically targeted towards these cells. The oligodendrocyte precursor cells are suspected to be these cells of origin, because they continue to proliferate through all the adult life. In this article, we present a model of the dynamics of these cells, first in the normal brain, and then we extrapolate our model to the pathological situation. We study several scenarios where, from the normal situation, a cell appears with one property different from those of the normal cells. We show that the alteration of only one of the properties of these cells in the model can lead to the formation of gliomas with different aggressiveness and very similar to real gliomas, reinforcing the suspicion that the precursor cells are at the origin of gliomas.
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Affiliation(s)
- Aloys Dufour
- IMNC Laboratory, CNRS, Univ Paris Saclay, Univ Paris-Sud, Univ Paris Diderot, France
| | - Emilie Gontran
- IMNC Laboratory, CNRS, Univ Paris Saclay, Univ Paris-Sud, Univ Paris Diderot, France
| | - Christophe Deroulers
- IMNC Laboratory, CNRS, Univ Paris Saclay, Univ Paris-Sud, Univ Paris Diderot, France
| | - Pascale Varlet
- Department of Neuropathology, Sainte-Anne Hospital, IMA-Brain, INSERM U894, Univ Paris Descartes, Paris, France
| | - Johan Pallud
- Department of Neurosurgery, Sainte-Anne Hospital, IMA-Brain, INSERM U894, Univ Paris Descartes, Paris, France
| | - Basile Grammaticos
- IMNC Laboratory, CNRS, Univ Paris Saclay, Univ Paris-Sud, Univ Paris Diderot, France
| | - Mathilde Badoual
- IMNC Laboratory, CNRS, Univ Paris Saclay, Univ Paris-Sud, Univ Paris Diderot, France
- * E-mail:
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14
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Konstorum A, Lowengrub JS. Activation of the HGF/c-Met axis in the tumor microenvironment: A multispecies model. J Theor Biol 2017; 439:86-99. [PMID: 29203124 DOI: 10.1016/j.jtbi.2017.11.025] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Revised: 10/24/2017] [Accepted: 11/30/2017] [Indexed: 02/06/2023]
Abstract
The tumor microenvironment is an integral component in promoting tumor development. Cancer-associated fibroblasts (CAFs), which reside in the tumor stroma, produce Hepatocyte Growth Factor (HGF), an important trigger for invasive and metastatic tumor behavior. HGF contributes to a pro-tumorigenic environment by activating its cognate receptor, c-Met, on tumor cells. Tumor cells, in turn, secrete growth factors that upregulate HGF production in CAFs, thereby establishing a dynamic tumor-host signaling program. Using a spatiotemporal multispecies model of tumor growth, we investigate how the development and spread of a tumor is impacted by the initiation of a dynamic interaction between tumor-derived growth factors and CAF-derived HGF. We show that establishment of such an interaction results in increased tumor growth and morphological instability, the latter due in part to increased cell species heterogeneity at the tumor-host boundary. Invasive behavior is further increased if the tumor lowers responsiveness to paracrine pro-differentiation signals, which is a hallmark of neoplastic development. By modeling anti-HGF and anti-c-Met therapy, we show how disruption of the HGF/c-Met axis can reduce tumor invasiveness and growth, thereby providing theoretical evidence that targeting tumor-microenvironment interactions is a promising avenue for therapeutic development.
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Affiliation(s)
- Anna Konstorum
- Center for Quantitative Medicine, UConn Health, Farmington, CT, USA.
| | - John S Lowengrub
- Department of Mathematics, University of California, Irvine, CA, USA; Center for Complex Biological Systems, University of California, Irvine, CA, USA; Department of Biomedical Engineering, University of California, Irvine, CA, USA; Chao Family Comprehensive Cancer Center, University of California, Irvine, USA.
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15
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Yang J, Axelrod DE, Komarova NL. Determining the control networks regulating stem cell lineages in colonic crypts. J Theor Biol 2017; 429:190-203. [PMID: 28669884 PMCID: PMC5689466 DOI: 10.1016/j.jtbi.2017.06.033] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Revised: 05/18/2017] [Accepted: 06/25/2017] [Indexed: 12/27/2022]
Abstract
The question of stem cell control is at the center of our understanding of tissue functioning, both in healthy and cancerous conditions. It is well accepted that cellular fate decisions (such as divisions, differentiation, apoptosis) are orchestrated by a network of regulatory signals emitted by different cell populations in the lineage and the surrounding tissue. The exact regulatory network that governs stem cell lineages in a given tissue is usually unknown. Here we propose an algorithm to identify a set of candidate control networks that are compatible with (a) measured means and variances of cell populations in different compartments, (b) qualitative information on cell population dynamics, such as the existence of local controls and oscillatory reaction of the system to population size perturbations, and (c) statistics of correlations between cell numbers in different compartments. Using the example of human colon crypts, where lineages are comprised of stem cells, transit amplifying cells, and differentiated cells, we start with a theoretically known set of 32 smallest control networks compatible with tissue stability. Utilizing near-equilibrium stochastic calculus of stem cells developed earlier, we apply a series of tests, where we compare the networks' expected behavior with the observations. This allows us to exclude most of the networks, until only three, very similar, candidate networks remain, which are most compatible with the measurements. This work demonstrates how theoretical analysis of control networks combined with only static biological data can shed light onto the inner workings of stem cell lineages, in the absence of direct experimental assessment of regulatory signaling mechanisms. The resulting candidate networks are dominated by negative control loops and possess the following properties: (1) stem cell division decisions are negatively controlled by the stem cell population, (2) stem cell differentiation decisions are negatively controlled by the transit amplifying cell population.
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Affiliation(s)
- Jienian Yang
- Department of Mathematics, University of California, Irvine, Irvine, CA 92697 USA
| | - David E Axelrod
- Department of Genetics and Cancer Institute of New Jersey, Rutgers University, Piscataway, NJ 08854-8082, USA
| | - Natalia L Komarova
- Department of Ecology and Evolutionary Biology, University of California, Irvine, Irvine, CA 92697, USA.
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16
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Radioresistance of the breast tumor is highly correlated to its level of cancer stem cell and its clinical implication for breast irradiation. Radiother Oncol 2017; 124:455-461. [PMID: 28923575 DOI: 10.1016/j.radonc.2017.08.019] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2017] [Revised: 08/24/2017] [Accepted: 08/25/2017] [Indexed: 11/24/2022]
Abstract
BACKGROUND AND PURPOSE Growing evidence suggested the coexistence of cancer stem cells (CSCs) within solid tumors. We aimed to study radiosensitivity parameters for the CSCs and differentiated tumor cells (TCs) and the correlation of the fractions of CSCs to the overall tumor radioresistance. MATERIAL AND METHODS Surviving fractions of breast cancer cell lines were analyzed using a dual-compartment Linear-quadratic model with independent fitting parameters: radiosensitive αTC, βTC, αCSC, βCSC, and fraction of CSCs f. The overall tumor radio-resistance, the biological effective doses and tumor control probability were estimated as a function of CSC fraction for different fractionation regimens. The pooled clinical outcome data were fitted to the single- and dual-compartment linear-quadric models. RESULTS CSCs were more radioresistant characterized by smaller α compared to TCs: αTC=0.1±0.2, αCSC=0.04±0.07 for MCF-7 (f=0.1%), αTC=0.08±0.25, αCSC=0.04±0.18 for SUM159PT (f=2.46%). Higher f values were correlated with increasing radioresistance in cell lines. Analysis of clinical outcome data is in accordance of a dual-compartment CSC model prediction. Higher percentage of BCSCs resulted in more overall tumor radioresistance and less biological effectiveness. CONCLUSIONS Percentage of CSCs strongly correlated to overall tumor radioresistance. This observation suggested potential individualized radiotherapy to account for heterogeneous population of CSCs and their distinct radiosensitivity for breast cancer.
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17
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18
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Application of pharmacometrics and quantitative systems pharmacology to cancer therapy: The example of luminal a breast cancer. Pharmacol Res 2017; 124:20-33. [PMID: 28735000 DOI: 10.1016/j.phrs.2017.07.015] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Revised: 06/09/2017] [Accepted: 07/14/2017] [Indexed: 12/12/2022]
Abstract
Breast cancer (BC) is the most common cancer in women, and the second most frequent cause of cancer-related deaths in women worldwide. It is a heterogeneous disease composed of multiple subtypes with distinct morphologies and clinical implications. Quantitative systems pharmacology (QSP) is an emerging discipline bridging systems biology with pharmacokinetics (PK) and pharmacodynamics (PD) leveraging the systematic understanding of drugs' efficacy and toxicity. Despite numerous challenges in applying computational methodologies for QSP and mechanism-based PK/PD models to biological, physiological, and pharmacological data, bridging these disciplines has the potential to enhance our understanding of complex disease systems such as BC. In QSP/PK/PD models, various sources of data are combined including large, multi-scale experimental data such as -omics (i.e. genomics, transcriptomics, proteomics, and metabolomics), biomarkers (circulating and bound), PK, and PD endpoints. This offers a means for a translational application from pre-clinical mathematical models to patients, bridging the bench to bedside paradigm. Not only can these models be applied to inform and advance BC drug development, but they also could aid in optimizing combination therapies and rational dosing regimens for BC patients. Here, we review the current literature pertaining to the application of QSP and pharmacometrics-based pharmacotherapy in BC including bottom-up and top-down modeling approaches. Bottom-up modeling approaches employ mechanistic signal transduction pathways to predict the behavior of a biological system. The ones that are addressed in this review include signal transduction and homeostatic feedback modeling approaches. Alternatively, top-down modeling techniques are bioinformatics reconstruction techniques that infer static connections between molecules that make up a biological network and include (1) Bayesian networks, (2) co-expression networks, and (3) module-based approaches. This review also addresses novel techniques which utilize the principles of systems biology, synthetic lethality and tumor priming, both of which are discussed in relationship to novel drug targets and existing BC therapies. By utilizing QSP approaches, clinicians may develop a platform for improved dose individualization for subpopulation of BC patients, strengthen rationale in treatment designs, and explore mechanism elucidation for improving future treatments in BC medicine.
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19
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Forouzannia F, Sivaloganathan S. Cancer Stem Cells, the Tipping Point: Minority Rules? CURRENT STEM CELL REPORTS 2017. [DOI: 10.1007/s40778-017-0095-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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20
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Yan H, Romero-López M, Benitez LI, Di K, Frieboes HB, Hughes CCW, Bota DA, Lowengrub JS. 3D Mathematical Modeling of Glioblastoma Suggests That Transdifferentiated Vascular Endothelial Cells Mediate Resistance to Current Standard-of-Care Therapy. Cancer Res 2017; 77:4171-4184. [PMID: 28536277 DOI: 10.1158/0008-5472.can-16-3094] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2016] [Revised: 02/24/2017] [Accepted: 05/16/2017] [Indexed: 01/17/2023]
Abstract
Glioblastoma (GBM), the most aggressive brain tumor in human patients, is decidedly heterogeneous and highly vascularized. Glioma stem/initiating cells (GSC) are found to play a crucial role by increasing cancer aggressiveness and promoting resistance to therapy. Recently, cross-talk between GSC and vascular endothelial cells has been shown to significantly promote GSC self-renewal and tumor progression. Furthermore, GSC also transdifferentiate into bona fide vascular endothelial cells (GEC), which inherit mutations present in GSC and are resistant to traditional antiangiogenic therapies. Here we use three-dimensional mathematical modeling to investigate GBM progression and response to therapy. The model predicted that GSCs drive invasive fingering and that GEC spontaneously form a network within the hypoxic core, consistent with published experimental findings. Standard-of-care treatments using DNA-targeted therapy (radiation/chemo) together with antiangiogenic therapies reduced GBM tumor size but increased invasiveness. Anti-GEC treatments blocked the GEC support of GSCs and reduced tumor size but led to increased invasiveness. Anti-GSC therapies that promote differentiation or disturb the stem cell niche effectively reduced tumor invasiveness and size, but were ultimately limited in reducing tumor size because GECs maintain GSCs. Our study suggests that a combinatorial regimen targeting the vasculature, GSCs, and GECs, using drugs already approved by the FDA, can reduce both tumor size and invasiveness and could lead to tumor eradication. Cancer Res; 77(15); 4171-84. ©2017 AACR.
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Affiliation(s)
- Huaming Yan
- Department of Mathematics, University of California, Irvine, California
| | - Mónica Romero-López
- Department of Biomedical Engineering, University of California, Irvine, California
| | - Lesly I Benitez
- Department of Molecular Biology and Biochemistry, University of California, Irvine, California
| | - Kaijun Di
- Chao Comprehensive Cancer Center, University of California, Irvine, California.,Department of Neurological Surgery, University of California, Irvine, California
| | - Hermann B Frieboes
- James Graham Brown Cancer Center, University of Louisville.,Department of Bioengineering, University of Louisville, Louisville, Kentucky
| | - Christopher C W Hughes
- Department of Biomedical Engineering, University of California, Irvine, California.,Department of Molecular Biology and Biochemistry, University of California, Irvine, California.,Chao Comprehensive Cancer Center, University of California, Irvine, California.,Center for Complex Biological Systems, University of California, Irvine, California
| | - Daniela A Bota
- Chao Comprehensive Cancer Center, University of California, Irvine, California.,Department of Neurological Surgery, University of California, Irvine, California.,Department of Neurology, University of California, Irvine, California
| | - John S Lowengrub
- Department of Mathematics, University of California, Irvine, California. .,Department of Biomedical Engineering, University of California, Irvine, California.,Chao Comprehensive Cancer Center, University of California, Irvine, California.,Center for Complex Biological Systems, University of California, Irvine, California
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21
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Stability of Control Networks in Autonomous Homeostatic Regulation of Stem Cell Lineages. Bull Math Biol 2017; 80:1345-1365. [PMID: 28508298 DOI: 10.1007/s11538-017-0283-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2016] [Accepted: 04/07/2017] [Indexed: 01/02/2023]
Abstract
Design principles of biological networks have been studied extensively in the context of protein-protein interaction networks, metabolic networks, and regulatory (transcriptional) networks. Here we consider regulation networks that occur on larger scales, namely the cell-to-cell signaling networks that connect groups of cells in multicellular organisms. These are the feedback loops that orchestrate the complex dynamics of cell fate decisions and are necessary for the maintenance of homeostasis in stem cell lineages. We focus on "minimal" networks that are those that have the smallest possible numbers of controls. For such minimal networks, the number of controls must be equal to the number of compartments, and the reducibility/irreducibility of the network (whether or not it can be split into smaller independent sub-networks) is defined by a matrix comprised of the cell number increments induced by each of the controlled processes in each of the compartments. Using the formalism of digraphs, we show that in two-compartment lineages, reducible systems must contain two 1-cycles, and irreducible systems one 1-cycle and one 2-cycle; stability follows from the signs of the controls and does not require magnitude restrictions. In three-compartment systems, irreducible digraphs have a tree structure or have one 3-cycle and at least two more shorter cycles, at least one of which is a 1-cycle. With further work and proper biological validation, our results may serve as a first step toward an understanding of ways in which these networks become dysregulated in cancer.
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22
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Lee M, Chen GT, Puttock E, Wang K, Edwards RA, Waterman ML, Lowengrub J. Mathematical modeling links Wnt signaling to emergent patterns of metabolism in colon cancer. Mol Syst Biol 2017; 13:912. [PMID: 28183841 PMCID: PMC5327728 DOI: 10.15252/msb.20167386] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2016] [Revised: 01/05/2017] [Accepted: 01/12/2017] [Indexed: 12/14/2022] Open
Abstract
Cell-intrinsic metabolic reprogramming is a hallmark of cancer that provides anabolic support to cell proliferation. How reprogramming influences tumor heterogeneity or drug sensitivities is not well understood. Here, we report a self-organizing spatial pattern of glycolysis in xenograft colon tumors where pyruvate dehydrogenase kinase (PDK1), a negative regulator of oxidative phosphorylation, is highly active in clusters of cells arranged in a spotted array. To understand this pattern, we developed a reaction-diffusion model that incorporates Wnt signaling, a pathway known to upregulate PDK1 and Warburg metabolism. Partial interference with Wnt alters the size and intensity of the spotted pattern in tumors and in the model. The model predicts that Wnt inhibition should trigger an increase in proteins that enhance the range of Wnt ligand diffusion. Not only was this prediction validated in xenograft tumors but similar patterns also emerge in radiochemotherapy-treated colorectal cancer. The model also predicts that inhibitors that target glycolysis or Wnt signaling in combination should synergize and be more effective than each treatment individually. We validated this prediction in 3D colon tumor spheroids.
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Affiliation(s)
- Mary Lee
- Department of Mathematics, University of California, Irvine, Irvine, CA, USA
| | - George T Chen
- Department of Microbiology and Molecular Genetics, University of California, Irvine, Irvine, CA, USA
| | - Eric Puttock
- Department of Mathematics, University of California, Irvine, Irvine, CA, USA
| | - Kehui Wang
- Department of Pathology, School of Medicine, University of California, Irvine, Irvine, CA, USA
- Chao Family Comprehensive Cancer Center, University of California, Irvine, Irvine, CA, USA
| | - Robert A Edwards
- Department of Pathology, School of Medicine, University of California, Irvine, Irvine, CA, USA
- Chao Family Comprehensive Cancer Center, University of California, Irvine, Irvine, CA, USA
| | - Marian L Waterman
- Department of Microbiology and Molecular Genetics, University of California, Irvine, Irvine, CA, USA
- Chao Family Comprehensive Cancer Center, University of California, Irvine, Irvine, CA, USA
- Center for Complex Biological Systems, University of California, Irvine, Irvine, CA, USA
| | - John Lowengrub
- Department of Mathematics, University of California, Irvine, Irvine, CA, USA
- Chao Family Comprehensive Cancer Center, University of California, Irvine, Irvine, CA, USA
- Center for Complex Biological Systems, University of California, Irvine, Irvine, CA, USA
- Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA
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23
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Yan H, Romero-Lopez M, Frieboes HB, Hughes CCW, Lowengrub JS. Multiscale Modeling of Glioblastoma Suggests that the Partial Disruption of Vessel/Cancer Stem Cell Crosstalk Can Promote Tumor Regression Without Increasing Invasiveness. IEEE Trans Biomed Eng 2016; 64:538-548. [PMID: 27723576 DOI: 10.1109/tbme.2016.2615566] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
OBJECTIVE In glioblastoma, the crosstalk between vascular endothelial cells (VECs) and glioma stem cells (GSCs) has been shown to enhance tumor growth. We propose a multiscale mathematical model to study this mechanism, explore tumor growth under various initial and microenvironmental conditions, and investigate the effects of blocking this crosstalk. METHODS We develop a hybrid continuum-discrete model of highly organized vascularized tumors. VEC-GSC crosstalk is modeled via vascular endothelial growth factor (VEGF) production by tumor cells and by secretion of soluble factors by VECs that promote GSC self-renewal and proliferation. RESULTS VEC-GSC crosstalk increases both tumor size and GSC fraction by enhancing GSC activity and neovascular development. VEGF promotes vessel formation, and larger VEGF sources typically increase vessel numbers, which enhances tumor growth and stabilizes the tumor shape. Increasing the initial GSC fraction has a similar effect. Partially disrupting the crosstalk by blocking VEC secretion of GSC promoters reduces tumor size but does not increase invasiveness, which is in contrast to antiangiogenic therapies, which reduce tumor size but may significantly increase tumor invasiveness. SIGNIFICANCE Multiscale modeling supports the targeting of VEC-GSC crosstalk as a promising approach for cancer therapy.
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24
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Badri H, Leder K. Optimal treatment and stochastic modeling of heterogeneous tumors. Biol Direct 2016; 11:40. [PMID: 27549860 PMCID: PMC4994177 DOI: 10.1186/s13062-016-0142-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2016] [Accepted: 07/07/2016] [Indexed: 12/24/2022] Open
Abstract
UNLABELLED In this work we review past articles that have mathematically studied cancer heterogeneity and the impact of this heterogeneity on the structure of optimal therapy. We look at past works on modeling how heterogeneous tumors respond to radiotherapy, and take a particularly close look at how the optimal radiotherapy schedule is modified by the presence of heterogeneity. In addition, we review past works on the study of optimal chemotherapy when dealing with heterogeneous tumors. REVIEWERS This article was reviewed by Thomas McDonald, David Axelrod, and Leonid Hanin.
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Affiliation(s)
- Hamidreza Badri
- Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA
| | - Kevin Leder
- Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN 55455 USA
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25
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Mathematical Modeling of the Role of Survivin on Dedifferentiation and Radioresistance in Cancer. Bull Math Biol 2016; 78:1162-88. [PMID: 27271121 DOI: 10.1007/s11538-016-0177-x] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2016] [Accepted: 05/13/2016] [Indexed: 12/27/2022]
Abstract
We use a mathematical model to investigate cancer resistance to radiation, based on dedifferentiation of non-stem cancer cells into cancer stem cells. Experimental studies by Iwasa 2008, using human non-small cell lung cancer (NSCLC) cell lines in mice, have implicated the inhibitor of apoptosis protein survivin in cancer resistance to radiation. A marked increase in radio-sensitivity was observed, after inhibiting survivin expression with a specific survivin inhibitor YM155 (sepantronium bromide). It was suggested that these observations are due to survivin-dependent dedifferentiation of non-stem cancer cells into cancer stem cells. Here, we confirm this hypothesis with a mathematical model, which we fit to Iwasa's data on NSCLC in mice. We investigate the timing of combination therapies of YM155 administration and radiation. We find an interesting dichotomy. Sometimes it is best to hit a cancer with a large radiation dose right at the beginning of the YM155 treatment, while in other cases, it appears advantageous to wait a few days until most cancer cells are sensitized and then radiate. The optimal strategy depends on the nature of the cancer and the dose of radiation administered.
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26
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Konstorum A, Hillen T, Lowengrub J. Feedback Regulation in a Cancer Stem Cell Model can Cause an Allee Effect. Bull Math Biol 2016; 78:754-785. [PMID: 27113934 DOI: 10.1007/s11538-016-0161-5] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2015] [Accepted: 03/15/2016] [Indexed: 12/24/2022]
Abstract
The exact mechanisms of spontaneous tumor remission or complete response to treatment are phenomena in oncology that are not completely understood. We use a concept from ecology, the Allee effect, to help explain tumor extinction in a model of tumor growth that incorporates feedback regulation of stem cell dynamics, which occurs in many tumor types where certain signaling molecules, such as Wnts, are upregulated. Due to feedback and the Allee effect, a tumor may become extinct spontaneously or after therapy even when the entire tumor has not been eradicated by the end of therapy. We quantify the Allee effect using an 'Allee index' that approximates the area of the basin of attraction for tumor extinction. We show that effectiveness of combination therapy in cancer treatment may occur due to the increased probability that the system will be in the Allee region after combination treatment versus monotherapy. We identify therapies that can attenuate stem cell self-renewal, alter the Allee region and increase its size. We also show that decreased response of tumor cells to growth inhibitors can reduce the size of the Allee region and increase stem cell densities, which may help to explain why this phenomenon is a hallmark of cancer.
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Affiliation(s)
- Anna Konstorum
- Department of Mathematics, University of California, Irvine, Irvine, CA, USA.
- Center for Complex Biological Systems, University of California, Irvine, Irvine, CA, USA.
- Center for Quantitative Medicine, University of Connecticut Health Center, Farmington, CT, USA.
| | - Thomas Hillen
- Centre for Mathematical Biology, University of Alberta, Edmonton, AB, Canada
| | - John Lowengrub
- Department of Mathematics, University of California, Irvine, Irvine, CA, USA.
- Center for Complex Biological Systems, University of California, Irvine, Irvine, CA, USA.
- Department of Biomedical Engineering, University of California, Irvine, Irvine, CA, USA.
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27
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Kunche S, Yan H, Calof AL, Lowengrub JS, Lander AD. Feedback, Lineages and Self-Organizing Morphogenesis. PLoS Comput Biol 2016; 12:e1004814. [PMID: 26989903 PMCID: PMC4798729 DOI: 10.1371/journal.pcbi.1004814] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2015] [Accepted: 02/15/2016] [Indexed: 01/31/2023] Open
Abstract
Feedback regulation of cell lineage progression plays an important role in tissue size homeostasis, but whether such feedback also plays an important role in tissue morphogenesis has yet to be explored. Here we use mathematical modeling to show that a particular feedback architecture in which both positive and negative diffusible signals act on stem and/or progenitor cells leads to the appearance of bistable or bi-modal growth behaviors, ultrasensitivity to external growth cues, local growth-driven budding, self-sustaining elongation, and the triggering of self-organization in the form of lamellar fingers. Such behaviors arise not through regulation of cell cycle speeds, but through the control of stem or progenitor self-renewal. Even though the spatial patterns that arise in this setting are the result of interactions between diffusible factors with antagonistic effects, morphogenesis is not the consequence of Turing-type instabilities.
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Affiliation(s)
- Sameeran Kunche
- Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
| | - Huaming Yan
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
| | - Anne L. Calof
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
- Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California, United States of America
- Department of Anatomy and Neurobiology, University of California, Irvine, Irvine, California, United States of America
- * E-mail: (ALC); (JSL); (ADL)
| | - John S. Lowengrub
- Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
- Department of Mathematics, University of California, Irvine, Irvine, California, United States of America
- * E-mail: (ALC); (JSL); (ADL)
| | - Arthur D. Lander
- Department of Biomedical Engineering, University of California, Irvine, Irvine, California, United States of America
- Center for Complex Biological Systems, University of California, Irvine, Irvine, California, United States of America
- Department of Developmental and Cell Biology, University of California, Irvine, Irvine, California, United States of America
- * E-mail: (ALC); (JSL); (ADL)
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28
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Tumours with cancer stem cells: A PDE model. Math Biosci 2016; 272:76-80. [PMID: 26719124 DOI: 10.1016/j.mbs.2015.12.003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Revised: 12/04/2015] [Accepted: 12/14/2015] [Indexed: 12/16/2022]
Abstract
The role of cancer stem cells (CSC) in tumour growth has received increasing attention in the recent literature. Here we stem from an integro-differential system describing the evolution of a population of CSC and of ordinary (non-stem) tumour cells formulated and studied in a previous paper, and we investigate an approximation in which the system reduces to a pair of nonlinear coupled parabolic equation. We prove that the new system is well posed and we examine some general properties. Numerical simulations show more on the qualitative behaviour of the solutions, concerning in particular the so-called tumour paradox, according to which an increase of the mortality rate of ordinary (non-stem) tumour cells results asymptotically in a faster growth.
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Borsi I, Fasano A, Primicerio M, Hillen T. A non-local model for cancer stem cells and the tumour growth paradox. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2015; 34:59-75. [DOI: 10.1093/imammb/dqv037] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2014] [Accepted: 10/01/2015] [Indexed: 12/15/2022]
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30
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MacLean AL, Kirk PDW, Stumpf MPH. Cellular population dynamics control the robustness of the stem cell niche. Biol Open 2015; 4:1420-6. [PMID: 26453624 PMCID: PMC4728354 DOI: 10.1242/bio.013714] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Within populations of cells, fate decisions are controlled by an indeterminate combination of cell-intrinsic and cell-extrinsic factors. In the case of stem cells, the stem cell niche is believed to maintain ‘stemness’ through communication and interactions between the stem cells and one or more other cell-types that contribute to the niche conditions. To investigate the robustness of cell fate decisions in the stem cell hierarchy and the role that the niche plays, we introduce simple mathematical models of stem and progenitor cells, their progeny and their interplay in the niche. These models capture the fundamental processes of proliferation and differentiation and allow us to consider alternative possibilities regarding how niche-mediated signalling feedback regulates the niche dynamics. Generalised stability analysis of these stem cell niche systems enables us to describe the stability properties of each model. We find that although the number of feasible states depends on the model, their probabilities of stability in general do not: stem cell–niche models are stable across a wide range of parameters. We demonstrate that niche-mediated feedback increases the number of stable steady states, and show how distinct cell states have distinct branching characteristics. The ecological feedback and interactions mediated by the stem cell niche thus lend (surprisingly) high levels of robustness to the stem and progenitor cell population dynamics. Furthermore, cell–cell interactions are sufficient for populations of stem cells and their progeny to achieve stability and maintain homeostasis. We show that the robustness of the niche – and hence of the stem cell pool in the niche – depends only weakly, if at all, on the complexity of the niche make-up: simple as well as complicated niche systems are capable of supporting robust and stable stem cell dynamics. Summary: Stem cell niche dynamics are very robust to external and physiological perturbations because proliferation and differentiation are naturally balanced and controlled by the reliance on a shared niche environment.
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Affiliation(s)
- Adam L MacLean
- Theoretical Systems Biology, Department of Life Sciences, Imperial College London, London SW7 2AZ, UK
| | - Paul D W Kirk
- MRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge CB2 0SR, UK
| | - Michael P H Stumpf
- Theoretical Systems Biology, Department of Life Sciences, Imperial College London, London SW7 2AZ, UK
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Fornari C, Balbo G, Halawani SM, Ba-Rukab O, Ahmad AR, Calogero RA, Cordero F, Beccuti M. A versatile mathematical work-flow to explore how Cancer Stem Cell fate influences tumor progression. BMC SYSTEMS BIOLOGY 2015; 9 Suppl 3:S1. [PMID: 26050594 PMCID: PMC4464028 DOI: 10.1186/1752-0509-9-s3-s1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Background Nowadays multidisciplinary approaches combining mathematical models with experimental assays are becoming relevant for the study of biological systems. Indeed, in cancer research multidisciplinary approaches are successfully used to understand the crucial aspects implicated in tumor growth. In particular, the Cancer Stem Cell (CSC) biology represents an area particularly suited to be studied through multidisciplinary approaches, and modeling has significantly contributed to pinpoint the crucial aspects implicated in this theory. More generally, to acquire new insights on a biological system it is necessary to have an accurate description of the phenomenon, such that making accurate predictions on its future behaviors becomes more likely. In this context, the identification of the parameters influencing model dynamics can be advantageous to increase model accuracy and to provide hints in designing wet experiments. Different techniques, ranging from statistical methods to analytical studies, have been developed. Their applications depend on case-specific aspects, such as the availability and quality of experimental data, and the dimension of the parameter space. Results The study of a new model on the CSC-based tumor progression has been the motivation to design a new work-flow that helps to characterize possible system dynamics and to identify those parameters influencing such behaviors. In detail, we extended our recent model on CSC-dynamics creating a new system capable of describing tumor growth during the different stages of cancer progression. Indeed, tumor cells appear to progress through lineage stages like those of normal tissues, being their division auto-regulated by internal feedback mechanisms. These new features have introduced some non-linearities in the model, making it more difficult to be studied by solely analytical techniques. Our new work-flow, based on statistical methods, was used to identify the parameters which influence the tumor growth. The effectiveness of the presented work-flow was firstly verified on two well known models and then applied to investigate our extended CSC model. Conclusions We propose a new work-flow to study in a practical and informative way complex systems, allowing an easy identification, interpretation, and visualization of the key model parameters. Our methodology is useful to investigate possible model behaviors and to establish factors driving model dynamics. Analyzing our new CSC model guided by the proposed work-flow, we found that the deregulation of CSC asymmetric proliferation contributes to cancer initiation, in accordance with several experimental evidences. Specifically, model results indicated that the probability of CSC symmetric proliferation is responsible of a switching-like behavior which discriminates between tumorigenesis and unsustainable tumor growth.
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32
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Yu VY, Nguyen D, Pajonk F, Kupelian P, Kaprealian T, Selch M, Low DA, Sheng K. Incorporating cancer stem cells in radiation therapy treatment response modeling and the implication in glioblastoma multiforme treatment resistance. Int J Radiat Oncol Biol Phys 2015; 91:866-75. [PMID: 25752402 DOI: 10.1016/j.ijrobp.2014.12.004] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2014] [Revised: 11/22/2014] [Accepted: 12/01/2014] [Indexed: 01/06/2023]
Abstract
PURPOSE To perform a preliminary exploration with a simplistic mathematical cancer stem cell (CSC) interaction model to determine whether the tumor-intrinsic heterogeneity and dynamic equilibrium between CSCs and differentiated cancer cells (DCCs) can better explain radiation therapy treatment response with a dual-compartment linear-quadratic (DLQ) model. METHODS AND MATERIALS The radiosensitivity parameters of CSCs and DCCs for cancer cell lines including glioblastoma multiforme (GBM), non-small cell lung cancer, melanoma, osteosarcoma, and prostate, cervical, and breast cancer were determined by performing robust least-square fitting using the DLQ model on published clonogenic survival data. Fitting performance was compared with the single-compartment LQ (SLQ) and universal survival curve models. The fitting results were then used in an ordinary differential equation describing the kinetics of DCCs and CSCs in response to 2- to 14.3-Gy fractionated treatments. The total dose to achieve tumor control and the fraction size that achieved the least normal biological equivalent dose were calculated. RESULTS Smaller cell survival fitting errors were observed using DLQ, with the exception of melanoma, which had a low α/β = 0.16 in SLQ. Ordinary differential equation simulation indicated lower normal tissue biological equivalent dose to achieve the same tumor control with a hypofractionated approach for 4 cell lines for the DLQ model, in contrast to SLQ, which favored 2 Gy per fraction for all cells except melanoma. The DLQ model indicated greater tumor radioresistance than SLQ, but the radioresistance was overcome by hypofractionation, other than the GBM cells, which responded poorly to all fractionations. CONCLUSION The distinct radiosensitivity and dynamics between CSCs and DCCs in radiation therapy response could perhaps be one possible explanation for the heterogeneous intertumor response to hypofractionation and in some cases superior outcome from stereotactic ablative radiation therapy. The DLQ model also predicted the remarkable GBM radioresistance, a result that is highly consistent with clinical observations. The radioresistance putatively stemmed from accelerated DCC regrowth that rapidly restored compartmental equilibrium between CSCs and DCCs.
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Affiliation(s)
- Victoria Y Yu
- Department of Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California
| | - Dan Nguyen
- Department of Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California
| | - Frank Pajonk
- Department of Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California
| | - Patrick Kupelian
- Department of Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California
| | - Tania Kaprealian
- Department of Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California
| | - Michael Selch
- Department of Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California
| | - Daniel A Low
- Department of Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California
| | - Ke Sheng
- Department of Radiation Oncology, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California.
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Getto P, Marciniak-Czochra A. Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation. Methods Mol Biol 2015; 1293:247-266. [PMID: 26040693 DOI: 10.1007/978-1-4939-2519-3_15] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.
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Affiliation(s)
- Philipp Getto
- TU Dresden, Fachrichtung Mathematik, Institut für Analysis, 01062, Dresden, Germany,
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34
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Abstract
This review discusses quantitative modeling studies of stem and non-stem cancer cell interactions and the fraction of cancer stem cells.
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Affiliation(s)
- Heiko Enderling
- Department of Integrated Mathematical Oncology
- H. Lee Moffitt Cancer Center & Research Institute
- Tampa
- USA
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35
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A mathematical-biological joint effort to investigate the tumor-initiating ability of Cancer Stem Cells. PLoS One 2014; 9:e106193. [PMID: 25184361 PMCID: PMC4153566 DOI: 10.1371/journal.pone.0106193] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2014] [Accepted: 07/29/2014] [Indexed: 01/06/2023] Open
Abstract
The involvement of Cancer Stem Cells (CSCs) in tumor progression and tumor recurrence is one of the most studied subjects in current cancer research. The CSC hypothesis states that cancer cell populations are characterized by a hierarchical structure that affects cancer progression. Due to the complex dynamics involving CSCs and the other cancer cell subpopulations, a robust theory explaining their action has not been established yet. Some indications can be obtained by combining mathematical modeling and experimental data to understand tumor dynamics and to generate new experimental hypotheses. Here, we present a model describing the initial phase of ErbB2+ mammary cancer progression, which arises from a joint effort combing mathematical modeling and cancer biology. The proposed model represents a new approach to investigate the CSC-driven tumorigenesis and to analyze the relations among crucial events involving cancer cell subpopulations. Using in vivo and in vitro data we tuned the model to reproduce the initial dynamics of cancer growth, and we used its solution to characterize observed cancer progression with respect to mutual CSC and progenitor cell variation. The model was also used to investigate which association occurs among cell phenotypes when specific cell markers are considered. Finally, we found various correlations among model parameters which cannot be directly inferred from the available biological data and these dependencies were used to characterize the dynamics of cancer subpopulations during the initial phase of ErbB2+ mammary cancer progression.
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36
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Weekes SL, Barker B, Bober S, Cisneros K, Cline J, Thompson A, Hlatky L, Hahnfeldt P, Enderling H. A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics. Bull Math Biol 2014; 76:1762-82. [PMID: 24840956 DOI: 10.1007/s11538-014-9976-0] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2013] [Accepted: 04/30/2014] [Indexed: 08/30/2023]
Abstract
Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan, and thus cannot initiate or reinitiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis--a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division--we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.
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Affiliation(s)
- Suzanne L Weekes
- Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA , 01609, USA,
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37
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Pei QM, Zhan X, Yang LJ, Bao C, Cao W, Li AB, Rozi A, Jia Y. Fluctuations of cell population in a colonic crypt. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032715. [PMID: 24730882 DOI: 10.1103/physreve.89.032715] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2013] [Indexed: 06/03/2023]
Abstract
The number of stem cells in a colonic crypt is often very small, which leads to large intrinsic fluctuations in the cell population. Based on the model of cell population dynamics with linear feedback in a colonic crypt, we present a stochastic dynamics of the cell population [including stem cells (SCs), transit amplifying cells (TACs), and fully differentiated cells (FDCs)]. The Fano factor, covariance, and susceptibility formulas of the cell population around the steady state are derived by using the Langevin theory. In the range of physiologically reasonable parameter values, it is found that the stationary populations of TACs and FDCs exhibit an approximately threshold behavior as a function of the net growth rate of TACs, and the reproductions of TACs and FDCs can be classified into three regimens: controlled, crossover, and uncontrolled. With the increasing of the net growth rate of TACs, there is a maximum of the relative intrinsic fluctuations (i.e., the Fano factors) of TACs and FDCs in the crossover region. For a fixed differentiation rate and the net growth rate of SCs, the covariance of fluctuations between SCs and TACs has a maximum in the crossover region. However, the susceptibilities of both TACs and FDCs to the net growth rate of TACs have a minimum in the crossover region.
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Affiliation(s)
- Qi-ming Pei
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and School of Physical Science and Technology, Yangtze University, Jingzhou 434023, China
| | - Xuan Zhan
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Li-jian Yang
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Chun Bao
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Wei Cao
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - An-bang Li
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Anvar Rozi
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and Department of Physics, Kashgar Teachers College, Kashgar 844007, China
| | - Ya Jia
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
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Abstract
Traditionally, scientific research has focused on studying individual events, such as single mutations, gene function, or the effect that mutating one protein has on a biological phenotype. A range of technologies is beginning to provide information that will enable a holistic view of how genomic and epigenetic aberrations in cancer cells can alter the homeostasis of signalling networks within these cells, between cancer cells and the local microenvironment, and at the organ and organism level. This process, termed Systems Biology, needs to be integrated with an iterative approach wherein hypotheses and predictions that arise from modelling are refined and constrained by experimental evaluation. Systems biology approaches will be vital for developing and implementing effective strategies to deliver personalized cancer therapy. Specifically, these approaches will be important to select those patients who are most likely to benefit from targeted therapies and for the development and implementation of rational combinatorial therapies. Systems biology can help to increase therapy efficacy or bypass the emergence of resistance, thus converting the current-often short term-effects of targeted therapies into durable responses, ultimately to improve patient quality of life and provide a cure.
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39
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Konstorum A, Sprowl SA, Waterman ML, Lander AD, Lowengrub JS. Predicting mechanism of biphasic growth factor action on tumor growth using a multi-species model with feedback control. JOURNAL OF COUPLED SYSTEMS AND MULTISCALE DYNAMICS 2013; 1:459-467. [PMID: 25075381 PMCID: PMC4112130 DOI: 10.1166/jcsmd.2013.1028] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
A large number of growth factors and drugs are known to act in a biphasic manner: at lower concentrations they cause increased division of target cells, whereas at higher concentrations the mitogenic effect is inhibited. Often, the molecular details of the mitogenic effect of the growth factor are known, whereas the inhibitory effect is not. Hepatoctyte Growth Factor, HGF, has recently been recognized as a strong mitogen that is present in the microenvironment of solid tumors. Recent evidence suggests that HGF acts in a biphasic manner on tumor growth. We build a multi-species model of HGF action on tumor cells using different hypotheses for high dose-HGF activation of a growth inhibitor and show that the shape of the dose-response curve is directly related to the mechanism of inhibitor activation. We thus hypothesize that the shape of a dose-response curve is informative of the molecular action of the growth factor on the growth inhibitor.
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Affiliation(s)
- Anna Konstorum
- Department of Mathematics, University of California, Irvine, CA 92697-3875, USA
- Center for Complex Biological Systems, University of California, 2620 Biological Sciences III, Irvine, CA 92697-2280, USA
| | - Stephanie A. Sprowl
- Center for Complex Biological Systems, University of California, 2620 Biological Sciences III, Irvine, CA 92697-2280, USA
- Department of Microbiology and Molecular Genetics, University of California, Irvine, CA 92697-4025, USA
| | - Marian L. Waterman
- Center for Complex Biological Systems, University of California, 2620 Biological Sciences III, Irvine, CA 92697-2280, USA
- Department of Microbiology and Molecular Genetics, University of California, Irvine, CA 92697-4025, USA
| | - Arthur D. Lander
- Center for Complex Biological Systems, University of California, 2620 Biological Sciences III, Irvine, CA 92697-2280, USA
- Department of Developmental and Cell Biology, University of California, 2011 Biological Sciences III, Irvine, CA 92697-2300, USA
| | - John S. Lowengrub
- Department of Mathematics, University of California, Irvine, CA 92697-3875, USA
- Center for Complex Biological Systems, University of California, 2620 Biological Sciences III, Irvine, CA 92697-2280, USA
- Department of Biomedical Engineering, University of California, 3120 Natural Sciences II, Irvine, CA 92697-2715, USA
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40
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Bravo R, Axelrod DE. A calibrated agent-based computer model of stochastic cell dynamics in normal human colon crypts useful for in silico experiments. Theor Biol Med Model 2013; 10:66. [PMID: 24245614 PMCID: PMC3879123 DOI: 10.1186/1742-4682-10-66] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2013] [Accepted: 11/07/2013] [Indexed: 12/27/2022] Open
Abstract
BACKGROUND Normal colon crypts consist of stem cells, proliferating cells, and differentiated cells. Abnormal rates of proliferation and differentiation can initiate colon cancer. We have measured the variation in the number of each of these cell types in multiple crypts in normal human biopsy specimens. This has provided the opportunity to produce a calibrated computational model that simulates cell dynamics in normal human crypts, and by changing model parameter values, to simulate the initiation and treatment of colon cancer. RESULTS An agent-based model of stochastic cell dynamics in human colon crypts was developed in the multi-platform open-source application NetLogo. It was assumed that each cell's probability of proliferation and probability of death is determined by its position in two gradients along the crypt axis, a divide gradient and in a die gradient. A cell's type is not intrinsic, but rather is determined by its position in the divide gradient. Cell types are dynamic, plastic, and inter-convertible. Parameter values were determined for the shape of each of the gradients, and for a cell's response to the gradients. This was done by parameter sweeps that indicated the values that reproduced the measured number and variation of each cell type, and produced quasi-stationary stochastic dynamics. The behavior of the model was verified by its ability to reproduce the experimentally observed monocolonal conversion by neutral drift, the formation of adenomas resulting from mutations either at the top or bottom of the crypt, and by the robust ability of crypts to recover from perturbation by cytotoxic agents. One use of the virtual crypt model was demonstrated by evaluating different cancer chemotherapy and radiation scheduling protocols. CONCLUSIONS A virtual crypt has been developed that simulates the quasi-stationary stochastic cell dynamics of normal human colon crypts. It is unique in that it has been calibrated with measurements of human biopsy specimens, and it can simulate the variation of cell types in addition to the average number of each cell type. The utility of the model was demonstrated with in silico experiments that evaluated cancer therapy protocols. The model is available for others to conduct additional experiments.
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Affiliation(s)
- Rafael Bravo
- Department of Genetics, Rutgers University, 604 Allison Rd, Piscataway, NJ 08854-8082, USA
- Department of Computer Science, Rutgers University, 110 Frelinghuysen Rd, Piscataway, NJ 08854-8019, USA
| | - David E Axelrod
- Department of Genetics, Rutgers University, 604 Allison Rd, Piscataway, NJ 08854-8082, USA
- Rutgers Cancer Institute of New Jersey, 195 Little Albany Street, New Brunswick, NJ 08901-1998, USA
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41
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Enderling H, Hlatky L, Hahnfeldt P. Cancer Stem Cells: A Minor Cancer Subpopulation that Redefines Global Cancer Features. Front Oncol 2013; 3:76. [PMID: 23596563 PMCID: PMC3625721 DOI: 10.3389/fonc.2013.00076] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2013] [Accepted: 03/24/2013] [Indexed: 01/06/2023] Open
Abstract
In recent years cancer stem cells (CSCs) have been hypothesized to comprise only a minor subpopulation in solid tumors that drives tumor initiation, progression, and metastasis; the so-called “cancer stem cell hypothesis.” While a seemingly trivial statement about numbers, much is put at stake. If true, the conclusions of many studies of cancer cell populations could be challenged, as the bulk assay methods upon which they depend have, by, and large, taken for granted the notion that a “typical” cell of the population possesses the attributes of a cell capable of perpetuating the cancer, i.e., a CSC. In support of the CSC hypothesis, populations enriched for so-called “tumor-initiating” cells have demonstrated a corresponding increase in tumorigenicity as measured by dilution assay, although estimates have varied widely as to what the fractional contribution of tumor-initiating cells is in any given population. Some have taken this variability to suggest the CSC fraction may be nearly 100% after all, countering the CSC hypothesis, and that there are simply assay-dependent error rates in our ability to “reconfirm” CSC status at the cell level. To explore this controversy more quantitatively, we developed a simple cellular automaton model of CSC-driven tumor growth dynamics. Assuming CSC and non-stem cancer cells (CC) subpopulations coexist to some degree, we evaluated the impact of an environmentally dependent CSC symmetric division probability and a CC proliferation capacity on tumor progression and morphology. Our model predicts, as expected, that the frequency of CSC divisions that are symmetric highly influences the frequency of CSCs in the population, but goes on to predict the two frequencies can be widely divergent, and that spatial constraints will tend to increase the CSC fraction over time. Further, tumor progression times show a marked dependence on both the frequency of CSC divisions that are symmetric and on the proliferation capacities of CC. Together, these findings can explain, within the CSC hypothesis, the widely varying measures of stem cell fractions observed. In particular, although the CSC fraction is influenced by the (environmentally modifiable) CSC symmetric division probability, with the former converging to unity as the latter nears 100%, the CSC fraction becomes quite small even for symmetric division probabilities modestly lower than 100%. In the latter case, the tumor exhibits a clustered morphology and the CSC fraction steadily increases with time; more so on both counts when the death rate of CCs is higher. Such variations in CSC fraction and morphology are not only consistent with the CSC hypothesis, but lend support to it as one expected byproduct of the dynamical interactions that are predicted to take place among a relatively small CSC population, its CC counterpart, and the host compartment over time.
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Affiliation(s)
- Heiko Enderling
- Center of Cancer Systems Biology, St. Elizabeth's Medical Center, Tufts University School of Medicine Boston, MA, USA
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42
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Bachman JWN, Hillen T. Mathematical optimization of the combination of radiation and differentiation therapies for cancer. Front Oncol 2013; 3:52. [PMID: 23508300 PMCID: PMC3600539 DOI: 10.3389/fonc.2013.00052] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2012] [Accepted: 02/28/2013] [Indexed: 11/13/2022] Open
Abstract
Cancer stem cells (CSC) are considered to be a major driver of cancer progression and successful therapies must control CSCs. However, CSC are often less sensitive to treatment and they might survive radiation and/or chemotherapies. In this paper we combine radiation treatment with differentiation therapy. During differentiation therapy, a differentiation promoting agent is supplied (e.g., TGF-beta) such that CSCs differentiate and become more radiosensitive. Then radiation can be used to control them. We consider three types of cancer: head and neck cancer, brain cancers (primary tumors and metastatic brain cancers), and breast cancer; and we use mathematical modeling to show that combination therapy of the above type can have a large beneficial effect for the patient; increasing treatment success and reducing side effects.
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Affiliation(s)
- Jeff W N Bachman
- Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta Edmonton, AB, Canada
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43
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Hillen T, Enderling H, Hahnfeldt P. The tumor growth paradox and immune system-mediated selection for cancer stem cells. Bull Math Biol 2012. [PMID: 23196354 DOI: 10.1007/s11538-012-9798-x] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Cancer stem cells (CSCs) drive tumor progression, metastases, treatment resistance, and recurrence. Understanding CSC kinetics and interaction with their nonstem counterparts (called tumor cells, TCs) is still sparse, and theoretical models may help elucidate their role in cancer progression. Here, we develop a mathematical model of a heterogeneous population of CSCs and TCs to investigate the proposed "tumor growth paradox"--accelerated tumor growth with increased cell death as, for example, can result from the immune response or from cytotoxic treatments. We show that if TCs compete with CSCs for space and resources they can prevent CSC division and drive tumors into dormancy. Conversely, if this competition is reduced by death of TCs, the result is a liberation of CSCs and their renewed proliferation, which ultimately results in larger tumor growth. Here, we present an analytical proof for this tumor growth paradox. We show how numerical results from the model also further our understanding of how the fraction of cancer stem cells in a solid tumor evolves. Using the immune system as an example, we show that induction of cell death can lead to selection of cancer stem cells from a minor subpopulation to become the dominant and asymptotically the entire cell type in tumors.
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Affiliation(s)
- Thomas Hillen
- Centre for Mathematical Biology, Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada.
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