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Almeida L, Denis JA, Ferrand N, Lorenzi T, Prunet A, Sabbah M, Villa C. Evolutionary dynamics of glucose-deprived cancer cells: insights from experimentally informed mathematical modelling. J R Soc Interface 2024; 21:20230587. [PMID: 38196375 PMCID: PMC10777142 DOI: 10.1098/rsif.2023.0587] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2023] [Accepted: 12/08/2023] [Indexed: 01/11/2024] Open
Abstract
Glucose is a primary energy source for cancer cells. Several lines of evidence support the idea that monocarboxylate transporters, such as MCT1, elicit metabolic reprogramming of cancer cells in glucose-poor environments, allowing them to re-use lactate, a by-product of glucose metabolism, as an alternative energy source with serious consequences for disease progression. We employ a synergistic experimental and mathematical modelling approach to explore the evolutionary processes at the root of cancer cell adaptation to glucose deprivation, with particular focus on the mechanisms underlying the increase in MCT1 expression observed in glucose-deprived aggressive cancer cells. Data from in vitro experiments on breast cancer cells are used to inform and calibrate a mathematical model that comprises a partial integro-differential equation for the dynamics of a population of cancer cells structured by the level of MCT1 expression. Analytical and numerical results of this model suggest that environment-induced changes in MCT1 expression mediated by lactate-associated signalling pathways enable a prompt adaptive response of glucose-deprived cancer cells, while fluctuations in MCT1 expression due to epigenetic changes create the substrate for environmental selection to act upon, speeding up the selective sweep underlying cancer cell adaptation to glucose deprivation, and may constitute a long-term bet-hedging mechanism.
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Affiliation(s)
- Luis Almeida
- Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions UMR 7598, Paris 75005, France
| | - Jérôme Alexandre Denis
- Sorbonne Université, Cancer Biology and Therapeutics, INSERM, CNRS, Institut Universitaire de Cancérologie, Saint-Antoine Research Center (CRSA), Paris 75012, France
- Department of Endocrinology and Oncology Biochemistry, Pitié-Salpetrière Hospital, Paris 75013, France
| | - Nathalie Ferrand
- Sorbonne Université, Cancer Biology and Therapeutics, INSERM, CNRS, Institut Universitaire de Cancérologie, Saint-Antoine Research Center (CRSA), Paris 75012, France
| | - Tommaso Lorenzi
- Department of Mathematical Sciences ‘G. L. Lagrange’, Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, Torino 10129, Italy
| | - Antonin Prunet
- Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions UMR 7598, Paris 75005, France
- Sorbonne Université, Cancer Biology and Therapeutics, INSERM, CNRS, Institut Universitaire de Cancérologie, Saint-Antoine Research Center (CRSA), Paris 75012, France
| | - Michéle Sabbah
- Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions UMR 7598, Paris 75005, France
| | - Chiara Villa
- Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions UMR 7598, Paris 75005, France
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Pérez-Aliacar M, Ayensa-Jiménez J, Doblaré M. Modelling cell adaptation using internal variables: Accounting for cell plasticity in continuum mathematical biology. Comput Biol Med 2023; 164:107291. [PMID: 37586203 DOI: 10.1016/j.compbiomed.2023.107291] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Revised: 07/20/2023] [Accepted: 07/28/2023] [Indexed: 08/18/2023]
Abstract
Cellular adaptation is the ability of cells to change in response to different stimuli and environmental conditions. It occurs via phenotypic plasticity, that is, changes in gene expression derived from changes in the physiological environment. This phenomenon is important in many biological processes, in particular in cancer evolution and its treatment. Therefore, it is crucial to understand the mechanisms behind it. Specifically, the emergence of the cancer stem cell phenotype, showing enhanced proliferation and invasion rates, is an essential process in tumour progression. We present a mathematical framework to simulate phenotypic heterogeneity in different cell populations as a result of their interaction with chemical species in their microenvironment, through a continuum model using the well-known concept of internal variables to model cell phenotype. The resulting model, derived from conservation laws, incorporates the relationship between the phenotype and the history of the stimuli to which cells have been subjected, together with the inheritance of that phenotype. To illustrate the model capabilities, it is particularised for glioblastoma adaptation to hypoxia. A parametric analysis is carried out to investigate the impact of each model parameter regulating cellular adaptation, showing that it permits reproducing different trends reported in the scientific literature. The framework can be easily adapted to any particular problem of cell plasticity, with the main limitation of having enough cells to allow working with continuum variables. With appropriate calibration and validation, it could be useful for exploring the underlying processes of cellular adaptation, as well as for proposing favourable/unfavourable conditions or treatments.
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Affiliation(s)
- Marina Pérez-Aliacar
- Mechanical Engineering Department, School of Engineering and Architecture, University of Zaragoza, C/ Maria de Luna, Zaragoza, 50018, Spain; Engineering Research Institute of Aragón (I3A), University of Zaragoza, C/ Mariano Esquillor, Zaragoza, 50018, Spain.
| | - Jacobo Ayensa-Jiménez
- Engineering Research Institute of Aragón (I3A), University of Zaragoza, C/ Mariano Esquillor, Zaragoza, 50018, Spain; Aragón Health Research Institute (IISAragón), Avda. San Juan Bosco, Zaragoza, 50009, Spain.
| | - Manuel Doblaré
- Engineering Research Institute of Aragón (I3A), University of Zaragoza, C/ Mariano Esquillor, Zaragoza, 50018, Spain; Aragón Health Research Institute (IISAragón), Avda. San Juan Bosco, Zaragoza, 50009, Spain; Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBERBBN), Avda. Monforte de Lemos, Madrid, 28029, Spain; Nanjing Tech University, South Puzhu Road, Nanging, 211800, China.
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3
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Spatio-temporal modelling of phenotypic heterogeneity in tumour tissues and its impact on radiotherapy treatment. J Theor Biol 2023; 556:111248. [PMID: 36150537 DOI: 10.1016/j.jtbi.2022.111248] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Revised: 08/02/2022] [Accepted: 08/17/2022] [Indexed: 11/20/2022]
Abstract
We present a mathematical model that describes how tumour heterogeneity evolves in a tissue slice that is oxygenated by a single blood vessel. Phenotype is identified with the stemness level of a cell and determines its proliferative capacity, apoptosis propensity and response to treatment. Our study is based on numerical bifurcation analysis and dynamical simulations of a system of coupled, non-local (in phenotypic "space") partial differential equations that link the phenotypic evolution of the tumour cells to local tissue oxygen levels. In our formulation, we consider a 1D geometry where oxygen is supplied by a blood vessel located on the domain boundary and consumed by the tumour cells as it diffuses through the tissue. For biologically relevant parameter values, the system exhibits multiple steady states; in particular, depending on the initial conditions, the tumour is either eliminated ("tumour-extinction") or it persists ("tumour-invasion"). We conclude by using the model to investigate tumour responses to radiotherapy, and focus on identifying radiotherapy strategies which can eliminate the tumour. Numerical simulations reveal how phenotypic heterogeneity evolves during treatment and highlight the critical role of tissue oxygen levels on the efficacy of radiation protocols that are commonly used in the clinic.
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Stochastic Fluctuations Drive Non-genetic Evolution of Proliferation in Clonal Cancer Cell Populations. Bull Math Biol 2022; 85:8. [PMID: 36562835 DOI: 10.1007/s11538-022-01113-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Accepted: 11/30/2022] [Indexed: 12/24/2022]
Abstract
Evolutionary dynamics allows us to understand many changes happening in a broad variety of biological systems, ranging from individuals to complete ecosystems. It is also behind a number of remarkable organizational changes that happen during the natural history of cancers. These reflect tumour heterogeneity, which is present at all cellular levels, including the genome, proteome and phenome, shaping its development and interrelation with its environment. An intriguing observation in different cohorts of oncological patients is that tumours exhibit an increased proliferation as the disease progresses, while the timescales involved are apparently too short for the fixation of sufficient driver mutations to promote explosive growth. Here, we discuss how phenotypic plasticity, emerging from a single genotype, may play a key role and provide a ground for a continuous acceleration of the proliferation rate of clonal populations with time. We address this question by combining the analysis of real-time growth of non-small-cell lung carcinoma cells (N-H460) together with stochastic and deterministic mathematical models that capture proliferation trait heterogeneity in clonal populations to elucidate the contribution of phenotypic transitions on tumour growth dynamics.
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Intermittent hypoxia enhances the expression of hypoxia inducible factor HIF1A through histone demethylation. J Biol Chem 2022; 298:102536. [PMID: 36174675 PMCID: PMC9597902 DOI: 10.1016/j.jbc.2022.102536] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Revised: 09/14/2022] [Accepted: 09/15/2022] [Indexed: 11/29/2022] Open
Abstract
The cellular response to hypoxia is regulated through enzymatic oxygen sensors, including the prolyl hydroxylases, which control degradation of the well-known hypoxia inducible factors (HIFs). Other enzymatic oxygen sensors have been recently identified, including members of the KDM histone demethylase family. Little is known about how different oxygen-sensing pathways interact and if this varies depending on the form of hypoxia, such as chronic or intermittent. In this study, we investigated how two proposed cellular oxygen-sensing systems, HIF-1 and KDM4A, KDM4B, and KDM4C, respond in cells exposed to rapid forms of intermittent hypoxia (minutes) and compared to chronic hypoxia (hours). We found that intermittent hypoxia increases HIF-1α protein through a pathway distinct from chronic hypoxia, involving the KDM4A, KDM4B, and KDM4C histone lysine demethylases. Intermittent hypoxia increases the quantity and activity of KDM4A, KDM4B, and KDM4C, resulting in a decrease in histone 3 lysine 9 (H3K9) trimethylation near the HIF1A locus. We demonstrate that this contrasts with chronic hypoxia, which decreases KDM4A, KDM4B, and KDM4C activity, leading to hypertrimethylation of H3K9 globally and at the HIF1A locus. Altogether, we found that demethylation of histones bound to the HIF1A gene in intermittent hypoxia increases HIF1A mRNA expression, which has the downstream effect of increasing overall HIF-1 activity and expression of HIF target genes. This study highlights how multiple oxygen-sensing pathways can interact to regulate and fine tune the cellular hypoxic response depending on the period and length of hypoxia.
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Liu Y, Kang Y, Li J, Zhang Y, Jia S, Sun Q, Ma Y, Zhang J, Wang Z, Cao Y, Shen Y. Estrogen Receptor and Claudin-6 Might Play Vital Roles for Long-Term Prognosis in Patients With Luminal A Breast Cancer Who Underwent Neoadjuvant Chemotherapy. Front Oncol 2022; 12:630065. [PMID: 35847894 PMCID: PMC9280129 DOI: 10.3389/fonc.2022.630065] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2020] [Accepted: 05/26/2022] [Indexed: 12/04/2022] Open
Abstract
Purpose It is well-known that the pathological complete response (pCR) rate in patients with luminal A cancer (LAC) is lower than those of other subtypes of breast cancer. The phenotype of cancer often alters after neoadjuvant chemotherapy (NAC) which may be related to hypoxia, and the latter might induce the drift of the estrogen receptor (ER). The phenotype drift in local advanced LAC after NAC might influence the long-term prognosis. Methods The oxygen concentration of cancer tissues during NAC was recorded and analyzed (n = 43). The expression of ER and claudin-6 was detected in pre- and post-NAC specimens. Results NAC might induce the cycling intracanceral hypoxia, and the pattern was related to NAC response. The median follow-up time was 61 months. Most of the patients (67%) with stable or increased ER and claudin-6 expression exhibited perfect prognosis (DFS = 100%, 61 months). About 20% of patients with decreased claudin-6 would undergo the poor prognosis (DFS = 22.2%, 61 months). The contrasting prognosis (100% vs. 22.2%) had nothing to do with the response of NAC in the above patients. Only 13% patients had stable claudin-6 and decreased ER, whose prognosis might relate to the response of NAC. Conclusion NAC might induce cycling intracanceral hypoxia to promote the phenotype drift in local advanced LAC, and the changes in ER and claudin-6 after NAC would determine the long-term prognosis.
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Affiliation(s)
- Yushi Liu
- Department of Breast Surgery, ShengJing Hospital of China Medical University, Shenyang, China
| | - Ye Kang
- Department of Pathology, Shengjing Hospital of China Medical University, Shenyang, China
| | - Jianyi Li
- Department of Breast Surgery, Liaoning Cancer Hospital, Shenyang, China
- *Correspondence: Jianyi Li,
| | - Yang Zhang
- Department of Breast Surgery, ShengJing Hospital of China Medical University, Shenyang, China
| | - Shi Jia
- Department of Breast Surgery, ShengJing Hospital of China Medical University, Shenyang, China
| | - Qiang Sun
- Department of Breast Surgery, Benxi Iron and Steel Co. General Hospital, Benxi, China
| | - Yan Ma
- Department of Breast Surgery, ShengJing Hospital of China Medical University, Shenyang, China
| | - Jing Zhang
- Department of Breast Surgery, ShengJing Hospital of China Medical University, Shenyang, China
| | - Zhenrong Wang
- Department of Breast Surgery, ShengJing Hospital of China Medical University, Shenyang, China
| | - Yanan Cao
- Department of Breast Surgery, ShengJing Hospital of China Medical University, Shenyang, China
| | - Yang Shen
- Department of Breast Surgery, ShengJing Hospital of China Medical University, Shenyang, China
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Foo J, Basanta D, Rockne RC, Strelez C, Shah C, Ghaffarian K, Mumenthaler SM, Mitchell K, Lathia JD, Frankhouser D, Branciamore S, Kuo YH, Marcucci G, Vander Velde R, Marusyk A, Hang S, Hari K, Jolly MK, Hatzikirou H, Poels K, Spilker M, Shtylla B, Robertson-Tessi M, Anderson ARA. Roadmap on plasticity and epigenetics in cancer. Phys Biol 2022; 19. [PMID: 35078159 PMCID: PMC9190291 DOI: 10.1088/1478-3975/ac4ee2] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Accepted: 01/25/2022] [Indexed: 11/22/2022]
Abstract
The role of plasticity and epigenetics in shaping cancer evolution and response to therapy has taken center stage with recent technological advances including single cell sequencing. This roadmap article is focused on state-of-the-art mathematical and experimental approaches to interrogate plasticity in cancer, and addresses the following themes and questions: is there a formal overarching framework that encompasses both non-genetic plasticity and mutation-driven somatic evolution? How do we measure and model the role of the microenvironment in influencing/controlling non-genetic plasticity? How can we experimentally study non-genetic plasticity? Which mathematical techniques are required or best suited? What are the clinical and practical applications and implications of these concepts?
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Affiliation(s)
- Jasmine Foo
- University of Minnesota System, School of Mathematics, Minneapolis, Minnesota, 55455-2020, UNITED STATES
| | - David Basanta
- Integrated Mathematical Oncology, H Lee Moffitt Cancer Center and Research Center Inc, H Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, MRC-3 West/IMO, Tampa, Florida 33612USA, Tampa, Florida, 33612-9416, UNITED STATES
| | - Russell C Rockne
- Computational and Quantitative Medicine; Division of Mathematical Oncology, Beckman Research Institute, 1500 E Duarte Rd, Rose Vogel Building (74), Duarte, California, 91010, UNITED STATES
| | - Carly Strelez
- Lawrence J. Ellison Institute , Transformative Medicine, Los Angeles, CA 90064, UNITED STATES
| | - Curran Shah
- Lawrence J. Ellison Institute , Transformative Medicine, Los Angeles, CA 90064, UNITED STATES
| | - Kimya Ghaffarian
- Lawrence J. Ellison Institute , Transformative Medicine, Los Angeles, CA 90064, UNITED STATES
| | - Shannon M Mumenthaler
- Lawrence J. Ellison Institute , Transformative Medicine, Los Angeles, CA 90064, UNITED STATES
| | - Kelly Mitchell
- Department of Cardiovascular & Metabolic Sciences, Cleveland Clinic, Lerner Research Institute, Cleveland, Ohio, 44195-5243, UNITED STATES
| | - Justin D Lathia
- Department of Cardiovascular & Metabolic Sciences, Cleveland Clinic, Lerner Research Institute, Cleveland, Ohio, 44195-5243, UNITED STATES
| | - David Frankhouser
- Computational and Quantitative Medicine; Division of Mathematical Oncology, Beckman Research Institute, 1500 E Duarte Rd, Rose Vogel Building (74), Duarte, California, 91010, UNITED STATES
| | - Sergio Branciamore
- Computational and Quantitative Medicine; Division of Mathematical Oncology, Beckman Research Institute, 1500 E Duarte Rd, Rose Vogel Building (74), Duarte, California, 91010, UNITED STATES
| | - Ya-Huei Kuo
- Hematologic Malignancies Translational Science, City of Hope National Medical Center, Beckman Research Institute, 1500 E Duarte Rd, Rose Vogel Building (74), Duarte, California, 91010, UNITED STATES
| | - Guido Marcucci
- Hematologic Malignancies Translational Science, City of Hope National Medical Center, Beckman Research Institute, 1500 E Duarte Rd, Rose Vogel Building (74), Duarte, California, 91010, UNITED STATES
| | - Robert Vander Velde
- Department of Cancer Physiology, H Lee Moffitt Cancer Center and Research Center Inc, H Lee Moffitt Cancer Center and Research Institute, 12902 Magnolia Drive, MRC-3 West/IMO, Tampa, Florida 33612USA, Tampa, Florida, 33612-9416, UNITED STATES
| | - Andriy Marusyk
- Cancer Physiology, Moffitt Cancer Center, 12902 USF Magnolia Drive, Tampa, Florida, 33612, UNITED STATES
| | - Sui Hang
- Institute for Systems Biology, Systems Biology, WA , WA 98109, UNITED STATES
| | - Kishore Hari
- Indian Institute of Science, 560012 Bangalore, Bangalore, 560012, INDIA
| | - Mohit Kumar Jolly
- Centre for BioSystems Science and Engineering,, Indian Institute of Science, 560012 Bangalore, Bangalore, 560012, INDIA
| | - Haralampos Hatzikirou
- Khalifa University, P.O. Box: 127788, Abu Dhabi, Abu Dhabi, NA, UNITED ARAB EMIRATES
| | - Kamrine Poels
- Early Clinical Development, Pfizer Global Research and Development, Early Clinical Development, Groton, Connecticut, 06340, UNITED STATES
| | - Mary Spilker
- Medicine Design, Pfizer Global Research and Development, Medicine Design, Groton, Connecticut, 06340, UNITED STATES
| | - Blerta Shtylla
- Early Clinical Development, Pfizer Global Research and Development, Early Clinical Development, Groton, Connecticut, 06340, UNITED STATES
| | - Mark Robertson-Tessi
- Integrated Mathematical Oncology Department, Moffitt Cancer Center, 12902 USF Magnolia Drive, Tampa, Florida, 33612, UNITED STATES
| | - Alexander R A Anderson
- Integrated Mathematical Oncology, Moffitt Cancer Center, Co-Director of Integrated Mathematical Oncology, 12902 Magnolia Drive, SRB 4 Rm 24000H, Tampa, Florida 33612, Tampa, 33612, UNITED STATES
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8
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Fiandaca G, Bernardi S, Scianna M, Delitala ME. A phenotype-structured model to reproduce the avascular growth of a tumor and its interaction with the surrounding environment. J Theor Biol 2021; 535:110980. [PMID: 34915043 DOI: 10.1016/j.jtbi.2021.110980] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Revised: 10/08/2021] [Accepted: 12/06/2021] [Indexed: 11/28/2022]
Abstract
We here propose a one-dimensional spatially explicit phenotype-structured model to analyze selected aspects of avascular tumor progression. In particular, our approach distinguishes viable and necrotic cell fractions. The metabolically active part of the disease is, in turn, differentiated according to a continuous trait, that identifies cell variants with different degrees of motility and proliferation potential. A parabolic partial differential equation (PDE) then governs the spatio-temporal evolution of the phenotypic distribution of active cells within the host tissue. In this respect, active tumor agents are allowed to duplicate, move upon haptotactic and pressure stimuli, and eventually undergo necrosis. The mutual influence between the emerging malignancy and its environment (in terms of molecular landscape) is implemented by coupling the evolution law of the viable tumor mass with a parabolic PDE for oxygen kinetics and a differential equation that accounts for local consumption of extracellular matrix (ECM) elements. The resulting numerical realizations reproduce tumor growth and invasion in a number scenarios that differ for cell properties (i.e., individual migratory behavior, duplication and mutation potential) and environmental conditions (i.e., level of tissue oxygenation and homogeneity in the initial matrix profile). In particular, our simulations show that, in all cases, more mobile cell variants occupy the front edge of the tumor, whereas more proliferative clones are selected at the more internal regions. A necrotic core constantly occupies the bulk of the mass due to nutrient deprivation. This work may eventually suggest some biomedical strategies to partially reduce tumor aggressiveness, i.e., to enhance necrosis of malignant tissue and to promote the presence of more proliferative cell phenotypes over more invasive ones.
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Affiliation(s)
- Giada Fiandaca
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
| | - Sara Bernardi
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
| | - Marco Scianna
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
| | - Marcello Edoardo Delitala
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
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Bridging cell-scale simulations and radiologic images to explain short-time intratumoral oxygen fluctuations. PLoS Comput Biol 2021; 17:e1009206. [PMID: 34310608 PMCID: PMC8341701 DOI: 10.1371/journal.pcbi.1009206] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 08/05/2021] [Accepted: 06/22/2021] [Indexed: 11/19/2022] Open
Abstract
Radiologic images provide a way to monitor tumor development and its response to therapies in a longitudinal and minimally invasive fashion. However, they operate on a macroscopic scale (average value per voxel) and are not able to capture microscopic scale (cell-level) phenomena. Nevertheless, to examine the causes of frequent fast fluctuations in tissue oxygenation, models simulating individual cells’ behavior are needed. Here, we provide a link between the average data values recorded for radiologic images and the cellular and vascular architecture of the corresponding tissues. Using hybrid agent-based modeling, we generate a set of tissue morphologies capable of reproducing oxygenation levels observed in radiologic images. We then use these in silico tissues to investigate whether oxygen fluctuations can be explained by changes in vascular oxygen supply or by modulations in cellular oxygen absorption. Our studies show that intravascular changes in oxygen supply reproduce the observed fluctuations in tissue oxygenation in all considered regions of interest. However, larger-magnitude fluctuations cannot be recreated by modifications in cellular absorption of oxygen in a biologically feasible manner. Additionally, we develop a procedure to identify plausible tissue morphologies for a given temporal series of average data from radiology images. In future applications, this approach can be used to generate a set of tissues comparable with radiology images and to simulate tumor responses to various anti-cancer treatments at the tissue-scale level. Low levels of oxygen, called hypoxia, are observable in many solid tumors. They are associated with more aggressive malignant cells that are resistant to chemo-, radio-, and immunotherapies. Recently developed imaging techniques provide a way to measure the magnitude of frequent short-term oxygen fluctuations, but they operate on a macro-scale voxel level. To examine the possible causes of rapid oxygen fluctuations at the cell level, we developed a hybrid agent-based mathematical model. We tested two different mechanisms that may be responsible for these cyclic effects on tissue oxygenation: temporal variations in vascular influx of oxygen and modulations in cellular oxygen absorption. Additionally, we developed a procedure to identify plausible tissue morphologies from data collected from radiological images. This can provide a bridge between the micro-scale simulations with individual cells and the longitudinal medical images containing average values. In future applications, this approach can be used to generate a set of tissues compatible with radiology images and to simulate tumor responses to various anticancer treatments at the cell-scale level.
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10
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Fiandaca G, Delitala M, Lorenzi T. A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer. Bull Math Biol 2021; 83:83. [PMID: 34129102 PMCID: PMC8205926 DOI: 10.1007/s11538-021-00914-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2020] [Accepted: 05/25/2021] [Indexed: 10/31/2022]
Abstract
Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatment. We present a mathematical model to study the influence of hypoxia and acidity on the evolutionary dynamics of cancer cells in vascularised tumours. The model is formulated as a system of partial integro-differential equations that describe the phenotypic evolution of cancer cells in response to dynamic variations in the spatial distribution of three abiotic factors that are key players in tumour metabolism: oxygen, glucose and lactate. The results of numerical simulations of a calibrated version of the model based on real data recapitulate the eco-evolutionary spatial dynamics of tumour cells and their adaptation to hypoxic and acidic microenvironments. Moreover, such results demonstrate how nonlinear interactions between tumour cells and abiotic factors can lead to the formation of environmental gradients which select for cells with phenotypic characteristics that vary with distance from intra-tumour blood vessels, thus promoting the emergence of intra-tumour phenotypic heterogeneity. Finally, our theoretical findings reconcile the conclusions of earlier studies by showing that the order in which resistance to hypoxia and resistance to acidity arise in tumours depend on the ways in which oxygen and lactate act as environmental stressors in the evolutionary dynamics of cancer cells.
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Affiliation(s)
- Giada Fiandaca
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino, Italy
| | - Marcello Delitala
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino, Italy
| | - Tommaso Lorenzi
- Department of Mathematical Sciences "G. L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino, Italy.
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11
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Celora GL, Byrne HM, Zois CE, Kevrekidis PG. Phenotypic variation modulates the growth dynamics and response to radiotherapy of solid tumours under normoxia and hypoxia. J Theor Biol 2021; 527:110792. [PMID: 34087269 DOI: 10.1016/j.jtbi.2021.110792] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2021] [Revised: 05/25/2021] [Accepted: 05/30/2021] [Indexed: 12/24/2022]
Abstract
In cancer, treatment failure and disease recurrence have been associated with small subpopulations of cancer cells with a stem-like phenotype. In this paper, we develop and investigate a phenotype-structured model of solid tumour growth in which cells are structured by a stemness level, which varies continuously between stem-like and terminally differentiated behaviours. Cell evolution is driven by proliferation and death, as well as advection and diffusion with respect to the stemness structure variable. Here, the magnitude and sign of the advective flux are allowed to vary with the oxygen level. We use the model to investigate how the environment, in particular oxygen levels, affects the tumour's population dynamics and composition, and its response to radiotherapy. We use a combination of numerical and analytical techniques to quantify how under physiological oxygen levels the cells evolve to a differentiated phenotype and under low oxygen level (i.e., hypoxia) they de-differentiate. Under normoxia, the proportion of cancer stem cells is typically negligible and the tumour may ultimately become extinct whereas under hypoxia cancer stem cells comprise a dominant proportion of the tumour volume, enhancing radio-resistance and favouring the tumour's long-term survival. We then investigate how such phenotypic heterogeneity impacts the tumour's response to treatment with radiotherapy under normoxia and hypoxia. Of particular interest is establishing how the presence of radio-resistant cancer stem cells can facilitate a tumour's regrowth following radiotherapy. We also use the model to show how radiation-induced changes in tumour oxygen levels can give rise to complex re-growth dynamics. For example, transient periods of hypoxia induced by damage to tumour blood vessels may rescue the cancer cell population from extinction and drive secondary regrowth.
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Affiliation(s)
- Giulia L Celora
- Mathematical Institute, University of Oxford, Oxford, United Kingdom.
| | - Helen M Byrne
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Christos E Zois
- Molecular Oncology Laboratories, Department of Oncology, Oxford University, Weatherall Institute of Molecular Medicine, John Radcliffe Hospital, Oxford, United Kingdom; Department of Radiotherapy and Oncology, School of Health, Democritus University of Thrace, 68100 Alexandroupolis, Greece
| | - P G Kevrekidis
- Department of Mathematics & Statistics, University of Massachusetts, Amherst 01003, USA
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Edwards J, Marusyk A, Basanta D. Selection-driven tumor evolution with public goods leads to patterns of clonal expansion consistent with neutral growth. iScience 2021; 24:101901. [PMID: 33364589 PMCID: PMC7753957 DOI: 10.1016/j.isci.2020.101901] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Revised: 10/07/2020] [Accepted: 12/01/2020] [Indexed: 12/18/2022] Open
Abstract
Cancers are the result of eco-evolutionary processes fueled by heritable phenotypic diversification and driven by environmentally dependent selection. Space represents a key growth-limiting ecological resource, the ability to explore this resource is likely under strong selection. Using agent-based modeling, we explored the interplay between phenotypic strategies centered on gaining access to new space through cell-extrinsic degradation of extracellular matrix barriers and the exploitation of this resource through maximizing cell proliferation. While cell proliferation is a cell-intrinsic property, newly accessed space represents a public good, which can benefit both producers and non-producers. We found that this interplay results in ecological succession, enabling emergence of large, heterogeneous, and highly proliferative populations. Even though in our simulations both remodeling and proliferation strategies were under strong positive selection, their interplay led to sub-clonal architecture that could be interpreted as evidence for neutral evolution, warranting cautious interpretation of inferences from sequencing of cancer genomes.
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Affiliation(s)
- Jack Edwards
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, 12902 USF Magnolia Drive, Tampa, FL 33612, USA
| | - Andriy Marusyk
- Cancer Physiology Department, H. Lee Moffitt Cancer Center & Research Institute, 12902 Magnolia Drive, SRB 4 Rm 24000H, Tampa, Florida 33612, USA
| | - David Basanta
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, 12902 USF Magnolia Drive, Tampa, FL 33612, USA
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Bader SB, Dewhirst MW, Hammond EM. Cyclic Hypoxia: An Update on Its Characteristics, Methods to Measure It and Biological Implications in Cancer. Cancers (Basel) 2020; 13:E23. [PMID: 33374581 PMCID: PMC7793090 DOI: 10.3390/cancers13010023] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2020] [Revised: 12/14/2020] [Accepted: 12/16/2020] [Indexed: 02/07/2023] Open
Abstract
Regions of hypoxia occur in most if not all solid cancers. Although the presence of tumor hypoxia is a common occurrence, the levels of hypoxia and proportion of the tumor that are hypoxic vary significantly. Importantly, even within tumors, oxygen levels fluctuate due to changes in red blood cell flux, vascular remodeling and thermoregulation. Together, this leads to cyclic or intermittent hypoxia. Tumor hypoxia predicts for poor patient outcome, in part due to increased resistance to all standard therapies. However, it is less clear how cyclic hypoxia impacts therapy response. Here, we discuss the causes of cyclic hypoxia and, importantly, which imaging modalities are best suited to detecting cyclic vs. chronic hypoxia. In addition, we provide a comparison of the biological response to chronic and cyclic hypoxia, including how the levels of reactive oxygen species and HIF-1 are likely impacted. Together, we highlight the importance of remembering that tumor hypoxia is not a static condition and that the fluctuations in oxygen levels have significant biological consequences.
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Affiliation(s)
- Samuel B. Bader
- Department of Oncology, The Oxford Institute for Radiation Oncology, Oxford University, Oxford OX3 7DQ, UK;
| | - Mark W. Dewhirst
- Radiation Oncology Department, Duke University School of Medicine, Durham, NC 27710, USA
| | - Ester M. Hammond
- Department of Oncology, The Oxford Institute for Radiation Oncology, Oxford University, Oxford OX3 7DQ, UK;
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Ardaševa A, Anderson ARA, Gatenby RA, Byrne HM, Maini PK, Lorenzi T. Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments. Phys Rev E 2020; 102:042404. [PMID: 33212726 PMCID: PMC10900972 DOI: 10.1103/physreve.102.042404] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Accepted: 09/14/2020] [Indexed: 06/11/2023]
Abstract
Deterministic continuum models formulated as nonlocal partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In light of these considerations, in this paper we develop a stochastic individual-based model for the coevolution of two competing phenotype-structured cell populations that are exposed to time-varying nutrient levels and undergo spontaneous, heritable phenotypic changes with different probabilities. Here, the evolution of every cell is described by a set of rules that result in a discrete-time branching random walk on the space of phenotypic states, and nutrient levels are governed by a difference equation in which a sink term models nutrient consumption by the cells. We formally show that the deterministic continuum counterpart of this model comprises a system of nonlocal partial differential equations for the cell population density functions coupled with an ordinary differential equation for the nutrient concentration. We compare the individual-based model and its continuum analog, focusing on scenarios whereby the predictions of the two models differ. The results obtained clarify the conditions under which significant differences between the two models can emerge due to bottleneck effects that bring about both lower regularity of the density functions of the two populations and more pronounced demographic stochasticity. In particular, bottleneck effects emerge in the presence of lower probabilities of phenotypic variation and are more apparent when the two populations are characterized by lower fitness initial mean phenotypes and smaller initial levels of phenotypic heterogeneity. The emergence of these effects, and thus the agreement between the two modeling approaches, is also dependent on the initial proportions of the two populations. As an illustrative example, we demonstrate the implications of these results in the context of the mathematical modeling of the early stage of metastatic colonization of distant organs.
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Affiliation(s)
- Aleksandra Ardaševa
- Wolfson Centre for Mathematical Biology, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - Alexander R A Anderson
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, Florida 33612, USA
| | - Robert A Gatenby
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, Florida 33612, USA
| | - Helen M Byrne
- Wolfson Centre for Mathematical Biology, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - Philip K Maini
- Wolfson Centre for Mathematical Biology, University of Oxford, Oxford OX2 6GG, United Kingdom
| | - Tommaso Lorenzi
- Department of Mathematical Sciences "G. L. Lagrange", Dipartimento di Eccellenza 2018-2022, Politecnico di Torino, Italy
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