1
|
Del Pino Herrera A, Ferrall-Fairbanks MC. A war on many fronts: cross disciplinary approaches for novel cancer treatment strategies. Front Genet 2024; 15:1383676. [PMID: 38873108 PMCID: PMC11169904 DOI: 10.3389/fgene.2024.1383676] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Accepted: 04/26/2024] [Indexed: 06/15/2024] Open
Abstract
Cancer is a disease characterized by uncontrolled cellular growth where cancer cells take advantage of surrounding cellular populations to obtain resources and promote invasion. Carcinomas are the most common type of cancer accounting for almost 90% of cancer cases. One of the major subtypes of carcinomas are adenocarcinomas, which originate from glandular cells that line certain internal organs. Cancers such as breast, prostate, lung, pancreas, colon, esophageal, kidney are often adenocarcinomas. Current treatment strategies include surgery, chemotherapy, radiation, targeted therapy, and more recently immunotherapy. However, patients with adenocarcinomas often develop resistance or recur after the first line of treatment. Understanding how networks of tumor cells interact with each other and the tumor microenvironment is crucial to avoid recurrence, resistance, and high-dose therapy toxicities. In this review, we explore how mathematical modeling tools from different disciplines can aid in the development of effective and personalized cancer treatment strategies. Here, we describe how concepts from the disciplines of ecology and evolution, economics, and control engineering have been applied to mathematically model cancer dynamics and enhance treatment strategies.
Collapse
Affiliation(s)
- Adriana Del Pino Herrera
- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, United States
| | - Meghan C. Ferrall-Fairbanks
- J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, United States
- University of Florida Health Cancer Center, University of Florida, Gainesville, FL, United States
| |
Collapse
|
2
|
Coggan H, Page KM. The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review. JOURNAL OF THE ROYAL SOCIETY, INTERFACE 2022; 19:20220346. [PMID: 35975562 PMCID: PMC9382458 DOI: 10.1098/rsif.2022.0346] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.
Collapse
Affiliation(s)
- Helena Coggan
- Department of Mathematics, University College London, London, UK
| | - Karen M Page
- Department of Mathematics, University College London, London, UK
| |
Collapse
|
3
|
In Silico Investigations of Multi-Drug Adaptive Therapy Protocols. Cancers (Basel) 2022; 14:cancers14112699. [PMID: 35681680 PMCID: PMC9179496 DOI: 10.3390/cancers14112699] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2022] [Revised: 05/21/2022] [Accepted: 05/25/2022] [Indexed: 11/17/2022] Open
Abstract
The standard of care for cancer patients aims to eradicate the tumor by killing the maximum number of cancer cells using the maximum tolerated dose (MTD) of a drug. MTD causes significant toxicity and selects for resistant cells, eventually making the tumor refractory to treatment. Adaptive therapy aims to maximize time to progression (TTP), by maintaining sensitive cells to compete with resistant cells. We explored both dose modulation (DM) protocols and fixed dose (FD) interspersed with drug holiday protocols. In contrast to previous single drug protocols, we explored the determinants of success of two-drug adaptive therapy protocols, using an agent-based model. In almost all cases, DM protocols (but not FD protocols) increased TTP relative to MTD. DM protocols worked well when there was more competition, with a higher cost of resistance, greater cell turnover, and when crowded proliferating cells could replace their neighbors. The amount that the drug dose was changed, mattered less. The more sensitive the protocol was to tumor burden changes, the better. In general, protocols that used as little drug as possible, worked best. Preclinical experiments should test these predictions, especially dose modulation protocols, with the goal of generating successful clinical trials for greater cancer control.
Collapse
|
4
|
Wölfl B, te Rietmole H, Salvioli M, Kaznatcheev A, Thuijsman F, Brown JS, Burgering B, Staňková K. The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer. DYNAMIC GAMES AND APPLICATIONS 2021; 12:313-342. [PMID: 35601872 PMCID: PMC9117378 DOI: 10.1007/s13235-021-00397-w] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 07/05/2021] [Indexed: 05/05/2023]
Abstract
Evolutionary game theory mathematically conceptualizes and analyzes biological interactions where one's fitness not only depends on one's own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer's eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. Moreover, we discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with evolutionary game theory has medically useful implications that can inform and create a lockstep between empirical findings and mathematical modeling. We suggest that cancer progression is an evolutionary competition between different cell types and therefore needs to be viewed as an evolutionary game.
Collapse
Affiliation(s)
- Benjamin Wölfl
- Department of Mathematics, University of Vienna, Vienna, Austria
- Vienna Graduate School of Population Genetics, Vienna, Austria
| | - Hedy te Rietmole
- Department of Molecular Cancer Research, University Medical Center Utrecht, Utrecht, The Netherlands
| | - Monica Salvioli
- Department of Mathematics, University of Trento, Trento, Italy
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Artem Kaznatcheev
- Department of Biology, University of Pennsylvania, Philadelphia, USA
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Frank Thuijsman
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Joel S. Brown
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL USA
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL USA
| | - Boudewijn Burgering
- Department of Molecular Cancer Research, University Medical Center Utrecht, Utrecht, The Netherlands
- The Oncode Institute, Utrecht, The Netherlands
| | - Kateřina Staňková
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
- Department of Engineering Systems and Services, Faculty of Technology, Policy and Management, Delft University of Technology, Delft, The Netherlands
| |
Collapse
|
5
|
Tavakoli F, Sartakhti JS, Manshaei MH, Basanta D. Cancer immunoediting: A game theoretical approach. In Silico Biol 2021; 14:1-12. [PMID: 33216021 PMCID: PMC8203245 DOI: 10.3233/isb-200475] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The role of the immune system in tumor development increasingly includes the idea of cancer immunoediting. It comprises three phases: elimination, equilibrium, and escape. In the first phase, elimination, transformed cells are recognized and destroyed by immune system. The rare tumor cells that are not destroyed in this phase may then enter the equilibrium phase, where their growth is prevented by immunity mechanisms. The escape phase represents the final phase of this process, where cancer cells begin to grow unconstrained by the immune system. In this study, we describe and analyze an evolutionary game theoretical model of proliferating, quiescent, and immune cells interactions for the first time. The proposed model is evaluated with constant and dynamic approaches. Population dynamics and interactions between the immune system and cancer cells are investigated. Stability of equilibria or critical points are analyzed by applying algebraic analysis. This model allows us to understand the process of cancer development and might help us design better treatment strategies to account for immunoediting.
Collapse
Affiliation(s)
- Fatemeh Tavakoli
- Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran
| | | | | | - David Basanta
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| |
Collapse
|
6
|
West J, Ma Y, Kaznatcheev A, Anderson ARA. IsoMaTrix: a framework to visualize the isoclines of matrix games and quantify uncertainty in structured populations. Bioinformatics 2020; 36:5542-5544. [PMID: 33325501 PMCID: PMC8016459 DOI: 10.1093/bioinformatics/btaa1025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Revised: 11/24/2020] [Accepted: 11/30/2020] [Indexed: 11/13/2022] Open
Abstract
Evolutionary game theory describes frequency-dependent selection for fixed, heritable strategies in a population of competing individuals using a payoff matrix. We present a software package to aid in the construction, analysis, and visualization of three-strategy matrix games. The IsoMaTrix package computes the isoclines (lines of zero growth) of matrix games, and facilitates direct comparison of well-mixed dynamics to structured populations on a lattice grid. IsoMaTrix computes fixed points, phase flow, trajectories, (sub)velocities, and uncertainty quantification for stochastic effects in spatial matrix games. We describe a result obtained via IsoMaTrix's spatial games functionality, which shows that the timing of competitive release in a cancer model (under continuous treatment) critically depends on the initial spatial configuration of the tumor. AVAILABILITY The code is available at: https://github.com/mathonco/isomatrix. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
Collapse
Affiliation(s)
- Jeffrey West
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa, 33612, Florida
| | - Yongqian Ma
- Department of Physics & Astronomy, University of Southern California, Los Angeles, CA, 90089-1191
| | - Artem Kaznatcheev
- Department of Translational Hematology & Oncology Research, Cleveland Clinic, Cleveland, OH, USA
| | - Alexander R A Anderson
- Integrated Mathematical Oncology Department, H. Lee Moffitt Cancer Center & Research Institute, Tampa, 33612, Florida
| |
Collapse
|
7
|
Cunningham J, Thuijsman F, Peeters R, Viossat Y, Brown J, Gatenby R, Staňková K. Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer. PLoS One 2020; 15:e0243386. [PMID: 33290430 PMCID: PMC7723267 DOI: 10.1371/journal.pone.0243386] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 11/19/2020] [Indexed: 12/16/2022] Open
Abstract
In the absence of curative therapies, treatment of metastatic castrate-resistant prostate cancer (mCRPC) using currently available drugs can be improved by integrating evolutionary principles that govern proliferation of resistant subpopulations into current treatment protocols. Here we develop what is coined as an 'evolutionary stable therapy', within the context of the mathematical model that has been used to inform the first adaptive therapy clinical trial of mCRPC. The objective of this therapy is to maintain a stable polymorphic tumor heterogeneity of sensitive and resistant cells to therapy in order to prolong treatment efficacy and progression free survival. Optimal control analysis shows that an increasing dose titration protocol, a very common clinical dosing process, can achieve tumor stabilization for a wide range of potential initial tumor compositions and volumes. Furthermore, larger tumor volumes may counter intuitively be more likely to be stabilized if sensitive cells dominate the tumor composition at time of initial treatment, suggesting a delay of initial treatment could prove beneficial. While it remains uncertain if metastatic disease in humans has the properties that allow it to be truly stabilized, the benefits of a dose titration protocol warrant additional pre-clinical and clinical investigations.
Collapse
Affiliation(s)
- Jessica Cunningham
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center & Research Institute, Tampa, Florida, United States of America
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Frank Thuijsman
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Ralf Peeters
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
| | - Yannick Viossat
- CEREMADE, Université Paris-Dauphine, Université PSL, Paris, France
| | - Joel Brown
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center & Research Institute, Tampa, Florida, United States of America
- Department of Biological Sciences, University of Illinois at Chicago, Chicago, Illinois, United States of America
| | - Robert Gatenby
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center & Research Institute, Tampa, Florida, United States of America
- Department of Diagnostic Imaging and Interventional Radiology, Moffitt Cancer Center & Research Institute, Tampa, Florida, United States of America
| | - Kateřina Staňková
- Department of Data Science and Knowledge Engineering, Maastricht University, Maastricht, The Netherlands
- Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands
| |
Collapse
|
8
|
Grimes DR, Jansen M, Macauley RJ, Scott JG, Basanta D. Evidence for hypoxia increasing the tempo of evolution in glioblastoma. Br J Cancer 2020; 123:1562-1569. [PMID: 32848201 PMCID: PMC7653934 DOI: 10.1038/s41416-020-1021-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Revised: 06/24/2020] [Accepted: 07/23/2020] [Indexed: 01/22/2023] Open
Abstract
BACKGROUND Tumour hypoxia is associated with metastatic disease, and while there have been many mechanisms proposed for why tumour hypoxia is associated with metastatic disease, it remains unclear whether one precise mechanism is the key reason or several in concert. Somatic evolution drives cancer progression and treatment resistance, fuelled not only by genetic and epigenetic mutation but also by selection from interactions between tumour cells, normal cells and physical micro-environment. Ecological habitats influence evolutionary dynamics, but the impact on tempo of evolution is less clear. METHODS We explored this complex dialogue with a combined clinical-theoretical approach by simulating a proliferative hierarchy under heterogeneous oxygen availability with an agent-based model. Predictions were compared against histology samples taken from glioblastoma patients, stained to elucidate areas of necrosis and TP53 expression heterogeneity. RESULTS Results indicate that cell division in hypoxic environments is effectively upregulated, with low-oxygen niches providing avenues for tumour cells to spread. Analysis of human data indicates that cell division is not decreased under hypoxia, consistent with our results. CONCLUSIONS Our results suggest that hypoxia could be a crucible that effectively warps evolutionary velocity, making key mutations more likely. Thus, key tumour ecological niches such as hypoxic regions may alter the evolutionary tempo, driving mutations fuelling tumour heterogeneity.
Collapse
Affiliation(s)
- David Robert Grimes
- School of Physical Sciences, Dublin City University, Dublin 9, Ireland.
- Cancer Research UK/MRC Oxford Institute for Radiation Oncology, Gray Laboratory, University of Oxford, Old Road Campus Research Building, Off Roosevelt Drive, Oxford, OX3 7DQ, UK.
| | - Marnix Jansen
- Departments of Endoscopy and Pathology, University College London Hospital, London, UK
| | - Robert J Macauley
- Department of Pathology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Jacob G Scott
- Departments of Translational Hematology and Oncology Research and Radiation Oncology, Cleveland Clinic, Cleveland, OH, USA
| | - David Basanta
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA.
| |
Collapse
|
9
|
Abstract
Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom but also on the cellular level. In cancer, for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory (EGT). The population structures arising due to cellular arrangement in tissues, however, are dynamic and thus cannot be accurately represented by either of these frameworks. In this work, we compare the conditions for cooperative success in an epithelium modelled using EGT, to those in a mechanical model of an epithelium—the Voronoi tessellation (VT) model. Crucially, in this latter model, cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the VT model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the EGT model.
Collapse
Affiliation(s)
- Jessie Renton
- Department of Mathematics, University College London , Gower Street, London WC1E 6BT , UK
| | - Karen M Page
- Department of Mathematics, University College London , Gower Street, London WC1E 6BT , UK
| |
Collapse
|
10
|
Rockne RC, Hawkins-Daarud A, Swanson KR, Sluka JP, Glazier JA, Macklin P, Hormuth DA, Jarrett AM, Lima EABF, Tinsley Oden J, Biros G, Yankeelov TE, Curtius K, Al Bakir I, Wodarz D, Komarova N, Aparicio L, Bordyuh M, Rabadan R, Finley SD, Enderling H, Caudell J, Moros EG, Anderson ARA, Gatenby RA, Kaznatcheev A, Jeavons P, Krishnan N, Pelesko J, Wadhwa RR, Yoon N, Nichol D, Marusyk A, Hinczewski M, Scott JG. The 2019 mathematical oncology roadmap. Phys Biol 2019; 16:041005. [PMID: 30991381 PMCID: PMC6655440 DOI: 10.1088/1478-3975/ab1a09] [Citation(s) in RCA: 97] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.
Collapse
Affiliation(s)
- Russell C Rockne
- Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, City of Hope National Medical Center, Duarte, CA 91010, United States of America. Author to whom any correspondence should be addressed
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
11
|
Gallaher JA, Brown JS, Anderson ARA. The impact of proliferation-migration tradeoffs on phenotypic evolution in cancer. Sci Rep 2019; 9:2425. [PMID: 30787363 PMCID: PMC6382810 DOI: 10.1038/s41598-019-39636-x] [Citation(s) in RCA: 58] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Accepted: 01/28/2019] [Indexed: 12/13/2022] Open
Abstract
Tumors are not static masses of cells but dynamic ecosystems where cancer cells experience constant turnover and evolve fitness-enhancing phenotypes. Selection for different phenotypes may vary with (1) the tumor niche (edge or core), (2) cell turnover rates, (3) the nature of the tradeoff between traits, and (4) whether deaths occur in response to demographic or environmental stochasticity. Using a spatially-explicit agent-based model, we observe how two traits (proliferation rate and migration speed) evolve under different tradeoff conditions with different turnover rates. Migration rate is favored over proliferation at the tumor's edge and vice-versa for the interior. Increasing cell turnover rates slightly slows tumor growth but accelerates the rate of evolution for both proliferation and migration. The absence of a tradeoff favors ever higher values for proliferation and migration, while a convex tradeoff tends to favor proliferation, often promoting the coexistence of a generalist and specialist phenotype. A concave tradeoff favors migration at low death rates, but switches to proliferation at higher death rates. Mortality via demographic stochasticity favors proliferation, and environmental stochasticity favors migration. While all of these diverse factors contribute to the ecology, heterogeneity, and evolution of a tumor, their effects may be predictable and empirically accessible.
Collapse
Affiliation(s)
- Jill A Gallaher
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL, USA.
| | - Joel S Brown
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL, USA
| | - Alexander R A Anderson
- Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL, USA.
| |
Collapse
|
12
|
Kaznatcheev A, Peacock J, Basanta D, Marusyk A, Scott JG. Fibroblasts and alectinib switch the evolutionary games played by non-small cell lung cancer. Nat Ecol Evol 2019; 3:450-456. [PMID: 30778184 PMCID: PMC6467526 DOI: 10.1038/s41559-018-0768-z] [Citation(s) in RCA: 71] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2017] [Accepted: 11/22/2018] [Indexed: 01/22/2023]
Abstract
Heterogeneity in strategies for survival and proliferation among the cells which constitute a tumour is a driving force behind the evolution of resistance to cancer therapy. The rules mapping the tumour’s strategy distribution to the fitness of individual strategies can be represented as an evolutionary game. We develop a game assay to measure effective evolutionary games in co-cultures of non-small cell lung cancer cells which are sensitive and resistant to the anaplastic lymphoma kinase inhibitor Alectinib. The games are not only quantitatively different between different environments, but targeted therapy and cancer associated fibroblasts qualitatively switch the type of game being played by the in-vitro population from Leader to Deadlock. This observation provides empirical confirmation of a central theoretical postulate of evolutionary game theory in oncology: we can treat not only the player, but also the game. Although we concentrate on measuring games played by cancer cells, the measurement methodology we develop can be used to advance the study of games in other microscopic systems by providing a quantitative description of non-cell-autonomous effects.
Collapse
Affiliation(s)
- Artem Kaznatcheev
- Department of Computer Science, University of Oxford, Oxford, UK. .,Department of Translational Hematology and Oncology Research, Cleveland Clinic, Cleveland, OH, USA.
| | - Jeffrey Peacock
- Department of Radiation Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - David Basanta
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, USA
| | - Andriy Marusyk
- Department of Cancer Physiology, Moffitt Cancer Center, Tampa, FL, USA.
| | - Jacob G Scott
- Department of Translational Hematology and Oncology Research, Cleveland Clinic, Cleveland, OH, USA. .,Department of Radiation Oncology, Cleveland Clinic, Cleveland, OH, USA.
| |
Collapse
|
13
|
De Jong MG, Wood KB. Tuning Spatial Profiles of Selection Pressure to Modulate the Evolution of Drug Resistance. PHYSICAL REVIEW LETTERS 2018; 120:238102. [PMID: 29932692 PMCID: PMC6029889 DOI: 10.1103/physrevlett.120.238102] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Indexed: 06/08/2023]
Abstract
Spatial heterogeneity plays an important role in the evolution of drug resistance. While recent studies have indicated that spatial gradients of selection pressure can accelerate resistance evolution, much less is known about evolution in more complex spatial profiles. Here we use a stochastic toy model of drug resistance to investigate how different spatial profiles of selection pressure impact the time to fixation of a resistant allele. Using mean first passage time calculations, we show that spatial heterogeneity accelerates resistance evolution when the rate of spatial migration is sufficiently large relative to mutation but slows fixation for small migration rates. Interestingly, there exists an intermediate regime-characterized by comparable rates of migration and mutation-in which the rate of fixation can be either accelerated or decelerated depending on the spatial profile, even when spatially averaged selection pressure remains constant. Finally, we demonstrate that optimal tuning of the spatial profile can dramatically slow the spread and fixation of resistant subpopulations, even in the absence of a fitness cost for resistance. Our results may lay the groundwork for optimized, spatially resolved drug dosing strategies for mitigating the effects of drug resistance.
Collapse
Affiliation(s)
- Maxwell G. De Jong
- Department of Physics, University of Michigan, Ann Arbor, Michigan
48109, USA
| | - Kevin B. Wood
- Department of Physics, University of Michigan, Ann Arbor, Michigan
48109, USA
- Department of Biophysics, University of Michigan, Ann Arbor,
Michigan 48109, USA
| |
Collapse
|
14
|
Warman PI, Kaznatcheev A, Araujo A, Lynch CC, Basanta D. Fractionated follow-up chemotherapy delays the onset of resistance in bone metastatic prostate cancer. GAMES 2018; 9. [PMID: 33552562 PMCID: PMC7864372 DOI: 10.3390/g9020019] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Prostate cancer to bone metastases are almost always lethal. This results from the ability of metastatic prostate cancer cells to co-opt bone remodeling leading to what is known as the vicious cycle. Understanding how tumor cells can disrupt bone homeostasis through their interactions with the stroma and how metastatic tumors respond to treatment is key to the development of new treatments for what remains an incurable disease. Here we describe an evolutionary game theoretical model of both the homeostatic bone remodeling and its co-option by prostate cancer metastases. This model extends past the evolutionary aspects typically considered in game theoretical models by also including ecological factors such as the physical microenvironment of the bone. Our model recapitulates the current paradigm of the "vicious cycle" driving tumor growth and sheds light on the interactions of heterogeneous tumor cells with the bone microenvironment and treatment response. Our results show that resistant populations naturally become dominant in the metastases under conventional cytotoxic treatment and that novel schedules could be used to better control the tumor and the associated bone disease compared to the current standard of care. Specifically, we introduce fractionated follow up therapy - chemotherapy where dosage is administered initially in one solid block followed by alternating smaller doeses and holidays - and argue that it is better than either a continuous application or a periodic one. Furthermore, we also show that different regimens of chemotherapy can lead to different amounts of pathological bone that are known to correlate with poor quality of life for bone metastatic prostate cancer patients.
Collapse
Affiliation(s)
- Pranav I Warman
- Duke University, Durham, NC, USA
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Artem Kaznatcheev
- Department of Computer Science, University of Oxford, Oxford, UK
- Department of Translational Hematology & Oncology Research, Cleveland Clinic, Cleveland, OH, USA
| | - Arturo Araujo
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - Conor C Lynch
- Department of Tumor Biology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| | - David Basanta
- Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA
| |
Collapse
|
15
|
Bifurcation Mechanism Design—From Optimal Flat Taxes to Better Cancer Treatments. GAMES 2018. [DOI: 10.3390/g9020021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
16
|
Böttcher MA, Held-Feindt J, Synowitz M, Lucius R, Traulsen A, Hattermann K. Modeling treatment-dependent glioma growth including a dormant tumor cell subpopulation. BMC Cancer 2018; 18:376. [PMID: 29614985 PMCID: PMC5883287 DOI: 10.1186/s12885-018-4281-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Accepted: 03/21/2018] [Indexed: 02/07/2023] Open
Abstract
Background Tumors comprise a variety of specialized cell phenotypes adapted to different ecological niches that massively influence the tumor growth and its response to treatment. Methods In the background of glioblastoma multiforme, a highly malignant brain tumor, we consider a rapid proliferating phenotype that appears susceptible to treatment, and a dormant phenotype which lacks this pronounced proliferative ability and is not affected by standard therapeutic strategies. To gain insight in the dynamically changing proportions of different tumor cell phenotypes under different treatment conditions, we develop a mathematical model and underline our assumptions with experimental data. Results We show that both cell phenotypes contribute to the distinct composition of the tumor, especially in cycling low and high dose treatment, and therefore may influence the tumor growth in a phenotype specific way. Conclusion Our model of the dynamic proportions of dormant and rapidly growing glioblastoma cells in different therapy settings suggests that phenotypically different cells should be considered to plan dose and duration of treatment schedules.
Collapse
Affiliation(s)
- Marvin A Böttcher
- Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306, Plön, Germany
| | - Janka Held-Feindt
- Department of Neurosurgery, University Medical Center Schleswig-Holstein UKSH, Campus Kiel, 24105, Kiel, Germany
| | - Michael Synowitz
- Department of Neurosurgery, University Medical Center Schleswig-Holstein UKSH, Campus Kiel, 24105, Kiel, Germany
| | - Ralph Lucius
- Department of Anatomy, University of Kiel, 24098, Kiel, Germany
| | - Arne Traulsen
- Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, 24306, Plön, Germany
| | | |
Collapse
|
17
|
Basanta D, Anderson ARA. Homeostasis Back and Forth: An Ecoevolutionary Perspective of Cancer. Cold Spring Harb Perspect Med 2017; 7:cshperspect.a028332. [PMID: 28289244 DOI: 10.1101/cshperspect.a028332] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The role of genetic mutations in cancer is indisputable: They are a key source of tumor heterogeneity and drive its evolution to malignancy. But, the success of these new mutant cells relies on their ability to disrupt the homeostasis that characterizes healthy tissues. Mutated clones unable to break free from intrinsic and extrinsic homeostatic controls will fail to establish a tumor. Here, we will discuss, through the lens of mathematical and computational modeling, why an evolutionary view of cancer needs to be complemented by an ecological perspective to understand why cancer cells invade and subsequently transform their environment during progression. Importantly, this ecological perspective needs to account for tissue homeostasis in the organs that tumors invade, because they perturb the normal regulatory dynamics of these tissues, often coopting them for its own gain. Furthermore, given our current lack of success in treating advanced metastatic cancers through tumor-centric therapeutic strategies, we propose that treatments that aim to restore homeostasis could become a promising venue of clinical research. This ecoevolutionary view of cancer requires mechanistic mathematical models to both integrate clinical with biological data from different scales but also to detangle the dynamic feedback between the tumor and its environment. Importantly, for these models to be useful, they need to embrace a higher degree of complexity than many mathematical modelers are traditionally comfortable with.
Collapse
Affiliation(s)
- David Basanta
- Integrated Mathematical Oncology Department, Moffitt Cancer Center, Tampa, Florida 33612
| | - Alexander R A Anderson
- Integrated Mathematical Oncology Department, Moffitt Cancer Center, Tampa, Florida 33612
| |
Collapse
|
18
|
Gerlee P, Altrock PM. Extinction rates in tumour public goods games. J R Soc Interface 2017; 14:20170342. [PMID: 28954847 PMCID: PMC5636271 DOI: 10.1098/rsif.2017.0342] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2017] [Accepted: 08/31/2017] [Indexed: 12/14/2022] Open
Abstract
Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.
Collapse
Affiliation(s)
- Philip Gerlee
- Department of Mathematical Sciences, Chalmers University of Technology, 41296 Gothenburg, Sweden
- Department of Mathematical Sciences, University of Gothenburg, 40530 Gothenburg, Sweden
| | - Philipp M Altrock
- Department of Integrated Mathematical Oncology, Moffitt Cancer Center and Research Institute, Tampa, FL 33612, USA
- University of South Florida Morsani College of Medicine, Tampa, FL 33612, USA
| |
Collapse
|
19
|
Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature. Br J Cancer 2017; 116:785-792. [PMID: 28183139 PMCID: PMC5355932 DOI: 10.1038/bjc.2017.5] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Revised: 11/06/2016] [Accepted: 12/20/2016] [Indexed: 12/13/2022] Open
Abstract
Background: Tumours are diverse ecosystems with persistent heterogeneity in various cancer hallmarks like self-sufficiency of growth factor production for angiogenesis and reprogramming of energy metabolism for aerobic glycolysis. This heterogeneity has consequences for diagnosis, treatment and disease progression. Methods: We introduce the double goods game to study the dynamics of these traits using evolutionary game theory. We model glycolytic acid production as a public good for all tumour cells and oxygen from vascularisation via vascular endothelial growth factor production as a club good benefiting non-glycolytic tumour cells. This results in three viable phenotypic strategies: glycolytic, angiogenic and aerobic non-angiogenic. Results: We classify the dynamics into three qualitatively distinct regimes: (1) fully glycolytic; (2) fully angiogenic; or (3) polyclonal in all three cell types. The third regime allows for dynamic heterogeneity even with linear goods, something that was not possible in prior public good models that considered glycolysis or growth factor production in isolation. Conclusions: The cyclic dynamics of the polyclonal regime stress the importance of timing for anti-glycolysis treatments like lonidamine. The existence of qualitatively different dynamic regimes highlights the order effects of treatments. In particular, we consider the potential of vascular normalisation as a neoadjuvant therapy before follow-up with interventions like buffer therapy.
Collapse
|
20
|
Simulation of avascular tumor growth by agent-based game model involving phenotype-phenotype interactions. Sci Rep 2015; 5:17992. [PMID: 26648395 PMCID: PMC4673614 DOI: 10.1038/srep17992] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2015] [Accepted: 11/06/2015] [Indexed: 01/01/2023] Open
Abstract
All tumors, both benign and metastatic, undergo an avascular growth stage with nutrients supplied by the surrounding tissue. This avascular growth process is much easier to carry out in more qualitative and quantitative experiments starting from tumor spheroids in vitro with reliable reproducibility. Essentially, this tumor progression would be described as a sequence of phenotypes. Using agent-based simulation in a two-dimensional spatial lattice, we constructed a composite growth model in which the phenotypic behavior of tumor cells depends on not only the local nutrient concentration and cell count but also the game among cells. Our simulation results demonstrated that in silico tumors are qualitatively similar to those observed in tumor spheroid experiments. We also found that the payoffs in the game between two living cell phenotypes can influence the growth velocity and surface roughness of tumors at the same time. Finally, this current model is flexible and can be easily extended to discuss other situations, such as environmental heterogeneity and mutation.
Collapse
|