1
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Kuo YP, Carja O. Evolutionary graph theory beyond single mutation dynamics: on how network-structured populations cross fitness landscapes. Genetics 2024; 227:iyae055. [PMID: 38639307 PMCID: PMC11151934 DOI: 10.1093/genetics/iyae055] [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: 02/07/2024] [Revised: 03/28/2024] [Accepted: 04/01/2024] [Indexed: 04/20/2024] Open
Abstract
Spatially resolved datasets are revolutionizing knowledge in molecular biology, yet are under-utilized for questions in evolutionary biology. To gain insight from these large-scale datasets of spatial organization, we need mathematical representations and modeling techniques that can both capture their complexity, but also allow for mathematical tractability. Evolutionary graph theory utilizes the mathematical representation of networks as a proxy for heterogeneous population structure and has started to reshape our understanding of how spatial structure can direct evolutionary dynamics. However, previous results are derived for the case of a single new mutation appearing in the population and the role of network structure in shaping fitness landscape crossing is still poorly understood. Here we study how network-structured populations cross fitness landscapes and show that even a simple extension to a two-mutational landscape can exhibit complex evolutionary dynamics that cannot be predicted using previous single-mutation results. We show how our results can be intuitively understood through the lens of how the two main evolutionary properties of a network, the amplification and acceleration factors, change the expected fate of the intermediate mutant in the population and further discuss how to link these models to spatially resolved datasets of cellular organization.
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Affiliation(s)
- Yang Ping Kuo
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15232, USA
| | - Oana Carja
- Computational Biology Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15232, USA
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2
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Tetrault E, Aaronson B, Gilbert MC, Albertson RC. Foraging-induced craniofacial plasticity is associated with an early, robust and dynamic transcriptional response. Proc Biol Sci 2024; 291:20240215. [PMID: 38654651 PMCID: PMC11040245 DOI: 10.1098/rspb.2024.0215] [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: 02/12/2024] [Accepted: 03/19/2024] [Indexed: 04/26/2024] Open
Abstract
Phenotypic plasticity is the ability of a single genotype to vary its phenotype in response to the environment. Plasticity of the skeletal system in response to mechanical input is widely studied, but the timing of its transcriptional regulation is not well understood. Here, we used the cichlid feeding apparatus to examine the transcriptional dynamics of skeletal plasticity over time. Using three closely related species that vary in their ability to remodel bone and a panel of 11 genes, including well-studied skeletal differentiation markers and newly characterized environmentally sensitive genes, we examined plasticity at one, two, four and eight weeks following the onset of alternate foraging challenges. We found that the plastic species exhibited environment-specific bursts in gene expression beginning at one week, followed by a sharp decline in levels, while the species with more limited plasticity exhibited consistently low levels of gene expression. This trend held across nearly all genes, suggesting that it is a hallmark of the larger plasticity regulatory network. We conclude that plasticity of the cichlid feeding apparatus is not the result of slowly accumulating gene expression difference over time, but rather is stimulated by early bursts of environment-specific gene expression followed by a return to homeostatic levels.
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Affiliation(s)
- Emily Tetrault
- Molecular and Cell Biology Graduate Program, University of Massachusetts, Amherst, MA 01003, USA
| | - Ben Aaronson
- Department of Biology, University of Massachusetts, Amherst, MA 01003, USA
| | - Michelle C. Gilbert
- Department of Biology, Pennsylvania State University, State College, PA 16802, USA
| | - R. Craig Albertson
- Department of Biology, University of Massachusetts, Amherst, MA 01003, USA
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3
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Lee ND, Kaveh K, Bozic I. Clonal interactions in cancer: integrating quantitative models with experimental and clinical data. Semin Cancer Biol 2023; 92:61-73. [PMID: 37023969 DOI: 10.1016/j.semcancer.2023.04.002] [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: 11/30/2022] [Revised: 02/16/2023] [Accepted: 04/03/2023] [Indexed: 04/08/2023]
Abstract
Tumors consist of different genotypically distinct subpopulations-or subclones-of cells. These subclones can influence neighboring clones in a process called "clonal interaction." Conventionally, research on driver mutations in cancer has focused on their cell-autonomous effects that lead to an increase in fitness of the cells containing the driver. Recently, with the advent of improved experimental and computational technologies for investigating tumor heterogeneity and clonal dynamics, new studies have shown the importance of clonal interactions in cancer initiation, progression, and metastasis. In this review we provide an overview of clonal interactions in cancer, discussing key discoveries from a diverse range of approaches to cancer biology research. We discuss common types of clonal interactions, such as cooperation and competition, its mechanisms, and the overall effect on tumorigenesis, with important implications for tumor heterogeneity, resistance to treatment, and tumor suppression. Quantitative models-in coordination with cell culture and animal model experiments-have played a vital role in investigating the nature of clonal interactions and the complex clonal dynamics they generate. We present mathematical and computational models that can be used to represent clonal interactions and provide examples of the roles they have played in identifying and quantifying the strength of clonal interactions in experimental systems. Clonal interactions have proved difficult to observe in clinical data; however, several very recent quantitative approaches enable their detection. We conclude by discussing ways in which researchers can further integrate quantitative methods with experimental and clinical data to elucidate the critical-and often surprising-roles of clonal interactions in human cancers.
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Affiliation(s)
- Nathan D Lee
- Department of Applied Mathematics, University of Washington, Seattle, WA, United States of America
| | - Kamran Kaveh
- Department of Applied Mathematics, University of Washington, Seattle, WA, United States of America
| | - Ivana Bozic
- Department of Applied Mathematics, University of Washington, Seattle, WA, United States of America; Herbold Computational Biology Program, Fred Hutchinson Cancer Center, Seattle, Washington, United States of America.
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4
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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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5
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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.
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Affiliation(s)
- Helena Coggan
- Department of Mathematics, University College London, London, UK
| | - Karen M Page
- Department of Mathematics, University College London, London, UK
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6
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Majic P, Erten EY, Payne JL. The adaptive potential of nonheritable somatic mutations. Am Nat 2022; 200:755-772. [DOI: 10.1086/721766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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7
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BONNEUIL NOËL. OPTIMAL CONTROL OF GENETIC DIVERSITY IN THE MORAN MODEL WITH POPULATION GROWTH. J BIOL SYST 2022. [DOI: 10.1142/s0218339022500012] [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
In the Moran model of drift and selection of a mutant allele with population growth, instead of examining the consequences of pre-specified selection and population growth, the coexistence of the wild allele and the mutant allele becomes the maximization of the expected sojourn time in a given set. The process is controlled by the additional mortality of the mutant and by population growth. This makes it possible to retroactively assign fitness values as functions of the constraints, thus guiding a conservation policy or the achievement of a wishful proportion of mutants. This also gives the optimal conditions that have allowed an observed coexistence.
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Affiliation(s)
- NOËL BONNEUIL
- Ined and Ehess, 54, bld Raspail 75006, Paris, France
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8
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Chen S, Xie ZX, Yuan YJ. Discovering and genotyping genomic structural variations by yeast genome synthesis and inducible evolution. FEMS Yeast Res 2021; 20:5809967. [PMID: 32188997 DOI: 10.1093/femsyr/foaa012] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Accepted: 03/06/2020] [Indexed: 12/21/2022] Open
Abstract
Genomic structural variations (SVs) promote the evolution of Saccharomyces cerevisiae, and play an important role in phenotypic diversities. Yeast genomic structures can be remodeled by design and bottom-up synthesis. The synthesis of yeast genome creates novel copy number variations (CNVs) and SVs and develops new strategies to discover gene functions. Further, an inducible evolution system SCRaMbLE, consisted of 3,932 loxPsym sites, was incorporated on synthetic yeast genome. SCRaMbLE enables genomic rearrangements at will and rapidly generates chromosomal number variations, and massive SVs under customized conditions. The impacts of genetic variations on phenotypes can be revealed by genome analysis and chromosome restructuring. Yeast genome synthesis and SCRaMbLE provide a new research paradigm to explore the genotypic mechanisms of phenotype diversities, and can be used to improve biological traits and optimize industrial chassis.
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Affiliation(s)
- Si Chen
- Frontier Science Center for Synthetic Biology and Key Laboratory of Systems Bioengineering (Ministry of Education), School of Chemical Engineering and Technology, Tianjin University, 300072 Tianjin, People's Republic of China.,Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), School of Chemical Engineering and Technology, Tianjin University, 300072 Tianjin, People's Republic of China
| | - Ze-Xiong Xie
- Frontier Science Center for Synthetic Biology and Key Laboratory of Systems Bioengineering (Ministry of Education), School of Chemical Engineering and Technology, Tianjin University, 300072 Tianjin, People's Republic of China.,Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), School of Chemical Engineering and Technology, Tianjin University, 300072 Tianjin, People's Republic of China
| | - Ying-Jin Yuan
- Frontier Science Center for Synthetic Biology and Key Laboratory of Systems Bioengineering (Ministry of Education), School of Chemical Engineering and Technology, Tianjin University, 300072 Tianjin, People's Republic of China.,Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), School of Chemical Engineering and Technology, Tianjin University, 300072 Tianjin, People's Republic of China
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9
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Pérez-García VM, Calvo GF, Bosque JJ, León-Triana O, Jiménez J, Perez-Beteta J, Belmonte-Beitia J, Valiente M, Zhu L, García-Gómez P, Sánchez-Gómez P, Hernández-San Miguel E, Hortigüela R, Azimzade Y, Molina-García D, Martinez Á, Rojas ÁA, de Mendivil AO, Vallette F, Schucht P, Murek M, Pérez-Cano M, Albillo D, Honguero Martínez AF, Jiménez Londoño GA, Arana E, García Vicente AM. Universal scaling laws rule explosive growth in human cancers. NATURE PHYSICS 2020; 16:1232-1237. [PMID: 33329756 PMCID: PMC7116451 DOI: 10.1038/s41567-020-0978-6] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
Most physical and other natural systems are complex entities composed of a large number of interacting individual elements. It is a surprising fact that they often obey the so-called scaling laws relating an observable quantity with a measure of the size of the system. Here we describe the discovery of universal superlinear metabolic scaling laws in human cancers. This dependence underpins increasing tumour aggressiveness, due to evolutionary dynamics, which leads to an explosive growth as the disease progresses. We validated this dynamic using longitudinal volumetric data of different histologies from large cohorts of cancer patients. To explain our observations we put forward increasingly-complex biologically-inspired mathematical models that captured the key processes governing tumor growth. Our models predicted that the emergence of superlinear allometric scaling laws is an inherently three-dimensional phenomenon. Moreover, the scaling laws thereby identified allowed us to define a set of metabolic metrics with prognostic value, thus providing added clinical utility to the base findings.
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Affiliation(s)
- Víctor M. Pérez-García
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Spain
- Correspondence and requests for materials should be addressed to V.M. Pérez-García (>)
| | - Gabriel F. Calvo
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Spain
| | - Jesús J. Bosque
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Spain
| | | | - Juan Jiménez
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Spain
| | | | | | - Manuel Valiente
- Brain Metastasis Group, Spanish National Cancer Research Centre (CNIO), Madrid, Spain
| | - Lucía Zhu
- Brain Metastasis Group, Spanish National Cancer Research Centre (CNIO), Madrid, Spain
| | - Pedro García-Gómez
- Brain Metastasis Group, Spanish National Cancer Research Centre (CNIO), Madrid, Spain
| | | | | | - Rafael Hortigüela
- Neuro-oncology Unit, Health Institute Carlos III-UFIEC, Madrid, Spain
| | | | | | - Álvaro Martinez
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Spain
- Department of Mathematics, Universidad de Cádiz, Spain
| | - Ángel Acosta Rojas
- Department of Radiation Oncology, Sanchinarro University Hospital, HM Hospitales, Spain
| | | | - Francois Vallette
- Inserm U1232, Centre de Recherche en Cancérologie et Immunologie Nantes-Angers, Nantes, F-44007, France
| | | | | | - María Pérez-Cano
- Mathematical Oncology Laboratory, Universidad de Castilla-La Mancha, Spain
| | - David Albillo
- Radiology Unit, MD Anderson Cancer Center, Madrid, Spain
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10
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Garaeva AY, Sidorova AE, Tverdislov VA, Levashova NT. A Model of Speciation Preconditions in Terms of Percolation and Self-Organized Criticality Theories. Biophysics (Nagoya-shi) 2020. [DOI: 10.1134/s0006350920050073] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
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11
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Aframian N, Eldar A. A Bacterial Tower of Babel: Quorum-Sensing Signaling Diversity and Its Evolution. Annu Rev Microbiol 2020; 74:587-606. [PMID: 32680450 DOI: 10.1146/annurev-micro-012220-063740] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Quorum sensing is a process in which bacteria secrete and sense a diffusible molecule, thereby enabling bacterial groups to coordinate their behavior in a density-dependent manner. Quorum sensing has evolved multiple times independently, utilizing different molecular pathways and signaling molecules. A common theme among many quorum-sensing families is their wide range of signaling diversity-different variants within a family code for different signal molecules with a cognate receptor specific to each variant. This pattern of vast allelic polymorphism raises several questions-How do different signaling variants interact with one another? How is this diversity maintained? And how did it come to exist in the first place? Here we argue that social interactions between signaling variants can explain the emergence and persistence of signaling diversity throughout evolution. Finally, we extend the discussion to include cases where multiple diverse systems work in concert in a single bacterium.
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Affiliation(s)
- Nitzan Aframian
- Faculty of Life Sciences, School of Molecular Cell Biology and Biotechnology, Tel-Aviv University, 6997801 Tel-Aviv, Israel; ,
| | - Avigdor Eldar
- Faculty of Life Sciences, School of Molecular Cell Biology and Biotechnology, Tel-Aviv University, 6997801 Tel-Aviv, Israel; ,
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12
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Lima JY, Moreira C, Nunes Freitas PN, Olchanheski LR, Veiga Pileggi SA, Etto RM, Staley C, Sadowsky MJ, Pileggi M. Structuring biofilm communities living in pesticide contaminated water. Heliyon 2020; 6:e03996. [PMID: 32462094 PMCID: PMC7240113 DOI: 10.1016/j.heliyon.2020.e03996] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2020] [Revised: 02/07/2020] [Accepted: 05/12/2020] [Indexed: 12/12/2022] Open
Abstract
The wide use of pesticides in agriculture expose microbiota to stressful conditions that require the development of survival strategies. The bacterial response to many pollutants has not been elucidated in detail, as well as the evolutionary processes that occur to build adapted communities. The purpose of this study was to evaluate the bacterial population structure and adaptation strategies in planktonic and biofilm communities in limited environments, as tanks containing water used for washing herbicide containers. This biodiversity, with high percentage of nonculturable microorganisms, was characterized based on habitat and abiotic parameters using molecular and bioinformatics tools. According to water and wastewater standards, the physicochemical conditions of the tank water were inadequate for survival of the identified bacteria, which had to develop survival strategies in this hostile environment. The biodiversity decreased in the transition from planktonic to biofilm samples, indicating a possible association between genetic drift and selection of individuals that survive under stressful conditions, such as heating in water and the presence of chlorine, fluorine and agrochemicals over a six-month period. The abundance of Enterobacter, Acinetobacter and Pseudomonas in biofilms from water tanks was linked to essential processes, deduced from the genes attributed to these taxonomic units, and related to biofilm formation, structure and membrane transport, quorum sensing and xenobiotic degradation. These characteristics were randomly combined and fixed in the biofilm community. Thus, communities of biofilm bacteria obtained under these environmental conditions serve as interesting models for studying herbicide biodegradation kinetics and the prospects of consortia suitable for use in bioremediation in reservoirs containing herbicide-contaminated wastewater, as biofilters containing biofilm communities capable of degrading herbicides.
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Affiliation(s)
- Jhenifer Yonara Lima
- Department of Structural and Molecular Biology and Genetics, Ponta Grossa State University, Ponta Grossa, Paraná, Brazil
| | - Cassiano Moreira
- Department of Structural and Molecular Biology and Genetics, Ponta Grossa State University, Ponta Grossa, Paraná, Brazil
| | - Paloma Nathane Nunes Freitas
- Department of Structural and Molecular Biology and Genetics, Ponta Grossa State University, Ponta Grossa, Paraná, Brazil
| | | | - Sonia Alvim Veiga Pileggi
- Department of Structural and Molecular Biology and Genetics, Ponta Grossa State University, Ponta Grossa, Paraná, Brazil
| | - Rafael Mazer Etto
- Department of Chemistry, Ponta Grossa State University, Ponta Grossa, Paraná, Brazil
| | - Christopher Staley
- The Biotechnology Institute, University of Minnesota, St. Paul, Minnesota, United States
| | - Michael Jay Sadowsky
- Department of Soil, Water, and Climate, The Biotechnology Institute, University of Minnesota, St. Paul, Minnesota, United States
| | - Marcos Pileggi
- Department of Structural and Molecular Biology and Genetics, Ponta Grossa State University, Ponta Grossa, Paraná, Brazil
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13
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Garaeva AY, Sidorova AE, Levashova NT, Tverdislov VA. A Percolation Lattice of Natural Selection as a Switch of Deterministic and Random Processes in the Mutation Flow. Biophysics (Nagoya-shi) 2020. [DOI: 10.1134/s0006350920030069] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
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14
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Lewin-Epstein O, Hadany L. Host-microbiome coevolution can promote cooperation in a rock-paper-scissors dynamics. Proc Biol Sci 2020; 287:20192754. [PMID: 32075531 PMCID: PMC7031668 DOI: 10.1098/rspb.2019.2754] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Cooperation is a fundamental behaviour observed in all forms of life. The evolution of cooperation has been widely studied, but almost all theories focused on the cooperating individual and its genes. We suggest a different approach, taking into account the microbes carried by the interacting individuals. Accumulating evidence reveals that microbes can affect their host's well-being and behaviour, yet hosts can evolve mechanisms to resist the manipulations of their microbes. We thus propose that coevolution of microbes with their hosts may favour microbes that induce their host to cooperate. Using computational modelling, we show that microbe-induced cooperation can evolve and be maintained in a wide range of conditions, including when facing hosts' resistance to the microbial effect. We find that host-microbe coevolution leads the population to a rock-paper-scissors dynamics that enables maintenance of cooperation in a polymorphic state. Our results suggest a mechanism for the evolution and maintenance of cooperation that may be relevant to a wide variety of organisms, including cases that are difficult to explain by current theories. This study provides a new perspective on the coevolution of hosts and their microbiome, emphasizing the potential role of microbes in shaping their host's behaviour.
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Affiliation(s)
- Ohad Lewin-Epstein
- Department of Molecular Biology and Ecology of Plants, Tel-Aviv University, Tel-Aviv 6997801, Israel
| | - Lilach Hadany
- Department of Molecular Biology and Ecology of Plants, Tel-Aviv University, Tel-Aviv 6997801, Israel
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15
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Saputra EC, Huang L, Chen Y, Tucker-Kellogg L. Combination Therapy and the Evolution of Resistance: The Theoretical Merits of Synergism and Antagonism in Cancer. Cancer Res 2018; 78:2419-2431. [PMID: 29686021 DOI: 10.1158/0008-5472.can-17-1201] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2017] [Revised: 09/29/2017] [Accepted: 02/12/2018] [Indexed: 11/16/2022]
Abstract
The search for effective combination therapies for cancer has focused heavily on synergistic combinations because they exhibit enhanced therapeutic efficacy at lower doses. Although synergism is intuitively attractive, therapeutic success often depends on whether drug resistance develops. The impact of synergistic combinations (vs. antagonistic or additive combinations) on the process of drug-resistance evolution has not been investigated. In this study, we use a simplified computational model of cancer cell numbers in a population of drug-sensitive, singly-resistant, and fully-resistant cells to simulate the dynamics of resistance evolution in the presence of two-drug combinations. When we compared combination therapies administered at the same combination of effective doses, simulations showed synergistic combinations most effective at delaying onset of resistance. Paradoxically, when the therapies were compared using dose combinations with equal initial efficacy, antagonistic combinations were most successful at suppressing expansion of resistant subclones. These findings suggest that, although synergistic combinations could suppress resistance through early decimation of cell numbers (making them "proefficacy" strategies), they are inherently fragile toward the development of single resistance. In contrast, antagonistic combinations suppressed the clonal expansion of singly-resistant cells, making them "antiresistance" strategies. The distinction between synergism and antagonism was intrinsically connected to the distinction between offensive and defensive strategies, where offensive strategies inflicted early casualties and defensive strategies established protection against anticipated future threats. Our findings question the exclusive focus on synergistic combinations and motivate further consideration of nonsynergistic combinations for cancer therapy.Significance: Computational simulations show that if different combination therapies have similar initial efficacy in cancers, then nonsynergistic drug combinations are more likely than synergistic drug combinations to provide a long-term defense against the evolution of therapeutic resistance. Cancer Res; 78(9); 2419-31. ©2018 AACR.
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Affiliation(s)
- Elysia C Saputra
- Cancer and Stem Cell Biology, Duke-NUS Medical School, Singapore.,Centre for Computational Biology, Duke-NUS Medical School, Singapore
| | - Lu Huang
- Computational Systems Biology, Singapore-MIT Alliance, National University of Singapore, Singapore.,Institute of Molecular Biology, Mainz, Germany
| | - Yihui Chen
- Cancer and Stem Cell Biology, Duke-NUS Medical School, Singapore.,Emerging Infectious Diseases, Duke-NUS Medical School, Singapore
| | - Lisa Tucker-Kellogg
- Cancer and Stem Cell Biology, Duke-NUS Medical School, Singapore. .,Centre for Computational Biology, Duke-NUS Medical School, Singapore.,Computational Systems Biology, Singapore-MIT Alliance, National University of Singapore, Singapore.,BioSystems and Micromechanics (BioSyM) Singapore-MIT Alliance for Research and Technology, Singapore
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16
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Obolski U, Ram Y, Hadany L. Key issues review: evolution on rugged adaptive landscapes. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:012602. [PMID: 29051394 DOI: 10.1088/1361-6633/aa94d4] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Adaptive landscapes represent a mapping between genotype and fitness. Rugged adaptive landscapes contain two or more adaptive peaks: allele combinations with higher fitness than any of their neighbors in the genetic space. How do populations evolve on such rugged landscapes? Evolutionary biologists have struggled with this question since it was first introduced in the 1930s by Sewall Wright. Discoveries in the fields of genetics and biochemistry inspired various mathematical models of adaptive landscapes. The development of landscape models led to numerous theoretical studies analyzing evolution on rugged landscapes under different biological conditions. The large body of theoretical work suggests that adaptive landscapes are major determinants of the progress and outcome of evolutionary processes. Recent technological advances in molecular biology and microbiology allow experimenters to measure adaptive values of large sets of allele combinations and construct empirical adaptive landscapes for the first time. Such empirical landscapes have already been generated in bacteria, yeast, viruses, and fungi, and are contributing to new insights about evolution on adaptive landscapes. In this Key Issues Review we will: (i) introduce the concept of adaptive landscapes; (ii) review the major theoretical studies of evolution on rugged landscapes; (iii) review some of the recently obtained empirical adaptive landscapes; (iv) discuss recent mathematical and statistical analyses motivated by empirical adaptive landscapes, as well as provide the reader with instructions and source code to implement simulations of evolution on adaptive landscapes; and (v) discuss possible future directions for this exciting field.
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17
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Farhang-Sardroodi S, Darooneh AH, Nikbakht M, Komarova NL, Kohandel M. The effect of spatial randomness on the average fixation time of mutants. PLoS Comput Biol 2017; 13:e1005864. [PMID: 29176825 PMCID: PMC5720826 DOI: 10.1371/journal.pcbi.1005864] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Revised: 12/07/2017] [Accepted: 10/26/2017] [Indexed: 12/03/2022] Open
Abstract
The mean conditional fixation time of a mutant is an important measure of stochastic population dynamics, widely studied in ecology and evolution. Here, we investigate the effect of spatial randomness on the mean conditional fixation time of mutants in a constant population of cells, N. Specifically, we assume that fitness values of wild type cells and mutants at different locations come from given probability distributions and do not change in time. We study spatial arrangements of cells on regular graphs with different degrees, from the circle to the complete graph, and vary assumptions on the fitness probability distributions. Some examples include: identical probability distributions for wild types and mutants; cases when only one of the cell types has random fitness values while the other has deterministic fitness; and cases where the mutants are advantaged or disadvantaged. Using analytical calculations and stochastic numerical simulations, we find that randomness has a strong impact on fixation time. In the case of complete graphs, randomness accelerates mutant fixation for all population sizes, and in the case of circular graphs, randomness delays mutant fixation for N larger than a threshold value (for small values of N, different behaviors are observed depending on the fitness distribution functions). These results emphasize fundamental differences in population dynamics under different assumptions on cell connectedness. They are explained by the existence of randomly occurring “dead zones” that can significantly delay fixation on networks with low connectivity; and by the existence of randomly occurring “lucky zones” that can facilitate fixation on networks of high connectivity. Results for death-birth and birth-death formulations of the Moran process, as well as for the (haploid) Wright Fisher model are presented. We study the influence of randomness on evolutionary dynamics, assuming that a newly arising mutant may experience a different set of environments compared to the wild type. We calculate the mean conditional fixation time of the mutant under different assumptions on spatial interactions, and show that randomness has a strong impact on the fixation time. In particular, it delays the fixation of mutants on 1D circles and accelerates it on complete graphs (the so called mass action, or complete mixing, model). This result holds for advantageous, disadvantageous, and neutral (on average) mutants. The reason for this pattern is quite intuitive: in a rigid, 1D structure, randomness can by chance put a “roadblock” and disrupt mutant spread, causing significant delay. In higher dimensions, there are many ways for a mutant to spread, and it is difficult to block all of them by chance; on the other hand, randomness can enhance fixation by providing an “easier” path. The effects of a random environment are important in biological models such as bacterial growth or cancer initiation/progression.
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Affiliation(s)
| | | | | | - Natalia L. Komarova
- Department of Mathematics, University of California Irvine, Irvine, California, United States of America
- * E-mail: (NLK); (MK)
| | - Mohammad Kohandel
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- * E-mail: (NLK); (MK)
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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.
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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
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19
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Essarioui A, LeBlanc N, Kistler HC, Kinkel LL. Plant Community Richness Mediates Inhibitory Interactions and Resource Competition between Streptomyces and Fusarium Populations in the Rhizosphere. MICROBIAL ECOLOGY 2017; 74:157-167. [PMID: 28058470 DOI: 10.1007/s00248-016-0907-5] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Accepted: 11/30/2016] [Indexed: 06/06/2023]
Abstract
Plant community characteristics impact rhizosphere Streptomyces nutrient competition and antagonistic capacities. However, the effects of Streptomyces on, and their responses to, coexisting microorganisms as a function of plant host or plant species richness have received little attention. In this work, we characterized antagonistic activities and nutrient use among Streptomyces and Fusarium from the rhizosphere of Andropogon gerardii (Ag) and Lespedeza capitata (Lc) plants growing in communities of 1 (monoculture) or 16 (polyculture) plant species. Streptomyces from monoculture were more antagonistic against Fusarium than those from polyculture. In contrast, Fusarium isolates from polyculture had greater inhibitory capacities against Streptomyces than isolates from monoculture. Although Fusarium isolates had on average greater niche widths, the collection of Streptomyces isolates in total used a greater diversity of nutrients for growth. Plant richness, but not plant host, influenced the potential for resource competition between the two taxa. Fusarium isolates had greater niche overlap with Streptomyces in monoculture than polyculture, suggesting greater potential for Fusarium to competitively challenge Streptomyces in monoculture plant communities. In contrast, Streptomyces had greater niche overlap with Fusarium in polyculture than monoculture, suggesting that Fusarium experiences greater resource competition with Streptomyces in polyculture than monoculture. These patterns of competitive and inhibitory phenotypes among Streptomyces and Fusarium populations are consistent with selection for Fusarium-antagonistic Streptomyces populations in the presence of strong Fusarium resource competition in plant monocultures. Similarly, these results suggest selection for Streptomyces-inhibitory Fusarium populations in the presence of strong Streptomyces resource competition in more diverse plant communities. Thus, landscape-scale variation in plant species richness may be critical to mediating the coevolutionary dynamics and selective trajectories for inhibitory and nutrient use phenotypes among Streptomyces and Fusarium populations in soil, with significant implications for microbial community functional characteristics.
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Affiliation(s)
- Adil Essarioui
- Department of Plant Pathology, University of Minnesota, Minneapolis, MN, USA.
- National Institute of Agronomic Research, Regional Center of Errachidia, Errachidia, Morocco.
| | - Nicholas LeBlanc
- Department of Plant Pathology, University of Minnesota, Minneapolis, MN, USA
| | - Harold C Kistler
- Department of Plant Pathology, University of Minnesota, Minneapolis, MN, USA
- Cereal Disease Lab, USDA-ARS, 1551 Lindig Street, St Paul, MN, USA
| | - Linda L Kinkel
- Department of Plant Pathology, University of Minnesota, Minneapolis, MN, USA
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20
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Obolski U, Lewin-Epstein O, Even-Tov E, Ram Y, Hadany L. With a little help from my friends: cooperation can accelerate the rate of adaptive valley crossing. BMC Evol Biol 2017. [PMID: 28623896 PMCID: PMC5473968 DOI: 10.1186/s12862-017-0983-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Background Natural selection favors changes that lead to genotypes possessing high fitness. A conflict arises when several mutations are required for adaptation, but each mutation is separately deleterious. The process of a population evolving from a genotype encoding for a local fitness maximum to a higher fitness genotype is termed an adaptive peak shift. Results Here we suggest cooperative behavior as a factor that can facilitate adaptive peak shifts. We model cooperation in a public goods scenario, wherein each individual contributes resources that are later equally redistributed among all cooperating individuals. We use mathematical modeling and stochastic simulations to study the effect of cooperation on peak shifts in both panmictic and structured populations. Our results show that cooperation can substantially affect the rate of complex adaptation. Furthermore, we show that cooperation increases the population diversity throughout the peak shift process, thus increasing the robustness of the population to sudden environmental changes. Conclusions We provide a new explanation to adaptive valley crossing in natural populations and suggest that the long term evolution of a species depends on its social behavior. Electronic supplementary material The online version of this article (doi:10.1186/s12862-017-0983-2) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Uri Obolski
- Department of Molecular Biology and Ecology of Plants, Tel-Aviv University, 6997801, Tel Aviv, Israel.,Current address: Department of Zoology, University of Oxford, Oxford, UK
| | - Ohad Lewin-Epstein
- Department of Molecular Biology and Ecology of Plants, Tel-Aviv University, 6997801, Tel Aviv, Israel
| | - Eran Even-Tov
- Department of Molecular Microbiology and Biotechnology, Tel-Aviv University, Tel-Aviv, Israel
| | - Yoav Ram
- Department of Molecular Biology and Ecology of Plants, Tel-Aviv University, 6997801, Tel Aviv, Israel.,Present Address: Department of Biology, Stanford University, Stanford, CA, USA
| | - Lilach Hadany
- Department of Molecular Biology and Ecology of Plants, Tel-Aviv University, 6997801, Tel Aviv, Israel.
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Wang X, Zhang L, Du X. The Effectiveness of Reward and Punishment in Spatial Social Games. INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE AND APPLICATIONS 2017. [DOI: 10.1142/s1469026817500079] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Punishment and reward are usually regarded as two potential mechanisms to explain the evolution of cooperation especially among multiple participators. However, the performance of these two scenarios in spatial environment needs to be discussed. To figure out this issue, we resort to the [Formula: see text]-player Iterated Snowdrift Dilemma (ISD) game and Iterated Prisoner’s Dilemma (IPD) game. More importantly, the evolution of punishment and reward in social network-structured populations has not been formally addressed. The numerical results show the equilibrium cooperation frequency can be influenced by cost-to-benefit ratio [Formula: see text], the punishment-to-benefit ratio [Formula: see text] and the reward-to-benefit ratio [Formula: see text]. And one intriguing observation is that under the same situation, the punishment is more effective than reward to the population. Then we further probe the effectiveness of neighborhood relationship to the cooperation, which is reflected by the random rewired probability [Formula: see text]. From the distribution of the four roles of the participator we can find that individuals can cooperate easily when they have close relationship. The results of this paper may be helpful to understand the cooperation in complex project or among industry–university–research cooperation project.
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Affiliation(s)
- Xiaoyang Wang
- Zhongshan Institute, University of Electronic Science and Technology of China, Zhongshan, Guangdong 528400, China
| | - Lei Zhang
- School of Physics and Engineering, Sun Yat-sen University, Guangzhou, Guangdong 510275, China
| | - Xiaorong Du
- School of Physics and Engineering, Sun Yat-sen University, Guangzhou, Guangdong 510275, China
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Hu Z, Sun R, Curtis C. A population genetics perspective on the determinants of intra-tumor heterogeneity. Biochim Biophys Acta Rev Cancer 2017; 1867:109-126. [PMID: 28274726 DOI: 10.1016/j.bbcan.2017.03.001] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Revised: 03/01/2017] [Accepted: 03/02/2017] [Indexed: 12/17/2022]
Abstract
Cancer results from the acquisition of somatic alterations in a microevolutionary process that typically occurs over many years, much of which is occult. Understanding the evolutionary dynamics that are operative at different stages of progression in individual tumors might inform the earlier detection, diagnosis, and treatment of cancer. Although these processes cannot be directly observed, the resultant spatiotemporal patterns of genetic variation amongst tumor cells encode their evolutionary histories. Such intra-tumor heterogeneity is pervasive not only at the genomic level, but also at the transcriptomic, phenotypic, and cellular levels. Given the implications for precision medicine, the accurate quantification of heterogeneity within and between tumors has become a major focus of current research. In this review, we provide a population genetics perspective on the determinants of intra-tumor heterogeneity and approaches to quantify genetic diversity. We summarize evidence for different modes of evolution based on recent cancer genome sequencing studies and discuss emerging evolutionary strategies to therapeutically exploit tumor heterogeneity. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.
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Affiliation(s)
- Zheng Hu
- Departments of Medicine and Genetics, Stanford University School of Medicine, Stanford, CA 94305, USA; Stanford Cancer Institute, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Ruping Sun
- Departments of Medicine and Genetics, Stanford University School of Medicine, Stanford, CA 94305, USA; Stanford Cancer Institute, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Christina Curtis
- Departments of Medicine and Genetics, Stanford University School of Medicine, Stanford, CA 94305, USA; Stanford Cancer Institute, Stanford University School of Medicine, Stanford, CA 94305, USA.
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Stewart AJ, Plotkin JB. Small groups and long memories promote cooperation. Sci Rep 2016; 6:26889. [PMID: 27247059 PMCID: PMC4887980 DOI: 10.1038/srep26889] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2016] [Accepted: 05/10/2016] [Indexed: 11/09/2022] Open
Abstract
Complex social behaviors lie at the heart of many of the challenges facing evolutionary biology, sociology, economics, and beyond. For evolutionary biologists the question is often how group behaviors such as collective action, or decision making that accounts for memories of past experience, can emerge and persist in an evolving system. Evolutionary game theory provides a framework for formalizing these questions and admitting them to rigorous study. Here we develop such a framework to study the evolution of sustained collective action in multi-player public-goods games, in which players have arbitrarily long memories of prior rounds of play and can react to their experience in an arbitrary way. We construct a coordinate system for memory-m strategies in iterated n-player games that permits us to characterize all cooperative strategies that resist invasion by any mutant strategy, and stabilize cooperative behavior. We show that, especially when groups are small, longer-memory strategies make cooperation easier to evolve, by increasing the number of ways to stabilize cooperation. We also explore the co-evolution of behavior and memory. We find that even when memory has a cost, longer-memory strategies often evolve, which in turn drives the evolution of cooperation, even when the benefits for cooperation are low.
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Affiliation(s)
- Alexander J Stewart
- Department of Biology, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Joshua B Plotkin
- Department of Biology, University of Pennsylvania, Philadelphia, PA 19104, USA
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24
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Bentley RA, O'Brien MJ. Collective behaviour, uncertainty and environmental change. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2015; 373:rsta.2014.0461. [PMID: 26460111 DOI: 10.1098/rsta.2014.0461] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
A central aspect of cultural evolutionary theory concerns how human groups respond to environmental change. Although we are painting with a broad brush, it is fair to say that prior to the twenty-first century, adaptation often happened gradually over multiple human generations, through a combination of individual and social learning, cumulative cultural evolution and demographic shifts. The result was a generally resilient and sustainable population. In the twenty-first century, however, considerable change happens within small portions of a human generation, on a vastly larger range of geographical and population scales and involving a greater degree of horizontal learning. As a way of gauging the complexity of societal response to environmental change in a globalized future, we discuss several theoretical tools for understanding how human groups adapt to uncertainty. We use our analysis to estimate the limits of predictability of future societal change, in the belief that knowing when to hedge bets is better than relying on a false sense of predictability.
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Affiliation(s)
- R Alexander Bentley
- Department of Comparative Cultural Studies, University of Houston, Houston, TX 77204, USA
| | - Michael J O'Brien
- Department of Anthropology, University of Missouri, 317 Lowry Hall, Columbia, MO 65211, USA
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25
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Waclaw B, Bozic I, Pittman ME, Hruban RH, Vogelstein B, Nowak MA. A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity. Nature 2015; 525:261-4. [PMID: 26308893 PMCID: PMC4782800 DOI: 10.1038/nature14971] [Citation(s) in RCA: 327] [Impact Index Per Article: 36.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2014] [Accepted: 07/23/2015] [Indexed: 01/01/2023]
Abstract
Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.
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Affiliation(s)
- Bartlomiej Waclaw
- School of Physics and Astronomy, University of Edinburgh, JCMB, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
| | - Ivana Bozic
- Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA
- Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138, USA
| | - Meredith E Pittman
- The Sol Goldman Pancreatic Cancer Research Center, Department of Pathology, Johns Hopkins University School of Medicine, 401 North Broadway, Weinberg 2242, Baltimore, Maryland 21231, USA
| | - Ralph H Hruban
- The Sol Goldman Pancreatic Cancer Research Center, Department of Pathology, Johns Hopkins University School of Medicine, 401 North Broadway, Weinberg 2242, Baltimore, Maryland 21231, USA
| | - Bert Vogelstein
- The Sol Goldman Pancreatic Cancer Research Center, Department of Pathology, Johns Hopkins University School of Medicine, 401 North Broadway, Weinberg 2242, Baltimore, Maryland 21231, USA
- Ludwig Center and Howard Hughes Medical Institute, Johns Hopkins Kimmel Cancer Center, 1650 Orleans Street, Baltimore, Maryland 21287, USA
| | - Martin A Nowak
- Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, Massachusetts 02138, USA
- Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138, USA
- Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, Massachusetts 02138, USA
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27
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In the light of evolution VIII: Darwinian thinking in the social sciences. Introduction. Proc Natl Acad Sci U S A 2014; 111 Suppl 3:10781-4. [PMID: 25202765 DOI: 10.1073/pnas.1411483111] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
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