The role of interventions in the cancer evolution–an evolutionary games approach

A. Swierniak; M. Krzeslak; D. Borys; M. Kimmel; A. Swierniak; M. Krzeslak; D. Borys; M. Kimmel

doi:10.3934/mbe.2019014

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 265-291. doi: 10.3934/mbe.2019014

Previous Article Next Article

Research article

The role of interventions in the cancer evolution–an evolutionary games approach

1.
Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland
2.
Department of Statistics, Rice University, Houston, Texas, USA

Received: 20 March 2018 Accepted: 10 August 2018 Published: 13 December 2018

We propose to endow evolutionary game models with changes of the phenotypes adjustment during the transient generations performed by the parameters in the payoff matrix which determine the fitness resulting from different interactions between players. These changes represent an alteration of access to external resources which, in turn, may reflect anticancer treatment. In the case of spatial games, these functions are represented by an additional lattice where another and parallel game based on cellular automata is performed. The main assumption of the spatial games is that each cell on the lattice is represented by a player following only one strategy. We propose to consider cells on the spatial lattice as heterogeneous (instead of homogeneous), so that each particular player may contain mixed phenotypes. Spatial games of the type, proposed by us, are called multidimensional spatial evolutionary games (MSEG). It may happen that within the population, all of the players have diverse phenotypes (which probably better describes biological phenomena). The additional lattice representing the evolution of resources increases only the dimension of the lattice in the MSEG.

Keywords:

Citation: A. Swierniak, M. Krzeslak, D. Borys, M. Kimmel. The role of interventions in the cancer evolution–an evolutionary games approach[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 265-291. doi: 10.3934/mbe.2019014

Related Papers:

[1]	Muhammad Farman, Ali Akgül, J. Alberto Conejero, Aamir Shehzad, Kottakkaran Sooppy Nisar, Dumitru Baleanu . Analytical study of a Hepatitis B epidemic model using a discrete generalized nonsingular kernel. AIMS Mathematics, 2024, 9(7): 16966-16997. doi: 10.3934/math.2024824
[2]	Weam G. Alharbi, Abdullah F. Shater, Abdelhalim Ebaid, Carlo Cattani, Mounirah Areshi, Mohammed M. Jalal, Mohammed K. Alharbi . Communicable disease model in view of fractional calculus. AIMS Mathematics, 2023, 8(5): 10033-10048. doi: 10.3934/math.2023508
[3]	Ashish Awasthi, Riyasudheen TK . An accurate solution for the generalized Black-Scholes equations governing option pricing. AIMS Mathematics, 2020, 5(3): 2226-2243. doi: 10.3934/math.2020147
[4]	Hui Han, Chaoyu Yang, Xianya Geng . Research on the impact of green finance on the high quality development of the sports industry based on statistical models. AIMS Mathematics, 2023, 8(11): 27589-27604. doi: 10.3934/math.20231411
[5]	Badr Aloraini, Abdulaziz S. Alghamdi, Mohammad Zaid Alaskar, Maryam Ibrahim Habadi . Development of a new statistical distribution with insights into mathematical properties and applications in industrial data in KSA. AIMS Mathematics, 2025, 10(3): 7463-7488. doi: 10.3934/math.2025343
[6]	Ahmad Bin Azim, Ahmad ALoqaily, Asad Ali, Sumbal Ali, Nabil Mlaiki . Industry 4.0 project prioritization by using q-spherical fuzzy rough analytic hierarchy process. AIMS Mathematics, 2023, 8(8): 18809-18832. doi: 10.3934/math.2023957
[7]	Maryam Amin, Muhammad Farman, Ali Akgül, Mohammad Partohaghighi, Fahd Jarad . Computational analysis of COVID-19 model outbreak with singular and nonlocal operator. AIMS Mathematics, 2022, 7(9): 16741-16759. doi: 10.3934/math.2022919
[8]	Mohamed S. Elhadidy, Waleed S. Abdalla, Alaa A. Abdelrahman, S. Elnaggar, Mostafa Elhosseini . Assessing the accuracy and efficiency of kinematic analysis tools for six-DOF industrial manipulators: The KUKA robot case study. AIMS Mathematics, 2024, 9(6): 13944-13979. doi: 10.3934/math.2024678
[9]	Geoffrey McGregor, Jennifer Tippett, Andy T.S. Wan, Mengxiao Wang, Samuel W.K. Wong . Comparing regional and provincial-wide COVID-19 models with physical distancing in British Columbia. AIMS Mathematics, 2022, 7(4): 6743-6778. doi: 10.3934/math.2022376
[10]	Massoumeh Nazari, Mahmoud Dehghan Nayeri, Kiamars Fathi Hafshjani . Developing mathematical models and intelligent sustainable supply chains by uncertain parameters and algorithms. AIMS Mathematics, 2024, 9(3): 5204-5233. doi: 10.3934/math.2024252

Abstract

Since its initiation in 1979, the Canadian Applied and Industrial Mathematics Society — Société Canadienne de Mathématiques Appliquées et Industrielles (CAIMS–SCMAI) has gained a growing presence in industrial, mathematical, scientific, and technological circles within and outside of Canada. Its members contribute to state-of-the-art research in industry, natural sciences, medicine and health, finance, physics, engineering, and more. The annual meetings are a highlight of the year. CAIMS–SCMAI is an active member society of the International Council for Industrial and Applied Mathematics, which hosts the prestigious ICIAM Congresses every four years.

Canadian Applied and Industrial Mathematics is at the forefront of scientific and technological development. We use advanced mathematics to tackle real-world problems in science and industry and develop new theories to analyse structures that arise from the modelling of real-world problems.

Applied Mathematics has evolved from traditional applications in areas such as fluids, mechanics, and physics, to modern topics such as medicine, health, biology, data science, finance, nano-tech, etc. Its growing importance in all aspects of life, health, and management increases the need for publication venues for high-level applied and industrial mathematics. Hence CAIMS–SCMAI decided to start a scientific journal called Mathematics in Science and Industry (MSI) to add value to the discussion of applied and industrial mathematics worldwide.

Submissions to MSI in all areas of applied and industrial mathematics are welcome (https://caims.ca/mathematics_in_science_and_industry/). We offer a timely and high-quality review process, and papers are published online as open access, with the publication fee being covered by CAIMS for the first five years.

MSI is honored that leading experts in industrial and applied mathematics have offered their support as editors:

Editors in Chief:

● Thomas Hillen (University of Alberta, thillen@ualberta.ca)

● Ray Spiteri (University of Saskatchewan, spiteri@cs.usask.ca)

Associate Editors:

● Lia Bronsard (McMaster University)

● Richard Craster (Imperial College of London, UK)

● David Earn (McMaster University)

● Ronald Haynes (Memorial University)

● Jane Heffernan (York University)

● Nicholas Kevlahan (McMaster University)

● Yong-Jung Kim (KAIST, Korea)

● Mark Lewis (University of Alberta)

● Kevin J. Painter (Heriot-Watt University, UK)

● Vakhtang Putkaradze (ATCO)

● Katrin Rohlf (Ryerson University)

● John Stockie (Simon Fraser University)

● Jie Sun (Huawei, Hong Kong)

● Justin Wan (University of Waterloo)

● Michael Ward (University of British Columbia)

● Tony Ware (University of Calgary)

● Brian Wetton (University of British Columbia)

The first eight papers of MSI, presented here, are published as special issue in AIMS Mathematics. They showcase a broad representation of applied mathematics that touches the interests of Canadian researchers and our many collaborators around the world. The science that we present here is not exclusively "Canadian", but we hope that through the new journal MSI, we can contribute to scientific dissemination of knowledge and add Canadian values to the scientific discussion.

The next issue of MSI is planned for the fall of 2020 and is expected to appear again as a special issue of AIMS Mathematics.

References

[1]	A. R. A. Anderson, K. A. Rejniak, P. Gerlee and V. Quaranta, Microenvironment driven invasion: a multiscale multimodel investigation, J. Math. Biol., 58 (2009), 579–624.
[2]	L. A. Bach, D. J. T. Sumpter, J. Alsner and V. Loeschcke, Spatial evolutionary games of interaction among generic cancer cells, J. Theor. Med., 5 (2003), 47–58.
[3]	L. Bach, S. Bentzen, J. Alsner and F. Christiansen, An evolutionary-game model of tumour-cell interactions: possible relevance to gene therapy, Eur. J. Cancer., 37 (2001), 2116–2120.
[4]	D. Basanta, H. Hatzikirou and A. Deutsch, Studying the emergence of invasiveness in tumours using game theory, Eur. Phys. J. B, 63 (2008), 393–397.
[5]	D. Basanta, J. G. Scott, M. N. Fishman, G. Ayala, S. W. Hayward and A. R. A. Anderson, Investigating prostate cancer tumour-stroma interactions: clinical and biological insights from an evolutionary game, Br. J. Cancer., 106 (2012), 174–181.
[6]	D. Basanta and A. R. A. Anderson, Exploiting ecological principles to better understand cancer progression and treatment, Interface focus, 3 (2013), 20130020.
[7]	D. Basanta, R. A. Gatenby and A. R. A. Anderson, Exploiting evolution to treat drug resistance: combination therapy and the double bind, Mol. Pharm., 9 (2012), 914–921.
[8]	D. Basanta, J. G. Scott, R. Rockne, K. R. Swanson and A. R. A. Anderson, The role of IDH1 mutated tumour cells in secondary glioblastomas: an evolutionary game theoretical view, Phys. Biol., 8 (2011), 015016.
[9]	D. T. Bishop and C. Cannings, A generalized war of attrition, J. Theor. Biol., 70 (1978), 85–124.
[10]	K. Bohl, S. Hummert, S. Werner, D. Basanta, A. Deutsch, S. Schuster, G. Theissen and A. Schroeter, Evolutionary game theory: molecules as players, Mol. Biosyst., 10 (2014), 3066–3074.
[11]	D. Dingli, F. A. C. C. Chalub, F. C. Santos, S. Van Segbroeck and J. M. Pacheco, Cancer phenotype as the outcome of an evolutionary game between normal and malignant cells, Br. J. Cancer., 101 (2009), 1130–1136.
[12]	M. Dolbniak, M. Kardynska and J. Smieja, Sensitivity of combined chemo-and antiangiogenic therapy results in different models describing cancer growth, Discrete Cont. Dyn. - B, 23 (2018), 145–160.
[13]	J. C. Fisher, Multiple-mutation theory of carcinogenesis, Nature, 181 (1958), 651–652.
[14]	R. A. Gatenby and T. L. Vincent, An evolutionary model of carcinogenesis, Cancer Res., 63 (2003), 6212–6220.
[15]	M. Gerstung, N. Eriksson, J. Lin, B. Vogelstein and N. Beerenwinkel, The temporal order of genetic and pathway alterations in tumorigenesis, PloS one, 6 (2011), e27136.
[16]	J. Hofbauer, P. Schuster and K. Sigmund, A note on evolutionary stable strategies and game dynamics, J. Theor. Biol., 81 (1979), 609–612.
[17]	S. Hummert, K. Bohl, D. Basanta, A. Deutsch, S. Werner, G. Theissen, A. Schroeter and S. Schuster, Evolutionary game theory: cells as players, Mol. BioSyst., 10 (2014), 3044–3065.
[18]	A. Kaznatcheev, R. Vander Velde, J. G. Scott and D. Basanta, Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature, Br. J. Cancer., 116 (2017), 785–792.
[19]	M. Krzeslak, D. Borys and A. Swierniak, Angiogenic switch - mixed spatial evolutionary game approach, Intell. Inf. Database Syst., 9621 (2016), 420–429.
[20]	M. Krzeslak and A. Swierniak, Multidimensional extended spatial evolutionary games, Comput. Biol. Med., 69 (2016), 315–327.
[21]	M. Krzeslak and A. Swierniak, Spatial evolutionary games and radiation induced bystander effect, Arch. Control Sci., 21.
[22]	J. M. Lasry and P. L. Lions, Mean field games, Jpn J. Math., 2 (2007), 229–260.
[23]	L. A. Loeb, Mutator phenotype may be required for multistage carcinogenesis, Cancer Res., 51 (1991), 3075–3079.
[24]	M. Mahner and M. Kary, What exactly are genomes, genotypes and phenotypes? And what about phenomes? J. Theor. Biol., 186 (1997), 55–63.
[25]	Y. Mansury, M. Diggory and T. S. Deisboeck, Evolutionary game theory in an agent-based brain tumor model: exploring the 'genotype-phenotype' link, J. Theor. Biol., 238 (2006), 146–156.
[26]	L. M. F. Merlo, J.W. Pepper, B. J. Reid and C. C. Maley, Cancer as an evolutionary and ecological process, Nat. Rev. Cancer, 6 (2006), 924–935.
[27]	J. V. Neumann, Theory of Self-Reproducing Automata, University of Illinois Press, Champaign, IL, USA, 1966.
[28]	K. Sigmund and M. A. Nowak, Evolutionary game theory, Curr. Biol., 9 (1999), R503–R505.
[29]	J. M. Smith and G. R. Price, The logic of animal conflict, Nature, 246 (1973), 15–18.
[30]	J. M. Smith, Evolution and the theory of games.
[31]	A. Swierniak, M. Kimmel, J. Smieja, K. Puszynski and K. Psiuk-Maksymowicz, System Engineering Approach to Planning Anticancer Therapies, Springer International Publishing, 2016.
[32]	A. Swierniak and M. Krzeslak, Application of evolutionary games to modeling carcinogenesis, Math. Biosci. Eng., 10 (2013), 873–911.
[33]	A. Swierniak and M. Krzeslak, Cancer heterogeneity and multilayer spatial evolutionary games., Biol. Direct, 11 (2016), 53.
[34]	A. Swierniak, M. Krzeslak, S. Student and J. Rzeszowska-Wolny, Development of a population of cancer cells: Observation and modeling by a mixed spatial evolutionary games approach, J. Theor. Biol., 405 (2016), 94–103.
[35]	I. P. Tomlinson and W. F. Bodmer, Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models., Proceedings of the National Academy of Sciences of the United States of America, 92 (1995), 11130–11134.
[36]	I. Tomlinson, Game-theory models of interactions between tumour cells, Eur. J. Cancer., 33 (1997), 1495–1500.
[37]	I. Tomlinson and W. Bodmer, Modelling the consequences of interactions between tumour cells, Br. J. Cancer., 75 (1997), 157–160.

Reader Comments

Your name:*

Email:*
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)