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Hodgkinson A, Trucu D, Lacroix M, Le Cam L, Radulescu O. Computational Model of Heterogeneity in Melanoma: Designing Therapies and Predicting Outcomes. Front Oncol 2022; 12:857572. [PMID: 35494017 PMCID: PMC9046868 DOI: 10.3389/fonc.2022.857572] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Accepted: 03/07/2022] [Indexed: 11/16/2022] Open
Abstract
Cutaneous melanoma is a highly invasive tumor and, despite the development of recent therapies, most patients with advanced metastatic melanoma have a poor clinical outcome. The most frequent mutations in melanoma affect the BRAF oncogene, a protein kinase of the MAPK signaling pathway. Therapies targeting both BRAF and MEK are effective for only 50% of patients and, almost systematically, generate drug resistance. Genetic and non-genetic mechanisms associated with the strong heterogeneity and plasticity of melanoma cells have been suggested to favor drug resistance but are still poorly understood. Recently, we have introduced a novel mathematical formalism allowing the representation of the relation between tumor heterogeneity and drug resistance and proposed several models for the development of resistance of melanoma treated with BRAF/MEK inhibitors. In this paper, we further investigate this relationship by using a new computational model that copes with multiple cell states identified by single cell mRNA sequencing data in melanoma treated with BRAF/MEK inhibitors. We use this model to predict the outcome of different therapeutic strategies. The reference therapy, referred to as “continuous” consists in applying one or several drugs without disruption. In “combination therapy”, several drugs are used sequentially. In “adaptive therapy” drug application is interrupted when the tumor size is below a lower threshold and resumed when the size goes over an upper threshold. We show that, counter-intuitively, the optimal protocol in combination therapy of BRAF/MEK inhibitors with a hypothetical drug targeting cell states that develop later during the tumor response to kinase inhibitors, is to treat first with this hypothetical drug. Also, even though there is little difference in the timing of emergence of the resistance between continuous and adaptive therapies, the spatial distribution of the different melanoma subpopulations is more zonated in the case of adaptive therapy.
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Affiliation(s)
- Arran Hodgkinson
- Living Systems Institute, University of Exeter, Exeter, United Kingdom
| | - Dumitru Trucu
- Division of Mathematics, University of Dundee, Dundee, United Kingdom
| | - Matthieu Lacroix
- IRCM, Institut de Recherche en Cancérologie de Montpellier, INSERM U1194, Univ Montpellier, Institut régional du Cancer de Montpellier, Montpellier, France
- Equipe Labélisée Ligue contre le cancer, Paris, France
| | - Laurent Le Cam
- IRCM, Institut de Recherche en Cancérologie de Montpellier, INSERM U1194, Univ Montpellier, Institut régional du Cancer de Montpellier, Montpellier, France
- Equipe Labélisée Ligue contre le cancer, Paris, France
| | - Ovidiu Radulescu
- LPHI, University of Montpellier and CNRS UMR 5235, Montpellier, France
- *Correspondence: Ovidiu Radulescu,
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Kirshtein A, Akbarinejad S, Hao W, Le T, Su S, Aronow RA, Shahriyari L. Data Driven Mathematical Model of Colon Cancer Progression. J Clin Med 2020; 9:E3947. [PMID: 33291412 PMCID: PMC7762015 DOI: 10.3390/jcm9123947] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Revised: 11/28/2020] [Accepted: 12/02/2020] [Indexed: 12/13/2022] Open
Abstract
Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. Here, we develop a data driven mathematical model for the interaction network of key components of immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients, and observe differences in the patterns of tumor growth between the groups. For instance, in tumors with a smaller density of naive macrophages than activated macrophages, a higher activation rate of macrophages leads to an increase in cancer cell density, demonstrating a negative effect of macrophages. Other tumors however, exhibit an opposite trend, showing a positive effect of macrophages in controlling tumor size. Although the results indicate that for all patients the size of the tumor is sensitive to the parameters related to macrophages, such as their activation and death rate, this research demonstrates that no single biomarker could predict the dynamics of tumors.
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Affiliation(s)
- Arkadz Kirshtein
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-9305, USA; (A.K.); (S.A.); (T.L.); (S.S.); (R.A.A.)
| | - Shaya Akbarinejad
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-9305, USA; (A.K.); (S.A.); (T.L.); (S.S.); (R.A.A.)
| | - Wenrui Hao
- Department of Mathematics, Pennsylvania State University, University Park, State College, PA 16802, USA;
| | - Trang Le
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-9305, USA; (A.K.); (S.A.); (T.L.); (S.S.); (R.A.A.)
| | - Sumeyye Su
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-9305, USA; (A.K.); (S.A.); (T.L.); (S.S.); (R.A.A.)
| | - Rachel A. Aronow
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-9305, USA; (A.K.); (S.A.); (T.L.); (S.S.); (R.A.A.)
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003-9305, USA; (A.K.); (S.A.); (T.L.); (S.S.); (R.A.A.)
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Delitala M, Lorenzi T. Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2017; 14:79-93. [PMID: 27879121 DOI: 10.3934/mbe.2017006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Accumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.
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Affiliation(s)
- Marcello Delitala
- Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
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Lorenzi T, Chisholm RH, Clairambault J. Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations. Biol Direct 2016; 11:43. [PMID: 27550042 PMCID: PMC4994266 DOI: 10.1186/s13062-016-0143-4] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Accepted: 07/20/2016] [Indexed: 02/06/2023] Open
Abstract
Background A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies. Results To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotype-structured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use. Conclusions Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a double-edged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anti-cancer therapeutic protocols that go beyond the ‘maximum-tolerated-dose paradigm’, as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones. Reviewers This article was reviewed by Angela Pisco, Sébastien Benzekry and Heiko Enderling. Electronic supplementary material The online version of this article (doi:10.1186/s13062-016-0143-4) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Tommaso Lorenzi
- School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK.
| | - Rebecca H Chisholm
- School of Biotechnology and Biomolecular Sciences, University of New South Wales, NSW, Sydney, 2052, Australia
| | - Jean Clairambault
- INRIA Paris Research Centre, MAMBA team, 2, rue Simone Iff, CS 42112, Paris Cedex 12, 75589, France.,Sorbonne Universités, UPMC Univ. Paris 6, UMR 7598, Laboratoire Jacques-Louis Lions, Boîte courrier 187, 4 Place Jussieu, Paris Cedex 05, 75252, France
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Pei QM, Zhan X, Yang LJ, Bao C, Cao W, Li AB, Rozi A, Jia Y. Fluctuations of cell population in a colonic crypt. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032715. [PMID: 24730882 DOI: 10.1103/physreve.89.032715] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2013] [Indexed: 06/03/2023]
Abstract
The number of stem cells in a colonic crypt is often very small, which leads to large intrinsic fluctuations in the cell population. Based on the model of cell population dynamics with linear feedback in a colonic crypt, we present a stochastic dynamics of the cell population [including stem cells (SCs), transit amplifying cells (TACs), and fully differentiated cells (FDCs)]. The Fano factor, covariance, and susceptibility formulas of the cell population around the steady state are derived by using the Langevin theory. In the range of physiologically reasonable parameter values, it is found that the stationary populations of TACs and FDCs exhibit an approximately threshold behavior as a function of the net growth rate of TACs, and the reproductions of TACs and FDCs can be classified into three regimens: controlled, crossover, and uncontrolled. With the increasing of the net growth rate of TACs, there is a maximum of the relative intrinsic fluctuations (i.e., the Fano factors) of TACs and FDCs in the crossover region. For a fixed differentiation rate and the net growth rate of SCs, the covariance of fluctuations between SCs and TACs has a maximum in the crossover region. However, the susceptibilities of both TACs and FDCs to the net growth rate of TACs have a minimum in the crossover region.
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Affiliation(s)
- Qi-ming Pei
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and School of Physical Science and Technology, Yangtze University, Jingzhou 434023, China
| | - Xuan Zhan
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Li-jian Yang
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Chun Bao
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Wei Cao
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - An-bang Li
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Anvar Rozi
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China and Department of Physics, Kashgar Teachers College, Kashgar 844007, China
| | - Ya Jia
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
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Kershaw SK, Byrne HM, Gavaghan DJ, Osborne JM. Colorectal cancer through simulation and experiment. IET Syst Biol 2013; 7:57-73. [DOI: 10.1049/iet-syb.2012.0019] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
- Sophie K. Kershaw
- Department of Computer ScienceComputational Biology GroupWolfson Building, Parks RoadOxfordOX1 3QDUK
| | - Helen M. Byrne
- Department of Computer ScienceComputational Biology GroupWolfson Building, Parks RoadOxfordOX1 3QDUK
- OCCAM, Mathematical Institute24-29 St. Giles’OxfordOX1 3LBUK
| | - David J. Gavaghan
- Department of Computer ScienceComputational Biology GroupWolfson Building, Parks RoadOxfordOX1 3QDUK
- Department of BiochemistryOxford Centre for Integrative Systems BiologySouth Parks RoadOxfordOX1 3QUUK
| | - James M. Osborne
- Department of Computer ScienceComputational Biology GroupWolfson Building, Parks RoadOxfordOX1 3QDUK
- Department of BiochemistryOxford Centre for Integrative Systems BiologySouth Parks RoadOxfordOX1 3QUUK
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Lo WC, Martin EW, Hitchcock CL, Friedman A. Mathematical model of colitis-associated colon cancer. J Theor Biol 2012; 317:20-9. [PMID: 23026764 DOI: 10.1016/j.jtbi.2012.09.025] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2012] [Revised: 08/28/2012] [Accepted: 09/18/2012] [Indexed: 02/07/2023]
Abstract
As a result of chronic inflammation of their colon, patients with ulcerative colitis or Crohn's disease are at risk of developing colon cancer. In this paper, we consider the progression of colitis-associated colon cancer. Unlike normal colon mucosa, the inflammed colon mucosa undergoes genetic mutations, affecting, in particular, tumor suppressors TP53 and adenomatous polyposis coli (APC) gene. We develop a mathematical model that involves these genes, under chronic inflammation, as well as NF-κB, β-catenin, MUC1 and MUC2. The model demonstrates that increased level of cells with TP53 mutations results in abnormal growth and proliferation of the epithelium; further increase in the epithelium proliferation results from additional APC mutations. The model may serve as a conceptual framework for further data-based study of the early stage of colon cancer.
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Affiliation(s)
- Wing-Cheong Lo
- Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA.
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A mathematical model for the dynamics of cancer hepatocytes under therapeutic actions. J Theor Biol 2011; 297:88-102. [PMID: 22138092 DOI: 10.1016/j.jtbi.2011.11.022] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2011] [Revised: 10/13/2011] [Accepted: 11/11/2011] [Indexed: 11/27/2022]
Abstract
This paper deals with the development of a mathematical model for the in vitro dynamics of malignant hepatocytes exposed to anti-cancer therapies. The model consists of a set of integro-differential equations describing the dynamics of tumor cells under the effects of mutation and competition phenomena, interactions with cytokines regulating cell proliferation as well as the action of cytotoxic drugs and targeted therapeutic agents. Asymptotic analysis and simulations, developed with an exploratory aim, are addressed to enlighten the role played by the biological phenomena under consideration in the dynamics of hepatocellular carcinoma, with particular reference to the intra-tumor heterogeneity and the response to therapies. The obtained results suggest that cancer progression selects for highly proliferative clones. Moreover, it seems that intra-tumor heterogeneity makes targeted therapeutic agents to be less effective than cytotoxic drugs and a joint action of these two classes of agents may mutually increase their efficacy. Finally, it is highlighted how targeted therapeutic agents might act as an additional selective pressure leading to the selection for the most fitting, and then most resistant, cancer clones.
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