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Bukkuri A. Modeling stress-induced responses: plasticity in continuous state space and gradual clonal evolution. Theory Biosci 2024; 143:63-77. [PMID: 38289469 DOI: 10.1007/s12064-023-00410-3] [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: 07/20/2023] [Accepted: 12/13/2023] [Indexed: 03/01/2024]
Abstract
Mathematical models of cancer and bacterial evolution have generally stemmed from a gene-centric framework, assuming clonal evolution via acquisition of resistance-conferring mutations and selection of their corresponding subpopulations. More recently, the role of phenotypic plasticity has been recognized and models accounting for phenotypic switching between discrete cell states (e.g., epithelial and mesenchymal) have been developed. However, seldom do models incorporate both plasticity and mutationally driven resistance, particularly when the state space is continuous and resistance evolves in a continuous fashion. In this paper, we develop a framework to model plastic and mutational mechanisms of acquiring resistance in a continuous gradual fashion. We use this framework to examine ways in which cancer and bacterial populations can respond to stress and consider implications for therapeutic strategies. Although we primarily discuss our framework in the context of cancer and bacteria, it applies broadly to any system capable of evolving via plasticity and genetic evolution.
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Affiliation(s)
- Anuraag Bukkuri
- Cancer Biology and Evolution Program and Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, USA.
- Tissue Development and Evolution Research Group, Department of Laboratory Medicine, Lund University, Lund, Sweden.
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Bukkuri A, Pienta KJ, Austin RH, Hammarlund EU, Amend SR, Brown JS. A mathematical investigation of polyaneuploid cancer cell memory and cross-resistance in state-structured cancer populations. Sci Rep 2023; 13:15027. [PMID: 37700000 PMCID: PMC10497555 DOI: 10.1038/s41598-023-42368-8] [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: 01/31/2023] [Accepted: 09/09/2023] [Indexed: 09/14/2023] Open
Abstract
The polyaneuploid cancer cell (PACC) state promotes cancer lethality by contributing to survival in extreme conditions and metastasis. Recent experimental evidence suggests that post-therapy PACC-derived recurrent populations display cross-resistance to classes of therapies with independent mechanisms of action. We hypothesize that this can occur through PACC memory, whereby cancer cells that have undergone a polyaneuploid transition (PAT) reenter the PACC state more quickly or have higher levels of innate resistance. In this paper, we build on our prior mathematical models of the eco-evolutionary dynamics of cells in the 2N+ and PACC states to investigate these two hypotheses. We show that although an increase in innate resistance is more effective at promoting cross-resistance, this trend can also be produced via PACC memory. We also find that resensitization of cells that acquire increased innate resistance through the PAT have a considerable impact on eco-evolutionary dynamics and extinction probabilities. This study, though theoretical in nature, can help inspire future experimentation to tease apart hypotheses surrounding how cross-resistance in structured cancer populations arises.
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Affiliation(s)
- Anuraag Bukkuri
- Cancer Biology and Evolution Program and Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, USA.
| | - Kenneth J Pienta
- The Brady Urological Institute, Johns Hopkins School of Medicine, Baltimore, USA
| | | | - Emma U Hammarlund
- Tissue Development and Evolution Research Group, Department of Laboratory Medicine, Lund University, Lund, Sweden
| | - Sarah R Amend
- The Brady Urological Institute, Johns Hopkins School of Medicine, Baltimore, USA
| | - Joel S Brown
- Cancer Biology and Evolution Program and Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, USA
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3
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Fischer MM, Blüthgen N. On tumoural growth and treatment under cellular dedifferentiation. J Theor Biol 2023; 557:111327. [PMID: 36341757 DOI: 10.1016/j.jtbi.2022.111327] [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: 05/29/2022] [Revised: 09/02/2022] [Accepted: 10/17/2022] [Indexed: 11/06/2022]
Abstract
Differentiated cancer cells may regain stem cell characteristics; however, the effects of such a cellular dedifferentiation on tumoural growth and treatment are currently understudied. Thus, we here extend a mathematical model of cancer stem cell (CSC) driven tumour growth to also include dedifferentiation. We show that dedifferentiation increases the likelihood of tumorigenesis and the speed of tumoural growth, both modulated by the proliferative potential of the non-stem cancer cells (NSCCs). We demonstrate that dedifferentiation also may lead to treatment evasion, especially when a treatment solely targets CSCs. Conversely, targeting both CSCs and NSCCs in parallel is shown to be more robust to dedifferentiation. Despite dedifferentiation, perturbing CSC-related parameters continues to exert the largest relative effect on tumoural growth; however, we show the existence of synergies between specific CSC- and NSCC-directed treatments which cause superadditive reductions of tumoural growth. Overall, our study demonstrates various effects of dedifferentiation on growth and treatment of tumoural lesions, and we anticipate our results to be helpful in guiding future molecular and clinical research on limiting tumoural growth in vivo.
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Affiliation(s)
- Matthias M Fischer
- Institute for Theoretical Biology, Humboldt Universität zu Berlin, 10115 Berlin, Germany; Charité Universitätsmedizin Berlin, Institut für Pathologie, 10117 Berlin, Germany.
| | - Nils Blüthgen
- Institute for Theoretical Biology, Humboldt Universität zu Berlin, 10115 Berlin, Germany; Charité Universitätsmedizin Berlin, Institut für Pathologie, 10117 Berlin, Germany.
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Italia M, Dercole F, Lucchetti R. Optimal chemotherapy counteracts cancer adaptive resistance in a cell-based, spatially-extended, evolutionary model. Phys Biol 2022; 19. [PMID: 35100568 DOI: 10.1088/1478-3975/ac509c] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Accepted: 01/31/2022] [Indexed: 11/12/2022]
Abstract
Most aggressive cancers are incurable due to their fast evolution of drug resistance. We model cancer growth and adaptive response in a simplified cell-based (CB) setting, assuming a genetic resistance to two chemotherapeutic drugs. We show that optimal administration protocols can steer cells resistance and turned it into a weakness for the disease. Our work extends the population-based (PB) model proposed by Orlando et al. (Physical Biology, 2012), in which a homogeneous population of cancer cells evolves according to a fitness landscape. The landscape models three types of trade-offs, differing on whether the cells are more, less, or equal effective when generalizing resistance to two drugs as opposed to specializing to a single one. The CB framework allows us to include genetic heterogeneity, spatial competition, and drugs diffusion, as well as realistic administration protocols. By calibrating our model on Orlando et al.'s assumptions, we show that dynamical protocols that alternate the two drugs minimize the cancer size at the end of (or at mid-points during) treatment. These results significantly differ from those obtained with the homogeneous model---suggesting static protocols under the pro-generalizing and neutral allocation trade-offs---highlighting the important role of spatial and genetic heterogeneities. Our work is the first attempt to search for optimal treatments in a CB setting, a step forward toward realistic clinical applications.
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Affiliation(s)
- Matteo Italia
- Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, Milano, 20133, ITALY
| | - Fabio Dercole
- Electronics, Information and Bioengineering, Politecnico di Milano, Via Ponzio 34/5, Milano, 20133, ITALY
| | - Roberto Lucchetti
- Mathematics, Politecnico di Milano, Via Edoardo Bonardi, 9, Milano, 20133, ITALY
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Lionetti MC, Cola F, Chepizhko O, Fumagalli MR, Font-Clos F, Ravasio R, Minucci S, Canzano P, Camera M, Tiana G, Zapperi S, Porta CAML. MicroRNA-222 Regulates Melanoma Plasticity. J Clin Med 2020; 9:jcm9082573. [PMID: 32784455 PMCID: PMC7464186 DOI: 10.3390/jcm9082573] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Revised: 07/31/2020] [Accepted: 07/31/2020] [Indexed: 12/27/2022] Open
Abstract
Melanoma is one of the most aggressive and highly resistant tumors. Cell plasticity in melanoma is one of the main culprits behind its metastatic capabilities. The detailed molecular mechanisms controlling melanoma plasticity are still not completely understood. Here we combine mathematical models of phenotypic switching with experiments on IgR39 human melanoma cells to identify possible key targets to impair phenotypic switching. Our mathematical model shows that a cancer stem cell subpopulation within the tumor prevents phenotypic switching of the other cancer cells. Experiments reveal that hsa-mir-222 is a key factor enabling this process. Our results shed new light on melanoma plasticity, providing a potential target and guidance for therapeutic studies.
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Affiliation(s)
- Maria Chiara Lionetti
- Center for Complexity and Biosystems, Department of Environmental Science and Policy, University of Milan, via Celoria 26, 20133 Milano, Italy; (M.C.L.); (M.R.F.)
| | - Filippo Cola
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy; (F.C.); (F.F.-C.); (G.T.); (S.Z.)
| | - Oleksandr Chepizhko
- Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck, Technikerstrasse 21a, A-6020 Innsbruck, Austria;
| | - Maria Rita Fumagalli
- Center for Complexity and Biosystems, Department of Environmental Science and Policy, University of Milan, via Celoria 26, 20133 Milano, Italy; (M.C.L.); (M.R.F.)
- CNR-Consiglio Nazionale delle Ricerche, Biophysics institute, via De Marini 6, 16149 Genova, Italy
| | - Francesc Font-Clos
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy; (F.C.); (F.F.-C.); (G.T.); (S.Z.)
| | - Roberto Ravasio
- Department of Experimental Oncology, European Institute of Oncology, Via Adamello 16, 20139 Milano, Italy; (R.R.); (S.M.)
| | - Saverio Minucci
- Department of Experimental Oncology, European Institute of Oncology, Via Adamello 16, 20139 Milano, Italy; (R.R.); (S.M.)
| | - Paola Canzano
- Centro Cardiologico Monzino I.R.C.C.S., Via Carlo Parea 4, 20138 Milano, Italy; (P.C.); (M.C.)
| | - Marina Camera
- Centro Cardiologico Monzino I.R.C.C.S., Via Carlo Parea 4, 20138 Milano, Italy; (P.C.); (M.C.)
- Department of Pharmacological and Biomolecular Sciences, University of Milan, Via Balzaretti 9/11/13, 20133 Milano, Italy
| | - Guido Tiana
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy; (F.C.); (F.F.-C.); (G.T.); (S.Z.)
| | - Stefano Zapperi
- Center for Complexity and Biosystems, Department of Physics, University of Milan, via Celoria 16, 20133 Milano, Italy; (F.C.); (F.F.-C.); (G.T.); (S.Z.)
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l’Energia, Via R. Cozzi 53, 20125 Milano, Italy
| | - Caterina A. M. La Porta
- Center for Complexity and Biosystems, Department of Environmental Science and Policy, University of Milan, via Celoria 26, 20133 Milano, Italy; (M.C.L.); (M.R.F.)
- CNR-Consiglio Nazionale delle Ricerche, Biophysics institute, via De Marini 6, 16149 Genova, Italy
- Innovation for Well-Being and Environment (CR-I-WE), University of Milan, via Celoria 26, 20133 Milano, Italy
- Correspondence:
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Sigal D, Przedborski M, Sivaloganathan D, Kohandel M. Mathematical modelling of cancer stem cell-targeted immunotherapy. Math Biosci 2019; 318:108269. [DOI: 10.1016/j.mbs.2019.108269] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Revised: 09/17/2019] [Accepted: 10/05/2019] [Indexed: 12/15/2022]
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Stiehl T, Marciniak-Czochra A. How to Characterize Stem Cells? Contributions from Mathematical Modeling. CURRENT STEM CELL REPORTS 2019. [DOI: 10.1007/s40778-019-00155-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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Jilkine A. Mathematical Models of Stem Cell Differentiation and Dedifferentiation. CURRENT STEM CELL REPORTS 2019. [DOI: 10.1007/s40778-019-00156-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
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Zhou D, Mao S, Cheng J, Chen K, Cao X, Hu J. A Bayesian statistical analysis of stochastic phenotypic plasticity model of cancer cells. J Theor Biol 2018; 454:70-79. [DOI: 10.1016/j.jtbi.2018.05.031] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2017] [Revised: 05/25/2018] [Accepted: 05/28/2018] [Indexed: 12/24/2022]
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Wodarz D. Effect of cellular de-differentiation on the dynamics and evolution of tissue and tumor cells in mathematical models with feedback regulation. J Theor Biol 2018; 448:86-93. [PMID: 29605227 PMCID: PMC6173950 DOI: 10.1016/j.jtbi.2018.03.036] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Revised: 03/26/2018] [Accepted: 03/28/2018] [Indexed: 12/12/2022]
Abstract
Tissues are maintained by adult stem cells that self-renew and also differentiate into functioning tissue cells. Homeostasis is achieved by a set of complex mechanisms that involve regulatory feedback loops. Similarly, tumors are believed to be maintained by a minority population of cancer stem cells, while the bulk of the tumor is made up of more differentiated cells, and there is indication that some of the feedback loops that operate in tissues continue to be functional in tumors. Mathematical models of such tissue hierarchies, including feedback loops, have been analyzed in a variety of different contexts. Apart from stem cells giving rise to differentiated cells, it has also been observed that more differentiated cells can de-differentiate into stem cells, both in healthy tissue and tumors, aspects of which have also been investigated mathematically. This paper analyses the effect of de-differentiation on the basic and evolutionary dynamics of cells in the context of tissue hierarchy models that include negative feedback regulation of the cell populations. The models predict that in the presence of de-differentiation, the fixation probability of a neutral mutant is lower than in its absence. Therefore, if de-differentiation occurs, a mutant with identical parameters compared to the wild-type cell population behaves like a disadvantageous mutant. Similarly, the process of de-differentiation is found to lower the fixation probability of an advantageous mutant. These results indicate that the presence of de-differentiation can lower the rates of tumor initiation and progression in the context of the models considered here.
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Affiliation(s)
- Dominik Wodarz
- Department of Ecology and Evolutionary Biology & Department of Mathematics, 321 Steinhaus Hall, University of California, Irvine, CA 92617, USA.
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