ArticleJournal of mathematical biology2016
Mass concentration in a nonlocal model of clonal selection.
Article in Journal of mathematical biology, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation.Journal of mathematical biology · 2022Article
- The role of memory in non-genetic inheritance and its impact on cancer treatment resistance.PLoS computational biology · 2021Article
- Computational Reconstruction of Clonal Hierarchies From Bulk Sequencing Data of Acute Myeloid Leukemia Samples.Frontiers in physiology · 2021Article
- Evolutionary dynamics of competing phenotype-structured populations in periodically fluctuating environments.Journal of mathematical biology · 2020Article
- Oscillations in a white blood cell production model with multiple differentiation stages.Journal of mathematical biology · 2020Article
- Modelling collective cell migration: neural crest as a model paradigm.Journal of mathematical biology · 2020Article
- A structured population model of clonal selection in acute leukemias with multiple maturation stages.Journal of mathematical biology · 2019Article
- Emergence of heterogeneity in acute leukemias.Biology direct · 2016Article
Corrections and comments
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To better understand this impact, we propose a mathematical model describing the dynamics of a continuum of cell clones structured by the self-renewal potential. The model is an extension of the finite multi-compartment models of interactions between normal and cancer cells in acute leukemias. It takes a form of a system of integro-differential equations with a nonlinear and nonlocal coupling which describes regulatory feedback loops of cell proliferation and differentiation. We show that this coupling leads to mass concentration in points corresponding to the maxima of the self-renewal potential and the solutions of the model tend asymptotically to Dirac measures multiplied by positive constants. Furthermore, using a Lyapunov function constructed for the finite dimensional counterpart of the model, we prove that the total mass of the solution converges to a globally stable equilibrium. Additionally, we show stability of the model in the space of positive Radon measures equipped with the flat metric (bounded Lipschitz distance). Analytical results are illustrated by numerical simulations.
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