Analysis of a model of dormancy in cancer as a state of coexistence between tumor and healthy stem cells

Djema, Walid; Bonnet, Catherine; Clairambault, Jean; Mazenc, Frédéric; Hirsch, Pierre; Delhommeau, François

doi:10.23919/acc.2017.7963751

Cited by 5 publications

(8 citation statements)

References 30 publications

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“…In light of Theorem 1, we deduce that zero is stable if we ensure that an upper-bound on κ is satisfied, i.e. if dedifferentiation does not cross the threshold defined by the condition a > 0 in (12). Medical practice supports this observation ( [16], [25]), as discussed in the sequel.…”

Section: Remarkmentioning

confidence: 64%

“…Next, let us assume that at t = 20 days, the dedifferentiation mechanism is triggered (by setting κ = 0.8 at t = 20 days). In that case, we still have s 1 > 0 and s 2 > 0, but, however, we note that the sufficient stability conditions (12), in Theorem 1, are not satisfied:…”

Section: A Numerical Illustration and Some Concluding Commentsmentioning

confidence: 94%

“…We particularly emphasize the case of hematopoietic SCs and early blood progeny (see some similar models in [20], [4], [1], [23], [12]). In fact, hematopoiesis provides a common paradigm for understanding all the mammalian SCs, in particular when it comes to study cell differentiation.…”

Section: Summary and Key Pointsmentioning

confidence: 99%

See 2 more Smart Citations

Introducing Cell-Plasticity Mechanisms into a Class of Cell Population Dynamical Systems

Djema

Bonnet

Mazenc

et al. 2018

2018 Annual American Control Conference (ACC)

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Abstract-Cells have amazing features that allow them to guide their development paths and determine their individual and collective fates. Dedifferentiation and transdifferentiation (cell plasticity) are littleunderstood phenomena that allow cells to regress from an advanced differentiated state to a less differentiated one, including the case where cells lose their specific function and become stem cells. In this paper, we introduce cell plasticity into a class of mathematical models we are interested in. We explore a new model involving a dedifferentiation function in the case of two cell maturity stages (stem cells and progeny). We highlight the role that dedifferentiation may have in the survival of cancer cells during therapy.The latter hypothesis appears to be in line with some medical observations.

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Section: Remarkmentioning

confidence: 64%

Section: A Numerical Illustration and Some Concluding Commentsmentioning

confidence: 94%

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Introducing Cell-Plasticity Mechanisms into a Class of Cell Population Dynamical Systems

Djema

Bonnet

Mazenc

et al. 2018

2018 Annual American Control Conference (ACC)

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“…x e ,ũ e and x e denote the equilibrium points of (6). By analogy with [11] the conditions bellow are necessary for the existence of the desired equilibrium points:…”

Section: Global Stability For Biological Healthy Steady Statẽmentioning

confidence: 99%

“…Section II of this paper provides a detailed mathematical exposition of an existing leukemic and healthy stem cells coupled model presented in [11] to which we introduce two important modifications that make it more realistic and permit reaching our purpose in this work. The first modification concerns a biological observation that some cells coming from proliferation phase, may become progenitors before their complete differentiation, because of the inhibition of their self-renewal capacity [2], [3].…”

Section: Introduction Tmentioning

confidence: 99%

Dynamical Behavior of Biological Healthy Steady State in Leukemia Using a New Leukemic & Healthy Stem Cells Cohabitation Model with Distributed Delay

Zenati

Chakir

Tadjine

et al. 2019

2019 American Control Conference (ACC)

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Acute Myeloid Leukemia (AML) treatment protocol from clinical point of view, aims to maintain a normal amount of healthy cells and to eradicate all malignant cells. This particular objective is biologically qualified as a positive healthy situation. In this paper, we give sufficient and necessary conditions for the global stability of such a healthy situation. To this end, we first propose a new distributed delay model of AML. The latter is an improvement of an existing delayed coupled model describing the dynamics of hematopoesis stem cells in AML. We modify the PDEs equations and transform them into a set of distributed delay equations. The proposed model is more suitable for biological phenomena than constant delay models as the proliferation time differs from a cell type to another. Furthermore in the proposed model, we consider the sub-population of cells that have lost their capacity of self-renewal and became progenitors. In second, we derive sufficient and necessary conditions for the global stability of healthy steady state. For this, the positivity of the obtained model and sequences of functions theory are used to construct new Lyapunov function candidates. Finally, we conduct numerical simulations to show that the obtained results complete and generalize those published in the literature.

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Control in dormancy or eradication of cancer stem cells: Mathematical modeling and stability issues

Djema

Bonnet

Mazenc

et al. 2018

Journal of Theoretical Biology

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We propose a biologically based model endowed with rich dynamics. It incorporates a new parameter representing immunoediting processes, including the case where proliferation of cancer cells is locally kept under check by the immune cells. It also considers the overproliferation of cancer stem cells, modeled as a subpopulation of mutated cells that is constantly active in cell division. The analysis that we perform here reveals the conditions of existence of several steady states, including the case of cancer dormancy, in the coupled model of interest. Our study suggests that cancer dormancy may result from a plastic sensitivity of mutated cells to their shared environment, different from that - fixed - of healthy cells, and this is related to an action (or lack of action) of the immune system. Next, the stability analysis that we perform is essentially oriented towards the determination of sufficient conditions, depending on all the model parameters, that ensure either a regionally (i.e., locally) stable dormancy steady state or eradication of unhealthy cells. Finally, we discuss some biological interpretations, with regards to our findings, in light of current and emerging therapeutics. These final insights are particularly formulated in the paradigmatic case of hematopoiesis and acute leukemia, which is one of the best known malignancies for which it is always hard, in presence of a clinical and histological remission, to decide between cure and dormancy of a tumoral clone.

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Analysis of a model of dormancy in cancer as a state of coexistence between tumor and healthy stem cells

Cited by 5 publications

References 30 publications

Introducing Cell-Plasticity Mechanisms into a Class of Cell Population Dynamical Systems

Introducing Cell-Plasticity Mechanisms into a Class of Cell Population Dynamical Systems

Dynamical Behavior of Biological Healthy Steady State in Leukemia Using a New Leukemic & Healthy Stem Cells Cohabitation Model with Distributed Delay

Control in dormancy or eradication of cancer stem cells: Mathematical modeling and stability issues

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