An Îto stochastic differential equations model for the dynamics of the MCF-7 breast cancer cell line treated by radiotherapy

Oroji, Amin; Omar, Mohd; Yarahmadian, Shantia

doi:10.1016/j.jtbi.2016.07.035

Cited by 19 publications

(10 citation statements)

References 27 publications

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“…In recent years, radio-and chemoresistant breast cancer cells or breast CSCs have been the therapeutic focus in numerous studies. [28][29][30][31][32][33][34] The TMZ, an alkylating agent, has been commonly used in clinical chemotherapy for treating malignant glioma. 35 However, low response to TMZ has been observed in cancers such as B cell lymphoma.…”

Section: Discussionmentioning

confidence: 99%

BMI-1 Promotes Self-Renewal of Radio- and Temozolomide (TMZ)-Resistant Breast Cancer Cells

et al. 2017

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Breast cancer is a hormone-dependent malignancy and is the most prevalent cause of cancer-related mortality among females. Radiation therapy and chemotherapy are common treatments of breast cancer. However, tumor relapse and metastasis following therapy are major clinical challenges. The importance of B-lymphoma Moloney murine leukemia virus insertion region-1 (BMI-1) was implicated in cell proliferation, stem cell maintenance, and tumor initiation. We established radio- and temozolomide (TMZ)-resistant (IRC-R) MCF-7 and MDA-MB-231 cell lines to investigate the mechanism involved in therapeutic resistance. Cell proliferation and sphere number were dramatically elevated, and BMI-1 was remarkably upregulated, in IRC-R cells compared to parental cells. Silencing BMI-1 by RNA interference only affected the cell proliferation of IRC-R but not parental cells, suggesting the critical role of BMI-1 in radio- and TMZ resistance. We used a xenograft mice model to elucidate that BMI-1 was necessary in tumor development by assessing tumor volume and Ki67 expression. We found that Hedgehog (Hhg) signaling exerted synergized functions together with BMI-1, implicating the importance of BMI-1 in Hhg signaling. Downregulation of BMI-1 could be an effective strategy to suppress tumor growth, which supports the potential clinical use of targeting BMI-1 in breast cancer treatment.

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Section: Discussionmentioning

confidence: 99%

BMI-1 Promotes Self-Renewal of Radio- and Temozolomide (TMZ)-Resistant Breast Cancer Cells

et al. 2017

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“…Remark 4 This result is new. Notice that λ < 0, 2λ + σ 2 < 0, and 2λ + ε 2 < 0 are necessary conditions for the MS-stability of (15). In [2], the particular test system (15) with b = 0 was discussed and the condition 2λ+σ 2 +ε 2 < 0 was shown.…”

Section: Theoremmentioning

confidence: 99%

A survey of mean-square destabilization of multidimensional linear stochastic differential systems with non-normal drift

Senosiaín

2023

Numer Algor

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Mean-square stability analysis of linear stochastic differential systems obtained perturbing ordinary systems by linear terms driven by independent Wiener processes is investigated. The so obtained stochastic regions are contractions of the asymptotic stability domain of the linear ordinary system. In this work, the mean-square stability regions exact shape is provided by means of necessary and sufficient conditions in terms of the eigenvalues of the drift and the intensities of the noises. Special attention is paid to how different structures of the perturbation affect the mean-square stability of systems with non-normal drifts. In each case, the obtained explicit stability condition reveals the role played by the parameter that controls the non-normality.

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“…The explicit drift and diffusion terms are derived from step-by-step modeling and not by simply adding some multiplicative noise to an ODE system describing in a more or less heuristic way the evolution of the tumor cell subpopulations. For instance, the form of the (negative) diffusion coefficients for the model in [48] is largely arbitrary and needs justification. The same applies to the simple multiplicative form of (positive) diffusions in the models from [51,64].…”

Section: Parameter Description Valuementioning

confidence: 99%

SDE-driven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness

Kroos¹,

Stinner²,

Surulescu³

et al. 2019

Discrete &Amp; Continuous Dynamical Systems - B

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We deduce cell population models describing the evolution of a tumor (possibly interacting with its environment of healthy cells) with the aid of differential equations. Thereby, different subpopulations of cancer cells allow accounting for the tumor heterogeneity. In our settings these include cancer stem cells known to be less sensitive to treatment and differentiated cancer cells having a higher sensitivity towards chemo-and radiotherapy. Our approach relies on stochastic differential equations in order to account for randomness in the system, arising e.g., due to the therapy-induced decreasing number of clonogens, which renders a pure deterministic model arguable. The equations are deduced relying on transition probabilities characterizing innovations of the two cancer cell subpopulations, and similarly extended to also account for the evolution of normal tissue. Several therapy approaches are introduced and compared by way of tumor control probability (TCP) and uncomplicated tumor control probability (UTCP). A PDE approach allows to assess the evolution of tumor and normal tissue with respect to time and to cell population densities which can vary continuously in a given set of states. Analytical approximations of solutions to the obtained PDE system are provided as well.

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An Îto stochastic differential equations model for the dynamics of the MCF-7 breast cancer cell line treated by radiotherapy

Cited by 19 publications

References 27 publications

BMI-1 Promotes Self-Renewal of Radio- and Temozolomide (TMZ)-Resistant Breast Cancer Cells

BMI-1 Promotes Self-Renewal of Radio- and Temozolomide (TMZ)-Resistant Breast Cancer Cells

A survey of mean-square destabilization of multidimensional linear stochastic differential systems with non-normal drift

SDE-driven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness

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