Fractional Order Mathematical Model for the Cell Cycle of a Tumour Cell

Abstract Background Doxorubicin (DOX) is widely used in both human and veterinary oncology although the onset of multidrug resistance (MDR) in neoplastic cells often leads to chemotherapy failure. Better understanding of the cellular mechanisms that circumvent chemotherapy efficacy is paramount. The aim of this study was to investigate the response of two canine mammary tumour cell lines, CIPp from a primary tumour and CIPm, from its lymph node metastasis, to exposure to EC50(20h) DOX at 12, 24 and 48 h of treatment. We assessed the uptake and subcellular distribution of DOX, the expression and function of P-glycoprotein (P-gp) and Breast Cancer Resistance Protein (BCRP), two important MDR mediators. To better understand this phenomenon the effects of DOX on the cell cycle and Ki67 cell proliferation index and the expression of p53 and telomerase reverse transcriptase (TERT) were also evaluated by immunocytochemistry (ICC). Results Both cell lines were able to uptake DOX within the nucleus at 3 h treatment while at 48 h DOX was absent from the intracellular compartment (assessed by fluorescence microscope) in all the surviving cells. CIPm, originated from the metastatic tumour, were more efficient in extruding P-gp substrates. By ICC and qRT-PCR an overall increase in both P-gp and BCRP were observed at 48 h of EC50(20h) DOX treatment in both cell lines and were associated with a striking increase in the percentage of p53 and TERT expressing cells by ICC. The cell proliferation fraction was decreased at 48 h in both cell lines and cell cycle analysis showed a DOX-induced arrest in the S phase for CIPp, while CIPm had an increase in cellular death without arrest. Both cells lines were therefore composed by a fraction of cells sensible to DOX that underwent apoptosis/necrosis. Conclusions DOX administration results in interlinked modifications in the cellular population including a substantial effect on the cell cycle, in particular arrest in the S phase for CIPp and the selection of a subpopulation of neoplastic cells bearing MDR phenotype characterized by P-gp and BCRP expression, TERT activation, p53 accumulation and decrease in the proliferating fraction. Important information is given for understanding the dynamic and mechanisms of the onset of drug resistance in a neoplastic cell population.

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Optimum multi-drug regime for compartment model of tumour: cell-cycle-specific dynamics in the presence of resistance

Journal of Pharmacokinetics and Pharmacodynamics ◽

10.1007/s10928-021-09749-w ◽

2021 ◽

Author(s):

Bharti Panjwani ◽

Vijander Singh ◽

Asha Rani ◽

Vijay Mohan

Keyword(s):

Cell Cycle ◽

Tumour Cell ◽

Compartment Model

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Fractional order generalized thermoelastic response in a half space due to a periodically varying heat source

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-04-2017-0022 ◽

2018 ◽

Vol 14 (1) ◽

pp. 2-15 ◽

Cited By ~ 2

Author(s):

Jitesh Tripathi ◽

Shrikant Warbhe ◽

K.C. Deshmukh ◽

Jyoti Verma

Keyword(s):

Mathematical Model ◽

Heat Source ◽

Laplace Transform ◽

Half Space ◽

Fractional Order ◽

Order Parameter ◽

Order Theory ◽

Numerical Inversion ◽

Content Type ◽

Copper Material

Purpose The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues. Design/methodology/approach Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates. Findings This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter. Research limitations/implications Constructed purely on theoretical mathematical model by considering different parameters and the functions. Practical implications The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations. Originality/value In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

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Mathematical Model of Tumour Spheroid Experiments with Real-Time Cell Cycle Imaging

Bulletin of Mathematical Biology ◽

10.1007/s11538-021-00878-4 ◽

2021 ◽

Vol 83 (5) ◽

Author(s):

Wang Jin ◽

Loredana Spoerri ◽

Nikolas K. Haass ◽

Matthew J. Simpson

Keyword(s):

Mathematical Model ◽

Cell Cycle ◽

Real Time ◽

Tumour Spheroid

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The Contribution of p53 in the Dynamics of Cell Cycle Response to DNA Damage Interpreted by a Mathematical Model

Cell Cycle ◽

10.4161/cc.6.8.4103 ◽

2007 ◽

Vol 6 (8) ◽

pp. 943-950 ◽

Cited By ~ 13

Author(s):

Monica Lupi ◽

Giada Matera ◽

Claudia Natoli ◽

Valentina Colombo ◽

Paolo Ubezio

Keyword(s):

Mathematical Model ◽

Cell Cycle ◽

Dna Damage

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A Branching Process to Characterize the Dynamics of Stem Cell Differentiation

10.1101/016295 ◽

2015 ◽

Cited By ~ 1

Author(s):

david miguez

Keyword(s):

Mathematical Model ◽

Cell Cycle ◽

Stem Cell ◽

Cycle Length ◽

Branching Process ◽

Stem Cell Differentiation ◽

Stem Cell Population ◽

Mathematical Framework ◽

Average Cell ◽

Cell Cycle Length

The understanding of the regulatory processes that orchestrate stem cell maintenance is a cornerstone in developmental biology. Here, we present a mathematical model based on a branching process formalism that predicts average rates of proliferative and differentiative divisions in a given stem cell population. In the context of vertebrate spinal neurogenesis, the model predicts complex non-monotonic variations in the rates of pp, pd and dd modes of division as well as in cell cycle length, in agreement with experimental results. Moreover, the model shows that the differentiation probability follows a binomial distribution, allowing us to develop equations to predict the rates of each mode of division. A phenomenological simulation of the developing spinal cord informed with the average cell cycle length and division rates predicted by the mathematical model reproduces the correct dynamics of proliferation and differentiation in terms of average numbers of progenitors and differentiated cells. Overall, the present mathematical framework represents a powerful tool to unveil the changes in the rate and mode of division of a given stem cell pool by simply quantifying numbers of cells at different times.

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Fractional-Order Modelling and Optimal Control of Cholera Transmission

Fractal and Fractional ◽

10.3390/fractalfract5040261 ◽

2021 ◽

Vol 5 (4) ◽

pp. 261

Author(s):

Silvério Rosa ◽

Delfim F. M. Torres

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Sensitivity Analysis ◽

Fractional Order ◽

Control Measures ◽

Time Interval ◽

Variable Order ◽

Effectiveness Analysis ◽

The Cost ◽

Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

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