A Mathematical Model of the Cell Cycle and Its Circadian Control

2007 ◽  
pp. 239-251 ◽  
Author(s):  
Jean Clairambault ◽  
Philippe Michel ◽  
Benoît Perthame
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Circadian Control

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

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

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

Cell Cycle ◽  
2007 ◽  
Vol 6 (8) ◽  
pp. 943-950 ◽  
Author(s):  
Monica Lupi ◽  
Giada Matera ◽  
Claudia Natoli ◽  
Valentina Colombo ◽  
Paolo Ubezio
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Dna Damage

scholarly journals A Branching Process to Characterize the Dynamics of Stem Cell Differentiation

2015 ◽  
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.

Bifurcation Analysis of a Model Accounting for the 14-3-3s Signalling Compartmentalisation

2012 ◽  
pp. 61-70
Author(s):  
S. Nikolov ◽  
J. Vera ◽  
O. Wolkenhauer
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Phase Portrait ◽  
Bifurcation Analysis ◽  
Subcellular Localisation ◽  
Loss Of Stability ◽  
Cycle Arrest ◽  
Reversible Loss ◽  
Analytical Tools

Bifurcation theory studies the qualitative changes in the phase portrait when we vary the parameters of the system. In this book chapter we adapt and extend a mathematical model accounting for the subcellular localisation of 14-3-3s, a protein involved in cell cycle arrest and the regulation of apoptosis. The model is analysed with analytical tools coming from Lyapunov-Andronov theory, and our analytical calculations predict that soft (reversible) loss of stability takes place.

Abstract 3411: Mathematical model of the cell cycle to determine mechanism of action and optimize dosing schedule.

2013 ◽  
Author(s):  
Jerome Mettetal ◽  
Derek Blair ◽  
Esha Gangoli ◽  
Patrick Vincent ◽  
Jeff Ecsedy ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Mechanism Of Action ◽  
Dosing Schedule ◽  
Determine Mechanism

scholarly journals Chemotherapeutic Effects on Hematopoiesis: A Mathematical Model

1998 ◽  
Vol 1 (3) ◽  
pp. 209-221 ◽  
Author(s):  
John Carl Panetta
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Cell Cycle ◽  
Growth Factors ◽  
Blood Cell ◽  
Blood Cells ◽  
Blood Stream ◽  
Hematopoietic Growth Factors ◽  
Cell Production ◽  
Delay Differential

Blood cell production is one of the major limiting effects of cell-cycle-specific chemotherapy. By studying the effects of the drugs on a mathematical model of hematopoiesis, a better understanding of how to prevent over-reduction of circulating blood may be investigated.In this model we will use a delay-differential equation developed by Mackey and Glass (1977) to show acceptable chemotherapeutic deses (i.e. survival of the circulating blood cells) as a function of: the period which the drugs are administered; the strength of the dose; and the delay from initiation of blood cell production to its release into the blood stream. We then make qualitative comparisons to know effects of cell-cycle-specific chemotherapy on circulating blood cell elements. Finally, we also consider how the effects of hematopoietic growth factors alter the outcome of the therapy.

scholarly journals A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity

2015 ◽  
Vol 12 (108) ◽  
pp. 20150276 ◽  
Author(s):  
María Fuentes-Garí ◽  
Ruth Misener ◽  
David García-Munzer ◽  
Eirini Velliou ◽  
Michael C. Georgiadis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Cell Lines ◽  
Phase Distribution ◽  
Initial Conditions ◽  
Cellular Heterogeneity ◽  
Cycle Phase ◽  
Biologically Relevant ◽  
Future Outcomes ◽  
Unique Cell

Acute myeloid leukaemia is characterized by marked inter- and intra-patient heterogeneity, the identification of which is critical for the design of personalized treatments. Heterogeneity of leukaemic cells is determined by mutations which ultimately affect the cell cycle. We have developed and validated a biologically relevant, mathematical model of the cell cycle based on unique cell-cycle signatures, defined by duration of cell-cycle phases and cyclin profiles as determined by flow cytometry, for three leukaemia cell lines. The model was discretized for the different phases in their respective progress variables (cyclins and DNA), resulting in a set of time-dependent ordinary differential equations. Cell-cycle phase distribution and cyclin concentration profiles were validated against population chase experiments. Heterogeneity was simulated in culture by combining the three cell lines in a blinded experimental set-up. Based on individual kinetics, the model was capable of identifying and quantifying cellular heterogeneity. When supplying the initial conditions only, the model predicted future cell population dynamics and estimated the previous heterogeneous composition of cells. Identification of heterogeneous leukaemia clones at diagnosis and post-treatment using such a mathematical platform has the potential to predict multiple future outcomes in response to induction and consolidation chemotherapy as well as relapse kinetics.

A mathematical model of the cell cycle of a hybridoma cell line

2001 ◽  
Vol 7 (1) ◽  
pp. 49-68 ◽  
Author(s):  
D.B.F Faraday ◽  
P Hayter ◽  
N.F Kirkby
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Cell Line
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