Tutorials in mathematical biosciences III. Cell cycle, prolifereation, and cancer.
type: Item
instance of: scholarly article
title: Tutorials in mathematical biosciences III. Cell cycle, prolifereation, and cancer.
zbMATH Open document ID: 1122.92030
DOI: 10.1007/11561606
published in: Lecture Notes in Mathematics
publication date: 2006-03-31T00:00:00Z
review text: The lectures in this volume are devoted to the cell division cycle, tumor growth and cancer chemotherapy. The first chapter discusses the Novak-Tyson model of the cell division cycle. The cell mass \(M\) is governed by \(dM/dt=\mu M\). The mitosis promoting factor \([MPF]\) is given by \([MPF]=[Cdc13_T]^{-1}(([Cdc13_T]-[preMPF])([Cdc13_T]-[Trimer]))\). The mass is coupled with \([Cdc13_T]\) (a B-type cyclin) given by \[ d[Cdc13_T]/dt=k_1M-k_2^{\prime}[Cdc13_T]-k_2^{\prime\prime} [Ste9][Cdc13_T]-k_2^{\prime\prime\prime}[Slp1][Cdc13_T]. \] The \([preMPF]\) is the total of the tyrosine-phosphorylated Cdc13/Cdc2 with or without Rum1 (a CDK-cyclin dependent kinase-inhibitor): \[ \begin{multlined} d[preMPF]/dt=k_{wee}([Cdc13_T]-[preMPF])-k_{25}[preMPF]+\\-k_2^{\prime} [preMPF] -k_2^{\prime\prime}[Ste9][preMPF]-k_2^{\prime\prime\prime}[Slp1][preMPF].\end{multlined} \] The antagonism between Cdc13/Cdc2 and APC (anaphase promoting complex) is described by the auxiliary factors Ste9 and Slp1 (its concentration is \([Slp1_T]\)): \[ d[Slp1_T]/dt=k_5^{\prime}+k_5^{\prime\prime}[MPF]^4/(J_5^4+[MPF]^4)-k_6[Slp1_T], \] \[ \begin{multlined} d[Slp1]/dt=k_7[IEP]([Slp1_T]-[Slp1])/(J_7+([Slp1_T]-[Slp1]))+\\ -k_8[Slp1]/(J_8+[Slp1])-k_6[Slp1], \end{multlined} \] \[ d[IEP]/dt=k_9[MPF](1-[IEP])/(J_9+(1-[IEP]))-k_{10}[IEP]/(J_{10} +[IEP]), \] \[ \begin{multlined} d[Ste9]/dt=(k_3^{\prime}+k_3^{\prime\prime}[Slp1])(1-[Ste9])/ (J_3+(1-[Ste9]))+\\-((k_4^{\prime}[SK]+k_4[MPF])[Ste9])/(J_4+[Ste9]). \end{multlined} \] The Rum1 concentration is given by \[ d[Rum1_T]/dt=k_{11}-(k_{12}+k_{12}^{\prime}[SK]) +k_{12}^{\prime\prime} [MPF])[Rum1_T]. \] The Cdc13/Cdc2 inhibits the SK (starter kinase) activity: \[ d[SK]/dt=k_{13}[TF]-k_{14}[SK], \] where \([TF]\) is the transcription factor. Several auxiliary equations, given by means of the Goldbeter-Koshland function, are also needed. The phase-plane and bifurcation analysis of the system is performed with the aim of getting some useful information for a s…
reviewed by: Octavian Mustafa
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 92C37
Mathematics Subject Classification ID: 92C45
Mathematics Subject Classification ID: 92-02
Mathematics Subject Classification ID: 92C40
zbMATH DE Number: 5016782
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/11561606
OpenAlex ID: W4244170134
description: scientific article; zbMATH DE number 5016782