The contribution of age structure to cell population responses to targeted therapeutics.

Cells grown in culture act as a model system for analyzing the effects of anticancer compounds, which may affect cell behavior in a cell cycle position-dependent manner. Cell synchronization techniques have been generally employed to minimize the variation in cell cycle position. However, synchronization techniques are cumbersome and imprecise and the agents used to synchronize the cells potentially have other unknown effects on the cells. An alternative approach is to determine the age structure in the population and account for the cell cycle positional effects post hoc. Here we provide a formalism to use quantifiable lifespans from live cell microscopy experiments to parameterize an age-structured model of cell population response.

[1]  G. Webb,et al.  Necessary and Sufficient Conditions for Asynchronous Exponential Growth in Age Structured Cell Populations with Quiescence , 1997 .

[2]  William Rundell.  Determining the Death Rate for an Age-Structured Population from Census Data , 1993, SIAM J. Appl. Math..

[3]  Daniel G. Mallet,et al.  A cellular automata model of tumorimmune system interactions , 2006 .

[4]  Determining a coefficient in a first-order hyperbolic equation , 1991 .

[5]  P. Maini,et al.  A cellular automaton model for tumour growth in inhomogeneous environment. , 2003, Journal of theoretical biology.

[6]  Delphine Picart,et al.  An innovative multistage, physiologically structured, population model to understand the European grapevine moth dynamics , 2011 .

[7]  Stéphane Gaubert,et al.  Synchronisation and control of proliferation in cycling cell population models with age structure , 2014, Math. Comput. Simul..

[8]  Numerical integration of nonlinear size-structured population equations , 2000 .

[9]  G. Webb.  Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

[10]  B. Perthame.  Transport Equations in Biology , 2006 .

[11]  Bedr'Eddine Ainseba,et al.  Parameter identification in multistage population dynamics model , 2011 .

[12]  R. Nagel,et al.  One-parameter semigroups for linear evolution equations , 1999 .

[13]  G. Webb,et al.  A nonlinear structured population model of tumor growth with quiescence , 1990, Journal of mathematical biology.

[14]  Tanya Kostova,et al.  An explicit third‐order numerical method for size‐structured population equations , 2003 .

[15]  Jocelyne Bédard,et al.  New-York, 1985 , 2005 .

[16]  Jean Clairambault,et al.  Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle , 2008, Math. Comput. Model..

[17]  Alissa M. Weaver,et al.  Mathematical modeling of cancer: the future of prognosis and treatment. , 2005, Clinica chimica acta; international journal of clinical chemistry.

[18]  Glenn F Webb,et al.  A mathematical model separates quantitatively the cytostatic and cytotoxic effects of a HER2 tyrosine kinase inhibitor , 2007, Theoretical Biology and Medical Modelling.

[19]  Laurent Pujo-Menjouet,et al.  Analysis of cell kinetics using a cell division marker: mathematical modeling of experimental data. , 2003, Biophysical journal.

[20]  Pierre Gabriel,et al.  The shape of the polymerization rate in the prion equation , 2010, Math. Comput. Model..

[21]  Jean Clairambault,et al.  An age-and-cyclin-structured cell population model for healthy and tumoral tissues , 2008, Journal of mathematical biology.

[22]  W. Rundell,et al.  Determining the initial age distribution for an age structured population. , 1991, Mathematical population studies.

[23]  Karyn L. Sutton,et al.  A new model for the estimation of cell proliferation dynamics using CFSE data. , 2011, Journal of immunological methods.

[24]  Azmy S. Ackleh,et al.  Parameter identification in size-structured population models with nonlinear individual rates , 1999 .

[25]  L. M. Tine,et al.  HIGH-ORDER WENO SCHEME FOR POLYMERIZATION-TYPE EQUATIONS ∗ , 2010, 1002.2174.

[26]  Bedr'Eddine Ainseba,et al.  CML dynamics: Optimal control of age-structured stem cell population , 2011, Math. Comput. Simul..

[27]  V. Quaranta,et al.  Invasion emerges from cancer cell adaptation to competitive microenvironments: quantitative predictions from multiscale mathematical models. , 2008, Seminars in Cancer Biology.

[28]  Odo Diekmann,et al.  On the stability of the cell size distribution , 1986 .

[29]  Joan Saldaña,et al.  A model of physiologically structured population dynamics with a nonlinear individual growth rate , 1995 .

[30]  Jorge P. Zubelli,et al.  Numerical solution of an inverse problem in size-structured population dynamics , 2008, 0810.1381.

[31]  E. Davies,et al.  One-parameter semigroups , 1980 .

[32]  L. D. de Pillis,et al.  A cellular automata model of tumor-immune system interactions. , 2006, Journal of theoretical biology.

[33]  Shyamal D Peddada,et al.  A random-periods model for expression of cell-cycle genes. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Gibin G Powathil,et al.  Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model. , 2012, Journal of theoretical biology.

[35]  S. Levin.  Lectu re Notes in Biomathematics , 1983 .

[36]  E. T. Gawlinski,et al.  A Cellular Automaton Model of Early Tumor Growth and Invasion: The Effects of Native Tissue Vascularity and Increased Anaerobic Tumor Metabolism , 2001 .

[37]  V. Quaranta,et al.  Fractional Proliferation: A method to deconvolve cell population dynamics from single-cell data , 2012, Nature Methods.

[38]  B. Perthame,et al.  General relative entropy inequality: an illustration on growth models , 2005 .

[39]  E. F. Codd,et al.  Cellular automata , 1968 .

[40]  Ignacio Ramis-Conde,et al.  Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach. , 2008, Biophysical journal.

[41]  S. B. Atienza-Samols,et al.  With Contributions by , 1978 .

[42]  John E Banks,et al.  Estimation of Dynamic Rate Parameters in Insect Populations Undergoing Sublethal Exposure to Pesticides , 2007, Bulletin of mathematical biology.

[43]  A. Golubev,et al.  Exponentially modified Gaussian (EMG) relevance to distributions related to cell proliferation and differentiation. , 2010, Journal of theoretical biology.

[44]  Mats Gyllenberg,et al.  The inverse problem of linear age-structured population dynamics , 2002 .

[45]  Azmy S. Ackleh,et al.  An implicit finite difference scheme for the nonlinear size-structured population model , 1997 .

[46]  Jim Douglas,et al.  Numerical methods for a model of population dynamics , 1987 .

[47]  Editors , 1986, Brain Research Bulletin.

[48]  G. Webb.  An operator-theoretic formulation of asynchronous exponential growth , 1987 .

[49]  Oscar Angulo,et al.  Numerical integration of fully nonlinear size-structured population models , 2004 .

[50]  Bedr'Eddine Ainseba,et al.  Optimal control problem on insect pest populations , 2011, Appl. Math. Lett..

[51]  Alan S Perelson,et al.  Modeling T Cell Proliferation and Death in Vitro Based on Labeling Data: Generalizations of the Smith–Martin Cell Cycle Model , 2008, Bulletin of mathematical biology.

[52]  B. Perthame,et al.  On the inverse problem for a size-structured population model , 2006, math/0611052.

[53]  On the Calibration of a Size-Structured Population Model from Experimental Data , 2009, Acta biotheoretica.

[54]  P. Hodgkin,et al.  Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age? , 2005, Journal of The Royal Society Interface.

[55]  W. Rundell.  Determining the birth function for an age structured population. , 1989, Mathematical population studies.

[56]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[57]  Philip K. Maini,et al.  The Use of Hybrid Cellular Automaton Models for Improving Cancer Therapy , 2004, ACRI.

[58]  William Rundell,et al.  A Regularization Scheme for an Inverse Problem in Age-Structured Populations , 1994 .

[59]  A. Anderson,et al.  A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype. , 2008, Journal of theoretical biology.

[60]  O. Diekmann,et al.  The Dynamics of Physiologically Structured Populations , 1986 .

[61]  G. Webb,et al.  Age-size structure in populations with quiescence , 1987 .