title: Regulatory effects on the population dynamics and wave propagation in a cell lineage model.
abstract: We consider the interplay of cell proliferation, cell differentiation (and de-differentiation), cell movement, and the effect of feedback regulations on the population and propagation dynamics of different cell types in a cell lineage model. Cells are assumed to secrete and respond to negative feedback molecules which act as a control on the cell lineage. The cell densities are described by coupled reaction-diffusion partial differential equations, and the propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. In particular, wavefront propagation speeds are obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effects of the feedback regulations on different stages in the cell lineage. It is found that when the progenitor cell is negatively regulated, the populations of the cell lineage are strongly down-regulated with the steady growth rate of the progenitor cell being driven to zero beyond a critical regulatory strength. An analytic expression for the critical regulation strength in terms of the model parameters is derived and verified by numerical solutions. On the other hand, if the inhibition is acting on the differentiated cells, the change in the population dynamics and wave propagation speed is small. In addition, it is found that only the propagating speed of the progenitor cells is affected by the regulation when the diffusion of the differentiated cells is large. In the presence of de-differentiation, the effect on down-regulating the progenitor population is weakened and there is no effect on the propagation speed due to regulation, suggesting that the effect of regulatory control is diminished by de-differentiation pathways.
authors.affiliation: National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China; School of Science, Nanjing University of Science and Technology, Nanjing 210094, China. Electronic address: wangmx@njust.edu.cn.
authors.forename: Mao-Xiang
authors.initials: MX
authors.lastname: Wang
authors.affiliation: National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China; Center for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou 215006, China.
authors.forename: Yu-Qiang
authors.initials: YQ
authors.lastname: Ma
authors.affiliation: Department of Physics, Graduate Institute of Biophysics, National Central University, Chungli 320, Taiwan, ROC. Electronic address: pylai@phy.ncu.edu.tw.
authors.forename: Pik-Yin
authors.initials: PY
authors.lastname: Lai
mesh_terms: D000818:Animals; D054337:Cell Dedifferentiation; D019070:Cell Lineage; D049109:Cell Proliferation; D025461:Feedback, Physiological; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D013234:Stem Cells / Q000166:cytology
keywords: Cell model; Differentiation; Population dynamics; Proliferation; Regulation; Wave propagation