(36c) Modelling of Cell Division and Proliferation Control in Eukaryotic Cell Populations

Over the past few decades, research in the biological sciences has tremendously increased our understanding of bacterial and mammalian cell populations. Simultaneously, considerable research has been undertaken into the development of mathematical models of important phenomena such as cell metabolism, cell cycle progression and signal transduction through various pathways. The enormous understanding of these processes can bear enhanced fruition by the application of systems engineering. Thus, there is a need for the development of detailed models for such processes [1]. Yet, there is a dearth of detailed mathematical models that integrate the information available today in a comprehensive manner.

In an attempt to redress this situation, a detailed cell population balance model with a comprehensive accounting of the underlying mechanisms has been presented in this paper. Cell metabolism is accounted for in this multi-dimensional framework by the incorporation of a six-parameter model of yeast metabolism [2]. The mitogen activated protein kinase (MAPK) [3] and transforming growth factor-beta (TGF-beta) [4] signalling pathways, responsible for cell progression, division and death, are modelled using a deterministic approach. Simple division and death kernels are adopted for demonstration purposes. Cell differentiation and apoptosis are also taken into consideration in the formulation of the model.

An efficient and accurate solution strategy [5] previously applied to one- and higher-dimensional population balance models has been adopted to solve the formulated population balance model. When only growth is considered, the model predicts the synchronisation of the cell population, a phenomenon seen previously [2]. This asymptotic behaviour is unaffected by the inclusion of MAPK signalling into the model. However, in the absence of signal transduction via the MAPK pathway, cell growth and division is suppressed, as has been observed previously [3].

In the absence of TGF-beta signalling, the model predicts a gradual increase in the fraction of differentiated cells. This gradual accumulation of differentiated cells is due to the assumption that these cells suffer apoptosis upon undergoing cell division. The inclusion of the TGF-beta signalling pathway results in a significant rise in the number of differentiated cells due to the suppression of cell division in these cells by signalling through this pathway, a phenomenon again observed previously [4].

Based on these results, it can be concluded that the model formulated in this study is qualitatively accurate and amenable to preliminary analysis studies. As the various phenomena in this model are accounted for using a relatively simple approach, this model thus represents a first step in the development of more detailed models of these cell populations. Such detailed models will have wide-ranging applications from bioreactor design, optimisation and control, to the study of diseases and their cures.

[1] Henson, M.A. 2003. Dynamic modelling of microbial cell populations. Current Opinion in Biotechnology 14:460-467.

[2] Henson, M. A., Muller, D., Reiss, M., 2002. Cell population modelling of yeast glycolytic oscillations. Biochemical Journal 368, 433-446.

[3] Downward, J., 2003. Targeting Ras signalling pathways in cancer therapy. Nature Reviews - Cancer 3, 11-22.

[4] Shi, Y., Massague, J., 2003. Mechanisms of TGF-beta signalling from cell membrane to the nucleus. Cell 113, 685-700.

[5] Pinto, M. A., Immanuel, C. D., Doyle III, F. J., 2006. A Feasible Solution Technique for Higher-Dimensional Population Balance Models. Computers and Chemical Engineering. In press.