(199f) Modeling of Fluorescent Protein-Labeled Cell Populations to Analyze Transcriptional and Division Effects On Fluorescent Intensity Distributions

Fluorescent proteins have been widely used as markers of gene expression and transcriptional regulation due to several reasons [1], such as that their plasmid can easily be integrated into the DNA of the cells, they do not have a toxic effect on cell growth and they can also be conveniently detected by illuminating the sample with suitable light. Thus, the fluorescence obtained in fluorescent protein based reporter systems can be used as an indicator of transcription and translation. However, there are phenotypic variations in cell populations as the observed fluorescence is affected by noise in gene expression [2] as well as physiological factors such as unequal partitioning of cellular material resulting from cell division [3]. Since most of the experimental data of fluorescence is obtained from techniques such as flow cytometry or fluorescence microscopy that utilize cell populations, using single cell models to estimate cell physiological parameters or transcriptional dynamics may lead to erroneous conclusions [4]. Furthermore, it is non-trivial to track individual cells in a population during the course of an experiment to analyze how fluorescence in a single cell evolves over time [5]. In this regard, we have developed a multiscale population balance model (PBM) that describes the dynamics of distributions of fluorescence intensity in a cell population labeled with a fluorescent protein. 

The developed PBM of a fluorescent protein expressing cell population is represented by an integro-partial differential equation (PDE) with time and fluorescence intensity as independent variables. It models the dynamic fluorescence intensity distribution of cells by taking into account processes such as cell birth and unequal partitioning due to cell division as well as the increase in fluorescence due to gene expression. The initial-boundary value problem of this PDE model has been solved using an implicit finite difference scheme which is second order accurate in time and fluorescent intensity space. The integral term in the PBM is approximated using trapezoidal rule. This work also includes using optimization techniques to estimate unknown physiological parameters such as the division rate, rate of fluorescence increase due to gene expression, cell partitioning distribution parameter, etc. in the model. For this purpose, the experimental data are obtained from a previously developed GFP (green fluorescent protein) reporter system for STAT3 [6]. The cells are stimulated with IL-6 to start the expression of GFP and timely samples are taken. The samples are fixed with paraformaldehyde and then analyzed using flow cytometry to obtain fluorescence intensity distributions. These data are then used for estimating the unknown parameters in the population balance model.      

Using the presented technique, it is possible to quantify the effects of gene expression and cell division on the observed fluorescence intensity distributions and analyze the time scales at which division becomes dominant in mammalian cells. The experimental data are also obtained for cell populations at different initial densities and different IL-6 concentrations to study their effect on division and death rate of cells and on GFP expression. Summarizing, this study integrates computational and experimental techniques to characterize certain aspects of fluorescent protein expressing cell populations and estimates unknown physiological population level parameters.

References

[1] M. Chalfie, Y. Tu, G. Euskirchen, W. W. Ward, and D. C. Prasher, "Green fluorescent protein as a marker for gene expression," Science, vol. 263, pp. 802-805, 1994.

[2] P. S. Swain, M. B. Elowitz, and E. D. Siggia, "Intrinsic and extrinsic contributions to stochasticity in gene expression " PNAS, vol. 99, pp. 12795-12800, 2002.

[3] M. A. Hjortsø, Population balances in biomedical engineering: Segregation through the distribution of cell states: McGraw-Hill, 2006.

[4] J. Hasenauer, S. Waldherr, M. Doszczak, N. Radde, P. Scheurich, and F. Allgöwer, "Identification of models of heterogeneous cell populations from population snapshot data," BMC Bioinformatics, vol. 12, pp. 1-15, 2011.

[5] Z. Huang, Y. Chu, and J. Hahn, "Computing transcription factor distribution profiles from green fluorescent protein reporter data," Chemical Engineering Science, vol. 68, pp. 340-354, 2012.

[6] C. Moya, Z. Huang, P. Cheng, A. Jayaraman, and J. Hahn, "Investigation of Il-6 and Il-10 signalling via mathematical modelling," IET Systems Biology, vol. 5, pp. 15-26, 2009.