(141h) Reduction Techniques and Hybrid Modelling Approaches for Cell Population Heterogeneity

Latest research on biological systems is steadily shifting from isolated single cells to entire cell populations. The latter are inherently heterogeneous, in the sense that the properties of the single cells that make up the population are typically not the same. To model such populations, three approaches that have been widely used are (i) the cell population balance, (ii) ensemble and (iii) continuum modelling frameworks. Each of these approaches focuses on different aspects of the processes of growth, division and intracellular reaction occurrence and can provide information at different levels of detail, with the corresponding computational expense. Continuum models neglect heterogeneity by assuming lumped biomasses, capture the dynamics of bulk intracellular concentrations and are easy to simulate. Ensemble models account for heterogeneity due to different initial conditions or kinetic constants, and are more computationally expensive. Finally, the cell population balance (CPB) approach captures cell growth, intracellular reactions, division and the partitioning of the intracellular contents in detail, but can quickly become intractable, as the number of biochemical species taken into consideration increases.

In this work, we show how one can reduce the CPB to hybrid modelling approaches that simulate cell population heterogeneity at a much lower computational expense. Under certain assumptions, these hybrid models are exact alternatives of the cell population balance; no approximation is involved.¹ We further demonstrate the use of these hybrid models to efficiently simulate cell population heterogeneity in a genetic network of a single gene with feedback.² Starting from a 4-species model we use singular perturbation analysis to derive a single equation for the intracellular protein concentration. We subsequently incorporate this equation to a hybrid model consisting of a CPB for the cell volume, and a continuum equation for the protein concentration. We finally compare the results obtained with the hybrid model with those of the full CPB, demonstrating the accuracy and computational efficiency of the hybrid methodology.

References

1. Stamatakis, M., Cell population balance, ensemble and continuum modeling frameworks: Conditional equivalence and hybrid approaches. Chemical Engineering Science, 2010. 65(2): p. 1008-1015.
2. Stamatakis, M., Cell Population Balance and Hybrid Modeling of Population Dynamics for a Single Gene with Feedback. Computers & Chemical Engineering, 2013. 53: p. 25-34.