A novel population balance model to investigate the kinetics of in vitro cell proliferation: Part I. model development

Abstract

In biotechnology and biomedicine reliable models of cell proliferation kinetics need to capture the relevant phenomena taking place during the mitotic cycle. To this aim, a novel mathematical model helpful to investigate the intrinsic kinetics of in vitro culture of adherent cells up to confluence is proposed in this work. Specifically, the attention is focused on the simulation of proliferation (increase of cell number) and maturation (increase of cell size and DNA content) till contact inhibition eventually takes place inside a Petri dish. Accordingly, the proposed model is based on a population balance (PB) approach that allows one to quantitatively describe cell cycle progression through the different phases the cells of the entire population experienced during their own life. In particular, the proposed model has been developed as a 2D, multi-staged, and unstructured PB, by considering a different sub-population of cells for any single phase of the cell cycle. These sub-populations are discriminated through cellular volume and DNA content, that both increase during the mitotic cycle. The adopted mathematical expressions of the transition rates between two subsequent phases and the temporal increase of cell volume and DNA content are thoroughly analyzed and discussed with respect to those ones available in the literature. Specifically, the corresponding uncertainties and pitfalls are pointed out, by also taking into account the difficulties and the limitations involved in the quantitative measurements currently practicable for these biological systems. A novel mathematical expression for contact inhibition in line with the PB model developed is also formulated, along with a proper comparison between modeled and measurable DNA distributions. The strategy for a reliable, independent tuning of the adjustable parameters involved in the proposed model along with its numerical solution is outlined in Part II of this work, where it is also shown how it can be profitably used to gain a deeper insight into the phenomena involved during cell cultivation under microgravity conditions.

Cell population balance and hybrid modeling of population dynamics for a single gene with feedback

“…More recently Fredrickson and Mantzaris (2002) and Fredrickson (2003) expanded the CPB formulation to account for the transitions between the different phases of the cell cycle. The CPB framework has been successfully used to model cell cycle dynamics (Faraday and Kirkby, 1992;Liu et al, 2007), capture cell population heterogeneity (Mantzaris, 2005b;Mantzaris, 2005a), predict and control the dynamics of fermentation processes in batch or continuous bioreactors (Godin et al, 1999;Mantzaris et al, 1999;Zhu et al, 2000;Mantzaris and Daoutidis, 2004;Sharifian and Fanaei, 2009), study aggregation dynamics in suspension cultures (Kolewe et al, 2012), as well as investigate in vitro cell proliferation patterns (Fadda et al, 2012b;Fadda et al, 2012a). The deterministic CPB framework just discussed does not include stochasticity in intracellular reaction occurrence.…”

A Framework for the Development of Integrated and Computationally Feasible Models of Large-Scale Mammalian Cell Bioreactors

“…Assuming spatial homogeneity and neglecting the effects of physical environmental parameters have been the basis of most culture models [19][20][21][22][23][24][25][26][27][28][29]. This reduces the problem of simulating relevant portions of cellular activities that control the production of a product of interest.…”

A novel quantitative model of cell cycle progression based on cyclin-dependent kinases activity and population balances

“…Models based on population balance (PB) are recognized to represent a very important theoretical tool for describing the proliferation of cells, as widely demonstrated by the growing literature addressing this topic (Liou et al, 1997;Fredrickson and Mantzaris, 2002;Pisu et al, 2003Pisu et al, , 2004Pisu et al, , 2006Pisu et al, , 2007Pisu et al, , 2008Fadda et al, 2012a,b). PB approach, combined with proper cell cycle kinetics, may represent a potentially powerful instrument to describe, quantitatively, the evolution of an entire population during in vitro/in vivo cell reproduction, thus overcoming the limits of the phenomenological equations (as exponential growth, logistic, and gompertzian functions) traditionally adopted to describe the classic growth profile (sigmoidal) of total cell counts (Fadda et al, 2012a). In classic PB models the cells are seen as maturing individuals, continuously traveling along their life cycle at a specific growth rate till mitosis, which occurs at a specific transition rate (Fadda et al, 2012a).…”

“…PB approach, combined with proper cell cycle kinetics, may represent a potentially powerful instrument to describe, quantitatively, the evolution of an entire population during in vitro/in vivo cell reproduction, thus overcoming the limits of the phenomenological equations (as exponential growth, logistic, and gompertzian functions) traditionally adopted to describe the classic growth profile (sigmoidal) of total cell counts (Fadda et al, 2012a). In classic PB models the cells are seen as maturing individuals, continuously traveling along their life cycle at a specific growth rate till mitosis, which occurs at a specific transition rate (Fadda et al, 2012a). Cells in a growing population may be discriminated in terms of their own age (Faraday et al, 2001;Sherer et al, 2008) and/or size (mass or volume) (Mantzaris et al, 1999;Pisu et al, 2003Pisu et al, , 2004Pisu et al, , 2006Pisu et al, , 2007Pisu et al, , 2008 which increase along cell life cycle.…”