A novel population balance model to investigate the kinetics of in vitro cell proliferation: Part II. numerical solution, parameters' determination, and model outcomes

Abstract

Based on the general theoretical model developed in Part I of this work, a series of numerical simulations related to the in vitro proliferation kinetics of adherent cells is here presented. First the complex task of assigning a specific value to all the parameters of the proposed population balance (PB) model is addressed, by also highlighting the difficulties arising when performing proper comparisons with experimental data. Then, a parametric sensitivity analysis is performed, thus identifying the more relevant parameters from a kinetics perspective. The proposed PB model can be adapted to describe cell growth under various conditions, by properly changing the value of the adjustable parameters. For this reason, model parameters able to mimic cell culture behavior under microgravity conditions are identified by means of a suitable parametric sensitivity analysis. Specifically, it is found that, as the volume growth parameter is reduced, proliferation slows down while cells arrest in G0/G1 or G2/M depending on the initial distribution of cell population. On the basis of this result, model capabilities have been tested by means of a proper comparison with literature experimental data related to the behavior of synchronized and not-synchronized cells under micro- and standard gravity levels.

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.…”

Cell mass and cell cycle dynamics of an asynchronous budding yeast population: Experimental observations, flow cytometry data analysis, and multi‐scale modeling

“…Parameter estimation from experimental data have been reported by Mancuso et al (2009) where two parameters corresponding to the maximum rate of cell growth and a power law order for a geometrical factor were tuned in order to minimize the differences between the experimental and predicted cell size distributions. Fadda et al (2012b) qualitatively compared model predictions to experimental observations previously reported in the literature. Common to all these cases is the use of parameters and/or assumptions previously reported on theoretical work on PBM for microbial populations, for example, the partition distribution shape parameter.…”

“…In a previous theoretical study by Mantzaris et al (2002), a symmetrical distribution with shape parameters, a and b, equal to 40 was assumed without experimental evidences. Other studies (Fadda et al, 2012b;Hatzis and Porro, 2006;Mancuso et al, 2009;Sidoli et al, 2006) assumed the same symmetrical distribution and shape parameter.…”

A numerical study on the estimation of the stable size distribution for a cell population balance model

“…Despite this early development, nowadays, it is an area of increasing applications, and it is used to describe quite different issues (see Ramkrishna and Singh and references therein). In recent years, they have evolved towards more complicated models: several structuring variables, various populations (describing, for example, proliferating and quiescent cells or the different stages in a cell cycle), non‐linear problems (with the consumption of a limited extracellular medium), and inverse problems to compute the vital functions . In our setting, we consider a cell population balance model structured by the cell size, in which the reproduction is performed by fission into 2 daughter cells with different sizes.…”

“…In recent years, they have evolved towards more complicated models: several structuring variables, various populations (describing, for example, proliferating and quiescent cells or the different stages in a cell cycle), non-linear problems (with the consumption of a limited extracellular medium), and inverse problems to compute the vital functions. [8][9][10][11] In our setting, we consider a cell population balance model structured by the cell size, in which the reproduction is performed by fission into 2 daughter cells with different sizes. Cell size is an attractive variable as a result of the relative ease and precision, with which it can be measured because the instrumentation to obtain it has improved considerably.…”