Ab initiophenomenological simulation of the growth of large tumor cell populations

Abstract

In a previous paper we have introduced a phenomenological model of cell metabolism and of the cell cycle to simulate the behavior of large tumor cell populations (Chignola R and Milotti E 2005 Phys. Biol. 2 8-22). Here we describe a refined and extended version of the model that includes some of the complex interactions between cells and their surrounding environment. The present version takes into consideration several additional energy-consuming biochemical pathways such as protein and DNA synthesis, the tuning of extracellular pH and of the cell membrane potential. The control of the cell cycle -that was previously modeled by means of ad hoc thresholds -has been directly addressed here by considering checkpoints from proteins that act as targets for phosphorylation on multiple sites. As simulated cells grow, they can now modify the chemical composition of the surrounding environment which in turn acts as a feedback mechanism to tune cell metabolism and hence cell proliferation: in this way we obtain growth curves that match quite well those observed in vitro with human leukemia cell lines. The model is strongly constrained and returns results that can be directly compared with actual experiments, because it uses parameter values in narrow ranges estimated from experimental data, and in perspective we hope to utilize it to develop in silico studies of the growth of very large tumor cell populations (10 6 cells or more) and to support experimental research. In particular, the program is used here to make predictions on the behaviour of cells grown in a glucose-poor medium: these predictions are confirmed by experimental observation.3

Statistical approach to the analysis of cell desynchronization data

“…We are now developing a numerical simulator of the growth of tumor spheroids and of dispersed tumor cell populations [4,5], and to produce a robust numerical model we must include stochastic effects in growth, as well as the known deterministic biochemical paths. For this reason we need a straightforward, intuitive, model-independent method for the estimation of the degree of randomness in different experimental settings.…”

Bridging the gap between the micro- and the macro-world of tumors

“…The simulation program includes some important checkpoint, which are modeled with different accuracies, mitosis, and several conditions for cell death. 14,15 Some of the events are partly stochastic, e.g., at mitosis, organelles are shared between daughter cells according to a binomial distribution. 16 Geometry and topology: to compute both diffusion and cell-cell forces we must know the proximity relations between cells.…”

“…These expressions are parameterizations of observed pH-and oxygen-dependent transport activity, and the related parameters are VMAX1, a2c slope, a2c thr, c2a slope, c2a thr, and O2st; we have introduced hyperbolic tangents as a practical way to avoid the sharp kinks associated to the spline functions quoted in the literature, 14,15 and at the same time keep the same general shape. The cells that are in direct contact with the environment require a slightly different form of the transport and diffusion equation:…”

Computer simulations and modeling in oncology: methods and applications

“…A convenient experimental tool that captures some of the most relevant features of tumor growth kinetics while allowing for a manageable description are the multicellular tumor spheroids (MTS) [17,19]. MTS are spherical aggregations of tumor cells that may be grown under strictly controlled conditions.…”

“…what is mainly of clinical interest from what can be learned from the bio-chemo-physics of the cells, e.g. by means of "ab initio" calculations [17]. Such an understanding is necessary not only to predict the emergence of macroscopic phenomena out of microscopic laws, but also to correlate microscopic and macroscopic parameters [18,19].…”