A phenomenological approach to the simulation of metabolism and proliferation dynamics of large tumour cell populations

Abstract

A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a simplified model of cell metabolism, growth and proliferation, suitable for inclusion in a multicell simulator, now under development (Chignola R and Milotti E 2004 Physica A 338 261-6). Nutrients regulate the proliferation dynamics of tumour cells which adapt their behaviour to respond to changes in the biochemical composition of the environment. This modelling of nutrient metabolism and cell cycle at a mesoscopic scale level leads to a continuous flow of information between the two disparate spatiotemporal scales of molecular and cellular dynamics that can be simulated with modern computers and tested experimentally.

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:…”

Ab initiophenomenological simulation of the growth of large tumor cell populations

“…The rationale behind the choice of the reactions in this minimal set has been discussed extensively in our previous paper [6], and we summarize again here the main arguments: 1. many parameters of the metabolic network are actually unknown; 2. even if we had a detailed knowledge of the actual metabolic network, a numerical model of a single cell's metabolic network would be computationally heavy, and the simulation of large cellular ensembles would be extremely impractical [5]; 3.…”

“…All these aspects and their mathematical modeling have been described and discussed in our previous paper [6]. were previously neglected [6] must now be taken into consideration. We include also protein and DNA synthesis and since these paths consume energy the global energy balance of the cell must also be extensively revised as well.…”

“…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.…”