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.
The growth dynamics of multicell tumour spheroids (MTS) were analysed by means of mathematical techniques derived from signal processing theory. Volume vs. time trajectories of individual spheroids were fitted with the Gompertz growth equation and the residuals (i.e. experimental volume determinations minus calculated values by fitting) were analysed by fast fourier transform and power spectrum. Residuals were not randomly distributed around calculated growth trajectories demonstrating that the Gompertz model partially approximates the growth kinetics of three-dimensional tumour cell aggregates. Power spectra decreased with increasing frequency following a 1/f(delta) power-law. Our findings suggest the existence of a source of 'internal' variability driving the time-evolution of MTS growth. Based on these observations, a new stochastic Gompertzian-like mathematical model was developed which allowed us to forecast the growth of MTS. In this model, white noise is additively superimposed to the trend described by the Gompertz growth equation and integrated to mimic the observed intrinsic variability of MTS growth. A correlation was found between the intensity of the added noise and the particular upper limit of volume size reached by each spheroid within two MTS populations obtained with two different cell lines. The dynamic forces generating the growth variability of three-dimensional tumour cell aggregates also determine the fate of spheroid growth with a strong predictive significance. These findings suggest a new approach to measure tumour growth potential.
Multicellular tumor spheroids are an important in vitro model of the pre-vascular phase of solid tumors, for sizes well below the diagnostic limit: therefore a biophysical model of spheroids has the ability to shed light on the internal workings and organization of tumors at a critical phase of their development. To this end, we have developed a computer program that integrates the behavior of individual cells and their interactions with other cells and the surrounding environment. It is based on a quantitative description of metabolism, growth, proliferation and death of single tumor cells, and on equations that model biochemical and mechanical cell-cell and cell-environment interactions. The program reproduces existing experimental data on spheroids, and yields unique views of their microenvironment. Simulations show complex internal flows and motions of nutrients, metabolites and cells, that are otherwise unobservable with current experimental techniques, and give novel clues on tumor development and strong hints for future therapies.
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