ABSTRACT

Variations and fluctuations are characteristic features of biological systems and are also manifested in cell cultures. Here we describe a computational pipeline for identifying the range of 3-dimensional (3D) cell aggregate sizes in which non-isometric scaling emerges in the presence of joint mass and metabolic rate fluctuations. 3D cell-laden spheroids with size and single cell metabolic rates described by probability density functions were randomly generated in silico. The distributions of the resulting metabolic rates of the spheroids were computed by modelling oxygen diffusion and reaction. Then, given that data collapse of joint probability distributions has not been reported, a new method for estimating scaling exponents of correlated variables through statistically significant data collapse was developed. The method was used to identify a physiologically relevant range of spheroid sizes where both non-isometric scaling and a minimum oxygen concentration (0.04 mol m^-3) is maintained. The in silico pipeline described enables the prediction of the number of experiments needed for an acceptable collapse and, thus, a consistent estimate of scaling parameters. We show that scaling exponents are significantly different and lower in the presence of joint mass and metabolic rate variations and that their deviation from the exponent estimated through means increases with increasing variability. Our study highlights the importance of incorporating fluctuations and variability in size and metabolic rates when estimating scaling exponents. It also suggests the need for taking into account their covariations for better understanding and interpreting experimental observations both in vitro and in vivo, and brings new insights for the design of more predictive and physiologically relevant in vitro models.