Fig. 3: Mathematical modelling predicts the type of ecological interactions in unirradiated mixed prostate spheroids.
a Schematic illustrating pipeline for mathematical modelling of ecological interactions. The logistic model of spheroid growth was fit to growth curves of homogeneous PC3 and DU145 spheroids to determine the growth rate r and carrying capacity K (the limiting volume of the spheroid) for parental and radioresistant populations. Interaction parameters in mixed curves were then estimated by fitting volume measurements and proportions of each population to a Lotka–Volterra model. The parameter λP indicates the effect of parental on radioresistant, while the parameter λRR indicates the effect of radioresistant on parental. b Estimated interaction parameters using biological data of mixed PC3 and DU145 spheroids. The nature of the interaction, i.e., competition vs. antagonism, depends on the sign of the interaction parameters. Error bars represent confidence intervals. c Experimental determination of proliferation (EdU+ cells) from cell cycle analysis for parental and radioresistant (RR) cell populations isolated from mixed (parental, green diamonds; RR, pink diamonds) and homogeneous spheroids (parental, white circles; RR, black circles; n = 4 experiments). Lines connecting symbols indicate the median value. ‡FDR < 0.05, overdispersed Poisson regression model fitting with Benjamini–Hochberg correction.
