Increased carrying capacity reduces the benefit of adaptive therapy by reducing spatial competition.

Abstract

(A) The blue and red boxplots show the TG from the 30 couple realizations (for both AT and CT-MTD) with respect to carrying capacities of K = 1 and 2, respectively. The triple asterisk (***) signifies that increasing the carrying capacity significantly reduced the TG (p − value B) The time evolution of the mean of the average number of empty sites in the VNHD of each R-cell in the 30 realizations () is shown for both CT-MTD (solid lines) and AT (dashed lines); K = 1 (blue) and 2 (red). K = 2 offers a greater number of empty sites in the VNHDs of R-cells than K = 1. For the clumped initial cell distribution, we investigated the effect of the spatial carrying capacity on the TG. The spatial carrying capacity was characterized as K = 1 (each lattice point could hold one cell) or K = 2 (each lattice point could hold, at most, two cells, regardless of their sensitivity or resistance). When K = 1 was used, a total of four cells could occupy the VNHD of each cell (i.e., ). For each cell in K = 2, a total of eight cells could occupy a VNHD, and one additional cell could be located in the respective cell’s site (i.e., ). S2A Fig shows that increasing the carrying capacity significantly decreased the TG (p − value K = 2, whereas it was below 2 for K = 1. Due to this ample space in their neighborhoods, R-cells hardly experienced any spatial competition and grew at a higher pace when K = 2 under both AT and CT-MTD. As the total cell population grew, decreased abruptly and tended to settle below 1. For K = 1, a similar trend was observed; however, the number of empty sites was lower than that for K = 2 (). Comparing the number of empty sites in each R-cell’s VNHD () for AT in the case of K = 1 with that in the case of K = 2 (S2B Fig, dotted lines)), we observed that, for K = 1, went through ups and downs several times, which suggested spatial competition with neighboring cells. On the other hand, for K = 2, this value monotonically decreased, and there was a very slight difference due to AT and CT-MTD. Therefore, we concluded that the short TG with K = 2 was due to the lack of spatial competition. We observed that the probabilities of having a negative TG were 0.03 and 0.4 for K = 1 and 2, respectively, i.e., an increase in carrying capacity reduces the benefit of AT over CT-MTD. (TIF)</p