Spatial competition constrains resistance to targeted cancer therapy

Abstract

Adaptive therapy (AT) aims to control tumour burden by maintaining therapy-sensitive cells to exploit their competition with resistant cells. This relies on the assumption that resistant cells have impaired cellular fitness. Here, using a model of resistance to a pharmacological cyclin-dependent kinase inhibitor (CDKi), we show that this assumption is valid when competition between cells is spatially structured. We generate CDKi-resistant cancer cells and find that they have reduced proliferative fitness and stably rewired cell cycle control pathways. Low-dose CDKi outperforms high-dose CDKi in controlling tumour burden and resistance in tumour spheroids, but not in monolayer culture. Mathematical modelling indicates that tumour spatial structure amplifies the fitness penalty of resistant cells, and identifies their relative fitness as a critical determinant of the clinical benefit of AT. Our results justify further investigation of AT with kinase inhibitors.

Fig. 1

Mathematical modelling of tumour evolutionary dynamics. a In mathematical modelling of cancer treatment outcomes, the function f describing the relationship between resistant cell relative fitness and frequency may be assumed to be linear (solid curve) or sigmoidal. Two example relationships are shown for the relative fitness of resistant cells when rare, f _min = 0.25 (dotted curve) and f _min = 0.75 (dashed curve). b Numerical results of a mathematical model for different therapy regimes, varied initial frequency of resistant cells, and varied function f. Population sizes are shown for sensitive cells (blue), resistant cells (red), and all cells (black). Days of progression-free survival (first vertical dashed line) and overall survival (second vertical dashed line) are shown. Grey vertical bars show the therapy dose. MTD = maximum tolerated dose; AT = adaptive therapy. c Mathematical model predictions for the progression-free survival benefit of adaptive therapy (relative to maximum tolerated dose therapy) vs. initial frequency of resistant cells. Symbols represent numerical results; lines are approximate analytical solutions; dotted lines are the upper bounds of the approximate analytical solutions. Outcomes are shown for five models assuming different functions f. The first model (black solid curve and square points) assumes a linear function, and assumes that the therapy slightly increases the mortality rate of resistant cells, μ _R. An analytical approximation is also shown for the case μ _R = 0 (dashed black line). Other models assume that f is sigmoidal. d Maximum relative survival benefit of adaptive therapy vs. f _min, assuming a sigmoidal function f. Curves are shown for different values of λ _R/λ _W, which is the maximum growth rate of resistant cells, relative to the growth rate of sensitive cells. The vertical asymptotes are at μ _RA/λ _R and the horizontal asymptote is at 1. Parameter values are taken from a previous study to facilitate comparison. Unless specified otherwise, λ _W = λ _R = log(2)/10, IC50_W = 1, IC50_R = 100, ρ _MTD = 1, θ = 5 days, N ₀ = 10⁹, k = 20, and c = 0.5

Fig. 2

Cell cycle rewiring in CDKi-resistant cells. a HCT116 WT and R50 early and late cells were grown in the absence or presence of 50 μM NU6102 and the cell number was evaluated every day for 6 days. Representative of three independent experiments. b Kinase activity assayed in vitro on CDK2 and cyclin A immunoprecipitates from WT, WT cells treated for 24 h with 20 µM NU6102, R50 and CDK2^−/− (KO) cells (mean±SD of 2 independent experiments performed in triplicates). c Heat-map of 2300 genes differentially expressed between WT, CDK2^−/− (KO), R50, and WT cells treated with 20 µM NU6102 for 24 h; analysis was performed in duplicates. Upregulated genes are indicated in yellow, downregulated in blue. d qRT–PCR analysis of CDK6 expression in WT, CDK2^−/− (KO) and R50 cells (mean±SD of three replicates). e Western blot analysis of the proteins indicated in WT, CDK2^−/− and R50 early and late cells. f Kinase activity assayed in vitro on CDK6 immunoprecipitates from WT, WT cells treated for 24 h with 20 µM NU6102, R50 and CDK2^−/− (KO) cells (mean±SD of two independent experiments performed in triplicates). g WT, R50 and CDK2^-/- cells were grown in the absence or presence of palbociclib (1 μM or 10 μM; PD0332991, PD) for 24 h, 48 h and 72 h, pulsed for 15 min with BrdU, and analysed for BrdU incorporation relative to untreated cells (mean±SD of a representative experiment performed in triplicates). h CDK6 was downregulated with siRNA in WT, CDK2^−/−, R50 and WT cells treated with 20 µM NU6102 for 24 h. After 24 h, the expression of indicated proteins (left) and cell cycle distribution (right) were analysed

Fig. 3

CDKi-resistant cells have lower proliferative fitness in vitro and in vivo. a WT and R50 cells were grown in 1% O₂. Percentage of viable cells (relative to cells cultured in 21% O₂) was quantified after 24 h, 48 h and 72 h (mean±SD of two independent experiments). b WT or R50 cells were grown in low serum (1%) or low glucose (1 g/L) and their number was analysed every 24 h (mean±SEM of 2 independent experiments). c Nude mice were injected subcutaneously with WT, CKD2^−/−, or R50 cells, and tumour volume was measured at 3-day intervals (n = 8 mice per condition; mean±SD). d Immunohistochemistry analysis of mitotic index, Ki67 expression and necrosis (Caspase 3a) in xenograft tumour samples from c (represented as % of cells, mean±SEM; t-test, ns, not significant). e, f Frequency dynamics (top row) and selection coefficients for competition assays, compared to predictions from growth rates (bottom row). In the bottom row, each point corresponds to a selection coefficient calculated from a competition assay (i.e., a period between consecutive points in the top row). Solid lines are means. Red dashed lines indicate predictions based on the growth rates of each cell type in isolation (Supplementary Methods). A single prediction is shown whenever growth curves were measured at the same time as competitions were conducted; otherwise pairs of lines show maximum and minimum predictions based on non-contemporaneous growth curves. Results are shown for competitions between GFP+CDKi-sensitive cells and drug-holiday GFP- CDKi-resistant (R50) cells (e), and for competitions between GFP+CDKi-sensitive cells and mCherry+R50 cells with different initial ratios (f)

Fig. 4

AT does not outperform MTD in limiting tumour growth in a monolayer culture. a Sensitive GFP+ and R50 mCherry+ cells were plated in monolayer at initial 99:1 ratio, in the presence of either DMSO as control or NU6102: AT condition (15 μM initial drug concentration, ±20% at 3-day intervals to maintain stable 70–80% confluence), MTD (50 μM for 24 h, with 48 h no drug) or MTDx (continuous 50 μM). Every 3 days, the proportion of GFP+ and mCh+ cells was determined by flow cytometry. b Flow cytometry analysis (forward scatter area, FSC-A, which increases with cell size, and side scatter area, SSC-A) of cell size of WT-GFP+ and R50-mCh+ cells from the experiment in a, at day 0 and day 12

Fig. 5

Spatial structure is a critical determinant of AT efficiency. a Time series of tumour spheroid cross-sections in a spatial computational model. In the upper four rows, cells are coloured according to their type (blue = sensitive, red = resistant) and shaded by local oxygen concentration (darker = more hypoxic); the medium surrounding the tumour spheroid and the necrotic core are coloured according to CDKi concentration (pale orange = high, dark orange = low) or, in the absence of CDKi, are coloured according to oxygen concentration (pale green = high, grey = low). In the lower two rows, cells are coloured according to their proliferation rate (grey = zero, red = low, yellow = high). Typical outcomes were chosen as those in which the final frequency of resistance most closely matched the median. See text and Supplementary Methods for parameter values and assumptions. b Tumour spheroid growth curves for different treatment regimens in the computational model. Medians (solid curves), means (dashed curves) and interquartile ranges (shaded) are shown for 1,000 stochastic simulations. c Frequency of resistance over time in the computational model. Medians (solid curves), means (dashed curves) and interquartile ranges (shaded) are shown for 1000 stochastic simulations. d–g Proportion of simulations in which the frequency of resistance exceeded 10% after 24 days of treatment with 20 μM CDKi, vs. the initial distance between the outermost resistant cell and the tumour spheroid periphery. Results are shown for 1000 stochastic simulations each of the default model (d); a model without a fitness cost of resistance (e); a model with no growth period prior to CDKi treatment (f); and a model in which cell crowding does not prohibit proliferation (g)

Fig. 6

Effective AT requires spatially structured tumour growth. a–c Tumour spheroids were initiated with WT-GFP+ and R50-mCh+, at different ratios (100% GFP+, 99%GFP+ / 1%mCh+, 100%mCh+), and when established, from day 4, grown either in the presence of DMSO or NU6102 at indicated concentrations. a Representative phase contrast and immunofluorescence images of spheroids at indicated time points. Bar, 1mm. b Flow cytometry analysis of GFP + and mCh+ cell content of spheroids at day 28 (cells of 4–5 spheroids per condition were dissociated and analysed). c Spheroid volume (mm³) at 3-day intervals (n≥5, mean±SD). Two independent experiments are presented