Fig 1.
(A) Cells grow as a blob in a specified volume of medium (0.1–0.2 mL). Cells consume O2 and glucose. O2 is supplied from the upper boundary and glucose is depleted from the medium unless replenished. Model parameters for diffusion and uptake of constituents, rate of cell growth and death, are acquired from experiments with monolayers and multicellular layers (MCL). Parameters were fitted using the monolayer ABM and Matlab MCL program as described in methods. Time-varying concentration fields of the constituents are solved for in the medium and within the spheroid on a course grid and fine grid respectively (see Figure C), the cells acting as sinks. (B) Simulation illustrating cell states as a function of local O2 and glucose concentrations. Once cells double in size they undergo mitosis (pink cells). As the spheroid grows, O2 and glucose levels decrease in medium near the spheroid (indicated by a cyan color gradient), and decrease in the spheroid core to very low levels with cells becoming hypoxic (< 0.15 μM O2, dark green cells). Cells starved of O2 or glucose eventually are tagged to die (blue cells) and then, after a delay, undergo cytolysis, creating a necrotic core (black). (C) Bright field image of a growing, 4-day HCT116 spheroid seeded at 1000 cells per well.
Fig 2.
Estimation of oxygen and glucose metabolism and glucose diffusivity.
(A) Simulated oxygen concentrations as a function of distance from the centre of the spheroid during growth under standard growth conditions of replacing 50% (100 μL) of the culture medium every 2nd day based on experimentally derived oxygen consumption rate and literature medium and tissue diffusion coefficients (see Table 1 and supplementary material). (B) Glucose consumption by HCT116 monolayers (105 cells in 0.2 mL/well) in glucose-free medium with no FCS and a range of D-glucose concentrations were measured by serially sampling 5 μL medium at each time point. Values are means ± SD for 4 replicates. D-glucose metabolism rate parameters (Vmax and Km) in HCT116 cells were then calculated using the MABM (lines) using parameters that minimize the sum of squared errors between observed and simulated glucose concentrations for the full data set simultaneously. (C) Correlation between observed and MABM predicted glucose concentration data in B (R2 = 0.977) using the optimized glucose metabolism parameters. (D) Schematic figure of apparatus for the measurement of glucose and drug diffusion and metabolism through MCLs grown on a porous support membrane. After drug is added to the donor compartment, samples were collected from the donor and receiver compartments at intervals for measurement of concentrations of glucose or drug and its metabolite(s). (E) Representative diffusion data showing transport of 3H-L-glucose or D-glucose through HCT116 MCL (grown for 3 days, ca 100 μm thickness). Concentrations are normalised to the initial concentration measured in the donor compartment. Lines are model fits (minimization of the sum of squared errors between observed and calculated concentrations) with fitted parameters Vmax for D-glucose, after fixing the glucose coefficient at its mean value determined for L-glucose curves. (F) Simulated D-glucose concentration as a function of distance from the centre of the spheroid during growth under standard growth conditions of replacing 50% (100 μL) of the culture medium every 2nd day.
Table 1.
The parameters used in the ABM are summarized here, including parameter name (units), value and source (either from literature, assumption, or measurement from experiment).
Fig 3.
Histological characteristics of spheroids visualised in central sections and comparison with outputs of the SABM.
S-phase cells in spheroids collected after the indicated days of growth were stained after incubation with EdU (panel A). Hypoxic cells in spheroids were visualised by immunostaining for EF5 binding (panel B). The same spheroid sections were stained with H&E to quantify the necrotic and viable rim size (lower panels of A, B). n = 48 spheroids for A and B, respectively. Panel C shows SABM simulations based on oxygen and glucose parameters fitted to monolayer ad MCL experimental data (See Table 1). 2D snapshots of a central plane through spheroids are shown in which pink cells represent dividing cells, light green cells are highly proliferative cells under well oxygenated microenvironment (>1 μM O2), dark green cells are slowly proliferative cells under hypoxia (<1 μM O2), blue cells have been hypoxic for > 24 hr and have been tagged for subsequent necrosis, and the black region in the centre represents the necrotic zone. Scale bars = 100 μm and a color-coded legend for oxygen concentration in the medium is shown.
Fig 4.
Quantitation of histological characteristics of spheroids and comparison with outputs of the SABM.
The overall diameter (circles), diameter of the necrotic region (triangle), and thickness of viable rim (plotted here as twice the viable rim thickness, rectangles) of HCT116 spheroids were quantitated using H&E stained histological sections illustrated in Fig 3. Values are means ± SD (n = 4 spheroids, 5 on day 7). The lines are the corresponding outputs of SABM simulations using oxygen and glucose parameters fitted to monolayer and MCL experimental data (See Table 1).
Fig 5.
Comparison of growth and cellular characteristics of HCT116 spheroids with outputs of the SABM.
On the indicated days, diameters of spheroids (A) were measured. Values are means ± SD (n ≥48 spheroids). After exposing spheroids to EdU or EF5, spheroids (n = 48 spheroids) were pooled and dissociated and the number of cells in cell suspension were counted to estimate total cell number per spheroid (B), followed by exposing cells in 1 μg/mL PI for 2 min to measure cell viability by flow cytometry (% PI negative, C). Hypoxic fraction (% EF5-positive cells, D) and S-phase fraction (% EdU-positive cells, E) were measured by flow cytometry. The predictions of the SABM (lines), using fitted parameters from monolayer and MCL experiments, plotted with experimental data (points) are: (A) spheroid diameter (A) total cell number, (B), fractions of cells not tagged for death (C), fraction of cells below 0.5μM O2 (D) and estimated S-phase fraction based on the assumption that 37% of cells were initially in S-phase.
Fig 6.
Development of a spatially resolved PK/PD model for SN30000 and testing by SABM simulation of spheroid response to SN30000 exposure.
Cellular bioreductive metabolism of SN30000 (A) and clonogenic cell killing (B) was measured by serial sampling of stirred HCT116 cell suspensions (2 × 106 cells/mL) under anoxia (0% oxygen gas mixture). The rate constants for SN30000 metabolism (kmet0) and cell killing (Kc) were estimated by fitting the data in panel A and panel B simultaneously using the MABM assuming the medium was fully stirred. Lines represent MABM predictions based on the parameters which minimize the overall error sum of squares (Table 1). (C) Diffusion parameters for SN30000 were estimated from HCT116 MCL transport studies illustrated for a single experiment. Lines are model fits using the reaction-diffusion program described in methods with fitted parameters for each MCL: DSN30000 estimated from MCL transport under hyperoxia (95% O2, filled symbols in panel C) assuming no metabolic consumption (confirmed by no production of SN30000-1-oxide); kmet0 estimated from SN30000 diffusion under anoxia (open symbols in panel C) by fixing DSN30000 at its mean value (Table 1) determined in hyperoxic experiments. (D) To quantitate cytotoxicity, spheroids seeded with 1000 cells were exposed on day 4 to a range of SN30000 concentrations for 2 hr under 20% or 5% O2 and clonogenic cell survival was measured (points in Panel D) and compared to predictions of SABM incorporating the optimized reaction-diffusion and cell kill parameters estimated from monolayer and MCL experiments from Table 1 (lines in Panel D). (E) To measure spheroid growth delay induced by SN30000, spheroids were exposed to 25 μM SN30000 under 5% O2 or to 100 μM SN30000 under 20% O2 for 2 hr and spheroid diameters were monitored (points in Panel E) and compared to the SABM predictions (lines in Panel E) using parameters from Table 1. Values are mean ± SD (n = 16 spheroids).
Fig 7.
Radiation model and simulation of spheroid response to radiation using the SABM.
(A) A LQ radiation model was parameterised by measuring clonogenic cell survival of HCT116 monolayer (105 cells/mL) in response to a range of radiation doses under anoxic (unfilled rectangles in A, 3 separate experiments) or oxic (unfilled triangles in A, 2 separate experiments) conditions. Values are means ± SEM. Lines represent LQ model fits (Eqn S12) to all monolayer data simultaneously (fitted parameters in Table 1) by minimization of the sum of squared errors between simulated and observed ln(SF). These parameters were used in the SABM to simulate clonogenic cell survival of cells in 4-day spheroids exposed to radiation under 20% O2 (solid line in A) and compared to measured clonogenic cell killing in HCT116 spheroids (filled circles in A). Values are means ± SD (n = 16 spheroids). To compare the measured spheroid growth delay induced by radiation to that predicted by the SABM, HCT116 spheroids were exposed to 4 Gy radiation under 5% (Panel B) or 20% O2 (Panel C) and spheroid growth was monitored as a function of time. Values are means ± SD (n = 16 spheroids) and lines are simulations by the SABM based on clonogenic cell killing alone (…), or with addition of parameters for cell growth inhibition and survival probability at each mitosis following radiation (—) as described in Table 1.
Fig 8.
Comparison of simulated and measured spheroid responses to SN30000 and radiation in combination.
The predicted and measured clonogenic cell killing (A) and growth (B) of spheroids seeded with 1000 cells and treated on day 4 under 5% ambient O2 with 25 μM SN30000 for 2 hr alone, 12 Gy radiation alone or both (25 μM SN30000 for 2 hr, followed by 12 Gy radiation 1 hr after SN30000 removal). Values are means ± SEM (n = 8 spheroids for A and n = 16 spheroids for B). SABM predictions are based on the optimized parameters in Table 1. 2D snapshots from the SABM (C) illustrate cell fate and spheroid regrowth after the treatments, with the D4 output immediately following irradiation. Yellow cells are tagged for treatment-induced death, pink cells represent dividing (mitotic) cells, light green cells were highly proliferative well-oxygenated cells, dark green cells were low proliferative hypoxic cells, blue cells are cells tagged for hypoxia-induced cell death, and central dark region represents necrosis. Cell motility and fluid flow, to simulated spheroid shrinkage, is not implement yet (see text). The scale bar = 100 μm and a color-coded legend for oxygen concentration in medium is shown.