Fig 1.
Model schematic and representative simulation result.
(A) Model schematic. T cells secrete IFN-γ, which promotes M1 differentiation. Tumor cells and M2 macrophages secrete IL-4, which promotes M2 differentiation. T cells kill tumor cells. M1 macrophages promote T cell function, while M2 macrophages inhibit it. (B) Representative spatial distribution of cells once the tumor reaches the equilibrium state. Tumor cells (black), T cells (yellow), active T cells (red), M0 macrophages (blue), M2 macrophages (purple). There are no M1 macrophages present at the end of this simulation.
Fig 2.
Time courses with baseline parameters and no treatment.
Time courses for tumors that were not removed by the immune system are shown in black; those for tumors that were removed are shown in red. There is only one simulation here that led to tumor removal. (A) Cancer cells, (B) M0 cells, (C) M1 cells, (D) M2 cells, (E) total T cells, (F) active T cells, (G) average IL-4, (H) maximum IL-4, (I) average IFN-γ, (J) Maximum IFN-γ. (G)–(J): units are number of molecules.
Fig 3.
Effects of continuous immunotherapy started at 100 days of simulation.
(A) Macrophage depletion, (B) recruitment inhibition, and (C) PI3K inhibition. (i) fraction of tumors removed after starting therapy. (ii) time (days) from starting treatment to tumor removal. It is averaged over the 100 simulations and is equal to zero if no tumors were removed at that treatment level. (iii) maximum number of M1 macrophages. (iv) maximum number of total T cells. (v) maximum number of active T cells. Note the differences in y-axis scales across treatment strategies. Asterisks signify that a result is statistically significant (p<0.01) from the result of the lowest treatment strength. We note that for the time needed to remove the tumor (ii), we plot the time averaged over only simulations where the tumor was removed. Therefore, while some bars may appear much higher than that of the lowest treatment strength, they only represent a small number of simulations out of 100 and thus were not found to be statistically significant.
Fig 4.
Effects of cycled immunotherapy started at 100 days of simulation.
For macrophage depletion (A), the fraction of macrophages removed at the beginning of each cycle is given as “Depletion Strength” and the length of each cycle is “Cycle Duration.” For recruitment inhibition (B) and PI3K inhibition (C), the number of days in the cycle that treatment is on for is given as “Days Treatment is On.” Recruitment inhibition is simulated at a strength of 1.0 (complete inhibition) and PI3K inhibition is simulated at a strength of 0.8. For recruitment inhibition and PI3K inhibition, spaces marked with an X are those where treatment-on time is equal or greater to the cycle duration, thus were not simulated. (i) fraction of tumors removed after starting therapy. (ii) time (days) from starting treatment to tumor removal. It is averaged over the 100 simulations and is equal to zero if no tumors were removed at that treatment level. (iii) maximum number of M1 macrophages. (iv) maximum number of total T cells. (v) maximum number of active T cells.
Fig 5.
PI3K inhibition of 0.8 for cycled immunotherapy.
Individual time courses for PI3K inhibition of 0.8 at a cycle duration of 25 days with treatment given for 2 days per cycle. Tumors that survived to the end of simulation are shown in black. Tumors that were eliminated are shown in green. One time course is shown in red for ease of understanding. (A) Cancer cells, (B) M0 macrophages, (C) M1 macrophages, (D) M2 macrophages, (E) T cells, (F) Active T cells, (G) Average IL-4, (H) Maximum IL-4, (I) Average IFN-γ, (J) Maximum IFN-γ.
Fig 6.
Time courses with increased tumor proliferation rate and no treatment.
The tumor proliferation rate is increased to 1.2/day. Time courses for tumors that were not removed by the immune system are shown in black; those for tumors that were removed are shown in red. (A) Cancer cells, (B) M0 cells, (C) M1 cells, (D) M2 cells, (E) Total T cells, (F) Active T cells, (G) Average IL-4, (H) Maximum IL-4, (I) Average IFN-γ, (J) Maximum IFN-γ.
Fig 7.
Constant PI3K inhibition at tumor proliferation rate of 1.2/day.
(A) fraction of tumors removed after starting therapy, (B) average time needed to remove the tumor, (C) the maximum number of M1 macrophages, (D) the maximum number of total T cells, (E) the maximum number of active T cells. Note the differences in y-axis scales across treatment strategies. Asterisks signify that a result is statistically significant (p<0.01) from the result of the lowest treatment strength. We note that for the time needed to remove the tumor (B), plotted is the time averaged over only simulations where the tumor was removed. Therefore, while some bars may appear much higher than that of the lowest treatment strength, they only represent a small number of simulations out of 100 and thus were not found to be statistically significant.
Fig 8.
Time courses with macrophage recruitment rate doubled and no treatment.
(A) Cancer cells, (B) M0 cells, (C) M1 cells, (D) M2 cells, (E) Total T cells, (F) Active T cells, (G) Average IL-4, (H) Maximum IL-4, (I) Average IFN-γ, (J) Maximum IFN-γ.
Fig 9.
Constant macrophage depletion started at 100 days with macrophage recruitment rate doubled.
(A) fraction of tumors removed after starting simulation, (B) average time needed to remove the tumor, (C) the maximum number of M1 macrophages, (D) the maximum number of total T cells, (E) the maximum number of active T cells. Note the differences in y-axis scales across treatment strategies. Asterisks signify that a result is statistically significant (p<0.01) from the result of the lowest treatment strength. We note that for the time needed to remove the tumor (B), plotted is the time averaged over only simulations where the tumor was removed. Therefore, while some bars may appear much higher than that of the lowest treatment strength, they only represent a small number of simulations out of 100 and thus were not found to be statistically significant.
Fig 10.
Time courses with increased tumor proliferation and macrophage recruitment rates, without treatment.
The macrophage recruitment rate is doubled, and tumor proliferation rate increased to 1.2/day. Time courses for tumors that were not removed by the immune system are shown in black; those for tumors that were removed are shown in red. (A) Cancer cells, (B) M0 cells, (C) M1 cells, (D) M2 cells, (E) Total T cells, (F) Active T cells, (G) Average IL-4, (H) Maximum IL-4, (I) Average IFN-γ, (J) Maximum IFN-γ.
Fig 11.
Constant PI3K inhibition at increased tumor proliferation and macrophage recruitment rates.
(A) fraction of tumors removed after starting therapy, (B) average time needed to remove the tumor, (C) the maximum number of M1 macrophages, (D) the maximum number of total T cells, (E) the maximum number of active T cells. Note the differences in y-axis scales across treatment strategies. Asterisks signify that a result is statistically significant (p<0.01) from the result of the lowest treatment strength. We note that for the time needed to remove the tumor (B), plotted is the time averaged over only simulations where the tumor was removed. Therefore, while some bars may appear much higher than that of the lowest treatment strength, they only represent a small number of simulations out of 100 and thus were not found to be statistically significant.
Fig 12.
Cycling macrophage depletion with increased tumor proliferation and macrophage recruitment rates.
The macrophage recruitment rate is doubled, and tumor proliferation rate increased to 1.2/day. (A) fraction of tumors removed after starting simulation, (B) average time needed to remove the tumor, (C) the maximum number of M1 macrophages, (D) the maximum number of total T cells, (E) the maximum number of active T cells.