Fig 1.
Core features of the early tumor-immune network model.
This schematic illustrates key processes captured in the HDC agent-based model. (A) Macrophage polarization and tumor killing. Naïve macrophages (MP) polarize to either an M1 state, in the presence of high levels of Activator signal, or an M2 state, with concomitant exposure to M2 signal (M2S). M1 cells secrete tumor lethality signal (TLS), high levels of which kills tumor cells. (B) Macrophage chemotaxis. All macrophages chemotax along gradients of M2S, which is secreted by the tumor and M2 cells. (C) Vascularization, tumor proliferation, and the effects of oxygen. Oxygen and naïve MP enter at sites of vascularization, which increases as a function of local levels of M2S. All cells die in anoxic conditions, and dead cells are retained (e.g., forming a necrotic tumor core, as depicted). Individual tumor cells divide at a fixed rate, expanding to “invade” neighboring lattice sites.
Fig 2.
Qualitative recapitulation of tumor physiology.
Qualitative behavior of the model is illustrated through snapshots in time from a single run of the HDC model using base parameter values. At each time point post-tumor initiation (in days), spatial distributions of cells (by type), M2S, oxygen, and vasculature are depicted. In this particular run, shortly after the final time point shown, all tumor cells were dead. Numerical ranges spanned by colored scale bars are: M2S (0–4 [pg/LS] x 10–6), oxygen (0–1 [pg/LS]), vasculature (0–40 au).
Fig 3.
Functional and spatial predictors of tumor clearance.
The model was run 200 times at base parameter values, and runs were grouped based upon simulation outcome (tumor survival or tumor death). (A,B) Time evolution of cell counts (by type) for runs in which the tumor survived (A) or died (B). Insets: Expanded views of early time points (same axes). (C) Macrophage polarization index (MPI) at 0.5 d post tumor-initiation, classified by simulation outcome. Error bars indicate standard error. (D) Distributions of MPI at t = 0.5 d observed across multiple simulations, classified by outcome. (E) Spatial metrics of the TME at t = 0.5 d: domain-wide maximum M2S value and mean local coefficient of variation (CV) of M2S, classified by outcome. Local CV of M2S was calculated within each 10 x 10 lattice site (LS) array, and mean of all 100 such arrays across the domain is shown. (F) Tumor survival probability evaluated across variations in average initial M2S level (p11) and M2 polarization threshold (p13). (G) MPI at t = 0.5 d evaluated across the same parameter variations used in F. (H) Tumor cell counts at t = 0.5 d evaluated across the same parameter values used in F. (I) Normalized MPI (blue) and normalized tumor cell count (green), both at t = 0.5 d, calculated across the same parameter values used in F and plotted against tumor survival probability. Linear regression was performed on data points for which tumor survival probability was less than 1.
Fig 4.
Systematic multi-parameter sensitivity analysis (MPSA).
Parameter sensitivity was evaluated by running simulations using 5 values of each parameter, spanning a single order of magnitude around the base value (see text), and this was performed for each combination of values for each parameter pair. 50 simulation runs were performed for each set of parameter values, and the tally of simulation outcomes is indicated by the color. The change in each parameter magnitude across its range is indicated by its corresponding purple ramps on the boundaries of the plot.
Fig 5.
Systematic evaluation of parameter contributions to model behaviors.
(A) Using the data from Fig. 4, sensitivities of four different metrics of model behavior were calculated over changes in each of the 18 model parameters. The range of each metric was different (indicated in key at top of panel). For each metric, normalized sensitivities were ranked by parameter (right column). (B) Illustration of M2 polarization probability “dose-response” curves (normalized) for different values of polarization stochasticity. (C) Illustrative spatial distributions of M2S for low and high values of the M2S heterogeneity parameter, p17, depicted at 0.1 d after tumor initiation, after which point initial diffusion had occurred but cellular contributions to the distribution were negligible. (D) Global correlation of tumor survival probability with MPI at t = 0.5 d across all parameter combinations evaluated in Fig. 4. Red lines depict linear regressions, with coefficients shown. (E) Pairwise contributions of polarization stochasticity and all other parameter values to tumor survival probability.
Fig 6.
Evaluation of potential engineered cell-based therapy strategies.
Three potential strategies to treat cancer with engineered macrophages (EMP) were evaluated for efficacy in promoting tumor clearance in this model of the early TME. Enhanced immunostimulation (left column): when polarized to the M1 state, EMP released four times the base case level of TLS. Decreased immunosuppression (center column): EMP could not polarize to the M2 state. Active conversion (right column): EMP could not polarize to the M2 state and constitutively secreted a diffusible signal that blocked the M2 receptor on normal (unmodified) macrophages. For each strategy, tumor survival probability was calculated over simulations varying the time at which the first EMP were introduced and the fraction of incoming MP that were MP (vs. unmodified); 50 simulations were performed for each case.