Mathematical model of tumor immunotherapy for bladder carcinoma identifies the limitations of the innate immune response

Abstract

Treatment for non-muscle invasive carcinoma of the bladder represents one of the few examples of successful tumor immunity. Six weekly intravesical instillations of Bacillus Calmette-Guerin (BCG), often followed by maintenance schedule, result in up to 50-70% clinical response. Current models suggest that the mechanism of action involves the non-specific activation of innate effector cells, which may be capable of acting in the absence of an antigen-specific response. For example, recent evidence suggests that BCG-activated neutrophils possess anti-tumor potential. Moreover, weekly BCG treatment results in a prime-boost pattern with massive influx of innate immune cells (107-108 PMN/ml urine). Calibrating in vivo data, we estimate that the number of neutrophil degranulations per instillation is approximately 106-107, more than sufficient to potentially eliminate ~106 residual tumor cells. Furthermore, neutrophils, as well as other innate effector cells are not selective in their targeting-thus surrounding cells may be influenced by degranulation and / or cytokine production. To establish if these observed conditions could account for clinically effective tumor immunity, we built a mathematical model reflecting the early events and tissue conditioning in patients undergoing BCG therapy. The model incorporates key features of tumor growth, BCG instillations and the observed prime / boost pattern of the innate immune response. Model calibration established that each innate effector cell must kill 90-95 bystander cells for achieving the expected 50-70% clinical response. This prediction was evaluated both empirically and experimentally and found to vastly exceed the capacity of the innate immune system. We therefore conclude that the innate immune system alone is unable to eliminate the tumor cells. We infer that other aspects of the immune response (e.g., antigen-specific lymphocytes) decisively contribute to the success of BCG immunotherapy.

Figure 1.

Diagram of our mathematical model. H and T denote the number of BCG-unassociated cells of the bladder tissue and tumor cells, respectively. E denotes the number of innate effector cells. B denotes the number of free BCG bacteria in the bladder. H_i and T_i denote the number of BCG-associated tissue and tumor cells, respectively. The model runs as follows. Before immunotherapy, only three of six cell populations are present: H, T and E. The interactions between these cell populations are negligible and their corresponding compartments are disconnected. The processes that take place for each of these independent compartments are “birth” (i.e., cell inflow and/or local proliferation) and “death” (i.e., cell outflow and/or homeostatic programmed cell death); see the vertical black arrows. During BCG instillations, three new populations of cells emerge creating dynamic interactions between all the compartments. Free BCG infects tissue and tumor cells (green arrows), inducing transitions of cells from H to H_i and T to T_i (horizontal black arrows). H_i and T_i cells activate innate immune effectors E (red arrows). In turn, E cells target H_i and T_i destroying them (blue continuous arrows) and neighboring H and T cells (blue dashed arrows) by innate effector mechanisms (e.g., cytokines, death receptor agonists, degranulations).

Figure 2.

Modeling results: The probability of tumor extinction was determined using a stochastic model for tumor growth. The results are bound by the number of bystander cells killed per innate effector mechanisms and the fraction of BCG-infected tumor cells infected by BCG during the last instillation. The probability map was obtained with the stochastic version of our model. The blue dashed line represents the necessary condition for tumor elimination that we obtained from the deterministic version of our model. Note that the stochastic and the deterministic results appear fairly close. The green shade defines the region of parameter values that are derived from clinical and observational data. The scaled color heat map indicates the probability of tumor extinction.

Figure 3.

Modeling results: The probability of tumor extinction after 6 instillations (error bars indicate 95% confidence intervals) vs. the number of bystander cells killed. The red region includes the values of the probability of tumor extinction observed in clinical practice.

Figure 4.

Estimation of bystander death by measurement of tumor cell apoptosis. (A) For detection of caspase-3 activity (apoptosis), we used EG7 cells expressing a FRET-based (Förster Resonance Energy Transfer) fluorescent probe sensitive to caspase-3 activity (see text). Apoptotic cells (loss of FRET and increase of CFP signal) were monitored by FACS. Here are shown two representative examples, for non- stimulated (Non-Stim) and staurosporin-stimulated cells. (B) The direct killing is measured by the percentage of apoptotic cells after 48 h incubation with no stimulus (NS), 5 × 10⁶ CFU/ml of BCG, 20 ng/ml of myeloperoxidase (MPO) or 1 μM of staurosporine (Stauro). C. The indirect killing is measured by the percentage of apoptotic cells after 48 h incubation with either supernatant from leukocytes alone (NS), or from leukocytes stimulated with 5 × 10⁶ CFU/ml of BCG. For the data presented in panels B and C, more than 1000 cells were analyzed (CV < 5%). The results are representative of three independent experiments.