An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers

Abstract

Interleukin (IL)-21 is an attractive antitumor agent with potent immunomodulatory functions. Yet thus far, the cytokine has yielded only partial responses in solid cancer patients, and conditions for beneficial IL-21 immunotherapy remain elusive. The current work aims to identify clinically-relevant IL-21 regimens with enhanced efficacy, based on mathematical modeling of long-term antitumor responses. For this purpose, pharmacokinetic (PK) and pharmacodynamic (PD) data were acquired from a preclinical study applying systemic IL-21 therapy in murine solid cancers. We developed an integrated disease/PK/PD model for the IL-21 anticancer response, and calibrated it using selected "training" data. The accuracy of the model was verified retrospectively under diverse IL-21 treatment settings, by comparing its predictions to independent "validation" data in melanoma and renal cell carcinoma-challenged mice (R(2)>0.90). Simulations of the verified model surfaced important therapeutic insights: (1) Fractionating the standard daily regimen (50 µg/dose) into a twice daily schedule (25 µg/dose) is advantageous, yielding a significantly lower tumor mass (45% decrease); (2) A low-dose (12 µg/day) regimen exerts a response similar to that obtained under the 50 µg/day treatment, suggestive of an equally efficacious dose with potentially reduced toxicity. Subsequent experiments in melanoma-bearing mice corroborated both of these predictions with high precision (R(2)>0.89), thus validating the model also prospectively in vivo. Thus, the confirmed PK/PD model rationalizes IL-21 therapy, and pinpoints improved clinically-feasible treatment schedules. Our analysis demonstrates the value of employing mathematical modeling and in silico-guided design of solid tumor immunotherapy in the clinic.

Figure 1. Scheme of the systemic IL-21 mathematical model.

A model of IL-21 PD effects on immune regulation of tumor growth is combined with a new IL-21 PK model based on data in mice . Under SC/IP administration, IL-21 is introduced at site (A) and is transported through 3 compartments to the plasma (P). Under IV administration, the drug is injected directly into the plasma. The drug is degraded via 3 additional compartments. IL-21 concentrations in the target tissue (T) are correlated with the plasma levels by parameter s. In the target site, IL-21 inhibits NK survival and promotes CTL expansion, while enhancing CPs of both cells and facilitating their tumor cell targeting. Abbreviations: PK- pharmacokinetics; PD- pharmacodynamics; IV- intravenous; SC- subcutaneous; IP-intraperitoneal; NK- natural killer cell; CTL- cytotoxic T lymphocyte; CPs- cytotoxic proteins.

Figure 2. Estimation and sensitivity analysis of model parameter s.

Curve-fits produced during estimation of parameter s, using experimental training data of B16 dynamics under an early-onset (day 3) IL-21 treatment (50 µg/day) . The parameter was evaluated per route of administration (see Table S1 in Text S1), and model-data approximation is indicated for both SC and IP treatment (“Model fit”). Predictions of the model under 2-fold increased or decreased s values (“Model prediction s×2” and “Model prediction s/2”, respectively) retrieving these experimental data (Exp), are plotted. Simulations (lines) are shown with respect to data (circles), given as means±SEM.

Figure 3. IL-21-induced antitumor effects: model simulations retrospectively verified in experimental murine tumors.

Model predictions (lines) retrieve experimental validation data (circles, triangles) of tumor dynamics from a preclinical study , where (A) B16-bearing mice were treated by a 50 µg/day IL-21 treatment applied SC or IP, starting on day 8 after tumor inoculation; (B) RenCa-challenged mice were treated by IL-21, 50 µg 3×/week, SC or IP, commencing either early (day 7) or late (day 12) after tumor inoculation; (C) RenCa-bearing mice were SC-administered various IL-21 doses between 1–20 µg (3×/week), or given a 30 µg (1×/week) regimen. Data are given as means±SEM.

Figure 4. Model-improved IL-21 therapies with modified onset and fractionation.

(A) Predicted outcomes (final B16 volumes; squares) of 20-day regimens (50 µg/day given SC) initiated on different days. (B) Predicted outcomes of regimens with the same total IL-21 dose (800 µg/treatment given SC) yet with different fractionations (i.e. number of injections, inter-dosing intervals and dose intensities). (C) Prospective validation of the model predictions (lines) in B16-bearing mice treated by a standard (std) 50 µg/day regimen vs. a fractionated (frac) 25 µg/twice daily schedule, both administered SC between days 3–20 (data in circles). Tumor growth in PBS controls is indicated as well. Means±SEM of data are given (n = 10; *p<0.001 for 25 µg-treated mice vs. PBS-treated mice, and for 50 µg-treated mice vs. PBS-treated mice; **p<0.05 for 25 µg-treated mice vs. 50 µg-treated mice).

Figure 5. Model-improved alternative-dosing IL-21 regimens.

(A) Predicted outcomes (final B16 volumes) of various 20-day treatments (initialized at day 3, and given SC), where different daily dose are applied (squares). (B) Experimental B16 dynamics following prospective treatments under the standard (std) 50 µg/day regimen, or under a model-based reduced-dosing (low) schedule (12 µg/day). Data (circles) are shown vs. model simulations (lines). Tumor growth in PBS controls appears as well. Means±SEM of data are indicated (n = 10; *p<0.05 for 12 µg-treated mice vs. PBS-treated mice; **p<0.001 for 50 µg-treated mice vs. PBS-treated mice; ns-not significant for 12 µg-treated mice vs. 50 µg -treated mice).