Mathematical model for non-monotone dose response to the PD-L1 blockade in vitro

Abstract Testing of new small molecules for oncotherapy often requires discrimination between the actual, target-specific bioactivity and non-specific toxicity. We present a mathematical model for T-cell reactivation under the action of therapeutic compounds targeting the PD-1/PD-L1 interaction in a co-culture in vitro setup. The model enables the estimation of the maximum safe concentration and the EC 50 value for T-cell activation from experimental data representing non-monotonic dose responses. The model describes the dose-dependent change in the strength of the luminescence signal using a system of ordinary differential equations. The estimates for the model parameters are based on experimental measurements of the signal for different concentrations of the compound. They are then used to calculate two parameters: C max_resp – the concentration of the tested molecule at which maximal T-cell activation is achieved (illustrating a maximal safe concentration), and EC 50 (reflecting the potency of the molecule) via a Monte Carlo method. By incorporating mechanistic assumptions regarding compound-induced T-cell activation and concentration-dependent toxicity, the model provides a coherent explanation of the observed luminescence trajectories across the entire dose range. The model serves as a platform supporting rational drug candidate optimization strategies within the domain of immune checkpoint modulation.