The human ex-vivo data, including initial concentrations and the dynamic range and changes of different Th1-related cell types and cytokines, were integrated into the systems biology model to determine a nominal parameter set, see Fig. 6a. First, the initial cytokine levels and T-cell populations used in numerical simulations were sampled from the patient (control) data. Then the MATLAB genetic algorithm with the ode15s solver was used to integrate the system of coupled ODEs, where the kinetic parameter ranges were set to previously reported biologically relevant ranges when possible (see Supplementary Section B for details). To simulate the 72-h experimental treatment protocol on the model system, we administered nivolumab treatment at t = 0, 24, 48 h. Drug washout between subsequent doses of nivolumab treatment was simulated by setting the free drug level to zero immediately before administering the next dose. The objective function was coded with the constraint that over the 72-hour treatment window, the simulated cytokine expression levels must fall within the range set by the average ±1 standard deviation of the patient data (with nivolumab treatment) at times t = 24, 48, 72 h. Similarly, the T-cell populations were forced to lie between average ±1 standard deviation at t = 72 h (with nivolumab treatment). Using this approach, it is conceivable that there could be many sets of parameters that fit the average patient data. The nominal parameter set that we obtained is presented in Supplementary Table 3.

a determine nominal parameter sets by matching to the average patient data and b use Latin hypercube sampling (LHS) to perform global sensitivity analysis and simulate a large patient clinical trial.

Importantly, this nominal parameter set led to a ‘responder’ phenotype. In this work, we define ‘responder’ as a patient whose tumor size at t = 72 h after treatment is less than or equal to the initial tumor size before treatment. However, it can be anticipated that in the ‘non-responder’ category there will be several sub-phenotypes. For example, for some patients, the treatment may have zero effect, thus their tumor will grow at its normal rate. For others, the treatment may have a negative effect and may accelerate tumor growth. Investigation of the hierarchy of these sub-phenotypes is left for a future work. However, given the variability in patient response to nivolumab treatment that was observed in the human ex-vivo experiments27, we aimed to capture such variability and understand more about the putative mechanisms of intrinsic drug resistance. To this end, we previously performed both local and global sensitivity analysis27. Importantly, we found that small perturbations to a single kinetic parameter and/or initial condition via local sensitivity analysis of the model were not sufficient to change the nature of the response to the treatment, i.e. to induce a ‘non-responder’ phenotype. Induction of a ‘non-responder’ phenotype was accomplished via global sensitivity analysis, see Fig. 6b, which involved randomly changing all the initial cytokine levels and initial T-cell populations and/or the values of the kinetic parameters of the model simultaneously to generate virtual patients in a large simulated clinical trial.

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