Cancer immunotherapy is a rapidly developing field, with numerous drugs and therapy combinations waiting to be tested in pre-clinical and clinical settings. However, the costly and time-consuming trial-and-error approach to development of new treatment paradigms creates a research bottleneck, motivating the development of complementary approaches. Computational modelling is a compelling candidate for this task, however, difficulties associated with the validation of such models limit their use in pre-clinical and clinical settings. Here we propose a bottom-up deterministic computational model to simulate tumour response to treatment with anti-programmed-death-1 antibodies (anti-PD-1). The model was built with validation in mind, and so contains minimum number of parameters, and only four free parameters. Moreover, all model parameters can be measured experimentally. Free parameters were tuned by fitting the model to experimental data from the literature, using B16-F10 murine melanoma implanted into wild type (C57BL/6), as well as into immunodeficient (NSG) mice strains, and treated with anti-PD-1 antibodies. The model's predictive ability was verified on two independent datasets from literature with different but well-known inputs. To identify possible biomarkers of response to anti-PD-1 immunotherapy, sensitivity study of key model parameters was performed. Good agreement between the simulated tumour growth curves and the experimental data was achieved, with mean relative deviations in the range of 13%-20%. Our sensitivity study demonstrated that major histocompatibility complex (MHC) class I expression was the only parameter able to clearly discriminate responders from non-responders to anti-PD-1 therapy. Additionally, the results of sensitivity studies suggest that MHC class I expression might affect the predictive ability of other biomarkers that are currently used in the clinics, such as PD-1 ligand (PD-L1) expression. Interestingly, our model predicts the best response to anti-PD-1 therapy for subjects with moderate PD-L1 values. Such computational models show promise to support, guide and accelerate future immunotherapy research.