Response of patients with melanoma to immune checkpoint blockade - insights gleaned from analysis of a new mathematical mechanistic model

J Theor Biol. 2020 Jan 21:485:110033. doi: 10.1016/j.jtbi.2019.110033. Epub 2019 Sep 30.


Immune checkpoint inhibitors (ICI) are becoming widely used in the treatment of metastatic melanoma. However, the ability to predict the patient's benefit from these therapeutics remains an unmet clinical need. Mathematical models that predict melanoma patients' response to ICI can contribute to better informed clinical decisions. Here, we developed a simple mathematical population model for pembrolizumab-treated advanced melanoma patients, and analyzed the local and global dynamics of the system. Our results show that zero, one, or two steady states of the mathematical system exist in the phase plane, depending on the parameter values of individual patients. Without treatment, the simulated tumors grew uncontrollably. At increased efficacy of the immune system, e.g., due to immunotherapy, two steady states were found, one leading to uncontrollable tumor growth, and the other resulting in tumor size stabilization. Model analysis indicates that a sufficient increase in the activation of CD8+ T cells results in stable disease, whereas a significant reduction in T-cell exhaustion, another process contributing CD8+ T cell activity, temporarily reduces the tumor mass, but fails to control disease progression in the long run. Importantly, the initial tumor burden influences the response to treatment: small tumors respond better to treatment than larger tumors. In conclusion, our model suggests that disease progression and response to ICI depend on the ratio between activation and exhaustion rates of CD8+ T cells. The analysis of the model provides a foundation for the use of computational methods to personalize immunotherapy.

Keywords: Cancer immunotherapy; Hopf bifurcation; Pembrolizumab; Phase-plane analysis; Simulation.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Antibodies, Monoclonal, Humanized* / therapeutic use
  • Humans
  • Immune Checkpoint Inhibitors*
  • Immunotherapy
  • Melanoma* / drug therapy
  • Models, Theoretical
  • Skin Neoplasms* / drug therapy


  • Antibodies, Monoclonal, Humanized
  • Immune Checkpoint Inhibitors