Combination therapy for melanoma with BRAF/MEK inhibitor and immune checkpoint inhibitor: a mathematical model

The B-raf gene is mutated in up to 66% of human malignant melanomas, and its protein product, BRAF kinase, is a key part of RAS-RAF-MEK-ERK (MAPK) pathway of cancer cell proliferation. BRAF-targeted therapy induces significant responses in the majority of patients, and the combination BRAF/MEK inhibitor enhances clinical efficacy, but the response to BRAF inhibitor and to BRAF/MEK inhibitor is short lived. On the other hand, treatment of melanoma with an immune checkpoint inhibitor, such as anti-PD-1, has lower response rate but the response is much more durable, lasting for years. For this reason, it was suggested that combination of BRAF/MEK and PD-1 inhibitors will significantly improve overall survival time.

It will be important to identify, by animal experiments or by early clinical trials, the zones of (γ B ,γ A ) where antagonism occurs, in order to avoid these zones in more advanced clinical trials.

This paper develops a mathematical model to address the question of the correlation between BRAF/MEK inhibitor and PD-1 inhibitor in melanoma therapy. The model includes dendritic and cancer cells, CD 4+ and CD 8+ T cells, MDSC cells, interleukins IL-12, IL-2, IL-6, IL-10 and TGF- β, PD-1 and PD-L1, and the two drugs: BRAF/MEK inhibitor (with concentration γ B ) and PD-1 inhibitor (with concentration γ A ). The model is represented by a system of partial differential equations, and is used to develop an efficacy map for the combined concentrations (γ B ,γ A ). It is shown that the two drugs are positively correlated if γ B and γ A are at low doses, that is, the growth of the tumor volume decreases if either γ B or γ A is increased. On the other hand, the two drugs are antagonistic at some high doses, that is, there are zones of (γ B ,γ A ) where an increase in one of the two drugs will increase the tumor volume growth, rather than decrease it. Conclusions: It will be important to identify, by animal experiments or by early clinical trials, the zones of (γ B ,γ A ) where antagonism occurs, in order to avoid these zones in more advanced clinical trials.