Mathematical modelling quantifies ERK-activity in response to vertical inhibition of the BRAFV600E-MEK-ERK cascade in melanoma

Vertical inhibition of the BRAF-MEK-ERK cascade has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanisms of how vertical inhibition synergistically suppresses intracellular ERK activity, and by extension cell proliferation, are yet to be fully elucidated. In this study, we develop a mechanistic mathematical model that describes how the BRAFV600E-inhibitor dabrafenib, and the MEK-inhibitor trametinib target the BRAFV600E-MEK-ERK cascade. We formulate a system of chemical reactions that describes cascade signalling dynamics. Using mass action kinetics, the system of chemical reactions is re-expressed as a system of ordinary differential equations, which we solve numerically to obtain the temporal evolution of cascade component concentrations.Our mathematical model provides a quantitative method to compute how dabrafenib and trametinib can be used in combination to synergistically inhibit ERK activity in BRAFV600E mutant cancer cells. Our work elucidates molecular mechanisms of vertical inhibition of the BRAFV600E-MEK-ERK cascade, and delineates how elevated cellular BRAF concentrations generate drug resistance to dabrafenib and trametinib. In addition, our model results suggest that elevated ATP levels lead to reduced sensitivity to dabrafenib.