AbstractSimultaneous inhibition of multiple components of the BRAF-MEK-ERK cascade (vertical inhibition) has become a standard of care for treating BRAF-mutant melanoma. However, the molecular mechanisms of how vertical inhibition synergistically suppress intracellular ERK activity, and as a consequence cell proliferation, are yet to be fully elucidated.In this study, we develop a mechanistic mathematical model that describes how the mutant BRAF-inhibitor, dabrafenib, and the MEK-inhibitor, trametinib, affect signaling through the BRAFV600E-MEK-ERK cascade. We formulate a system of chemical reactions that describes cascade signaling dynamics and, using mass action kinetics, the chemical reactions are re-expressed as ordinary differential equations. Using model parameters obtained from in vitro data available in the literature, these equations are solved numerically to obtain the temporal evolution of the concentrations of the components in the signaling cascade.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 melanoma cells. This 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, the computational simulations suggest that elevated ATP levels could be a factor in drug resistance to dabrafenib. The mathematical model that is developed in this study will have generic application in the improved design of anticancer combination therapies that target BRAF-MEK-ERK pathways.
Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance