The Bcl-2-associated death promoter (BAD) lowers the threshold at which the Bcl-2-interacting domain death agonist (BID) triggers mitochondria disintegration

The Bcl-2-associated death promoter (BAD) protein, like many other BH3-only proteins, is known to promote apoptosis through the intrinsic mitochondrial pathway. Unlike the BH3-interacting domain death agonist (BID) protein, BAD cannot directly trigger apoptosis but, instead, lowers the threshold at which apoptosis is induced. In many mathematical models of apoptosis, BAD is neglected or abstracted. The work presented here considers the incorporation of BAD and its various modifications in a model of the tBID-induction of BAK (Bcl-2 homologous antagonist killer) or the tBID-induction of BAX (Bcl-2-associated X protein). Steady state equations are used to develop an explicit formula describing the total concentration level of tBID, guaranteed to trigger apoptosis, as a bilinear function of the total BAD concentration level and the total anti-apoptotic protein concentration level (usually Bcl-2 or Bcl-x_L). In particular, the formula explains how the pro-apoptotic protein BAD lowers the threshold at which tBID induces BAK/BAX activation—reducing the level of total Bcl-2/Bcl-x_L available to inhibit tBID signaling in the mitochondria. Attention is then turned to the experimental data surrounding BAD phosphorylation, a process known to inhibit the pro-apoptotic effects of BAD. To address this data, the phosphorylation process is modeled following two separate kinetics in which either free unbound BAD is the assumed substrate or Bcl-x_L/Bcl-2-bound BAD is the assumed substrate. Bifurcation analysis and further analysis of the bilinear equation validate experiments, which suggest that BAD phosphorylation prevents irreversible BAK/BAX-mediated apoptosis, even when phosphorylation-induced dissociation of Bcl-x_L/Bcl-2-bound BAD is blocked. It is also shown that a cooperative, even synergistic, removal of mitochondrial BAD is seen when both types of phosphorylation are assumed possible. The presented work, however, reveals that the balance between BAD phosphorylation and dephosphorylation modulates the degree to which BAD influences the signaling from tBID to BAK/BAX. Our model shows that both the mode(s) of phosphorylation and the BAD dephosphorylation rate become important factors in determining whether BAD influences the activation of the BAK/BAX signal or not. Such potential variations in the pro-apoptotic effects of BAD are used to explain some of the inconsistent experimental data surrounding BAD phosphorylation. Nonetheless, our model serves to evaluate BAD and its sensitizing effects on the tBID-induction of BAK/BAX and thus aid in predicting when the incorporation of BAD in an apoptosis signaling model is important and when it is not.