Figure 4

Adaptation-dependent fractional killing in an apoptosis model. (a) Some mammalian cell-death pathways associated with fractional killing including the stress-induced mitochondrial pathway of apoptosis (left panel). The detailed model of this study couples the coarse-grained model of stress-induced adaptation module (Eqs. 4a, b) and a published model of the mitochondrial apoptosis initiation module²⁴ (right panel). (b) Death probability as function of the relative stimulus level \(s/s_{50}\) obtained through numerical simulation of Eq. (1) with \(\sigma =0.002\), where \(\eta\) is about four-fold higher with adaptation (\(\beta =1\)) compared to without (\(\beta =0\)). (c–d) Temporal trajectories of \(x_1\) and \(\hbox {Bax}_m\) in the presence or the absence of adaptation (c: \(\beta =1\); d: \(\beta =0\)). Adaptation timescale is set to \(\tau =1.25\mathrm {hr}\) to match with the timescale of the apoptotic switch (time unit is hour). Right panels show a 2D state-space projection of the high-dimensional dynamics with respect to the stable and saddle fixed points (brown and white circles) of the deterministic system.