(A) Simplified schematic of receptor-mediated apoptosis signaling, with fluorescent reporters for initiator caspases (IC FRET) and effector caspases (EC FRET) indicated. The MOMP reporter measures mitochondrial outer membrane permeablization.
(B) Steps involved in converting a biochemical cartoon into a reaction diagram and ordinary differential equations. C8* indicates active caspase-8. Lower panels show a model-based 12 hr simulation of the increase in tBid relative to the time of MOMP and analysis of the sensitivity of MOMP time to Bid levels. The simulation in (B) was adapted from Albeck et al. (2008b).

(A and B) Composite plot of effector caspase substrate cleavage measured using a CFP-DEVDR-YFP reporter (A) or initiator caspase substrate cleavage measured using CFP-IETDG-GIETD-YFP (B) for >50 HeLa cells treated with 50 ng/ml TRAIL in the presence of cycloheximide and aligned by the average time of MOMP (red line).
(C) Fitted trajectories for initiator caspase substrate cleavage (assayed using CFP-IETDG-GIETD-YFP) in single HeLa cells treated with 10 ng/ml TRAIL in the presence of cycloheximide (fits are based on sampling at 3 min intervals). Concomitant expression of a reporter for MOMP permits a determination of the time at which mitochondria permeabilize and thus an estimation of the height of the MOMP threshold (yellow circles) and the rate of approach to the threshold (the “slope” of the green lines).
(D) Histograms of time of death in HeLa cells treated with various death ligands in the presence of cycloheximide, as determined by live-cell microscopy.
(A), (B), and (D) were adapted from Albeck et al. (2008b); (C) was adapted from Spencer et al. (2009).

(A) Energy landscape showing frameworks for achieving two distinct states. Left: A bistable system has two stable steady states for all time (once equilibrium is reached), corresponding to alive and dead. Right: A monostable system starts with a single stable “alive” state; once the model starts to evolve, the landscape morphs as proteins are created and destroyed, producing a single stable “dead” state at late times. Making the transition unidirectional requires processes such as a threshold.
(B) Top: Immunoblot analysis of PARP cleavage in HeLa cells treated with 10 ng/ml TRAIL in the presence of cycloheximide; PARP is an effector caspase substrate. Bottom: Simulation of the time course of effector caspase (EC) substrate cleavage in individual cells (blue lines), overlaid with an average (pink line) that depicts the fraction of cells in which caspases have been activated; this average mimics the data obtained by immunoblotting.
(C) Idealized single-cell time course for effector caspase substrate cleavage. The dynamics have the form of a sigmoidal Boltzmann equation in which c(t) is the amount of substrate cleaved at time t, f is the fraction cleaved at the end of the reaction, T_d is the delay period between TRAIL addition and half-maximal substrate cleavage, and T_s is the switching time between initial and complete effector caspase substrate cleavage (the reciprocal of the slope at t = T_d).
(D) Effector caspase substrate cleavage in individual HeLa D98 cells expressing myc-CFP-DEVD-YFP in response to the indicated doses of TNF. Data from each cell have been fit with the sigmoidal Boltzmann function.
(E) Simulation showing effector caspase substrate cleavage as a function of XIAP concentration. At high concentrations, effector caspase substrate cleavage is blocked; at low concentrations, effector caspases are activated rapidly; and at concentrations of XIAP between 0.15 and 0.30 μM, effector caspase substrate cleavage proceeds slowly and only reaches submaximal levels.
(F) A simulation showing how the initial concentrations of procaspase-8 and cFLIP_L determine whether NF-κB is activated, effector caspases are activated, or both after Fas stimulation. The white circle indicates the estimated level of procaspase-8 and cFLIP_L in HeLa-CD95 cells.
(A) and (C) were adapted from Albeck et al. (2008b); (D) was adapted with permission from Rehm et al. (2002), J. Biol. Chem. 277, 24506–24514, copyright 2002 The American Society for Biochemistry and Molecular Biology. All rights reserved; (E) was adapted from Rehm et al. (2006) by permission from Macmillan Publishers Ltd: EMBO J. 25, 4338–4349, copyright 2006. (F) was adapted from Neumann et al. (2010) by permission from Macmillan Publishers Ltd: Mol. Syst. Biol. 6, 352, copyright 2010.