Table 1.

Summary of cell death mechanism models.

Authors, Year, Cell Death Mechanism Modeled	Methods. Death Rule (DR)	Results
Fussenegger et al., 2000 [7], receptor- and stress-induced apoptosis	ODE approach. DR: the ratio of executioner caspase to free Bcl-xL is greater than a threshold value	Qualitative explanation of observed caspase activation dynamics
Eissing et al., 2004 [21], receptor-induced apoptosis	ODE approach, stability and bifurcation analysis methods. DR: The bistable system is in apoptotic steady state	Bistable behavior of caspase-3 activation
Bentele et al., 2004 [25], receptor-induced apoptosis	ODE approach, sensitivity analysis. DR: receptor–ligand ratio is greater than a threshold value	A threshold mechanism for induction of receptor-induced apoptosis
Hua et al., 2005 [43], receptor-induced apoptosis	ODE approach, sensitivity analysis. DR: caspase-3 activation	Bcl-2 blocks the mitochondrial apoptosis pathway by binding to proapoptotic proteins
Legewie et al., 2006 [22], intrinsic apoptosis	ODE approach, stability and bifurcation analysis methods. DR: irreversible caspase-3 activation	Bistable and irreversible caspase-3 activation arises in the system due to XIAP-mediated feedback
Rehm et al., 2006 [26], intrinsic apoptosis	ODE approach, sensitivity analysis. DR: complete caspase-dependent substrate cleavage	All-or-none apoptotic response depends on caspase-3-dependent feedback signaling and XIAP
Bagci et al., 2006 [23], mitochondria-dependent apoptosis	ODE approach. DR: caspase-3 activation is above a threshold that depends on Bax degradation and expression rates.	The transition from bistable to monostable (survival) cell behavior is controlled by the number of mitochondrial permeability transition pores
Chen and Cui et al., 2007, 2008 [38,45,46], intrinsic apoptosis	Deterministic and stochastic approaches, robustness analysis. DR: one-way bistable switch of Bax-activation	Apoptotic switches are bistable and robust to noise
Albeck et al., 2008 [27], extrinsic apoptosis	ODE approach, compartmental modeling. DR: mitochondria-to-cytosol cytochrome c and Smac translocation in an all-or-none manner	Permeabilization of the mitochondrial membrane and relocalization of proteins are the key factors in all-or-none death decision
Spencer et al., 2009 [33], extrinsic apoptosis	ODE approach. DR: levels of activated tBid, Bax, and Bak exceed a threshold set by inhibitory Bcl-2 proteins	Cell-to-cell variability in time-to-death depends on activation of the pore-forming proteins Bax and Bak
Neumann et al., 2010 [32], crosstalk between receptor-mediated apoptosis and NF-κB signaling	ODE approach, sensitivity analysis. DR: the maximum level of active caspase-8 is used as a readout for apoptosis	Assembly of DISC acts as a signal processor determining life/death decisions in a nonlinear manner
Hong et al., 2012 [28], crosstalk between apoptosis and ER stress response mechanisms	ODE approach, sensitivity analysis. DR: the level of apoptosis is determined by an ODE that depends on caspases-2,3,9,8 and apoptosis-inducing factor	Crosstalks among the mitochondrial, death receptor and ER stress response pathways contribute to the level of apoptosis
Tavassoly et al., 2015 [29], crosstalk between autophagy and apoptosis	ODE approach. DR: apoptosis occurs as soon as proapoptotic BH3 exceeds antiapoptotic Bcl2 protein	Time courses of the relative level of autophagy for different levels of stressor and percentage of apoptotic cells
Ballweg et al., 2017 [30], crosstalk between p53 signaling and apoptosis	ODE approach, dynamical analysis. DR: the level of p53 is elevated higher than a threshold that depends on cIAP level	The probability of apoptosis depends on the dynamics of p53
Schlatter et al., 2009 [34], apoptosis	Boolean logic and multi-value logic approach	High connectivity, crosstalks, and feedback loops in apoptosis regulatory network are significant and essential for apoptosis signaling
Mai et al., 2009 [35], intrinsic and extrinsic apoptosis	Boolean logic approach. DR: the “DNA Damage Event’’ node has remained in the ON state for 20 successive steps	The feedback loops directly involving the caspase 3 are essential for maintaining irreversibility of apoptosis
Calzone et al., 2010 [36], apoptosis and non-apoptotic cell death (necroptosis)	Boolean logic approach. DR: “Apoptosis” node or “NonACD” node is in ON state	Transient activation of key proteins in necroptosis and mutual inhibitory crosstalks among apoptosis, survival and necroptosis pathways
Xu et al., 2021 [8], cellular necroptosis signaling circuits	ODE approach, sensitivity analysis, bifurcation and potential landscape methods.	The structure and distribution characteristics of all parameters are essential for stable oscillation behavior of necroptosis circuits
Ildefonso et al., 2022 [59], necroptosis regulation	ODE approach, DREAM parameter estimation method, sensitivity analysis. DR: phosphorylated MLKL exceeds a hard threshold of 2772 molecules	Four distinct necroptosis execution modes
Li et al., 2021 [65], crosstalk between apoptosis and necroptosis regulatory networks.	ODE approach. DR: apoptosis occurs when RIP1 level < ∼1000 molecules/cell, co-occurrence of apoptosis and necroptosis when ∼46,000 mpc< RIP1 > ∼1000 mpc, necroptosis alone when RIP1 >∼46,000 mpc	Characterization of RIP1’s biphasic roles in necroptosis
Zhu et al. [9], crosstalk between caspase-1 and caspase-3 driven pyroptosis pathways	ODE approach, bifurcation and sensitivity analysis methods. DR: Cell death rate is defined using a ratio of dying cell population to the initial cell population	The change in expression levels of caspase-1, caspase-3, and GSDMD can switch between GSDMD- and GSDME-executed pyroptosis death modes
Li et al., 2022 [73], crosstalk between pyroptosis and apoptosis regulations	ODE and potential energy landscape approaches. DR: by levels of cleaved GSDMD (pyroptosis) and cleaved caspase-3 (apoptosis)	Caspase-1 and GSDMD are key proteins that regulate the switching between pyroptosis and apoptosis
Konstorum et al., 2020 [10], ferroptosis regulation	Stochastic, multistate, discrete mathematical approach. DR: intermediate and high levels of the lipid radical LO*	Ferroptosis sensitivity depends on PUFA synthesis, PUFA incorporation into the phospholipid membrane, and the balance between levels of pro-oxidant species and antioxidant factors
Checcoli et al., 2020 [11], immunogenic cell death (ICD) mechanism	Boolean Kinetic Monte-Carlo approach. DR: Death node is at 1	The succession of events resulting in ICD. Points of intervention that had the strongest effect on ICD