Computational insights on the competing effects of nitric oxide in regulating apoptosis

Abstract

Despite the establishment of the important role of nitric oxide (NO) on apoptosis, a molecular-level understanding of the origin of its dichotomous pro- and anti-apoptotic effects has been elusive. We propose a new mathematical model for simulating the effects of nitric oxide (NO) on apoptosis. The new model integrates mitochondria-dependent apoptotic pathways with NO-related reactions, to gain insights into the regulatory effect of the reactive NO species N(2)O(3), non-heme iron nitrosyl species (FeL(n)NO), and peroxynitrite (ONOO(-)). The biochemical pathways of apoptosis coupled with NO-related reactions are described by ordinary differential equations using mass-action kinetics. In the absence of NO, the model predicts either cell survival or apoptosis (a bistable behavior) with shifts in the onset time of apoptotic response depending on the strength of extracellular stimuli. Computations demonstrate that the relative concentrations of anti- and pro-apoptotic reactive NO species, and their interplay with glutathione, determine the net anti- or pro-apoptotic effects at long time points. Interestingly, transient effects on apoptosis are also observed in these simulations, the duration of which may reach up to hours, despite the eventual convergence to an anti-apoptotic state. Our computations point to the importance of precise timing of NO production and external stimulation in determining the eventual pro- or anti-apoptotic role of NO.

Figure 1. (A) Mitochondria-dependent apoptotic pathways in Model I.

The dotted box includes the interactions considered in the model. Solid arrows indicate chemical reactions or upregulation; those terminated by a bar indicate inhibition or downregulation; and dashed arrows indicate subcellular translocation. The components of the model are procaspase-8 (pro8), procaspase-3 (pro3), procaspase-9 (pro9), caspase-8 (casp8), caspase-9 (casp9), caspase-3 (casp3), IAP (inhibitor of apoptosis), cytochrome c (cyt c), Apaf-1, the heptameric apoptosome complex (apop), the mitochondrial permeability transition pore complex (PTPC), p53, Bcl-2, Bax, Bid, truncated Bid (tBid). The reader is referred to our previous work for more details. Three compounds (N₂O₃, FeL_nNO and ONOO⁻) not included in the original Model I are highlighted. These compounds establish the connection with the nitric oxide pathways delineated in panel B. (B) Nitric oxide (NO)-related reactions in Model II. The following compounds are included: ONOO⁻ (peroxynitrite), GPX (glutathione peroxidase), O₂ ⁻ (superoxide), GSH (glutathione), GSNO (nitrosoglutathione), GSSG (glutathione disulfide), CcOX (cytochrome c oxidase), SOD (superoxide dismutase), FeL_n (non-heme iron compounds), FeL_nNO (non-heme iron nitrosyl compounds), NADPH (reduced form of nicotinamide adenine dinucleotide phosphate), NADP+ (oxidized form of nicotinamide adenine dinucleotide phosphate). FeL_nNO, ONOO⁻ and N₂O₃, highlighted in both panels A and B, bridge between Models I to II. Model III integrates both sets of reactions/pathways through these compounds. GSH modulates their concentrations by reacting with them. GSH is converted by these reactions to GSNO, which is then converted to GSSG and finally back to GSH. Those compounds and interactions are shown in blue. See Table 1 for the complete list of reactions and rate constants.

Figure 2. Time evolution of [casp3] predicted by a bistable model in response to different strengths of apoptotic stimuli, A) in a cell subjected to a weak EC apoptotic signal (reflected by the low concentration [caps8]₀); B) in a cell that is subjected to a stronger EC pro-apoptotic signal.

Caspase-3 is activated at 60 minutes; C) in a cell that is subjected to a stronger EC pro-apoptotic signal than one in panel B. Caspase-3 is activated at 30 minutes. Panels A and B illustrate two opposite effects induced by different initial concentrations of caspase-8. The threshold concentration of [caps8]₀ required for the switch from anti-apoptotic to pro-apoptotic response is calculated to be 8.35×10⁻⁵ µM. Panels B and C illustrate the shift in the onset time of apoptosis depending on [casp8]₀. D) Dependence of apoptotic response time on the initial caspase-8 concentration. The ordinate is the onset time of caspase-3 activation, and the abscissa is the initial concentration of caspase-8 in excess of the threshold concentration required for the initiation of apoptosis (evidenced by increase in [casp3], see panels B–C). The onset time of caspase-3 activation exhibits a logarithmic decrease with Δ[casp8]₀ ([casp8]₀–8.35×10⁻⁵ µM).

Figure 3. Time evolutions of A) GSH, B) N₂O₃, C) FeL_nNO, and D) ONOO⁻ predicted by Model II.

N₂O₃ and FeL_nNO increase to high concentrations by a switch-like mechanism induced by a decrease in GSH concentration due to conversion of GSH to GSNO and subsequently to GSSG. [ONOO⁻] does not follow a similar switch-like increase in its concentration. Solid curve is for [GSH]₀ = 10⁴ µM, dotted curve for [GSH]₀ = 10³ µM, and dashed curve with diamonds for [GSH]₀ = 10² µM. The response is thus sharper and earlier in the presence of lower initial concentrations of GSH.

Figure 4. Time evolutions of [GSH] and [casp3] predicted by Model III in the presence of N₂O₃ effects.

Here, in order to visualize the effect of N₂O₃ exclusively, the reaction (xxii) in Table 4 is included in the model while those involving FeL_nNO and ONOO⁻ (reactions (xx, xxiii-xxv) are not, assuming FeL_n concentration and rate of formation of superoxide to be zero. The solid curves depict the time evolution of [casp3], and dotted curves refer to [GSH]. The three rows of panels are the counterparts of those in Figure 2 A–C, with the different columns referring to different initial concentrations of GSH: A–C) [GSH]₀ = 10³ µM; D–F) [GSH]₀ = 10² µM; G–I) [GSH]₀ = 0 µM.

Figure 5. Time evolutions of [GSH] and [casp3] predicted by Model III in the presence of N₂O₃ and FeL_nNO.

N₂O₃ is present in the model ([O₂] is non-zero) as well as FeL_nNO ([FeL_n]₀ is non-zero). Each column is a counterpart of Figure 2A–C with different initial concentrations of GSH. A–C) [GSH]₀ = 10⁴ µM; D–F) [GSH]₀ = 10³ µM. Solid curve shows the time evolution of [casp3] and dotted curve that of [GSH].

Figure 6. Time evolutions of [GSH] and [casp3] predicted by Model III in the presence of N₂O₃, FeL_nNO and ONOO⁻.

The initial concentration of PTPC is 0.01 µM. Each column is a counterpart of Figure 2A–C and has a different initial concentration for GSH. A–C) [GSH]₀ = 10⁴ µM; D–F) [GSH]₀ = 10³ µM. Solid line is for time evolution of [casp3] and dashed line is for time evolution of [GSH]. Caspase-3 concentrations at long times are 2.4 ×10⁻⁴ µM and 2.5×10⁻⁸ µM for panels A–C and D–F, respectively.

Figure 7. Time evolutions of [GSH] and [casp3] predicted by Model III in the absence of N₂O₃, FeL_nNO and presence of ONOO⁻.

The initial concentration of PTPC is 0.0001 µM. A–C) [GSH]₀ = 10⁴ µM; D–F) [GSH]₀ = 10² µM. Solid line is for time evolution of [casp3] and dashed line is for time evolution of [GSH].