Fig 1.
Steps for modeling NO˙-cGMP signaling pathway.
The reaction schema: NO˙ is synthesized in a generator cell and freely diffuses, either within the same cell or to a target cell, to activate sGC; sGC is oxidized by H2O2 and inactivated. Either sGC or NO˙-sGC can convert GTP to cGMP, which is degraded by PDE to GMP. Note that oxidative stress drives the system toward the oxidative limb, and that the goal of pharmacological modulation of this pathway is to reverse the adverse effects of oxidative stress and to minimize PDE inhibition in order to optimize cGMP levels. NAC can be used as an antioxidant (impairing hydrogen peroxide-dependent oxidation of SGC and, perhaps, oxidation of NO˙), sildenafil as a PDE5 inhibitor, and SNAP as an NO˙ donor to modulate this pathway experimentally. Abbreviations: cGMP, cyclic guanosine 3', 5'-monophosphate; GMP, guanosine-5'-monophosphate; GTP, guanosine-5'-triphosphate; H2O2, hydrogen peroxide; NAC, N-acetylcysteine; NO˙, nitric oxide; NOx, oxidized (inactive) nitrogen oxides; PDE, phosphodiesterase; SNAP, S-Nitroso-n-nacetylpenicillamine; sGC, soluble guanylyl cyclase.
Fig 2.
Monitoring cGMP levels after single perturbation of oxidatively impaired NO˙-cGMP pathway.
(A) The effect of H2O2 on cGMP dynamics. H2O2 caused ~6-fold reduction in cGMP levels. (B and C) Reducing either k3 or k10 during oxidative stress was not an effective perturbation for restoring cGMP to the normal level. The value of k3 or k10 was reduced to 10% of their original values (S1 Table), with perturbation of k3 or k10 denoted as ρk3 and ρk10, respectively. While these perturbations can be effective strategies in enhancing cGMP levels in the absence of H2O2, they are not effective in restoring cGMP levels to normal in the presence of H2O2. (D) All single perturbations of the NO˙-cGMP pathway in the presence of H2O2. The cGMP levels were monitored in the absence of H2O2. Subsequently, in the presence of H2O2, the system was perturbed by reducing one of thirteen rate constants (k1‒k13) to 10% of their original values, denoted as ρks, and then the cGMP levels calculated. Note that ρk1, ρk3, ρk10, and ρk12 markedly increased the cGMP levels beyond other perturbations.
Fig 3.
Relative cGMPT levels after single, paired, and triple kinetic perturbations of the oxidatively impaired NO˙-cGMP pathway.
The relative level of cGMPT as a function of all possible single (13 brown bars), paired (78 gray bars), and triple (286 green bars) perturbations is shown. Values of the rate constants were reduced to 10% of their original values (S1 Table). Each bar shows the relative integrated cGMP levels over the period of simulation, or . Note that some of the optimal perturbations are highlighted in this figure.
Fig 4.
The effects of linear reduction of values for three individual rate constants on cGMP dynamics.
Using the linear reduction of values for k1, k3, and k10, we created a vector of eleven different values for each of these rate constants. We next generated three linearly spaced vectors for each of the rate constants by fractionally reducing each decrementally. Using these vectors of rate constants, cGMP dynamics were calculated. The cGMP levels after serial reduction of (A) k1, (B) k2, and (C) k3. (D) The relative cGMP levels. Data are shown as mean (dashed lines) ± S.E.M (shaded lines) of 11 simulated replicates. Note: k3 was the most sensitive parameter in cGMP accumulation as compared with k1 and k10. In addition, the highest cGMP levels were achieved at ~40 seconds.
Fig 5.
Pairwise perturbation of optimal rate constants increased cGMP levels beyond that predicted by the Bliss model.
Comparison of cGMP levels after individual and pairwise perturbation of (A) k1 + k3, (B) k1 + k10, and (C) k3 + k10 with the Bliss model [generated using the perturbation of corresponding individual rate constants and applying eq (15) in the Supplement]. Single perturbations were used to predict paired perturbation signatures. The simulated combination produced cGMP levels that were greater than those predicted by the Bliss model.
Fig 6.
Pairwise or triple perturbations of three agents additively enhance the cGMPT levels.
(A-C) The cGMPT dose matrix-responses to all possible combined perturbations of three rate constants. We iteratively reduced the rate constants by fractional decrements with ρ defined as the (normalized) perturbation ratio with values either 0.3 or 0.5 for pairwise or triple perturbations, respectively. For pairwise perturbations, two vectors of rate constants were combined in 11×11 matrices in which the value of each rate constant was fractionally reduced by linear decrements along each axis. The combined effects of (A) k1 plus k3, (B) k1 plus k10, and (C) k3 plus k10 on cGMPT levels. (D-E) The contour plots illustrate that the pairwise perturbations exerted additive effects on cGMPT levels. (G-I) The cGMP dose matrix responses to the triple perturbation of k1, k3, and k10. Three vectors of rate constants were combined in 11×11×11 matrices in which the value of each rate constant was linearly reduced along each axis. (J-L) The contour plots reveal additive augmentation of cGMPT levels.
Fig 7.
Increases in cGMP in PAVSM cells in the presence and absence of pharmacological agents that affect the cGMP pathway.
In (A) and (B), PAVSM cells were pre-incubated for 90 min with buffer, 10 mM NAC (N-acetylcysteine), or 100 nM sildenafil (sild), followed by 30 min incubation with 500 μM hydrogen peroxide. Cells were then incubated with 100 μM SNAP for 10 min prior to harvesting for cGMP determination. Panel (A) shows a representative experiment, with three biological replicates under each condition. Shown in (B) are the averages of 3–4 separate experiments with each condition tested in duplicate or triplicate. Sildenafil, NAC, H2O2, plus SNAP condition was not significantly different from the sildenafil plus SNAP condition; these two conditions (* indicates p<0.05 by ANOVA followed by a Newman-Keuls test) were significantly different from all other conditions.