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Modeling the Interaction of Peroxynitrite with Low-density Lipoproteins. I. Plasma Levels of Peroxynitrite
J. theor. Biol. (2000) 205, 457}464 doi:10.1006/jtbi.2000.2079, available online at http://www.idealibrary.com on
Modeling the Interaction of Peroxynitrite with Low-density Lipoproteins. I. Plasma Levels of Peroxynitrite WILLIAM D. STANBRO* 1632 Camino Redondo, ¸os Alamos, NM 87544, ;.S.A. (Received on 8 October 1999, Accepted in revised form on 15 April 2000)
Peroxynitrite is a strong candidate for the material responsible for the initiation of peroxidation of low-density lipoproteins (LDLs) which is considered the "rst step in the formation of atherosclerotic plaque. Recent advances in the understanding of peroxynitrite chemistry allow the construction of a kinetic model that can be used to understand the factors controlling levels in plasma. These results indicate that the carbon dioxide catalysed decomposition of peroxynitrite produces large quantities of reactive species, but the rapid decomposition of this intermediate, ONOOCO\, may limit its availability to attack LDLs at points distant from the site of production. In this case, peroxynitrite itself may be of greater quantitative importance in LDL peroxidation. 2000 Academic Press
Introduction In 1996, 476 818 Americans died of coronary heart disease (CHD) (National Heart, Lung and Blood Institute, 1998). It is generally agreed that the "rst step in the development of CHD is peroxidation of low-density lipoproteins (LDLs). This is believed to occur by a free radical chain reaction. While there are a number of candidates for the initiator of this chain reaction, the identity of the agent is currently unknown (Stanbro, 1999). One possible mechanism is through the intermediary of peroxynitrite, ONOO\, an unstable molecule formed from the reaction of NO and O\. This is the "rst of three planned papers that will use modeling techniques to examine the processes involved in the interaction of ONOO\ with LDLs. This paper will center on the factors governing the levels of ONOO\ in plasma. This will form the boundary conditions for a di!u-
sion/reaction model of the dynamics of ONOO\ with LDLs which will be described in the second paper. The third paper of this series will examine the role of antioxidants in mitigating LDL peroxidation. Model
* E-mail: [email protected]
The general conceptual model for this series of papers is that ONOO\ and related reaction products are produced at some concentration in plasma. The resultant products must then di!use to or into the LDL particle. Once inside the particle ONOO\ would continue to decompose and release reactive products. This paper will produce estimates of the amount of ONOO\ and related species using a chemical kinetic model. The various factors controlling ONOO\ chemistry in plasma will also be examined. Kinetic modeling has proven to be a valuable tool in illuminating the relative importance of individual processes in complex reacting systems (Stanbro, 1998, 1999). The results of this study will provide
0022}5193/00/150457#08 $35.00/0
2000 Academic Press
458
W. D. STANBRO
guidance on the species most likely to be available to penetrate into an LDL particle. The general procedures to be followed include developing a list of the key chemical reactions and their rate constants, using the mass action law to produce di!erential equations describing the time history of each species, numerically solving the equations and varying the pertinent input parameters to further elucidate the nature of the interactions between the various elements in the reacting system (Stanbro, 1998). REACTION CHEMISTRY AND RATE CONSTANTS
The chemistry of the ONOO\ has been the subject of considerable study for a number of years but has proven quite di$cult to understand. However, a number of recent papers have gone quite far in resolving the apparent contradictions in the data (Hurst & Lymar, 1999). The work described in this paper takes advantage of these advances in understanding. Figure 1 is a schematic diagram of ONOO\ chemistry. Note that when ONOO\ is referred to in this paper it includes not only the ONOO\ ion, but also its conjugate acid, ONOOH, unless they are speci"cally di!erentiated. The balanced reactions and the associated rate constants in the model are shown in Table 1. The sources of the rate constants are presented below. ONOO\ is formed by the near-di!usionlimited reaction of NO and O\. Pulse radiolysis studies of this reaction provides estimates of the
rate constant of from 4.3;10 (Huie & Padmaja, 1993) to 6.7;10 M\ s\ (Goldstein & Czapski, 1995). This paper assumes a value of 5;10 M\ s\. Once formed ONOO\ can undergo a backreaction to the products. The measured rate constant for this process in 0.017 s\ (Logager & Sehested, 1993). This rate constant was also determined by a pulsed radiolysis study. Once formed the ONOO\ ion is relatively stable. However, the conjugate acid readily decays. The overall rate constant for the decay process has been measured under physiological conditions (7.4 pH, 373C) to be 0.69 s\ (Pfei!er et al., 1997). It has been observed that approximate 60}70% of the product of the decay is the nitrate ion (NO\). The balance seems to be the hydoxide radical ('OH) and nitrogen dioxide ('NO ) (Goldstein et al., 1998; Coddington et al., 1999). The interpretation of the reaction is that HONOO homolyses to 'OH and 'NO , but that the radicals are trapped in a solvent cage. The majority of the radicals combine and rearrange to form NO\. The remainder escape the cage and are responsible for the observed oxidizing capabilility of ONOO\. This paper takes the rate constant for the formation to NO\ to be 70% of the total rate constant (0.69 s\) and the rate constant for the formation of 'OH and 'NO to be 30% of the total. Further complicating the chemistry of ONOO\ was the discovery that its decomposition is catalysed by CO (Keith & Powell, 1969; Radi et al., 1993). The "rst step in this process is formation of a ONOO\/CO adduct (ONOOCO\) (Lymar & Hurst, 1995). This is
TABLE 1 Model Reactions and rate constants* Reactions
FIG. 1. Schematic diagram of the formation and decay reactions of peroxynitrite considered in the model. The k's refer to the rate constants in Table 1.
(1) (2) (3) (4) (5) (6) (7)
Rate constants
NO#O\PONOO\ k "5;10 M\ s\ ONOO\PNO#O\ k "0.017 s\ ONOO\P)NO #)OH k "0.207 s\ HONOOPNO\#H> k "0.483 s\ ONOO\#CO PONOOCO\ k "5.8;10 M\ s\ ONOOCO\P)NO #)CO\ k "3;10 s\ ONOOCO\PNO\#CO k "7;10 s\
* Sources of all rate constants are given in the text.
PLASMA PEROXYNITRITE LEVELS
signi"cant because of the bu!ering of many biological systems by the CO /bicarbonate/carbon ate system. In plasma, the expected CO levels are of the order of 1.3 mM (corresponding to 25 mM bicarbonate). Based on a measurement of the formation of ONOOCO\ under physiolo gical conditions (Denicola et al., 1996), the model uses a rate constant of 5.8;10 M\ s\. ONOOCO\ rapidly decomposes with the ma jor products being NO\ and CO . As in the case of HONOO decomposition, the reaction proceeds through the formation of two radicals in a solvent cage. In this case, the radicals are the carbonate radical anion, 'CO\, and 'NO (Lymar & Hurst, 1996; Lymar et al., 1996; Goldstein & Czapski, 1997; Lymar & Hurst, 1998, Goldstein & Czapski, 1998, 1999). Again, some of the radicals escape the cage to participate in oxidation reactions (Goldstein & Czapski, 1997). The formation of 'CO\ has been demonstrated experimentally (Meli et al., 1999; Bonini et al., 1999). In aqueous solution, the proportion escaping is about 30}35% (Goldstein & Czapski, 1997, 1998, 1999). There are no measurements of the decomposition rate of ONOOCO\. On thermodynamic grounds, the total rate constant is expected to be 1.5;10 s\ (Merenyi & Lind, 1997). In this model, the rate of decomposition to NO\ is taken to be 70% of 1;10 and 30% of 1;10 for the formation of the free radicals. The e!ect of varying this rate constant is examined below. The model neglects any direct reaction between either ONOO\ or ONOOCO\ and other components of plasma. While such reactions are possible, they would have to compete with the reaction of CO and the rapid decomposition of the adduct. Experimental data seem to indicate that direct reaction is limited and that the primary means by which ONOO\ exerts is oxidizing e!ect is through its decomposition products (Squadrito et al., 1995; Jackson et al., 1998). This will be considered in more detail in the third paper in this series. Although not considered in this model, the free radical products of ONOO\ and ONOOCO\ decomposition do react readily with plasma components (Squadrito et al., 1995; Bartlett et al., 1995; Lymar et al., 1996; Jackson et al., 1998; Alvarz et al., 1999) such as human serum albumin
459
and ascorbate ion. These reactions may be expected to rapidly scavenge highly reactive species so few will survive to directly attack LDL particles. MODEL IMPLEMENTATION
From the reactions in Table 1 the appropriate ordinary di!erential equations (ODEs) were formed for each of the species of interest using the mass action law. A di!erential equation is written for each species whose concentration may change during the simulation. The di!erential equations are shown in Table 2. The terms in the di!erential equation are the products of the appropriate rate constants and the concentrations of the reactants (the species on the left hand of the arrows in Table 1) with any suitable stoichiometric coe$cients. As is usual in studies in aqueous solution, the concentrations of the components of the water system (H O, H>, OH\) are held constant and subsumed into the pH-dependent rate constants. Most naturally occurring systems are open, that is matter and energy are exchanged with the rest of the environment. In the blood stream, components are being swept along while di!erent chemical species are di!using into and out of the various structures in suspension in the plasma or are interacting with the walls of the circulatory system. An exact model of such a system would require representation of not only of the chemical processes, but also the three-dimensional di!usion of all of the components. Such a model would be very computationally intensive, require a level of detailed knowledge about blood that is not available, and probably obscure an understanding of the fundamental chemical processes involved. Fortunately, a simpler model structure is available that is often used to study complex chemical processes both in the laboratory and in the computer. This approximation is the continuously stirred tank reactor (CSTR) (Scott, 1991.) A CSTR is a system in which reactants are introduced continuously into a tank by an input stream while the tank's contents are continuously discharged. It is normally assumed, as in this case, that the #ow rate into the CSTR equals the #ow rate out. The contents of the tank are stirred so there is a uniform concentration at all times
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W. D. STANBRO
TABLE 2 Di+erential equations in model d[NO] "!k [NO][O\]#k [ONOO\]#f [NO] !f [NO] GLNSR dt d[O\] "!k [NO][O\]#k [ONOO\]#f [O\] !f [O\] GLNSR dt d[ONOO\] "k [NO][O\]!(k #k #k )[ONOO\] dt !k [CO ][ONOO\]#f [ONOO\] !f [ONOO\] GLNSR d[NO\] "k [ONOO\]#k [ONOOCO\]#f [NO\] !f [NO\] GLNSR dt d['OH] "k [ONOO\]#f ['OH] !f ['OH] GLNSR dt d['NO ] "k [ONOO\]#k [ONOOCO\]#f ['NO ] !f ['NO ] GLNSR dt d['CO\] "k [ONOOCO\]#f ['CO\] !f ['CO\] GLNSR dt d[ONOOCO2\] "k [CO ][ONOO\]!(k #k )[ONOOCO\] dt #f [ONOOCO\] !f [ONOOCO\] GLNSR
in the tank. This results in additional terms being added in the ODE for each compound for in#ow (at the input concentration which is set equal to the initial concentration) and out#ow (at the current concentration). These extra terms are re#ected in the di!erential equations in Table 2. The input concentrations used in the base case are shown in Table 3. They are derived from values measure in human plasma (Brovkovych et al., 1997; Huk et al., 1997). The #ow in and out of the reaction volume is paramaterized in the #ow parameter, f, which is equal to the #ow divided by the reaction volume. f is the reciprocal of the average time a nonreacting species will spend in the reaction volume. This formalism also provides a convenient mechanism for comparison of the e!ects of varying conditions. By allowing reactions to relax to an equilibrium between input plus production vs. discharge plus destructions, it is possible to evaluate the relative amounts of various products produced. Comparisons in this paper are in terms
TABLE 3 Base case initial concentrations and conditions* NO O\ CO pH Temperature f
50 nM 50 nM 1.3 mM 7.4 373C 0.5
* All other species are set initially to zero.
of the concentrations of the compounds of interest at 100 s after the initiation of the reaction. Where helpful, the time course of the approach to equilibrium is also plotted. In this study, f was usually set at 0.5 s\, and all reactions run for 100 s so that equilibrium of the system was attained. To summarize, the reactor is considered to contain plasma, the species input into the reactor are NO and O\. The output will in general contain these species plus ONOO\, ONOOCO\, 'OH,
PLASMA PEROXYNITRITE LEVELS
, NO , and NO\. CO is kept constant 'CO\ ' at 1.3 mM. The resulting system of di!erential equations was solved using the multi-step Gear numerical ODE solver (Gear, 1971) in the Maple V Release 5.1 software package (Waterloo Maple Inc., 450 Phillip Street, Waterloo, ON, Canada N2L 5J2.) With this type of ODE solver, the time step is automatically set to maintain a maximum allowed error in each species at each step. For this study the error was set to no more than one part in 10.
Results This section will show the levels of a number of species as a function of the input NO concentration. Because NO and O\ react on a one-to-one basis and in the model have no other reactions with other components, the e!ect of varying O\ would be the same as varying NO. Therefore, for the sake of brevity the variation with O\ is not shown explicitly. Figure 2 shows the variation in NO and O\ with a change in the input levels of NO. As expected, increasing the level of NO increasingly scavenges available O\ and leaves unreacted NO. The leveling o! occurs because of the nearly total comsumption of O\. It should be noted that in itself this should be protective of LDL since an oxidant, O\, is removed and NO is known to react with LDL-peroxy radicals to terminate the radical chain reaction that lead to
FIG. 2. Variation in equilibrium NO (E) and O\ (£) concentrations as a function of initial NO concentration.
461
peroxidation (Hogg et al., 1993). Unfortunately, as shown in Fig. 3 there is a concomitant increase in a number of reactive free radicals: 'OH, 'CO\ and NO . NO\ is of course also formed as the major product of ONOO\ decomposition. It is also clear that formation of 'CO\ dominates production of ' OH by two orders of magnitude. This is due to the rapid formation of ONOOCO\ followed by its even more rapid decay. Indeed, the decay of the adduct is so fast that under physiological conditions adduct formation is the rate-determining step in the production of ONOOCO\ decay products (Lyman & Hurst, 1998). Figure 4 shows the variation in the formation of the two intermediaries ONOO\ and
FIG. 3. Variation in equilibrium 'OH (E), 'CO\ (£), () concentrations as a function of 'NO (䊏) and NO\ initial NO concentration. Note that 'NO plots on top of . 'CO\
FIG. 4. Variation of equilibrium ONOO\ (E) and ONOOCO\ (£) concentrations as a function of initial NO concentration.
462
FIG. 5. Time history of NO (E), ONOO\ ONOOCO\ (䊏) and NO\ () concentrations.
W. D. STANBRO
(£),
ONOOCO\. Even though the free radical prod ucts of ONOOCO\ decomposition are greater than those from ONOO\, ONOOCO\ is found at a lower concentration. Again this is due to its very rapid rate of decomposition once formed. This trend is clearly seen in Fig. 5 which shows the time history of the consumption of NO, the formation and decay of ONOO\ and ONOOCO\, and the formation of NO\. Notably, ONOO\ is found in nM concentrations and above despite the competition to react with CO , ONOOCO\ is never found above the pM levels and declines from this point with time. Figure 6 addresses the issue of the sensitivity of concentrations of ONOO\ and ONOOCO\ to the rate constants for decomposition of ONOOCO\, k and k which as noted above has not, to be determined experimentally. While the sum of the two rate constants have a large e!ect on the level of ONOOCO\, the varia tion over four orders of magnitude does not change the conclusion that ONOOCO\ is expected to be found in much lower concentration than ONOO\. However, quantitative calculations of the relative amounts of the radical products produced by these substances are clearly dependent on the value chosen for k #k . The lack of variation in ONOO\ concentration is due to the competition to form ONOOCO\. Once this molecule is formed, the lifetime has no futher impact on ONOO\ levels.
FIG. 6. Variation in the equilibrium ONOO\ (£) and ONOOCO\ (E) concentration as a function of the sum of k and k .
FIG. 7. Variation in the time history of the ONOOCO\ concentration for three di!erent values of f. They are 0.1 (E), 0.5 (£) and 1.0 (䊏).
In addition to the processes of chemical production and decay another factor controlling the availability of a substance to react with an LDL particle is the e!ect of transport from the site of production to the location of the LDL. The CSTR model gives some insight into this process by examining the e!ect of varying the #ow parameter, f. Figures 7 and 8 show the results for ONOOCO\ and ONOO\, respectively. In each case, rapid transport (higher values of f ) result in higher concentrations of the molecules. This is true because there is less time for decomposition to occur before discharge. However, even a rapid #ow rate does not fully compensate for the very rapid decomposition of ONOOCO\.
463
PLASMA PEROXYNITRITE LEVELS
quirement for signi"cant impact on peroxidation rate. In this respect, ONOO\ would have a considerably larger radius of action than ONOOCO\. In summary, ONOO\ appears to be the species most available for reaction with LDL. Based on model results ONOO\ should be found in plasma in nM concentrations.
REFERENCES
FIG. 8. Variation in the time history of the ONOO\ concentration for three di!erent values of f. They are 0.1 (E), 0.5 (£) and 1.0 (䊏).
Discussion The processes controlling the levels of ONOO\ in plasma are clearly dominated by the reaction with CO , i.e. CO -catalysed. Forma tion of the adduct causes a rapid formation of highly reactive free radical species. While the uncatalysed reaction would also eventually produce reactive materials, the rate would be much slower. This leads to the expectation that formation of ONOO\ in plasma results in most of the reactive species being released in the plasma, before the parent molecule can penetrate the LDL particle. If as we have assumed these radicals are rapidly consumed by components of the plasma, CO would appear to exert a protective e!ect on the LDL while increasing the free radical burden in the plasma. Corroboration of this is found in the demonstration a reduction in the toxicity of ONOO\ to E. coli in the presence of CO (Zhu et al., 1992). The rapid decay of ONOOCO\ also controls the identity of the residual species available for penetration of the LDL particle. Based on model results very few ONOOCO\ mole cules (pM levels) would be available. Instead, ONOO\ will be the dominant species (nM levels) available to move from the aqueous to the lipid phase. The rate of decomposition of both ONOO\ and ONOOCO\ suggests that generation in close proximity to target LDL particles is a re-
ALVAREZ, B., FERRER-SUETA, G., FREEMAN, B. A. & RADI, R. (1999). Kinetics of peroxynitrite reaction with amino acids and human serum albumin. J. Biol. Chem. 274, 842} 848. BARTLETT, D., CHURCH, D. F., BOUNDS, P. L. & KOPPENOL, W. H. (1995). The kinetics of the oxidation of L-ascorbic acid by peroxynitrite Free Rad. Biol. Med. 18, 85}92. BONINI, M. G., RADI, R., FERRER-SUETA, G., DA C. FERREIRA, A. M. & AUGUSTO, O. (1999). Direct EPR detection of the carbonate radical anion produced from peroxynitrite and carbon dioxide. J. Biol. Chem. 274, 10802}10806. BROVKOVYCH, V., PATTON, S., BROVKOVYCH, S., KIECHLE, F., HUK, I. & MALINSKI, T. (1997). In-situ measurement of nitric oxide, superoxide and peroxynitrite during endotoxemia. J. Physiol. Pharmacol. 48, 633}644. CODDINGTON, J. W., HURST, J. K. & LYMAR, S. V. (1999). Hydroxyl radical formation during peroxynitrous acid decomposition. J. Am. Chem. Soc. 121, 2438}2443. DENICOLA, A, FREEMAN, B. A., TRUJILLO, M. & RADI, R. (1996). Peroxynitrite reaction with carbon dioxide/bicarbonate: kinetics and in#uence on peroxynitrite-mediated oxidation. Arch. Biochem. Biophys. 333, 49}58. GEAR, C. W. (1971). Numerical Initial
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HUK, I., NANOBASHVILI, J., NEUMEYER, C., PUNZ, A., MUELLER, M.., AFKHAMPOUR, K., MITTLBOECK, M., LOSERT, U., POLTERAUER, P., ROTH, E., PATTON, S. & MALINSKI, T. (1997). L-Arginine treatment alters the kinetics of nitric oxide and superoxide release and reduces ischemia/reperfusion injury in skeletal muscle. Circulation 96, 667}675. JACKSON, T. S., XU, A., VITA, J. A. & KEANEY, JR., J. F. (1998). Ascorbate prevents the interaction of superoxide and nitric oxide only at very high physiological concentrations. Circ. Res. 83, 916}922. KEITH, W. G. & POWELL, R. E., (1969). Kinetics of decomposition of peroxynitrous acid. J. Chem. Soc. A 1969, 90}90. LOGAGER, T. & SEHESTED, K. (1993). Formation and decay of peroxynitrous acid: a pulse radiolysis study. J. Phys. Chem. 97, 5554}6669. LYMAR, S. V. & HURST, J. K. (1995). Rapid reaction between peroxynitrite ion and carbon dioxide: implications for biological activity. J. Am. Chem. Soc. 117, 8867. LYMAR, S. V. & HURST, J. K. (1996). Carbon dioxide: physiological catalyst for peroxynitrite-mediated cellular damage or cellular protectant? Chem. Res. ¹oxicol. 9, 845}850. LYMAR, S. V. & HURST, J. K. (1998). CO -catalyzed one electron oxidation by peroxynitrite: properties of the reactive intermediate. Inorg. Chem. 37, 294}301. LYMAR, S. V., JIANG, Q. & HURST, J. K. (1996). Mechanism of carbon dioxide-catalyzed oxidation of tyrosine by peroxynitrite. Biochemistry 35, 7855}7861.
MELI, R., NAUSER, T. & KOPPENOL, W. H. (1999). Direct observation of intermediates in the reaction of peroxynitrite with carbon dioxide. Helv. Chim. Acta 82, 722}725. MERENYI, G. & LIND, J. (1997). Thermodynamics of peroxynitrite and its CO adduct. Chem. Res. ¹oxicol. 10, 1216}1220. NATIONAL HEART, LUNG AND BLOOD INSTITUTE. (1998). Morbidity and Mortality: 1998 Chartbook on Cardiovascular, ¸ung and Blood Diseases, p. 9. Rockville, MD: U. S. Department of Health and Human Services. PFEIFFER, S., GORREN, A. C. F., SCHMIDT, K., WERNER, E. R., HANSERT, R., BOHLE, D. S. & MAYER, B. (1997). Metabolic fate of peroxynitrite in aqueous solution. J. Biol. Chem. 272, 3465}3470. RADI, R., COSGROVE, T. P. & BECKMAN, J. S. (1993). Peroxynitrite-induced luminol chemiluminescence Biochem. J. 290, 51}57. SCOTT, S. K. (1991). Chemical Chaos, pp. 12}13. Oxford: Oxford University Press. SQUADRITO, G. L., JIN, X. & PRYOR, W. A. (1995). Stopped#ow kinetic study of the reaction of ascorbic acid with peroxynitrite Arch. Biochem. Biophys. 322, 53}59. STANBRO, W. D. (1998). A kinetic model of the myeloperoxidase-hydrogen peroxide-chloride ion system in phagolysosomes. J. theor. Biol. 193, 59}68. STANBRO, W. D. (1999). A kinetic model of the system: tyrosyl radical-nitrogen oxide-superoxide. J. theor. Biol. 197, 557}567. ZHU, L., GUNN, C., & BECKMAN, J. S. (1992). Bactericidal activity of peroxynitrite. Arch. Biochem. Biophys. 298, 452}457.
Modeling the Interaction of Peroxynitrite with Low-density Lipoproteins. I. Plasma Levels of Peroxynitrite WILLIAM D. STANBRO* 1632 Camino Redondo, ¸os Alamos, NM 87544, ;.S.A. (Received on 8 October 1999, Accepted in revised form on 15 April 2000)
Peroxynitrite is a strong candidate for the material responsible for the initiation of peroxidation of low-density lipoproteins (LDLs) which is considered the "rst step in the formation of atherosclerotic plaque. Recent advances in the understanding of peroxynitrite chemistry allow the construction of a kinetic model that can be used to understand the factors controlling levels in plasma. These results indicate that the carbon dioxide catalysed decomposition of peroxynitrite produces large quantities of reactive species, but the rapid decomposition of this intermediate, ONOOCO\, may limit its availability to attack LDLs at points distant from the site of production. In this case, peroxynitrite itself may be of greater quantitative importance in LDL peroxidation. 2000 Academic Press
Introduction In 1996, 476 818 Americans died of coronary heart disease (CHD) (National Heart, Lung and Blood Institute, 1998). It is generally agreed that the "rst step in the development of CHD is peroxidation of low-density lipoproteins (LDLs). This is believed to occur by a free radical chain reaction. While there are a number of candidates for the initiator of this chain reaction, the identity of the agent is currently unknown (Stanbro, 1999). One possible mechanism is through the intermediary of peroxynitrite, ONOO\, an unstable molecule formed from the reaction of NO and O\. This is the "rst of three planned papers that will use modeling techniques to examine the processes involved in the interaction of ONOO\ with LDLs. This paper will center on the factors governing the levels of ONOO\ in plasma. This will form the boundary conditions for a di!u-
sion/reaction model of the dynamics of ONOO\ with LDLs which will be described in the second paper. The third paper of this series will examine the role of antioxidants in mitigating LDL peroxidation. Model
* E-mail: [email protected]
The general conceptual model for this series of papers is that ONOO\ and related reaction products are produced at some concentration in plasma. The resultant products must then di!use to or into the LDL particle. Once inside the particle ONOO\ would continue to decompose and release reactive products. This paper will produce estimates of the amount of ONOO\ and related species using a chemical kinetic model. The various factors controlling ONOO\ chemistry in plasma will also be examined. Kinetic modeling has proven to be a valuable tool in illuminating the relative importance of individual processes in complex reacting systems (Stanbro, 1998, 1999). The results of this study will provide
0022}5193/00/150457#08 $35.00/0
2000 Academic Press
458
W. D. STANBRO
guidance on the species most likely to be available to penetrate into an LDL particle. The general procedures to be followed include developing a list of the key chemical reactions and their rate constants, using the mass action law to produce di!erential equations describing the time history of each species, numerically solving the equations and varying the pertinent input parameters to further elucidate the nature of the interactions between the various elements in the reacting system (Stanbro, 1998). REACTION CHEMISTRY AND RATE CONSTANTS
The chemistry of the ONOO\ has been the subject of considerable study for a number of years but has proven quite di$cult to understand. However, a number of recent papers have gone quite far in resolving the apparent contradictions in the data (Hurst & Lymar, 1999). The work described in this paper takes advantage of these advances in understanding. Figure 1 is a schematic diagram of ONOO\ chemistry. Note that when ONOO\ is referred to in this paper it includes not only the ONOO\ ion, but also its conjugate acid, ONOOH, unless they are speci"cally di!erentiated. The balanced reactions and the associated rate constants in the model are shown in Table 1. The sources of the rate constants are presented below. ONOO\ is formed by the near-di!usionlimited reaction of NO and O\. Pulse radiolysis studies of this reaction provides estimates of the
rate constant of from 4.3;10 (Huie & Padmaja, 1993) to 6.7;10 M\ s\ (Goldstein & Czapski, 1995). This paper assumes a value of 5;10 M\ s\. Once formed ONOO\ can undergo a backreaction to the products. The measured rate constant for this process in 0.017 s\ (Logager & Sehested, 1993). This rate constant was also determined by a pulsed radiolysis study. Once formed the ONOO\ ion is relatively stable. However, the conjugate acid readily decays. The overall rate constant for the decay process has been measured under physiological conditions (7.4 pH, 373C) to be 0.69 s\ (Pfei!er et al., 1997). It has been observed that approximate 60}70% of the product of the decay is the nitrate ion (NO\). The balance seems to be the hydoxide radical ('OH) and nitrogen dioxide ('NO ) (Goldstein et al., 1998; Coddington et al., 1999). The interpretation of the reaction is that HONOO homolyses to 'OH and 'NO , but that the radicals are trapped in a solvent cage. The majority of the radicals combine and rearrange to form NO\. The remainder escape the cage and are responsible for the observed oxidizing capabilility of ONOO\. This paper takes the rate constant for the formation to NO\ to be 70% of the total rate constant (0.69 s\) and the rate constant for the formation of 'OH and 'NO to be 30% of the total. Further complicating the chemistry of ONOO\ was the discovery that its decomposition is catalysed by CO (Keith & Powell, 1969; Radi et al., 1993). The "rst step in this process is formation of a ONOO\/CO adduct (ONOOCO\) (Lymar & Hurst, 1995). This is
TABLE 1 Model Reactions and rate constants* Reactions
FIG. 1. Schematic diagram of the formation and decay reactions of peroxynitrite considered in the model. The k's refer to the rate constants in Table 1.
(1) (2) (3) (4) (5) (6) (7)
Rate constants
NO#O\PONOO\ k "5;10 M\ s\ ONOO\PNO#O\ k "0.017 s\ ONOO\P)NO #)OH k "0.207 s\ HONOOPNO\#H> k "0.483 s\ ONOO\#CO PONOOCO\ k "5.8;10 M\ s\ ONOOCO\P)NO #)CO\ k "3;10 s\ ONOOCO\PNO\#CO k "7;10 s\
* Sources of all rate constants are given in the text.
PLASMA PEROXYNITRITE LEVELS
signi"cant because of the bu!ering of many biological systems by the CO /bicarbonate/carbon ate system. In plasma, the expected CO levels are of the order of 1.3 mM (corresponding to 25 mM bicarbonate). Based on a measurement of the formation of ONOOCO\ under physiolo gical conditions (Denicola et al., 1996), the model uses a rate constant of 5.8;10 M\ s\. ONOOCO\ rapidly decomposes with the ma jor products being NO\ and CO . As in the case of HONOO decomposition, the reaction proceeds through the formation of two radicals in a solvent cage. In this case, the radicals are the carbonate radical anion, 'CO\, and 'NO (Lymar & Hurst, 1996; Lymar et al., 1996; Goldstein & Czapski, 1997; Lymar & Hurst, 1998, Goldstein & Czapski, 1998, 1999). Again, some of the radicals escape the cage to participate in oxidation reactions (Goldstein & Czapski, 1997). The formation of 'CO\ has been demonstrated experimentally (Meli et al., 1999; Bonini et al., 1999). In aqueous solution, the proportion escaping is about 30}35% (Goldstein & Czapski, 1997, 1998, 1999). There are no measurements of the decomposition rate of ONOOCO\. On thermodynamic grounds, the total rate constant is expected to be 1.5;10 s\ (Merenyi & Lind, 1997). In this model, the rate of decomposition to NO\ is taken to be 70% of 1;10 and 30% of 1;10 for the formation of the free radicals. The e!ect of varying this rate constant is examined below. The model neglects any direct reaction between either ONOO\ or ONOOCO\ and other components of plasma. While such reactions are possible, they would have to compete with the reaction of CO and the rapid decomposition of the adduct. Experimental data seem to indicate that direct reaction is limited and that the primary means by which ONOO\ exerts is oxidizing e!ect is through its decomposition products (Squadrito et al., 1995; Jackson et al., 1998). This will be considered in more detail in the third paper in this series. Although not considered in this model, the free radical products of ONOO\ and ONOOCO\ decomposition do react readily with plasma components (Squadrito et al., 1995; Bartlett et al., 1995; Lymar et al., 1996; Jackson et al., 1998; Alvarz et al., 1999) such as human serum albumin
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and ascorbate ion. These reactions may be expected to rapidly scavenge highly reactive species so few will survive to directly attack LDL particles. MODEL IMPLEMENTATION
From the reactions in Table 1 the appropriate ordinary di!erential equations (ODEs) were formed for each of the species of interest using the mass action law. A di!erential equation is written for each species whose concentration may change during the simulation. The di!erential equations are shown in Table 2. The terms in the di!erential equation are the products of the appropriate rate constants and the concentrations of the reactants (the species on the left hand of the arrows in Table 1) with any suitable stoichiometric coe$cients. As is usual in studies in aqueous solution, the concentrations of the components of the water system (H O, H>, OH\) are held constant and subsumed into the pH-dependent rate constants. Most naturally occurring systems are open, that is matter and energy are exchanged with the rest of the environment. In the blood stream, components are being swept along while di!erent chemical species are di!using into and out of the various structures in suspension in the plasma or are interacting with the walls of the circulatory system. An exact model of such a system would require representation of not only of the chemical processes, but also the three-dimensional di!usion of all of the components. Such a model would be very computationally intensive, require a level of detailed knowledge about blood that is not available, and probably obscure an understanding of the fundamental chemical processes involved. Fortunately, a simpler model structure is available that is often used to study complex chemical processes both in the laboratory and in the computer. This approximation is the continuously stirred tank reactor (CSTR) (Scott, 1991.) A CSTR is a system in which reactants are introduced continuously into a tank by an input stream while the tank's contents are continuously discharged. It is normally assumed, as in this case, that the #ow rate into the CSTR equals the #ow rate out. The contents of the tank are stirred so there is a uniform concentration at all times
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TABLE 2 Di+erential equations in model d[NO] "!k [NO][O\]#k [ONOO\]#f [NO] !f [NO] GLNSR dt d[O\] "!k [NO][O\]#k [ONOO\]#f [O\] !f [O\] GLNSR dt d[ONOO\] "k [NO][O\]!(k #k #k )[ONOO\] dt !k [CO ][ONOO\]#f [ONOO\] !f [ONOO\] GLNSR d[NO\] "k [ONOO\]#k [ONOOCO\]#f [NO\] !f [NO\] GLNSR dt d['OH] "k [ONOO\]#f ['OH] !f ['OH] GLNSR dt d['NO ] "k [ONOO\]#k [ONOOCO\]#f ['NO ] !f ['NO ] GLNSR dt d['CO\] "k [ONOOCO\]#f ['CO\] !f ['CO\] GLNSR dt d[ONOOCO2\] "k [CO ][ONOO\]!(k #k )[ONOOCO\] dt #f [ONOOCO\] !f [ONOOCO\] GLNSR
in the tank. This results in additional terms being added in the ODE for each compound for in#ow (at the input concentration which is set equal to the initial concentration) and out#ow (at the current concentration). These extra terms are re#ected in the di!erential equations in Table 2. The input concentrations used in the base case are shown in Table 3. They are derived from values measure in human plasma (Brovkovych et al., 1997; Huk et al., 1997). The #ow in and out of the reaction volume is paramaterized in the #ow parameter, f, which is equal to the #ow divided by the reaction volume. f is the reciprocal of the average time a nonreacting species will spend in the reaction volume. This formalism also provides a convenient mechanism for comparison of the e!ects of varying conditions. By allowing reactions to relax to an equilibrium between input plus production vs. discharge plus destructions, it is possible to evaluate the relative amounts of various products produced. Comparisons in this paper are in terms
TABLE 3 Base case initial concentrations and conditions* NO O\ CO pH Temperature f
50 nM 50 nM 1.3 mM 7.4 373C 0.5
* All other species are set initially to zero.
of the concentrations of the compounds of interest at 100 s after the initiation of the reaction. Where helpful, the time course of the approach to equilibrium is also plotted. In this study, f was usually set at 0.5 s\, and all reactions run for 100 s so that equilibrium of the system was attained. To summarize, the reactor is considered to contain plasma, the species input into the reactor are NO and O\. The output will in general contain these species plus ONOO\, ONOOCO\, 'OH,
PLASMA PEROXYNITRITE LEVELS
, NO , and NO\. CO is kept constant 'CO\ ' at 1.3 mM. The resulting system of di!erential equations was solved using the multi-step Gear numerical ODE solver (Gear, 1971) in the Maple V Release 5.1 software package (Waterloo Maple Inc., 450 Phillip Street, Waterloo, ON, Canada N2L 5J2.) With this type of ODE solver, the time step is automatically set to maintain a maximum allowed error in each species at each step. For this study the error was set to no more than one part in 10.
Results This section will show the levels of a number of species as a function of the input NO concentration. Because NO and O\ react on a one-to-one basis and in the model have no other reactions with other components, the e!ect of varying O\ would be the same as varying NO. Therefore, for the sake of brevity the variation with O\ is not shown explicitly. Figure 2 shows the variation in NO and O\ with a change in the input levels of NO. As expected, increasing the level of NO increasingly scavenges available O\ and leaves unreacted NO. The leveling o! occurs because of the nearly total comsumption of O\. It should be noted that in itself this should be protective of LDL since an oxidant, O\, is removed and NO is known to react with LDL-peroxy radicals to terminate the radical chain reaction that lead to
FIG. 2. Variation in equilibrium NO (E) and O\ (£) concentrations as a function of initial NO concentration.
461
peroxidation (Hogg et al., 1993). Unfortunately, as shown in Fig. 3 there is a concomitant increase in a number of reactive free radicals: 'OH, 'CO\ and NO . NO\ is of course also formed as the major product of ONOO\ decomposition. It is also clear that formation of 'CO\ dominates production of ' OH by two orders of magnitude. This is due to the rapid formation of ONOOCO\ followed by its even more rapid decay. Indeed, the decay of the adduct is so fast that under physiological conditions adduct formation is the rate-determining step in the production of ONOOCO\ decay products (Lyman & Hurst, 1998). Figure 4 shows the variation in the formation of the two intermediaries ONOO\ and
FIG. 3. Variation in equilibrium 'OH (E), 'CO\ (£), () concentrations as a function of 'NO (䊏) and NO\ initial NO concentration. Note that 'NO plots on top of . 'CO\
FIG. 4. Variation of equilibrium ONOO\ (E) and ONOOCO\ (£) concentrations as a function of initial NO concentration.
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FIG. 5. Time history of NO (E), ONOO\ ONOOCO\ (䊏) and NO\ () concentrations.
W. D. STANBRO
(£),
ONOOCO\. Even though the free radical prod ucts of ONOOCO\ decomposition are greater than those from ONOO\, ONOOCO\ is found at a lower concentration. Again this is due to its very rapid rate of decomposition once formed. This trend is clearly seen in Fig. 5 which shows the time history of the consumption of NO, the formation and decay of ONOO\ and ONOOCO\, and the formation of NO\. Notably, ONOO\ is found in nM concentrations and above despite the competition to react with CO , ONOOCO\ is never found above the pM levels and declines from this point with time. Figure 6 addresses the issue of the sensitivity of concentrations of ONOO\ and ONOOCO\ to the rate constants for decomposition of ONOOCO\, k and k which as noted above has not, to be determined experimentally. While the sum of the two rate constants have a large e!ect on the level of ONOOCO\, the varia tion over four orders of magnitude does not change the conclusion that ONOOCO\ is expected to be found in much lower concentration than ONOO\. However, quantitative calculations of the relative amounts of the radical products produced by these substances are clearly dependent on the value chosen for k #k . The lack of variation in ONOO\ concentration is due to the competition to form ONOOCO\. Once this molecule is formed, the lifetime has no futher impact on ONOO\ levels.
FIG. 6. Variation in the equilibrium ONOO\ (£) and ONOOCO\ (E) concentration as a function of the sum of k and k .
FIG. 7. Variation in the time history of the ONOOCO\ concentration for three di!erent values of f. They are 0.1 (E), 0.5 (£) and 1.0 (䊏).
In addition to the processes of chemical production and decay another factor controlling the availability of a substance to react with an LDL particle is the e!ect of transport from the site of production to the location of the LDL. The CSTR model gives some insight into this process by examining the e!ect of varying the #ow parameter, f. Figures 7 and 8 show the results for ONOOCO\ and ONOO\, respectively. In each case, rapid transport (higher values of f ) result in higher concentrations of the molecules. This is true because there is less time for decomposition to occur before discharge. However, even a rapid #ow rate does not fully compensate for the very rapid decomposition of ONOOCO\.
463
PLASMA PEROXYNITRITE LEVELS
quirement for signi"cant impact on peroxidation rate. In this respect, ONOO\ would have a considerably larger radius of action than ONOOCO\. In summary, ONOO\ appears to be the species most available for reaction with LDL. Based on model results ONOO\ should be found in plasma in nM concentrations.
REFERENCES
FIG. 8. Variation in the time history of the ONOO\ concentration for three di!erent values of f. They are 0.1 (E), 0.5 (£) and 1.0 (䊏).
Discussion The processes controlling the levels of ONOO\ in plasma are clearly dominated by the reaction with CO , i.e. CO -catalysed. Forma tion of the adduct causes a rapid formation of highly reactive free radical species. While the uncatalysed reaction would also eventually produce reactive materials, the rate would be much slower. This leads to the expectation that formation of ONOO\ in plasma results in most of the reactive species being released in the plasma, before the parent molecule can penetrate the LDL particle. If as we have assumed these radicals are rapidly consumed by components of the plasma, CO would appear to exert a protective e!ect on the LDL while increasing the free radical burden in the plasma. Corroboration of this is found in the demonstration a reduction in the toxicity of ONOO\ to E. coli in the presence of CO (Zhu et al., 1992). The rapid decay of ONOOCO\ also controls the identity of the residual species available for penetration of the LDL particle. Based on model results very few ONOOCO\ mole cules (pM levels) would be available. Instead, ONOO\ will be the dominant species (nM levels) available to move from the aqueous to the lipid phase. The rate of decomposition of both ONOO\ and ONOOCO\ suggests that generation in close proximity to target LDL particles is a re-
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