Modeling the energy transfer pathways. Creatine kinase activities and ...
Modeling the energy transfer pathways. Creatine kinase activities and heterogeneous distribution of ADP in the perfused heart. Joubert, F., Hoerter, J.A. and M azet, J.-L. U446 INSERM , Université Paris-Sud, 92260, Châtenay-M alabry, France Address : U-446 INSERM, Cardiologie cellulaire et moléculaire, Faculté de Pharmacie, 5 rue J.-B. Clément, 92260 – Châtenay-Malabry (France) e-mail : jean-luc.mazet@cep .u-psud.fr ; phone : (33) 1 46 83 57 69 ; FAX : (33) 1 46 83 54 75
Summary The exchange scheme of high energy phosphate transport in a whole heart relies on a system of CK functioning in different ways. This suggests that the CKs are able to act both like a shuttle and like a buffer for the energy transfer. The challenge is to understand how these two functions are balanced in the CK system. One key of this balance is the knowledge of the local concentrations of the ADP nucleotide. These concentrations cannot be directly measured, but they may be derived by computation. In the present report we introduce the known properties of the enzymes catalyzing the exchange of high energy phosphate into the model of flux pathways derived from NM R experiments to compute both the maximum activity of each enzyme and the local concentrations of all the substrates. We show that the ADP distribution must be heterogeneous for the system to work. Its concentration is 50% higher in the vicinity of ATPase sites and 50% lower in the intermembrane space of the mitochondria than in the cytosol. Another result of this analysis is that the apparent large unbalance of the CKmito pathway is imposed by the adenosine nucleotide transferase fluxes. This analysis proves that it is possible to deduce the local concentrations of a substrate by combining data originating from NM R, biochemistry and enzymology into a common model. Keywords : creatine kinase shuttle, energy transfer, heart muscle, mathematical modeling Abbreviations : ADPx and ATPx : matrix nucleotides ADPcyto and ATPcyto : cytosolic nucleotides ADPmyos and ATPmyos : nucleotides close to the ATPase ADPim and ATPim : mitochondrial intermembrane nucleotides ANT : adenosine nucleotide translocase CK : creatine kinase, adenosine triphosphate creatine phosphotransferase, E.C 2.7.3.1 CKcyto : cytosolic CK Kmito : mitochondrial CK CKmyos : particulate CK close to the ATPase Cr : creatine PCr (phosphocreatine
Introduction In the muscle, the energy is transferred from the mitochondria to the sites of utilization via high energy phosphates carried by ATP and PCr. In this pathway, the CK, which is the only enzyme able to catalyze the reversible transfer of high energy phosphate to Cr, should play a major role. In the heart, which does not possess large energy stores, the adequacy of oxygen consumption to the energy demand is tight and permanent. In the course of the adjustment to increased work, no variations of CK substrates can be measured. This suggests that the CKs plays a buffering role. Recently we developed a methodology (Joubert et al., 2001) which allows separation of the activities of three CKs located at various sites within the rat myocyte. These three enzymes have
different kinetics in normoxic conditions (Joubert et al., 2002). A cytosolic CKcyto works at equilibrium, a particulate CKmyos close to ATPase favors ATP synthesis, the CKmito functions far from equilibrium in the direction of PCr synthesis. This proves that the CKs are able to act like an energy carrier. Since the some CK function out of equilibrium, the ADP concentration cannot be inferred at all sites from the thermodynamic equilibrium. M oreover the local ADP concentrations should depend on the working load of the heart. The knowledge of these variations would thus enlighten the understanding of how the CKs share their activity between buffering and transporting the energy. Unfortunately, it is not possible at present to measure directly the ADP concentration in subcellular spaces of a perfused heart. A particular difficulty arises from the fact that the CKmito pathway is composed of two enzymes the CKmito itself and the ANT, separated by a small intermembrane space of the mitochondria, which escapes the NM R investigations. Nevertheless the mitochondrial activity is regulated by the nucleotides present in this space. Here we have combined the knowledge from NM R analysis, from biochemical measurements and from the enzyme characteristics into a model to determine the nucleotide concentration in each of the subcellular compartments.
Theory
Figure 1. Enzyme organization used to represent the scheme of the exchange fluxes in perfused rat heart derived from NMR experiments (Joubert et al., 2001 ; 2002a). In control conditions, three CK activities were estimated, transferring phosphate between a PCr compartment and three ATP compartments (mitochondrial, cytosolic and closely bound to ATPases). For modeling, the mitochondria pathway was split into CKmito and ANT separated by a small intermembrane compartment non visible in NMR experiments. Note that the myosine ATPase is assumed to represent most of the ATPases.
Each flux of exchange was represented in terms of enzymatic reactions between four compartments (Fig. 1) : the cytosol, two mitochondrial compartments (the matrix and the intermembrane space) and a restricted space close to the ATP utilizing sites, which we consider to be mainly myosine
ATPase in the present work. Both flux PCr Û ATPcyto and PCr Û ATPmyos were carried by the same enzyme M M -CK. The mitochondrial pathway ATP Û PCr was replaced by two enzymes working in series, the ANT between the matrix and the intermembrane space and the CKmito between the intermembrane space and the cytosol. The functioning of the enzymes is described in the Table 2 and the appendix 1. The ATPase were supposed to work at a constant rate. The phosphate exchanger was a non limiting reaction imposing an instantaneous gradient (.15 ratio) between the cytosol and the matrix. Its rate was therefore imposed by the rate of the ATPase. For simplification, the ATP synthase was assumed to work like a non reversible mass Table 1 : Kinetic representation of the enzymes used to describe the energy fluxes in the model. Enzyme
equation
kinetics
ATPase
ATPmyos Ë ADPmyos + Pi
v = constant (see appendix 2)
phosphate exchanger
Pi Û Px
v = constant (see text)
ATP synthase
ADPx + Px Ë ATPx
v = k1 . [ADPx] . [Px]
ANT
ATPx + ADPim Û ADPx + ATPim antiport (see appendix 1 and 2)
CKcyto and CKmyos PCr + ADPcyto Û Cr + ATPcyto
antiport (see appendix 1 and 2)
PCr + ADPmyos Û Cr + ATPmyos antiport (see appendix 1 and 2) CKmito
PCr + ADPim Û Cr + ATPim
antiport (see appendix 1 and 2)
action reaction. The CKs and the ANT were described by antiport equations. The volume of each compartment was fixed as a fraction of the cell water volume : matrix (.24) intermembrane space ( .001), restricted space close to the ATPase (.1) and cytosol (.659). The computation was made in two steps. The substrates were assigned initial values to account for their measured values in the control conditions (Joubert et al., 2001) : ATPmyos (1.29 mmoles.l H2O cell-1.s-1), ATPcyto (3.95 mmoles.l H2O cell-1.s-1), ATPmito (1.56 mmoles.l H2O cell-1.s-1), PCr (10.6 mmoles.l H2O cell-1.s-1 = total PCr minus the non exchangeable PCr trapped in the mitochondria), Cr (10 mmoles.l H2O cell-1.s-1) and Pi (2.9 mmoles.l H2O cell-1.s-1). Then the system was solved for all the concentrations at a steady state. In the second step, the maximum activity of the three CKs and of the ANT were adjusted the fit the constraints : energy consumption (2.3 mmoles ATP.l H2O cell-1.s-1), CKcyto fluxes (3.3 mmoles ATP.l H2O cell-1.s-1), flux ratio of the CKmyos (Ff/Fr = 1.7). It was assumed that the ANT is tightly coupled with the CKmito on a mole to mole basis. The computations were made with the program Gepasi 3.21 (M endes, 1993, 1997 ; M endes &Kell, 1998).
Results and discussion Investigating the kinetic behavior of a physiological system by considering its known enzymatic properties greatly enhances the possibilities of understanding its mechanisms. In the present study we have been able to infer some information both on the non equilibrium state of the CKs at the subcellular level and on the substrate concentrations, especially ADP which otherwise cannot be estimated in different cellular compartments.
Figure 2. The enzyme fluxes (mmoles.l H2 O cell-1 .s-1 ) and the substrates concentrations were calculated as described in the Theory section. The fluxes were fit to the values measured on rat heart perfused in control conditions. The methodology used here allows to compute the metabolites concentrations, including ADP, in subcellular spaces (Joubert et al., 2002b).
Since the M M -CK fluxes were constraint parameters, they obviously fit closely to the experimental results. But an unexpected result concerns the mitochondrial pathway (Fig. 2). The global unbalance of the unidirectional ATP fluxes result mainly from the far from equilibrium ANT activity (Ff/Fr = 43), while the unbalance of the CKmito (Ff/Fr = .5) is of the same order of magnitude as that of the CKmyos (Ff/Fr = 1.7), in the reverse direction. As a consequence of these unbalances, there is a gradient of ADP from the ATPase vicinity (106 µM) to the cytosol (70 µM ) and to the intermembrane space (37 µM ). Our result suggests that the cytosolic value does not reflect the one which really regulates the mitochondrial respiration. Table 2 : Maximum values of the CKs reverse and ANT forward activities (Vmax) units : mmoles.l H2O cell-1.s-1 Parameter
CKmito
CKcyto
CKmyos
ANT
Vmax
9.54
15.15
19.06
8.48
Another Information which may be derived via the present methodology is the enzyme maximum activities (table 2). The maximum activities of CKmito and ANT are similar due to their tight coupling considered by the present model. In a further study, this constraint will be released to take into account a possible direct pathway for ATP. The transport capability of the mitochondrial pathway is consistent with previously published data, On the other hand, the maximum activity of both the CKcyto and CKmyos are higher than the maximum ATPase requirement. The actual working points for the reverse fluxes of the CKs are respectively 50% (CKmito), 22% (CKcyto) and 17% (CKmyos). This figures are apparently low for the M M -CK. However if one consider that the maximum forward activity of these cytoplasmic enzymes are smaller than the reverse one (appendix 1), the forward working points are 30% (CKcyto) and 40% (CKmyos). These values are close to half activities. In its present state, this model is able to determine the local concentrations of a substrate in subcellular compartments. The present method is also designed to incorporate information from other sources, for instance experiments on skinned cardiac fibers. Given the fact that the computed values are model dependent, it will be refined to account for other experimental conditions. In particular the different energy pathway evidenced by partial respiration inhibition (Joubert et al., 2002a) and cardiac arrest (Joubert et al., 2002b) has to be considered. References Aliev, M. K. & Saks, V. A. (1993) BBA 1143(3), 291-300. Joubert, F., Hoerter, J. A. and Mazet, J.-L. (2001) Biophysical Journal 81, 2995-3004. Joubert, F., Mazet, J.-L., Mateo, P. and Hoerter, J. A. (2002a) J. Biol. Chem. 277, 18469-18476. Joubert, F., Mazet, J.-L., Mateo, P. and Hoerter, J. A. (2002b) (submitted to the present session) Korzeniewski, B. & Froncisz, W. (1991) BBA 1060(2), 210-223. Mendes, P. (1993) Comput. Appl. Biosci. 9, 563-571. Mendes, P. (1997) T rends Biochem. Sci. 22, 361-363. Mendes, P. & Kell, D. B. (1998) Bioinformatics 14, 869-883. Schimerlik, M. I. & Cleland, W. W. (1973) J Biol Chem. 248(24), 8418-23.
Appendix 1 Four enzymes are of antiport type : A + B Û P + Q where A, B, P, and Q depend on the selected enzyme. Each variable refer to the metabolite in the same position of the enzyme equation (see table 1, second column). We used the following equations to calculate the forward and reverse fluxes. Vr ⋅ K Eq ⋅ Ff =
Fr =
A⋅ B K pq
D P⋅Q Vr ⋅ K pq D
where D = 1+
A B P Q A⋅ B P ⋅Q A⋅Q B ⋅ P + + + + + + + Ka Kb K p Kq Kab K pq Kaq Kbp
Appendix 2 The following table gathers the value of the kinetics parameters used for the computation. The affinity coefficients for ATP and ADP were corrected to account for the affinity of these nucleotides for M g2+ (Korzeniewski & Froncisz, 1991). ATPase
CKmito (Schimerlik & Cleland, 1973)
v = 2.3e-03
Kab = 3.62e-07 M2 Keq = 1.6e+02 Ka = 1.6e-03 M Kb = 3.62e-04 M Kp = 2.6e-02 M Kq = 7.84e-04 M Kpq = 4.08e-06 M2 Kaq = 1.88e-05 M2 Kbp = 1.88e-06 M2
ATP synthase k1 = 1.00e+03
CKcyto and CKmyos (Aliev & Saks, 1993) Kab = 1.34e-07 M2 Keq = 1.6e+02 Ka = 3.9e-03 M Kb = 2.68e-04 M Kp = 1.0 e+21 M Kq = 3.4e-03 M Kpq = 2.89e-05 M2 Kaq = 1.33e-05 M2 Kbp = 1.47e-05 M2
ANT (Korzeniewski & Froncisz, 1991) Kab = 1.5e-09 M2 Keq = 6.67e+02 Ka = 5.0e-05 M Kb = 3.0e-05 M Kp = 4.0e-04 M Kq = 2.5e-03 M Kpq = 1.0e-06 M2 Kaq = 1.25e-07 M2 Kbp = 1.2e-08 M2
Summary The exchange scheme of high energy phosphate transport in a whole heart relies on a system of CK functioning in different ways. This suggests that the CKs are able to act both like a shuttle and like a buffer for the energy transfer. The challenge is to understand how these two functions are balanced in the CK system. One key of this balance is the knowledge of the local concentrations of the ADP nucleotide. These concentrations cannot be directly measured, but they may be derived by computation. In the present report we introduce the known properties of the enzymes catalyzing the exchange of high energy phosphate into the model of flux pathways derived from NM R experiments to compute both the maximum activity of each enzyme and the local concentrations of all the substrates. We show that the ADP distribution must be heterogeneous for the system to work. Its concentration is 50% higher in the vicinity of ATPase sites and 50% lower in the intermembrane space of the mitochondria than in the cytosol. Another result of this analysis is that the apparent large unbalance of the CKmito pathway is imposed by the adenosine nucleotide transferase fluxes. This analysis proves that it is possible to deduce the local concentrations of a substrate by combining data originating from NM R, biochemistry and enzymology into a common model. Keywords : creatine kinase shuttle, energy transfer, heart muscle, mathematical modeling Abbreviations : ADPx and ATPx : matrix nucleotides ADPcyto and ATPcyto : cytosolic nucleotides ADPmyos and ATPmyos : nucleotides close to the ATPase ADPim and ATPim : mitochondrial intermembrane nucleotides ANT : adenosine nucleotide translocase CK : creatine kinase, adenosine triphosphate creatine phosphotransferase, E.C 2.7.3.1 CKcyto : cytosolic CK Kmito : mitochondrial CK CKmyos : particulate CK close to the ATPase Cr : creatine PCr (phosphocreatine
Introduction In the muscle, the energy is transferred from the mitochondria to the sites of utilization via high energy phosphates carried by ATP and PCr. In this pathway, the CK, which is the only enzyme able to catalyze the reversible transfer of high energy phosphate to Cr, should play a major role. In the heart, which does not possess large energy stores, the adequacy of oxygen consumption to the energy demand is tight and permanent. In the course of the adjustment to increased work, no variations of CK substrates can be measured. This suggests that the CKs plays a buffering role. Recently we developed a methodology (Joubert et al., 2001) which allows separation of the activities of three CKs located at various sites within the rat myocyte. These three enzymes have
different kinetics in normoxic conditions (Joubert et al., 2002). A cytosolic CKcyto works at equilibrium, a particulate CKmyos close to ATPase favors ATP synthesis, the CKmito functions far from equilibrium in the direction of PCr synthesis. This proves that the CKs are able to act like an energy carrier. Since the some CK function out of equilibrium, the ADP concentration cannot be inferred at all sites from the thermodynamic equilibrium. M oreover the local ADP concentrations should depend on the working load of the heart. The knowledge of these variations would thus enlighten the understanding of how the CKs share their activity between buffering and transporting the energy. Unfortunately, it is not possible at present to measure directly the ADP concentration in subcellular spaces of a perfused heart. A particular difficulty arises from the fact that the CKmito pathway is composed of two enzymes the CKmito itself and the ANT, separated by a small intermembrane space of the mitochondria, which escapes the NM R investigations. Nevertheless the mitochondrial activity is regulated by the nucleotides present in this space. Here we have combined the knowledge from NM R analysis, from biochemical measurements and from the enzyme characteristics into a model to determine the nucleotide concentration in each of the subcellular compartments.
Theory
Figure 1. Enzyme organization used to represent the scheme of the exchange fluxes in perfused rat heart derived from NMR experiments (Joubert et al., 2001 ; 2002a). In control conditions, three CK activities were estimated, transferring phosphate between a PCr compartment and three ATP compartments (mitochondrial, cytosolic and closely bound to ATPases). For modeling, the mitochondria pathway was split into CKmito and ANT separated by a small intermembrane compartment non visible in NMR experiments. Note that the myosine ATPase is assumed to represent most of the ATPases.
Each flux of exchange was represented in terms of enzymatic reactions between four compartments (Fig. 1) : the cytosol, two mitochondrial compartments (the matrix and the intermembrane space) and a restricted space close to the ATP utilizing sites, which we consider to be mainly myosine
ATPase in the present work. Both flux PCr Û ATPcyto and PCr Û ATPmyos were carried by the same enzyme M M -CK. The mitochondrial pathway ATP Û PCr was replaced by two enzymes working in series, the ANT between the matrix and the intermembrane space and the CKmito between the intermembrane space and the cytosol. The functioning of the enzymes is described in the Table 2 and the appendix 1. The ATPase were supposed to work at a constant rate. The phosphate exchanger was a non limiting reaction imposing an instantaneous gradient (.15 ratio) between the cytosol and the matrix. Its rate was therefore imposed by the rate of the ATPase. For simplification, the ATP synthase was assumed to work like a non reversible mass Table 1 : Kinetic representation of the enzymes used to describe the energy fluxes in the model. Enzyme
equation
kinetics
ATPase
ATPmyos Ë ADPmyos + Pi
v = constant (see appendix 2)
phosphate exchanger
Pi Û Px
v = constant (see text)
ATP synthase
ADPx + Px Ë ATPx
v = k1 . [ADPx] . [Px]
ANT
ATPx + ADPim Û ADPx + ATPim antiport (see appendix 1 and 2)
CKcyto and CKmyos PCr + ADPcyto Û Cr + ATPcyto
antiport (see appendix 1 and 2)
PCr + ADPmyos Û Cr + ATPmyos antiport (see appendix 1 and 2) CKmito
PCr + ADPim Û Cr + ATPim
antiport (see appendix 1 and 2)
action reaction. The CKs and the ANT were described by antiport equations. The volume of each compartment was fixed as a fraction of the cell water volume : matrix (.24) intermembrane space ( .001), restricted space close to the ATPase (.1) and cytosol (.659). The computation was made in two steps. The substrates were assigned initial values to account for their measured values in the control conditions (Joubert et al., 2001) : ATPmyos (1.29 mmoles.l H2O cell-1.s-1), ATPcyto (3.95 mmoles.l H2O cell-1.s-1), ATPmito (1.56 mmoles.l H2O cell-1.s-1), PCr (10.6 mmoles.l H2O cell-1.s-1 = total PCr minus the non exchangeable PCr trapped in the mitochondria), Cr (10 mmoles.l H2O cell-1.s-1) and Pi (2.9 mmoles.l H2O cell-1.s-1). Then the system was solved for all the concentrations at a steady state. In the second step, the maximum activity of the three CKs and of the ANT were adjusted the fit the constraints : energy consumption (2.3 mmoles ATP.l H2O cell-1.s-1), CKcyto fluxes (3.3 mmoles ATP.l H2O cell-1.s-1), flux ratio of the CKmyos (Ff/Fr = 1.7). It was assumed that the ANT is tightly coupled with the CKmito on a mole to mole basis. The computations were made with the program Gepasi 3.21 (M endes, 1993, 1997 ; M endes &Kell, 1998).
Results and discussion Investigating the kinetic behavior of a physiological system by considering its known enzymatic properties greatly enhances the possibilities of understanding its mechanisms. In the present study we have been able to infer some information both on the non equilibrium state of the CKs at the subcellular level and on the substrate concentrations, especially ADP which otherwise cannot be estimated in different cellular compartments.
Figure 2. The enzyme fluxes (mmoles.l H2 O cell-1 .s-1 ) and the substrates concentrations were calculated as described in the Theory section. The fluxes were fit to the values measured on rat heart perfused in control conditions. The methodology used here allows to compute the metabolites concentrations, including ADP, in subcellular spaces (Joubert et al., 2002b).
Since the M M -CK fluxes were constraint parameters, they obviously fit closely to the experimental results. But an unexpected result concerns the mitochondrial pathway (Fig. 2). The global unbalance of the unidirectional ATP fluxes result mainly from the far from equilibrium ANT activity (Ff/Fr = 43), while the unbalance of the CKmito (Ff/Fr = .5) is of the same order of magnitude as that of the CKmyos (Ff/Fr = 1.7), in the reverse direction. As a consequence of these unbalances, there is a gradient of ADP from the ATPase vicinity (106 µM) to the cytosol (70 µM ) and to the intermembrane space (37 µM ). Our result suggests that the cytosolic value does not reflect the one which really regulates the mitochondrial respiration. Table 2 : Maximum values of the CKs reverse and ANT forward activities (Vmax) units : mmoles.l H2O cell-1.s-1 Parameter
CKmito
CKcyto
CKmyos
ANT
Vmax
9.54
15.15
19.06
8.48
Another Information which may be derived via the present methodology is the enzyme maximum activities (table 2). The maximum activities of CKmito and ANT are similar due to their tight coupling considered by the present model. In a further study, this constraint will be released to take into account a possible direct pathway for ATP. The transport capability of the mitochondrial pathway is consistent with previously published data, On the other hand, the maximum activity of both the CKcyto and CKmyos are higher than the maximum ATPase requirement. The actual working points for the reverse fluxes of the CKs are respectively 50% (CKmito), 22% (CKcyto) and 17% (CKmyos). This figures are apparently low for the M M -CK. However if one consider that the maximum forward activity of these cytoplasmic enzymes are smaller than the reverse one (appendix 1), the forward working points are 30% (CKcyto) and 40% (CKmyos). These values are close to half activities. In its present state, this model is able to determine the local concentrations of a substrate in subcellular compartments. The present method is also designed to incorporate information from other sources, for instance experiments on skinned cardiac fibers. Given the fact that the computed values are model dependent, it will be refined to account for other experimental conditions. In particular the different energy pathway evidenced by partial respiration inhibition (Joubert et al., 2002a) and cardiac arrest (Joubert et al., 2002b) has to be considered. References Aliev, M. K. & Saks, V. A. (1993) BBA 1143(3), 291-300. Joubert, F., Hoerter, J. A. and Mazet, J.-L. (2001) Biophysical Journal 81, 2995-3004. Joubert, F., Mazet, J.-L., Mateo, P. and Hoerter, J. A. (2002a) J. Biol. Chem. 277, 18469-18476. Joubert, F., Mazet, J.-L., Mateo, P. and Hoerter, J. A. (2002b) (submitted to the present session) Korzeniewski, B. & Froncisz, W. (1991) BBA 1060(2), 210-223. Mendes, P. (1993) Comput. Appl. Biosci. 9, 563-571. Mendes, P. (1997) T rends Biochem. Sci. 22, 361-363. Mendes, P. & Kell, D. B. (1998) Bioinformatics 14, 869-883. Schimerlik, M. I. & Cleland, W. W. (1973) J Biol Chem. 248(24), 8418-23.
Appendix 1 Four enzymes are of antiport type : A + B Û P + Q where A, B, P, and Q depend on the selected enzyme. Each variable refer to the metabolite in the same position of the enzyme equation (see table 1, second column). We used the following equations to calculate the forward and reverse fluxes. Vr ⋅ K Eq ⋅ Ff =
Fr =
A⋅ B K pq
D P⋅Q Vr ⋅ K pq D
where D = 1+
A B P Q A⋅ B P ⋅Q A⋅Q B ⋅ P + + + + + + + Ka Kb K p Kq Kab K pq Kaq Kbp
Appendix 2 The following table gathers the value of the kinetics parameters used for the computation. The affinity coefficients for ATP and ADP were corrected to account for the affinity of these nucleotides for M g2+ (Korzeniewski & Froncisz, 1991). ATPase
CKmito (Schimerlik & Cleland, 1973)
v = 2.3e-03
Kab = 3.62e-07 M2 Keq = 1.6e+02 Ka = 1.6e-03 M Kb = 3.62e-04 M Kp = 2.6e-02 M Kq = 7.84e-04 M Kpq = 4.08e-06 M2 Kaq = 1.88e-05 M2 Kbp = 1.88e-06 M2
ATP synthase k1 = 1.00e+03
CKcyto and CKmyos (Aliev & Saks, 1993) Kab = 1.34e-07 M2 Keq = 1.6e+02 Ka = 3.9e-03 M Kb = 2.68e-04 M Kp = 1.0 e+21 M Kq = 3.4e-03 M Kpq = 2.89e-05 M2 Kaq = 1.33e-05 M2 Kbp = 1.47e-05 M2
ANT (Korzeniewski & Froncisz, 1991) Kab = 1.5e-09 M2 Keq = 6.67e+02 Ka = 5.0e-05 M Kb = 3.0e-05 M Kp = 4.0e-04 M Kq = 2.5e-03 M Kpq = 1.0e-06 M2 Kaq = 1.25e-07 M2 Kbp = 1.2e-08 M2
