Adjustment of K′ to Varying pH and pMg for the Creatine Kinase, Adenylate Kinase and Atp Hydrolysis Equilibria Permitting Quantitative Bioenergetic Assessment

Knowledge of the thermodynamics of creatine kinase (EC 2.7.3.2), adenylate kinase (EC 2.7.4.3) and adenosinetriphosphatase (EC 3.6.1.3) reactions is central to studying the biochemical and physiological processes of the cell. The maintenance of near-equilibrium of the creatine kinase and adenylate kinase reactions in vivo (Lawson and Veech, 1979; Teague and Dobson, 1992; Veech et al. 1979) has led to their widespread use in estimating free cytosolic [ADP], free [AMP], cytosolic phosphorylation ratio ([ATP]/[ADP][P_i]) and [PCr]/[P_i] (where PCr is phosphocreatine and P_i is orthophosphate) ratio (Chance et al. 1985, 1986; Gyulai et al. 1985; Veech et al. 1979). The cytosolic phosphorylation ratio provides an index of the energy status of the cell. Free [ADP] and [P_i] have been implicated as the primary kinetic controllers of steady-state rates of oxygen consumption (Balaban, 1990; Chance et al. 1986; Chance and Williams, 1955; Headrick et al. 1994; Lardy and Wellman, 1952; Ugurbil et al. 1987), while free [AMP] has been shown to be involved in the regulation of a number of key glycogenolytic and glycolytic enzymes (Dobson et al. 1986; Matherne et al. 1993) and IMP levels (Matherne et al. 1993) and is possibly linked to cytosolic adenosine production (Headrick and Willis, 1990). The transformed Gibbs energy of the system (Δ_fG′_ATP) can be calculated from knowledge of the standard transformed Gibbs energy of formation (Δ_fG′ °_ATP) and from the phosphorylation ratio derived from the creatine kinase equilibrium and inorganic orthophosphate concentration. Δ_fG′_ATP may also be used to estimate the thermodynamic efficiency in forming 3 mol of ATP along the mitochondrial respiratory chain from NADH to O₂ for every 2 electrons cycled (Dobson and Headrick, 1995).

The aim of this study is to provide quantitative mathematical expressions for the adjustment of an equilibrium constant to varying pH and free [Mg²⁺], thereby permitting more accurate bioenergetic assessment of mammalian organs and tissues. It is argued that such parameters have little quantitative meaning without the K′ of each reaction being adjusted to the intracellular pH, free [Mg²⁺], temperature (T) and ionic strength (I) of the biological system under investigation (symbols are defined in Table 1). The importance of adjustment of the apparent equilibrium constant of creatine kinase (K′_CK) to the pH and pMg of the cell may be illustrated in the anaesthetized rat brain. The widely used value for the K′_CK constant for bioenergetic calculations is 166, which is specified at pH 7.0, free [Mg²⁺], 1.0 mmol l⁻¹; I, 0.25 mol l⁻¹ and T, 38 °C. However, the adjusted constant accounting for pH and pMg of anaesthetized rat brain is 122 (pH, 7.0; free [Mg²⁺], 0.5 mmol l⁻¹; I, 0.25 mol l⁻¹; T, 38 °C). In this case, if K′ is not adjusted there would be significant errors (26 %) in the calculation of free cytosolic [ADP] and the cytosolic phosphorylation ratio ([ATP]/[ADP][P_i]). Moreover, in muscle during vigorous exercise, pH may fall by up to 1 unit (from 7.2 to 6.2) (Fitts, 1994), which would require an adjustment of K′_CK by nearly an order of magnitude from 85 to 726.

In order to clarify the situation, Alberty (1992, 1994b) has defined two equation types, a biochemical equation and a chemical equation. A biochemical equation is one describing an equilibrium mixture of total reactants followed by K′ at specified pH, pMg, I, P and T. The value of K′ may be analytically measured in the laboratory or calculated from in vitro experimental data using a system of equations as described by Teague and Dobson (1992). The point of emphasis here is that a biochemical equation deals with total concentrations and therefore does not balance charge, but it must balance elements, except for H⁺ and Mg²⁺ when pH and free [Mg²⁺] are specified. A chemical equation, in contrast, is defined as one comprising ionic species of reactants at specified I, P and T. By definition, a chemical reaction must balance charge and atoms of elements. Furthermore, because it is a reference equation, it may be part of a mathematical expression with the appropriate metal-binding and acid-dissociation constants with which to calculateK′ with varying pH and pMg (Teague and Dobson, 1992). The equilibrium constant of a chemical equation is thus abbreviated K_ref and is dependent on I, P and T (Alberty and Goldberg, 1992). In contrast to a biochemical equation, there exist numerous chemical equations, each with specified ionic species and corresponding K_ref values. It is important to realize that chemical and biochemical equations are two separate systems and cannot be added or subtracted from one another to form one equation (Alberty and Goldberg, 1992).

This distinction between biochemical and chemical equations serves to promote understanding of complex physiological processes using precise thermodynamic language. What follows is the use of such nomenclature in the adjustment of K′ with varying pH and free [Mg²⁺] at I=0.25 mol l⁻¹ and T=38 °C. Computations were performed using a Macintosh computer (Microsoft Excel software).

The primary aim of this study is to provide biochemists and physiologists with a number of thermodynamic expressions that will enable them to adjust K′ of key equilibria to the pH and free [Mg²⁺] of their experimental system at I=0.25 mol l⁻¹ and 38 °C. Such information is essential for quantifying the bioenergetic state of a tissue or organ. The reactant concentrations ATP and PCr and the parameters pH and pMg may be obtained by phosphorus magnetic resonance spectroscopy (³¹P MRS) and the total creatine concentration by conventional metabolic analysis methodology (Chance et al. 1988; Conway and Radda, 1991; Gadian, 1982; Gadian and Radda, 1981; Ingwall, 1982; Kushmerick and Meyer, 1985; Meyer et al. 1982). It is important to convert the tissue enzymatic measurements from units of μmol g⁻¹ wet mass to mol l⁻¹, which requires estimations of the total tissue water space and the intra- and extracellular water distribution of that total water space for the organ system under investigation (Dobson et al. 1992; Masuda et al. 1990).

The present study has provided mathematical expressions for calculating the apparent equilibrium constant (K′) of the creatine kinase, adenylate kinase and ATP hydrolysis reactions in terms of K_ref and the appropriate acid-dissociation and magnesium-binding constants. We have calculated K_ref for each reaction and demonstrated how K′ can be adjusted to varying levels of experimental pH and free [Mg²⁺]. Tables of K′ as a function of pH and free [Mg²⁺] at I=0.25 mol l⁻¹ and T=38 °C have also been provided for convenience. Finally, we have indicated some of the biochemical applications for using the equilibrium constants in assessing cellular bioenergetics taking place under physiological and pathophysiological conditions.

The authors would like to thank R. A. Alberty, Professor Emeritus, Department of Chemistry, Massachusetts Institute of Technology, for critical comments on the manuscript. We thank members of the Department of Molecular Sciences, Division of Chemistry (Dr P. Duggan) and Division of Biochemistry, James Cook University, for their interest and lively discussions on some aspects of this study. This work was supported by an ARC small grant 1.91380.9821 (G.P.D.).