Adjustment of K′ for the Creatine Kinase, Adenylate Kinase and Atp Hydrolysis Equilibria to Varying Temperature and Ionic Strength

Temperature is directly linked to the metabolism and distribution of organisms because it affects reaction rates (Arrhenius, 1915) and thermodynamic equilibria (Van’t Hoff, 1898; Teague and Dobson, 1992). In the polar regions, marine fish and invertebrate life are found at temperatures of −1.8 °C (Schmidt-Nielsen, 1991; Withers, 1992), whereas in the hot springs, some organisms survive water temperatures above 50 °C (Wickstrom and Castenholz, 1973). Some subarctic insects, intertidal marine bivalves, gastropods and barnacles, and at least four species of terrestrial hibernating frogs, survive temperatures below freezing by depressing the supercooling point of their body fluids (Storey and Storey, 1988). Other organisms have been found in hydrothermal vents and can survive temperatures in excess of 100 °C (Prosser, 1986).

In a previous study we showed (i) how to adjust a number of key near-equilibrium kinase reactions to pH and pMg at 38 °C and ionic strength of 0.25 mol l^-1, and (ii) how to use these expressions to calculate the cytosolic phosphorylation ratio ([ATP]/[ADP][P_i]), free cytosolic [ADP] and free cytosolic [AMP] (Golding et al. 1995). Because many organisms maintain body temperatures below 38 °C and because many are subjected to wide daily or seasonal temperature fluctuations (Schmidt-Nielsen, 1991), the aim of the present study is to extend the utility of the methods of adjustment of equilibria to include temperature (T) and ionic strength (I). We calculate, for example, that K′ of creatine kinase increases by a factor of nearly two as temperature decreases from 38 to 5 °C. If these temperature adjustments are not taken into account, in combination with the effects of pH and pMg (Golding et al. 1995), serious errors can enter our calculations and affect our understanding of the strategies of metabolic adaptation of vertebrates and invertebrates, including the bioenergetics of scaling (Dobson and Headrick, 1995).

In order to adjust the K′ of a biochemical reaction to a new T and I, it is important first to understand the difference between a K′ and a K_ref (Alberty, 1994; Golding et al. 1995; Teague and Dobson, 1992). We will use the creatine kinase equilibrium as an example.

PCr is phosphocreatine, ADP is adenosine 5′-diphosphate, ATP is adenosine 5′-triphosphate, Cr is creatine and all concentrations are expressed in mol l^-1. Each reactant represents the sum of all the ionic and metal complex species. The chemical equation for the above reaction can now be written.

From the above equation, we can see that K′ equals K_ref multiplied by an expression consisting of pH, pMg and all the appropriate acid-dissociation (K_a) and magnesium-binding constants (K_b) of the major ionic species in our equilibrium system. Thus, the effect of pH and pMg on K′ is exerted through their participation in the right-hand side of equation 5 (Golding et al. 1995). For our present calculations, K_ref and the acid-dissociation constants (K_a values) and magnesium-binding constants (K_b values) must all be adjusted to T and I because it is through these chemical equations that temperature and ionic strength influence K′.

Given K_ref (at specified values of T and I) from the published literature, the sequence of mathematical operations required to adjust K′ to new experimental T and I is as follows.

1. Adjust K_ref from ionic strength 0.25 mol l^-1 to the condition of I=0 mol l^-1 using the extended Debye–Hückel equation.

2. Adjust K_ref (now at I=0 mol l^-1 ) to the new temperature (18 °C) using the Van’t Hoff equation.

3. Adjust K_ref to the new ionic strength (I=0.15 mol l^-1 ), again using the extended Debye–Hückel equation.

4. Adjust all metal-binding and acid-dissociation constants in the same way and substitute them into the right-hand side of equation 5.

5. K′ can now be calculated at specified pH, pMg, T, and I (Golding et al. 1995).

From published thermodynamic data on creatine kinase (Teague and Dobson, 1992): K_ref for CK is 4.959X10⁸ l mol^-1 (25 °C, I=0.25 mol l^-1 ) and enthalpy (H) for K_ref CK (equation 3) is -16.73 kJ mol^-1 at I=0.25 mol l^-1.

Using the extended form of the Debye–Hückel equation (Clarke and Glew, 1980; Alberty and Goldberg, 1992), adjust K_ref from I=0.25 mol l^-1 to I=0 mol l^-1. This adjustment is important because the H° value used in the next calculation is given at I=0 mol l^-1 (Table 1).

and γ is the activity coefficient of each separate ionic species in the K_ref, A_m is the Debye–Hückel constant (‘ion-size parameter’), where A_m=3[-16.390+(261.337/T)+3.369lnT-1.437(T/100)+0.112(T/100)² ] with T in K (Clarke and Glew, 1980; Alberty and Goldberg, 1992) and T(K)=273.15+t, I is ionic strength (mol l^-1 ), B is 1.6 kg^1/2 mol^-1/2, z is charge; II indicates the product of the specified values, and t is temperature (°C).

where 1.4775 and 1.60 are constants and Σz² is the sum of the squared individual charges of the reactant species (Goldberg and Tewari, 1991).

where K₁ is the value of the equilibrium constant at I=0 mol l^-1 and at the given temperature, T₁ is the temperature given for K₁ in Kelvin, and K₂ is the unknown value of the equilibrium constant at the new temperature T₂ (R=8.3145 J K^-1 mol^-1, ΔH° must be in J mol^-1 ).

For the K_ref reaction (equation 3), H°=-17.55 kJ mol^-1 at I=0 mol l^-1 (see Table 1). Substitution of K₁, T₁ and T₂ values in equation 10 yields a K_ref of 5.332X10⁸ at 18 °C (I=0 mol l^-1 ).

Once the K_ref has been adjusted to the required temperature (in our example 18 °C), the K_ref must then be adjusted from I=0 mol l^-1 to the desired ionic strength (in our example 0.15 mol l^-1 ). This is performed as described using the extended form of the Debye–Hückel equation (equation 6), ensuring that the value for A_m in equation 8 is calculated for the new temperature by using the Clarke and Glew data (Clarke and Glew, 1980; Alberty and Goldberg, 1992).

Now that K_ref is adjusted to I=0.15 mol l^-1, all of the magnesium-binding constants and acid-dissociation constants (a total of eight in the case of the creatine kinase reaction) must be adjusted in a similar manner. Following adjustment of all the constants, and having substituted these new values into equation 5 at specified pH and pMg, K′ may now be calculated. For our example using creatine kinase, K′=3.127Ò10² (T=18 °C, I=0.15 mol l^-1, pH 7.0, pMg 3.0).

The thermodynamic data necessary to permit similar adjustment calculations for K′ of adenylate kinase and ATP hydrolase reactions have been tabulated in Table 1.

Conclusions

A series of mathematical operations has been provsided to facilitate adjustment of K′ of a biochemical equilibrium to T and I at specified pH and pMg. It was shown that temperature and ionic strength exert their effect on K′ through K_ref and the values of K_a and K_b (equation 5). In order to ensure accurate bioenergetic comparisons between organs and tissues from a single species and across species spanning different vertebrate classes, the appropriate biochemical equilibria must be adjusted to the temperature, pH, pMg and ionic strength conditions of the cell. Assuming a constant value for any of these equilibrium constants can lead to errors which could conceivably show significant differences which did not really exist or, conversely, mask important differences that may affect conceptual advancement. We have provided information and theory in this study and in a companion paper dealing with pH and pMg (Golding et al. 1995) to make the necessary adjustments of K′, thereby permitting quantitative bioenergetic assessment.

The authors would like to thank R. N. Goldberg, Chemical Thermodynamics Division, National Institute of Standards and Technology, Gaithersburg, Maryland, USA, for his assistance on ionic strength calculations. This work was supported by an ARC small grant 91380.9821 (G.P.D.).