THE STATE OF MAGNESIUM IN CELLS AS ESTIMATED FROM THE ADENYLATE KINASE EQUILIBRIUM* BY TRWIN A. RoSE THE INSTITUTE FOR CANCER RESEARCH, PHILADELPHIA Communicated by Thomas F. Anderson, August 30, 1968 Magnesium functions in many enzymatic reactions as a cofactor and in com- plex with nucleotides acting as substrates. Numerous examples of a possible regulatory role of Mg can be cited from studies with isolated enzymes,'- and it is known that Mg affects the structural integrity of macromolecules such as trans- fer RNA" and functional elements such as ribosomes.'0 The major problem in translating this information on isolated preparations to the functioning cell is the difficulty in determining the distribution of Mg and the nucleotides among the free and complexed forms that function in the region of the cell for which this information is desired. Nanningall based an attempt to calculate the free Mg2+ and Ca2+ ion concentrations of frog muscle on the total content of these metals and of the principal known ligands (adenosine 5'-triphosphate (ATP), creatine-P, and myosin) and the dissociation constants of the complexes. However, this method suffers from the necessity of evaluating the contribution of all ligands as well as from the assumption that all the known ligands are contributing their full complexing capacity. During studies concerned with the control of glycolysis in red cells and the control of the phosphoglycerate kinase step in particular, it became important to determine the fractions of the cell's ATP and adenosine 5'-diphosphate (ADP) that were present as Mg complexes. Just as the problem of determining the distribution of protonated and dissociated forms of an acid can be solved from a knowledge of pH and pKa of the acid, so it would be possible to determine the liganded and free forms of all rapidly established Mg complexes from a knowledge of Mg2+ ion concentration and the appropriate dissociation constants. An esti- mate of (Mg2+) could be made from the position of equilibrium of a reaction in the cell if the equilibrium value were strongly Mg-dependent. To be useful in this regard such a reaction must be at thermodynamic equilibrium in the cell and must have all reactants in suitably measurable amounts. Preferably, the posi- tion of equilibrium should be insensitive to pH in the physiological range, since the pH within the compartment of the cell containing the components of the reaction will generally be unknown. The present study concerns the use of the adenylate kinase equilibrium for this purpose and the application of this method to the intact red cell. Theory.-When 32Pi is incubated with glycolyzing human erythrocytes, the isotope is found to be incorporated into the 9-phosphoryl position of ATP at about the same time as it is into the 7-position.12' 13 The 7-position is first to be labeled in the course of glycolysis, since phosphoglycerate kinase reacts with ADP and not with adenosine 5'-phosphate AMP.14 Thus randomization of radio- activity requires two cycles of the adenylate kinase reaction: ATP7* + AMP -- ADP + ADP,-* AMP + ATPP*, which must be very rapid relative to the initial labeling. Since, in the cell, the rate of ATP generation through glycolysis 1079 Downloaded by guest on September 27, 2021 1080 BIOCHEMISTRY: I. A. ROSE PRoc. N. A. S. TABLE 1. Dissociation constants for Mg2+, H+, and K+ complexes of AMP, ADP, and A TP at 350 and 0.1 ionic strength. Dissociation Dissociation reaction constant Reference (AMP)H- * (AMP)2- + H+ 10^ 4 M 16 (AMP)Mg (AMP)2- + Mg2+ 10 mM 17 (ADP)H2- (ADP)3- + H+ 106.8 M 18 (ADP)Mg- (ADP)3- + Mg2+ 0.30 mM 18 (ADP)HMg (ADP)H2- + Mg2+ 7.6 mM 18 (ADP)K2- (ADP)3- + K+ 200 mM 19 (ATP)H3- (ATP)4- + H+ 10-7.05 M 18 (ATP)Mg2- (ATP)4- + Mg2+ 0.019 mM 18 (ATP)HMg-, (ATP)H3- + Mg2+ 1.35 mM 18 (ATP)K3- (ATP)4- + K+ 100 mM 19 is sufficient to maintain the ATP level, the adenylate kinase step must also be much more rapid than the degradative steps such as ATPase and adenylate deaminase. Hence, the adenylate kinase reaction must be close to equilibrium. Bowen and Kerwin15 demonstrated that the position of equilibrium of the adenylate kinase reaction is a biphasic function of magnesium concentration. At concentrations of Mg very low compared with the nucleotide concentrations, the value of [(2AMP) (ZATP) ]/(2ADP)2 = 0.37 was obtained when the reaction was started in either direction at pH 7.5, , = 0.02. (The temperature used in these determinations was unstated.) The observed equilibrium value first increased with added Mg as the ATP was preferentially titrated and then, due to the squared term in the denominator, the value decreased as the ADP became complexed. Whereas this behavior of Keq when related to total Mg (as done by Bowen and Kerwin) is a function of the adenylate concentration, it is possible to obtain an expression for the equilibrium constant that is independent of the total amounts of both the nucleotides and Mg and which depends only on the concentration of free MgS+ ion. Define the observed mass action ratio K' in terms of the significant free, pro- tonated, and complexed forms of AMP (M), ADP (D), and ATP (T): (M2- + MH + MMg)- (T4- + TMg2- + TH3- + THMg + TK3-) K =. (D3- + DMg- + DH2- + DHMg + DK2-)2 (1) Using the values of the dissociation constants at 350 and , = 0.1 that are listed in Table 1, one obtains equation (2), which relates K' to the millimolar concen- trations of K+ and Mg2+, x. (M2-) (T4-) (D3-)2 (1 + 10.4pH + +1 0.019 + 107l6pH 1 + 13) + (K+)1 -L0 + 0O8019 1+.35)+~j 100 (2) [1 + 0 3 + 106,8-pH (1 + 6 + (0) 7e0.30 2001 From the zero-Mg experimental value of Bowen and Kerwin, at pH 7.5 and K+ Downloaded by guest on September 27, 2021 VOL. 61, 1968 BIOCHEMISTRY: 1. A. ROSE 1081 = 20 mM, one can calculate, using equation (2), the pH- and K+-independent constant [(M2-) (T4-) ]/(D3-)2 which, due to compensating effects in the secon- dary pKa's of the nucleotides, remains at 0.37. Figure 1 presents the computed values K' as a function of (Mg2+) in the pH range 6.5-8.0. It will be noted that K' increases most sensitively with (Mg2+) in the range 0-0.25 mM, and that it becomes insensitive to (Mg2+) in a peak region the width of which is strongly influenced by pH. At higher (Mg2+), K' falls slowly to a limiting value of 0.17. Methods.-The nucleotides were determined by standard methods:20 ATP by yeast hexokinase and glucose-6-P dehydrogenase; ADP by pyruvate kinase and lactate de- hydrogenase; and AMP by prior addition of ATP and adenylate kinase, acidification, and determination of the two equivalents of ADP formed thereby. For the determination of ATP in the presence of deoxyglucose, a tenfold excess of glucose was added to mini- mize the side reaction of ATP with deoxyglucose. At these high levels of glucose a small correction for its direct oxidation by glucose-6-P dehydrogenase was necessary. In the assay of AMP, cognizance was taken of the presence of AMP in commercial preparations of reduced diphosphopyridine nucleotide (DPNH).20 Failure to correct for this is re- sponsible for the high values previously determined21 for the adenylate kinase equilibrium. The DPNH used in these assays was purified by chromatography22 to reduce the level of AMP, although a more satisfactory method exists.21 Glycerate-2,3-diP was determined as glycerate-2-P plus glycerate-3-P after treatment with glycerate-P mutaseY20 Total Mg was kindly determined by Dr. Stuart Blum by atomic absorption. Human red cells were prepared from normal donors just prior to study.2' Experimertal.-Estimate of (Mg2+) in frozen-thawed preparations of red cells: Since human erythrocytes are known to be impermeable to the entry of Mg2+ ion,24' 25 studies were begun with disrupted preparations. One may add MgCl2 or ethylenediaminetetraacetate (EDTA) and determine the effect on the equi- librium distribution of the adenylate kinase reactants. In this way it would be possible to determine where in the K' versus (Mg2+) function the (Mg2+) of the initial hemolysate was poised. This was done with a water hemolysate (2 vol of water/vol of cells), prepared by successive freezings and thawings, that had been reconstituted by lyophilization to the original cell volume, and to which .8 .7- K FIG. 1.-Effect of (Mg2+) on the 2 3 4 5 6 mass action ratio K' of adenylate Mg. mm kinase according to equation (2), .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 T = 35°, , = 0.1. Mg , mM Downloaded by guest on September 27, 2021 1082 BIOCHEMISTRI': I. A. ROSE PROC. N. A. S. AMP was added to provide greater amounts of AMP and ADP in the equilibrium for increased accuracy and freedom from artifact (see below). The results of such an experiment are given in Table 2. The value for K' of 0.77, observed for the earliest sample, could be attributed to (Mg2+) at either 134 or 1770'Al[ (Fig. 1, pH 7.2). A sample taken five minutes later gave a higher value of K'. A reasonable basis for this increased K', assuming the lower value of (Mg2+) to be the real one, would be the observed loss of 0.45 Mmole of ATP/ml due to an ATPase, thus making an almost equivalent amount of Mg available for complex formation.