Equilibrium Constants under Physiological Conditions for the Reactions of Polynucleotide Phosphorylase and RNA Polymerase*

The observed equilibrium constants (K,& for the polynucleotide phosphorylase reaction (EC 2.7.7.8) have been determined under physiological conditions of temperature (38°C) and ionic strength (0.25 M) and physiological ranges of pH and free [Mg”]. Using B and square brackets to indicate total concentration: The value of Kobs has been found to be sensitive to variations in free [M$+] but relatively insensitive to At and 38”C, K,,hs = 4.08 at free free and 1.04 at free of K at Z is calculated

and eukaryotic cells (3), catalyzes the reversible polymerization of 5'-nucleoside diphosphates with the release of Pi (4,5). The enzyme can catalyze the polymerization of either a mixture of nucleoside diphosphates or of a single species such as the polymerization of ADP ( Equation  1) (1): The polymer formed from mixtures of nucleoside diphosphates cannot be distinguished chemically from natural RNA (6).
The equilibrium constant of this reaction has been suggested to be approximately 1.5 to 2 (3O"C, pH 8.1, MgCl* = lo-' M) (1) and sensitive to variations in magnesium concentration (2). Unfortunately, however, no actual data on the equilibrium constant of this reaction seem to be available and there seem to be no estimates of the constant under physiological conditions. Therefore, in the current study using the synthesis and degradation of poly(A) as a model, we have examined in detail the observed equilibrium constant (K,,J' of the polynucleotide phoshorylase reaction under physiological ranges of pH and free [Mg'+]. Combining these results with the equilibrium constants determined previously under the same conditions for the reactions of adenylate kinase (7), the hydrolysis of ATP to ADP and Pi (8), and the hydrolysis of ATP to AMP and PPi (9) has allowed the calculation of the I=& for the RNA polymerase reaction (EC 2.7.7.6) (Equation [ The values of the appropriate constants for ATP, ADP, AMP, and P, have been determined or cited previously (8,9,17). Only acid groups with a pK, between 5 and 9 have been considered.
For calculations at 25"C, the AH" values cited by Alberty (18)  For all calculations, unit activity has been taken to be the standard state of liquid water.

RESULTS
AND DISCUSSION

Apparent Binding Constants of Magnesium to Poly(A)-
The Scatchard plot of the interaction of magnesium with the poly(A) polymer is shown in Fig. 1. A curve rather than a straight line results probably reflecting cooperativity of the multiple binding sites on the molecule, although exact interpretation of such plots seems to be complicated (16). As an approximation, however, the graph can be interpreted as demonstrating roughly two types of binding sites. From the initial slope, it can be estimated that there are 40 binding sites/molecule each with an intrinsic binding constant of 2.3 X 10" M-'. Extrapolation of the terminal portion of the curve also predicts 100 sites/molecule of lower affinity (I&, = 2.2 x 10' M-l).
The total number of binding sites per molecule (estimated at 140) is in reasonable agreement with the 150 sites expected assuming 2 AMP residues per site and assuming a molecular weight of 10" for the polymer. The binding of magnesium to the polymer under the current conditions is slightly lower than that found by Sanders     The value of K can be used to back-calculate the value of Kobs for the reaction at a specified pH, K+, and free [Mg"'] concentration (Fig. 2). Equation 3 can be rewritten as Equation 11.
The relative insensitivity of Kobs of the polynucleotide phosphorylase reaction to pH (Fig. 3)  The value of K for the RNA polymerase reaction, therefore, can be calculated to be 2.89 X 10m7 M (AG" = 38.91 kJ/mol (9.30 kcal/mol)).
The value at pH 7.0 of K/rH+l (2.89) is not very different from that of polynucleotide phosphorylase reaction (K = 6.10). The values for Kobs under physiological conditions and the sensitivity to the free [Mg'+] (Fig. 4) and the pH (Fig. 3)  Although the synthesis of poly(A) has been used in this case as a model for the RNA polymerase reaction, the value of K would not be expected to be very different when the base composition of the polymer varies since there is no evidence for any but minimal difference among the bond energies of the various nucleoside triphosphates.
There are, however, significant differences among the stacking energies of RNA and DNA of differing base pair compositions (21, 22) which would have to be taken into account in describing the overall thermodynamics of RNA or DNA synthesis. The value found in the current work for the Kubs of the RNA polymerase reaction is very close to that found by Kato et al. (23) The value of Kobs for hydrolysis of the polymer at free [Mg2+] = 0 is 7.30 X lo4 (AGib, = -29.1 kJ/mol (-6.92 kcal/ mol)) and at free [Mg2+] = lo-" M is 7.63 x lo* (AebS = -29.1 kJ/mol (-6.94 kcal/mol)).