RIOi~VORGAXiC CIIEMISTR Z’ 9, 35-45 (I 978)
Apparent Stability Ctrwtnnts of H+ and 31~~* Complexes of S-Phosphoribosyl Q- 1 -Pyrophospha te*
INTROIXK’TION’
3s
R. E. THOMPSON ET AL. complete in vivo. To properly plan and interpret kinetic studies of PRPP uti. lizing enzymes under these conditions, it is often necessary to know the Mg2+-PRPP stability constants. Since the proton competes significantly with the Vg2+ for the PRPP ligand at pH values G 7.5, it is important to have protonstability constants as well. Apparently, neither of these constants has been determined by accurate methods, and only crude and widely different estimates have geen used in past enzyme kinetic studies. The objective of this study was to obtain accurate values of these stability constants with conditions of ionic strength (-0.2 M) and monovalent cation concentrations (0.17 M Na+ or K+) comparable to many physiological media. We have used the pH titration method [5] at 25*C, since it provides both H+- and Mg2+- ligand stability constants from simple pH titrations. From these constants the concentrations of each significant H+- and Mg2*-PRPP complex may be calculated at any pH [6, 7] with these conditions of ionic strength and Na+ or K+ concentrations. Accurate extrapolation of constants to other ionic strengths within 0.14 .2 M, and other monovalent cation concentrations should also be poss:Sle as described under the Results and Discussion section, and in analogy to other organophosphate complexes, the temperature dependence of the constants should be small. EXPERIMENTAL Materials The PRPP (?-la+ salt ). Ba2+ -ribosc-S-P. fruc:tose-I ,~~-rl~pll~rspl~~ttc, FiskeSubbaRow reducer, orcinol. Dowex resin, and the enzymes, orotidinc-S’-P pyrophosphorylase and orotidine-5’.P decarboxylase from yeast were purchased from Sigma Chemical Co. Thin-layer chromatographic plates were type Q2 from Quantum Industries (cellulose) and Polygram CEL 300 PEI (polyethyleneiminc impregnated cellulose) from Brinkmann. All other chemicals were of reagent grace. Heavy metal contaminants were extracted from the commercial MgClz with dithizone [8], and the MgCl, was recrystallized. Aqueous MgClz stock solutions were prepared from the recrystallized MgC12. and Mg2+ concentrations were determined either by NaOH titration of Ha0 cluates from a column of Dowex-50 (.H’ form) to which a!iquuts ~bf the Fvi~?l~ solution were applied (experiment I). or by complcxometric titrations \vith EDTA using Eriochromc Black T as indicator [o] (experiments 11 and 111). Sodium hydroxide stock solutions were prepared from supernatant fractions of centrifuged, saturated solutions and were stored in polyethylene bottles. kept inside glass bottles filled with argon to exclude CO,. Sodium hydrosidc titrant (-+.II\~) was standardized by titration with standard HCI (J. T. Baker DILUT-IT) to a bromothymol blue end point.
STABILITY
CONSTANTS
OF H+ AND Mg2+ COMPLEXES
37
PRPP Purification and Purity Determinations For titrations of experiment I wirh 0 mM. 3 mM. and 60 ml\1 MgCi,. the PRPP was further purified by the technique of Khorana et al. [lo]. except that the pooled PRPP sample eluted from the column was concentrated by lyophilization instead of by rotary evaporation. and the sample was increased to of Dowex I-2X. 100 mg for chromatography on a 2.2 cm X 4.2 cm column Cl-. The resultant PRPP was stored in a vacuum desiccator over phosphorous pentoside at -20°C. The preparation was found to be stable within reproducCommercial analysis ibility of the enzymatic assay ( -5%) for about 2 monrhs. showed a 1 :I carbon:lithium ratio. The second and third sets of titrations (experiments II and IIIj with 0 mM. 3 mM. 10 mhi. and 60 mM MgCI2 were made with commercial PRPP without further purification. The PRPP for experiment II was obtained and used as soon as possible after the synthesis of the PRPP by Sigma Chemical Co. The PRPP for experiments I and II were assayed enzymatically [ 1 1] utilizing a reference cell containing orotate at the same initial concentration as in the sample celI to permit use of the expanded scale of the Coleman 124 spectrophotometer with No. 165 recorder. Assay concentrations were 0.2-O-3 mM orotate. 2.0 mM MgCI,. about 0.04 m&f PRPP. 0.5 units/ml of orotidine-5’-P pyrophosphorylase. and 1 unit/ml of orotidine-5’-P decarboxylase in 20 mM Tris-CI at pH 8.0 in a l-cm-path cuvette. Thin-layer-chromatography (TLC) of PRPP was made on precoated microcrys:alline cellulose plates (experiment I) seilulose plates. These results. together or on polyethylenimine impregnated with the enzymatic iss2y, indicated a maximum of 7.5 mol% of impurity in the PRPP. However. the varisble sensitivity of the Haynes/Isherwood spray [ 121 . and the poor resolution of spots left us unconvinced of the PRPP purity. For column method was developed for separating this reasoxl. an ion.eschange PRPP and its likely contaminants. and the details on TLC are omitted here. The recommendations of Cohn on ion-exchange chromatography of nucleotides 1131 were used on solutions of Pi_ ribose-s-Pi. PP,, fructose-l.rj-diphosphate, and PRPP, either separately or as mixtures to establish elution conditions. The fructose diphosphare served as an analog of ribose-15diphosphate, which was not commercially available. Ribose and phosphate analyses were made on aliquots of each of the five fractions obtained by chromatography of about 20 pmol PRPP. Further details are given by I_i [ 14]_ Results of the analyses indicated that PRPP used in experiment III contained 2.0% Pi, 2.2% ribose-5-P, ?.6% PPi. and 15 ribose-I-5-diphosph3te. each specified as mol% of the PRPP. Potentiometric Titrations Titrations of about 10 ml of 3.0 mM instruments. including: (I) PHM 25/TTTl
PRPP were made with Radiometer 1 titrator. (2) PHA 925a scale es-
R. E. THOMPSON
38
ET AL.
pander, (3) TTA31 titrz-.on assembly. and (4) SBUl syringe burette. Either a G2222C glass electrode with K41 I_q calomel electrode and titration cell at roo::I temperature (~27°C; experiment 1) or a GK2320C combined electrode II and 111) was used. with a water-jacketed cell kept at 25°C (experiments Argon saturated with Hz0 was layered on top of the solutions, which were magnetically stirred. The ionic strengths. cc’, of solutions titrated were increased to initial values of 180 mM calculated as 1-1’= 3[MgC12JI + [MeCI] 1. where brackets and subscript indicate total concentrations, and Me = Na+ (experiment 1) or K+ (experiments II and 111). These PRPP solutions were titrated with about O.iN HCI (experiment I). or about O.lN NaOH (experiments II and Ill) after addition of about 50 mequiv HCI to achieve pH 2 4.0. and tlushing for an additional 2 min with argon. The SBUI and Hamilton No. 1002 syringes were both calibrated within 0.25 precision by weights of water or glycerin delivered to weighing bottles. The pH and titrant micrometer were read following about 0.2 ph unit increments of titrant. Each titration wx completed within 1-O-30 min, and TLC and enzymatic analyses on aliquots from the titrated solutions revealed no breakdown of the PRPP during the titrations. Titrations of the PRPP-free solutions (blanks) were made. but they did not affect the calculations and were omitted in the final calculations. Calculations Data analyses \vere made with the least-squares computer program SCOGSII developed at our university as a modified version tlf SCOGS [l-C 1 It differs from SCOGS in using 3 Marquardt minimizing subroutine [ lb] . ;tllowing f’or four different metal and ligand species and permitting other constants (e.g. titrant normality. total tigand concentrarron ). in addition to the metal-ligand stability constants to he fitted by the least-sqrrares method, if desired. Any of these parameters may be declared fixed (no: fitted) or free (fitted) on input (set Li [ 141 fl>r further details of the program). The quality of the fits were judged in part by the values of the chi-square statistic. x2 [ 17). This statistic was computed using estimated values of the statistical errors in the data. TI:e con-ditionsl stepwise stability constants c’3lcul;1ted were defined ;IS in the esample
where [ j 4. : denote concentrations and activities ( 10-P” keeping vvith the practice of Saycc [ 151. They rare “practical” in terms of experimentally measured quantities alone.
). respcctivcly. in c~mstants defined
STABILITY
CONSTANTS
OF I I+
86
KESULTSANDDISCUSSION
AND !blg"+ COMPLEXES
39
R. E. THOMPSON TABLE Mg’+
ET AL.
1
and HC Stability Constants of PRPP Complexes in Fig. 2 at 25OC. 0.17 M NaC1 or KCl, and 0.20 M Ionic Strength”
Exp x0.
Iog x-1
log x-r,
log kq
log k5
log k,
logk,
I
6.68 (0.0 I!
5.87 (0.01)
3.‘36 (0.03)
6.23 (0.04)
3.78 (0.15)
I .67b (0.10)
II
6.48 (0.0 1)
5.73
io.01)
3-17 (0.04)
6.34 (0.06)
4.20 (0.11)
1.73 to.081
6.52 (0.02)
5.91 (0.02)
3.16 (0.03)
6.22 (0.04)
4.15 (0.12)
1.60 (0.06)
III
o Standard deviations in parenthesis are those calculated by the least-squares program from the random errors only. Total errors, equal to random and systematic errors (e-g., from sample impurities) are likely to be several fold larger. Species 3 and 8 were found to contribute negligibly to the equilibria (see text). Experimental conditions were the same as in Fig. 1 except for rxperiment I, where titrations were in the presence of approximately 0 mM. 3 mM, and 60 mM total Mg*+ only. b The experimental log k, t= 3-18) and log ki (= 1.65) values were corrected for Li’ binding by extension of Eq. (1). This correction factor for ksfe is (1 + k, [ KC ] i k,i[Li+] )/( 1 + Xr, [ K’J ). giving a A iog k, = 0.05 and a 1 log ki = 0.02 with constants given by Smith and Alberty [ 18 ] and [ Li+ ] = 15 mM. Since these corrections are so small relative to standard deviations and their quantitative contributions to the isomeric HL and LH species uncertain without accurate microscopic constants, similar corrections of other constants of experiment I are omitted.
other (arbitrarily chosen) independent equilibria. Only the underlined species are concluded to be significant over the data range used as described below. and MLHhi species by deleting them from This was verified for the HLH2*the mode1 in one fit. When present, Iog k3 and log kg were fixed at reasonable values of 2.05 and 4.0, respectiveiy. since the fits were insensitive to a wide choice of values. The HLHM-species is only significant at extremes of pH and
Mg2’ concentrations equal to or greater than between the I-PP and 5-P groups is considered
10 mM. A Mg*+ complexed
unfavorable J3i3species due to charge repulsions between the phosphates. Results of fitting the constants of this model to all three given in Tabie I. The effects of PPi and ribose-1.5diphosphate
the
List data
set were incfuded
in the model
as ligands
relative
to
the
experiments are impurities in 2 and 3 (L9 and J-3).
STABILITY
CONSTANTS
OF H* AND Mg2+ COMPLEXES
41
respectively. The logarithms of overall stability constants (log 0) were taken from titrations in our laboratory on PPi as follows (unpublished results): L3.H. 8.5 1; L2*H2, 14.79; LZ-Mg, 5.08; L2-Mg-H, 11.6; LZ-hlg2. 7.41. The log /3 values for ribose-1 S-diphosphate were estimated from data on fructose-l .6diphosphate at ionic strengths and [Na’] close to our experiments as follows [19]: L3.H, 6.56; L3=H2. 12.39; L3*Mg, 2.73; L3mH*Mg. 9.29; L3-Mg,, 4.87. To test the sensitivity of the model to errors in these constants for the impurities, each stepwise constant for ribose-I Jdiphosphate complex was doubled (A log k = 0.30) and the data retltted. The resulting best-fit constants were not significantly changed. The effects of 1% systematic errors in the titrant and micrometer calibranormality. total Mg2+ and total PBPP concentrations, tion were also tested by intentionally fixin g them one at a time to nonoptimal values and refitting. These errors did not cause significant changes in the stability constants, although the quality of fits were noticeably poorer. The reason for this insensitivity to systematic errors is undoubtedly due to the high correlations among some of these parameters: (1) titrant normality, (2) total Mg2+ and PRPP concentrations, and (3) micrometer calibration. Thus an error in one was compensated for by altering the best-fit value of a correlated parameter otlrer than the stability constants. This emphasizes the advantage of fitting these parameters rather than assuming the experimental values, as emphasized by Briggs and Stuehr 1201 for excess acid (fitted in our analyses also)_ Of course, only one of the highly correlated parameters can be freed at a time, but any one suffices. None of the fitted stQbilit_v COZZStQlZtS had correlation coefficients with other parameters greater than 0.84. however. The only other measurements of which we are aware for any of these constants utilize a spectroscopic method. Berlin estimated k4 to be “approximately with either 0.1 M K’ or Na’ present in 50 mM Tris (pH 7.5) and IO3 M-l” Morton and Parsons obtained X-, = 3.8 X low3 M-l with 0.15 M KC1 in 0.1 M Tris (pH 8.5) [3]. Applicable
Solution
Conditions
The range of ionic strengths calculated by summation over all species was approximately 0.19-0.22 M. Since most activity coefficients 3re fairly constant in this range. a nominal value of 0.20 M may be assumed. The Na+ or K+ concentrations were I SO mM, 171 mhl. 150 mhl, and 0 mM for MgCl, concentrations of 0 mM, 3 mM_ 10 mM, and 60 mhl, respectively. A weighted average of 170 mM Na’ or K’ may be assumed for ail titrations with insignificant error. since concentrations of Na’- or K’-ligand species tiould be negligible, with 60 mM MgC12, even if 170 mM Na’ or K’ were present. This may be verified by calculations using the stability constants of Na+ for NaADP2- and NaAMP-, since these appear to mimic the I-PP and 5-P groups of PRPP as discussed below. (The stability constants of Na’ and K’ complexes are similar
42
R. E. THOMPSON ET AL.
STABILITY CONSTANTS OF H’ AND Mg2+ COMPLEXES
43
respectively. If species 9 (MLH) is omitted, the models of Figs. 2 and 3 are equivalent in that each macroscopic constant is an exact and known function of the microscopic constants alone. Species 9 (MLH) prevents the equivalence because it cannot be converted to HLHM as can its isomers in the ke step of Fig. 2. Fortunately, MLH concentrations were most likely negligible throughout the data, as deduced below, and will in any event only affect the magnitude of kg. In fact, ks and HLHM may be deleted from the Fig.2 mode, without significantly changing the results in Table 1, if a few extreme pH data are deleted. Although the models are then equivalent in the sense citfined, the microscopic model and constants give us more chemical information, such as the proportion of ML and LM species present under given conditions. Fortunately, it appears that only the underlined species are significant over the wide range of data pH and Mg2+ concentrations. We conclude this as follows. All 12 of the microscopic constants were estimated by using five of the eight exact equations between the macro- and microconstants, plus seven microconstants estimated from analogous reactions (e.g., MgADP- + H+ e MgHADP [22]) and reasonable charge effects. The concentration of each microscopic species was then calculated at each third pH datum of all titrations (“0.6 pH intervals) using the calculated microconstants, pH, and best-fit values of L and Mg2+ concentrations. None of the minor species (those not underlined) in Fig. 3 were found to contribute to more than 5% of the total ?RPP species. This conclusion was valid even when reasonable maximum microconstants were used to estimate upper limits of the minor species (derails will be sent to the reader on request). We conclude that tl.e simple model of Fig. 2 can be used omitting all species not underlined to calculate many nlicrospecies with the constants of Table 1. In particular, ML species are negligible. Extents of Complex Formation
For enzymatic studies, where the uncomplexed ligand. L. may inhibit the enzyme, it is important to maintain the ratio, [MgL] /[L] , constant [8]. which is equivalent to a constant [Mgz’] . The fractions of total I?RPP (,L,) as L, MgL, and Mg,L are then independent of [L] t and are calculated from the hganc! 1 conservation equation as [L] /[L] t = \1 t k4[Mg2+) + k&[Mg2+)*)-’ [MgLI/[Ll, = k4!Mg2’] [L]/(Llt,and [MgaLl/[Lll =k&7[Mg2+12[L1/IL\~ if the proton equilibria are ignored (good estimate for pH 27.5, although corcr., -re e*~ciltr inti~llldd\ Assuming ;1 !Mg*+] = (I.8 rnM. com~i?Cii~iX IV* 1 tO%‘ei -I-I ~8~ u,w -.,.., .,._.____,. ____ parable to mammalian cytoplasm [ 3] . calculated values are [L] /[L] t = 0.46, LMgLl IILl f = 0.51, and \MgzL]/[L] t = Q.02. For conditions ill rink where [Ca2+] would be appreciable, however, [MgL] and [Mg2L] would be lowered by the competitive binding of Ca 2+ . The [Caa’] concentratron in heparic cytoplasm is generally considered negligible relative to [Mg2’1 , however.
R. E. THOMPSON
Extrapolation to Ion Concentrations
Other
Temperatures,
Ionic
Strengths,
and
ET AL.
Monovalent
Conditions simuIating physiological media were chosen for these measurements Calculations of both relative and absolute species’ concentrations at other solution conditions would appear possible with good accuracy, however. since dependence of the H+- and Mg*’ -organophosphate stability constants on temperature and ionic strength (at 0.1-0.2 M) are small. The effects of different concentrations of aikali metal ions (Me) may also be estimated by assuming the values for Me-ADP or Me-AMP for the I-PP and 5-P groups of PRPP, respectively, since these analogs appear to bind Mg** to a similar extent. The general relation for the resulting apparent (sometimes called conditional) constant is 161
aw-bg =
.
kMg 1 + kH{H+}+ kM,
(Me]
0)
for the exampie of MgPRPP. The stability constants kMMeof Smith and Alberty [IS] for ADP and AMP appear accurate, although their Mg2+-nucleotide constants are substantially lower than accepted values [22j, and Mohan and Rechnitz [21] claimed that the Me-nucleotide constants of Smith and Alberty were also unreasonabIy sn-..I!_ This dnd related criticisms by Mohan and Rechnitz which have motivated us [2 I] have potentially la* dz- and ,erious consequences, to experimentally test i hese claims. We have concluded that these criticisms are not valid [ 143 and that the reported differences between Me-nucleotide stability strength are real. If the stability conconstants at 0 [21] and 0.20 M [18] Ionic _ stants of monovalent ion-&and compiexes were as high as those claimed by Mohan and Rechnitz [21], the resulting Li+ corrected log k4 of experiment I (Table 1) would be considerably larger than the values obtained in experiments II and III without L.i+. It is important to remember that the extrapolations described here are based on the assumptions that PRPP behaves similarly to ADP and AMP, and on the validity of other data. In addition to providing at least reasonable estimates for extrapolations, however, we hope that this discussion will emphasize the usefulness of these general relations, thereby motivating further studies to extend the data to verify or correct the conclusions and assumptions we have suggested.
REFERENCES 1.
T. A. Krenitsky, S.
M. Neil. G. B. Elion. and G. H. Hitchines.1
Biol. Chem- 244.4779
(1969). 2-
E. W. Holmes. J. A_ McDonald. J. M. McCord, J. B. Wyngaardcn. and W. N. KeUey, J. Bioi. Chem
248,144
(1973).
ST-ABILITY
CONSTANTS
OF H’
AND
Mg2+
45
COMPLEXES
3-
R. D. Berlin, Arch. Biochem. Biophys. 134. 120 Parsons, Arch. Biochem. Biophys. 175,677 (I 976).
4. 5. 6.
R. L. Switzer.J. Biol. Chem. 246. 2447 (1971). W. J. O’Sullivan and D. D. Prrrin. Biochemisrry 3. 18 (1964). hi. J. Johnson. in The Enzymes (P. D. Boyer. H. Lxdy. rind K. Myrb;ick,
7.
demic Press, Nrw York, 1960, Vol. 2. 2nd Ed., pp. 415 ff: D. D. Perrin and I. G. Ssyce. TaIanra 14.833 (1967).
8.
9.
(1969);
D. P. Morton
J. F. Morrison nnd M. L. Uhr. Biochim. Biophys. Acra 122.57 (1966). D. A. Skoog rend D. M. West, Fundamentals of _4na!_vtical Chemistr_v. Rinehart 2nd Winston. Nrw York, 1969. p. 343.
and S. M.
Eds.),
Aca-
2nd Ed.,
Holt,
H. G. Khomna. J. F. Fernandes. and A. Kornberg, J. A. Kornberg, I. Liebermxr. ;ind E. S. Simms, J. Biol. C. S. Haynrs nnd I-. A. Isherwood.L%rfure 164. 1107 W. E.Cohcn. in.Merhodsin En~_vmo!o~ Vol. 3 (S. P. Academic Press. New York, 1957, p_ 724.
Biol. Chem. 230. 941 (1958). Chem. 215, 389 (1955). Colowick
;Ind N:. 0.
14.
E. L.-F.
Stillwater
(1977),
15.
I. G. Sayce. Talanra 15, 1397 (1968). D. W. Mxquardt,/SI4M 11,431 (1963). W. C. Hsmilton. Sratisrics in rhe Physical
Ronald
Press.
10.
11. 12. 13.
16. 17.
Li, hf. S. thesis. Oklnhomtl
Stste
University,
Sciences,
(1949).
Ksphn,
Eds.),
p 39.
New
York
1969.
p. 90.
18. 19. 20. 21. 22.
23_
R. M. Smith nnd R. A. A1berty.J. Ph_vs. Chem. 60, 180 (1956). R. W. McGiIvery. Biochemistry 4. I924 (1965). T. N. Briggs and J. E. Stuehr.A~l. Chem. 46 1517 (1974). %f. S. Mohan and G. A. Rechnitz, J. Am. Chem. Sot. 92.5839 (1970). R. C. Phillips, P. George. and R. J. Rurman. J. Am. Chem. Sot. 88. 2631 (1966). L. G. Silien and A. E. %fiartell. Srabitity Constants of Feral-Ion Compleses. Chemical Society, No. 2.5.
24.
2.5.
26. 27. 28. 29.
London.
1964.
Special
Publication
No.
17 end
(1971).
Spcci31
Publication
hf. hf. Tnqui Khan end A. E.. hfartell, J. Amer. Chem. Sot. 89. 5585 (1967): L. B. Nanninpa. 1. Ph_Lx Chenr 61. 1144 (1957): E. W&as. ilcta Clrem. Stand_ 12. 528 (1958). H. Sigel and H. Brintzingcr, Hcfv. Chim. tlctu 47. 170! (1964). G. Weitzel and T. Speer, Z. Physiol. Chem. 313,212 (19.58). G. Schwarzenbach and G. Andercgg. Heir. Chim. Acta 40, 1229 (19.57). H. B. Clarke. D. C. Curworth. and S. P. D;ttta. Boic/rem- /. 58. 146 (1954). D. Veloso, R. W. Gunn, M. Oskarsson. and R. L. Leach. J. Biol. Chem. 248, 4811 (1973).
Received
29 August
1977
Apparent Stability Ctrwtnnts of H+ and 31~~* Complexes of S-Phosphoribosyl Q- 1 -Pyrophospha te*
INTROIXK’TION’
3s
R. E. THOMPSON ET AL. complete in vivo. To properly plan and interpret kinetic studies of PRPP uti. lizing enzymes under these conditions, it is often necessary to know the Mg2+-PRPP stability constants. Since the proton competes significantly with the Vg2+ for the PRPP ligand at pH values G 7.5, it is important to have protonstability constants as well. Apparently, neither of these constants has been determined by accurate methods, and only crude and widely different estimates have geen used in past enzyme kinetic studies. The objective of this study was to obtain accurate values of these stability constants with conditions of ionic strength (-0.2 M) and monovalent cation concentrations (0.17 M Na+ or K+) comparable to many physiological media. We have used the pH titration method [5] at 25*C, since it provides both H+- and Mg2+- ligand stability constants from simple pH titrations. From these constants the concentrations of each significant H+- and Mg2*-PRPP complex may be calculated at any pH [6, 7] with these conditions of ionic strength and Na+ or K+ concentrations. Accurate extrapolation of constants to other ionic strengths within 0.14 .2 M, and other monovalent cation concentrations should also be poss:Sle as described under the Results and Discussion section, and in analogy to other organophosphate complexes, the temperature dependence of the constants should be small. EXPERIMENTAL Materials The PRPP (?-la+ salt ). Ba2+ -ribosc-S-P. fruc:tose-I ,~~-rl~pll~rspl~~ttc, FiskeSubbaRow reducer, orcinol. Dowex resin, and the enzymes, orotidinc-S’-P pyrophosphorylase and orotidine-5’.P decarboxylase from yeast were purchased from Sigma Chemical Co. Thin-layer chromatographic plates were type Q2 from Quantum Industries (cellulose) and Polygram CEL 300 PEI (polyethyleneiminc impregnated cellulose) from Brinkmann. All other chemicals were of reagent grace. Heavy metal contaminants were extracted from the commercial MgClz with dithizone [8], and the MgCl, was recrystallized. Aqueous MgClz stock solutions were prepared from the recrystallized MgC12. and Mg2+ concentrations were determined either by NaOH titration of Ha0 cluates from a column of Dowex-50 (.H’ form) to which a!iquuts ~bf the Fvi~?l~ solution were applied (experiment I). or by complcxometric titrations \vith EDTA using Eriochromc Black T as indicator [o] (experiments 11 and 111). Sodium hydroxide stock solutions were prepared from supernatant fractions of centrifuged, saturated solutions and were stored in polyethylene bottles. kept inside glass bottles filled with argon to exclude CO,. Sodium hydrosidc titrant (-+.II\~) was standardized by titration with standard HCI (J. T. Baker DILUT-IT) to a bromothymol blue end point.
STABILITY
CONSTANTS
OF H+ AND Mg2+ COMPLEXES
37
PRPP Purification and Purity Determinations For titrations of experiment I wirh 0 mM. 3 mM. and 60 ml\1 MgCi,. the PRPP was further purified by the technique of Khorana et al. [lo]. except that the pooled PRPP sample eluted from the column was concentrated by lyophilization instead of by rotary evaporation. and the sample was increased to of Dowex I-2X. 100 mg for chromatography on a 2.2 cm X 4.2 cm column Cl-. The resultant PRPP was stored in a vacuum desiccator over phosphorous pentoside at -20°C. The preparation was found to be stable within reproducCommercial analysis ibility of the enzymatic assay ( -5%) for about 2 monrhs. showed a 1 :I carbon:lithium ratio. The second and third sets of titrations (experiments II and IIIj with 0 mM. 3 mM. 10 mhi. and 60 mM MgCI2 were made with commercial PRPP without further purification. The PRPP for experiment II was obtained and used as soon as possible after the synthesis of the PRPP by Sigma Chemical Co. The PRPP for experiments I and II were assayed enzymatically [ 1 1] utilizing a reference cell containing orotate at the same initial concentration as in the sample celI to permit use of the expanded scale of the Coleman 124 spectrophotometer with No. 165 recorder. Assay concentrations were 0.2-O-3 mM orotate. 2.0 mM MgCI,. about 0.04 m&f PRPP. 0.5 units/ml of orotidine-5’-P pyrophosphorylase. and 1 unit/ml of orotidine-5’-P decarboxylase in 20 mM Tris-CI at pH 8.0 in a l-cm-path cuvette. Thin-layer-chromatography (TLC) of PRPP was made on precoated microcrys:alline cellulose plates (experiment I) seilulose plates. These results. together or on polyethylenimine impregnated with the enzymatic iss2y, indicated a maximum of 7.5 mol% of impurity in the PRPP. However. the varisble sensitivity of the Haynes/Isherwood spray [ 121 . and the poor resolution of spots left us unconvinced of the PRPP purity. For column method was developed for separating this reasoxl. an ion.eschange PRPP and its likely contaminants. and the details on TLC are omitted here. The recommendations of Cohn on ion-exchange chromatography of nucleotides 1131 were used on solutions of Pi_ ribose-s-Pi. PP,, fructose-l.rj-diphosphate, and PRPP, either separately or as mixtures to establish elution conditions. The fructose diphosphare served as an analog of ribose-15diphosphate, which was not commercially available. Ribose and phosphate analyses were made on aliquots of each of the five fractions obtained by chromatography of about 20 pmol PRPP. Further details are given by I_i [ 14]_ Results of the analyses indicated that PRPP used in experiment III contained 2.0% Pi, 2.2% ribose-5-P, ?.6% PPi. and 15 ribose-I-5-diphosph3te. each specified as mol% of the PRPP. Potentiometric Titrations Titrations of about 10 ml of 3.0 mM instruments. including: (I) PHM 25/TTTl
PRPP were made with Radiometer 1 titrator. (2) PHA 925a scale es-
R. E. THOMPSON
38
ET AL.
pander, (3) TTA31 titrz-.on assembly. and (4) SBUl syringe burette. Either a G2222C glass electrode with K41 I_q calomel electrode and titration cell at roo::I temperature (~27°C; experiment 1) or a GK2320C combined electrode II and 111) was used. with a water-jacketed cell kept at 25°C (experiments Argon saturated with Hz0 was layered on top of the solutions, which were magnetically stirred. The ionic strengths. cc’, of solutions titrated were increased to initial values of 180 mM calculated as 1-1’= 3[MgC12JI + [MeCI] 1. where brackets and subscript indicate total concentrations, and Me = Na+ (experiment 1) or K+ (experiments II and 111). These PRPP solutions were titrated with about O.iN HCI (experiment I). or about O.lN NaOH (experiments II and Ill) after addition of about 50 mequiv HCI to achieve pH 2 4.0. and tlushing for an additional 2 min with argon. The SBUI and Hamilton No. 1002 syringes were both calibrated within 0.25 precision by weights of water or glycerin delivered to weighing bottles. The pH and titrant micrometer were read following about 0.2 ph unit increments of titrant. Each titration wx completed within 1-O-30 min, and TLC and enzymatic analyses on aliquots from the titrated solutions revealed no breakdown of the PRPP during the titrations. Titrations of the PRPP-free solutions (blanks) were made. but they did not affect the calculations and were omitted in the final calculations. Calculations Data analyses \vere made with the least-squares computer program SCOGSII developed at our university as a modified version tlf SCOGS [l-C 1 It differs from SCOGS in using 3 Marquardt minimizing subroutine [ lb] . ;tllowing f’or four different metal and ligand species and permitting other constants (e.g. titrant normality. total tigand concentrarron ). in addition to the metal-ligand stability constants to he fitted by the least-sqrrares method, if desired. Any of these parameters may be declared fixed (no: fitted) or free (fitted) on input (set Li [ 141 fl>r further details of the program). The quality of the fits were judged in part by the values of the chi-square statistic. x2 [ 17). This statistic was computed using estimated values of the statistical errors in the data. TI:e con-ditionsl stepwise stability constants c’3lcul;1ted were defined ;IS in the esample
where [ j 4. : denote concentrations and activities ( 10-P” keeping vvith the practice of Saycc [ 151. They rare “practical” in terms of experimentally measured quantities alone.
). respcctivcly. in c~mstants defined
STABILITY
CONSTANTS
OF I I+
86
KESULTSANDDISCUSSION
AND !blg"+ COMPLEXES
39
R. E. THOMPSON TABLE Mg’+
ET AL.
1
and HC Stability Constants of PRPP Complexes in Fig. 2 at 25OC. 0.17 M NaC1 or KCl, and 0.20 M Ionic Strength”
Exp x0.
Iog x-1
log x-r,
log kq
log k5
log k,
logk,
I
6.68 (0.0 I!
5.87 (0.01)
3.‘36 (0.03)
6.23 (0.04)
3.78 (0.15)
I .67b (0.10)
II
6.48 (0.0 1)
5.73
io.01)
3-17 (0.04)
6.34 (0.06)
4.20 (0.11)
1.73 to.081
6.52 (0.02)
5.91 (0.02)
3.16 (0.03)
6.22 (0.04)
4.15 (0.12)
1.60 (0.06)
III
o Standard deviations in parenthesis are those calculated by the least-squares program from the random errors only. Total errors, equal to random and systematic errors (e-g., from sample impurities) are likely to be several fold larger. Species 3 and 8 were found to contribute negligibly to the equilibria (see text). Experimental conditions were the same as in Fig. 1 except for rxperiment I, where titrations were in the presence of approximately 0 mM. 3 mM, and 60 mM total Mg*+ only. b The experimental log k, t= 3-18) and log ki (= 1.65) values were corrected for Li’ binding by extension of Eq. (1). This correction factor for ksfe is (1 + k, [ KC ] i k,i[Li+] )/( 1 + Xr, [ K’J ). giving a A iog k, = 0.05 and a 1 log ki = 0.02 with constants given by Smith and Alberty [ 18 ] and [ Li+ ] = 15 mM. Since these corrections are so small relative to standard deviations and their quantitative contributions to the isomeric HL and LH species uncertain without accurate microscopic constants, similar corrections of other constants of experiment I are omitted.
other (arbitrarily chosen) independent equilibria. Only the underlined species are concluded to be significant over the data range used as described below. and MLHhi species by deleting them from This was verified for the HLH2*the mode1 in one fit. When present, Iog k3 and log kg were fixed at reasonable values of 2.05 and 4.0, respectiveiy. since the fits were insensitive to a wide choice of values. The HLHM-species is only significant at extremes of pH and
Mg2’ concentrations equal to or greater than between the I-PP and 5-P groups is considered
10 mM. A Mg*+ complexed
unfavorable J3i3species due to charge repulsions between the phosphates. Results of fitting the constants of this model to all three given in Tabie I. The effects of PPi and ribose-1.5diphosphate
the
List data
set were incfuded
in the model
as ligands
relative
to
the
experiments are impurities in 2 and 3 (L9 and J-3).
STABILITY
CONSTANTS
OF H* AND Mg2+ COMPLEXES
41
respectively. The logarithms of overall stability constants (log 0) were taken from titrations in our laboratory on PPi as follows (unpublished results): L3.H. 8.5 1; L2*H2, 14.79; LZ-Mg, 5.08; L2-Mg-H, 11.6; LZ-hlg2. 7.41. The log /3 values for ribose-1 S-diphosphate were estimated from data on fructose-l .6diphosphate at ionic strengths and [Na’] close to our experiments as follows [19]: L3.H, 6.56; L3=H2. 12.39; L3*Mg, 2.73; L3mH*Mg. 9.29; L3-Mg,, 4.87. To test the sensitivity of the model to errors in these constants for the impurities, each stepwise constant for ribose-I Jdiphosphate complex was doubled (A log k = 0.30) and the data retltted. The resulting best-fit constants were not significantly changed. The effects of 1% systematic errors in the titrant and micrometer calibranormality. total Mg2+ and total PBPP concentrations, tion were also tested by intentionally fixin g them one at a time to nonoptimal values and refitting. These errors did not cause significant changes in the stability constants, although the quality of fits were noticeably poorer. The reason for this insensitivity to systematic errors is undoubtedly due to the high correlations among some of these parameters: (1) titrant normality, (2) total Mg2+ and PRPP concentrations, and (3) micrometer calibration. Thus an error in one was compensated for by altering the best-fit value of a correlated parameter otlrer than the stability constants. This emphasizes the advantage of fitting these parameters rather than assuming the experimental values, as emphasized by Briggs and Stuehr 1201 for excess acid (fitted in our analyses also)_ Of course, only one of the highly correlated parameters can be freed at a time, but any one suffices. None of the fitted stQbilit_v COZZStQlZtS had correlation coefficients with other parameters greater than 0.84. however. The only other measurements of which we are aware for any of these constants utilize a spectroscopic method. Berlin estimated k4 to be “approximately with either 0.1 M K’ or Na’ present in 50 mM Tris (pH 7.5) and IO3 M-l” Morton and Parsons obtained X-, = 3.8 X low3 M-l with 0.15 M KC1 in 0.1 M Tris (pH 8.5) [3]. Applicable
Solution
Conditions
The range of ionic strengths calculated by summation over all species was approximately 0.19-0.22 M. Since most activity coefficients 3re fairly constant in this range. a nominal value of 0.20 M may be assumed. The Na+ or K+ concentrations were I SO mM, 171 mhl. 150 mhl, and 0 mM for MgCl, concentrations of 0 mM, 3 mM_ 10 mM, and 60 mhl, respectively. A weighted average of 170 mM Na’ or K’ may be assumed for ail titrations with insignificant error. since concentrations of Na’- or K’-ligand species tiould be negligible, with 60 mM MgC12, even if 170 mM Na’ or K’ were present. This may be verified by calculations using the stability constants of Na+ for NaADP2- and NaAMP-, since these appear to mimic the I-PP and 5-P groups of PRPP as discussed below. (The stability constants of Na’ and K’ complexes are similar
42
R. E. THOMPSON ET AL.
STABILITY CONSTANTS OF H’ AND Mg2+ COMPLEXES
43
respectively. If species 9 (MLH) is omitted, the models of Figs. 2 and 3 are equivalent in that each macroscopic constant is an exact and known function of the microscopic constants alone. Species 9 (MLH) prevents the equivalence because it cannot be converted to HLHM as can its isomers in the ke step of Fig. 2. Fortunately, MLH concentrations were most likely negligible throughout the data, as deduced below, and will in any event only affect the magnitude of kg. In fact, ks and HLHM may be deleted from the Fig.2 mode, without significantly changing the results in Table 1, if a few extreme pH data are deleted. Although the models are then equivalent in the sense citfined, the microscopic model and constants give us more chemical information, such as the proportion of ML and LM species present under given conditions. Fortunately, it appears that only the underlined species are significant over the wide range of data pH and Mg2+ concentrations. We conclude this as follows. All 12 of the microscopic constants were estimated by using five of the eight exact equations between the macro- and microconstants, plus seven microconstants estimated from analogous reactions (e.g., MgADP- + H+ e MgHADP [22]) and reasonable charge effects. The concentration of each microscopic species was then calculated at each third pH datum of all titrations (“0.6 pH intervals) using the calculated microconstants, pH, and best-fit values of L and Mg2+ concentrations. None of the minor species (those not underlined) in Fig. 3 were found to contribute to more than 5% of the total ?RPP species. This conclusion was valid even when reasonable maximum microconstants were used to estimate upper limits of the minor species (derails will be sent to the reader on request). We conclude that tl.e simple model of Fig. 2 can be used omitting all species not underlined to calculate many nlicrospecies with the constants of Table 1. In particular, ML species are negligible. Extents of Complex Formation
For enzymatic studies, where the uncomplexed ligand. L. may inhibit the enzyme, it is important to maintain the ratio, [MgL] /[L] , constant [8]. which is equivalent to a constant [Mgz’] . The fractions of total I?RPP (,L,) as L, MgL, and Mg,L are then independent of [L] t and are calculated from the hganc! 1 conservation equation as [L] /[L] t = \1 t k4[Mg2+) + k&[Mg2+)*)-’ [MgLI/[Ll, = k4!Mg2’] [L]/(Llt,and [MgaLl/[Lll =k&7[Mg2+12[L1/IL\~ if the proton equilibria are ignored (good estimate for pH 27.5, although corcr., -re e*~ciltr inti~llldd\ Assuming ;1 !Mg*+] = (I.8 rnM. com~i?Cii~iX IV* 1 tO%‘ei -I-I ~8~ u,w -.,.., .,._.____,. ____ parable to mammalian cytoplasm [ 3] . calculated values are [L] /[L] t = 0.46, LMgLl IILl f = 0.51, and \MgzL]/[L] t = Q.02. For conditions ill rink where [Ca2+] would be appreciable, however, [MgL] and [Mg2L] would be lowered by the competitive binding of Ca 2+ . The [Caa’] concentratron in heparic cytoplasm is generally considered negligible relative to [Mg2’1 , however.
R. E. THOMPSON
Extrapolation to Ion Concentrations
Other
Temperatures,
Ionic
Strengths,
and
ET AL.
Monovalent
Conditions simuIating physiological media were chosen for these measurements Calculations of both relative and absolute species’ concentrations at other solution conditions would appear possible with good accuracy, however. since dependence of the H+- and Mg*’ -organophosphate stability constants on temperature and ionic strength (at 0.1-0.2 M) are small. The effects of different concentrations of aikali metal ions (Me) may also be estimated by assuming the values for Me-ADP or Me-AMP for the I-PP and 5-P groups of PRPP, respectively, since these analogs appear to bind Mg** to a similar extent. The general relation for the resulting apparent (sometimes called conditional) constant is 161
aw-bg =
.
kMg 1 + kH{H+}+ kM,
(Me]
0)
for the exampie of MgPRPP. The stability constants kMMeof Smith and Alberty [IS] for ADP and AMP appear accurate, although their Mg2+-nucleotide constants are substantially lower than accepted values [22j, and Mohan and Rechnitz [21] claimed that the Me-nucleotide constants of Smith and Alberty were also unreasonabIy sn-..I!_ This dnd related criticisms by Mohan and Rechnitz which have motivated us [2 I] have potentially la* dz- and ,erious consequences, to experimentally test i hese claims. We have concluded that these criticisms are not valid [ 143 and that the reported differences between Me-nucleotide stability strength are real. If the stability conconstants at 0 [21] and 0.20 M [18] Ionic _ stants of monovalent ion-&and compiexes were as high as those claimed by Mohan and Rechnitz [21], the resulting Li+ corrected log k4 of experiment I (Table 1) would be considerably larger than the values obtained in experiments II and III without L.i+. It is important to remember that the extrapolations described here are based on the assumptions that PRPP behaves similarly to ADP and AMP, and on the validity of other data. In addition to providing at least reasonable estimates for extrapolations, however, we hope that this discussion will emphasize the usefulness of these general relations, thereby motivating further studies to extend the data to verify or correct the conclusions and assumptions we have suggested.
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ST-ABILITY
CONSTANTS
OF H’
AND
Mg2+
45
COMPLEXES
3-
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Received
29 August
1977
