10
E. H. FRIEDEN, M. S. DUNK AND C. D. CORYELL
QUANTITATIVE INVESTIGATIOSS OF AMINO ACIDS A S D PEPTIDES. X EQUILIBRIA BETWEEN
AMINOACIDSAND FORMALDEHYDE : LEUCINEAND N-METHYLLEUCI~
EDWARD H. FRIEDEN,z MAX S. DUNN, AND CHARLES D. CORPELL
Department of Chemistry, Unzversiiy of Calzfornia, Los Angeles, Calafornza Received September 11, 1942
In paper VI1 of this series (4), attention was called to the fact that the equilibria between amino acids and formaldehyde could be studied conveniently by a polarimetric procedure, and the application of the method to the reaction of formaldehyde and I ( - )-proline was described. Similar studies have now been completed for a number of other amino acids. This paper demibes the application of the polarimetric procedure to the reaction of formaldehyde with the anions of d( -)-N-methylleucine and Z( -)-leucine. In addition, a potentiometric study of the former reaction is reported for comparison. EXPERIMENTAL
1( -)-Leucine3 was obtained from Amino Acid Manufactures. d( -)-N-
Methylleucine was prepared from crude I ( - )-leucine by first converting the latter to active a-bromoisocaproic acid with nitrosyl bromide, and allowing the freshly distilled bromo acid to react with an excess of methylamine in aqueous solution. The solid obtained upon evaporation of the solvent was twice recrystallized from methyl ethyl ketone (Analysis: [a]:'" = -18.9' (c = 0.614 1 = 2.00, a = -0.232°)4. Calculated for C ~ H I ~ O C ~ N=: 57.80, H = 10.40; found: C = 57.60, 57.78; H = 10.32, 10.14.)5 The polarimetric studies were made using the apparatus and procedure described previously, with one modification. The sodium-vapor lamp was replaced by a General Electric 3H mercury-vapor lamp. When equipped with a combination of -Corning HR yellow shade and didymium-glass filters, no lines other than 5461 A. were detectable with a Beckman quartz spectrophotometer. The intensity of the light makes this lamp admirably suited to polarimetry. 1
For the ninth communication in this series, see Dnnn, Frieden, Stoddard, and Brown:
J. Biol. Chem. 144, 487 (1942). This paper is part of a thesis submitted by Edward H. Frieden to the Graduate School of the University of California in partial fulfillment of the requirements for the degree of Doctor of Philosophy, October, 1942. Some of the material herein was presented a t the Boston Meeting of the American Society of Biological Chemists, April, 1942. This work was aided by grants from Merck and Company and from the University of California. 2 Present address: Department of Chemistry, University of Texas, Austin, Texas. a A.P., lot 6 4 . 4 Fischer and Mechel ( 3 ) give [a]:' = -19.77". 6 The carbon and hydrogen analyses were made by hfr. Edward Duncan.
INVESTIGATIONS O F AMINO ACIDS AND PEPTIDES.
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X
The potentiometric study of the formaldehyde-methylleucine equilibrium was made according to the procedure of Levy (5), except that pH measurements were made with a Beckman industrial model pH meter instead of the hydrogen electrode. The pH of a solution of N-methylleucine to which half an equivalent of sodium hydroxide had been added was measured as a function of the concentration of added formaldehyde. RESULTS
The data obtained from the potentiometric titration of half-neutralized N methylleucine with 12.6 M formaldehyde are given in table 1. The results of the polarimetric titrations are listed in tables 2 and 3. The results of each study will be discussed separately. The data of table 1 can be adequately treated by the method of Levy (5). From structural considerations, it would be expected that but 1 mole of forTABLE 1 Titration of 0.0167 M N-methylleucine with 18.66 M formaldehyde
II
POPYALDEBYDE
POPYAIDEEYDE
PH Volume
Concentration
ml.
moles per liter
0.00 0.11 0.21 0.29 0.40 0.61 0.86 1.10 1.50 2.00
O.Oo0 0.0646
0.1198 0.1889 0.2320 0.347 0.488 0.618 0.835 1.079
Concentration
ml.
moles par liter
____9.89 9.79 9.69 9.60 9.62 9.42 9.31 9.27 9.18 9.08
I PH
Volume
2.50 3.01 4.00 5.00 7.50 10.00 15.00 20.00 30.00 40.00
1.321 1.556 1.973 2.388 3.272 4.01 5.19 6.09 7.35 8.20
9.00 8.95 8.87 8.79 8.64 8.59 8.48 8.39 8.30 8.23
~~
maldehyde reacts per mole of methylleucine. The limiting slope of the curve relating pH and the log of the formaldehyde concentration is 1 if 1 mole of formaldehyde reacts, and 2 if 2 moles of the aldehyde are concerned in the reaction. Figure 1 confirms the prediction that the former reaction is concerned. This reaction a,nd the equilibrium constant associated with it can be formulated as:
As shown by Levy, the evaluation of L1 from the potentiometric date merely requires that the concentration of formaldehyde be plotted as a function of the quantity
g)
, where KZis the second acidic dissociation constant of methyl-
leucine, 9.89. The slope of this line is LI. Figure 2 indicates that the slope,
12
E. H. FRIEDEN, M. S. DUXX AXD C. D. CORYELL
and hence the value of LI, is 4.77. (Following Levy's notation, we have used Gf to represent (H') in the presence of formaldehyde.)
U6
20 I2
14 16
-?Y LOG
F
FIG.1. The pH of an equimolar solution of anionic and zwitter-ionic S-methylleucine as a function of formaldehyde concentration.
FIG.2. Analytic treatment of the pH-formaldehyde titration data for hr-methylleucine, G, is measured (H+) in the presence of formaldehyde.
I n figure 3, the molecular rotation of methylleucine anion is plotted as a function of the total added formaldehyde. The data of table 2 are represented
INVESTIGATIONS OF AMINO ACIDS AND PEPTIDES.
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by the points, superimposed upon the predicted curve derived from the analysis shown below. Figure 3 i s qualitative confirmation of the potentiometric analyTABLE 2 Results of the polarimetric titration of 0.1880 M d(-)-N-methylleucine with 18.66 M formaldehyde FOBWLDEEYDE
N-METRYLLEVCINE
Volume
Concentration
mi.
moles per Iilcr
0.00 0.160 0.300 0.6Gi-I
0.760 1 .ooo 1.310 1.755 2.255 3.000 4.005 5.00 7.00 10.00 13.00 20.00
O.Oo0 0.0250 0.0496 0.0831 0.1250 0.1652 0.2155 0.2865 0.3660 0.483 0.636 0.785 1.071 1.477 1.854 2.640
mdes per likr
0.1220 0.1217 0.1214 0.1212 0.1208 0.1203 0.1m 0.1191 0.1183 0.1173 0.1159 0.1143 0.1116 0.1077 0.1040 0.0964
OBSEPVED POTATION
dara
degrees
-2.867 -2.891 -2.913 -2.939 -2.961 -2.982 -3.016 -3.050 -3.074 -3.100 -3.115 -3.110 -3.062 -2.976 -2.860 -2.602
-68.8 -59.5 -60.0 -60.6 -61.3 -62.0 -62.8 -64.0 -65.0 -66.1 -67.2 -68.0 -68.7 -69.1 -68.7 -67.7
; at o.+ a6 a8 LZ 16 AO ~4 f0RMAI DFHVDE, MOLES PER L ITCR
FIG.3. The molecuiar rotation of anionic d(-)-N-methylleucine as & function of total formaldehyde concentration. The line is that calculated from the constants derived in the text.
sis, since it is obvious that a single complex between formaldehyde and methylleucine is formed. The method of evaluating LI from the data presented pre-
14
E. H. FRIEDEK, h.1. S. DUNW AKD C. D. CORYELL
viously for poline involves the estimation of cyz, the asymptote of the curve of figure 3. The estimation of cy2 is difficult in the case of figure 3 because of the falling off of the curve at higher concentrations of formaldehyde. Another method of calculat,ing the constants involved is available. If cy1 represents the molecular rotation of the anion (A-), and cy2 that of the complex (AF-), the observed molecular rotation can be related to the concentration of free formaldehyde by equation 2.
For any mass-action equilibrium, similar to reaction 1, the relation between some property linear with the amount of reaction [as ( M ) ]and the concentration of one of the reactants [as (F)]is a hyperbolic function, an example of which
LOG (fl FIG.5
FIG.4
FIG.4. Relations in the hyperbola representing rotation as a function of free formaldehyde.
FIG.5. Logarithmic treatment of N-methylleucine-formaldehyde equilibrium.
is given in figure 4. The curve is a simple rectangular hyperbola, of the general type (F)(M) = -C, displaced SO that the asymptotes, instead of being the F and AI axes, are -l/L and CYZ. The general equation is, therefore:
( M - ez)(F
+ 1/Li) = -C
(3)
Since equations 2 and 3 describe the same phenomenon, the constant C can be evaluated by substituting from equation 2 into equation 3. Performing this operation, and solving for ill gives:
+
If ( M ) is plotted as a function of 1/(F ~ / L I ) ,a straight line of slope (a1 - a n ) / L and intercept cy2 will result. A preliminary estimation of L, is
INVESTIGATIONS OF AMINO ACIDS AND PEPTIDES.
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15
necessary, as the reciprocal of the value of (F) when the reaction is half completed. a~is known as the value of ( M ) a t F = 0. (F) is calculated from the total added formaldehyde, the ratio of (AF-) to (A-), and the total amino acid concentration as described for proline. For accurate values of 012 and LI, several approximations may be required. For methylleucine, the second approximation gave a2and L1 values which were changed only slightly in the third approximation. The values obtained were: Li = 2.37,
a2
=
-73.4"
As a check upon this value of Ll, the data can be used to calculate a series of log (AF-)/(A-)'and log (F) terms, using the value of 012 given above. Figure 5 is a graph of log (AF-)/(A-) os. log (F). The data fit satisfactorily on a straight line of unit slope. At log (AF-)/(A-) = 0, log (F) = -0.355; hence LI is 2.27. The agreement of this value with that calculated using equation 4 is quite satisfactory. The very considerable discrepancy between the polarimetric figure and that calculated as a result of the potentiometric study (4.77) has not been satisfactorily explained. That the value of LI = 2.27 is very nearly the correct one is indicated by another reference to figure 3. The solid line representing the predicted curve was drawn using equation 2 and the constants Ll = 2.27, a1 = -58.8", and a2 = -73.4'. The data of table 3 are represented graphically in figure 6, in which the molecular rotation of the leucine-formaldehyde mixture is plotted as a function of the total added formaldehyde. The curve offers direct evidence that leucine and formaldehyde react to form two compounds, characteriaed by daerent, molecular rotations. If it is assumed that the reactions involved are:
it can be shown that at any point along the curve the molecular rotation observedl is related to the free formaldehyde concentration by equation 7:
In equation 7, (YI, "2, and aa are the molecular rotations of A-, AF-, and AF;, respectively. Equation 7 as given, however, cannot be used to evaluate the unknown terms. I n the first place, (F) is a complicated function of total added formaldehyde and the two equilibrium constants. I n the second place, the labor involved in the solution of equation 7 is considerable. An alternative method of solution is available, using the principles described in the section on methylleucine. Figure 6 may be considered to be a composite of two equilibrium curves, as shown in figure 7. Curve 1 of figure 7 corresponds to reaction 5, while curve
16
E. H. FRIEDEN, M. S. DUNN AND C. D. CORYELL
TABLE 3 Results of the polarimetric titTation of 0.0606 M K-l-leucine with 12.66 M formaldehude FORMALDEHYDE OBSEBVEDROIATION
Volume
Concentration
ml.
moles per liter
moles per liter
degrees
degreer
0.00 0.10 0.20 0.30 0.45 0.55 0.65 0.75 0.85 0.95 1.10 1.25 1.50 1.75 2.25 3.00 4.00 5.00 7.50 10.05 12.50 17.50 25.00 35.00
O.Oo0
0.0605 0.0604 0.0603 0.0603 0.0602 0.0601 0.0600 0.06oO 0.0599 0.0598 0.0597 0.0596 0.0594 0.0592 0.0589 0.0583 0.0576 0.0570 0.0553 0.0537 0.0524 0.0496 0.0460 0.0420
0.332 0.122 -0.028 -0.144 -0.262 -0.312 -0.341 -0.363 -0.372 -0.375 -0.375 -0.366 -0.335 -0.300 -0.218 -0,103 0.046
13.7 5.1 -1.2 -6.0 -10.9 -13.0 -14.2 -15.2 -15.6 -16.0 -16.0 -15.4 -14.1 -12.7 -9.3 -4.4 2.0 7.9 18.2 24.9 29.4 35.5 40.8 42.6
0.0159 0:0318 0.0475 0.0712 0.0867 0.1022 0.1180 0.1339 0.1495 0.1722 0.1954 0.2340 0.2721 0.348 0.524 0.605 0.748 1.090 1.418 1.718 2.282 3.022 3.858
0.1m 0.402 0.533 0.615 0.704 0.750 0.733
I
:
-
$
-Po -11
a2 O P a6 08 LO
fOR#ALDEHYD€,
/2 14 / b
MOLES
/B
20 ZP ~f
PER L / T f R
FIG.6. The molecular rotation of anionic Z(-)-leucine as a function of total formnldehyde concentration.
The line is that calculated from the constants derived in the text.
INVESTIGATIONS OF AMINO ACIDS AND PEPTIDES.
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17
2 represents the reaction:
It is observed that a summation of the ordinates of the two curves of figure 6 will result in a curve of the shape found experimentally for leucine. It is most convenient to divide the problem presented by figure 6 into two parts, solving first for the constants involved in curve 2. For leucine, this involves making use of the data when ZF is greater than 0.2 M . Equation 4, appropriately modified, can utilized, the first approximation again necessitating a rough estimate of Lz . Free formaldehyde can be calculated as before, estimating a2 and CQ, and noting that reaction 5 has already used up an amount
c
4,
---------- --- -----------_-
FIQ. 7. Schematie representation of rotation curve when two complexes form
of formaldehyde equivalent to the concentration of amino acid present. Inasmuch as only a3is directly obtained from equation 4, and since a2 must be known in order to calculate L: , a transformation of equation 4 to equation 4a is useful:
Hence, plotting (F) vs. l/[(M) - W ]gives a straight line of slope (a2- a ~ ) / Land i intercept -l/L;. It may be noted that the slopes of equations 4 and 4a are identical, and we thus have a valuable check upon the accuracy of the method. Three approximations were found sufficient to establish a ~ as, , and LZ with fair accuracy, the values being a2 = -44.6', a8 = 58.9', and L: = 1.56. The latter value can be checked by calculating log (AFT)/(AF-) and log (F). A graph relating these two quantities is reproduced in figure 8. The slope of the straight line is quite precisely 1, and the value of the log (F) at log (AFF)/(AF-) = 0 is -0.192, indicating L: = 1.56,in excellent agreement with equation 4a. The evaluation of LIcan be accomplished by using the data at low formaide hyde concentrations. From the calculations given above, 02 has been determined and LYIis known. By calculating the ratio (AF-)/(A-), the free formaldehyde concentration, and plotting the logarithms of these quantities, LI is
18
E. H. FRIEDEN, M. S. DUNN AND C. D. CORYELL
obtained directly as the intercept. However, at low formaldehyde concentrations an accurate estimation of (F) is difficult, while at higher concentrations of (F) the calculation of (AF-)/(A-) is affected because of the presence of increasing amounts of AFT. The first calculation, then, merely gives a rough estimate of h. It is now possible to calculate approximate concentrations of (A-), (AF-), (AFT), and (F) for various values of ZF. The data of table 3 at low formaldehyde can now be corrected for the rotational contribution of (AF;), by means of the expression:
-
Mc = M o b a d . - (013 az)(AF;)* (9) in which iM,is the corrected rotation and (AFT)* is the relative concentration of AF2. The calculation of (F) is also dected somewhat. Log (AF-)/(A-)
':E
0.5
i
FIG.8. Logarithmic treatment of the equilibrium involving the addition of the second formaldehyde molecule to leucine.
and log (F) can now be calculated with more assurance. The graph relating these quantities is reproduced in figure 9. When log (AF-)/(A-) = 0, log (F) = - 1.310, and Ll = 19.9. From LI and L:, LZcan be calculated t o be 31.0. The reliability of the constants (LI = 19.9, LZ = 31.0, 012 = -44.6', 013 = +58.9') is indicated by referring again to figure 6, in which the solid line indicates the curve predicted by their use, and the points are the experimental observations. I t is estimated that the values presented by the present authors are reliable to 1 5 per cent. Potentiometric studies of the equilibria between leucine and formaldehyde have been reported by Levy (5), and by Balson and Lawson (1). Dunn and Weiner (2) have published data on the change of pK:! of leucine upon the addition of formaldehyde, from which the equilibrium constants involved can be
INVESTIQATIONS OF AMINO ACIDS AND PEPTIDES.
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19
calculated. Levy's values of LI and Lf, respectively, are 16 and 35, while calculations by the authors using the data of Dunn and Weiner give 11 and 27 for these constants. Balson and Lawson report the figures 17 and 32, but claim that the system is inadequately characterized by equations 5 and 6. These workers postulated a further reaction involving 1 mole of the amino acid and 3 moles of formaldehyde. The agreement between the values of the equilibrium constants obtained from the polarimetric study and those derived from potential measurements i s quite satisfactofy. Since the possibility of the reaction of leucine zwitter ion with formaldehyde was eliminated in the authors' study, it appears that such a reaction does not occur even when an appreciable quantity of zwitter ion is present.
LO6
(fl
FIQ.9. Logarithmic treatment of the equilibrium involving the addition of the first formaldehyde molecule to leucine.
There is no evidence, either from the potentiometric studies of Levy or Dunn and Weiner, or from the polarimetric study reported in this paper, to indicate that any reactions other than 5 and 6 are of significance in controlling the equilibria between leucine anion and formaldehyde. SUMMARY
The polarimetric investigation of amino acid-formaldehyde equilibria, described in an earlier publication, has been extended to include N-methylleucine and 1(-)-leucine. A potentiometric investigation of the former compound is also described. A considerable discrepancy has been observed between equilibrium constants obtained by each method for the reaction of N-methylleucine and formaldehyde. The constants calculated by the authors 'for the leucineformaldehyde reaction are in good agreement with those reported previously.
20
E. H. FRIEDEN, M. S. DUNN AND C. D. CORYELL
A general solution has been described for the four parameter equations denoting the change in rotation of leucine solutions upon the addition of formaldehyde. REFEREXCES (1) BALSON, E. W., AND LAWSON, A.: Biochem. J. 90, 1257 (1936). (2) D u ” , M. S., AND WEINER,J. G.: J. Biol. Chem. 117,381 (1937). (3) FISCHER,E., AND MECHEL,L.: Ber. 49, 1355 (1916). (4) FRIEDEN, E. If., DUNN,M. S., AND CORYELL, C. D.: J. Phys. Chem. 46, 216 (1942). (5) LEVY,M.: J. Biol. Chem 99, 767 (1933).
QUANTITATIVE IKVESTIGATIONS OF AMINO ACIDS AND PEPTIDES. X I EQUILIBRIA BETWEEK AMINO ACIDSAKD FORMALDEHYDE : GLUTAMIC ACID’ EDWARD H. FRIEDENa, MAX S. DUNN,
AND
CHARLES D. CORYELL
Department of Chemistry, University of California, Los Angeles, Calzfornia Received September 11, 19@
The polarimetric study of the equilibria between amino acids and formaldehyde, applied by the authors to the reaction of formaldehyde with I ( -)-proline, d(-)-N-methylleucine, and I(-)-leucine (1, 2), has been extended in this paper to include the equilibria between formaldehyde and I( +)-glutamic acid. EXPERIMENTAL
The apparatus used for the polarimetric titrations has been described previously (1). I( +)-Glutamic acid3was obtained from Amino Acid Manufactures. A 0.1020 M solution of glutamic acid, containing enough sodium hydroxide to convert 99.5 per cent of the amino acid to the dianionic form, was titrated with 12.60 M formaldehyde. The filtered mercury arc (5461 A.) was used. The data obtained are given in table 1. The reaction was shown to be reversible by the addition of distilled water tu the solution, thus restoring the formaldehyde concentration to a value obtained earlier in the experiment. The rotation of the resulting solution was identical with that observed earlier under these same conditions. KO further change in For the preceding communication in this series, see Frieden, Dunn, and Coryell: J. Phys. Chem. 47, 10 (1943). This paper is part of a dissertation submitted by Edward H. Frieden to the Graduate School of the University of California in partial fulfillment of the requirements for the degree of Doctor of Philosophy, February, 1943. The authors were aided in this work by grants from the University of California and from Merck and Company. 2 Present Address: Department of Chemistry, University of Texas, Austin, Texas. 8 C.P., lot x 5 .
