G5lG
PHOEBUS AI. CHRISTOPHER
On the other hand, the iodine chloride fundamental vibration is also shifted to 310 cm.-l by 2,2’-bipyridine in solution.13 This shows that the donor strengths of P M T and of 2,2’-bipyridine vis-a-vis IC1 are approximately the same. Yet P M T does not show any appreciable coordinating tendency toward hydrogen while 2,2’-bipyridine is a moderately strong base with a pKb of 9.56.14 One, therefore, should not necessarily relate the donor strength of a compound with its proton affinity, especially if the latter were determined in aqueous solutions. Conclusions I n general, i t is seen that P M T is a moderately strong donor molecule. I t s basic strength vis-a-vis iodine halides places i t in an intermediate position between weak donors such as aromatic substances and acetonitrile on one hand and the strong donors such as pyridine and trialkylamines on the other. It is interesting to note that most of the convulsant agents, such as strychnine, metathamide, hydra(13) R a y E. Humphrey, Ph.D. Thesis, State University of Iowa. June 1958. (14) P. Krumholz, THISJ O U R N A L ,73, 3487 (1951).
zides, etc., likewise have donor properties which seem to be of approximately the same magnitude Irl a recent publiction Jenney and Pfeiffcr report a study on convulsant activity of hydrazideslb and conclude that there is only- a very gross correlation between the pk’, values of compounds and thc convulsant activity. I t is possible that electron donor properties and coinplexirig ability of these compounds may zhow a better correlation with their physiological properties. Acknowledgments.-This work was supported by the Research Grant B-1095 from the National Institute of Neurological Diseases and Blindness, Public Health Service. The authors are also indebted to Professor €1. Keasling, Pharmacology Department, State University of Iowa, and t o Dr. R. 0. Hauck of Knoll Pharmaceutical Company for helpful discussions. The determination of the infrared data was aided by ;1 grant from the National Science Foundation (1.5) E H. Jenney and C C I’fclfler, J Plinrmac. E x p e r . T h c r a p , l a % ,110 (1958).
IOWACITY Iowa
[CONTRIBUTION FROM THE DEPARTMENT O F CHEXISTRY, h-EWARK COLLEtiE O F ESC:IXEsRTNti]
Some Octet and Bond Refractivities Involving Boron BY PHOEBUS M. CHRISTOPHER AND THOMAS J. TULLY RECEIVED JANU.4RY 27, 1955 The Lorentz-Lorenz molar refractivity R has been calculated from literature data for n and d for a fairly !arge number of organoboron compounds. A preliminary attempt has been made t o evaluate some octet and bond refractivities involving boron. The resulting values show deviations up to 1 cc./mole, and merely approximate average refractivities can be given (in cc./mole for the D-line and 20’) for the octets B : G : c (3.1) and B:C,‘: (6.8) as well as for the bond B :C.liph (1.75). If one assumes in aromatic compounds the Kekul6 structure for the Cg ring, an average apparent value of 3 0 cc./mole results A satisfactory additivity of molar refractivity obtains for homologous series of organoboron comfor the bond B : C,,,. b have been derived, in which n is the number of carbon pounds. For six such series, equations of the type Rob.d = an atoms in an alkyl chain.
+
A search of the literature has disclosed no information regarding the refractivity of any bonds or octet groups in which both elements boron and carbon are involved. An early investigation based on only a few cornpounds was made’ in order to evaluate an atomic refraction for boron. However, according to certain investigators, the ordinary atomic refractivitiesa have no simple physical significance, and account must be taken of the electronic structure of the molecules, since optical properties depend on the state of the valence electrons. Values for bond and octet refractivities have been tabulated4J for the generally known Lorentz-Lorenz molar refraction. This molar refraction R is a measure of the looseness or tightness with which the valence electrons are held by the atomic cores, and is expressed in cc./mole. (1) A. Ghira, A f f i R. Accad. Litzcci, 2, i, 312 (1893); Z . p k y s i k . Chcm., I S , 764, 768 (1893). ( 2 ) K. F a j a n s and C. A. Knorr, Ber., 59, 249 (1926). (3) F.Eisenlohr. Z.physik. C h e w . 7 6 , 585 (1910);79, 129 (1912). (4) J. R. Partington, “An Advanced Treatise on Physical Chemistry,” Vol. 4, Longmans, Green and Co., 1953,pp. 69-71. ( 5 ) K. F a j a n s in A. Weissberger, “Physical Methods of Organic Chemistry,” 2nd ed., Vol. I , Interscience Publishers, Inc., New York, N. Y..1949,p. 1164.
The present investigation is concerned with the evaluation of some octet and bond refractivities involving boron. Values for the refractive index n (for the D-line) and the density d for a large number of organoboron compounds were selected from a recent comprehensive report on the organic compounds of boron.6 This information was used to calculate the observed molar refraction, R o b s . Assuming, as a first approximation, exact additivity, the sum of the shares of known6 bond and octet refractions, R k n , was subtracted from R o b s , in order to calculate the unknown value, Rx, involving boron. The difference between R o b s and R k n has been divided by the number of such bonds or octets present in the compound. For the compounds selected, these octet and bond refractivities were evaluated: B :0 ..:C, B : Ci I , B :..C a l i p h and B : C a r o m . The resulting values for the B : O : C octet range in Table I from 2.92 (compound lij7to 3.51 (compound 9). This variation is hardly due to experi(6) M. F. Lappert, Chcm. Rem., 66, 151 959 (1956). (7) A still lower value, 2 74, is obtained from compound 1 9 , which contains a phenyl group. See the discussion of Table IV.
OCTETAND BONDREFRACTIVITIES INVOLVING BORON
Dec. 20, 10,55
REFRACTIVITY R, OF
a
B(OCHa)a B(0CzHa)r n-B(OC4Hg)a t-B(OC4Hw)v n-B(OCaHii)o i-B(OCsHii)i B [OCH(CHa)CaH71a t-B [OCH(CHa)C4Hg]: n-B(OC7Hida n-B(OCsHi7)r n-B(OCloHzJr B[OCH(OCHa)CHa]r B[OCH(Cl)CHa], B [OCHzCOOCzHs]r B [OCH(CHa)COOCnHs]r B(OCHZCHZCOOCIH~)~ B [OCH(COOCzH6)CHzCOOCzHsla B [OCH(CHLl),]r B [OCH(CHa)Cd&h ~-CIHQOB(OCHZ)~ HOCHzCHzOB (O-n-C4Hp) I
0.9547 ,8635 .8560 .814 .8549 .8514 .8375 .841 .8398 .8548 .8581 1.0096 1.2780 1.160 1.070 1.108 1.167 1. a 2 8 1.064 0.9976" 0.9141"
IN
CC./MOLE
lEPoD
M
1.3610 1.3741 1,4085 1.3883 1.4190 1 ,4156 1.4075 1.4151 1.4280 1.4377 1.4440 1.4059, 1.4556 1.4290 1.4215 1.4331 1.4408 1.4883 1.5347 1 .4280" 1.4129'
103.9 146.0 230.2 230.2 272.2 272.2 272.2 314.3 356.39 398.47 482.62 236.1 249.3 320.1 362.2 362.2 578.37 394.8 374.28 144.0 218.1
d2%
Compound
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
TABLE I OCTETB :0 :C
THE
Compound
1 ClB(O-n-CsH7)z
9 10 11 12 13 14
15.30 29.19 56.97 56.70 70.86 70.50 70.50 84.30 98.64 112.53 140.31 47.85 43.80 61.83 75.54 75.72 122.07 72.30 101.25 26.99 50.44
ClB(O-n-CJIw)z ClB(O-i-C4Hp)* ClB(O-s-C4He)* CIB [OCH~C(CHI)B]Z C1B [O-t-CH(CHs)CaHg]z ClB(O-n-C,H17)z C1B [O-n-CH(CHI)CeHi312 n-CsH70BClz n-CIHgORC12 i-C4HgOBClz (CH3)aCCH20BCIz TZ-C~HI~OBC~~ Cl(CHz)cOBClz
d 20,
..
TABLE I1 THE OCTETB : C1: n~
0.959 ,941 ,938 ,924 ,906 ,901 .906 ,897 1.138 1.079 1.047 1.032 1.015 1.254
.. MIN
O D
1.4028 1.4132 1.4055 1.4017 1.4102 1.4165 1.4380 1.4277 1.4094 1.4162 1,4088 1.4097 1.4315 1.4522
cc./hiom RX
Rkn
Rob,
164.4 192.5 192.5 192.5 220.6 248.6 304.7 304.7 140.8 154.8 154.8 168.9 211.0 189.3
41.81 51.03 50.35 50.70 60.35 69.31 88.28 87.34 30.62 36.02 36.54 40.52 53.87 40.74
35.00 44.26 44.08 44.08 53.28 62.48 81.30 80.88 17.50 22.13 22.04 26.64 40.65 26.94
6.81 6.77 6.27 6.62 7.07 6.83 6.98 6.46 6.56 6.95 7.25 6.94 6.61 6.90
Av. (rounded off)
REFRACTIVITY R, FOR Compound
1 2 3 4 5 6 7
2.93 3.14 3.15 3.36 3.18 3.22 3.20 3.10 3.51 3.26 3.03 3.19 3.06 3.10 3.46 3.09 2.92 2.94 2.74 3.38 3.01
Av. (rounded off) 3 . 1
REFRACTIVITY R, OF
7 8
R.
Rkn
&hi
24.08 38.62 66.42 66.78 80.41 80.16 80.09 93.61 109,18 122.30 149.40 57.43 52.99 71.14 85.93 84.98 130.82 81.13 109.46 37.14 59.48
dz6r,n Z 6 D .
2 3 4 5 6
6317
B(n-CsH,)s B(i-C4Hs)a B(i-CsHds n-CdHgB (0-n-CIHw)2 n-CJIgO(n-CIH9)BCl (n-ChHi1)zBOCHzCHzOB(n-CsHi1)z (n-CsHi7)pBO-n-C4Hg a dad, n26~. b d 2 2 . 8 2 2 . 6 ~ . 4 n
THE
TABLE 111 BONDB : C WHEN C
$04
0. 7225b .7400* .7607b .8300 .898 .8276" .8036
mental uncertainties and confirms the conclusion that the multitude of the presently available data cannot be satisfactorily reproduced by a limited number of constant additive increments. Therefore the average value 3.14 f 0.14 is rounded off a t the end of Table I to 3.1 cc./rnole. The mean value, 3.14, for the B : O : C octet refractivity from Table I was used in &e calculation
? mD I
1.41359 1,42445b 1 .43207* 1.4169 1.4170 1.4378" 1.4312
IS
6.8
ALIPHATIC,IN cc ./MOLE M
Rob,
140.1 182.2 224.2 214.2 176.5 366.24 310.4
'
48.41 62.89 76.46 64.89 49.43 116.12 100.02
Rkn
R*
43.08 56.70 70.50 63.25 47.91 108,76 97.15
1.78 2.06 1.99 1.64 1.52 1.84 1.44
Av . 1.7,
of R k__n for the compounds listed in Table I1 when needed. The values for the B : 21: octet refractivity in Table 11 range between 6:27 and 7.25, and the average 6.79 Oa2' has been rounded Off to 6.8 cc./mole. The mean refractivity values for the B : O : C octet, 3.14, and the B :%I: .. octet, 6.79, from Tables
*
,l?Q
1 2
1 . -1926"
1.1785 1 ,4738"
,
4 5
1.4751 1 4711 I ,4658
6 7
1.4666 1 ,4870" 1 ,4737" 1.4721" 1.4706" 1 ,4926" 1.4796" 1 ,4757" 1 ,4744" 1 ,4948" I ,4793" 1 ,4770' 1.4758" 1 ,4880" 1 ,4864"
8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 33 24 25 26 37
I , 544ii" 1 ,54117" 1 54211" 1.4mi 1 ,4865 1 ,5:L% ,
160
140
IB(0 R), 2-ClB(OR),
120
5 -C,HsB(OR), 6-C,HtCH,B(OR),
3-ROBCI, 4-0R,
100
:
G
XO
60
40
d
20
0
0
-9
6
4
8
10
12
I2
Fig. 1 -Dependence of Robad ( r h h e , 20') for members of homologous series on the number n of carbon atoms in the alkyl chains, R.
I and 11, respectively, were used wheii needed in the calculation of Rkn in Table 111. The values
for the B : C bond refractivity, when the carbon is aliphatic, range in Table I11 between 1.4-1 aiicl 2.06, with an average 1.75 h 0.19 cc. 'mole. In Table I, an especially low value (2.i4) was obtained for B : .. 0 :C from compound 19, I3 [OCEI(CH3)C&]3, which alone contained an aromatic ring, although separated from the oxygen by :L methylene group. I n calculating this value, the phenyl group was assumed to have the Kekuli. structure. This might appear to be justifiable because the refractivity of benzene, 26.18, is close to the sum, 26.30, expected for 6 C : H , 3 C : C am1 3 C : : C bonds. However, if Oile uses this assunip tion for the evaluation of the refractivity of the H : C bond for the compounds of Table IV, in ~vliicli the carbon is aromatic, a considerable systeiiintir deviation from additivity becomes evident. n a t a i'or compounds cdntaining B :ii . . : c octets in wliicli the carbon is aroixitic werc riot available iii t l i v report.'j The mean values for the octet and bond relractivities from Tables I (3.14), I1 (6.79) and 111 (1.75), were used when needed in the calculation of Rkn for the compounds listed in Table IV. The range of the resulting apparent values for B : Car,, is from 2.43 to 3.50, hence the average value 2.96 + 0.23 has been rounded off to 3.0 cc./mole, as cornpared with 1.76cc./mole for B :Caliph in Table 111. Markedly smaller deviations from additivity result when one limits the comparison to series of homologous compounds which differ only with respect to the number of carbon atoms in the alkyl chain. Among the lig compounds listed in 'Tablrs
Dec. 20, 1058
INFLUENCE OF STJBSTR.4TE IONIZATION ON
ENZYME KINETICS
6519
+ + + + + +
R = an b; a RCH~ I-IV, 46 may be classified into one of these six types: (1) B(OR)3--compounds 1 to (1) B(OR)3 Robed = 14.04% 10.05; 14.04 = 3 x 4.68 11, Table I ; ( 2 ) CIB(0R)Z--conipounds ( 5 ) ciB(oR), R a b s d = 9.18ff 14.27; 9 . 1 8 2 x 4.59 1 to 8, Table 11; ( 3 ) RORCl?-compounds (3) 1 ~ 0 ~ ~ 1&hnd~ = 4.92ff 15.73; 4.92 = 1 X 4.92 0 to 13, Table 11; ( 3 ) UR3-compounds 1 (4) BR3 Robsd = 14.14n 6 . 0 4 ; 14.14 = 3 x 4.712 to 3, Table 111; ( 5 ) C&B(OR)z--com( 5 ) C&& (OR)2 Robsd = 9.34% 34.10; 9.34 = 2 x 4.67 pounds 1 to 7 , Table IV; (6) C6H&H3B- (6) CsHdCH3B(OR)z Robed 9.42ff 38.94; 9 . 4 2 2 X 4.71 (OR)z-conipounds 8 to 19, Table IV. If the values for R o b s are plotted against n, where n is cc. observed for long homologous series. These the number of carbon atoms in a single alkyl group, equations may therefore be used to calculate the the following graph is produced. molar refractions for any organoboron compounds ‘Since the R o b s values for isomeric compounds of the six types mentioned without the need of show no systematic deviations (the n-isomers have density and/or refractive index data. partly larger, partly smaller values than the The accuracy of equations 3 and 4 is questioni-isomers), the average value was used in the plot. able, since the derivation of the latter is based on The fact that almost all of the points fall directly only three points (see graph) and for the former the on straight lines may be taken as an indication of experimental points deviate relatively more from the reliability of the values for the density and re- the straight line than for the other equations. fractive index as given in the report6 From the Achowledgment.-The authors gratefully acslopes and intercepts of the straight lines shown, one knowledge the advice and helpful suggestions given can derive a set of equations of the type by Professor Kasiinir Fajans of the University of The resulting increment RCH> agrees, except in Michigan, Ann Arbor, Michigan. the series ( 3 ) , within 0.07 cc. with the value 4.64 NEWARK,N. J.
+
[COSTRIBUTION FROM THE
DEPARTMEKT OF BIOLOGICAL CHEMISTRY,
WASHINGTON UNIVERSITY SCHOOL O F MEDICINE]
The Influence of the Ionization of a Group in the Substrate Molecule on the Kinetic Parameters of Enzymatic Reactions BY CARLFRIEDEN RECEIVED MARCH 28, 1958 Equations have been derived for the single substrate case to include the effects of the ionization of a group in the substrate molecule upon the over-all rate of an enzymatic reaction. These equations have been described in terms of changes in the maximum velocity and Michaelis constant of the reaction. It is shown that there are several distinguishable kinetic cases even when the effects of substrate ionization are complicated by those of groups in the enzymatically active site. These cases may be distinguished by differences in plots of kinetic constants as a function of PH for the forward and reverse reaction. Provided that enough data are available and that the assumptions made in the derivations are correct, it is possible to tell whether (1)one of both ionic forms of the substrate are utilizable or ( 2 ) if only one form is utilizable, whether the other form is a good or poor competitive inhibitor.
The substrates for many enzymes contain groups which ionize in the pH range most frequently investigated. Since most substrate molecules are of low molecular weight the change in charge associated with the change in degree of ionization of substrate probably will affect the substrate-enzyme interaction in some way and thus will influence the rate of the over-all reaction. The changes in the over-all reaction may in turn be attributed to changes in the kinetic parameters, that is, the maximum velocity and Michaelis constant of the reaction. There has been little attention paid to the effect of substrate ionization on over-all rates of enzymatic reactions. Undoubtedly, much of this lack arises from the already complicated pH-dependence of the kinetic parameters due to enzymatic ionizations alone.1-6 However, under suitable conditions, equations describing the over-all reac(1) L. Michaelis and H. Davidson, Biochem. Z., 3S, 386 (1911). (2) L. Michaelis and H. Pechstein, ibid., S9, 77 (1914).
(3) J. B. S. Haldane, “Enzymes,” Longmans, Green and Co., London, 1930. (4) R. A. Alberty and V. Massey, Biochim. et Biophys. Acta, 13, 347 (1954). (5) SI. Dixon, Biochem. J . . 55, 161 (1953). (a) C!. Frieden and R. A. Alberty, J . Bid Chem.. 212, 839 (1935).
tion rate in the presence of an ionizable substrate may be derived. Provided that there is some difference either in the binding of two different ionized forms of substrate to the enzyme or in the rate of breakdown of the two different enzyme-substrate complexes there will always be some effect of the substrate ionization on the kinetic parameters of the reaction. The derived equations show that changes in enzyme-substrate interaction and breakdown due to changes in the ionization state of the substrate molecule may be detected from a complete study of the kinetic parameters as a function of pH for the forward and reverse reaction. The ionization constant of the substrate must, of course, be known. There are two major assumptions made in this paper: first, that the enzyme contains either 0, 1 or 2 ionizable groups which control the pH dependence of the reaction rate in a “total” way. It will be assumed that there are no more than two such groups. Such an assumption does not seem unlikely in view of the fact that this appears to be the situation for many enzymes as exemplified by fumarase.6 Secondly, i t is assumed that hydrogen ion equilibria are established rapidly.
