Introduction
I t is well known that sedimentation constants of prateins and o k materials depend upon the density and the viscosity of the medium. For this r e m , i t is customary to iiieasurc sedinigntatian rates under convenient experimental conditions, and then correct the rates to correspond to what they mutd have been if sedimentation had been d e d out in a medium with the viscosity and density of water at 20'. Svedberg and Pedersenla have presented an equation, exactly analogous to equation 1 of this conimunication, for carrying out this correction. It was painted out by them that hydratiou might affect the validity of the equation, but the subject was not treated quantitatively. Since i t is mcogrdzed that proteins are probably hydrated to an appreciable extent, it seenied worthwhile to coasider the possible effect of hydration upoil the cmreeted value of the sedimentation constant obtained through the use of equation 4. I t was found that the error can be quite appreciable.
Theory and Discussion Consider a particle of mass m which displaces ;i volume v in a medium of density p . Suppose that this particle becomes solvated in such 3 way that the iiicrease in the voluinc' displaccd is It and the increase in mass is hi. In this notation, cl amounts to the density- of that portiori of the medium attached to the particle. I t could be the same as p , but it also could be different from p ; for example, if the iiiediuiil ctmtained inorganic salts or sucrose sild the solvating metiiuni wits solely water, then d would riot equal p. In general, i n it ternary system, d will differ frorii p unless ii has thc same coiiim i o n as the two-cwmponent solvent arid (other sources of difference are negligible. 111 a centrifuge, the force acting (111 tlic solvated particle is w2.u[(m Id) -.- j z ~ hip , where w is the angular velocity ; I I ~.u is tlw (lis tance from the axis oi rot:itioii. 'I'hc. irictinnal force will be f'a ti.\. '(I!, \vIirre f'",i s tlic, covITic*irii~ friction of the solvated particle, q is the (:(I efficient nf viscosity nf the solvent uii(1 c1.v (1: is the velocity oi scdiirieiitatioii. ' I ' h t w . t iorces can be ecjuatctl, atld one c ~ t i \wit(, i
-
+
i1.1
- .. -.- -
.
(VI
-1- l:d
-. I c
-
N )p =
>8''7)
/ I
where .\, the settimeiltation constant, is defined as (d.x,'df)/c~?s. Since L' ) I T is the partial specific volume, I., of thc solute a t the concentratinn = .I/, present in the solution, and since -VYI>Z where .V is -1vogadro's number and .Vis rnolerul~r weight, t h r following equation results.
If sedimentation experiments are carried out in two media with viscosities q1 and q2 and densities pI +l p z , l C respectively, in general two different sedimentation constants, sl and s2, will be observed. I f -11 mid ,I' are tlie same in the two
inc.di:i. one ran ivrito
'Tliis is the equation ior correcting an observetl setlilneiltation constant, s2, to that, sI, at soiiic* standard condition such as the viscosity and delisity of water a t 20'. If hl and lzz arc 0, i.e., thew is no solvation, or if dl = p1 aud dz = p 2 , i. e., the density of the solvent illaterial attached to the particle is the same as the density of the medium, regardless of the density of the medium, equation 3 reduces to equatian 4, the one usually given for correcting. sedimentation constants.
I*, aiitl 1 itrc usually assumed to be the saiiic'. Svedberg and Eriksson-Quensel,' in studies oi the sedimentation of hemocyanin in heavy water, found that correction of their observed sedimentation constants according to equation 4 gave values for sifl equal to that obtained in ordinarv water. I t seeins likely that the solvating medium in each mixture ot' heavy and ordinary water had a density equal to that of the itiediuili. 'Thus equatioii .Iheld, Izquation 3 can be derived irorii equation 1 i i i tlw same manner as equation 3 was deri\wt
I
1
( 1 ) Publication Xi) I of thc Department of Biophysics (la) Svedberg ancl l J < 4 c . r % t , i i"The , iltracrritrifiigr," t )xford Prr.,, Phgland, 1940. (Ib) The coefficient of friction, as delined by Svedberg, lnclude the viscosity roeflicient and a teriti relatrd t o the size, shape, i l l i t 1 Iiydrdtion of the sedimenting particles. 111 this treatment the two terms are separated in ordcr t o relate tlic scdinieiitation constant t o the viscositv of the solvent 'I'buq, oiir /'n i < tlrr Sam? as Svrdberg'a )..
I IC) Some discusiioii IIAS been ilirectrd t o thc density t i . r i I i it) tquation I The work of C.ofrnan, cl ai., (J. H i d (''hrm , 179, ! l i : ; i 1949)) on tlie sedimentation of lipoproteins iudicutes that t h e prc5. t'iice of other protein niolecules influences the direction as ' ~ ~ a 1 s1 the rate of sedinientation of the lipoprotein molecules, tliercl)) aha* inp that solution density is important. 111 most studies the dciisitir\ 01 the solvent and solution are very siniilnr and either cnii bc u h c < l without introducing a significant c'rror. 'l'hrrc is general aprccinciit that tllc density of the solutiou i. tlic ~ o n t r o l l ilaictor ~ i ~ iii smlini, r i t i i t i o n equilibrium. 12) 4rcdhrrK and lirikwon-Quimrrl, V n f i c r r 197. 400 (1936).
DENSITYCORRECTION OF SEDIMENTATION CONSTANTS
Sept., 10.50
+
If m, v , h, d and f' (which depends upon ZJ h ) are all constant in different media, and if V h is defined as (v Iz)/(m hd), equation 5 reduces to equation 6.
+ 71
-
52
+
'T"
'I-- clhpl)
111
(1
-
vhP2)
(61
I n such a case, 7s will be a linear function of p and v h will equal the reciprocal of p when s is 0. Data obtained with tobacco mosaic virus3 meet this requirement, and data obtained with Southern bean mosaic virus4 deviate only slightly from this requirement. If m, Y, h a n d f ' are held constant but d is a linear function of p (d = a k ( p - u), where a and k are constants), as in the experiments of Mchleekin, et U Z . , ~ equation 5 reduces to equation 7 , in which v h is defined as (v h - h k ) / ( m ha - hku).
+
+
+
426 7
Beard6 on the Sedimentation of swine influenza virus in DzO, sucrose and Serum albumin solutions. TABLE I SEDIMENTATION OF TORACCO MOSAIC VIXUS IS 0.01 M PHOSPHATE BUFFER SOLUTIONS CONTAININGJ'ARYING AMOUNTSOF SUCROSE Sucrose concn.,
S%
S;O,
%
smat./ S
g./cc.
V = 0.73 eq.'6, vh = 0.789 S S
0 0 5 12.4 20 30 40
182 188 148 98 71.4 41.3 22.5
0.999 0.999 1,018 1.045 1.079 1.113 1.151
169 170 163 159 152 139 128
P,
e q . 4,
169 170 166 168 170 168 174
Since i t is probable that many proteins are hydrated to an appreciable extent, it is evident that many of the published sedimentation constants corrected to water a t 20' by means of equation 4 may be in error. The larger the value of V , It is possible that other assumptions can be made the greater will be the error if hydration is negwhich yield equations of the form of 6 and 7 lected. The only solutions to the problem are t o except that v h or Vi will be replaced by V:, carry out sedimentation experiments under condiVL", etc. This means that, while a constant tions such that the density correction is not imequal to the reciprocal of p when sedimentation portant or else to attempt to obtain a measure of rate is zero, can be evaluated in experiments like those of Schachman and Lauffer, its meaning, VI, (or Vi, etc.). In general, sedimentation in terms of the composition and amount of solvate, studies are carried out in dilute buffers of density is ambiguous in the absence of additional jn- about 1.01 g./cc. Under such circumstances the error in si, will be small, amounting to only a few formation. I n spite of the ambiguity in the meaning of v h , per cent. The preceding discussion deals only with the VL, etc., equation 6 is an exact equivalent of equation 3 whenever qs is a linear function of p . question of obtaining the right value for siofrom Table I shows the results obtained in the studies st when the sedimentating particles are solvated. on the sedimentation of tobacco mosaic virus The next question is whether the correct value for in sucrose solutions of different d e n ~ i t i e s . ~I n the unsolvated molecular weight can be calculated the calculations, the value for Vh (or vi, etc.) from the correct value of si,, and the diffusion was obtained from the density of solution, ob- constant, Die. The relationship between the tained by extrapolation, in which the virus would diffusion constant and the coefficient of friction is have zero sedimentation rate. Comparison of given by the Einstein-Sutherland equation, column 4 with 5 shows the magnitude of the error equation 8. if Vis used instead of Vh. It is clear that reasonD = kT/f'v (81 ably constant values of si,, are obtained for all In this equation, T is the absolute temperature, k solutions if v h is used, whereas an error of 26% is the Boltzman constant, and f' has the same results if V is used for studies in 40% sucrose. It meaning as in equation 2 . By combining equais, of course, not surprising that correcting the tions 2 and 8, one obtains equation 9, where R s values in Table I by equation 6 leads to essenti- is the gas constant. ally constant values while correcting by equation M = RTSs/D[l - VP (Iz/m)(d - ,011 (9) 4 does not; the original sedimentation data3 show that qs is proportional to (1 - Vhp) and not When d+p or when h/m-+O or both, equation to (1 - Vp). The point to the calculations in- 9 reduces t o the familiar Svedberg equation, volving equation 4 is that they illustrate how large equation 10. Under these conditions the molecthe error can be in an extreme case when the usual ular weight of the unsolvated particles procedure (involving equation 4)is used to correct M RTs/(l - Vp)D (10) sedimentation constants. Similar calculations can be made from the data of Sharp, Beard and can be determined from the correct values of si, and Dio of the solvated particles and the partial (3) Schachman and Lauffer, THIS JOURNAL, 71, 536 (1949). (4) Taylor and Lauffer, paper read b e f m Divisioa of Biological specific volume, V , of the unsolvated particle. Chemistry, American Chemical Society, in Atlantic City, September, Since Vp usually has a value of about 0.7 for 1949. 51 - '12 (1 - VLPd (7) 52 VI (1 - V h 2 ) I n this case, too, sq will be a linear function of p and Vi will equal the reciprocal of p when s is 0.
+
-
( 5 ) McMeekin, Groves and Hipp,
THISJOURNAL, 72, 3662 ( 1 9 5 0 ) .
.
(6) Sharp, Beard and Beard, J . 81ol. Chum., 183, 279 (1960).
Vo1. 72
NOTES
4268
experiments carried out on proteins dissolved in aqueous media, when h/m is less than 1 and d - p is less than 0.01, a value for the unsolvated moIecular weight, -11,within about 3y0 of the correct value should be obtained. Whenever (h/m) (d - p ) exceeds 0.01, unsolvated molecular weights of proteins determined by means of equation 10 will be too low by 3% or more. When allowance is made for the differences in symbols, it is evident that equation 9 divided by equation 10 yields the equation derived previously by Lansing and Kraemer' for sedimentation equilibrium. Their equation 9 applies to the case of sedimentation equilibrium in a ternary system where the solute combines with only one of the other two components. In the same paper, of course, Lansing and Kraerner showed that the molecular weight of solute determined (7) Lansing and Kracmer, Tnrs JomxNa~,68, 1471 (1936).
by sedimentation equilibrium of a dilute binary solution was virtually independent of solvation. Just as Lansing and Kraemer's equation 9 in no way contradicts their own equation 7, our treatment is in no way inconsistent with theirs. Summary The effect of hydration on the density correction of sedimentation constants is considered. Equations are presented to show the influence of hydration and a comparison is made between these new equations and the equation of Svedberg and Pedersen which is shown to represent a special case. Calculations involving previously published data show errors due to neglecting hydration ranging from 5 to 26% in an extreme case. BERKELEY, CALIF. PITTSBURGH, PENNA.
RECEIVED JANUARY 11, 1950
NOTES Synthesis of C14-SodiumCyanide from Carbon Dioxide BY B.
BELLE-4U2 AND
R.D. B. HEARD
The two methods in current use for the conversion of radiocarbonate to radiocyanide, namely, the interaction3 of C1*02, NH:, and R in a sealed tube a t 620°, and the fusion of B a C 1 4 0 ~with sodium azide,4 have in our experienee proved to be tricky, inconvenient and distinctiy limited in size [see also61. Just recently an improved synthesis has been ted by Abra.mss; C1402 is um to elementary carbon, which is then converted in 6&70% over-all yield to cyanide by treatment with ammonia a t 1000O. The desirability of producing radiocyanide by simple organic reactions not requirkg high temperature or pressure techniques prompted the adaptation of the following sequence of reactions. SOC1, then
1
I1
(1) The investiption was supported by research grants from the National Cancer Institute, U. S. Public Health Service. and the Medical Resedrch Division, National Research Council of Canada. (2) Quebec Scientific Research Bureau Bursar. Contributed in partial fultiliment of the requirements for the degree of Doctor of Philosophy. (3) Cramer and Kistiakowsky, 1. Biol. Chrm., laV, 547 (1941); Loftfield, Nucleonics, 1, No. 3, 54 (1947). (4) Adamson, Trns JOURNAL, 69, 2564 (1947) ( 5 ) Abrams, i b i d , 71, 3835 (1949).
(~sHs)sCC"OO"2
97% 111
Na, EtOH
pzos
&(CRH~)~CC~~N
90%
1V (C8Hs)XH
v
+ NaC14N VI
Triphenylmethylsodium (I)6carbonates' readily to the crystalline triphenylacetic acid 11. The corresponding amide IPI,8 prepared in the usual way through the acid chloride,8 dehydrates smoothly to the nitrile IV, which, because of the pronounced electrophilic properties of the component goups facilely undergoesg hydrogenolysis to triphenylmethane (V) and cyanide (VI) rather than hydrogenation to triphenylethylamine. A consistent yield of 90% or better has been achieved in each of the steps, with the overall realization of 68 to 72% of NaC14N from BaC1403. The purification of intermediates is not necessary. The method offers several worthwhile advantages: (a) in one convenient reaction, a g seous low molecular weight starting material (8140*; m, w., 46) leads to a solid high molecular weight product (11, m. w., 290, m. p., 267'); (b) it is equally adaptable to a micro- or a macroscale; and, (c) other useful one carbon compounds such as formate, methylamine, etc., may be obtainable directly (in the course of exploration). (6) Renfrow and Hauser, Org. Sys~hcscs,Col. Vol. 11, 607 (1943).
(7) Schlenk and Marcus. Be?., 47, 1668 (1914). (€4) Schmidlin and Hodgson. ibrd., 41, 445 (1908). (9) Biltz. Ann., 896, 253 (1897).
