ON T H E DISSOCIATION O F SERUM GLOBULIN AT VARYING HYDROGEN ION CONCENTRATIONS BY T. BRAILSFORD ROBERTSON
(From the Rudolfih Spreckels Physiological Laboratory of the University of California) I. INTRODUCTION I n recent papers’ I have suggested that the proteins may be regarded as amphoteric electrolytes (“ ampholytes ”) and I have pointed ,out that certain phenomena exhibited by proteins in solution and in the process of hydrolysis by enzymes meet with a simple explanation upon the basis of this hypothesis. If, however, regarding proteins as amphoteric electrolytes, we endeavor to estimate their dissociation constants when acting as bases, on the one hand, and as acids on the other, it is evident that we cannot, in general, regard one of the functions as negligible while estimating the value of the other. For example, we cannot consider serum globulin in the presence of acid t o be acting purely as a base and, regarding it as if it were a simple base, calculate its basic function ; for a t a definite and comparatively high concentration of acid (in the neighborhood of IO-~N)more than sufficient to carry the globulin into solution, the globulin is “isoelectric,” i. e., migrates equally in both directions in an electric field, or, in other words, the concentration of the globulin anion is equal to that of the globulin cation and the protein is acting equally as an acid and as a base, while at lower concentrations of acid, so long as the protein remains in homogeneous solution, the greater part of the protein migrates as an anion, that is, is acting as an acid; and similar considerations doubtless hold good in regard to other ampholytes. Nevertheless, this method of neglecting the acid while estimal’. Brailsford Robertson : Jour. Phys. Chem., Biol. Cheni., 2 , 317 ( 1 9 0 7 ) .
IO,
524 (1906). Jour,
438
T. Brnilsford Robeidsoiz
ting the basic function and vice versa, which amounts to neglecting the most characteristic property of the ampholyte while estimating its characteristic constants, has been frequently employed in investigations upon the properties and dissociation constants of ampholytes. As I will show later on, this method can only give even approximately accurate values for the larger function if it be sufficiently large compared with the other; otherwise the dissociation constants obtained in this way are subject to considerable error. It is, however, possible to estimate the acid and basic functions of an ampholyte by a method which is free from the above objections. Consider the ampholyte HXOH in solution in the presence of the acid HA, and let the concentrations of the various molecules and ions which are present in equilibrium be represented as follows : H+ OHXOHHX+ HXOH X X A- HXA a
b
d
C
e
f
Y
P
Then we have, for the equilibrium of the positive and negative ions in pairs:
.
ab = K . . ........................... ac = k,e.. ........................... bd = K b e . . ........................... cd -=Qf............................. dy=Sp
.............................
(I> (2)
(3) (4) (5 )
and since the sum of the concentrations of the positive ions must be equal t o the sum of the concentrations of the negative ions, we have: ...................... ( 6 ) a+d=b+c+y In these equations K is the ionic product for water, k, and kb are respectively profiortional to the acid and basic affinity constants of the ampholyte,' and Q and S are constants. From ( I ) , (2) and (3) we obtain the relation:
J. Walker: Proc. Roy. SOC.,73, 157 (1904). Jour. Phys. Chem., IO, 533 and foot-iiote, 534 [ 1906).
T.Brailsford Robertson:
Dissociation of S e m n i Globzdin
439
Consider the conductivity of this solution, let U be the velocity of the hydrogen ion, V that of the anion A, and v that of the protein ions, assuming that the protein anions and cations, since their mass is practically the same, have identical velocities. From (6), since b is so small compared with a that it can be neglected, we have:
.........................
y=a+d-c
(8)
and, if x be the conductivity in reciprocal ohms, we have: 1.037 X IO-* x = UU V ( U d - C ) vd vc Let x, be the conductivity the solution would have were the ampholyte absent, then : 1.037 x IO-* X , = UU V U , the acid HA being supposed to be completely dissociated. Hence : 1.037 x 10-2(X-XI) = (v + V ) d - ( v - V ) C Representing 1.037 X IO-' (x- xi)by X we have :
+
+ +
+
+
From (7) and (9), by substitution and rearrangement, we have : k K AX c= kb vK k a ) . . . . . . . . . . . . . . . . .(IO) (V
+ "'("-vi-y.
Let a, be the total amount of the acid HA which is present, combined or uncombined, in the solution, then, from (8), the amount ( p ) which is combined with the ampholyte to form the salt HXA is a, - a - d c; let a , - a = m, then from (8) and ( 5 ) we have: d(a d - C) = S ( M - d c). . . . . . . . . . . . . . . . . .(12) From (9) :
+
+
(j-cc=---. v h ~
+
vv+22, vc
...................
440
T. Brailsford Robertsoiz Substituting from
Let
(IO), (11)
V - v Kka I , = H and -___ v + v hb S W v)
+
~
and (13) in
=
(12) we
have:
J, then equation 14 becomes:
In practice it is found that the term Ju'A
2v
(
x
V"v2 a+-V + ~v a=--H a'-H
is negligible, when the ampholyte is chiefly acid, except at comparatiGely high concentrations of the acid HA, so that for low concentrations of the acid HA we have: 22,
pz
",A
= -~-v = - v V+v a'--H h
...........
If, however, the basic function is much larger than the acid function, then H is negligible except at very low concentrations of the acid HA and the equation (15) becomes:
x
m=--+JA
v+v
(a+- V S V
................
If, instead of considering the equilibrium of the ampholyte HXOH in the presence of the non-amphoteric acid HA we consider its equilibrium in the presence of the base COH, we obtain equations similar in form except that instead of the
constant H we obtain a constant G which
U
=
the velocity of the cation C.
=
U-v Kkb . where U + V ka
-
~
If the basic function is
441
Dissociation of Serziiiz Globzrliiz
larger than the acid function then at low concentrations of the base COH we have for equilibrium: 2v
GX m= - U”v2 - ___ .... . . . . . . . . . . . . . . (18) U+V 6’-G h
>
while if k , k b , then except at very low concentrations of COH, G is negligible and we have: h
m=----+RRX . . ...... U+V In the equations (16) to ( I S ) , V and U are, in general, known and the quantities m, and a or b can be measured.
Hence from two observations v and the remaining constant in the equation can be obtained. In practice, however, when using the equations (16) and (IS) into which v enters as the square as well the first power, it is more convenient t o assume a value for v and then, calculating the value of H or of G from one observation, to investigate how closely the equation thus obtained fits the observations. By repeated approximations the values of v and of H or G can in this way be fairly accurately ascertained. 11. EXPERIMENTAL If the amount of the acid HA which has been added to a solution of an ampholyte and the volume of the solution be accurately known then a, is known and if a , the final hydrion gives us m. The concentration, be measured, then a , - a conductivity x, of a solution of the acid HA of concentration a can be obtained from tables or from the formula a(U V) = I .037 x IO-’ x , where U and V are the velocities of the hydrion and of the anion A respectively, and x, is the conductivity of the solution in reciprocal ohms1 The conductivity x of the solution of the ampholyte plus the acid HA can be directly measured and (x - xl)1.037 x IO-’ gives us X. The ampholyte which was used throughout in these experiments was the “ insoluble ” serum globulin’ prepared
+
~
_
_
_
_
W. C. D. Whetham : “Theory of Solution,” p. 2 1 4 (1902). See Clarence Quiiian : Univ. of Calif. Piibl. Patliol., I, I (1903);W. B. Hardy : Jour. Physiol., 33, 251 (1905) ; Far literature see Gustav Mann : “ Chewistry of the Proteids,” p. 363 (1906). I
’
442
T. BrniGsJord Robertsoiz
from ox-serum by diluting ten times and saturating with CO,. The precipitate thus obtained was washed several times with water by allowing the precipitate to settle in tall glass cylinders and then siphoning off the supernatant fluid. It was then dissolved in a minimal amount of normal KCl solution plus a trace of alkali, diluted, precipitated again by CO, and repeatedly washed with distilled water. The precipitate, which was never allowed to dry, was then kept standing under water to which toluene had been added as a sterilizer.' When globulin was required, the water and precipitate were shaken up and the fine and homogeneous suspension thus obtained was diluted as required. The ash, estimated by igniting slowly a t a dull red heat in a platinum crucible, amounted to 0.77 percent of the dried globulin. The final hydrion concentration, a, of the solution was measured by the gas-chain. A calomel electrode in which the solution covering the mercury was N / I O KC1 saturated with HgCl formed one extremity of the chain,' while an electrode of platinized platinum gauze saturated with hydrogen formed the other extremity. The platinum electrode, which Dr. F. G. Cottrell very kindly 'prepared for me, consisted of a glass tube bent at right angles a t the upper end. A cylinder of platinum gauze was sealed into the lower end and its lower extremity closed by welding the gauze together ; a fine platinum wire was threaded in and welded to the gauze and carried up through the glass tube as far as the bend where it passed out into a little cup closed at the bottom and sealed into the tube. Contact was made by means of mercury placed in this cup. The hydrogen was led into the tube and before bubbling through the solution had to pass through the platinized gauze -hence equilibrium was very quickly attained. The hydrogen was prepared from arsenic-free zinc and sulphuric acid and was passed through three Mohr potash bulbs containing ( I ) alkaline pyrogallol, ( 2 ) potassium perman1 2
Hardy, LOC.cit., has shown that toluene has no action on globulin. Richards : Zeit. phys. Chern., 24, 37 (1897).
Dissociation of Serzinz Globziliiz
443
ganate, and (3) silver nitrate and, finally, through a vessel containing granular calcium chloride. Since KC1 or other neutral salts could not be added to the solutions of serum globulin without, in all probability, displacing the very equilibrium which it was desired to measure, some other device had to be resorted to in order to eliminate the error due to the contact difference of potential between the solution in which the hydrion concentration was being measured and the calomel electrode. The device which was used was to place a saturated solution of KCI in the chain between the solution which was being measured and the calomel electrode. As Bjerrum has shown, this procedure eliminates the contact difference of potential between the solution under investigation and the calomel electrode, and introduces only a small and fairly constant error into the determination. Owing to the foaming of the protein solutions under investigation and the slight pressure thus established, a certain amount of flow was liable to take place in the tube connecting the solution under investigation with the next link in the chain. This tube was therefore not allowed to dip directly into the saturated KCI, but connection was established through another vessel filled with the same solution. In order to detect the zero point on the bridge a sensitive d'ilrsonval galvanometer was employed instead of the capillary electrometer; this method was found in most cases to be very satisfactory, the instrument giving a very distinct throw for I mm displacement on the bridge. When measuring the hydrion concentration of solutions of very low conductivity, however, owing to the high internal resistance of the cell formed by the electrodes and the solution, a very low amperage was obtained in the external circuit and the deflection obtained was small. Trouble was not experienced until the conductivity fell to about 2 to 3 X 1oW4reciprocal ohms, but below this the experimental errors in the determination of a from this and other causes are considerably increased. Tower : Zeit. phys. Clieui,, ('905).
20)
198 (1896); N. Bjerrum : Ibid., 53? 428
'
444
T. Brailsford Robertsoiz
The general arrangement of the connections was the same as that shown in the figure in Ostwald-Luther’s Physicochemische Messungen 2 Aufl., S. 372. According to Nernst’ the difference of potential between the hydrogen electrode and r / I N hydrogen ion solution is So.277 volt. The potential difference between Hg and N / I O KC1 saturated with HgCl is fo.613 volt.’ Hence the measured difference of potential between the hydrogen electrode and the Hg would be 0.613 volt -0.277 volt = 0.326 volt. Using carefully standardized3 N/IOO HC1 the value of this potential difference which was actually found, using the method of determination described above, was 0.313 volt. According to the Nernst formula
T
=
R T - log nat 77e
c2 -?
(1
where T is the potential difference between two different concentrations of the same ion, R is the‘ gas-constant in voltcoulombs, T is the absolute temperature, the valency of the ion, and e the Faraday constant. Hence we have at zoo, at which most of the determinations were made:
Given that r1 = 0.313 volt for normal H+, then if T~ is the potential difference in volts when C,- is xN, we have: 0.313-
?Tx=
0.0581 log,,
X
or 0.313- r r log,, X = ~ _ 0.0581
_
determinations made upon standard acids and alkali solutions diluted to various strengths gave results agreeing excellently with the titrations of the undiluted solutions. The following procedure was adopted in all the determinations. The hydrogen was allowed to bubble through the electrode and the solution for 1/2 hour and then a reading a +;
Quoted after Ostwald-Luther : LOC.cit., S. 384. Richards : Zeit. phys. Chern., 2 4 , 37 (1897). Standardized gs described below.
Dissociation of Ser2int GZoobuZin
445
was taken. After a further hour a second reading was taken, and if the neutral point had not shifted more than 0 .j mm this reading was taken as correct; if a greater shift than this had taken place, a third determination was made after another 1 5 minutes and so on until a constant reading was obtained. Usually, equilibrium was quickly attained since the solutions under investigation were sufficiently far from neutrality. It was observed, however, that the first determination after the electrode had been allowed to dry and stand in contact with air for some hours was always a long while in coming to equilibrium, so that finally I adopted the plan of simply dipping the electrode in water and passing hydrogen for to ’//,hour before commencing a fresh series of determinations. The experimental procedure was as follows : A suspension of globulin in distilled water was made up and its concentration determined by evaporating 2 5 0 cc and drying at 110’ until no further loss of weight could be detected. To 2 0 0 cc of this suspension were added 4, 6, 8 cubic centimeters, etc., of acid or alkali of known concentration (approx. N/Io) and the total volume of the solution made up to 2 5 0 cc with distilled water. The alkali used had been standardized against normal oxalic acid, using lacmoid as indicator; the oxalic acid had been standardized against a solution made up from Kahlbaum’s potassium permanganate. The hydrochloric acid solution used was standardized against the KOH thus prepared, using lacmoid indicator, and, finally, a solution of KC1 was made by neutralizing the KOH with the HC1; this solution was diluted to N/5o and its conductivity measured; the conductivity was exactly that of a N/5o KC1 solution. The following were the experimental results obtained with HC1. Concentration of globulin suspension : 0.62 percent. Hence concentration of globulin in each solution : 0.496 percent. Conductivity of the water employed 7.3 X IO-^ reciprocal ohms.
.
446
T. Braihfoyd Robevisoiz
Conductivity of globulin suspension alone g x IO-^ reciprocal ohms. Concentration of the HC1 employed : 0. I 203 N. The tabulated values of x are the conductivities actually measured less the conductivity of the distilled water. The values tabulated under x, are cafculated from the formula 1.037 X roA2x1= a(U V) and U and V are taken as 316 X 1 0 c 5 and 65 X IO+ respectively, and the figures thus obtained are multiplied by 1.12 to reduce t o 2 5 O . l Since, in serum-globulin the acid function is much stronger than the basic function,' the equation which we have to apply to the above observations is equation (16). Hardy found by direct measurement by the boundary r n e t h ~ d ,that ~ v for globulin was about I O X IO-^, but since He had to use very dilute acid and alkali in order t o observe the movement of an opalescent boundary, the velocity observed is probably too high on account of the presence of pseudo-ions, " the movements of which in an electric field are due to electric endosmose, as Hardy has pointed out, and are much more rapid than those of true ions. On the other hand, were the observed velocity an ionic velocity, it would be lower than the true value, since the migration of the boundary represents the excess of migration in one direction over the migration in the other. I assumed the values 0, 2.5 X IO-^, 5 X IO-^, 7 x IO-" and IO X 10-5 for v and substituting them in equation (16) calculated the value of H which most nearly fitted the observations. Of these assumed velocities the one which gave by far the best results was 7 X IO-^ and the value of H which best fitted the observations was found to be 55 X IO-^. Hence, since V = 65 X IO-^ equation (16)becomes:
+
m=-----72
h
X
10-5
1.8425 x IO-4h 5 5 X IO-^'
2-
See table of ionic velocities in Kohlrausch und Holborn : Leitvermogen der Elektrolyte (18gS),S. zoo ; also table of temperature-coefficients, S . 199. W. B. H a r d y : LOC.cit., p. 255. W. B, Hardy : Loc. cit.
Dissociation of Serzim Globulin
3
N V C n W N
u
?uI-‘popo\p cn
w 0 mm\D N
xxxxxx - u u C I c (
irooooo I I I I I I e
P
P
e
P
P
xxxxxx Y
C
.
l
i
U
U
W
0 0 0 0 0 0
I eI PI PI eI CI
e
01
xxxxxx u u u u u u
0 0 0 0 0 0
I I I I I I
P e P e e e
2 W
E n
xxxxxx
xxxxxx
447
In the following table the experimental and calculated values of m are compared. TABLEI1 ~~~~~
~~
~
47.6 X 10-4 46.9 X 40.25 x IO-4 45.23 x 34.00 X r b ' ~ 2 8 . 9 x 26.1 X 1 0 - 4 29.93 X 20.2 X 10-4 18.86 X 14.9 A 10-4 10.83X
~
10-4 5285.00 IOV41 1347.00
X X
0.126 X 10-4 46.77 0.492 x 10-4 44.74 566.44 x 0.7945X 10-4,28.1 153.76 X IO-* 4.02 x IO-4~25.91 12.09 X 10-1 6.77 75.7 x I O 19.4 X IO-^ -4.05 x 10-4114.88
10-41
IO-4~ 10-41
10-4
IO-~ IO-'
X X X
10-4 10-4 10-4
x
10-4
j
