The Quantitative Interpretation of the Electrophoretic Patterns of

STUDIES O S FETUIN

171

acid value for a plasma protein, where all the globulins have their Z.P.’s above pH 5 and the albumin has an I . P . of 4.8.

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SUMMARY

Methods for preparing fetuin from calf and fetal sera have been described. The sedimentation constant for fetuin varies strongly with concentration. For infinite dilution s20 seems to vary somewhat with the origin of the fetuin, but the molecular w i g h t always comes out a t about 50,000. Fefuin has its isoelectdc point a t pH 3.5, which is a very acid value for a plasma protein. The expenses connected with this study have been defrayed by grants from the Nobel Fund and The Rockefeller Foundation. REFERENCES (1) CLEMENTE, C. L. SAN,ASD HUDDLESON, J. F . : l l i c h . State College Agr Esptl. Sta., Tech. Bull. 182, 3 (1943). (2) HOWE,P. E . : J . Biol. Chem. 49, 115 (‘1921); 63, 479 (1922). (3) JAMESON, E., ALVAREZ-TOSTADO, C., A N D S O R T ~ R H,. H . : Proc. Soc. Esptl. 3 0 1 . N e d . 51, 163 (1942). (4) MOORE,D. H . , SIIEN, S. C., IND ALEXANDER, C. S.: Proc. SOC. Esptl. Biol. Med. 58, 307 (1945). (5) PEDERSEN, K. 0. : I n T h e Svedberg 1884-1944, p. 490. Almqvist and Wikseils, Upsala (1944). (6) PEDERSEN, K. 0.: S a t u r e 164, 575 (1944). (7) PEDERSEK, K. 0.: Ultracentrifugd Studies on S e r u m and S e r u m Fractions. Almqvist and Wiksells, Upsala (1945). ( 8 ) POLSOS, A . G.: S a t u r e 152, 413 (1943).

THE QGAXTITATIT’E ISTERPRETATIOS OF T H E ELECTROPHORETIC PATTERNS OF PROTEINS’ L. G. LOKGSWORTH Laboratories of T h e Rockefeller Institute f o r Medical Research, New York, X e w York Received August 8 , 1945 INTRODUCTIOS

I n the moving-boundary method as adapted by Tiselius (14) for the analysis of protein mixtures, the initial boundary is formed between the two solutions that result from the dialysis of the protein solution against a large volume of an appropriate buffer solution. The diffusible buffer ions are then present on both sides of the initial boundary at concentrations corresponding t o a Donnan equilibrium. On passage of the current this boundary generally splits into a number of separate boundaries, one of which remains near the initial boundary 1 Presented a t the Twentieth Sational Colloid Symposium, Tvhich was held at Madison, Wisconsin, May 2&-29, 1946.


172

L. G. LONGSWORTH

position while the others move away from this position a t different rates. At each of the moving boundaries the concentration of one of the protein components varies from a constant value below the boundary to zero above and is thus said to disappear in the boundary. Moreover, the variation of the refractive index with the height due to the disappearance of this species may be recorded photographically by either the schlieren-scanning or the cylindrical-lens method (7). In the complete pattern each boundary appears as a separate peak whose area is proportional to the difference of refractive index between the two solutions forming the boundary. At pH values not too different from the isoelectric pH the equivalent weights of most proteins are large in comparison with those of the buffer ions. Consequently, a relatively low equivalent concentration of protein may still be one a t which this constituent makes a major contribution to the density and refractive index of the solution. The conductance, on the other hand, is determined largely by the buffer ions. Thus the limiting case is approached in which one of the solutions meeting a t the original boundary contains small concentrations of one, or more, species in a large excess of other ions, whereas only the dominant species are present in the other end solution and at the same concentrations. The dominant species, the buffer ions, then insure throughout the boundary system a uniform electric field in which the constituents a t low equivalent concentrations, the protein ions, drift. At a moving boundary in which a protein ion disappears there are then no superimposed gradients of other species, and the area of the corresponding peak in the pattern is a direct measure of the concentration of the disappearing species. Moreover, in this case the boundary pattern is independent of the direction in which the current is passed. Consequently, if boundaries are formed initially in each of the two sides of the U-shaped channel of the Tiselius cell, as is the usual procedure, the pattern obtained from one side is the mirror image of that from the other side. Such patterns may be said to be enantiogrophic. This limiting or ideal case is the basis of the current method for obtaining what will be called the apparent composition of a protein mixture. In this approximate method the superimposed gradients are ignored, and the relative concentration of a component is taken as the ratio of the area of the peakin the pattern due to this component to the sum of the areas due t o all constituents. A glance a t the deviations of almost any pair of patterns from enantiography will convince one, however, that actual systems may approach, but do not attain, the ideal conditions. With the aid of the moving-boundary theory developed by Kohlrausch ( 5 ) and Weber (16),and recently extended by Dole (4) and Svensson (11, 12, 13), it is the purpose of this report t o compute the behavior of some typical systems and to compare the results with experiment. THREE-ION SYSTEMS

Since the theory assumes that the relative ion mobilities are constant throughout the system, it is applicable to protein ions only insofar as the presence of the buffer electrolytes insures a uniform pH and hence a constant protein-ion mobility. In Dole’s theory t.he displacements of the boundaries and the composi-

173


ELECTROPHORETIC PATTERNS O F PROTEINS

tions of the solutions formed by their separation are computed from the relative mobilities and concentrations of the two solutions forming the original boundary, the so-called end solutions. The inverse problem of computing the mobilities and concentrations of the ions in the end solutions from the boundary pattern is, however, the one that arises in the electrophoretic analysis of protein mixtures. As a matter of fact this problem is not solvable in the general case without additional information and even then the computations are laborious. illthough results for more complex mixtures will be presented later in this paper, it is only in the case of a three-ion system that simple relations are obtained. h single protein dissolved in a buffer having a pH a t 11 hich the conductance of the hydrogen-ion constituent can be neglected is an important special case of such a system. Notation In this paper .4,B, C . . . will refer to cations whose mobilities, u , are in the order > uB > uc nhile R , S, T . . . indicate anions for which 1 uR > 1 us 1 > 1 uT 1 . . . . The mobility of one species relative to that of another taken as unity is called the relative mobility and is denoted as r. Both the relative and absolute mobility and the concentration of a given ion retain the sign of the charge on that species. The initial boundary is indicated by separating with a dash, -, the symbols for the ions in the two end solutions. In the system that develops on passage of the current a moving boundary is denoted by an arrow, -+, while a double colon, :: , will be used for the concentration boundary remaining near the site of the original boundary. The current is always taken as flowing from left to right, and the solutions meeting a t the boundaries will be denoted by Greek letters in the order of decreasing density. Owing to the nature of the end solutions in the case of proteins, no difficulty will be experienced in determining this order, since the protein components disappear progressively with increasing height at each moving boundary and thus the density decreases with the number of species in a solution. The end solution containing the protein ions is thus always the CY solution. Except a t low ionic strengths the mobility of the protein ion is generally less in magnitude than that of either the buffer cation or anion and these are denoted, therefore, as B and R , respectively. At pH values below its isoelectric pH the protein ion is the cation B, whereas above this pH it is the anion 8. Here the protein solution mill be taken as ABR, since the necessary modifications when the protein is an anion will be obvious. As will be shown below, the buffer acid, or base, may be considered as part of the solvent if it is uncharged. The special case in which the buffer acid and its conjugate base are both charged, e.g., the H2PO; and HPOT- ions in phosphate buffers, offers no difficulty if the concentration and mobility of the buffer-ion constituent are used. In that side of the channel in which the protein ions descend the boundary system for three ions is AR(-y) :: AR@) -+ .4BR(a), \Thereas in the other side it is ABR(a) :: ABR(@)-+ AR(-y). Wherever it is necessary in order to avoid confusion, the subscripts r (rising) and d (descending) will be added t o distinguish between the two systems. ~


1i4

L. G. LONGSWORTH

T h e protein mobility At the descending boundary cy0 in the system AR(7) :: AR(P) -+ ABR(cy) the protein ion B disappears from the end solution cy of known conduct,ance, P . Its mobility, up,, in this solution may be computed (9) directly ryith the aid of the relation, t i g = u ~ @ K in ~ , which v u @ is the displacement, in milliliters, of the first moment of the gradient curve per coulomb of electricity passed. Although the ~$3 boundary is generally diffuse, the modern schlieren methods for recording the refractive-index gradients usually make it possible to locate this moment with an uncertainty of less than 0.03 mm. If the boundary moves 3 cm., for example, this represents an error of 0.1 per cent in the mobility. If the mobility of the protein in pure buffer solution is required, determinations are made a t t v o or more protein concentrations and extrapolated. T h e biifler-concentration boundary The earlier designation (8) of the buffer-concentration boundary fir as the e boundary was unfortunate, since it has been confused with the moving boundaries due to the serum globulins that are also identified n i t h Greek letters. The corresponding boundary in the other side of the channel, heretofore called the 6 boundary, will be termed the protcin-concentration boundary. In the ideal case that the relative mobilities of all species are constant throughout the channel, the buffer- and protein-concentration boundaries are stationary. In real systems they generally move slightly on passage of the current. Since the protein solu6on cy is prepared by dialysis against a large excess of the buffer solution 7, its composition is not arbitrary but is given, t o a close approximation, by the first term in the expansion of the Donnan equation, Le.

e; = e: - +c; c; = c; - *e;

(1)

(2) With the aid of these relations and the electroneutralitg conditions, XC, = 0, the Xohlrausch regulating functions (4,5)of tbe tlvo end solutions become

and

Since wU'/w' is the dilution factor for all species a t the concentration boundaries in both sides of the channel and occurs frequently in the theory, it will be designated E .

At sufficiently lox- protein concentrations ( becomes unity and deviation6 therefrom are, therefore, a measure of the divergence of real systems from the ideal behavior that is assumed in the usual electrophoretic analysis.

175

ELECTROPHORETIC PATTERSS O F PROTEISS

I n the case of the buffer-concentration boundary the difference in refractive index is


n@ -

n7

=

KAI((C1 -

c.i)

= IC.kR(4

- 1)ci

where KAR is the increment of refractive indes per equivalent of AR. -4t a given p H and ionic strength the area of the buffer-concentration peak in the pattern is thus proportional to the protein concentration. I n the special case that the mobilities of the buffer ions are equal, Le., r.k = - T R , equation 4 becomes

At a constant ionic strength and protein concentration of p grams per 100 ml. of solution, both Cg and rB varynith the pH. This variation is due to the change of the valence, zB, of the protein ion. Since Cg is directly proportional to Z B TABLE 1 T h e buffer-concentration boundary in a three-ion system Ovalbumin in 0.1 N sodium acetate a t p H 3.92 (e = 2 34 X IO-*) : rxa = 1 000, rAa = -0 7875, rprOteln = 0.1392, K A R= 0 01235 1 2 3 4 5

.I ..I

p ( g r a r n s p e r ~ ~ r n l. .. ). . . . . . . . , I I C," (equivalents per liter) . . . . . . I nB - n7 (equation 4 ) . . . . . . . . . . .. I ~

~

I

n@ - n y (observed) . . . . . . . . . . . e (computed) . . . . . . . . . . . . .

0.a

0.00150 0.000060 O.OOOO1~ 0.0001g

I

I

I

1.36 0.00318 0.000127 0.000121 0.000227

I

1

I ~

2.74 0.00641 0.000255 0.00024, 0.000227

and rB is approximately so, and they occur in equation 5 as the ratio, compensation occurs. With a given buffer salt n b - n7 should, therefore, be almost independent of the pH. The variation of nb - n7 Jvith the ionic strength a t constant pH and protein concentration, p , is more obscure. In this case zB, and hence C;, generally increases with increasing ionic strength (2, 6), whereas the relative mobility of the protein ion decreases (15). Both of these effects should, if ZJAR is independent of the salt concentration, cause n3 - 727 to increase somewhat with increasing ionic strength. Although the foregoing conclusions appear t o be in accord with experiment, no data of sufficient precision t o test equation 4 are available escept for a variation of the protein concentration a t constant pH and ionic strength (9). The results of this test are summarized in table 1. The equivalent concentrations of protein, line 2, are given by the relation, C s = l o p e , \There e is the net charge in Faraday equivalents per grem of protein and is taken from the titration data of Cannan, Kibrick, and Palmer (2). hlthough the molecular wight, V,of the protein is not required for the computation of Cg, if Jf for ovalbumin (15) is 45,000 the valence of these ions in the present esainple is zB = 1 1 s = 10.5.

176

L. G. LONGSWORTH

The relative mobilities of table 1 are based on the measured value, uB, for the protein ion, the conductance, ,'K of the buffer solution, and the cation transference number, !/', of 0.1 N sodium acetate, Le.,


UA

= 1000K'T/FCi and

UR

= 1000ny(l

-

T)/FCz

Since K Y is the conductance of sodium acetate in the presence of acetic acid, provision is thereby made for the effe& on the buffer-ion mobilities of the viscosity due t o the weak buffer acid. In any given system allowance can also be made as follows for the viscosity due to the protein. Since U R / U A is taken as equal t o (T - 1 ) / T throughout the system, the specific conductance of the protein solution may be written

and may be solved for uA. Since refractive-index differences, as computed from pattern areas, are uncertain by a t least 1 X lOW, the agreement between the observed and computed values of np - ny (lines 3 and 4 of table 1 ) is essentially complete. A conductometric analysis of the p solution after its removal from the channel would doubtless yield a more precise value for C i than the refractometric method and will be used in the future. If the procedure is reversed and the net charge, e, computed from the observed values of np - n', the results given in the last line of table 1 are obtained. I t is clear that this affords a method for the determination of the net charge on the protein that compares favorably with the value, 0.000234, obtained from titration data. The ratao o j the displacements of the rising and descending boundaries In the other side of the channel where the system is ABR(a) :: ABR(@)-+ AR(r), the protein ion R disappears in the rising boundary By. The displacement of this boundary is given by the relation ug = v @ ' K ~ . Since the @ solution has been formed by the passage of the current its conductance, K @ , is not known and the rising boundary cannot, therefore, be used for direct mobility measurements. i n terms of the relative conductances, u , and mobilities, r, the relations a t the rising and descending boundaries are ?'B = V

~

m8 d

~TB

= ~

Since the cy solution is the same in both sides of the channel, u: = u: ande/v;@ = u:/& The ratio of the relative conductances a t either concentration boundary is also the dilution factor, 5, from which vy/vd

=

5

(6)

where the superscripts have been dropped, since there is only one moving boundary in each side of the channel with three-ion systems. With the aid of this

177


ELECTROPHORETIC PATTERNS OF PROTEINS

relation values of v r / v d for the solutions listed in table 1 were computed and are given in the second line of table 2. The agreement with the observed values in the third line is poor. In seeking to explain this discrepancy it will be recalled that the theory assumes the constancy of the relative ion mobilities. The deviation of v J v d from unity predicted by equation 6 is due to the stronger field, i.e., loFer conductance, in the solution above the protein-concentration boundary resulting from the dilution a t this boundary. Equation 6 may thus be said to correctfor the conductivity change a t this boundary. I t does not provide, however, for any change in the relative mobility of an ion. If, for example, the pH is different on the two sides of the protein-concentration boundary the mobility of the protein ion, relative to the mobilities of the buffer ions, is also different. A correction for such a pH effect may be made as follows.

The inJluence of p H gradients Evidence to be presented below indicates that the concentration of the weak buffer acid, HR, remains constant throughout the boundary system. In the diluted protein solution fi the concentration of the buffer salt AR differs, however, TABLE 2 T h e displacement ratio of the rising and descending boundarzes in a three-ion system Ovalbumin in 0 1 N sodium acetate a t p H 3.92 1 2 3 1

ip ~

,

i

.......... ............ (equation 6 ) . . . . . , . . . . . . , . . v,/ud (observed)* . . . . . . . . . . . . . . . . . Z ' , / L ' ~ (corrected for p H effect). . . . .

0.64 1.018 1.091 1.078

t',./ud

~

11 1

1.36 1.103 1.180 1.166

I ~

2.71 1.207 1.333 1.341

* These values differ slightly from those previously published (9), since here the boundary position is correctly taken as the position of the first moment of the gradient curve instead of the bisecting ordinate t h a t was used in the earlier work. from the concentration of this material in the original protein solution a. For small variations in composition the relation pH = const.

+ log

may be assumed and the difference of pH across the protein-concentration boundary is pHu

- pHP

= log

(Ci/Ci)

= log (

Since 5 > 1 the pH of the solution above this boundary is less than that underneath. Below the isoelectric pH the protein-ion mobility increases with decreasing pH, and these ions thus move faster above the ap boundary than below it. If du/dpH is the slope of the mobility curve a t the pH in question &/rE = 1 - (l/uB)(duB/dpH) log 5 (7) and the value of vJvd given by equation 6 must be increased by this factor. At pH 3.92 and 0.1 N , (l/uB)(duB/dpH) = - 3.8 for ovalbumin (6) and the cor-


178

L. G . LONGSWORTH

rected values of L',/Vd are given in the last line of table 2. The improved agreement with the observed values constitutes part of the evidence for the validity of the assumption that the concentration of the weak buffer acid remains essentially uniform throughout the system. Additional evidence has been obtained as follows: If, prior to forming the boundaries, the protein soiution is dilJted by the factor t.with a solution of HR at the concentration C H R , the concentration boundaries are eliminated from the resulting patterns. In the case of a buffer system in which the acid and its conjugate base are both charged, e.g., phosphate buffers, the dilution is made xith water. This is a useful device in countercurrent electrolysis n hcre one of the concentration boundaiies mould normally be drawn into the bottom section of the cell, thereby initiating convection. TABLE 3 T h e protean-concentratton boundary i n a three-ion system Ovalbumin in 0.1 N sodium acetate at pH 3.93 2 3 4

'

I P

nu - n6 (equation 9) 1 nu - nP (obseived) n" - n@(corrected for pH effect) 1

061 0 003114 0 033150 0 003146

1 36

0 001351 0 00H9r 0 032476

1

I1

2 0 0 0

74 031085 03149s 001509

T h e protean-concentratzon boundaru If the p H change at the protein-concentration boundary is ignored, the expression for the difference in refractive index becomes

- nS

- ~9 + KBR(CE - CS,) = [ K A R C+ ~ (RBR- +K.m)Cg](l - 1/51 =

KAR(c~

(8)

(9)

The equivalent refraction, KBR,is that of the protein salt, ovalbumin acetate in the present example. Its relation t o the specific refraction, k , of the isoelectric protein is k(l

+ ae)p = K B R C ~

where a is a constant for a given buffer salt (1). The product ae represents a small correction for the effect of the charge, e , of the protein ion on its refractivity and for the refractivity of the buffer ions that balance this charge. The values of nu - nB given in the second line of table 3 were computed with the aid of equation 9 for the solutions of table 1. As in the case of the boundary displacement ratio before correction for the pH effect, the agreement with the observed values, line 3, is poor. The increased mobility of the protein ions at the lower pH of the p solution leads, hoTvever, to a concentration, Cg,that must satisfy, approximately, the relation Cg& = C $ T ~ .In order to correct for the pH effect, C i in equation 8 is replaced by C",a/&, where rg/& is given by equation 7 . The values obtained in this manner, line 4 of table 3, are in good


ELECTROPHORETIC PATTERNS OF PROTEINS

179

agreement with those observed. I n a more exact treatment of the problem the concentrations of the buffer ions in the p solution would also be adjusted to preserve electrical neutrality, but the effect of this adjustment on the refractive index of the solution is small. Although there is a similar pH change a t the buffer-concentration boundary, the relative mobilities of the buffer ions are not appreciably altered thereby. It is for this reason that an analysis of the buffer solution below this boundary probably affords the most direct method for determining, with the aid of moving boundaries, the net charge on the protein.

The conductivity and p H effects The conductivity and pH changes a t the boundaries do not always combine, as in the examples given above, to decrease the enantiography of the patterns

1.

1.363ovalbumin as cations in 0.1NNaAc at pH 3.93 a

1.30% ovalbumin a3 anions

in O.1NNaAc at pH5.34 b

FIG. 1

from the two sides of the channel. Above the isoelectric p H of the protein the coefficient (l,’u)(du/dpH), equation 7, is positive and the pH effect thentends to cancel the conductivity effect. I n buffers of the uncharged-acid type, the patterns obtained above the isoelectric pH tend to be more neariy mirror images of each other than below this pH. This is illustrated in figure 1, ivhere the patterns at n are those of the 1.36 per cent ovalbumin solution of table 1, whereas a similar concentration, 1.30 pe: cent, of this protein in a 0.1 h‘ sodium acetate buffer at pH 5.34 gave the patterns of figure l b . Even when allowance is made for the inhomogeneity of this protein a t the higher pH, the increased enantiography of the patterns ivhen the protein is an anion is clearly evident. The deviations from enantiography shown here are those most commonly encountered. If, hoivever, the buffer is of the uncharged-base type, e.g., glycine hydrochloride, a reversal in the sign of the pH effect can be expected.

180

L. G. LONQSWORTH


Sharpening and spreading of the moving boundaries An additional deviation from enantiography illustrated in figure 1 is the relative sharpness of the rising boundary. If the conductivity is lower behind a moving boundary than ahead of it, the boundary generally spreads less rapidly than from diffusionalone and is thus sharper than if the conductivity change aids diffusion. If A and R are the buffer ions, the conductance increases with increasing height a t each moving boundary in both sides of the channel (13). A rising boundary thus tends to be sharper than the corresponding descending one. If, however, the mobility of the protein ion is greater than that of the buffer ion of the same sign, the conductivity change is reversed and the rising boundary then becomes, in the absence of a pH effect, the diffuse one. As is apparent in figure l a the p H change may also enhance the sharpening effect of the conductivity change a t the rising boundary and the spreading effect of this change a t the descending boundary or, as in figure l b , the pH effect may partially counteract the conductivity effect. In a t least one system that the author has studied, namely, 0.1 M sodium hydroxide, 0.2 M glycine, 0.05 M glutamic acid (a)4.1 M sodium hydroxide, 0.2 M glycine ( y ) , the p H effect outweighed the conductivity change so that the sharp boundary moved into the solution with the low conductance. In the case of a 0.3 per cent solution of ovalbumin in 0.01 N sodium diethylbarbiturate a t pH 8.6 the conductivity effect is so small, since the protein and diethylbarbiturate ions have respectively, that the the similar mobilities of -10.8 X lO-land -11.9 X pH effect dominates and causes the descending boundary to be the sharp one. SYSTEMS CONTAINING TWO OR MORE PROTEINS

In the absence of sufficiently precise data on mixtures of two or more proteins it has appeared most practicable to compute, with the aid of Dole’s theory, the pattern characteristics for hypothetical systems. If these patterns are then analyzed in the conventional manner the apparent compositions may be compared with those assumed in making the computations and the differences will indicate the errors in the apparent values. The hypothetical mixture selected for the computations consists of the two proteins, S and T, each a t a concentration of 1 per cent, with relative mobilities of rs = -0.3 and rT = -0.15 and equivalent concentrations of CS = -0.0036 and CT = -0.0018. Insofar as it is permissible to lump the serum globulins together as the single component, T, such a solution could represent serum, diluted with two to three volumes of buffer, a t p H 8.6 in which the albumin*globulin ratio is unity. The results of the computations for this protein mixture in 0.1 N solutions of the sodium salts of the commonly used buffers are given in table 4. As is clear from the second column of the table, the buffer anions in the first column are arranged in the order of increasing negative mobility. The equivalent refractions of the buffer salts in column 3 were measured a t 0°C. in a hollow-prism cell with the aid of the schlieren-scanning camera (7).

181

ELECTROPHORETIC PATTERNS OF PRmEINS


As in the case of a single protein (13) the displacement ratios for the fast boundary, column 4 of table 4, and for the slow one, column 5 , increase as the buffer anion mobility, I rR I, increases. In a given buffer this ratio is greater for the slow than for the fast boundary and is in accord, therefore, with experiment. In an analysis of twenty-five human plasmas, diluted 1 to 3 in a 0.1 N sodium diethylbarbiturate buffer a t p H 8.6, Dole (3) obtained 1.06 as the average displacement ratio for the albumin boundary and 1.13 for the globulin boundaries TABLE 4 Results of computations for a mizture of the two proteins S and T i n 0.1 N solutions of sodium buffer salts Data assumed: F N . = 1; rs = -0.3; rT = -0.15; Cs = -0.0036; CT = -0.0018 (1)

Buffer ion, R . . . . . . . . . . . . . . . . . . . . . Diethylbarbiturate . . . . . . . . . . . . . . . Lactate, . . . . . . . . . . . . . . . . . . . . . . . . . . Glycinate . . . . . . . . . . . . . . . . . . . . . . . . . Acetate. . . . . . . . . . . . . . . . . . . . . . . . . . . Phosphate (dibasic). . . . . . . . . . . . . . . Chloride, . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(6)

(3)

lp/@- v p o a

KAR lp/vd"P 0.04055 1.0371 0.01914 1.0443 0.01746 1.0515 0.01235 1.0550 0,01484 1.0595 0.01120

-rR

0.4640* 0.5795t 0.7098t 0.7825: 1.1008" 1.6810*

1.085 1.111 1.138 1.150 1.189

0.1471 0.1459 0.1444 0.1437 0.1411 0.1381 (11)

Buffer

1

Protein

Rising

I Descending

AVERAGE EPPOP

psr cen1

Diethylbarbiturate . . . . . . . . . . . . . . . . Lactate. . . . . . . . . . . . . . . . . . . . . . . . . . . Glycinate . . . . . . . . . . . . . . . . . . . . . . . . Acetate. . . . . . . . . . . . . . . . . . . . . . . . . Phosphate (dibasic). . . . . . . . . . . . . . . Chloride . . . . . . . . . . . . . . . . . . . . . . . . . .

268 155 166 126

473 412 473 458 57.12

~

53.44

1.42 2.20 2.83 3.25 4.13 5.28

* From transference measurements at 0.1 N and 0.5? t Assuming additivity of ion conductances a t 0.1 N and 0.5% $ From transference measurements a t 0.1 N and 25.0"C.

If the mobility of the slow protein, T, is computed from the displacement of the slow, descending boundary and the known conductance of the protein solution a,the (relative) values of column G are obtained. In the limit of vanishingly small concentrations of protein all of the figures in this column would have the assumed value of -0.15. The deviations from this are a measure of the errors that are made in the conventional method of determining this mobility. The computed differences in refractive index a t the concentration boundaries, columns 7 and 8 of table 4,indicate the magnitude of these effects in different buffers. Of most interest, however, are the effects of the superimposed gradients a t a boundary due to ions other than the one that disappears. These cause the relative concentration of the fast component S to appear greater than the assumed


182

L. 0. LONGSWORTH

value of 50 per cent. Moreover, in the examples of table 4 the error increases with increasing mobility of the buffer anion and is more serious in the pattern of the rising boundaries, column 9 , than in that of the descending boundaries, column 10. If the apparent composition from the two patterns is averaged, the deviation from the true value of 50 per cent is then given in column 11. The available results on mixtures of proteins are in qualitative accord, a t least, with the theory as represented by the computations of table 4. As equation 3 indicates, the regulating functions for the two end solutions approach equality as the ratio of the protein to the buffer salt concentration approaches 0

I

0

2

I

1

1

I

I

I

4 6 8 10 12 14 Recippocal of buffer salt concn. in cgsJlitee

1

5

FIG.2

zero. Thus the true composition of a protein mixture may be obtained by extrapolation of the apparent composition either to zero protein concentration a t constant ionic strength or to infinite salt concentration at constant protein content. Both methods have been used. Thus Svensson (11) analyzed a hog serum at a total protein concentration of 3.75 per cent in a 0.068 N sodium phosphate buffer at p H 7.7 to vhich increasing amounts of sodium chloride nere added. From the patterns of the rising boundaries he found the apparent albumin content to decrease from 59.1 pel cent n ith no added sodium chloride to 42.9 per cent when the concentration of this salt was 0.37 AV,vhereas the corresponding variation in the patterns of the descending boundaries was from 51.9 per cent t o about 44 per cent. These results are in accord with the computations of table 4 insofar as the theory predicts larger errors from the rising-boundary pattern than from that of the descending boundpries and also the relatively large errors to be expected in phosphate-chloride buffers. However, with increasing salt concentration the apparent composition approaches the true value asymp-


ELECTROPHORETIC PATTERNS OF PROTEIXS

183

totically and the plot used by Svensson is not suitable for extrapolation. As equation 3 suggests and as is s h o w by the circles in figure 2, a plot of his apparent values against the reciprocal of the salt concentration is approximately linear and extrapolates to an albumin content of 39.4 per cent. With the aid of a 0.1 sodium diethylbarbiturate buffer a t pH 8.G Perlmann and Kaufman (10) have studied the apparent composition of a human plasma with varying amounts of added sodium chloride. ,is Irould be expected from table 4 for this buffer and as is shonn graphically by the crosses of figure 2 , they observed errors similar to those of Svensson but of smaller magnitude. They also studied the same plasma a t different concentrations of total protein. At a constant buffer salt concentration of 0.1 .Ir they observed a change in the apparent albumin content from 58.2 to 51.0 per cent as the absolute protein concentration iyas reduced from 2.66 to 1.0 per cent. In this case the variation was approximately linear and extrapolated to the same albumin content, 53 per cent, as do the crosses of figure 2. .ilthough additional experiments of this type will be necessary in order to establish the relative merits of the two methods of extrapolation, it is clear that a determination of the true composition of a protein mixture will involve at least two experiments in which either the protein concentration or the salt concentration is varied. SUMMARY

With the aid of the moving-boundary theory developed by S'incent, P. Dole the electrophoretic behavior of some typical protein systems has been computed and compared viith experiment. Satisfactory agreement is obtained in the case of a single protein if a correction is made for the p H changes at the boundaries as well as for the conductivity changes predicted by the theory. I n the case of solutions containing more than one protein both the computations and the available experimental results indicate that appreciable errors may be made in the usual electrophoretic analysis of such mixtures. Procedures for minimizing these errors are suggested. REFERESCEY (1) ADAIR,G. S.:ASD ROBISSOS, 11.E.: Biochem. J. 24, 993 (1930). R . K., KIBRICK, A , ASD PALMER, A. H.: Ann. S . T.Acad. Sci. 41,243 (1941). . P . : J. Clin. Investigation 23, i o 8 (1944). (4) DOLE,V. P.: J. .4m. Chem. Soc. 67, 1119 (1945j. (5) KOHLRIUSCH, F.: .Inn. Physik 62, 209 (1897). (6) Loscsn.oRTH, L. G . :Ann. S . 1.;\cad. Sei. 41, 267 (1941). ( 7 ) LOSGSWORTH, L . G . : Ind. Eng. Chem., .Anal. Ed., 18, 219 (1946). ( 8 ) LOSGSU-ORTH. L. G., ASD X i c I s m a , D . A . : Chem. Rev. 24,271 (1939). (9) LOSGSWORTH, L. G., ASD hIacIsxvns, D . .I.: J. Am. Cheni. SOC.62, 705 (1940). (10) PERLHANN, G . E., AKD 1

The Quantitative Interpretation of the Electrophoretic Patterns of

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