4242
YORKTSANG AND T. E. THOMPSON
It is well known that polished metal surfaces are not nascently clean, crystalline lattice planes. However, such a surface (and for that matter an oxidized metal) otherwise free from organic contamination should have a critical surface tension of wetting” which would cause a sessile drop of water to spread spontaneously on the metal. A metal surface entirely free from oxides would have a higher surface energy than an oxidized metal ; consequently, water should spread more readily on the former surface rather than the latter. If a sessile water drop does not spontaneously wet a “clean” metal surface, it is probably an
indication of measurable contamination by a hydrophobic organic impurity. An exception to this would be contamination by an organic wetting agentla having a polar group in the outermost surface of the adsorbed molecule; such an impurity on a metal surface would promote the spontaneous spreading of a sessile drop of water. (17) W. A. Zisman, Advances in Chemistry Series, No. 43,American Chemical Society, Washinpton, D. C., 1964,p. 12. (18) 8. J. Gregg, “The Surface Chemistry of Solids,” 2nd Ed., Reinhold Publishing Gorp., New York, N. Y., 1961,p. 220.
The Use of Combined Schlieren and Absorption Optics in an Electrophoretic Study of the Reversibly Interacting System Dextran Sulfate-CarboxyhemoglobinlJ
by York Tsang and T. E. Thompson Department of Phusiological Chemietry, Johns Hopkins Univorsitg, School of Medicine, Baltimore, Maryland (Received J u l y 6, 1966)
The behavior during moving-boundary electrophoresis of interacting dextran sulfatescarboxyhemoglobin in aqueous solution has been studied utilizing combined schlieren and absorption optics. Interaction was studied over a pH range of 7.4 to 8.5 and ionic strength range of 0.05 to 0.20 M and at various concentration ratios of interactants. The variation of the interaction, decreasing with increasing pH and ionic strength, can be explained as due to attraction between the anionic sulfate groups of the dextran sulfates and cationic groups on the hemoglobin. Interaction constants have been calculated by two different methods. The information provided by the combined schlieren and absorption optical systems enables a more accurate estimate of the effects of nonideal electrophoresis and reduces uncertainties involved in the interpretation of the moving-boundary patterns of interacting macromolecules to a level comparable with that involved for noninteracting systems of macromolecules.
Kumerous studies have been reported on the behavior in free-boundary electrophoresis of systems of interacting macrom~lecules.~For many of these systems, the behavior as reflected in the refractometrically determined nioving-boundary patterns is such as to suggest that continuous readjustment Of the ConThe Journal of Physical Chemistry
centrations of each species is occurring in the boundary region. The patterns can no longer be related in any (1) Presented in part at the 145th National Meeting of the American Chemical Society, New York, N. Y.,Sept. 1963. (2) Portions of this paper are derived from the Ph.D. dissertation of Y. T., Johns Hopkins University, 1964.
REVERSIBLY INTERACTING SYSTEM DEXTRAN SULFATE-CARBOXYHEMOGLOBIN
4243
-.__
simple manner to conditions in the homogeneous solution. Several methods have been developed to evaluate the patterns of rapidly equilibrating systems. Calculations have usually utilized the relationships derived from the moving-boundary equation^.^ Alternately, the differential equations describing the transport behavior of the interacting systems can be used. Analytical solutions have been obtained for the equaB C, assuming Intions describing the reaction A stantaneous equilibration and neglecting the effects of diff usiom6 Computer solutions6 have been obtained for the equations describing the isomerization reaction A e B for different reaction rates and diffusion constants and, more recently, for equations7 describing the reaction A C, assuming instantaneous equilibration. nB The problem of interpreting the moving-boundary pattern obtained with interacting systems is complicated by the fact that the usual refractometric methods for recording concentration distributions sum the contributions of all species present in the boundary. What, in fact, is desired is the concentration distribution of each individual interactant in the boundary region. This information can be obtained in a twointeractant system by employing light absorption measurements in conjunction with a refractometric method, provided that one interactant has suitable absorption characteristics. I n this investigation the electrophoretic boundaries of the interacting system carboxyhemoglobin-dextran sulfate have been investigated using a Tiselius apparatus equipped with both schlieren and absorption optics. This interactant system was selected for study because of the convenient light absorption characteristics of the carboxyhemoglobin and because of the general interest in interaction between proteins and charged polysaccharide^.^-^^
tion and electrophoretic properties are given in Tables I and 11. D-8 and E 4 were gifts of Dr. Colin Rickets of the University of Birmingham, England. Ph150 was synthesized according to the procedure of Ricketts. The ascending electrophoretic peak was Table I: Properties of Dextran Sulfates
+ +
Prepn.
Mol. wt. (numberaverage)
D-8
1.0
E-4 Ph-150
6.0
x x
106 104
3 . 0 X lo6
% sulfur
18.9 11.1 16.7
No. of sulfate groups per glucose
2.3 1.4 2.0
+
Experimental Section Human carboxyhemoglobin (COHb) was twice crystallized by the method of Drabkin.I6 Stock solutions ranging from 8 to 12% (g./lOO ml. of solution) were kept under CO a t 4”. I n the buffer systems used, the electrophoretic mobility was linear with pH over the range 6.0 to 9.0 with the isoelectric point a t pH 6.8. No variation in mobility with ionic strength was observed in the experimental range 0.05 to 0.20 2M. Single symmetrical boundaries were obtained in both cell limbs under all conditions of pH and ionic strength employed. Sodium dextran sulfates (DS) were synthesized from dextran samples prepared by acetone fractionation of acid hydrolysates of native dextrans. The composi-
Table I1 : Electrophoretic Mobilities of Dextran Sulfates
x
105,
r/2, M
cm.2 sec.-1
7.4
0.05 0.10 0.20
17.8 14.4 11.9
8.0
0.05 0.10 0.20
15.5 14.2 11.9
8.5
0.05 0.10 0.20
15.6 14.2 11.8
E-4
7.4
0.10 0.20
14.4 12.0
Ph-150
7.4
0.10 0.20
14.4 12.0
Prepn.
D-8
PH
V. -1
(3) R. A. Brown and S. N. Timasheff in “Electrophoresis,” M. Bier, Ed., Academic Press Inc., New York, N. Y., 1959. (4) L. G. Longsworth in “Electrophoresis,” M. Bier, Ed., Academic Press Inc., New York, N. Y., 1959. (5) G. A. Gilbert and R. C. L1. Jenkins, Proc. Roy. SOC.(London),
A253, 420 (1959). (6) J. R. Cann and H. R. Bailey, Arch. Biochem. Biophys., 93, 576 (1961). (7) J. R. Cann and W. M. Goad, J . Biol. Chem., 240, 148 (1965). (8) P. Bernfeld, V. M. Donahue, and M. E. Berkowitz, ibid., 226, 51 (1957). (9) S. E. Kornguth and M. A. Stahmann, Arch. Biochem. Biophys., 9 1 , 3 2 (1960). (10) M. Schubert and E. C. Franklin, J . Am. Chem. Sac., 83, 2920 (1961). (11) P. Bernfeld and T. Kelley, J. Biol. Chem., 238, 1236 (1963). (12) H. Noguchi, Biochim. Biophys. Acta, 22, 459 (19b9). (13) H. Noguohi, J . Phys. Chem., 64, 185 (1960). (14) T. E. Thompson and W. M. MoKernan, Biochem. J., 81, 12 (1961). (15) D. A. Drabkin, Arch. Biochem. Biophys., 21, 224 (1949). (16) C. R. Ricketts, Biochem. J., 51, 129 (1952).
Volume 69. Number 13 December 1966
4244
always hypersharp, and the descending peak, broad and asymmetrical. The moving-boundary apparatus was of the KlettLongsworth type equipped with phase plate and cylinA single set of optical components proved drical adequate for both schlieren and absorption measurements. The modifications necessary for absorption measurements included the installation of a precisely adjustable mount for the light source, the use of a penciltype tungsten filament lamp (GE T3Q/C1 Quartzline), interference filters to isolate the desired wave length, and a mechanical scanner located at the image plane of the camera lens. The search-head unit carrying a photomultiplier (IP 21) was mounted on a 0.5-in. no. 16 brass screw driven by a Bodine synchronous motor (KYC-23RB). The unit was positioned to scan a 2.5 cm. wide strip at the image plane located on the opposite side from the schlieren base line. Thus, except when the gradient was very steep, the scan was not cut by the schlieren peak. Scanning slit width was 0.6 mm. Microswitches served to limit the scan to 7.5 cm. Scanning time was fixed at 20 sec. corresponding to a recorder strip of 17.2 cm. The recording circuit consisted of the IP21 tube, a d.c. amplifier, a logarithmic conversion circuit, and a 10-mv. Brown recorder. The photomultiplier signal was d.c. amplified, converted to its logarithm, and read out into the recorder. The logarithmic conversion circuit was of the biased diode type and used four 6A15’s to approximate the log of the amplified signal over a two-decade range. The linearity was f1%,full scale. Photomultiplier power was supplied by 67.5-v. batteries. Current drain was below 100 ma. with maximum anode current 0.3 ma. Drift of the over-all circuit when in continuous operation over several days was 0.2% of the full-scale input.17 Typical linearity and reproducibility are shown in Figure 1. Points for different preparations of COHb all fell within the circIes. Linearity was preserved up to 0.4% COHb concentration (one decade) with the 596-mp interference filter and up to 0.8% with the 610mp filter. Point reproducibility was better than =k2%, full scale. Tubes were aged, as were the batteries, and matched if necessary, before use. For comparison, the linearity of the integrated schlieren pattern vs. concentration of COHb is shown in Figure 2. The agreement of these two types of measurement is shown in Figure 3. The nonlinearity at higher COHb concentrations observed with the absorption record was probably due to the finite band width of the light isolated by the interference filter. Both the extinction coefficient of COHb and the sensitivity of the photoThe Journal of Physical Chemistry
YORKTSANG AND T. E. THOMPSON
Yo COH b
Figure 1. Linearity and reproducibility of absorption scanning system. Plot of pen deflection 11s. COHb concentration.
l
/
i
I
.I
l
I
.2
l
I
.3
1
1
1
1
.4 .5 %COH b
1
1
.6
1
1
1
.7
1
1
1
.8
Figure 2. Linearity and reproducibility of schlieren system. Plot of integrated schlieren area (arbitrary square units) us. COHb concentration.
multiplier in the wave length region of the filters used decreased appreciably with increasing wave length. Calibrated neutral density filters gave linear response up to 1.8 decades. The concentration of COHb was determined with a Beckman DU spectrophotometer at 538 and 568 mp using E:?,, = 8.55. Dextran sulfate concentrations were determined by dry weight. Sodium phosphate buffers were used at pH 7.5 and 7.0. Cacodylate buffer was used at pH 6.0. Tris(hydroxymethy1)aminomethane (Tris) buffers were used at all other pH values. All solutions were 0.05 ionic strength in the buffer with sodium chloride making up the rest of the ionic strength. Solution conductivities were determined in a dipping-type cell with either an Industrial Instrument bridge (Model RC16B2) or an LKB Type 3216 B instrument. All pH and con(17) Y.Tsang, Thesis, Johns Hopkins University, 1964.
4245
REVERSIBLY INTERACTING SYSTEM DEXTRAN SULFATE-CARBOXYHEMOGLOBIN
u 2 0 3.63 7.26 10.9 14.5 18.2 X
Figure 3. Superposition of absorption and integrated schlieren patterns. COHb alone; phosphate buffer; pH 7.4; r/2 = 0.20.
ductance determinations were corrected to lo, the temperature at which the electrophoretic measurements were made. A minimum of three sets of schlieren and absorption patterns was taken during each run. The schlieren photograph was first taken, then the search-head unit swung into place, and the absorption scan made. A maximum of 4 min. was required for these operations. Before comparing the absorption scan with the integrated schlieren pattern, correction was made for the absorption base line, the resulting pattern reduced by dividing the density at each point by the maximum density, and the reduced pattern then multiplied by the refractive index increment in arbitrary square units.
Results
metric, fast boundary consisted entirely of dextran sulfate and moved with the mobility of free dextran sulfate. The slow, ascending boundary was an asymmetric reaction boundary. The electrophoretic results are summarized in Table 111. I n the table, a! is the fraction of total COHb moving with the mobility of free COHb in the descending cell unit. The free COHb concentration was obtained directly from the absorption pattern. The empirical measure of interaction used was 1 a which may vary from 0 for no interaction to 1 for maximum interaction without equilibration. l 4 It can be seen that, at constant ionic strength, the interaction as measured by 1 - a! decreased sharply with increasing pH. At pH 8.5, the patterns were those of a simple, noninteracting system of two macromolecular components. At constant pH, the interaction decreased rapidly with increasing ionic strength. The interaction increased somewhat with increasing molecular weight of the dextran sulfate. It should be mentioned that preliminary experiments with dextran sulfates of the same molecular weight as the E-4 preparation but with sulfur contents of 15.2 and 18.2% gave nearly identical patterns, with the degree of interaction increasing only slightly with increasing sulfur content. Variation of the concentration ratios or the total concentrations did not appreciably change the value of 1 - a. Additional information can be obtained by considering the relative mobilities, r, of the reaction boundaries. A relative mobility ~ D Scan be defined for the fast, descending boundary as TDS
= (U’DS
- WOHb)/(UDS - WOHb)
and in a similar manner slow, ascending boundary
rCOHb
can be defined for the
The interaction studies were carried out over a pH YCOHb = 1 - (UDS - U’COHb)/(UDS - WOIIb) range of 7.4 to 8.5, at an ionic strength range of 0.05 to 0.20 M, and at different interactant concentration Here UDS and W O H b are the mobilities of uncomplexed dextran sulfate and carboxyhemoglobin, respectively, ratios. The criteria for ascertaining whether interaction occurs have been discussed in other s t u d i e ~ . ~ 1 ~U’DS 4 and U’COHb are the weight-average mobilities of By these criteria the systems studied here were of the the fast, descending boundary and the slow, ascending reversible, rapidly equilibrating type. Both schlieren boundary, respectively, calculated from the controidal and absorption patterns indicated that the concentraordinate of the gradient curve.4 If the weight-average tion distributions in all runs showing interaction could mobilities of the reaction boundaries are taken as measures of the constituent mobilities,ls then it is evident be classified as of the “two-moving-boundary” type. In the descending limb, the slow boundary, which was that the relative mobility is a convenient measure of symmetric or only very slightly skewed, moved with the difference between the constituent mobility and the mobility of free hemoglobin. A comparison of the mobility of the corresponding free interactant. schlieren and absorption patterns showed that this It can be seen by examination of Table I11 that rDS boundary consisted of hemoglobin only. The fast, descending boundary was an asymmetric reaction (18) R. A. Alberty and H. H. Marvin, J. Phv8. Colloid Chem., 54, b ~ u n d a r y . ~I n the ascending limb, the sharp, sym47 (1950). Volume 69,Number lb December 1966
4246
YORKTSANG AND T. E. THOMPSON
Table HI: Summary of Electrophoretic Data COHb,
DS,
PH
r/2
g./lOO ml.
g . / l O O ml.
DS, mol. wt.
1-a
rDS
TCOHb
7.42 8.00 8.52
0.10 0.10 0.10
0.205 0.208 0.305
0.470 0.455 0.455
1.0 x 108 1 . 0 x 108 1 . 0 x 106
0.85 0.32 0.02
0.88 0.92 1.0
0.70 0.50 0.10
5.5 2.0
7.40 7.96 8.45
0.20 0.20 0.20
0.207 0,209 0.202
0.450 0.460 0.415
1 . 0 x 106 1.0 x 108 1 . 0 x 106
0.45 0.07 0
0.92 0.91 1.0
0.45 0.10 0
3.0 0.5
7.44 7.42 7.40
0.05 0.10 0.20
0.208 0.205 0.207
0.302 0.470 0.450
1.0 x 106 1.0 x 106 i . 0 x 106
1.00 0.85 0.45
0.85 0.88 0.92
7.98 8.00 7.96
0.05 0.10 0.20
0.205 0 * 208 0.209
0.460 0.455 0.460
1.0 1.0 1.0
106 106 106
0.92 0.32 0.07
7.43 7.40
0.10 0.20
0.170 0.156
0.420 0.245
6.0 6.0
104 104
7.43 7.43 7.43
0.10 0.10 0.10
0.170 0.271 0.205
0.420 0.435 0.470
x x x x x x
7.43 7.43 7.42
0.10 0.10 0.10
0.298 0.360 0.170
0.63 0.265 0.420
6.0 6.0 6.0
8.00 8.00
0.10 0.10
0,208 0.77
0.455 0.390
7.96 7.96
0.20 0.20
0.209 0.395
0.460 0,440
AF/2
n'
...
10 6 I . .
0.0085 0.004 0.004
9
...
... ...
0.008 0.005 0.004
0.85 0.70 0.45
10.2 5.5 3.0
15 10 9
0.004 0.0085 0.008
0.86 0.92 0.91
0.95 0.50 0.10
6.0 2.0 0.5
18 6
0.003 0.004 0.005
0.25 0
0.98 1.0
0.30 0
0.1
...
...
3
0.007 0.005
6.0 104 3.0 X lo6 1.0 x 106
0.25 0.22 0.85
0.98 0.84 0.88
0.30 0.10 0.70
0.10 0.7 5.5
3 2 10
0.007 0.0095 0.0085
x x x 1.0 x 1.0 x 1.0 x 1.0 x
104 104 104
0.29 0.15 0.25
0.95 0.92 0.98
0.30 0.20 0.30
0.12 0.18 0.10
2 4 3
0.011 0.004 0.007
106 106
0.32 0.37
0.92 0.77
0.50 0.40
2.0 10.8
6 26
0.004 0.004
106 106
0.07 0.08
0.91 0.93
0.10 0.05
0.5 1.5
*..
0.005 0.005
is equal to 1 or very nearly so in all cases. This can obtain only if the mobilities of all the complexes are essentially equal toIum If this is the case, then YCOHb should decrease as the degree of interaction decreases. Examination of Table I11 shows that this is indeed the case. Hence, it is apparent that all DS-COHb complexes present in the system, regardless of their stoichiometry, have mobilities essentially equal to UDB-
The minimum number of moles, n, of COHb complexed per mole of dextran sulfate can be directly estimated from the known concentrations of total COHb and total dextran sulfate and from the concentration of uncomplexed COHb &s determined from the slow, descending boundary assuming that all the dextran sulfate is available for association. The maximum quantity, n', of moles of COHb complexed per mole of dextran sulfate can be obtained from the uncomplexed dextran sulfate concentration in the fast, ascending boundary. As the mobilities of the complexes are not very different from that of the dextran sulfate, the quantity n cannot be very much less than the actual value in the homogeneous interaction solution. The Journal of Physical Chemistru
n
...
...
It can be seen in Table 111 that these quantities run parallel to the degree of interaction. With the mole ratios used, it can be concluded that, except at low degrees of interaction, the average composition of the complex changed with both pH and ionic strength. Interaction (dissociation) constants were calculated from the moving-boundary equation^^^^* or from the partial differential equations of Gilbert and Jenkins.6 For the moving-boundary calculations, the interaction was considered to be of the type A nB ," AB,, where A is the dextran sulfate, B is the carboxyhemoglobin, and n is the number of moles of COHb associated per mole of dextran sulfate. I n the Gilbert calculations, n = 1. I n utilizing the Gilbert and Jenkins equations, a procedure employing information derived from both absorption and schlieren patterns was developed. The asymptotic equations were rearranged to give d@ -=-- V A - VC: v - VB V B - vc v - V A dbT
+
+
+
where UT = u c and bT = b c. The symbols are those of Gilbert and Jenkins.5 Here u represents the
4247
REVERSIBLY INTERACTING SYSTEM DEXTRAN SULFATE-CARBOXYHEMOGLOBIN
Table IV : Summary of Interaction Constant Calculations
PH r/2 [COHbl, M X 10-5 [DS], M X [COHb], free, M X 10-6 U'DS X cm.2 sec. -1 v. -1
n
K, M VA
x
= vDS
Mol. wt. of DS 1.0 X 108 1.0 X 106
-
6.0 X 104
6.0 >: 104
7.43 0.10 4.40
7.43 0.10 5.30
7.43 0.10 2.50
8.00 0.10 3.06
8.00 0.10 11.3
7.95 0.20 3.07
7.95 0.20 5.80
7.43 0.10 4.00
10.5 3.10
4.4 4.50
7.0 1.85
0.46 2.10
0.39 7.1
0.46 2.85
0.44 5.20
1.40 3.10
6.0
x
104
13.8
13.3
14.1
13.2
1
105
1 12.5
12.5
Moving boundary 1 12 13.0 25 X
x
104,
6.6
6.6
Gilbert-Jenkins 6.6 5.4
x
0.33
0.33
0.33
5.5 0.63 0.0085
4.1 0.18 0.0110
5.6 0.63 0.011
0.185
0.30
0.65
11.3
12 86 X
1.0 X 106
11.2
2 18 X
1.0 X 106
11.1
3.0 X 106
12.2
2 12 X low6
1 1.3
5.4
2.31
2.31
6.7
5.3 0.96
2.10 0.80
2.10 0.80
6.2 0.85
cm./sec. UB
= VCOHb
10'9
cm./sec.
vc = VAB x lo4, cm./sec. K , M X lo5, eq. 16, ref. 5 K , M X lo6, eq. 19, ref. 5 K , M x 105 (VA
22
20
5.3 0.96
18
1.7
= VC)
concentration of uncomplexed DS, b represents the concentration of uncomplexed COHb, and c represents the concentration of the 1-1 complex. The value of the derivative, daT/dbT, was obtained by differentiation of a plot of the values of a~ vs. b~ in the boundary regions. The value of vc could thus be unequivocally determined. With vc known, the dissociation constants were calculated using either eq. 16 or 19 of ref. 5. I n addition, dissociation constants were calculated assuming vc is equal to VA. It is of interest to note that with the combined schlieren and absorption data, such a procedure, using only the derivatives of the partial differential system, could, in principle, be extended to higher order complexes to include the effect of changes in conductances through the reaction boundary. However, the precision of the data obtained in this study did not warrant such a procedure. The results of calculations using both the movingboundary equations and the Gilbert-Jenkins differential equations for selected runs are summarized in Table IV. I n the case of the interaction of E-4 and Ph-150 with COHb a t pH 7.3, (r/z) - 0.10, the best fit with the moving-boundary equations was obtained for n = 1. I n these systems dissociation constants calculated
by the two methods agree well, provided V A = VC. The agreement is poor when eq. 16 or 19 of ref. 5 are used with values of vc calculated from daT/dbT. At higher values of pH and ionic strength, the movingboundary equations required values of n > 1. Under these circumstances, application of the Gilbert-Jenkins equations leads to negative values for the dissociation constants.
Discussion I n addition to the assumptions of homogeneous solutes and of simple stoichiometry, both the treatment utilizing the moving-boundary equations and the Gilbert-Jenkins equations assume that experimentally attainable constant weight-average velocities can be reached and that electrophoresis is in all other respects ideal. I n fact, electrophoresis was nonideal as evidenced by the large area due to the stationary boundaries. At the ionic strength and p H range for which interaction was observed, nonideality can be attributed to the large equivalent concentration of the dextran sulfate. Thus, in runs with dextran sulfate alone, the descending, stationary boundary accounted for 15Vo'oEume69. Number 12 December 1966
4248
30% of the total area under the schlieren curves. The area was usually linear with respect to the per cent concentration of dextran sulfate but varied with the buffer system used. For a given concentration it was nearly independent of ionic strength. The areas of the stationary boundaries in runs with COHb alone were near the experimental error for area measurements. An estimate of the ionic strength change through the reaction boundaries can be obtained by use of the moving-boundary equation^.^^^^ The results are shown in the last column of Table 111. Sodium or Tris dextran sulfate was assumed to behave as a univalent electrolyte in its contribution to the ionic strength.20 Equivalent concentrations were estimated from the area of the descending, stationary boundary in runs with dextran sulfate alone. Comparison of the absorption and schlieren patterns indicated that the stationary areas in the interaction experiments were the same as those estimated for the interacting systems. These results are in agreement with counterion binding studies on other polyelectrolytes.21 The two types of boundary systems assumed for the calculations were
YORKTSANG AND T. E. THOMPSON
1.0 -
-
.8 -
.6
%,
.4
-
-
.2 -
-
n ”-
1 1 1 1 1 1 1 1 1 l I I I I I I I ~
-3.2 -2.6
0
1.6 3.2 V”
4.8
6.4
8.0 8.6 11.2
X/t
Figure 4. Variation of concentration distribution with time: 50 min.; , 95 min. p H 7.43; r/2 = 0.10; COHb and DS concentrations 0.170 and 0.420 g./lOO ml., respectively; DS molecular weight 6.0 x 104.
-----__ , 20 min.; -,
-
through the reaction boundary was linear in the change in refractive index due to changes in the sodium (or Tris) dextran sulfate concentration. For the concentration range used, a given per cent deviation in the assumed linear relation would cause an error in the C1-, H2PO4-,HP042-, Na+, C1-, H 2 P 0 4 HP042-jlNa+, , experimental value ranging from 0.25 to 0.50 of the per COHb (p) -+-Na+, C1-, cent deviation. The point at which the original homogeneous soluH2P04-, HP0d2-, COHb, tion begins and the point at which the solution containDS, complexes (a) (I) ing uncomplexed components begins were difKcult to Naf, TrisH+, Cl-/IR’a+, TrisH+, C1-, COHb (p) + determine with precision. Plots of v(x/t) vs. C/CO (Figure 4) indicate that, for all systems studied, a Na+, TrisH+, C1-, COHb, DS, “quasi-steady-state” was reached within the expericomplexes (a) (11) mental time limits. There have been numerous studies on the interaction Since the interaction as measured by the parameter between different macromolecules carrying net charges 1 - a decreased with increasing ionic strength at a of the same Usually, there are other attracgiven pH, it may be expected that, owing to this effect tive forces which compensate for the long-range realone, the observed degree of interaction would be pulsion. Thus, for antibody-antigen interaction, the 0.02-0.05 lower than in the homogeneous interaction large surface area available for short-range attraction solution. I n addition, the conductivity of the p contributing to steric fit is sufficient to balance out the solution would be higher than that of the CY solution. coulombic repulsion. For interactions involving polyThe increase in the degree of interaction would be electrolytes, the flexible-coil properties are probably small since the mobility of the reaction boundary is as important as the charge densities. Dipole and nonclose to that of free dextran sulfate. polar effects are probably not sufficient.12 The effects of nonideal electrophoresis would be The marked variation of interaction with ionic more serious in calculations involving the Gilbertr strength and pH observed in this study indicates that Jenkins equations than with the moving boundary equathe interaction probably involves the sulfate anion of tions. For the latter, the increase of the ?A-DS - %OHb the dextran sulfate and cationic groups on the COHb.14 would be offset by a decrease in [COHb] - [COH~IT. I n the former calculations, [DSIT,the total concentra(19) J. de Wael and E. Wegelin, Rec. trav. chim., 71, 1035 (1952). tion of dextran sulfate, was obtained by subtracting (20) C. Tanford, “Physical Chemistry of Macromolecules,” John the absorption pattern from the schlieren pattern and Wiley and Sons, Ino., New York, N. Y.,1901,p. 468. assuming that the change in refractive index caused by (21) G. Sitaramaiah and D. A. I. Goring, J . Polvmer Sei., 58, 1107 changes in the concentration of buffer and salt ions (1962). The Journal of PhyaicaS Chemistry
REVERSIBLY INTERACTING SYSTEM DEXTRAN SULFATE-CARBOXYHEMOGLOBIN
While the total charge per polyelectrolyte molecule is high (even with extensive counterion binding), it is distributed through a large volume. Thus, for example, E-4, which has approximately the same average molecular weight as COHb, can be calcu1at:d to have an equivatent hydrodynamic radius of 280 A. as compared to 32 A. for COHb.22123The near neutrality of this large permeable sphere,24 in addition to the nearly random motions of the fixed charges within the volume, is favorable for a close approach by the COHb molecule and multiple interactions of the local field of unlike charges. With increasing pH, the decrease in the available cationic groups on the COHb would be a cause for decreased interactions. The titration charges of COHb are -2, -7, and -14 a t pH 7.4, 8.0, and 8.5, re~pectively,~~ and the calculated electrophoretic charges are -2, -4, and -6,2s The disappearance of interaction occurs at a much lower charge than that observed for dextran sulfatebovine serum albumin interaction.ld This correlateswith the extensive anionbinding properties of BSA which is in contrast with the behavior of human hemoglobin which exhibits little or no binding of monovalent and divalent cations and monovalent anions. The decrease in interaction may also be partly attributed to counterion binding of TrisH+ ion resulting in a greater excluded volume within the equivalent sphere. It has been observed that values of interaction constants obtained from transport experiments usually
4249
do not agree with values obtained from equilibrium experiment^.^^^^ It has been suggested that transport and equilibrium experiments constitute two general classes of experiments from which two different quantities can be obtained.29 An applied field will modify the charge density in the ionic atmosphere, quite apart from any effect due to the finite mobilities of the ionem I n the studies reported here, as has been mentioned, the field strength was varied over a sixfold range with currents from 2.5 to 15 ma. with only slight changes occurring in the patterns. Acknowledgments. We wish to thank the Johns Hopkins School of Medicine for Post-Sophomore fellowships for Y. T. Some of the calculations were done at the Rockefeller Institute, and we wish to thank Dr. G. E. Perlmann for providing facilities. This research was supported by U. S. Public Health Service Research Grant GM-08411.
(22) (23) (24) (25) (26) (27) (28) (29) (30)
P.J. Napjus and J. J. Hermans, J . Colloid Sci., 14, 252 (1959). J. J. Hermans, J . Polymer Sci., 18, 529 (1955). P. Debye and A. M. Beuche, J . Chem. Phys., 16, 573 (1948). K. F. Guthe, J . Biol. Chem., 234, 3167 (1959). D. C. Henry, Proc. Roy. SOC.(London), A133, 106 (1931). C. Van Os and W. Moeller, Rec. trav. chim., 77, 297 (1958). 0. Redem and A. Katchalsky, J . Polymer Sci., 15, 32 (1955). Z. Alexandrowicz and E. Daniels, Biopolymers, 1, 447 (1963). F. Booth, Proc. Roy. SOC.(London), A203, 514 (1950).
Volume 69,Number 11 December 1066
