THERMODYNAMIC PROPERTIEB OF BOVINE ALBUMIN AT Low pH
Dec., 1956
1633
in this work and as previously reported, has already taken place in a significant amount, Le., at the end of 30 minutes the gain in weight is 3.5 pg./ The results of these studies are shown in Table V and are compared with those reported by Gulbransen and Wysong on the oxidation." AI does not show any significant reaction with Nz until the temperature is raised to 530' where an apTABLEV preciable amount of nitridation has been observed. INITIALNITRIDATION PERIOD OF ALUMINUM;COMPARISON This is to be contrasted with the report by TeremIO OF NITRIDATION WITH OXIDATION OF ALUMINUM IN THE that the nitridation begins a t 760". As in the case SAMETEMPERATURE REQION of Mg, Terem's technique was probably not sensiWt. gain at the end of 30 min., tive enough to observe the reaction taking place a t t , oc. G8S rg./cm.r lower temperatures.
colors ranging from gold to blue or purple, depending on the thickness of the nitride film formed. (c) Initial Nitridation Period.-Studies were carried out to find the lowest temperature where nitridation may be observed with the sensitivity of this apparatus. At 450" there was no reaction a t all for nitridation, whereas oxidation, as observed
400
02
450 450
0 2
Nz
475 475 500
0 2
515
N2
N2 0 2
2.90 3.50 No reaction 6.80 0.10 8.80 0.25
Acknowledgment.-This research was in part conducted under Contract No. AF 33(616)-338 with the United States Air Force, the sponsoring agency being the Aeronautical Research Laboratory of the Wright Air Development Center, Air Research and Development Command.
HYDRODYNAMIC AND THERMODYNAMIC PROPERTIES OF BOVINE SERUM ALBUMIN AT LOW pH1 BY GEORGE I. LOEBAND HAROLD A. SCHERAGA Departmed of Chemistry, Cornel2 University, Ithaca, New Yorlc Received Jdzl 87, 1066
Hydrodynamic measurements (sedimentation and viscosity) have been carried out on bovine serum albumin at PH 4.0 and 5.13 in 0.5 M KC1 in order to assess the influence of the molecular configuration on the a parently anomalous ionization behavior of the carboxyl groups. From the sedimentation-diffusion molecular weight a n 8 the computed hydrodynamic parameter j3 it is concluded that the hydrodynamic properties of bovine serum albumin can be interpreted in terms of an equivalent sphere a t both H 4.0 and 5.13, the volume at pH 4.0 being only about 11% greater than that at.pH 5.13. This incL-easein volume a t the Tower pH can account for only a small part of the anomalous reactivit insofar as it influences the electrostatic contribution to the free energy of ionization. To circumvent this difficulty Tanforland co-workers have introduced a discontinuity into the description of the molecular model by allowin for penetration of ions a t low pH but not above pH 4.3. Even with this discontinuity, the analysis of Tanford and co-worgers accounts only for the slopes but not the absolute values of the pH dependence of the thermodynamic parameters. On the other hand, with the use of a reasonable empirical electrostatic contribution (Le., WZus. p H curve), both the slopes and absolute values can be accounted for by exanding on a previous suggestion of reversible ormation and breakage of internal hydrogen bonds. Calculations on this gasis are reported here to show that the anomalous behavior can be understood if it is assumed that some of the carboxyl groups .are mvolved in carboxyl-carboxyl acetic acid dimer type hydrogen bonds. Upon ionization, carboxylate ion groups form hydrogen bonds with hydroxyl donors. The reversible formation and breakage of these internal hydrogen bonds is presumably accompanied b some penetration of solvent into the molecular domain to give rise to the 11% difference in volume a t the two pH's. $he calculations of the effects of h dro en bonding thus account f?r both the hydrodynamic and thermodynamic properties of bovine serum albumin at low p 8 . i t the same time they provide some details of the chanees taking place on specific groups within the albumin molecule, and provide a basis for the so-called configurationaladaptability of the albumin molecule.
Introduction The free energy change for such reactions as the binding of small ions by proteins contains an electrostatic contribution which depends upon several factors including the net charge Z of the protein and an electrostatic interaction factor w, the latter depending on the size and shape of the protein mole~ u l e . 2 - ~For example, the standard free energy of ionization AFO and the pK, respectively, of a particular group on a protein are (1) This work was supported b y the O 5 c e of Naval Researoh (Contract NB-onr 26414), by the National Science Foundation (Grant G-507), and by Eli LiUy and Co. Reproduction in whole or in part is
permitted for any purpose of the United Stated Government. (2) IC. Linderatrfjm-Lang, Compt. rand. Lrou. lab. Carlaberg. 16, No. 7 (1924). (a) G. Scatchard, Ann. N. Y. Acod. Sci., 61, 660 (1049). (4) T. L. Hill, Arch. Bioohem. Biophgn., 67, 239 (1966).
AL\Fo = (AF')'
- 2RTwZ
(1)
and pK
pKo
2wz -2.303
if the ionizing group is influenced only by electrostatic effects (e.g., if the group is not involved in a hydrogen bond). In these equations, R is the gas constant, T is the absolute temperature, (AFO)" is the value of AFO when Z = 0, and Kand K O are the ionization constants corresponding to AFo and (AFo)O, respectively. The quantity w is given by the following formula for a n impenetrable sphere with uniform surface charge (3)
where N is Avogadro's number,
B
is the electronic
GEORGE I. LOEBAND HAROLD A. SCHERACA
1634
charge, D is the dielectric constant, K is the inverse of the radius of the ionic atmosphere, and b and a are the hypothetical radii of the molecule and of exclusion, respectively. Whereas 2 varies with pH, w (and, therefore, the size and shape of the molecule) is usually found to be constant over a considerable part of the pH range.6 However, recent studies of the binding of protons6s6and other low molecular weight ions and molecules7 by bovine serum albumin (BSA) show that the thermodynamics of such reactions cannot be accounted for adequately if only 2,but not w, is assumed to vary with pH. I n other words, eqs. 1 and 2, with wasHumed constant with changing pH, fail to apply in t,hese cases. In the case of BSA this anomalous behavior manifests itself a t low pH by an abnormal steepening of the titration curve in the region where carboxyl groups are ionizing, i.e., whereas eq. 2 would predict a given increase in the observed pK as the pH rises (or as 2 decreases), the experimental titration curve is excessively steep because the pK of the carboxyl groups increases less rapidly than the simple electrostatic theory requires if both w and pKo remain constant. Also,the experimental pKo is found6 to be lower than expected. These effects, which make the carboxyl groups appear more acidic than normal, are illustrated in Fig. 1.
4.5
L
3.5 I 3
1
1
I
I
I
5
4
PH. Fig. l.-variation of p&bad with p H . for the carboxyl groups of BSA: curve A, expected behavior (eq. 2) asRuming w constant (0.023) and p K o = 4.6; curve B, same as curve A except that w was assumed to vary slightly with pH according to the hydrodynamic behavlor; curve C, experimental curve6at ionic strength 0.15.
--
Curve A represents the expected variation in p K o b s d assuming the carboxyl groups of BSA to be normal (pKo = 4.6)and w to have the value 0.023, independent of pH. I n order to obtain this curve, the Z us. pH data were taken from Tanford, et aZ.,8 and w was assumed equal t o the value found in the neutral pH regions (evaluated from titration data6 using eq. 2 in the neighborhood of the isoionic point). Curve B was computed on the same basis as curve A except that the slight variation of w with p H (due to a small pH dependence of b to be discussed below) was taken into account (eq. 3). Curve C is the experimental curve a t ionic strength 0.15 (see Fig. 4 of reference 6). It should be noted ( 5 ) C. Tanford, Proc. I o w a Acad. Sci., 69,
206 (1952).
(6) C.Tanford, 8. A. Swanson and W. 8. Shore, J . A m . Chern. Sac., 77,6414 (1955). We are indebted to Dr. Tanford for sending us the manuscripts for references 0 and 8 in advance of publicaton. (7) I. M.Klotz and J. Ayem, Disc. Farodas Soc., 13, 189 (1953). (8) C. Tanford. J. G. Buzzell, D. G. Rands and 5. A. Swanson, J . Am. Chsm. SOC.,7 7 , 0421 (1955).
Vol. 60
that the slope of curve C is smaller than that of curve A or B,and also that curve C lies lower than curves A and B. Two explanations have been proposed to account for the abnormal ionization behavior of the carboxyl groups in BSA. The first of these6.6.scan account for the slope of the pK vs. pH curve in terms of electrostatic effects by suggesting that the molecular weight remains unchanged but that the molecular configuration changes with pH5.698-10 giving rise to a pHdependent w factor. However, this explanation cannot account for the magnitude of pK". The second explanation accounts for the slope partly in terms of electrostatic effects, and the magnitude in terms of an additional factor over and above those included in eqs. 1 and 2. Specifically, the abnormal steepness of the titration curve a t low pH may be due to an additional pH dependence of the observed pK's of the groups being titrated because of the reversible formation and rupture of carboxyl-carboxyl hydrogen bonds of the acetic acid dimer type." It is also possible that both effects are present, Le., reversible changes in size or shape may accompany the change in the hydrogen bonding between the side chain polar R groups of the protein This investigation of the effect of pH on the hy-, drodynamic properties of BSA was undertaken in order to learn about the extent to which configurational changes occur as the pH region of anomalous reactivity is approached. Thus, we should be able to decide whether phenomena other than configurational changes must be considered in order to account for the reactivity. Similar investigation~,8~10~1~-15 making use of hydrodynamic methods, have been carried out on human and bovine serum albumin but most of them involve the measurement of only one hydrodynamic quantity, e.g., viscosity. Since two independent quantities are required, le some of the previous investigations have substituted an arbitrary assumption about the shape in order to deduce the size from the measurement of only one quantity.'' By coincidence this arbitrary assumption, that the molecule is essentially spherical, is compatible with the results obtained in this investigation. While it would have been desirable to apply the hydrodynamic method16 over a wide pH range, it is unfortunate that albumin does not remain homogeneous a t low and high pH9.18-zo where most of the (9) M . E. Reichmann and P. A. Charlwood, Can. J. Chem., $1, IO92 (1954). (IO) J. T. Yang and J. F. Foster, J . A m . Cham. Soc., 7 6 , 1588 (1954). (11) M.Laskowski, Jr.. and H. A. Soheraga, ibid.. 76, 0305 (1954). (12) C. Tanford and J. G. Buzzell, THIS.IOURNAL,60, 225 (1966). (13) J. M. Creeth, Bioehem. J . , 61, 10 (1952). (14) P. A. Charlwood, ibid., 66, 259 (1954). (15) J. R. Colvin, Can. J . Chem., 31, 734 (1953). (16) H.A. Scheraga and L. Mandelkern, J . A m . Chsm. SOC.,76, 179 (1953). (17) K. 0. Pedersen, Diac. Faraday Soc., 13, 49 (1953), has also called attention to the danger of drawing conclusions from a singlii measurement. (18) H.A. Saroff, G. I. Loeb and H. A. Scheraga. J . A m . Clan.. Soc.. 77, 2908 (1955). (19) P. Bro, 8. J. Singer and J. M. Sturtevant, ibid., 77, 4924 (1955). (20) M. J. Kronman, M. D. Stern and 5. N. Timasheff. THISJOURN A L , 60, 829 (1950).
Dec., 1956
THERMODYNAMIC PROPERTIES OF BOVINE ALBUMIN AT Low pH
1635
anomalies in the reactivity occur. Since the inter- coiled for compactness. The flow time of water in these viscometers was about 10 min. With such long flow times, the pretation of hydrodynamic data is not unambigu- kinetic energy correction was negligible. The viscosity ous for polydispersed systems,21this investigation measurements were carried out at 25.00", the bath temhas been confined to the isoionic point (pH 5.13) perature being constant to j=0.003". The viscosity data and to an acid pH (4.0) in 0.5 M KC1 where the were expressed in terms of the flow times t c and t of solvent solution, respectively, and plotted as ( 1 - t o ) / & us. c. protein is still homogeneous in the ultracentrifuge and Spring-driven stopwatches were used rather than electrical and where some of the titration anomalies (e.g., the timers because the fluctuations in the electric power line abnormally high reactivity of carboxyl groups) be- frequency were large enough to lead to significant errors. Calculations carried out with Booth's equation26indicate come apparent. Some previous interpretations of at an ionic strength of 0.5, the viscosity of the protein hydrodynamic data in the acid pH range have not that, solution is not affected by the charge of the prot.ein at pH taken cognizance of this heterogeneity. 4.0. It is worth noting that, in the pH range investiSedimentation.-Sedimentation constants s were used, gated here, a reversible reaction has been detected in conjunction with diffusion data obtained on the same of BSA,*o to compute molecular weights M ; also calorimetrically, 2 2 and anomalies have been found samples the values of s, together with [7] and M , permitted the in the behavior of the depolarization of fluores- hydrodynamic parameter @ to be calculated.lB cence2a; also studies of chloride and thiocyanate Sedimentation measurements were made with the Spinco binding by human serum albumin revealedz4that Model E ultracentrifuge. In order to encompass a wide of protein concentrations, cells with light paths of 3, the binding sites had to be cohsidered as divided range 12 and 30 mm., respectively, were used. The runs were into two non-equivalent sets if the data were to be carried out a t 59,780 r.p.m. except when the 30 mm. cell explained by electrostatic effects only. was used, the speed in the latter case being 50,740 r.p.m. All runs were made at room temperature. The reversible Experimental cooling on acceleration observed by Waugh and YphantisP'
Materials and Solutions .--Armour crystallized bovine serum albumin (lot No. N67009) was dissolved in 0.5 M KC1 to a concentration of about 10 g./100 cc. and dialyzed for 24 hours against this same salt solution in a rocking dialyzer at 2". The pH of this solution was 5.13. Solutions to be used a t pH 4.0 were then acidified; the amount of HCi required to lower the pH did not contribute appreciably to the ionic strength. These stock solutions were diluted with the corresponding solvents ( i . e . , the outside solution from the dialysis) to obtain more dilute protein solutions. The concentrations of the stock solutions were determined by dry weight measurements (heating to 105"), using the solvent as a tare. The estimated amount of bound chloride was taken into account in computing the concentration. The ionic strength was maintained at 0.5 in order to eliminate the Donnan effect. At lower ionic strengths at pH's away from the isoelectric oint the net charge and attendant Donnan effect are sugciently high so that the solvent in the protein solution contains unequal amounts of low molecular weight positive and negative ions; the viscosity of this solvent, 70, is therefore undefined. This problem was circumvented in computations of s ecific viscosity (pp= (7 70)/70where q is the viscosity of t i e protein solution) by using 0.5 M KCl. The solutions used for viscosity measurements were clarified by centrifugation at 1600 X g. I n a check experiment the solutions were filtered through Pyrex fine-grade sintered glass funnels; both clarification procedures yielded identical viscosity results. Solutions used for sedimentation measurements were naturally clarified during the acceleration period of the ultracentrifuge. All non-protein materials were Mallinckrodt analytical reagents, aqueous solutions being made up with conductivity water. The Beckman model G pH meter, standardized a t pH 4 and 7 with Beckman buffers, was used for p H measurements. Since the intrinsic viscosity [7]of dilute solutic%?%A< very small (-0.04 for concentration expressed in g./100 cc.) good precision in measurements of specific viscosity can be obtained only by using viscometers with very long flow times, e.g., for a 1% solution an error of 0.1 sec. in flow time corresponds to an error in specific viscosity of 5% for a flow time of 100 sec. and 0.8% for a flow time of 10 min. Ostwald viscometers with a 15-cm. hydrostatic head were used. The capillary portion of the viscometer was 90 cm. long with a bore diameter of about 0.6 mm. and was (21) Except for homologous polymers of known molecular weight distribution, &a discussed b y E. V. Gouinlock, P. J. Flory and H. A. Scheraga, J . PoEymsr Sci., 16, 383 (1955). (22) H. Gutfreund and J. M. Sturtevant, J . Am. Chcm. Soc.. 1 6 , 5447 (1953). (23) G. Weber, Biochem. J . , 61, 155 (1952); Diec. Faraday Soc., 18, 33 (1953). (24) G. Bcatchard, I. H. Scheinberg and 8. H. Armatrong, J . Am. Chsm. Soc., 79, 535, 540 (1950).
and by Biancheria and Kegeless was taken into account by subtracting 0.9 and 0.7" from the inter olated temperatures a t 59,780 and 50,740 r. .m., respectiveyy. The optics were focused according to t i e procedure recommended by Kegeles and Gutterm in order to obtain a set of symmetrical fringes on both sides of the peak, making it easier to measure its position. The photogra hs were read with a projection comparator previously &scribed26 with a precision corresponding to a distance of 5 p movement of the boundary in the ultracentrifuge cell. The sedimentation constants were corrected to 25" in 0.5 M KCl in the usual manner. Calculations similar to those made by Bro, Singer and Sturtevantl@indicate that a t this ionic strength the sedimentation constant depends on charge at pH 4.0 to the extent of only 0.5% which is about the limit of experimental error. The artial specific volume was taken" as T = 0.734 at 25' a t &oth pH 4.0 and 5.13. The concentration dependence of s is expressed in a plot of s us. c .
Results At both pH 4.0 and Fj.13 there was no time dependence of the viscosity or sedimentation behavior within 5 hr. after the solutions were brought from 2' to room temperature. Aging at room temperature apparently produces changes in the viscosity*at pH values below 4. Aging for several days at pH values of 4 and above at 2" produces no apparent change in the viscosity or sedimentation behavior. Since all measurements repolted here were completed within the 5 hr. period at room temperature, the subsequent reaction of BSA was of no concern. In assessing the sedimentation patterns for evidence of polydispersity it was estimated that about 2 to 3% of a faster sedimenting component was present a t pH 4.0 and 5.13. Typical sedimentation patterns are shown in Fig. 2. If the pH were lower than 4, the more extensive polydispersity previously reportedls-20 is evident. This poly(25) F. Booth, Proc. Roy. Soc. (London), APOS, 533 (1950). (26) M. L. Wagner and H. A. Soheraga, THISJOURNAL, 60, 1060 (1956). (27) D. F. Waugh and D. A. Yphantis, Rcv. Sci. Inatr., 18, 609 (1952). (28) A. Biancrheria and G. Kegeles, J . Am. Cham. Soc., 16, 3737 ('954). (29) G. Kegeles and F. J. Gutter, ibid., 1 3 , 3770 (1951). (30) M. 0. Dayhoff,G. E. Perlmann and D. A. MacInnea, ibid., 1 4 , 2515 (1952).
GEORGE I. LOEBAND HAROLD A. SCHERAGA
1636
A
B
A
B
Fig. 2.-Typical sedimentation patterna of BSA in 0.5 M KC1 at room temperature: A, pH 4.00, 6 g./100 cc.; B, pH 5.13,2 g./100 cc.
Fig. 3.-Sedimentation evidence for polydispersity in 0.5 M KC1 at p H 3.6: A, BSA stored at 2O, but run at
/ pH
Lot No
1
Vol. 60
low temperatures. By keeping the temperature at 2O, it should be possible to make diffusion, sedimentation and viscosity measurements a t lower pH's where the magnitude of the aforementioned anomalies in the reactivity increases at 25". Having indicated that the solutions at pH 4.0 and '5.13 are essentially monodispersed within the first 5 hours at room temperature we present the data obtained under these conditions. The viscosity and sedimentation data are shown in Figs. 4 and 5, respectively. In both figures the various lines shown were obtained by the method of least squares enabling extrapolations to be carried out to zero protein concentration. It may be noted that the sedimentation curves in Fig. 5 cross, This is simply a reflection of the fact that the concentration dependence of s is greater for the sample with the larger so value as has often been noted previously, for example for polyisobutylenes2 and cellulose trinitrate.s8 This behavior illustrates that a comparison of s values at some Jinite concentration, say 1 g./100 cc., would not provide information about relative configurations. The intercepts of the ( I - to)/toc vs. c plots are not the true intrinsic viscosities, but the limiting kinematic viscosities. To account for the difference in density between the pure solvent and the protein solution the term (1 - 52po)/100po must be added.a4 In this term, which has the value 0.0025 for our data, the quantity po represents the solvent density and O2 the partial specific volume of the protein. The corrected values, representing the intrinsic viscosities, are shown in Table I. TABLE I VISCOSITY AND SEDIMENTATION DATAOF BSA AT 25" pH 4.00
[VI, 100 cc./g.
IN
0.5 M KCl
pH 6.13
0.0457 i 0.0004 0.0413 i 0.0004
Svedberg units at 25' in 0.5 M KC1 4.43 f 0.03
80,
0.055
A 4.00 N67009 5.1 3 N67009 0 5.39 M66909 0 5.59 3701958
d
5uo 0.050 l
0.045 0.040 2.0 3.0 4.0 5.0 6.0 Concn. (g./lOO ml.). Fig. 4.-Viscosity data for BSA in 0.5 M KCl at 25'. 0
1.0
dispersity casts doubt on previous interpretations of low pH studies of BSA which have been based only on viscosity measurements. Examples of this polydispersity are shown in Fig. 3 in which Fig. 3A indicates the relative stability of BSA even after aging for several days a t pH 3.6 at 2". If the same solution stands at room temperature, then the polydispersity evident in Fig. 3B develops within a few hr. The sedimentation constants could not be determined for the solutions which were stable at pH 3.6 a t 2" because of the inability to maintain adequate temperature control in the ultracentrifuge a t
4.59 f 0.04
The limits of error are the standard deviations of the intercepts. It may be noted from Fig. 4 that the viscosity data are independent of the albumin lot. Preliminary studies not reported here indicate that this is not true of sedimentation and diffusion data. The sedimentation data presented here, and diffusion data126pertain to lot No. N67009. The sedimentation constants, extrapolated to zero concentration are given in Table I in terms of Svedberg units (1 Svedberg unit = sec.). It may be noted that aging of the solution at p H 4.0 for 2 days at 2O, the ultracentrifuge runs being completed within 5 hours after warming to room temperature, had no appreciable effect on the sedimentation data. Discussion Comparison with Literature Values.-The values of [v] reported in the literature for isoionic BSA (31) A temperature oontrol and temperature measuring device has reoently been developed b y Spinoo for the model E ultracentrifuge. This auxiliary equipment has not been installed on our ultracentrifuge. (32) L. Mandelkern, W. R . Krigbaum, H. A. Scheraga and P. J. Flory,J . Chem. Phys., 90, 1392 (1962). (33) M. L. Hunt, 8. Newman, H. A. Sohersga and P.J. Flory, THIS JOURNAL, 60, 1278 (1966). (34) C. Tanford, ibid., 69, 798 (1956).
Dec., 1956
THERMODYNAMIC PROPERTIES OF BOVINE ALBUMIN AT Low pH
show some scatter (see Table 11). As noted above, differences in lot in our own work do not a.ppear to affect the viscosity. It does not seem probable that differences in ionic strength are altogether responsible for these discrepancies. It may, however, be noted that measurements reported in the literature were carried out with viscometers having 100-200 sec. flow times. I n contrast, our flow times were about 10 min., .giving better precision in t - to. This difference in procedure need not of itself account for the discrepancies. TABLE I1 INTRINSIC VISCOSITIES OF ISOIONIC BSA Is1 Ref. 0.03, 0.15 0.037 8, 12 ( O ) , (0.1) .038" 10 .2 .041 35 .2 .042b 36 .5 .0413 This work a This value includes the kinetic energy and density corrections estimated by Tanford, et d.* This value was obtained a t pH 7. Ionic strength
1637
,
5.0 2' 4.5
2 X
4.0 YI
4 3.5 0
2.0 3.0 4.0 5.0 6.0 Concn. (g./lOO ml.). Fig. 5.-Sedimentation data-for BSAo(Lot No. N67009) in 0.5 M KCl a t 25 . 1.0
this component alone. While it is of interest to have information about the major component, it should be emphasized that our primary interest in the configuration of BSA arises from the desire to account for its anomalous reactivity. Since the titration data6were obtained on the whole albumin sample (lot No. N67009, as in our work) we are also interested in the average values of M and p. The sedimentation constant at pH 5.13 is com- We shall, therefore, carry out the computations in pared with literature values in Table 111. For this both ways, recognizing that the differences in the purpose our value given in Table I has been cor- results will be small since the impurity is estimated rected to 20" in water in the usual manner, using to be present only to the extent of about 3%. The measured values of [v] and D are average the same correction data reported elsewhere.26 values for the whole sample, while the value of s TABLE I11 pertains to a particular component. With this in SEDIMENTATION CONSTANTS OF ISOIONIC BSA CORRECTED mind we shall calculate first the molecular weight TO 20" IN WATER of the major component. For this purpose we use Ref. ema em,& the value of s20,w = 4.41 X sec. reported in 4.32 4.41 Taylor (see ref. 37) Table I11 for the major component at pH 5.13. 4.30 4.39 Miller and Golder (see ref. 37) Diffusion data on the same samples, reported else4.31 4.40 Creeth (see ref. 37) where126give = 5.90 X lo-' cm.2/sec. for the 4.29 4.38 37 major component. This value was computed26 .. 4.40 36 from the observed average diffusion coefficient on 4.29" 4.34" 29 the basis that the major component represents 4.40 4.49 35 97% of the total protein, and that the ratio of .. 4.41 This work the diffusion coefficients of the major and minor a As reported in literature. *This column is obtained components is 1.5. Both of these assumptions by multiplying the data in the previous column by 1.02 are compatible with a heterogeneity analysis car(ref. 37) to account for the Waugh-Yphantis or BiancheriaKegeles effect. The value of Kegeles and Gutterm is multi- ried out, on the diffusion data126while the 3% value plied by 1.01 since they took the correction into account is, in addition, in agreement with the appearance but used only one-half the correct value. c The value of of the sedimentation patterns of Fig. 2. The literaKegeles and Gutter20 is slight1 lower than the others. This is probably due to the fact tiat their value corresponds ture valueaOof 5 = 0.734 at 25" may be corrected to to pH 4.4. As can be seen from Table I, the sedimentation 0.730 at 20" using the generalized temperature coconstant decreases with decreasing p H in the pH range 5.13 efficient for 5 for proteins.38 The density of water to 4.0 in the presence of chloride where no cations except at 20" is 0.9982 g./cc. Using these data in the hydrogen ion are bound. Svedberg equation Molecular Weight and Configuration.-We may sRT M = use the data of Table I t o compute a sedimentation(4) D(l - Vp) diffusion molecular weight M for BSA and also the hydrodynamic parameter16 p. In such calculations we obtain for the major component the value M = we must take account of the presence of about 301, 67,000 f 3000 g./mole. We shall assume that the of the faster sedimenting component (see Fig. 2). molecular weight of the major component, as well If we use hydrodynamic data which pertain to the as the average molecular weight to be computed whole albumin sample, then we will have computed below, is the same at pH 4.0 as the value calculated average values of M and P. On the other hand, above from data at pH 5.13. This seems justified if we use data which pertain to the major compo- in light of previously reported light scattering nent, which represents 97% of the total protein, data.a-IO In order to compute the average molecular weight then the computed values of M and p will pertain to we use the observed average value26of the diffu(35) V. L. Koenig and J. D. Perrings, Arch. Biochsm. Biophya.. 41, sion coefficient at pH 5.13. B2~,w = 5.81 X 10-7 367 (1952). (36) P. A. Charlwood, Can. J . Chem., 88, 1043 (1955). (37) S. Bhulman, Arch. Biochem. Biophya., 44, 230 (1953).
(38) T. Svedberg and K. 0. Pedersen, "The Ultrscestrifuge," Appendix 11, Oxford, 1940.
GEORGEI. LOEBAND HAROLD A. SCHERAGA
1638
Vol. 60
cm.2/sec. The average sedimentation constant is computed as follows. The sedimentation constant of the faster, minor component is about 6.6 X sec., this value being subject to a large experimental error since the concentration of this component is very small. However, since the faster component is present to the extent of only 3%, such a large error will not seriously affect the final result. The average value of s is taken as [(0.97). (4.41) (0.03)(6.6)] X 10-13 or 4.48 X 10-13 sec. We thus obtain from equation 4 a value of M = 69,200 g./mole as an average molecular weight of the albumin sample. We can now compute the hydrodynamic parameter p defined by the equation16
2.5, the value for a sphere, and v2 = 2.91, the value for a prolate ellipsoid of revolution of axial ratio 2. I n such a case the observed intrinsic viscosity would be 2.51/2.50 times the value for the major component. Since this difference in [v] is well within the experimental error, and since this error is further reduced by the fact that we take the cube root of [ q ]in computing B from eq. 5, we are justified in assigning the measured value of [ q ] to the major component. Using then the measured values of [ T ] and the values of s for the major component, as given in Table I, we obtain the values of p for the major component which are given in Table IV. From the data shown in Table IV it can be seen that the presence of about 3% of the faster sedimenting (5) component has no significant effect on the resulting value of p even though it increases the average Since the measured value of [ q ] is an average for the molecular weight by 3%. whole protein, we shall first compute an average The values obtained for p indicate16 that an efvalue of p using the [T J data of Table I, the average fective hydrodynamic sphere" will account for all values s = 4.50 X 10-13 sec. and 4.66 X 10-13 sec. of the measurements of BSA, i.e., sedimentation, for 0.5 M KC1 at 25" at pH 4.0 and 5.13, respec- diffusion and viscosity, without any arbitrary astively, and values of 5, p and 70 pertaining to 0.5 sumption about the density or hydration of the M KC1 at 25". The results obtained are given in molecule. Further, from the similar values42of /3 Table IV. at both pH's we see that the shape is independent of p H in the pH region encompassed by the measTABLE IV urements reported here. The different viscosities VALUES~ OF 6 FOR THE MAJORCOMPONENT OF BSA AND FOR are thus to be accounted for in terms of a greater THE WHOLEPROTEIN AT 25' IN 0.5 M KC1 hydrodynamic volume at pH 4.0 compared to pH M pH 4.0 p H 5.13 5.13. Similarly, the different sedimentation con2.05 X 106 2.05 X 106 Major component 67,000 stants at these pH's reflect the different hydrodyWhole protein 69,200 2.04 2.04 namic radii. The ratio of the radius at p H 4.0 to a The standard deviation in 6 is 4~0.06X 106. This includes an estimate of the error in the diffusion coefficient. that at pH 5.13 is
+
I n this connection it may be mentioned that variations in D for BSA in the literature are approximately 5%. This may be due, in part, to the observation made in this LaboratorylB that D varies with the albumin sample. Further, the standard deviation cited above is believed to be a minimum value which would be augmented by determinate errors in any of the measured values from which 6 was computed. For example, the intrinsic viscosity may be slightly in error because of an uncertainty in c arising from an unknown amount of bound chloride ion.
where f is the translational frictional coefficient. If this value is cubed, we obtain for the ratio of the volumes at the two pH's a value of 1.12. This value is in excellent agreement with the ratio of the intrinsic viscosities 0.0457/0.0413 or 1.11. Thus, the configuration of the albumin molecule is presuch that its volume is 11% greater at pH In order to compute /3 for the major component sumably than at pH 5.13. The agreement between the we must know the value of [ q ]for this species. We 4.0 ratios obtained from f and [ q ]is compatible with the can make the following reasonable assumptions to spherical model for albumin. Further, the moleshow that the measured value of [ q ] for the whole cule presumably possesses sufficient flexibility to protein is, within the experimental error of the de- allow for this increase in volume, i.e., the volume termination of [TI, equal to [ q ] for the major com- change is envisaged as arising from the entrance of ponent. The intrinsic viscosity is solvent between the peptide helices. 171 = ( N v / l O O ) ( V e / M ) (6) It is of interest to emphasize a point made where v is a shape factorag and Ve is the effective previously, l6 that while hydrodynamic measurements are carried out in order to ascertain sizes and hydrodynamic volume.lB If we assume that Ve (40) When the 6 value is near 2.1 X lo8 the distinction between a M , then the ratio Ve/M for both components is the and an oblate ellipsoid cannot be made from 6 alone.ln Ae dissame, irrespective of the values of Y . Neglecting sphere cussed elsewhere" the absence of flow birefringence suggests the absence protein-protein interaction, we can write, as a of high asymmetry for BSA. However, for moleaules as small as BSA consequence of eq. 6, the following equation for the the results of flow birefringence are not very reliable. W e ehall, therefore, interpret the data in terms of a sphere. In view of the errors in observed value of the intrinsic Viscosity.
-
[T]
[ 0 . 9 7 ~f 0.03uz](N/100)( V o / M )
(7)
If both components were spherical v1 would equal v2 and the observed intrinsic viscosity would be equal to that of either component separately. If the major component were spherical and component 2 were an aggregate of 2 spheres we could take V I = (39) R . Simha TH!S JOURNAL, 44: 25 (1040),
the measured hydrodynamic quantities, and also in light of the comments in footnote a of Table IV, the deviation of the experimental 6 values from the minimum theoretical's value of 2.12 X 10s should not be regarded as a failure of the theory. (41) H. A. Scheraga, W. R. Carroll, L. F. Nims, E. Sutton, J. K. Backus and J. M. saunders, J . Polymer Sci., 14, 427 (1954). (42) This comparison of 6 values at two pH's is essentially a comparison of the values of s[n]l'a. Hence, since errors in D and M do not affect this quantity, this comparison is more preciae than an individual ¶, value.
Dec., 1956
THERMODYNAMIC PROPERTIES OF BOVINE ALBUMIN AT Low pH
1639
shapes of protein molecules in dilute solution, it does urements of two hydrodynamic quantities, then not follow that the hydrodynamic volume is identical the procedure of reference 16 will provide the size with the particle volume. This erroneous identifi- and shape without requiring arbitrary assumptions cation of the two volumes is embodied in eq. 7 of ref- about the shape (or hydration). This procedure has erence 12.43 If the two volumes were identical, been applied above in the evaluation of @ for BSA then Stokes’ law would hold for small spherical par- at pH 4.0 and 5.13. Reactivity (in Terms of Varying w).-We may ticles, i.e., for macromolecules. However, it is precisely because Stokes’ law does not always hold now consider the question of the anomalous carfor spherical macromolecules4~(and correspond- boxyl ionization, first from the point of view that w ingly, Perrin’s equation for ellipsoidal macromole- may vary with pH, to see if the 11% increase in hycules) that the procedure of reference 16 used the drodynamic volume at pH 4.0 (interpreted to mean concept of the efective hydrodynamic volume. It is an increase in the volume of the solvated protein thus impossible at present to relate the hydrody- molecule) will account for the steepness of the titranamic volume to the partial specific volume, as tion curve49at low pH. We have seen from equation 8 that the ratio of equation 7 of reference 12 tries t o do. Further, the claimI2 that the hydrodynamic properties of BSA the radius at pH 4.0 to that at pH 5.13 is 1.04. cannot be represented by t b theory previously Such a ratio of radii corresponds to a very small citedl6 is based on the departure of @ from the ratio of w values (see eq. 3) for the impenetrable minimum value of 2.12 X los. When experimental sphere model. The viscosity datas at ionic errors are taken in account this discrepancy be- strength 0.15 correspond to a slightly greater excomes i n s i g n i f i ~ a n t . ~Further ~ , ~ ~ support for this pansion. If the titration data on BSA6 are interin terms of a variation in w with pH, the point of view has been provided by C h a r l ~ o o d . ~preted ~ It is thus worthwhile to re-emphasize that hydro- experimental variation* in w is in excess by several dynamic measurements (a) give sizes and shapes of orders of magnitude of that computed from eq. 3 effective hydrodynamic particles, not real particles using the value 1.04 for the ratio of radii. We and (b) that hydrodynamic methods are not very may thus conclude that the anomalous reactivity sensitive to changes in shape. This insensitivity is a of the carboxyl groups of BSA cannot be accharacteristic feature of hydrodynamic methods. counted for by a changing molecular size (in terms While a single hydrodynamic property, such as vis- of the impenetrable sphere model). To circumvent this conclusion, but still precosity or sedimentation, is highly sensitive to changes in shape, it is unfortunate, as shown previ- serving the concept of a varying w, Tanford, et ~ l . , ~ ously, that a single hydrodynamic property does ignoring the heterogeneity previously cited, 18-20 not lead to a unique size or shape. Rather, a pair have interpreted the configurational changes over a of quantities is required, and the combination of two wide, acid pH range in terms of an alternative model hydrodynamic quantities is not very sensitib e to in which the salt ions penetrate some distance into particle shape.48 If one has carried out meas- the interior of the protein ion (with the protein fixed charges remaining on the “surface”). They (43) Essentially this same error is committed by Harrington, Johnson and Ottewill44 who attempt t o correlate hydrodynamic volume then change the model, above pH 4.3, to that of an with G. Further, these authors critlcize the procedure of Scheraga impenetrable sphere. In view of the fact that there and Mandelkernl8 by stating t h a t “for axial ratios smaller than 20 an is an 11% volume expansion at low pH there is cerapproximate form of the Simha equation has to be used.” This statetainly justification for assuming penetration of the ment is incorrect since the exact Simha equation is availableso and its solution has been given in connection with numerical viscosity calculaprotein ion by low molecular weight species. Howtione46 for axial ratios from 1 t o 300, as well as by Mehl, Oncley and ever, one may question, without being able to show Simha.“ Further, Scheraga and Mandelkern used the ezoct Simha conclusively,whether the discontinuity in the model equation in the evaluation of their B function. Thus the contention a t pH 4.3 represents a realistic description of the of Harrington, Johnson and Ottewill t h a t the Simha or Perrin equations do not hold accurately for nearly spherical particles is unfounded. configurational changes of BSA. Whereas the imWe suggest here t h a t the difficulties of Harrington, Johnson and Ottepenetrable sphere model leads to equation 3, the will could be circumvented b y a precision analysis of their @-values,as penetrable sphere model leads to an alternative carried out here.40 The same remarks about reliability and precision expressions for w. By using these two different of hydrodynamic data apply to their calculations of B for southern bean mosaic virus and tobacco mosaic virus. models (the penetrable sphere at pH 4.0and the im(44) W . F. Harrington, P. Johnson and R. H. Ottewill, Biochem. J., penetrable sphere a t pH 5.13), the. ratio of radii 62, 569 (1956). becomes 1.03, in reasonable agreement with the (45) H. A. Scheraga. J. Chem. Phys., 28, 1526 (1955). value 1.04 of eq. 8. This better agreement arises (46) J. W. Mehl, J. L. Oncley and R. Simha, Science, 93, 132 (1940). (47) The well-known failure of Stokes’ law for macromolecules was because the variation in w with pH, ascribed to taken into account in the treatment of Scheraga and Mandelkern.10 variation in protein size in the impenetrable sphere The failure of Stokes’ law for molecules has again been discussed remodel, is attributed to penetration by ions in the cently by A. Spernol, THISJOURNAL, 60,703 (1956). penetrable sphere model at p H 4.0. However, the (48) For example, the large change in intrinsic viscosity with particle shape a t constant volume might seem to provide a sensitive tool assumption of a discontinuity in the model at p H for measurement of shape changes (a change from a sphere to a prolate 4.3 does not appear realistic. As stated in footnote ellipsoid of axial ratio 4 leads to a n 85% change in [ q ] if the volume stays constant). Unfortunately, however, we have no way of knowing whether a change in viscosity is due to a change in shape, or volume, or both. I n order to determine which factor is responsible, anpther measurement, e.&, sedimentation, is needed. The B function which isolates the shape factor’s effects is a function of both s and 171. Now, if [ q ] increases, 8 will decrease [both are associated with increased frictional effects), and thus there is internal compensation In the function of 8 and [ q ] (as indeed there must be to eliminate size effect$) which make4 the B function comparatively insensitive. 4 n y
method of separating the shape and size effects will suffer from such internal compensation. The combined function will only undergo a change of 4% as against 85% for viscosity alone in the example cited. (49) Whereas the titration data’ were obtained a t several ionic strengths, the highest being 0.16, we shall assume t h a t the conclusions reached about chongss in particle shape from hydrodynamia data a t ionic strength 0.6 may be applied t o the titration data a t ionic strenqt,h
0,16,
1640
GEORGE I. LOEBAND HAROLD A. SCHERAGA
VOl. 60
26 of reference 8, neither the penetrable nor the impenetrable sphere models are individually adequate to account for the thermodynamic and hydrodynamic properties without switching the model a t pH 4.3. Further, even with this discontinuity in the model, the explanation of reference 8 can account only for the slope of the pK 1)s. pH curve but not for the difference in pKo values t i e . , an “observed” pKo value of 4.0 compared to the “normal” value of 4.6), as pointed out in the Introduction in the discussion of Fig. 1. We therefore propose an alternative explanation below.
we may investigate the various possibilities to see whether the results so obtained can be correlated with the experimentally determined thermodynamic parameters. It must be recognized, however, that the following discussion is essentially qualitative because the hydrogen bonding theory“ to be’used applies only in cases where the polar R groups involved are attached t o polypeptide chains which are rigidly fixed in position relative to each other. This is not true in the case of BSA in the acid region since the molecule has been shown to expand. The effect of such expansion on the hydrogen bonding between the polar R groups would Reactivity (in Terms of Hydrogen Bondiug).The alternative explanation discussed here is not be expected to be negligible since the equilibconcerned with the effects of hydrogen bonds“ rium constants for the formation of such hydrogen between un-ionized carboxyl groups, and of hydro- bonds are strongly dependent upon the distance begen bonds between ionized carboxyl groups and the tween the polar groups concerned.l1 However, the expansion is small so that we may expect our results OH groups of tyrosine, serine and threonine. Considering first the tyrosyl ionization, if the ty- to be qualitatively correct. In the following treatment we shall deal with rosy1 residues are assumed to be involved in heterologous single hydrogen bonds with ionized carboxyl three plausible models. These are not the only groups, then according to eq. 1-38 of reference 11the possibilities but they cover a wide range of values of observed standard free energy change for the tyro- the thermodynamic parameters. I n all of these models the un-ionized COOH groups are doubly syl ionization is hydrogen bonded and the ionized COO- groups AhFoob.a AFO1 -k RT In (1 Kij) (9) are potentially capable of functioning as hydrogen in the pH region of tyrosyl ionization. I n this bonding acceptors. If all these types of hydrogen equation Molcorresponds to the normal, non-hy- bonding situations were present it is doubtful drogen bonded tyrosyl group, and K i j is a hydrogen whether present methods of interpreting titration bonding equilibrium constant previously defined. l1 curves could distinguish between the various kinds In order to make AFoobsd agree with the experi- of carboxyl groups. mental value6 of 14.1 kcal./mole (assuming AFol = I n all the models those un-ionized COOH groups 13.1 kcal./mole6), K i j must have the value60 4 ac- which are hydrogen bonded are assumed to-be incording to eq. 9. The calculated Values of A H o o b s d volved in acetic acid dimer type bonds. The and ASoobsd are then 11 kcal./mole and -10 e.u., models differ according to the behavior of the carrespectively, which agree very well with the ob- boxyl group after ionization. In formulating these served6 values of 11.5 kcal./mole and -9 e.u., re- models we shall distinguish between the left and spectively. Such hydrogen bonding accounts for right carboxyl groups in the hydrogen bond and the thermodynamic parameters of the tyrosyl compute the expected thermodynamic parameters ionization. lipsi for the ionization of either the left or right carWe now consider the ionization of the carboxyl boxyl. In model A we allow only the left but not groups. Since there are only 18 or 19 tyrosyl the right carboxyl group to form a heterologous groups, only a t most 18 or 19 ionized carboxyl single hydrogen bond with an OH donor when the groups can be hydrogen bonded to tyrosyls. How- carboxyl group is ionized. For this model we shall ever, we may postulate that the 57 seryl and thre- consider separately the ionization behavior of both onyl hydroxyl groups may also hydrogen bond the left and right carboxyl groups. I n model B with ionized carboxyl groups.62 We thus have we consider that the ionized carboxyl groups can available a total of 76 donors for hydrogen bonding form cooperative hydrogen bonds (two OH donor with ionized carboxyl groups. Since there are at groups to each COO- group). Finally, in model C least 90 carboxyl groups, it i s implied that some of we assume that the ionized carboxyl groups are not them are not hydrogen bonded in the ionized form. hydrogen bonded. This model was considered preWhen the carboxyl groups are un-ionized it is pos- viously. l1 In models B and C we shall consider the tulated that some of them are involved in COOH- ionization of the left COOH group, but the same HOOC acetic acid dimer type bonds’l and some of equations would be derived if the ionization of the them are not hydrogen bonded a t all. The treat- right COOH group were considered. ment given below considers the possible fates of the Since the method of computing the thermodyhydrogen bonded COOH groups upon ionization. namic parameters is the same for all the models, we While a direct test of such hydrogen bonding phe- shall illustrate the details for model B and merely nomena is not yet feasible for the carboxyl ionization, state the results for the other, simpler cases.6a The ionization process may be generalized as (50) A revision6 in the values of AFOI and AFoobad leads to the
+
value of 4 for Kij, rather than 2.5 as reported previously.11 (51) As noted previously.11 tyrosyl groups may be involved in a cooperative hydrogen bonding situation. If such is the case, the values of Kij would have to be revised. In any event, the previous estimate” that Kij is of the order of unity seems reasonable. (52) I t may be, howover, that such hydrogen bonds are not as readily formed 88 tyrosyl hydrogen bonds since the acid pK’e of seryl pnd threonyl hydroxyl groups are quite high.
I,H++II
(10)
In the case of model B, the symbol I represents species A-D, whereas I1 represents species E-J (see (53) In all the models we shall make the simplifying and justifiable approximation that two COOH groups can be bonded only when two not one, hydrogen bonds are formed.
THERMODYNAMIC PROPERTIES OF BOVINE ALBUMIN AT Low pH
Dee., 1956
t
-
I i :1 I
0
c4° ' 0 n
no
on
on
c4O -
'0
'0
on
on
on
on
e
.
..
no
A
..
0
.no
E
F
no
0
HO
8
-c
cd-
\
'0
c4 O ' 0
1641
n
on on
C
D
-
o . . .
no
OH
- on
0
-\ 0
G
2
H
- cP -
'0
0
no
-OH
0
-'c o/
c
on
8-
... ...
o . . .
'0
OH
*
*
-OH
on
e
.
-on
no * * '
... . -
no
. O
0
\c
I
0
0
//
J
I Fig.6.-Speoies designated as I and I1 in model B (see eq. IO).
Fig. 6). The observed ionization constant &bed for From these we obtain the left carboxyl group in model B can be computed by the method of Appendix I of reference 11. The relative concentrations ni of the various species are listed below, where Kij, K1, and K,, are hydro- where [H+]is the hydrogen ion activity. Substitugen bonding equilibrium constants defined in ref- tion for the n's gives erence 11. The normal value for the ionization constant of a non-hydrogen bonded COOH group in a protein of charge Z is KP. By the usual thermodynamic procedures we can obtain AFOobsd, As'obsd and AH'obsd from eq. 12. Speoiee The relation for AFoobsd is A B A F o o b s d = -RT In &bad C
D E F G H
I J
= AF'2
-
The equations for ASoobsd and m o o b e d are somewhat cumbersome. However, they can be simplified if we recall that M"z = 0 for carboxyl groups. The simplified equations are then
GEORQE I. LOEBAND HAROLD A. SCHNRAGA
1642
Vol. 60
The experimental thermodynamic parameters6 lie between curves calculated from the above equations for the various models using the values Kij = 4, KI, = 100, K r a 40, K'z = 2.5 XlO", w US. pH data from the hydrodynamic behavior, and Z vs. pH data from Tanford, et aLB However, the slopes of the resulting AF' us. pH curves do not match the experimental slopes. On the other hand, it must be kept in mind, as stated in reference 6, that the Z us. pH data have been estimated on the basis of measurements of chloride binding at one or two pH's, and assumptions about potassium binding. Thus, there is considerable uncertainty in the Z us. pH data for BSA, and consequently in the w us. pH data. We have, therefore, introduced an empirical WZ us. pH dependence, chosen so that the slopes of the AFO us. pH curves (computed from the above models) would be compatible with the experimental ones. This empirical curve is compared in Fig. 7 with theoretical curves computed from the Z us. pH data postulated by Tanford, et al.,Band from w us. pH data using the impenetrable and penetrable models.6' It is also of interest to examine the pH
Model C
Z. The expressions for AFoobsd and ASoobsd follow readily from those given, and have therefore been omitted.
.
PH.
Fi &-Dependence of 2 on pH: curve A, values assumed by anford, el aL8; curve B, values computed from Fig. 7, using the impenetrable model for w (allowing for the small expansion a t low pH).
3
-Oe4
dependence of the empirical charge, Zemp, computed from the empirical WZ us. pH curve of Fig. 7, using the impenetrable model for w. The resultant curve is compared with that postulated66 by Tanford, et a1.,8 in Fig. 8. We do not feel that sufficient data are available at present to provide an accurate W Z us. pH curve. If we use the empirical W Z us.
t
3
(54) The empirical YZ V U . pH curve oould be inaccurate at the low pH end since the hydrogen bonding theory,rl on which it is based,
5
4
pH. Fig. 7.-Dependence of WZ on pH: curve A, penetrable model; curve B, impenetrable model; curve C, empirical.
does not hold rigorously because of the molecular expansion. (65) I t is obvious that there is 8 need for a completestudy on BSA of the simultaneous binding of CI-,K + and H Cin order to obtain 2 at any pH. Such studies are being carried out by Saroff (private gommunication) with the aid of perm-selective membranes.
Dec., 1956
1643
THERMODYNAMIC PROPERTTES OF BOVINE A L ~ U M I AT N Low ],TI
pH curve we can account not only for the slope of AF0 us. p H curves, but also for the AHoand ASo parametersssand resolve the anomaly of the carboxyl ionization. Thus, the curves of Figs. 9, 10, and 11 were computed using this empirical WZ us. pH curve and the above values of K i j , Kim, K r s and Koz. It can be seen that the experimental curves lie between the theoretical curves for the models chosen, both with respect to absolute values and slopes. Thus, the experimental curve may be considered as representing some average among these models plus a few possibly normal COOH groups. This average cannot be evaluated quantitatively because the theory of reference ll assumes that the helices are maintained in fixed positions with respect to each other, whereas the small expansion deduced from the hydrodynamic data suggests that solvent may force the helices apart.67 Nevertheless, we can see qualitatively that the hydrogen bonding picture is plausible and accounts for the thermodynamic behavior of the carboxyl groups of BSA ( i e . , both the slopes and absolute values of the t,hermodynamicparameters) .68 Further, in view of the possibility of making and breaking various kinds of hydrogen bonds reversibly, permitting expansion as the charge on the molecule increases, we can see how the configurational adaptability commonly ascribed to the albumin molecule can arise. Thus, the foregoing analysis provides a compatible picture to account for both the hydrodynamic and thermodynamic data on BSA a t low pH. As the pH rises the hydrogen bonds between OH groups and COO- groups may bring the peptide helices closer together, squeeze solvent out of the molecular domain, and account for the decrease in volume in going from pH 4.0to pH 5.3. No ahaiigc! in configuration then occurs until high pH wherc tyrosyl groups ionize. Finally, we should emphasize the limited range of conditions under which our conclusions apply. First of all, they apply to fresh solutions (less than 5 hours at room temperature), and not to older solutions which a t the lower pH exhibit the time-
,6
5
Mob%. 4
3-
4 3
PH. Fig. 9.-Dependence of AFoob.d on p H . Curves AR, AL, B, C correspond to the hydrogen bonded models given in the text. The normal curve was computed using p K o = 4.6 and the empirical wZ us. pH data of Fig. 7. The experimental curve6 is also shown.
+I5 1
-
3
4 5 PH. Fig. 10.-Dependence of AHoot,don pH. The curves corw spond to those of Fig. 9.
+20
(56) It should be noted that the empirical W ZV I . pH relation is not
required t o give the proper range of AFO, AH' and AS'; it was chosen only t o make the slopes of the A F " curves agree with experiment. T h e range of values of these parameters, obtained from the aeveral hydrogen bonding models, is sufficient to account for the experimental data even with the w Z m. pH data of Tanford, et 01.8 (57) It should be noted t h a t contributions to the observed free energy of ionization due t o configurational changes (#.e., the volume change acaompanying the shifting of helices relative to each other) have been neglected in this treatment. (58) It may be mentioned t h a t the experimental curve lies between the normal ourve and curve B in Fig. 9 whereas in Figs. 10 and 11 it lies between the normal curves (not shown in the Figures) and curve AL. This shift. however, corresponds t o relatively small changes in the parsmeters K,j, Krs, Kim and in the values selected for AH",, A H o i r , AHora, A H o i m . For example, if A H % were not zero au assumed, there would be errors in AHoobad arising not only from the nonzero value of A H % but alao from the differentiation processof eq. 14, carried out a t constant [I€+]. ( I t should be noted that AHoDbsd of eq. 14 corresponds t o constant [H+I whereas the experimental value usually corresponds to constant r ) . Finally, since a n error of 2 kcal. in the enthalpy would correspond to an error of about 7 e.u. in the entropy, such errors in AHoobsd will also appear in ASoobad. Hence, the change in the sequence of the curves 88 calculated is not outside the expected range of uncertainty inherent in these calculations, especially since the averaging procedure is different for the diflerent thermodynamic parameters.
5
4
0
I
c
E = = = = t Exptl.
j w
-40 - 60 3
4
5
PH. Fig. 11.-Dependence of A S " on pH. The curves correspond to those of Fig. 9.
dependent phenomena observed by Tanford and coworkers.8 The titration datas were obtained with fresh solutions and, therefore, are comparable to our hydrodynamic data. Secondly, because of the
1644
ALFRED P. MILLSAND WARREN E. BECKER
heterogeneity18-20 at low pH our investigation was confined to the homogeneous region a t pH 2 4.0. Thus, the conclusions of previous investigators,*,"J based on hydrodynamic data, are open to question. For this reason, also, we cannot confirm or deny the idea of an CY-@transformation a t pH's below 4 proposed by Yang and Foster,'O and discussed recently by HiIl.h9 It may be pointed out that the heterogeneous sedimentation patterns of Fig. 3 are compatible with the existence of two forms. However, our sedimentation observations are too meager to identify these as CY- and 0-forms. It is our opinion that the nature of the configurational changes below pH 4 is still an unsettled matter. However, insofar as these changes already manifest themselves to a small extent as the pH is lowered from 5.13 to 4.0,we may conjecture at this time that the combined effects of reversible formation and breakage of hydrogen bonds be(59) T. L. Hill, THISJOURNAL, 60, 358 (1956).
VOl. 60
tween side chain polar R groups of BSA, and the concomitant penetration of solvent into the molecular domain (ie., swelling), will account for the abnormal steepening of the titration curve in the pH region of the ionization of carboxyl groups. However, it must be emphasized that, without a determination of p for each species present below pH 4,we have no assurance that a sphere is a good model a t t,he low pH. Therefore, conclusions drawn from only one hydrodynamic quantity (ie., viscosity) plus the assumption of spherical symmetry811OB60 could be erroneous. It is quite conceivable that the changes taking place below pH 4 would require the use of asymmetrical equivalent ellipsoids to account for the hydrodynamic properties of BSA. I n fact recent experiments of Harrington, Johnson and O t t e ~ i l lindicate ~~ that such may be the case. (60) The lack of flow birefringence in a molecule is no guarantee of spherical symmetry.
88
small
88
BSA
THE SILICON-BROMINE AND SILICON-CARBON(ARYL) BOND PARACHORS AND THE SILICON-BROMINE BOND REFRACTION' BY ALFREDP. MILLSAND WARREN E. BECKER Contribution from the Department of Chemistry, University of Miami, Coral Gables, Florida Received Julu 87, 1.966
Trimethylphen Isilane, dimethyldiphenylsilane, trimethylbromosilane, dimethylphenylbromosilane, dimethyldibromosilane and methy h e t h ylbromosilane were repared and purified and thelr refractive mdices, densities, surface tensions and viscosities were measured. Using the bonfparachor system of Mills and MacKensie as a basis, values of 74.1 and 1.8 were derived for the silicon-bromine and silicon-carbon( aryl) bond arachors, respectively. Using the system of Vogel and coworkers as a basis, a new value of 10.24 was derived for the s&con-bromine bond refraction from data on 14 compounds. For the six compounds listed above, values of Trouton's constant were found to range from 21.1 to 25.5 and the ratio AILap/ AEvis ranged from 2.96 to 3.86.
The organosilicon bond parachor system developed by Mills and MacKenzie2 did not contain a value for the Si-Br bond and the value for the Si-C(aryl) bond was based on a high temperature measurement of only one compound. Since most parachors change slightly with temperature it was considered desirable to obtain a new value based on measurements made a t 25". The Si-Br bond refraction in Vogel's systema was based on only three compounds. A new value was obtained by also considering the molar refractions of four compounds measured in this research and eight compounds measured by McCusker and Experimental Materials.-Trimethylphenylsilane and dimethyldiphenylsilane were prepared by the addition of phenylmagnesium bromide to trimethylchlorosilane and dimethyldichlorosilm e , respectively. The silicon-phenyl bonds were then cleaved with bromine by the method of McBride and (1) Presented in part at the Meeting-in-Miniature of the Florida Section of the American Chemical Society, Orlando, Florida, May, 1956. Abstracted in part from the M.S. Thesis of Warren E. Becker, University of Miami, May, 1955. (2) A. P. Mills and C. A. MacKeneie, J . Am. Chem. Soc., 7 6 , 2673 (1954).
(3) A. I. Vogel, W. T . Cresswell and J. Leicester. THISJOURNAL, 68,
177 (1954). (4) P. A. McCusker and E. L. Reilly, J . Am. Chem. SOC.,76, 1583 (1953).
Beachell' to form trimethylbromosilane, dimethylphenylbromosilane and dimethyldibromosilane. Methyldiethylbromosilane was prepared by the addition of appropriate quantities of ethylmagnesium bromide and p-tolylmagnesium bromide to methyltrichlorosilane to form methyldiethyl-p-tolylsilane (b.p. 132' a t 20 mm. and 143' a t 30 mm.) which was then cleaved with bromine. AI1 of the above compounds were purified by reduced pressure fractionation6 using a column packed with glass helices and having about 15 theoretical plates. Density.-The densities were determined in stoppered density bulbs by the method of MacKensie, Mills and Scott,' a cathetometer being used for the measurements. Refractive Index.-The refractive indices were measured with an Abbe refractometer. Measurements were made rapidly in order to minimize errors due to oxidation and hydrolysis. Surface Tension.-The surface tensions were determined by the capillary rise method in the double capillary type of apparatus, the two capillaries having internal diameters of 0.3 and 0.55 mm., respectively. A cathetometer was used to measure the capillary rise. Viscosity.-The viscosities were measured with a Drucker viscometer. The experimental data are listed in Table I.
Results and Discussion Bond Parachors.-Using the bond parachor (5) J. J. McBride, Jr., and H. C. Beachell, ibid., 74, 5247 (1952).
(6) We wish to thank Louia H. Dunlop (MoKeesport High School, McKeesport, Pa.) Future Scientists of America Summer Fellow, for his help with mme of the fractionations. (7) C. A. MacKeneie, A . P. Mills and J. M. Scott, J . Am. Chsm. Soc., 74, 2032 (1950).
