Chemical Physics 166 ( 1992) 299-302 North-Holland

Application of the Yukawa potential to the auto-controlled mechanism of the ovalbumin molecule in aqueous systems

Takayoshi Matsumoto and Hiroshi Inoue Department of Polymer Chemistry, Kyoto Universrty, Kyoto 606, Japan

Received 10 March 1992

The rigidity of ovalbumin (OA) aqueous colloids remains almost constant over a wide range of OA concentration c from z 0.1 to z 17 wt%, this is called the auto-controlled mechanism. The Yukawa potential was applied to explain the auto-controlled mechanism and revealed that the effective charge 2’ of the OA molecule is relatively small. Further, the z* value is almost constant at extremely low concentrations and is proportional to c- w in the concentration range where the rigidity remains approximately constant.

1. Introduction

Ovalbumin (OA) is a globular protein with a mo- lecular weight of z 44000 [ 1,2]. The complete se- quence of amino acids in an OA molecule was deter- mined by McReynolds et al. and Nisbet et al. [ 3,4]. However, little is known of the secondary and ter- tiary structure of the OA molecule [ 5,6] and the bi- ological function of the OA molecule has not been clarified. It has been considered that the OA mole- cule in an aqueous system disperses in a form in which hydrophobic groups are withdrawn from water and polar groups or hydrophilic residues are exposed near the surface of the molecule. According to our pre- vious studies, it has been found that the electron den- sity transition is relatively sharp at the interface be- tween the OA molecule and the medium and that the surface of the native OA molecule has x 1.7 times the surface area of a smooth sphere with the same vol- ume [ 7,8]. On the other hand, there is little infor- mation on the electrostatic or ionic properties of the OA molecular surface. We have reported another characteristic property of the aqueous colloids of the A0 molecule, i.e. that the rigidity of the OA colloid remains almost constant over a wide range of OA concentration from 0.1 to 17 wtO#~ [ 9 1. We discussed

Correspondence to: T. Matsumoto, Department of Polymer Chemistry, Kyoto University, Kyoto 606, Japan.

fully this unusual phenomenon, designated the auto- controlled mechanism, using rheological data. We have also reported that the Yukawa potential modi- fied for the finite size of the dispersing particle can represent with sufficient accuracy the influence of ionic concentration on the rigidity of colloidal sys- tems of polystyrene spheres and OA molecules [ 10,111.

In the present paper, we will try to apply the Yu- kawa potential to the auto-controlled mechanism and estimate the effective charge of the OA molecule.

2. The potential model

The Yukawa potential modified for the finite size of the particle, which is called the DLVO potential, is given by

V(r)= & ( > 2 Z2e2 e-Kr

cr ’ (1)

Here r is the distance between the dispersing parti- cles, a is the radius of the particle, Z is the surface charge of the particle, e is the electronic charge, t is the relative permittivity of the medium and K is the Debye-Hiickel parameter given by

0301-0104/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.

300 T. Matsumoto and H. Inoue / Chemrcal Phyucs 166 (1992) 299-302

Here, Y is the number density of the colloidal parti- cle, n, and z, are the number and charge of free-state (diffusible) ions in the unit volume, k is the Boltz- mann constant and Tis the absolute temperature. The number of surface charge of the particle Z is approx- imately related to the surface potential !PO of the par- ticle as follows [ 121,

z= ae(l+KQ) yy 0. (3)

e

The shear modulus G for the bee arrangement of the colloidal particles is given by

G=$cV(d) rc2d2, (4)

where d is the nearest-neighbor distance between the particles [ 13 1. In this theoretical consideration, the number of surface charge Z is usually replaced by the number of effective charge Z* ( = j?Z). The effective charge Z* is not directly measurable and is usually

determined from shear modulus measurements [ 13 I. Fig. 1 shows a qualitative relationship between G

and K by eq. (4). The value of G increases with in- creasing K in a range of small values of ic (region A) and after that decreases through a maximum (region B). In almost all colloidal systems reported hitherto, the rigidity due to the solid structure decreases with increasing ionic concentration or K value of the sys- tem [ 10,13,14]. That is, the situation of the colloidal system is in the region B in fig. 1. On the other hand, the rigidity of the OA colloid, which is discussed in

log x

Fig. 1. Qualitative relationship between G and K using eq. (4).

this paper, increases with increasing K value of the system as reported in the previous paper [ 111. This means that the situation of the OA colloid is in the region A.

3. Experimental

Crystallized, lyophilized, and salt-free ovalbumin (Sigma, Grade V, Lot No. 19F-8105), which was

electrophoretically pure, was used. The weight aver- age molecular weight of the native OA molecule ob- tained by light scattering measurements is 43700. The zeta-potential c of the native OA molecule measured with electrophoretic light scattering at various pH values is shown in table 1. Approximate values of the Z of the OA molecule which are calculated by eq. ( 3 ) using c for !Po are relatively small ( x 10). The iso- electric point, where the [ potential equals to zero, is approximately pH 4.4 in the native state. The native OA molecule is almost spherical with the radius of ~25 A and associates slightly with increasing con-

centration [ 2,7 1. A more detailed characterization of the OA molecule is described elsewhere [ 9- 111. A sodium phosphate buffer solution of 20 mM was used for preparation of the colloid of pH 7.0.

Rheological measurements were carried out with a cone-plate type Weissenberg rheogoniometer (San- gamo Controls, R 18 ). The diameter and angle of the cone used were 7.0 cm and 1.77”. Measurements of conductivity and pH of the OA colloids were made using a conductivity outfit (MY8, Yanako, Tokyo) and an ion meter (N8F, Horiba, Kyoto), respectively.

4. Results and discussion

In previous papers [ 9 1, we reported that the col-

Table 1

Zeta-potential of the OA molecule in aqueous solutions at var-

ious pH values

PH C (mv)

3.76 8.39

4.09 2.78

4.34 0.92

4.76 - 3.93

5.30 -9.95

7.0 -21.6

T. Matsumoto and H. Inoue / Chewcal Phyws 166 (1992) 299-302 301

loid systems of native OA molecules in buffer solu- tion have a certain solid-like structure due to the ar- rangement of the OA molecules and show a remark- able yield stress a, and rigidity G even at extremely low concentration such as 0.027 wt%. The yield stress is a useful parameter describing a solid-like property and the value of a, almost coincides with the value of G’ in the OA colloid [ 111. In fig. 2, the yield stress (open circles) and the dynamic modulus G’ (closed circles) at angular frequency w=O. 1 s-l are loga- rithmically plotted against the OA concentration c. It has been confirmed that the dynamic modulus re- tains almost constant over a relatively wide range of angular frequency from 0.01 to 5 s-‘. In fig. 2, an- other plot which will be discussed later is also shown. The value of a, is proportional to c below 0.1 wt% where the OA molecules disperse in a monomeric state. The concentration dependence of oY and G’ be- comes very weak in a higher concentration region where the OA molecules disperse in a dimeric and a tri- or tetrameric state. We considered that this phe- nomenon can be ascribed to spontaneous control (auto-control) of the OA molecule in order to sup- press the increase in the rigidity. It should be noted that the yield stress and rigidity are proportional to c3-5 in normal colloids [ 14,15 1. The auto-controlled process remains over a relatively wide pH range from 4 to 7 and also remains in heat denatured systems below an OA concentration of = 5.9 wt% [ 2,161.

1 I I

OA Cb. ZOmM

Fig. 2. Yield stress a, (open circles) and dynamic modulus G’

(closed circles) plotted logarithmically against the OA concen- tration c. The number of effective charge zf (open triangles) of

the OA molecule is also plotted against c.

Considering that there is little change in the shape, size and surface roughness of the OA molecule during the auto-controlled process as was described previ- ously [ 2,7,8], the auto-controlled mechanism is likely to be attributed to the electronic properties of the OA molecular surface.

In fig. 3, the specific conductivity/i and pH values are plotted against the OA concentration for the 20 mM phosphate buffer systems at 20’ C. The value of A of the buffer solution is 3.588x lop6 Q-’ cm-’ as designated by an arrow. The values of n are almost constant in the concentration range where the rigid- ity is proportional to the OA concentration and in- crease very slightly with increasing OA concentra- tion. The pH values also increase slightly with increasing OA concentration. That is, /i and pH val-

ues are proportional to c 0°3. The dependence of/i

and pH values on the OA concentration is essentially negligible. This means that the number of diffusible (free-state) ions remains approximately constant over a relatively wide range of OA concentration and that the number of effective charge Z* of the OA molecule is relatively small. The most suitable method to obtain Z* is to estimate through the relationship between the measured rigidity and the theoretical value using eqs. (l)-(3) [ 12,171. In fig. 2, the val- ues of Z* estimated by the above method are plotted (open triangles) using a K value of 1.33X lo5 cm-‘. The K value is the most suitable value for fitting the experimental values of rigidity to the theoretical val-

370

OA 2oac

Fig. 3. Logarithm of specific conductivity n and pH value plotted

agamst the OA concentration. The value of ,4 of the 20 mM buffer

solutron is 3.588X 10-6Q-’ cm-‘.

302 T. Matsumoto and H. Inoue / Chemical Physics 166 (1992) 299-302

ues in the colloidal systems in the 20 mM buffer so- lution using the Yukawa potential [ 111. It is likely that the K value does not depend on the OA concen- tration, because the term of YZ is much smaller than the term of Cn,zf in eq. (2). As shown in fig. 2, the value of Z* is constant and approximately equal to unity at extremely low concentrations below 0.1 wt% where the rigidity is proportional to the OA concen- tration. The value of Z* decreases in proportion to c-‘14 at higher concentrations where the rigidity is almost constant. There is little information on the charge of the OA molecule. If the value of the C-PO- tential of 21.6 mV of the OA molecule at pH 7.0 is used for !PO, the value of Z can be estimated to 12.7. Tanford and Roberts Jr. reported that the number of surface charge Z on a bovine serum albumin mole- cule which was obtained from the ionization curve at various pH values was less than 50 [ 18,191. For the colloidal systems studied hitherto, the ratio ji be- tween the effective charge Z* which contributes to the rigidity of the system and the surface charge Z is

scattered widely over a range from = 0.003 to x 0.8 [ 201. Fig. 2 shows that the values of Z* of the OA molecule are ranging from = 1 to G 0.4. These values correspond to the /I values of 0.07-0.03. Considering that the /I value of 0.03 was most suitable for fitting the measured rigidity to the theoretical value for the colloids with the polystyrene spheres [ lo], the val-

ues of Z* of the OA molecule shown in fig. 2 seem to be reasonable. Moreover, from the following consid- eration, it turns out that the values of Z* for the OA system are adequate. In comparison with the value of other systems, it is more reasonable to compare the effective charge per unit surface of the colloidal par- ticle, Z: ( =Z*/4na2), or the effective charge per unit volume (or unit mass) of the particle, Zt

( = 3Z*/47ca3), rather than the value of Z* itself. The values of Z:=1.3~10-~ Ae2 and Z,*=1.5~10-~ A -’ are approximately estimated for the OA system (Z*=l, a=25 A), Z:=8.0~10-~ AP2 and Z,*= 4.4 x lo-’ A -’ for the system of the polystyrene sphere (Z*=300, a= 545 A) used by Lindsay and Chaikin [ 13 1, and Thirumalai [ 2 11, and Z: = 2.7 x 10-4A-2andZ,*=3.2x10-6A-3forthesystemof the polystyrene sphere (Z* = 2 10, a = 250 A) used by Rosenberg and Thirumalai [ 221. According to these data, the values of Zt are approximately congruent

( = 10 -’ AW2) for the three systems. On the other

hand, Z,* is the largest in the OA colloid. At the present time, although the biophysical

meaning of the dependence of Z* N c-‘/~ is not clear, it is one of the possibilities to explain the auto-con- trolled mechanism in the rigidity of the OA colloids.

Acknowledgement

This work was supported by the Cosmetology Re- search Foundation.

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