VOL. 15, 2263-2275 (1976)

BIOPOLYMERS

Interaction of Sodium Decyl Sulfate with Poly(Lornithine) and Poly(L-lysine) in Aqueous Solution IWAO SATAKE* and JEN TSI YANG,+Cardiovascular Research Institute and Department of Biochemistry and Biophysics, University of California, S a n Francisco, California 94143 Synopsis The binding isotherms of sodium decyl sulfate to poly(L-ornithine), poly(D,L-ornithine), and poly(1,-lysine)at neutral pH were determined potentiometrically. The nature of a highly cooperative binding in all three cases suggests a micelle-like clustering of the surfactant ions onto the polypeptide side groups. The hydrophobic interaction between the nonpolar groups overshadows the coulombic interaction between the charged groups. The titration curves can be interpreted well by the Zimm-Bragg theory. The average cluster size of bound surfactant ions is sufficiently large to promote the @-structureof (L-LYS),even at a very low binding ratio of surfactant to polypeptide residue, whereas the onset of the helical structure for (L-Orn), begins after about 7 surfactant ions are bound to two turns of the helix. The CD results are consistent with this explanation.

INTRODUCTION The hydrophobic interaction between proteins and ionic surfactants results in a conformational change of the polymers even when the concentration of the ligands is remarkably 10w.l But the nature of such surfactant-induced changes in conformation remains unclear even for simple polypeptides. For instance, addition of sodium dodecyl sulfate (NaDodSO4)to poly(L-ornithine)((L-Om),) and poly(L-lysine)((L-Lys),) in neutral solutions induces coil-to-helixand coil-to-@transitions, respecti~ely.~,~ The only difference between the two polypeptides is that the monomer ornithine has one less methylene group than lysine. P r e v i ~ u s l ywe , ~ have reported the effect of chain length in sodium alkyl sulfates (CH3(CH2),S04Na with n = 7,9, 11, 13, and 15) on the conformations of the (L-Om), and (L-LYS),at neutral pH. In all five surfactant solutions, (L-Orn), adopts a helical conformation, but (L-LYS),becomes helical only in octyl sulfate solution and adopts the @-formin the other four homologs. These conformational transitions can occur both below and above the critical micelle concentration of the surfactants. For example, M with a 1 X M (residue) polypeptide solution, as low as 2 x NaDodS04 would be sufficient enough to induce an appreciable change * Present address: Department of Chemistry, Faculty of Science, Kagoshima University, Kagoshima City, Japan. t To whom correspondence should be addressed. 2263 hC>

1976 by John Wiley & Sons, Inc.

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SATAKE AND YANG

in the conformation of the polypeptide. The percent helix or @-formappeared to increase almost linearly with the NaDodS04 concentration. These observations suggest a cooperative affinity between the positively charged polypeptides and the anionic surfactant. In this work we determine potentiometrically the binding isotherms of sodium decyl sulfate (NaDecSO4)to (L-Om), and (L-LYS),and correlate the degree of binding of decyl sulfate ions with the helical and @-content of the polypeptides as inferred from the CD spectra. As a control, poly(D,L-ornithine)((D,L-Om),) is also used for the binding study. NaDecS04 has a smaller binding constant than NaDodS04; the use of the former makes precise measurements possible.

EXPERIMENTAL Materials (L-Om-HBr), ( M , = 200,000) and (L-Lys-HBr), (Mr = 125,000) were purchased from Pilot Chemicals and (D,L-Orn-HBr), ( M , = 15,600) was purchased from the Sigma Chemical Company. The polypeptide hydrobromides were converted into the corresponding hydrochlorides through dialysis against 0.1 M HC1 and then water. The polypeptide concentrations were determined by micro-Kjeldahl nitrogen analysis. NaDecS04 was synthesized by esterification of decyl alcohol (from Aldrich Chemical Company) that had been purified by vacuum distillation. Dodecyl trimethylammonium decyl sulfate [(Dod(CH3)3N)+(S04Dec)-] was prepared by mixing dodecyl trimethylammonium chloride (Eastman) and NaDecS04 solutions. After filtration the precipitate was washed with water and then recrystallized twice from acetone. Fisher certified nitrobenzene was used without further purification.

Potentiometric Measurement A cell with a liquid membrane that is selectively permeable for surfactant ions was constructed as fol10ws:~ Calomel I 1M NH4NO3 agar bridge I Reference solution (6.06 X low4 M NaDecSO4; 2.13 X NaC1) I Nitrobenzene (1 X lo4 M [(Dod(CH3)3N)+(S04Dec)-] I Sample solution (polypeptide, Cp; NaM NaCI) I 1 M NH4N03 agar bridge I CaloDecS04, C,; 2.13 X mel All measurements were carried out a t neutral pH. The electromotive force (emf) of cell was measured with a Leeds & Northrup potentiometric-type recorder, Speedomax model XL-680, which had an error within 0.1 mV. The temperature of the solutions in a concentric cylinder was controlled by circulating constant-temperature water through it. The concentrations of the polypeptide and added salt were kept constant throughout a series of experiments. The concentrations of Na-

POLYPEPTIDE-SURFAC'rANT

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COMPLEXES

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4 .O

3.5

3.0

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I

-log [Na DecS04] Fig. 1. Plots of emf of the cell vs. the logarithm of the concentration of sodium decyl sulfate at 25" and 40°C.

DecS04 were so chosen that they were well below its critical micelle concentration even in the presence of the salt used. To check the accuracy of the apparatus, we measured the emf of the cell with the sample solution containing NaDecS04 but no polypeptide. Figure 1 shows that the semilogarithmic plots of emf versus NaDecS04 concentration (above 5 X M ) are linear with a slope of 57.7 mV at 25°C and 61.0 mV at 4OOC. They agreed well with the ideal Nernst slopes (59.1 mV at 25°C and 62.1 mV at 4OoC), suggesting that the liquid membrane responds exclusively to the surfactant ions. Assuming that the polypeptide ions in a salt solution do not affect appreciably the activity coefficient of free surfactant ions, a decrease in the surfactant activity represents a decrease in the free surfactant concentration. The degree of binding of the surfactant ion by the polypeptide (x) can be given as

(C, - C,)/C, (1) where Ct is the total surfactant concentration, Cf the free surfactant concentration as determined from Figure 1,and C, the polypeptide (residue) concentration.

x

=

Circular Dichroism

The CD spectra were recorded with a Jasco J-10 at 25°C under constant nitrogen flush. The data were expressed in terms of mean residue ellipticity.

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SATAKE AND YANG

3 8

I I

ct

I

I

I

2

3

4

x ~ ~ 4 ( ~ )

Fig. 2. Plots of free and bound surfactant concentration vs. total surfactant concentration M (residue), salt concentration = 2.13 X M. for (L-LYS), at 25OC. C, = 2.48 X

c t x lo4 (MI

Fig. 3. Plots of free and bound surfactant concentration vs. total surfactant concentration for (L-Om), and (D,L-Om), a t 25OC. C, = 2.06 X lo-* M (residue), salt concentration = 2.13 x 10-2 M . 0,(L-Om),; 0 , (D,L-Om),.

RESULTS Binding Isotherm The free and bound surfactant concentrations (cf and c b ) at 25°C in salt M (residue)] and (L-Om), and solutions of (L-LYS),[Fig. 2; C,, 2.48 X M (residue)] are plotted against the total (D,L-Om), [Fig. 3; C,, 2.06 X surfactant concentration (C,) used. Below a certain surfactant concentration (1.1X lO-4M in Fig. 2 and 1.6 X M in Fig. 3), decyl sulfate ions do not bind appreciably with the two polypeptides. Above this concentration, the salt solution of (L-LYS),has virtually constant Cf over a wide

POLYPEPTIDE-SURFACTANT C O M P L E X E S 1.01

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cf

I

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I

xio4 (M)

Fig. 4. The binding isotherms of sodium decyl sulfate to (L-Om),, (D,L-Orn),, and (L-LYS), a t 25°C.

range of C t , followed by a gradual increase in Cf with further increase in Ct. But Cb first increases linearly with Ct and then approaches a plateau close to the polypeptide concentration (C,). On the other hand, the dependence of Cf on Ct for (L-Om), and (D,L-Om), solutions differs from that for (L-LYS), in that their Cf increases gradually with increasing Ct (above 1.6 X M). Figure 4 shows the binding isotherm of NaDecS04 to (L-L~s),,(L-Or&, and (D,L-Orn), in a salt solution, where the degree of binding (x), that is, the ratio of Cb/C,, is plotted against Cf a t equilibrium. For the (L-LYS), solution a sharp increase in x over a narrow range of Cf suggests a highly cooperative binding. The binding isotherm is less sharp for the two polyornithines than for (L-LYS),. Nevertheless, the binding process in the two cases may still be cooperative. Although (L-Om), adopts a helical conformation, and (D,L-Orn), does not, the two curves are similar t o each other. At neutral pH, the three positively charged polypeptides are typical polyelectrolytes. The binding of surfactant anions can be regarded as the formation of ion pairs and the association equilibrium written as

where M + is the polypeptide residues (monomer), R - the free surfactant ion, and ( M + R - ) the ion pair. Thus the apparent binding constant, K,, is defined as

K, = X/Cf(l - x)

(3)

SATAKE AND YANG

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X 0.6

0.8

I0 I

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0

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0#4

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1

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0.8

X Fig. 5. Plots of log K , vs. x at 2 5 O and 4OOC.

Figure 5 shows that the x versus log K, plots are inverse S-shaped. K , increases rapidly with x in all three cases. This is exactly the opposite of the hydrogen ion titration of poly(L-glutamic acid)6 and poly(~-lysine),~ whose apparent association constant (protonation) decreases with increasing binding ratio ( x ) . Thus the contribution of electrostatic free energy alone cannot account for the deviations observed in Figure 5 (see Discussion). Apart from the theoretical analysis of a titration curve (see Discussion), we can estimate the cooperative binding constant (K')of the decyl sulfate ion to the polypeptides from K, at x = 1(Fig. 5). The curvature of the titration curves as x approaches 1 makes extrapolation difficult; some inherent errors are unavoidable. With this reservation in mind, the values of K' are about 1.0 X lo5 for (L-Om), and (D,L-Orn), and 2.3 X lo5 for (L-LYS),at 25OC. The corresponding standard free-energy changes, AGO, are -6.9 kcal/mol (residue) for the polyornithines and -7.4 kcal/mol (residue) for (L-LYS),. The values of K' a t 40°C (1.1X lo5 for (L-Orn), and 2.1 X lo5 for (L-LYS),)(see Fig. 5 inset) are not so different from those a t 25°C. Thus the interaction between the surfactant ion and polypeptide side chain probably originates from the entropy changes rather than the enthalpy changes. The estimated values of A G O are almost the same as the predicted values for the micelle formation of nonionic surfactants such as dimethyl alk-

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POLYPEPTIDE-SURFACTANT COMPLEXES I

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3

--a

-10

3

0 X (D

0

N N

-20 -

- 30 I

0

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0.4

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0.8

X Fig. 6. Plots of CD minimum vs. x at 25°C. Values a t x solutions above the critical micelle concentration.

=

1are those in sodium decyl sulfate

ylamine oxide with chain length ( n )of 13 and 14 (AGO = -6.8 and -7.4 kcal/mol, respectively).8 On the other hand, the intrinsic binding constant, of decyl sulfate ion to a protein such as bovine serum albumin (Kint= 1.4 X lo6, AGO = -8.4 kcal/mol)l, p.272 is considerably larger than that of homopolypeptides reported herein.

Circular Dichroism Figure 6 shows the change in CD minimum for the @form and helix (I81219 for (L-LYS),and [el226 for (L-Om),) with respect t o the binding ratio ( x ) . In 2.13 X lop2M NaCl a t 25"C, the &content of (L-LYS),in the presence of NaDecS04 increases almost linearly with increasing x , except a t the initial stage where x is close to zero. In contrast, the helical content of (L-Om), in surfactant solution a t first does not increase appreciably; it increases sharply only when x is larger than about 0.3.

DISCUSSION Nature of the Binding Isotherm The sharpness of the binding isotherm in Figure 4 indicates a cooperative process just as for the potentiometric titration of poly(~-lysine).~But unlike the latter, the apparent binding constant, K,, in the present case increases rather than decreases with the increasing degree of binding, x (Fig.

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SATAKE A N D YANG

5). Thus the cooperative interaction cannot be attributed only to a conformational transition such as helix-coil or &coil. Rather, it must arise from the hydrophobic interaction among the bound surfactant molecules on the surface of polypeptide molecules, which overshadows the electrostatic interaction. The leveling-off phenomenon of Cf in Figure 2 also resembles the micelle formation of the surfactant alone above its critical micelle ~oncentration.5>~ This has been interpreted as a pseudo-phase separation or the formation of micellar aggregates of about 100 molecules.1° It is, therefore, likely that in the binding process of NaDecSO4 with (L-LYS),, the nonpolar alkyl chains of the bound surfactant are in an environment similar to the micellar interior. Binding isotherms have been observed for the complexes of NaDodS04 with nonionic polymers such as methyl cellulose and polyvinyl alcoho1,’l and of sodium alkyl sulfate with varying chain lengths with polyvinylpyrrolidone.I2 In all cases, the incipient bindings occurred well below the critical micelle concentration of the surfactants. An abrupt increase in x again suggests a cooperative process, although the mechanism of the complex formation might be different from that reported in this work. Arai et a1.12 have found a linear relationship between the logarithm of the surfactant concentration for incipient binding and the chain length of the surfactant, which is similar to the plot of log (critical micelle concentration) versus the chain length for pure surfactant solutions. Thus the free-energy group from an aqueous medium to the change for transferring a -CH2polymer-surfactant complex is nearly identical with that for the micelle formation. These authors conclude that the bound surfactant ions contact one another and are not uniformly distributed on the surface of polyvinylpyrrolidone molecules. Our results also suggest a strong hydrophobic interaction between the nonpolar groups of surfactant molecules. Of course, the electrostatic interaction between the cationic polypeptides and anionic surfactants must also play a role, perhaps a minor one (see below).

Theoretical Analysis Theoretical considerations of the titration curve of a polymer chain with a strongly interacting ligand have been given by Marcus13and Lifson.14 By assuming the nearest neighbor interaction, they have derived an expression that is equivalent to each other. Recently, Schmitz and Schurr15have also developed the cooperative binding theory in connection for polyuridylic acid-adenosine complexes. Alternatively, we can adopt the Zimm-Bragg theory16 for helix-coil transition to the cooperative binding isotherm (assuming that the thermodynamic contribution of any conformational transition is comparatively insignificant in such a process). The Zimm-Bragg theory defines two parameters: the equilibrium constants and an initiation factor u. If the

POLYPEPTIDE-SURFACTANT COMPLEXES

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digit 0 represents an unbound polypeptide side chain and 1a surfactantbound polypeptide side chain, a state of the polypeptide chain can schematically be described by a sequence as 00001111100011100 Furthermore, the association equilibrium between the polypeptide side chain and surfactant molecule can be written as follows:

(00)

+ R-

KO

tr (01)

(4)

where KOis the binding equilibrium constant of the surfactant molecule to a site which has two unoccupied nearest neighbors, and Kou that to a site which follows one or more 1's. Here, u can be described in terms of the interaction energies of the neighboring groups, i.e., u = exp

[ ( ~ E o-IEll - Eoo)/kT]

(6)

If we denote the average electrical potential a t the polymer surface by *o, KOin Eqs. (4) and (5) can be written as

KO = K exp (-&o/kT)

(7)

(in the case of electrostatic attraction). Thus, denoting the concentration by the bracket, we may write as = [Ol]/[OO] = KCf

(8)

and s = [11]/[10] = KuCf

with a = [Ol][lO]/[OO][ll]

= l/u

According to the Zimm-Bragg theory, the degree of binding ( x ) becomes x = d In Ao/d In s

(11)

where A0 represents the larger of the two eigenvalues for the statistical weight matrix and is given by A0 =

+ + [(l- s ) 2 + 4as]'/2)/2

{l s

(12)

It follows, therefore, from Eqs. (8), (9), (ll),and (12) that 2x - 1 = ( s - l)/[(l- s ) 2

+ 4as]1/2 = (KuCf - l)/[(il - KuCf)'

+ 4KCf]1'2

(13)

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SATAKE AND YANG

Equation (13) is equivalent to the potentiometric equation as derived by Lifson.14 The cooperative binding theory of Schmitz and Schurr15 also gives the same result. If the bound surfactant ions cluster side by side onto the polypeptide chain, the electrical potential ( 9 0 )on the polymer surface will remain virtually constant unless the size of successive vacant sites become extremely small. This is especially true in the presence of salt as counterions. For simplicity, therefore, we assume a constant coulombic term independent of x (i.e., K is a constant independent of x ) . Since from Eq. (13) Ku(Cf)x=o.!j= 1

(14)

we have

2x - 1 = (y - l)/[(l- y)'

+ 4y/u]1/'

(15)

where Y = Cf/(Cf)r=O.B

(16)

Substitution of Eq. (15) into Eq. (3) gives K, = ~ ( [ ( y)' l

+ ~Y/U]'/' + (y - 1))'/4yCf

(17)

and K,/(K,),=o.s = ~ { [-(Y)' l

+ ~ Y / u ] ~+/ ' (Y - 1)1'/4~'

(18)

In the above equations, u = 1corresponds to an ideal mixing of the M+ and ( M + R - ) groups, whereas u = 03 is the limiting case for extremely strong interactions among the ( M + R - ) groups. By differentiating x in Eq. (13) with respect to Cf and substituting (Cf)r=0.5by 1/Ku in Eq. (141, it can easily be shown that (dx/dCf)x=0.5= Ku3/'/4

(19)

( d x / d In Cf)x=o,5= u1/2/4

(20)

or

Equation (20) is equivalent to Eq. 26 of the theory of Schmitz and Schurr.I5 (The authors thank Dr. J. M. Schurr for calling to their attention this relationship.) From the results in Figure 4 we obtained u = 77 for (L-Om),, 161 for (D,L-Om), I lo4 for (L-LYS),according to Eq. (20). Figures 7 and 8 show the experimental (points) and calculated (solid lines for u = 77) binding isotherm and titration curve of (L-Om),. The agreement is good to about x = 0.7. The interchange energy (2Eol- Ell - Em) for u = 77 is about 2.6 kcal/mol bonds at 25°C. Since the above equations neglect any conformational transition, they can approximately be applied to the L-polypep tides which undergo a coil-to-helix or coil-to-0 transition. However, the close similarity in binding isotherm and titration curve between (D,L-Orn), and (L-Om), (Figs. 4 and 5) seems to indicate that the contributions of any

POLYPEPTIDE-SURFACTANT COMPLEXES I .I

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Fig. 7. Comparison of calculated and observed binding isotherm for (L-Om), a t 25°C. 0 , observed; solid line, calculated titration curve from Eq. (15) with u = 77.

conformational change may not significantly complicate our analysis. Indeed, good fits similar to those in Figures 7 and 8 were obtained for (D,L-Orn), with u = 161 and (L-LYS), with u 2 10. As x approaches unity, the average size of vacant binding site clusters (p)becomes small and the assumption of a constant \ko is no longer valid. This can account for the deviation of the calculated isotherm found a t higher x values. According to the foregoing analysis, the number of bound surfactant ion clusters is given by d In hon/d In c.l6 Hence, the average cluster size of bound surfactant ions (E)and unoccupied binding sites ( j 3 ) can easily be derived from Eq. (12). -

m = 2x(u - 1)/{[4x(1- x ) ( u - 1)

+ 1]1/2- 1)

(21)

and j 3 = (1 - x ) E / x

(22)

For (L-Om), with u = 77 the calculated p was about 7 a t x = 0.7. In this case \ko in Eq. (7) can be regarded as a constant without introducing serious errors when p > 7. But 90is anticipated to vary rapidly with x (or p)when x > 0.7 (or j 3 < 7 ) . Table I lists the calculated T i vaues for the three polypeptides as a function of x. The cluster size of the bound surfactant ions is much larger for (L-LYS),than for (L-Orn),. A clue for this difference might be found from the change in CD minimum with respect to the binding ratio ( x ) (Fig.

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SATAKE AND YANG I

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1

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0.8

0.4

X

Fig. 8. Comparison of calculated and observed titration curve for (L-Om), at 25OC. 0, observed;solid line, calculated titration curve from Eq. (18) with u = 77.

6). Uncharged (L-Om), in aqueous solution without surfactant (at pH 12) is known to be only 20% helical at room ternperat~re.~J~ An additional hydrophobic interaction between bound surfactant ions is therefore essential for the stability of a helical structure. Since a-helix has 3.6 residues per turn, a cluster of at least 4 or 5 bound surfactant ions is necessary for the hydrophobic interaction. Each bound surfactant ion can further interact with another one that is one turn above or below. It is reasonable to assume that E = 7 or 8 (two helical turns) would stabilize the helical structure. This consideration also provides a plausible explanation for TABLE I The Average Cluster Size, E , o f Bound Decyl Sulfate Ions t o Polypeptides at Different Binding Ratios, x X

0.1 0.2 0.3 0.4 0.5

( L -Om), u = 77

3.5 5 .O 6.5 8.0 9.8

(D,L-Om), u = 161

4.8 7.0 9.0 11.2 13.7

(L-LYS), =

104

3 3.9 50.6 66.2 82.5 101.0

POLYPEPTIDE-SURFACTANT COMPLEXES

2275

the breaking point a t x = 0.3 of the (L-Om), curve in Figure 6. On the other hand, the average cluster size of bound surfactant ions on the (L-LYS), chain is large enough for the formation of the 0-structure even a t x = 0.1. (D,L-Om), in surfactant solution adopts no secondary structure. However, the values of i?i seem to be similar t o that of (L-Orn),. The above considerations are based on the assumption of a uniform distribution of bound surfactant ion cluster having an average size over the whole polypeptide molecule in solution. Other explanations are not entirely ruled out. This work was aided by the USPHS Grants GM-10880 and HL-06285. T h e authors wish t o thank Prof. L. Peller for a valuable discussion of the theoretical analysis.

References 1. Steinhardt, J. & Reynolds, J. A. (1969) Multiple Equilibria in Proteins, Academic, New York, ch. 7. 2. Grourke, M. J. & Gibbs, J. H. (1967) Biopolymers 5,586-588. 3. Sarkar, P. K. & Doty, P. (1966) Proc. Nut. Acad. Sci. U.S. 55,981-989; Li, L.-K. & Spector, A. (1969) J . Amer. Chem. SOC.91,220-222. 4. Satake, I. & Yang, J. T. (1973) Biochem. Biophys. Res. Commun. 54,930-936. 5. Gavach, C. (1969) Chim. Phys. A p p l . Prat. Ag. Surface (C. R. Congr. Int. Deterg. 5th 1968) 2,859-868. 6. Nagasawa, M. & Holtzer, A. (1964) J . Amer. Chem. SOC.86,538-543. 7. Grourke, M. J. & Gibbs, J. H. (1971) Biopolymers 10,795-808. 8. Benjamin, L (1964) J . Phys. Chem. 68,3575-3581. 9. Ekwall, P. & Stenius, P. (1967) Acta Chem. Scand. 21,1767-1772; Kaibara, K., Nakahara, T., Satake, 1. & Matuura, R. (1970) Mem. Fac. Sci. K y u s h u Uniu. Ser. C 7,l-4. 10. See for example, Shinoda, K., Nakagawa, T., Tamamushi, B. & Isemura, T. (1963) Colloidal Surfactants, Academic, New York, ch. 1. 11. Lewis, K. E. & Robinson, C. P. (1970) J . Colloid Interfac. Sci. 32,539-546. 12. Arai, H., Murata, M. & Shinoda, K. (1971) J . Colloid Interfac. Sci. 37, 223-227. 13. Marcus, R. A. (1954) J. Phys. Chem. 58,621-623. 14. Lifson, S. (1957) J. Chem. Phys. 26, 727-734. 15. Schmitz, K. S. & Schurr, J. M. (1970) Biopolymers 9,697-715. 16. Zimm, B. H. & Bragg, J. K. (1959) J . Chem. Phys. 31,526-535. 17. Chaudhuri, S. R. & Yang, J. T. (1968) Biochemistry 7,1379-1383.

Received January 5,1976 Returned for revision March 2,1976 Accepted May 19,1976

Interaction of sodium decyl sulfate with poly(L-ornithine) and poly(L-lysine) in aqueous solution.

VOL. 15, 2263-2275 (1976) BIOPOLYMERS Interaction of Sodium Decyl Sulfate with Poly(Lornithine) and Poly(L-lysine) in Aqueous Solution IWAO SATAKE*...
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