electrostatic interactions in ionic homopolypeptides in solutions of moderate ionic strength

Electrostatic Interactions in Ionic Homopolypeptides in Solutions of Moderate Ionic

Strength

GERMAN SANTIAGO, RACHID C. MAROUN, ERIN R. HAWKINS, and WAYNE L. MATTICE, Department of Chemistry, Louisiana

S ta te University, Baton Rouge, Louisiana 70803

Synopsis

At sufficiently high ionic strength, long-range electrostatic interactions in a polyelectrolyte such as poly(L-glutamic acid) might be adequately approximated in matrix calculations by use of statistical weights representing second-order interactions. The validity of this as- sumption has been investigated making use of experimental observations (CD spectra and titration curves) for poly(L-glutamic acid) as a function of temperature in 0.1-0.5M sodium chloride. Theoretical analysis, using a statistical weight matrix proposed by Warasbina and Ikegami, is based on the Zimm-Rice theory. Implementation differs from that of Warashina and Ikegami in one respect. Refinement of the initial estimates is achieved using a form of the configuration partition function which does not assume diagonalization of the statistical weight matrix. This difference is of no consequence for the values of o and s, but it does produce somewhat different values for the statistical weights used to represent the electrostatic interactions. The method used to treat electrostatic interactions in poly(L-glutamic acid) in 0.1M sodium chloride can be viewed as successful in that it properly reproduces the helix-coil transition and titration curves in this solvent and the molecular-weight dependence of the titration curves yields values for s in harmony with those obtained using a treatment which is independent of model, and gives a reasonable ionic-strength dependence for the electrostatic parameters. Furthermore, the model can account for measured helix-coil transitions and titration curves in homopolypeptides in which the side chain is -(CHZ)~- NHCO(CHd,COOH. The model, however, is not exact. It does not properly account for the molecular-weight dependence of the helical content for polymers of low degree of polymerization.

INTRODUCTION

Ionized homopolypeptides interact strongly with detergents bearing charges of the opposite sign.'-12 This interaction frequently induces a disorder-order transition in the polypeptides.'-'' One such detergent, sodium dodecyl sulfate, is also a powerful protein denat~rant.l~-~O Several physical properties of complexes formed by proteins and sodium dodecyl sulfate can be rationalized using a matrix treatment. This matrix treatment is based on the assumptions that the native structure of the protein is disrupted and amino acid residues bearing cationic side chains in the denatured protein have an enhanced probability of populating a helical state.20,21 Among properties susceptible to rationalization in this manner are CD spectra, radius of gyration, molecular-weight dependence of

Biopolymers, Vol. 20,2181-2194 (1981) 0 1981 John Wiley & Sons, Inc. CCC 0006-3525/8l/l02l8l-14$01.40

2182 SANTIAGO E T AL.

transport properties, and the “abnormal” transport properties of a few proteins in aqueous sodium dodecyl sulfate.20-22 Recent work indicates this approach can also rationalize several of the changes observed in 0-li- potropin, 0-endorphin, and myelin basic protein when they interact with anionic lipids.23

Success of this matrix treatment of protein-sodium dodecyl sulfate and myelin basic protein-anion lipid complexes is particularly noteworthy because the theoretical calculation uses rather crude estimates for parameters describing the interaction of the detergent or anionic lipid with the various amino acid residues. Since the crude model is reasonably successful, it becomes important to replace the crude estimates with more exact values for these interaction constants. This objective can be realized through study of suitable homo- and copolypeptides. It is expected that these studies will not only improve the accuracy of the matrix calculations, but will also shed added light on the means by which detergents and anionic lipids interact with polypeptides and proteins.

Improvement in crude estimates for the interaction parameters demands that special attention be given to electrostatic interactions. That this is the case is apparent from two considerations. First, synthetic detergents exert dramatic effects on ionic homopolypeptides only if they bear a charge opposite to that on the amino acid side chains.’-’l No important interaction occurs if the detergent bears a charge of the same sign as the polypeptide or if the polypeptide is n ~ n i o n i c . ~ , ~ ~ Hence there must be an appreciable electrostatic contribution to the binding process. Secondly, binding has the effect of discharging a side chain in the polyelectrolyte. Binding therefore modifies the conformational properties of the polypeptide by changing long-range electrostatic interactions. It will be of interest to separate these electrostatic contributions to the interaction from other contributions (e.g., hydrophobic) which may be present.

Incorporation of long-range interactions of any kind into a matrix treatment of the configuration-dependent properties of chain molecules is a formidable task. It can be accomplished reasonably well in simple cases, such as a polymethylene chain significantly perturbed by long-range interactions.25 For molecules with the complexity of those of current interest, however, it is desirable to restrict attention to circumstances where the effects of long-range electrostatic interactions can be incorporated into the matrix treatment by approximating them as second-order, short-range interactions. This approximation should be reasonable if application is restricted to solutions of sufficiently high ionic strength.

A study of poly(L-glutamic acid) by Warashina and IkegamP suggests that an ionic strength of O.1M might suffice to permit successful treatment of the electrostatic interaction of charged side chains via statistical weights representing second-order interactions. We wish to extend the range of their experimental observations. The validity of approximating intra- molecular electrostatic interactions by statistical weights which formally represent second-order interactions can be assessed by seeing which pa-

INTERACTIONS IN HOMOPOLYPEPTIDES 2183

rameters in the matrix treatment must be treated as being ionic-strength dependent in order to account for the measured properties. Therefore, we have examined the behavior of poly(L-glutamic acid) in 0.5M, as well as 0.1M, sodium chloride. It is also desirable to extend the temperature range covered, because many measurements with proteins are conducted at lower temperatures than those studied by Warashina and Ikegami.26

The method used by Warashina and Ikegami26 is based on an approximate diagonalization of the statistical weight matrix. In the present study, initial estimates of the statistical weights are obtained using this approximate treatment and then refined through application of an expression for the configuration partition function, which does not assume diagonalization of the statistical weight matrix. Statistical weights for electrostatic interactions, evaluated in this manner, should prove useful in the detailed analysis of detergent-polypeptide interactions.

EXPERIMENTAL

Materials

Poly(L-glutamic acid), as the sodium salt, was obtained from Sigma Chemical Company. Molecular weights for samples used were reported by the supplier to be 26 X lo3, 98 X lo3, and 103 X lo3. Solutions were prepared using deionized water. All other chemicals were reagent grade and were used without further purification.

Fractionation of poly(L-glutamic acid) was achieved by passage through a 5.0 X 60-cm borosilicate glass column packed with Sephacryl S-200 su- perfine resin. Samples applied to the column had a polymer concentration, c , of about 10 mg ml-l. The solvent was 0.1OM sodium chloride containing 0.5% n-butyl alcohol. Each solution was passed through a filter with 1.2 pm-pore size before application to the column. Equivalent fractions from multiple sample applications were combined, exhaustively dialyzed against deionized water, and recovered by lyophilization.

Viscosity Measurements

Flow times, t , for poly(L-glutamic acid) solutions of various concentrations were measured using Cannon-Ubbelohde semimicro dilution vis- cometers immersed in a bath whose temperature was 28.0 f 0.2OC. The solvent, with flow time to, was 0.2M sodium chloride, pH 7.3. Polypeptide concentrations were determined from the absorbance, measured using a Cary 14 spectrophotometer and 0.1-cm quartz cells, of the random-coil form a t 200 nm. A mean residue extinction coefficient of 5660 L cm mol-1 was assumed.27 The intrinsic viscosity, [ q ] , was obtained from linear extrapolation of (t - to)/toc to zero concentration.

Molecular weights for the poly(L-glutamic acid) fractions were obtained from measured intrinsic viscosities using the relationship

[q] = KMa (1)

2184 SANTIAGO ET AL.

with K = 41 X and a = 0.94 for [77] expressed in dL g-1.28929 These values for K and a are based on measurements performed at 25"C, but they should also apply at 28°C because d ln[q]ldT is extremely small for ionized poly(L-glutamic acid). Fractions selected for further study had degrees of polymerization of 55,70,80, 110, and 190.

Titrations

Samples for potentiometric titration were prepared by dissolving 20-35 mg of poly(L-glutamic acid) in 10-15 ml aqueous sodium chloride of the desired ionic strength (0.10,0.25,0.50M sodium chloride). The solution was placed in a jacketed vessel, kept at a constant temperature by circu- lating water from a constant temperature bath, and a stream of nitrogen was passed over the solution to eliminate potential interference from carbon dioxide. Measurements of pH were made with a Beckman 3500 digital pH meter equipped with a combination electrode. Burets with a total dis- charge volume of 5 ml were used.

Each solution was titrated with 0.1M sodium hydroxide prepared the same day from a saturated solution. Solutions were back-titrated with 0.1M hydrochloric acid prepared from a standard 1.OM solution. Further use of the results was made only when good agreement was found between the two titrations. The titrants' ionic strengths were kept close to those of the poly(L-glutamic acid) solutions examined. Negligible contributions were found in blank titrations. Titrations were performed at temperatures between 7 and 47°C.

Circular Dichroism

A Jasco 5-20 recording spectropolarimeter was used for CD measurements. These measurements were performed in the wavelength range 190-260 nm using calibrated quartz cells with path lengths ranging from 0.01 to 0.2 cm. The solutions examined were prepared from a stock solution of the specified ionic strength. Poly(L-glutamic acid) concentration was about 1 mg mL-l. The degree of ionization, a, was adjusted by addition of appropriate amounts of standard sodium hydroxide or hydrochloric acid until the desired pH was obtained. A portion of the solution was then withdrawn and the process repeated until a wide range of a was obtained. The pH of each solution was checked after the CD measurement at each temperature. Temperatures used correspond to those chosen for the titrations.

MATRIX CALCULATIONS

Theoretical analysis of the titration and CD data is achieved using a matrix treatment based on the Zimm-Rice theory.30 A 4 X 4 statistical weight matrix, U, which permits treatment only of nearest-neighbor in-


teractions, was employed. This matrix is formulated in a fashion identical to that of Warashina and Ikegami.26 An estimation of the behavior of in- finitely long chains can be obtained from an approximation to the largest eigenvalue of the statistical weight matrix.26 The resulting equations were employed to obtain trial values for four parameters in the matrix expression. Our approach differs from that of Warashina and Ikegami26 in the refinement of these initial trial values. Their refinement utilizes approximate equations for the limiting behavior a t high molecular weight. These equations may, unfortunately, introduce significant bias because diagonalization of U is not exact. In our refinement of the initial estimates, we return to the original (undiagonalized) matrix expression. In this manner any bias introduced in the approximate diagonalization is removed.

The statistical weight matrix, Ui, is

4-1 N O ) h(-) Y 0-S

f l s y u c h

crsy SYUhh 1 i SY US

h(O) [ yu,, Y S

ui = c(-)

h(-) Y u h c S

This matrix differs from that employed by Warashina and IkegamP only in the significance of the rows and columns, i.e., our U is the transpose M T ,

of their M. Columns in Ui index the state of residue i, rows index the state of residue i - 1, and the order of indexing is c(O), c(-), h(O), h(-). Here h denotes a residue in a helical state, c denotes a residue in a nonhelical state, and the charge state of the side chain occurs in parentheses. Zimm-Bragg31 parameters cr and s refer to the electrically neutral polypeptide. The intrinsic dissociation constant and pH determine y according to y = 10pH-pKo. The contribution to statistical weights made by the electrostatic interaction of neighboring charged side chains is denoted by ucc, uchr uh,, and Uhh. The expectation is 1 > u,, > Uhh because electrostatic interactions are repulsive and more severe in the helix than in the random coil. As pointed out by Warsashina and Ikegami,26 the relatively infrequent occurrence of helix ends in the charged polypeptide should permit use of an approximate form for uch and uhc. We adopt their approximation, u c h = uhc = (u u )1/2.26,30 cc hh

The configuration partition function, Z,32 is

Z = row (1,0,0,0) Un col (l,l,l,l) (3) for a polypeptide containing n residues. The row is formulated assuming the imaginary zeroth residue should be treated as being uncharged and in a nonhelical state. The configuration partition function used by Warashina and Ikegami26 was row (l,l,l,l) (UT)" col (l , l , l , l) , which contains four times as many terms as ours due to the difference in treatment of chain ends.

Following the customary development used in rotational isomeric state calculation^,^^ the probability that a residue will be ionized is

(4) a = n-1Z-1 row (I,o,o,o,o,o,o,o) U: col (O,O,O,OJJ,I,I)


and the probability that a residue will occupy a helical state is

f = n-1Z-1 row (I,o,o,o,o,o,o,o) U? col(0,0,0,0,1,1,1,1) (5)

Here Ux is defined as

u u: Ox = [o u ]

where U: is obtained from U by nulling all elements in two columns. The columns nulled are the first and third for x = a and the first and second forx = f .

Initial estimates for several of the parameters occurring in U were obtained using a simplified, approximate version of 2. This form of 2 is written for infinite n , but since it is based on an approximate, rather than exact, diagonalization G f U, it may not be correct even a t infinite n. The procedure used to obtain the initial estimates for ucc, U h h , IT, and s is es- sentially that described by Warashina and Ikegami26 after correction of what appear to be typographical errors in the matrices defined by their equation (A-6). This correction is as follows: The statistical weight matrix in Eq. (2) is rewritten as

where

Jx, = [1 ] 1 U,,Y

= A,.,. [ t19xv 0 ] B,, x2 ,x . v

Initial estimates for the statistical weights were refined using Eqs. (4) and (5), thereby removing any errors introduced by the inexact diagonalization of u.

RESULTS AND DISCUSSION

Titrations

Data obtained from potentiometric titrations were treated in the con- ventional manner.",28,~o,3.-:(8 The apparent pK, pH - log [a/(1 - a ) ] , is plotted as a function of cy. These plots were similar to those obtained in


several earlier s t ~ d i e s . ~ ~ , ~ ~ , ~ ~ The intrinsic dissociation constant, KO, was obtained by linear extrapolation of the helix and coil portions of the titration curve to 01 = 0. It was found to be independent of temperature and molecular weight. This constant did, however, depend on ionic strength. The values for pKo were 4.60,4.44, and 4.30 in 0.10,0.25, and 0.50M sodium chloride, respectively. The temperature independence of pKo is in agreement with results of measurements with poly(D1-glutamic acid).37 Our pKo at the higher ionic strength is also in agreement with that for the racemic polypeptide. At low ionic strength, our pKo is somewhat higher, which may be attributed, at least in part, to our choice of a linear, rather than curved, extrapolation. The pKo reported here in 0.1M sodium chloride is in excellent agreement with that measured in 0.1M potassium chloride.36

Thermodynamic parameters for the transition from the uncharged helix to uncharged random coil were determined from the titration curves in the usual manner.37 The free energy change per mole of residues in 0.1M sodium chloride is compared with that obtained by Olander and H ~ l t z e r " ~ in Fig. 1. Excellent agreement is found between results in the two studies. The free-energy changes depicted as the filled circles in Fig. 1, as well as similar data in 0.25 and 0.50M sodium chloride, can be reproduced using temperature- and ionic-strength-independent enthalpy and entropy changes of 900 f 85 cal and 2.5 f 0.3 cal K-l, respectively. These enthalpy and entropy changes are in excellent agreement with previous determina- tions for poly(L-glutamic acid)26,34,37 and copolymers containing L-glutamic acid.39

- 'J 200 0 I J a 0

0 20 40 60 T, "C

Fig. 1. Free-energy changes, per residue, for the helix-coil transition in un-ionized poly(L-glutamic acid) in 0.1M sodium chloride. Filled circles are data from the present work, and open circles are results reported by Olander and Holtzer (Ref. 37).


Helical Content

CD spectra were those expected for a polypeptide in which each residue must either be in a helical or random-coil state. Helical content was calculated from the mean residue ellipticity, [O], at 222 nm:

(13)

Here [O], and [el, are the mean residue ellipticities for the completely disordered and completely helical polypeptide, respectively. A value of -40,700 deg cm2 dmol-I was used for [el,. It is the most negative value measured on our spectropolarimeter for poly(L-glutamic acid).40 This value is in reasonable agreement with that measured for helical poly(L- glutamic a ~ i d ) . ~ ' - ~ 3 The mean residue ellipticity a t 222 nm is extremely small in disordered poly(L-glutamic acid), permitting approximation of [O], as zero.

Representative curves depicting the dependence off on a at two ionic strengths and four temperatures are shown in Fig. 2. The helical content increases with a decrease in a or temperature, as expected. An increase in sodium chloride concentration also stabilizes the helix. Figure 3 shows a representative dependence off and a on pH.

f = ([dl - [O]c)<[d]h - [O]c)-'

Refinement of Initial Values

Table 1 summarizes initial estimates and refined values for ucc, Uhh, 0,

and s. Refinement was achieved by varying each parameter, in turn, until the a and f , computed using Eqs. (4) and (5), gave the best fi t to the experimental results. In only one case (s a t 47°C in 0.5M sodium chloride) did refinement cause the the value of a statistical weight to move outside the range established by the initial estimate. A representative indication of the agreement between experimental and calculated curves is depicted in Fig. 3.

Sensitivity of computed a and f to independent adjustment of several parameters is depicted in Fig. 4. In this figure "R" denotes calculated

f

I .0

0.5

0.0 0.2 0.5 0.80.2 0.5 08

a

Fig. 2. Representative curves depicting the dependence off on a for poly(L-glutamic acid), degree of polymerization 70, a t 7°C ( O ) , 22°C (A) , 37°C (u), and 47°C (+).


4.5 5.0 5.5 6.0 PH

Fig. 3. Calculated (lines) and experimental (points) results for poly(L-glutamic acid), degree of polymerization 70, at 22OC in 0.1M sodium chloride. The calculation uses pKo = 4.60, u,, = 0.35, U h h = 0, U = 2.5 x w 3 , S = 1.22.

curves from Fig. 3. Both f and a are seen to be affected by a 10% change in s. The increase in s elevates the helical content, as expected. It also produced a decrease in a because Uhh < uCc, reflecting the greater difficulty in ionizing residues in helical states. Helical content is more sensitive than is a to changes in s. This result is expected because s only occurs in the statistical weight of helical residues, and does so whether they are ionized or not.

An increase in c causes both f and a to change less rapidly with pH, as expected. As was the case with s, f is found to be more sensitive than a to changes in c. Thus, refined values reported for c and s are determined primarily by the experimentally observed behavior off.

In contrast to the results seen with c and s , a change in u,, is seen to produce effects of comparable size on a and f. An increase in u,, produces an increase in a and a decrease in f because this statistical weight is called upon only when two neighboring residues are ionized and nonhelical. An increase in Uhh by the same amount, 0.10, produces an increase in both f and a. A larger statistical weight is now being given to chains in which two

TABLE I Initial and Refined Values

0.1M Sodium Chloride 0.5M Sodium Chloride Parameter Initial Refined Initial Refined

uc, 0.30-0.35 0.35 0.35-0.45 0.4 u hh 0 0 0 0 103a 2-8 2.5 2-8 5 S

7°C 1.27-1.33 1.33 1.31-1.42 1.35 22°C 1.21-1.25 1.22 1.22-1.29 1.25 37°C 1.11-1.13 1.13 1.10-1.13 1.13 47°C 1.06-1.08 1.08 1.10-1.13 1.06


I .o

0.0 1 8 I . I .o

f 0 .5

0.0 4.5 5.0 5.5 4.5 5.0 5.5

PH Fig. 4. Sensitivity of a and f to changes in u, s , u,,, and uhh. Curves denoted by R are

computed using u = 2.5 X lop3, s = 1.22, u,, = 0.35, Uhh = 0, pK0 = 4.60. In the other curves one parameter has been changed to the value indicated.

neighboring residues are both ionized and helical. The change in a occurs at lower pH when U h h is increased than is the case when the increment is made in ucc. Figure 4 shows that f is much more sensitive than a to the change in Uhh. When U h h is zero, helical sequences of any length are pro- hibited if even one pair of adjacent residues is ionized. Such helical seg- ments become allowed when Uhh is 0.1. Therefore, f is quite sensitive to the change in Uhh.

Comparison with Previous Studies

Previous estimates for u for poly(L-glutamic acid) under the conditions used here include 5 X lop3 in O.1M sodium chloridez6 and (3 f 1) X lop3, the latter value being independent of ionic strength.44 In 0.2M sodium chloride, u has been found to be (5 f 2) X lop3 and (2.5 f 0.5) X by Rifkind and Applequist45 and Bychkova et a1.,46 respectively. Refined u in Table I are therefore in the expected range. Figure 4 demonstrates that a twofold change in u will produce a small effect on f and only an inconse- quential effect on a. Measured f in 0.1 and 0.5M sodium chloride can be reproduced best if a different u is used in each solvent. However, the improvement in quality of the fit gained thereby is small. Thus, a reasonable conclusion from our work is that u is (3.75 f 1.25) X lop3 in sodium chloride of concentration 0.1-0.5M.


-0.1 I 2.8 3.2 3.6

lo'/ T

Fig. 5. Temperature dependence of s for un-ionized poly(L-glutamic acid) in 0.1M sodium chloride. Filled circles are data from the present work, and open circles are results reported by Warashina and Ikegami (Ref. 26). A least-squares straight line has been drawn through the solid circles.

Figure 5 compares s obtained in 0.1M sodium chloride in the present study with those reported by Warashina and IkegamP in the same solvent. Agreement is excellent in the upper end of the temperature range common to both sets of measurements. Somewhat larger s have been obtained a t pH 2.3 for L-glutamyl residues incorporated into poly(hydroxybuty1-L- gl~tamine)."~ Differences, however, do not exceed the standard deviation reported by Maxfield et al.39

While our u and s are in reasonable agreement with those obtained by Warashina and Ikegami,26 there is a significant difference in values found for the second-order statistical weights used for neighboring ionized residues. In 0.1M sodium chloride we find u,, = 0.35, while the value reported by Warashina and Ikegami is 0.5. A smaller difference is seen in Uhh, which they assign as 0.035 and for which we use zero. Reference to Fig. 4 shows the difference in values for Uhh is of no consequence for the titration curve. It will, however, produce a significant effect on the helix-coil transition. If U h h is increased from zero to 0.035, f will increase a t each a. Figure 3 compares the measured f with the best calculated curve. The calculated curve uses u h h = 0. Most points fall on the curve, but two are slightly below it. No points lie above the calculated curve. If Uhh were increased to 0.035, the computed curve would rise (Fig. 4), causing a deterioration in the quality of the fit.

A more important discrepancy concerns the size of ucc. Curves in Fig. 4 show that both the titration and helix-coil transition curves will be dis- placed to lower pH if u,, is increased from our value of 0.35 to Warashina and Ikegami's value of 0.5. The magnitude of the shift is about 0.2 pH units a t N = and f = I l2. Half of this discrepancy can be attributed to a difference of 0.1 in the values used for pKo. There remains, however, a significant difference in the size of the statistical weight used to account for the electrostatic interaction of charged side chains in random-coil poly(L- glutamic acid) in 0.1M sodium chloride. An explanation for the discrepancy may lie in the methods adopted for analysis of the experimental re-


sults. Our refined values are obtained by returning to Eqs. (4) and (5), which are based on the undiagonalized formulation of the configuration partition function.

We conclude that the differences in data analysis employed by Warashina and Ikegami26 and by us are of little consequence insofar as B and s are concerned. However, appreciable differences are found for terms used to account for electrostatic interaction of charged side chains. If the major objective is evaluation of the consequences of the electrostatic interaction of charged side chains, the method used here is preferred.

Adequacy of the Treatment of Electrostatic Interactions

The statistical weight matrix in Eq. (2) adequately describes the observed pH dependence of Q and f in 0.1M sodium chloride (Figs. 3 and 4). Fur- thermore, the response of the statistical weights to an increase in ionic strength to 0.5M is in reasonable accord with expectation. The most important change is an increase in ucc, which would be expected upon an increase in salt concentration. These two observations show that Eq. (2) accounts for the most important electrostatic interactions in poly(L-glutamic acid) in 0.1M sodium chloride in a manner which permits a reasonable rationalization of optical activity and titration data. The success of the model may be due in part to the strongly repulsive nature of the long-range electrostatic interactions in the helix. If these electrostatic interactions are sufficiently repulsive, stable helices cannot have a high charge density. Then any approximate treatment of electrostatic interactions in the helix should be moderately successful if that treatment severely penalizes helices of high charge density. That objective is achieved with the present model when Uhh is made small.

Additional important information concerning the range of validity of the model comes from analysis of data reported for homopolypeptides in which a larger number of bonds, m, separates the ionized carboxyl group and Ca atom. Hydrogen ion titration curves and pH-induced helix-coil transitions at 25OC, ionic strength 0.12M, have been reported for poly- (succinyl-L-ornithine), poly(glutary1-L-ornithine), poly(succiny1-L-lysine), and poly(glutaryl-~-lysine).~~ In these polypeptides m is 8-10, while m is only 3 in poly(L-glutamic acid). Murai and S ~ g a i ~ ~ present figures which depict the titration curves (as pK,,, vs a) and helix-coil transitions (as f vs a) for these four polypeptides. These data were converted to a vs pH and f vs pH. Values for s were calculated from the free energies for helix propagation reported by Murai and Sugai for the uncharged polypeptides. Analysis then proceeded in the fashion described above for poly(L-glutamic acid). The hydrogen ion titration curves and pH-induced helix-coil transitions reported for the four derivatives of poly(L-ornithine) and poly(L-lysine) are successfully described. Parameters reproducing the data are collected in Table 11. The pertinent value for u,, is found to be 0.50 f 0.01 if m is &lo, which is decidedly larger than the value of 0.35 required


TABLE I1 Statistical Weights for Various Homopolypeptides Bearing Ionized Carbonyl Groups in

Their Side Chains

Side Chain m 0 x 103 S u cc Uhh

-(CH2)2COO- 3 2.5 1.20 0.35 0 -(CH2)3NHCO(CH&COO- 8 2.0 1.13 0.50 0.25 -(CH2)3NHCO( CH2)3COO- 9 2.0 1.29 0.49 0.17 -(CHP)~NHCO(CH~)~COO- 9 1.5 1.18 0.51 0.26 -(CH2)4NHCO(CHrJ$OO- 10 3.0 1.33 0.51 0.25

at nearly the same ionic strength when m is 3. These limited results are in harmony with the expectation that u,, must approach unity as m becomes infinite. Similarly, uhh lies between 0.17 and 0.26 at m = 8-10, which is significantly larger than the result of zero required at m = 3. As expected, Uhh remains smaller than u,, even when m is as large as 10.

Taken together, the results reported above demonstrate that Eq. ( 2 ) provides an adequate description of the conformational effects produced in high-molecular-weight poly(L-glutamic acid) in 0.1M sodium chloride. This treatment can be expected to see successful application to other ionic homopolypeptides of high molecular weight.

Finally, it is important to recognize that the above treatment, while successful for homopolypeptides of high molecular weight, does have lim- itations. Equation (4) provides an excellent description of a for all poly(L-glutamic acid) fractions examined. This equation predicts very little dependence of a on n in the pertinent range, which is the result obtained experimentally. However, Eq. (5) predicts f should fall off somewhat more rapidly at small n than is observed for the fractions studied. For example, the best fit to the data for the fraction with a degree of polymerization of 70 was obtained using an n of about 250 in Eq. ( 5 ) . This inade- quacy of the theoretical treatment undoubtedly arises because the range of electrostatic interactions in poly(L-glutamic acid) in 0.1M sodium chloride extends beyond nearest neighbors and therefore cannot be treated rigorously using Eq. ( 2 ) . For the same reason, the present treatment may require modification if it is to be extended to copolypeptides containing L-glutamyl residues and un-ionized amino acid residues.

This research was supported by the National Science Foundation through Research Grant PCM 78-22916.

1. 2. 3. 4. 5. 6. 7.

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1329.

polymers 18,1889-1900.

1260.

Biophys. Res. Commun. 60,140-145.

1036.

1483-1498.

8,479-491.

3553.

2179.

Received December 1980 Accepted March 24,1981

electrostatic interactions in ionic homopolypeptides in solutions of moderate ionic strength

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