VOL. 16, 1541-1555 (1977)
BIOPOLYMERS
Viscosity and Potentiometric Measurements of Poly( L-Histidyl-L-Alanyl-a-L-Glutamic Acid) and Acid) Poly (L-Lysyl-L-Alanyl-a-L-Glutamic H. JOSEPH GOREN* and LORETTA GRANDAN, Division of Medical Biochemistry, ALFRED W. L. JAY, Division of Medical Biophysics, Faculty of Medicine, T h e University of Calgary, Calgary, Alberta, Canada T 2 N l N 4 , and NOAH LOTAN, Biophysics Department, T h e Weizmann Institute of Science, Rehovot, Israel
Synopsis Poly( His-Ala-Glu) and poly(Lys-Ala-Glu) were examined by viscosity and potentiometric titration. These measurements were interpreted in terms of the hydrodynamic size of the above sequential polypeptides. Effects of polymer, size and concentration, and solution-salt concentration were demonstrated. Although the sequential polypeptides generally behave like polyampholytes, they d o demonstrate some differences. These differences my be attributed to the ability of ionized side chains three residues apart to repel themselves, in the order His > Glu > Lys.
INTRODUCTION+ Poly(His-Ala-Glu)' and poly(Lys-Ala-Glu)2 are two ampholytic sequential polypeptides whose secondary structure in water is essentially a random coil.3 The inability of these polymers to form ordered structures in water may be attributed to the repulsive forces between the ionized side chains of the ith and the (i 3rd) residue. In the present report we present evidence that the same forces are also responsible for some hydrodynamic properties of the macromolecules.
+
MATERIALS AND METHODS Poly(His-Ala-Glu) and poly(Lys-Ala-Glu) were fractionated on a Sephadex G-50 column with 0.01N HC1.2 Water was distilled and deionized. All other reagents were of the highest grade commercially available. * To whom correspondence should be addressed. t A set of computer simulated curves [aus pH, Eq. (91, A us a,Eq. (lo),and B us a,Eq. ( I l ) , has been drawn where the effect of K1, K z , n , and w has been tested. Since polymers may
undergo tertiary structural changes on deprotonation, a set of curves using the above equations has been simulated where the value of w changed during the titration. Equation (9) has been adjusted to include polyanions and polycations of two different ionizable groups and simulated curves are included. These figures (Figs. 1M-6M) are stored in the microfiche repository and may be ordered from the publisher.
1541 Q 1977 by John Wiley & Sons, Inc.
GOREN ET AL.
1542
Potentiometric Titration Potentiometric titrations were performed with a Radiometer T T l C (Copenhagen) titration apparatus in connection with Titrigraph SBR2C at room temperature (-22 "C). Table I lists the polymer fractions, solvents, and polymer concentrations used in the experiments. The titration data were analyzed using Eqs. (10) and ( l l ) , whose derivation is described below. The average number of hydrogen ions, F, dissociated per polyelectrolyte molecule of two types of ionizable groups may be approximated from4 -
r=
nlKintl. e z w z / a H + 1 Kintl e Z w z / a H +
+
Kint2- e z w Z/a H + + nz. 1 + KintZ- ezwz/aH+
(1)
where nl and n2 are the total number of protons dissociable from ionizable group 1 and ionizable group 2, respectively, Kintl and Kintz are the respective intrinsic dissociation constants (hereafter written as K1 and Kz, respectively), Z is the net average charge per polymer molecule, aH+ is the hydrogen ion activity, and w = A/kT, where k is Boltzman's constant and T is the absolute temperature. A is a function relating the electrostatic free energy of a single macroion (W,J to the molecule's average charge, i.e.,
We,= A(Z)'
(2)
The choice of A and therefore the interpretation of w depends on the model TABLE I Conditions for Potentiometric Titration of Poly(X-Ala-Glu)"
Polymer (His-Ala-Glu), n N 30
n
N
70
(Lys-Ala-Glu),d n N 70
Concentration (mg/ml)
Solvent
pKib
pKzb
4.2 13.0 40.6" 1.7 1.1
0.1M KCI 0.1M KCl Dz0 0.1M KC1 1.OM KC1
4.03 4.15
6.03 6.15
4.75 4.87
6.75 6.62
5.6 2.1 4.2
0.1M KCI 0.5M KCl 1.OM KCl
4.5 4.5 4.5
9.5 9.5 9.5
a X is equal to His or Lys. All titrations were carried out on polymer using appropriately diluted standardized potassium hydroxide solutions a t 22 "C. For poly(His-Ala-Glu) the value of pK2 is A a t a = 0.5. Since K z / K , was assumed to have a certain value, pK1 is also defined by the value of A at a = 0.5. The concentration reported here is slightly high since the solution was slightly turbid and had to be filtered (Millipore) prior to the titration. (Temperature was 30 "C.) The titrant wa 3N NaOD. The pKo's have been assumed and not determined as described in b.
POLY(H1S-ALA-GLU), POLY (LYS-ALA-GLU)
1543
chosen to represent the macromolecule (rod us sphere, and regions of counterion permeability and impermeability) and on the various parameters which appear in the equation for We1.5-9 (Rice and Harris'O and Katchalsky and Miller" have derived expressions for Wel specifically for polyampholytes.) For this report we are assuming the sequential polypeptides to be flexible linear polyelectrolytes such that hydrodynamically they may be approximated as sphere^.^ It may be shown that by using the Hermans-Overbeek equation12 for We,that w qualitatively reflects the reciprocal of the effective radius of the macroion, i.e., an increase in w indicates a contracting macromolecule, and a decrease indicates the reverse. Thus Eq. (1)has been simplified in order that w may be calculated as a function of the degree of proton dissociation, a , from the polyampholyte where
Since in poly(His-Ala-Glu)and poly(Lys-Ala-Glu)nl = n2, where 1refers to glutamic and 2 refers to either histidine or lysine, and if n is twice the degree of polymerization (calculated from molecular weight), then n = nl n2. Allowing e2wz to be X , then Eq. (1)may be simplified to
+
If K2/K1 is less than 1 (e.g., equal to or less than 0.01) then Eq. (4) becomes
Equation (5) is a quadratic whose solution is
+
-
[(0.5 - a)' 4(K:!/K1) (1 - ~ ) C U ] ~ ' ~ ) (6) 2K2(1 - a ) Assuming that the average charge on the macromolecules is described by
X =
U H + { ( a- 0.5) f
z= n(0.5 - a )
(7) (at extreme pH's this assumption may not be valid as counterions would lower then
z),
-log10 X = 0.868 wn(a - 0.5)
(8) Incorporating Eq. (8) into the logarithmic form of Eq. (6), the following is obtained: pH
+ loglo 2(1 - a ) - loglo ( ( a- 0.5) + [(0.5- a)*
+ 4(K:!/K1) - (1- a)a]1/2)= 0.868 wn(a - 0.5) + pK2
(9)
1544
GOREN ET AL. I .o
0.78
a
0 5(
0 2!
PH
Fig. 1. Titration of (His-Ala-Glu),: in 0.1M KCl, where n N 30 at 13 mg/ml (A)and 4 rng/ml (0); where n N 70 at 1.7 mg/ml (A). In 1M KC1, where n N 70 at 1.1mg/ml(O). And in DzO, where n N 30 at 40.6 m g h l ( 0 ) . See Table I.
where pKz = -loglo Kz and pH = -loglo UH+. Since a glass electrode was used to measure pH, hydrogen ion concentration and not activity was measured and therefore K1 and K Zare not intrinsic but apparent dissociation constants.6 In going from Eq. (6) to Eq. (9), the negative sign in front of the square-root term has been removed. Leaving in the negative sign would make the log expression containing the square-root term the log of a negative number. Equation (10)has been written in a form such that the left-hand side of the equation ( A ) contains the experimentally determined variables pH and a:
A = pH
+ loglo 2(1 - a ) - loglo ( ( a- 0.5) -I-[(0.5 - a)’ + 4(Kz/K1)
Defining B as
*
(1 - C Y ) ~ ] ~ ’ ~(10) )
POLY (HIS-ALA-GLU), POLY(LYS-ALA-GLU)
1545
B
A
a or
"I
05
I .d
m 04.
6.
6.
'00
P d
0O'l2
I 2
6
1
8
1 3
nip*+?
ltP""
Fig. 2. Plot of Eqs. (10) A) and (11) B) from titration data for (His-Ala-Glu),. Top pair are theoretical curves where pK1 = 4.0, p K 2 = 7.0, n = 50,100, and 150, and w = 0.05 - 0.05 sin ( 2 n . x). Lower two pairs where n N 30 in 0.1M KCI I) 13 mg/ml and 11) 4 mg/rnl.
B=
A - PK2 0.868 n ( a - 0.5)
then R = w if pK2 is known. In order to calculate A, K2IKl needs to be known. For poly(His-Ala-Glu) this was assumed to be (except for the titration of polymer in 1.OM KC1 where it was assumed to be 1.8 X The ratio of the ionization constant for poly(Lys-Ala-Glu) was assumed to be In determining
1546
GOREN ET AL.
"I
1.0.
IV
c6.5.
iiwnn
Fig. 3. Plot of Eqs. (10) A) and (11)B) from titration data for (His-Ala-Glu),. Top pair are theoretical curves where pK1 = 4.0, pK2 = 7.0, n = 50,100, and 150, and w = 0.05 + 0.05 sin (a.T). Lower two pairs where n = 70 111) a t 1.7 mg/ml in 0.1M KCI and IV) at 1.1mg/ml in 1.OM KCl.
B, pK2 was taken as A at a = 0.5 [consequence of Eq.(ll)].All calculations and graphics were performed a t the University of Calgary Computer Center (CDC Syber 172). The curves (see ftn.+, p. 1541) drawn for A and B us LY used a program where the best hyperbola was drawn between each three successive data points. Viscosity. Three aliquots of poly(His-Ala-Glu) (approximately 22,000 molecular weight) were dissolved in distilled-deionized water and pH was adjusted to 2.97,4.99, and 9.70. Dilutions were made by adding distilled
POLY (HIS-ALA-GLU), POLY (LYS-ALA-GLU)
O4
1547
t
Fig. 4. A) Reduced viscosity of (His-Ala-Glu), where n N 70, in distilled water at pH 2.97 (0) plotted against the polymer concentration. B) The reciprocal of the reduced viscosity of poly(His-Ala-Glu) plotted against the square root of the polymer concentration. Data and symbols are those of Fig. 4A).
(o), 9.70 (A),and 4.99
water at the appropriate pH. A fourth sample of poly(His-Ala-Glu),3 mg, was dissolved in 1ml0.2M NaCl at pH 1.55. Flow times were taken of this solution and when it was diluted with 1ml0.2M NaCl. The diluted solution was adjusted with single drops of 2M NaOH and the pH measured after flow times were taken. These were pH 1.55, 2.09,2.97, and 7.12. Poly(Lys-Ala-Glu), approximately 20,000 molecular weight, was dissolved in 1.OM KC1. The initial concentrations and pH's were: 2.49 mg/ml, pH 2.15; 2.11 mg/ml, pH 4.50; and 2.49 mg/ml, pH 12.15. The viscosity of these solutions and their dilutions (with 1.OM KC1 adjusted to the appropriate pH) were measured. A Cannon viscometer (K727) was used in these experiments. The temperature was maintained a t 25.2 f 0.1 "C, for poly(His-Ala-Glu),and 25.0 f 0.1 "C, for poly(Lys-Ala-Glu), with a constant temperature water bath. A t least three flow times were taken for each sample and the time agreed within 1%of the mean value.
RESULTS Poly(His-Ala-Glu) Potentiometric titration. Figure 1 illustrates the titration of the different solutions of poly(His-Ala-Glu). These data were applied to Eqs. (10) and (11)with the resultant curves illustrated in Figures 2 and 3. The pKz's reported in Table I are the values of A at CY = 0.5. This permitted the calculation of pK1. The apparent dissociation constants calculated in this manner are different for each experiment (Table I). The values of p K , appear dependent on the size of the polymer and the solution salt content. B in Eq. (11)is the parameter w ,a term assumed to be inversely proportional to the effective radius of a polyelectrolyte. Figures 2B) and 3B)
GOREN ET AL.
1548
illustrate that poly(His-Ala-Glu) undergoes expansion and contraction during its titration. A t a < 0.5 (polycation) the polymer is more expanded than at a > 0.5 (polyanion) (Bu0.5). The polyampholyte form of the sequential polypeptide, a = 0.5, shows the largest value of B and is therefore the most compact form. Comparison of the experimental curves for poly(His-Ala-Glu) with computer simulated curves indicates that the effective radius of unfractionated poly(His-Ala-Glu) follows a sine wave as it is being deprotonated. Initially the molecule is expanding (decreasing B ) then it rapidly contracts around a = 0.5, and above a = 0.6 appears to remain constant or else slowly expands (Fig. 2). The effective radius of the high-molecular-weight fraction of poly(His-Ala-Glu) follows a bellshaped curve, the width being proportional to the ionic strength of the polymer solution (Fig. 3). Thus, poly( His-Ala-Glu) of 22,000 molecular weight, in going to either of its pure ionic forms from its polyampholyte form, expands. High salt content in the polymer solution stabilizes a compact form of the sequential polypeptide [compare Fig. 3B) (111)to Fig. 3B) ( W I . Viscosity. Figure 4A) illustrates the relationship of viscosity of poly(His-Ala-Glu) to concentration. I t appears that at high pH (9.7) the polymer behaves like a polyelectrolyte, that is, with decreasing concentration the viscosity appears to increase. A possible explanation is that polymer expansion occurs as a result of decreased ionic screening.13 The polyelectrolyte behavior of anionic poly(His-Ala-Glu) is confirmed since the viscosity of the sequential polypeptide at pH 9.7 follows the relationship of Fuoss and Strauss14 [Fig. 4 B)] for polyelectrolytes:
where Y equals the intrinsic viscosity of the polymer. Since the degree of expansion (as measured by the magnitude of viscosity) of polyelectrolytes is also dependent on the degree of ionization of the macromolecule,15poly(His-Ala-Glu) in the polyanionic (pH 9.7) or polycationic (pH 3.0) form TABLE I1 Reduced Viscositv of Polv(His-Ala-GluP
NaCl ( M )
Polymer Concentration (g/dU
PH
(dl/g)
0 0.2 0.2 0 0.2
0.21 0.3,0.15 0.15 0.15 0.15
2.97 1.55 2.09,2.89 9.70 7.12
0.6 0.1 0.1 0.13 0.25
Ilsplc
a Viscosity measurements were made on poly(His-Ala-Glu) of approximately 22,000 molecular weight.
1549
POLY(H1S-ALA-GLU), POLY(LYS-ALA-GLU) 1.0
0.7
4
x a
0,s
L;1
4
0.2
a
I
3.0
5.0
I
7.0
9.0
11.0
PH Fig. 5. Titration of (Lys-Ala-Glu), where n KC1 (0).
N
70 in 0.1M KC1 (O), 0.5M KCI (A),and 1.OM
has a higher viscosity (0.2 and 0.55 dl/g, respectively, a t 0.5 mg/ml) than when the sequential polypeptide is neutral (pH 5,0.07 dl/g a t 0.4 mg/ml). The low viscosity observed for poly(His-Ala-Glu) a t pH 5.0 may be explained by the presence of internal salt bridges. These salt bridges would prevent the macromolecule from expanding on dilution. The reduced viscosities of the two ionic forms of poly(His-Ala-Glu) appear to be quite different [Fig. 4A)l; however, the intrinsic viscosities are approximately equivalent [Fig. 4B)]. Salts are known to eliminate the dilution and ionization effect of polyelectrolyte^.^*-'^ Thus the viscosity of poly(His-Ala-Glu) as a polycation in 0.2M NaCl is unchanged with dilution (Table 11) and is less (0.1 dl/g) than in the absence of added salt (0.6 dl/g). The internal charge repulsions which had produced the expanded form of the polymer are now decreased or removed. On the other hand, the internal salt bridges which had maintained the low viscosity of poly(His-Ala-Glu) a t pH 5.0 are exchanged for external salt bridges in 0.2M NaC1. This would produce an expanded form of the macromolecule and therefore a higher viscosity. Thus a t pH 7.1, where poly(His-Ala-Glu) is still relatively neutral, the viscosity is 0.25
GOREN ET AL.
1550
A
.2
M.0;
.6
.4
B
.8
1 .O
RLPHR
.GO9 m
,006 ,003
8.5 9.01
L
8.00
.2
.4
-6
.8
1.0
‘0
RLPHR I1
.2
.6
.4
.B
1.0
RL PIIR
.o-
10.5.
111
10.0.
a 9.5.LO
9 .O.
8.5.
.05
.2
.4
.6
.8
1.0
RLPHR
Fig. 6. Plot of Eqs. (10) A) and (11) B) for (Lys-Ala-Glu), where n 11) 0.5M KCl, and 111) 1.OM KCl.
N
70 in I) 0.1M KCI,
dl/g in 0.2M NaCl while in the absence of salt the viscosity is approximately 0.1 dl/g (at 1.5mg/ml). The changes in viscosity of poly(His-Ala-Glu)with pH and ionic strength are consistent with earlier studies on the behavior of polyampholytes in aqueous s ~ l u t i o n . ~ ~ J ~
Poly(Lys- Ala-Glu)
Potentiornetric titrution. Figure 5 illustrates the titration of poly(Lys-Ala-Glu) in 0.1,0.5, and 1.OM KCl. The application of the titration
data to Eqs. (10) and (11) gave the unexpected results of Figure 6, that is values of A at a < 0.5 were greater than A at a = 0.5 and values of A at a > 0.5 were less than A at a = 0.5 (theoretically not permissible). Since the true values of A in the region of a = 0.5 were in doubt, pK:!was assumed to be 9.5. As a result the values of B in this a region were negative. The information in Table I11 may be used to explain the unexpected results of Figure 6. It is apparent that the final term of Eq. (10) is the largest contributing factor to A . Its contribution is greatest below a = 0.5, where its magnitude is inversely proportional to the ratio of the
ionization constants, K21K1. Thus the further apart are the pK,’s of the ionizable groups in a polyampholyte, the more sensitive is A to a, especially for 0.55 > a > 0.45. To calculate a the concentration of polymer and the volume of titrant added over and above the volume of titrant used to titrate the solvent is needed. In this report concentration was determined from the weight of polymer sample dissolved. Aside from possible error in weighing, presence of water or counterions in the dried polymer sample could easily produce wrong values for concentration. In the titrations of the two sequential polypeptides the most significant data were between pH 3.5 and 10.5. Below pH 3.5 the difference between polymer titration and solvent titration is small and therefore small errors in measurement produce large percentage errors. Above pH 10.5 the titration curves for both solvent and polymer rise sharply. Since differences between two sharply rising curves are difficult to measure, errors may readily arise. and with the Thus with the sensitivity of A to a , (when K2IK1 N TABLE 111 Contribution of Components of Eq. (10) to A a t Various KzIK1 Ratios” A = PH
0.40 0.45 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.55 0.60
+ loglo 2(1 - a)- loglo { ( a- 0.5) + [(0.5- a)’+ 4(Kz/K1)
0.08 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.05 -0.10
5.32 5.00 4.78 4.60 4.30 3.00 1.70 1.40 1.22 1.00 0.70
4.32 4.00 3.78 3.61 3.31 2.50 1.69 1.40 1.22 1.00 0.70
3.32 3.01 2.79 2.63 2.38 2.00 1.62 1.37 1.21 1.00 0.70
(1 - a)a]1’2)
2.33 2.04 1.87 1.76 1.64 1.50 1.36 1.24 1.13 10.96 0.69
a Figures are given to two decimal places. In the computer simulated curves many more places are stored in the calculation.
1552
GOREN ET AL.
possible inaccuracies of a, it follows that in the region of 0.45 < a < 0.55, poly(Lys-Ala-Glu) could produce the A data observed in Figure 6. Since the ionization of the glutamyl and the lysyl residues in poly(LysAla-Glu) are sufficiently different, it may be assumed that below a = 0.5 only (y-) carboxyl groups are being ionized and above a = 0.5 only (t-) ammonium ions are being deprotonated. Under these conditions the titration data for poly(Lys-Ala-Glu) may be analyzed by the method of Arnold and Overbeeklg: a’
pH - loglo -= 0.868 wn’a‘ 1 - a‘
- pKint
where for pKi,t = pK1, a’ = 2a and for pKint = pK2, a‘ = 2(a - 0.5) and in both instances n’ = n/2 [a,pK1, pK2, n, and w are the values used in Eq. (lo)]. Figure 7 illustrates the titration data analyzed by the latter method. From Eq. (13) it is seen that the slope of these curves is representative of w. Thus an increasing slope is indicative of an increasing w or a decreasing effective radius of the polymer. Figure 7 illustrates that the polyampholyte form of poly(Lys-Ala-Glu) is the most condensed form. From Figure 6 it may be concluded that the polyanionic form, in 0.1 and 0.5M KC1, has a larger effective radius than the polycationic form. Viscosity. The viscosity of poly(Lys-Ala-Glu) in 1M KCl was measured at pH 2.15, pH 7.50, and pH 12.15 [Fig. 8A)]. Despite the presence of 1M KC1, poly(Lys-Ala-Glu) at pH 12.15 expands on dilution [Fig. 8B)], an unexpected result in view of the shielding effect of salts on the dilution effect on polyelectrolytes. l6
DISCUSSION Hydrodynamic Properties of Poly(His-Ala-Glu) and Poly(Lys-Ala-Glu). Poly(His-Ala-Glu) and poly(Lys-Ala-Glu) in some respects behave hydrodynamically similarly to p o l y a m p h ~ l y t e s ~ ~i)- ~The ~ : most compact form of the polymers occurs when they are ionicly neutral. ii) Dilution of the polyanionic form of the sequential polypeptides results in increasing hydrodynamic size. iii) Increasing the ionic strength of a poly(His-Ala-Glu) solution below pH 3 decreases the size of the polymer (Table 11). The reduced viscosity of poly(Lys-Ala-Glu) a t 3 mglml in 0.1M NaCl at pH 3.6 and a t pH 11.5 is 0.15 and 0.18 dl/g, respectively.2 These values may be compared with the reduced viscosities, 0.14 and 0.16 dl/g, respectively [Fig. 8A)], of the sequential polypeptide in a comparable ionized state in 1M KCl. Thus poly(Lys-Ala-Glu)also decreases in size with increasing solution ionic strength. Although the two sequential polypeptides behave similarly in some respects they are different in other respects: i) The sensitivity of poly(HisAla-Glu) to its solution’s salt content is much greater than for PO~Y(LYS-
POLY (HIS-ALA-GLU), POLY (LYS-ALA-GLU) 11.0
1
B
0 5 U'
Fig. 7. Plot of titration data of Fig. 5 according to Eq. 13where A) pK,,,
1553
10
U'
= pK1 and
B) pK,,,
= pK2. Symbols are those of Fig. 5.
Ala-Glu). ii) The histidine containing polymer is larger as a polycation while the lysine containing one is larger as a polyanion. These observations may be discussed in view of the secondary structural analyses of the two sequential polypeptides.'J In the latter studies it was concluded that prevention of a-helix formation may be due to charge repulsion between the i t h and the (i 3rd) residue. The order of ability to disrupt a-helix formation by the ionized form of the amino acid was Glu > His > Lys. If this order is correct then the polyanionic form of the seqential polypeptides would be the larger ionized specie. Poly(His-Ala-Glu),however, is larger as a polycation. This implies that the ionized form of histidine would repel itself more strongly than would the ionized form of glutamic acid. On the basis of the size of the monoionic species of poly(His-Ala-Glu) and poly(Lys-Ala-Glu) the order of ability of ionized side chains three residues apart to repel themselves is His > Glu > Lys. (The difference to the secondary structure interpretation could be explained if the assumption is made that uncharged glutamic acid is a stronger a-helix former than is histidine.'O) T he effect of solution ionic strength on the sequential polypeptides' hydrodynamic size is consistent with the interpretation that the ionized forms of histidine, glutamic acid, and lysine repel themselves with decreasing strength in the latter order. With increasing ionic strength intramolecular forces of polyelectrolytes are r e d ~ c e d . ~ ~ The ~ ~ ' strength ~-'~ of intramolecular repulsive forces would be expected to be inversely proportional to the solution's salt content. Thus if ionized histidine side chains repel each other more strongly than do ionized lysine side chains poly(His-Ala-Glu) would demonstrate greater sensitivity to ionic strength than would poly (Lys-Ala-Glu). I t has been proposed that poly(Lys-Ala-Glu) is more a-helical a t low p H than a t high pH because the charge repulsion between the ionized lysyl side
+
1554
GOREN ET AL. 0.3
A A
o.a
-
-
M
-
a
_---
'=.
-
i_
0
0
0 0.1-
01 0
1
L
.1
CONCENTRATION
1
.8
( g/dl)
Fig. 8. A) Reduced viscosity of (Lys-Ala-Glu), where n N 70 in 1.OM KC1 a t pH 2.15 (a), pH 7.50 (m),and pH 12.15 (A)plotted against the polymer concentration. B) The reciprocal of the reduced viscosity of poly(Lys-Ala-Glu) a t pH 12.15 plotted against the square root of the polymer concentration.
chains is less than between the ionized glutamyl side chain^.^ In the present study using viscosity and potentiometric measurements on poly(Lys-Ala-Glu) and poly(His-Ala-Glu) the order of strength of charge repulsion includes histidine, i.e., His > Glu > Lys. This is also the order of increasing distance and flexibility of the ionic group away from the peptide backbone. Thus the ability of ionized amino acids three residues apart to interact with each other may be dependent on the distance andlor flexibility of the charged side chain from the peptide backbone. This research was supported by the Medical Research Council of Canada, MA 5521 and the United States-Israel Binational Science Foundation (BSF 456). H.J.G. thanks the De-
POLY (HIS-ALA-GLU), POLY (LYS-ALA-GLU)
1555
partment of Macromolecular Science, Case Western Reserve University, for offering its facilities, where some of the present studies were performed, and Dr. M. McDonnell for fruitful discussions.
References 1. Goren, H. J., Katchalski, E. & Fridkin, M. (1973) Int. Cong. Biochem. 9,89. 2. Goren, H. J., Fletcher, T . & Epand, R. M. (1977) Biopolymers 16,1513-1525. 3. Goren, H. J., McMillin, C. R. & Walton, A. G. (1977) Biopolyrners 16,1527-1540. 4. Tanford, C. (1965) Physical Chemistry of Macromolecules, Wiley, New York, pp. 549-552. 5. Tanford, C. (1965) Physical Chemistry of Macromolecules, Wiley, New York, pp. 461 -488. 6. Nagasawa, M. (1971) Pure Appl. Chem. 26,519-536. 7. Nagasawa, M. (1974) in Polyelectrolytes, SBIBgny, E., Mandel, M. & Strauss, U. P., Eds., Reidel, Boston, pp. 57-77. 8. Katchalsky, A,, Shavit, N. & Eisenberg, H. (1954) J . Polymer Sci. 13,69-84. 9. Manning, G. S. (1974) in Polyelectrolytes, SBIBgny, E., Mandel, M. & Strauss, U. P., Eds., Reidel, Boston, pp. 9-37. 10. Rice, S. A. & Harris, F. E. (1956) J . Chem. Phys. 24,326-335. 11. Katchalsky, A. & Miller, I. R. (1954) J . Polymer Sci. 13,57-68. 12. Hermans, J. J. & Overbeek, J. Th. G. (1948) Rec. Trau. Chim. 67,761-776. 13. Strauss, U. P. (1974) in Polyelectrolytes, S k g n y , E., Mandel, M. & Strauss, U. P., Eds., Reidel, Boston, pp. 79-85. 14. Fuoss, R. M. & Strauss, U. P. (1948) J . Polymer Sci. 3,246-263. 15. Oth, A. & Doty, P. (1952) J . Phys. Chem. 56,43-50. 16. Fuoss, R. M. (1951) Discuss. Faraday Soc. 11, 125-134. 17. Alfrey, T., Jr., Fuoss, R. M., Morawetz, H. & Pinner, H. (1952) J . Amer. Chem. SOC. 74,438-441. 18. Ehrlich, G. & Doty, P. (1954) J . Amer. Chem. SOC. 76,3764-3777. 19. Arnold, R. & Overbeek, J. Th. G. (1950) Rec. Trau. Chim. 69,192-206. 20. Chou, P. Y. & Fasman, G. D. (1974) Biochemistry 13,222-245.
Received June 6,1976 Accepted November 29,1976
BIOPOLYMERS
Viscosity and Potentiometric Measurements of Poly( L-Histidyl-L-Alanyl-a-L-Glutamic Acid) and Acid) Poly (L-Lysyl-L-Alanyl-a-L-Glutamic H. JOSEPH GOREN* and LORETTA GRANDAN, Division of Medical Biochemistry, ALFRED W. L. JAY, Division of Medical Biophysics, Faculty of Medicine, T h e University of Calgary, Calgary, Alberta, Canada T 2 N l N 4 , and NOAH LOTAN, Biophysics Department, T h e Weizmann Institute of Science, Rehovot, Israel
Synopsis Poly( His-Ala-Glu) and poly(Lys-Ala-Glu) were examined by viscosity and potentiometric titration. These measurements were interpreted in terms of the hydrodynamic size of the above sequential polypeptides. Effects of polymer, size and concentration, and solution-salt concentration were demonstrated. Although the sequential polypeptides generally behave like polyampholytes, they d o demonstrate some differences. These differences my be attributed to the ability of ionized side chains three residues apart to repel themselves, in the order His > Glu > Lys.
INTRODUCTION+ Poly(His-Ala-Glu)' and poly(Lys-Ala-Glu)2 are two ampholytic sequential polypeptides whose secondary structure in water is essentially a random coil.3 The inability of these polymers to form ordered structures in water may be attributed to the repulsive forces between the ionized side chains of the ith and the (i 3rd) residue. In the present report we present evidence that the same forces are also responsible for some hydrodynamic properties of the macromolecules.
+
MATERIALS AND METHODS Poly(His-Ala-Glu) and poly(Lys-Ala-Glu) were fractionated on a Sephadex G-50 column with 0.01N HC1.2 Water was distilled and deionized. All other reagents were of the highest grade commercially available. * To whom correspondence should be addressed. t A set of computer simulated curves [aus pH, Eq. (91, A us a,Eq. (lo),and B us a,Eq. ( I l ) , has been drawn where the effect of K1, K z , n , and w has been tested. Since polymers may
undergo tertiary structural changes on deprotonation, a set of curves using the above equations has been simulated where the value of w changed during the titration. Equation (9) has been adjusted to include polyanions and polycations of two different ionizable groups and simulated curves are included. These figures (Figs. 1M-6M) are stored in the microfiche repository and may be ordered from the publisher.
1541 Q 1977 by John Wiley & Sons, Inc.
GOREN ET AL.
1542
Potentiometric Titration Potentiometric titrations were performed with a Radiometer T T l C (Copenhagen) titration apparatus in connection with Titrigraph SBR2C at room temperature (-22 "C). Table I lists the polymer fractions, solvents, and polymer concentrations used in the experiments. The titration data were analyzed using Eqs. (10) and ( l l ) , whose derivation is described below. The average number of hydrogen ions, F, dissociated per polyelectrolyte molecule of two types of ionizable groups may be approximated from4 -
r=
nlKintl. e z w z / a H + 1 Kintl e Z w z / a H +
+
Kint2- e z w Z/a H + + nz. 1 + KintZ- ezwz/aH+
(1)
where nl and n2 are the total number of protons dissociable from ionizable group 1 and ionizable group 2, respectively, Kintl and Kintz are the respective intrinsic dissociation constants (hereafter written as K1 and Kz, respectively), Z is the net average charge per polymer molecule, aH+ is the hydrogen ion activity, and w = A/kT, where k is Boltzman's constant and T is the absolute temperature. A is a function relating the electrostatic free energy of a single macroion (W,J to the molecule's average charge, i.e.,
We,= A(Z)'
(2)
The choice of A and therefore the interpretation of w depends on the model TABLE I Conditions for Potentiometric Titration of Poly(X-Ala-Glu)"
Polymer (His-Ala-Glu), n N 30
n
N
70
(Lys-Ala-Glu),d n N 70
Concentration (mg/ml)
Solvent
pKib
pKzb
4.2 13.0 40.6" 1.7 1.1
0.1M KCI 0.1M KCl Dz0 0.1M KC1 1.OM KC1
4.03 4.15
6.03 6.15
4.75 4.87
6.75 6.62
5.6 2.1 4.2
0.1M KCI 0.5M KCl 1.OM KCl
4.5 4.5 4.5
9.5 9.5 9.5
a X is equal to His or Lys. All titrations were carried out on polymer using appropriately diluted standardized potassium hydroxide solutions a t 22 "C. For poly(His-Ala-Glu) the value of pK2 is A a t a = 0.5. Since K z / K , was assumed to have a certain value, pK1 is also defined by the value of A at a = 0.5. The concentration reported here is slightly high since the solution was slightly turbid and had to be filtered (Millipore) prior to the titration. (Temperature was 30 "C.) The titrant wa 3N NaOD. The pKo's have been assumed and not determined as described in b.
POLY(H1S-ALA-GLU), POLY (LYS-ALA-GLU)
1543
chosen to represent the macromolecule (rod us sphere, and regions of counterion permeability and impermeability) and on the various parameters which appear in the equation for We1.5-9 (Rice and Harris'O and Katchalsky and Miller" have derived expressions for Wel specifically for polyampholytes.) For this report we are assuming the sequential polypeptides to be flexible linear polyelectrolytes such that hydrodynamically they may be approximated as sphere^.^ It may be shown that by using the Hermans-Overbeek equation12 for We,that w qualitatively reflects the reciprocal of the effective radius of the macroion, i.e., an increase in w indicates a contracting macromolecule, and a decrease indicates the reverse. Thus Eq. (1)has been simplified in order that w may be calculated as a function of the degree of proton dissociation, a , from the polyampholyte where
Since in poly(His-Ala-Glu)and poly(Lys-Ala-Glu)nl = n2, where 1refers to glutamic and 2 refers to either histidine or lysine, and if n is twice the degree of polymerization (calculated from molecular weight), then n = nl n2. Allowing e2wz to be X , then Eq. (1)may be simplified to
+
If K2/K1 is less than 1 (e.g., equal to or less than 0.01) then Eq. (4) becomes
Equation (5) is a quadratic whose solution is
+
-
[(0.5 - a)' 4(K:!/K1) (1 - ~ ) C U ] ~ ' ~ ) (6) 2K2(1 - a ) Assuming that the average charge on the macromolecules is described by
X =
U H + { ( a- 0.5) f
z= n(0.5 - a )
(7) (at extreme pH's this assumption may not be valid as counterions would lower then
z),
-log10 X = 0.868 wn(a - 0.5)
(8) Incorporating Eq. (8) into the logarithmic form of Eq. (6), the following is obtained: pH
+ loglo 2(1 - a ) - loglo ( ( a- 0.5) + [(0.5- a)*
+ 4(K:!/K1) - (1- a)a]1/2)= 0.868 wn(a - 0.5) + pK2
(9)
1544
GOREN ET AL. I .o
0.78
a
0 5(
0 2!
PH
Fig. 1. Titration of (His-Ala-Glu),: in 0.1M KCl, where n N 30 at 13 mg/ml (A)and 4 rng/ml (0); where n N 70 at 1.7 mg/ml (A). In 1M KC1, where n N 70 at 1.1mg/ml(O). And in DzO, where n N 30 at 40.6 m g h l ( 0 ) . See Table I.
where pKz = -loglo Kz and pH = -loglo UH+. Since a glass electrode was used to measure pH, hydrogen ion concentration and not activity was measured and therefore K1 and K Zare not intrinsic but apparent dissociation constants.6 In going from Eq. (6) to Eq. (9), the negative sign in front of the square-root term has been removed. Leaving in the negative sign would make the log expression containing the square-root term the log of a negative number. Equation (10)has been written in a form such that the left-hand side of the equation ( A ) contains the experimentally determined variables pH and a:
A = pH
+ loglo 2(1 - a ) - loglo ( ( a- 0.5) -I-[(0.5 - a)’ + 4(Kz/K1)
Defining B as
*
(1 - C Y ) ~ ] ~ ’ ~(10) )
POLY (HIS-ALA-GLU), POLY(LYS-ALA-GLU)
1545
B
A
a or
"I
05
I .d
m 04.
6.
6.
'00
P d
0O'l2
I 2
6
1
8
1 3
nip*+?
ltP""
Fig. 2. Plot of Eqs. (10) A) and (11) B) from titration data for (His-Ala-Glu),. Top pair are theoretical curves where pK1 = 4.0, p K 2 = 7.0, n = 50,100, and 150, and w = 0.05 - 0.05 sin ( 2 n . x). Lower two pairs where n N 30 in 0.1M KCI I) 13 mg/ml and 11) 4 mg/rnl.
B=
A - PK2 0.868 n ( a - 0.5)
then R = w if pK2 is known. In order to calculate A, K2IKl needs to be known. For poly(His-Ala-Glu) this was assumed to be (except for the titration of polymer in 1.OM KC1 where it was assumed to be 1.8 X The ratio of the ionization constant for poly(Lys-Ala-Glu) was assumed to be In determining
1546
GOREN ET AL.
"I
1.0.
IV
c6.5.
iiwnn
Fig. 3. Plot of Eqs. (10) A) and (11)B) from titration data for (His-Ala-Glu),. Top pair are theoretical curves where pK1 = 4.0, pK2 = 7.0, n = 50,100, and 150, and w = 0.05 + 0.05 sin (a.T). Lower two pairs where n = 70 111) a t 1.7 mg/ml in 0.1M KCI and IV) at 1.1mg/ml in 1.OM KCl.
B, pK2 was taken as A at a = 0.5 [consequence of Eq.(ll)].All calculations and graphics were performed a t the University of Calgary Computer Center (CDC Syber 172). The curves (see ftn.+, p. 1541) drawn for A and B us LY used a program where the best hyperbola was drawn between each three successive data points. Viscosity. Three aliquots of poly(His-Ala-Glu) (approximately 22,000 molecular weight) were dissolved in distilled-deionized water and pH was adjusted to 2.97,4.99, and 9.70. Dilutions were made by adding distilled
POLY (HIS-ALA-GLU), POLY (LYS-ALA-GLU)
O4
1547
t
Fig. 4. A) Reduced viscosity of (His-Ala-Glu), where n N 70, in distilled water at pH 2.97 (0) plotted against the polymer concentration. B) The reciprocal of the reduced viscosity of poly(His-Ala-Glu) plotted against the square root of the polymer concentration. Data and symbols are those of Fig. 4A).
(o), 9.70 (A),and 4.99
water at the appropriate pH. A fourth sample of poly(His-Ala-Glu),3 mg, was dissolved in 1ml0.2M NaCl at pH 1.55. Flow times were taken of this solution and when it was diluted with 1ml0.2M NaCl. The diluted solution was adjusted with single drops of 2M NaOH and the pH measured after flow times were taken. These were pH 1.55, 2.09,2.97, and 7.12. Poly(Lys-Ala-Glu), approximately 20,000 molecular weight, was dissolved in 1.OM KC1. The initial concentrations and pH's were: 2.49 mg/ml, pH 2.15; 2.11 mg/ml, pH 4.50; and 2.49 mg/ml, pH 12.15. The viscosity of these solutions and their dilutions (with 1.OM KC1 adjusted to the appropriate pH) were measured. A Cannon viscometer (K727) was used in these experiments. The temperature was maintained a t 25.2 f 0.1 "C, for poly(His-Ala-Glu),and 25.0 f 0.1 "C, for poly(Lys-Ala-Glu), with a constant temperature water bath. A t least three flow times were taken for each sample and the time agreed within 1%of the mean value.
RESULTS Poly(His-Ala-Glu) Potentiometric titration. Figure 1 illustrates the titration of the different solutions of poly(His-Ala-Glu). These data were applied to Eqs. (10) and (11)with the resultant curves illustrated in Figures 2 and 3. The pKz's reported in Table I are the values of A at CY = 0.5. This permitted the calculation of pK1. The apparent dissociation constants calculated in this manner are different for each experiment (Table I). The values of p K , appear dependent on the size of the polymer and the solution salt content. B in Eq. (11)is the parameter w ,a term assumed to be inversely proportional to the effective radius of a polyelectrolyte. Figures 2B) and 3B)
GOREN ET AL.
1548
illustrate that poly(His-Ala-Glu) undergoes expansion and contraction during its titration. A t a < 0.5 (polycation) the polymer is more expanded than at a > 0.5 (polyanion) (Bu0.5). The polyampholyte form of the sequential polypeptide, a = 0.5, shows the largest value of B and is therefore the most compact form. Comparison of the experimental curves for poly(His-Ala-Glu) with computer simulated curves indicates that the effective radius of unfractionated poly(His-Ala-Glu) follows a sine wave as it is being deprotonated. Initially the molecule is expanding (decreasing B ) then it rapidly contracts around a = 0.5, and above a = 0.6 appears to remain constant or else slowly expands (Fig. 2). The effective radius of the high-molecular-weight fraction of poly(His-Ala-Glu) follows a bellshaped curve, the width being proportional to the ionic strength of the polymer solution (Fig. 3). Thus, poly( His-Ala-Glu) of 22,000 molecular weight, in going to either of its pure ionic forms from its polyampholyte form, expands. High salt content in the polymer solution stabilizes a compact form of the sequential polypeptide [compare Fig. 3B) (111)to Fig. 3B) ( W I . Viscosity. Figure 4A) illustrates the relationship of viscosity of poly(His-Ala-Glu) to concentration. I t appears that at high pH (9.7) the polymer behaves like a polyelectrolyte, that is, with decreasing concentration the viscosity appears to increase. A possible explanation is that polymer expansion occurs as a result of decreased ionic screening.13 The polyelectrolyte behavior of anionic poly(His-Ala-Glu) is confirmed since the viscosity of the sequential polypeptide at pH 9.7 follows the relationship of Fuoss and Strauss14 [Fig. 4 B)] for polyelectrolytes:
where Y equals the intrinsic viscosity of the polymer. Since the degree of expansion (as measured by the magnitude of viscosity) of polyelectrolytes is also dependent on the degree of ionization of the macromolecule,15poly(His-Ala-Glu) in the polyanionic (pH 9.7) or polycationic (pH 3.0) form TABLE I1 Reduced Viscositv of Polv(His-Ala-GluP
NaCl ( M )
Polymer Concentration (g/dU
PH
(dl/g)
0 0.2 0.2 0 0.2
0.21 0.3,0.15 0.15 0.15 0.15
2.97 1.55 2.09,2.89 9.70 7.12
0.6 0.1 0.1 0.13 0.25
Ilsplc
a Viscosity measurements were made on poly(His-Ala-Glu) of approximately 22,000 molecular weight.
1549
POLY(H1S-ALA-GLU), POLY(LYS-ALA-GLU) 1.0
0.7
4
x a
0,s
L;1
4
0.2
a
I
3.0
5.0
I
7.0
9.0
11.0
PH Fig. 5. Titration of (Lys-Ala-Glu), where n KC1 (0).
N
70 in 0.1M KC1 (O), 0.5M KCI (A),and 1.OM
has a higher viscosity (0.2 and 0.55 dl/g, respectively, a t 0.5 mg/ml) than when the sequential polypeptide is neutral (pH 5,0.07 dl/g a t 0.4 mg/ml). The low viscosity observed for poly(His-Ala-Glu) a t pH 5.0 may be explained by the presence of internal salt bridges. These salt bridges would prevent the macromolecule from expanding on dilution. The reduced viscosities of the two ionic forms of poly(His-Ala-Glu) appear to be quite different [Fig. 4A)l; however, the intrinsic viscosities are approximately equivalent [Fig. 4B)]. Salts are known to eliminate the dilution and ionization effect of polyelectrolyte^.^*-'^ Thus the viscosity of poly(His-Ala-Glu) as a polycation in 0.2M NaCl is unchanged with dilution (Table 11) and is less (0.1 dl/g) than in the absence of added salt (0.6 dl/g). The internal charge repulsions which had produced the expanded form of the polymer are now decreased or removed. On the other hand, the internal salt bridges which had maintained the low viscosity of poly(His-Ala-Glu) a t pH 5.0 are exchanged for external salt bridges in 0.2M NaC1. This would produce an expanded form of the macromolecule and therefore a higher viscosity. Thus a t pH 7.1, where poly(His-Ala-Glu) is still relatively neutral, the viscosity is 0.25
GOREN ET AL.
1550
A
.2
M.0;
.6
.4
B
.8
1 .O
RLPHR
.GO9 m
,006 ,003
8.5 9.01
L
8.00
.2
.4
-6
.8
1.0
‘0
RLPHR I1
.2
.6
.4
.B
1.0
RL PIIR
.o-
10.5.
111
10.0.
a 9.5.LO
9 .O.
8.5.
.05
.2
.4
.6
.8
1.0
RLPHR
Fig. 6. Plot of Eqs. (10) A) and (11) B) for (Lys-Ala-Glu), where n 11) 0.5M KCl, and 111) 1.OM KCl.
N
70 in I) 0.1M KCI,
dl/g in 0.2M NaCl while in the absence of salt the viscosity is approximately 0.1 dl/g (at 1.5mg/ml). The changes in viscosity of poly(His-Ala-Glu)with pH and ionic strength are consistent with earlier studies on the behavior of polyampholytes in aqueous s ~ l u t i o n . ~ ~ J ~
Poly(Lys- Ala-Glu)
Potentiornetric titrution. Figure 5 illustrates the titration of poly(Lys-Ala-Glu) in 0.1,0.5, and 1.OM KCl. The application of the titration
data to Eqs. (10) and (11) gave the unexpected results of Figure 6, that is values of A at a < 0.5 were greater than A at a = 0.5 and values of A at a > 0.5 were less than A at a = 0.5 (theoretically not permissible). Since the true values of A in the region of a = 0.5 were in doubt, pK:!was assumed to be 9.5. As a result the values of B in this a region were negative. The information in Table I11 may be used to explain the unexpected results of Figure 6. It is apparent that the final term of Eq. (10) is the largest contributing factor to A . Its contribution is greatest below a = 0.5, where its magnitude is inversely proportional to the ratio of the
ionization constants, K21K1. Thus the further apart are the pK,’s of the ionizable groups in a polyampholyte, the more sensitive is A to a, especially for 0.55 > a > 0.45. To calculate a the concentration of polymer and the volume of titrant added over and above the volume of titrant used to titrate the solvent is needed. In this report concentration was determined from the weight of polymer sample dissolved. Aside from possible error in weighing, presence of water or counterions in the dried polymer sample could easily produce wrong values for concentration. In the titrations of the two sequential polypeptides the most significant data were between pH 3.5 and 10.5. Below pH 3.5 the difference between polymer titration and solvent titration is small and therefore small errors in measurement produce large percentage errors. Above pH 10.5 the titration curves for both solvent and polymer rise sharply. Since differences between two sharply rising curves are difficult to measure, errors may readily arise. and with the Thus with the sensitivity of A to a , (when K2IK1 N TABLE 111 Contribution of Components of Eq. (10) to A a t Various KzIK1 Ratios” A = PH
0.40 0.45 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.55 0.60
+ loglo 2(1 - a)- loglo { ( a- 0.5) + [(0.5- a)’+ 4(Kz/K1)
0.08 0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.05 -0.10
5.32 5.00 4.78 4.60 4.30 3.00 1.70 1.40 1.22 1.00 0.70
4.32 4.00 3.78 3.61 3.31 2.50 1.69 1.40 1.22 1.00 0.70
3.32 3.01 2.79 2.63 2.38 2.00 1.62 1.37 1.21 1.00 0.70
(1 - a)a]1’2)
2.33 2.04 1.87 1.76 1.64 1.50 1.36 1.24 1.13 10.96 0.69
a Figures are given to two decimal places. In the computer simulated curves many more places are stored in the calculation.
1552
GOREN ET AL.
possible inaccuracies of a, it follows that in the region of 0.45 < a < 0.55, poly(Lys-Ala-Glu) could produce the A data observed in Figure 6. Since the ionization of the glutamyl and the lysyl residues in poly(LysAla-Glu) are sufficiently different, it may be assumed that below a = 0.5 only (y-) carboxyl groups are being ionized and above a = 0.5 only (t-) ammonium ions are being deprotonated. Under these conditions the titration data for poly(Lys-Ala-Glu) may be analyzed by the method of Arnold and Overbeeklg: a’
pH - loglo -= 0.868 wn’a‘ 1 - a‘
- pKint
where for pKi,t = pK1, a’ = 2a and for pKint = pK2, a‘ = 2(a - 0.5) and in both instances n’ = n/2 [a,pK1, pK2, n, and w are the values used in Eq. (lo)]. Figure 7 illustrates the titration data analyzed by the latter method. From Eq. (13) it is seen that the slope of these curves is representative of w. Thus an increasing slope is indicative of an increasing w or a decreasing effective radius of the polymer. Figure 7 illustrates that the polyampholyte form of poly(Lys-Ala-Glu) is the most condensed form. From Figure 6 it may be concluded that the polyanionic form, in 0.1 and 0.5M KC1, has a larger effective radius than the polycationic form. Viscosity. The viscosity of poly(Lys-Ala-Glu) in 1M KCl was measured at pH 2.15, pH 7.50, and pH 12.15 [Fig. 8A)]. Despite the presence of 1M KC1, poly(Lys-Ala-Glu) at pH 12.15 expands on dilution [Fig. 8B)], an unexpected result in view of the shielding effect of salts on the dilution effect on polyelectrolytes. l6
DISCUSSION Hydrodynamic Properties of Poly(His-Ala-Glu) and Poly(Lys-Ala-Glu). Poly(His-Ala-Glu) and poly(Lys-Ala-Glu) in some respects behave hydrodynamically similarly to p o l y a m p h ~ l y t e s ~ ~i)- ~The ~ : most compact form of the polymers occurs when they are ionicly neutral. ii) Dilution of the polyanionic form of the sequential polypeptides results in increasing hydrodynamic size. iii) Increasing the ionic strength of a poly(His-Ala-Glu) solution below pH 3 decreases the size of the polymer (Table 11). The reduced viscosity of poly(Lys-Ala-Glu) a t 3 mglml in 0.1M NaCl at pH 3.6 and a t pH 11.5 is 0.15 and 0.18 dl/g, respectively.2 These values may be compared with the reduced viscosities, 0.14 and 0.16 dl/g, respectively [Fig. 8A)], of the sequential polypeptide in a comparable ionized state in 1M KCl. Thus poly(Lys-Ala-Glu)also decreases in size with increasing solution ionic strength. Although the two sequential polypeptides behave similarly in some respects they are different in other respects: i) The sensitivity of poly(HisAla-Glu) to its solution’s salt content is much greater than for PO~Y(LYS-
POLY (HIS-ALA-GLU), POLY (LYS-ALA-GLU) 11.0
1
B
0 5 U'
Fig. 7. Plot of titration data of Fig. 5 according to Eq. 13where A) pK,,,
1553
10
U'
= pK1 and
B) pK,,,
= pK2. Symbols are those of Fig. 5.
Ala-Glu). ii) The histidine containing polymer is larger as a polycation while the lysine containing one is larger as a polyanion. These observations may be discussed in view of the secondary structural analyses of the two sequential polypeptides.'J In the latter studies it was concluded that prevention of a-helix formation may be due to charge repulsion between the i t h and the (i 3rd) residue. The order of ability to disrupt a-helix formation by the ionized form of the amino acid was Glu > His > Lys. If this order is correct then the polyanionic form of the seqential polypeptides would be the larger ionized specie. Poly(His-Ala-Glu),however, is larger as a polycation. This implies that the ionized form of histidine would repel itself more strongly than would the ionized form of glutamic acid. On the basis of the size of the monoionic species of poly(His-Ala-Glu) and poly(Lys-Ala-Glu) the order of ability of ionized side chains three residues apart to repel themselves is His > Glu > Lys. (The difference to the secondary structure interpretation could be explained if the assumption is made that uncharged glutamic acid is a stronger a-helix former than is histidine.'O) T he effect of solution ionic strength on the sequential polypeptides' hydrodynamic size is consistent with the interpretation that the ionized forms of histidine, glutamic acid, and lysine repel themselves with decreasing strength in the latter order. With increasing ionic strength intramolecular forces of polyelectrolytes are r e d ~ c e d . ~ ~ The ~ ~ ' strength ~-'~ of intramolecular repulsive forces would be expected to be inversely proportional to the solution's salt content. Thus if ionized histidine side chains repel each other more strongly than do ionized lysine side chains poly(His-Ala-Glu) would demonstrate greater sensitivity to ionic strength than would poly (Lys-Ala-Glu). I t has been proposed that poly(Lys-Ala-Glu) is more a-helical a t low p H than a t high pH because the charge repulsion between the ionized lysyl side
+
1554
GOREN ET AL. 0.3
A A
o.a
-
-
M
-
a
_---
'=.
-
i_
0
0
0 0.1-
01 0
1
L
.1
CONCENTRATION
1
.8
( g/dl)
Fig. 8. A) Reduced viscosity of (Lys-Ala-Glu), where n N 70 in 1.OM KC1 a t pH 2.15 (a), pH 7.50 (m),and pH 12.15 (A)plotted against the polymer concentration. B) The reciprocal of the reduced viscosity of poly(Lys-Ala-Glu) a t pH 12.15 plotted against the square root of the polymer concentration.
chains is less than between the ionized glutamyl side chain^.^ In the present study using viscosity and potentiometric measurements on poly(Lys-Ala-Glu) and poly(His-Ala-Glu) the order of strength of charge repulsion includes histidine, i.e., His > Glu > Lys. This is also the order of increasing distance and flexibility of the ionic group away from the peptide backbone. Thus the ability of ionized amino acids three residues apart to interact with each other may be dependent on the distance andlor flexibility of the charged side chain from the peptide backbone. This research was supported by the Medical Research Council of Canada, MA 5521 and the United States-Israel Binational Science Foundation (BSF 456). H.J.G. thanks the De-
POLY (HIS-ALA-GLU), POLY (LYS-ALA-GLU)
1555
partment of Macromolecular Science, Case Western Reserve University, for offering its facilities, where some of the present studies were performed, and Dr. M. McDonnell for fruitful discussions.
References 1. Goren, H. J., Katchalski, E. & Fridkin, M. (1973) Int. Cong. Biochem. 9,89. 2. Goren, H. J., Fletcher, T . & Epand, R. M. (1977) Biopolymers 16,1513-1525. 3. Goren, H. J., McMillin, C. R. & Walton, A. G. (1977) Biopolyrners 16,1527-1540. 4. Tanford, C. (1965) Physical Chemistry of Macromolecules, Wiley, New York, pp. 549-552. 5. Tanford, C. (1965) Physical Chemistry of Macromolecules, Wiley, New York, pp. 461 -488. 6. Nagasawa, M. (1971) Pure Appl. Chem. 26,519-536. 7. Nagasawa, M. (1974) in Polyelectrolytes, SBIBgny, E., Mandel, M. & Strauss, U. P., Eds., Reidel, Boston, pp. 57-77. 8. Katchalsky, A,, Shavit, N. & Eisenberg, H. (1954) J . Polymer Sci. 13,69-84. 9. Manning, G. S. (1974) in Polyelectrolytes, SBIBgny, E., Mandel, M. & Strauss, U. P., Eds., Reidel, Boston, pp. 9-37. 10. Rice, S. A. & Harris, F. E. (1956) J . Chem. Phys. 24,326-335. 11. Katchalsky, A. & Miller, I. R. (1954) J . Polymer Sci. 13,57-68. 12. Hermans, J. J. & Overbeek, J. Th. G. (1948) Rec. Trau. Chim. 67,761-776. 13. Strauss, U. P. (1974) in Polyelectrolytes, S k g n y , E., Mandel, M. & Strauss, U. P., Eds., Reidel, Boston, pp. 79-85. 14. Fuoss, R. M. & Strauss, U. P. (1948) J . Polymer Sci. 3,246-263. 15. Oth, A. & Doty, P. (1952) J . Phys. Chem. 56,43-50. 16. Fuoss, R. M. (1951) Discuss. Faraday Soc. 11, 125-134. 17. Alfrey, T., Jr., Fuoss, R. M., Morawetz, H. & Pinner, H. (1952) J . Amer. Chem. SOC. 74,438-441. 18. Ehrlich, G. & Doty, P. (1954) J . Amer. Chem. SOC. 76,3764-3777. 19. Arnold, R. & Overbeek, J. Th. G. (1950) Rec. Trau. Chim. 69,192-206. 20. Chou, P. Y. & Fasman, G. D. (1974) Biochemistry 13,222-245.
Received June 6,1976 Accepted November 29,1976
