α-Helix nucleation constant in copolypeptides of alanine and ornithine or lysine

Article abstract of DOI:10.1021/ja982319d

The α-helix is one of a small number of fundamental structural motifs of the peptide backbone that are abundant in native proteins. The forces responsible for its stability have attracted a great deal of theoretical and experimental attention. Helix formation can naturally be considered in terms of two processes, initial nucleation of a helix from a sequence of disordered residues and propagation or growth of helical structure from such a nucleus. Data from a variety of short peptide and polypeptide models have revealed more details about the propagation of helix structure than about helix nucleation. To investigate helix nucleation, we have synthesized two series of high molecular weight polypeptides containing differing ratios of alanine and one of the basic side chains, ornithine or lysine; poly L-alanine is insoluble in water. The CD signals of these copolymers have been analyzed by a program that evaluates the helix content in terms of the experimental chain-length distribution and composition, with the helix nucleation constant (σ value) and the propagation constants (s values) for the amino acids involved. Fitting the CD data allows the determination of the propagation constants for Orn (s = 0.45) and Lys (s = 0.8) in addition to that of the helix nucleation constant once the s value for Ala is specified. The value of σ is sensitive to the dependence of the CD signal on helix length; using the Yang equation, [θ]₂₂₂ = -41000(n - x)/n, with x = 2.5, the nucleation constant value is σ = 0.004 ± 0.002 at 4 °C in the presence of 1 M salt. This value is consistent with earlier estimates based on analysis of the helix-coil transition in poly(Lys), poly(Glu), and shorter Ala-rich peptides. However, if x is taken to be zero, the resulting σ value is 0.02, considerably larger than the above estimates.

Full text of DOI:10.1021/ja982319d

10646
J. Am. Chem. Soc. 1998, 120, 10646-10652
R-Helix Nucleation Constant in Copolypeptides of Alanine and
Ornithine or Lysine
Jianxin Yang, Kang Zhao, Youxiang Gong, Alexander Vologodskii, and
Neville R. Kallenbach*
Contribution from the Department of Chemistry, New York UniVersity, New York, New York 10003
ReceiVed July 2, 1998
Abstract: The R-helix is one of a small number of fundamental structural motifs of the peptide backbone that
are abundant in native proteins. The forces responsible for its stability have attracted a great deal of theoretical
and experimental attention. Helix formation can naturally be considered in terms of two processes, initial
nucleation of a helix from a sequence of disordered residues and propagation or growth of helical structure
from such a nucleus. Data from a variety of short peptide and polypeptide models have revealed more details
about the propagation of helix structure than about helix nucleation. To investigate helix nucleation, we have
synthesized two series of high molecular weight polypeptides containing differing ratios of alanine and one of
the basic side chains, ornithine or lysine; poly L-alanine is insoluble in water. The CD signals of these
copolymers have been analyzed by a program that evaluates the helix content in terms of the experimental
chain-length distribution and composition, with the helix nucleation constant (σ value) and the propagation
constants (s values) for the amino acids involved. Fitting the CD data allows the determination of the propagation
constants for Orn (s ) 0.45) and Lys (s ) 0.8) in addition to that of the helix nucleation constant once the s
value for Ala is specified. The value of σ is sensitive to the dependence of the CD signal on helix length;
using the Yang equation, [θ]222 ) -41000(n - x)/n, with x ) 2.5, the nucleation constant value is σ ) 0.004
( 0.002 at 4 °C in the presence of 1 M salt. This value is consistent with earlier estimates based on analysis
of the helix-coil transition in poly(Lys), poly(Glu), and shorter Ala-rich peptides. However, if x is taken to
be zero, the resulting σ value is 0.02, considerably larger than the above estimates.
Introduction
fragments from proteins, primarily relying on CD spectroscopy
to assess the extent of helical structure present. While the helix
propagation constants of most natural side chains apart from
alanine do not stabilize R-helical structure, hydrophobic interac-
tions, salt bridges, and packing interactions can all exert
significant helix-stabilizing effects.1,8 One objective of these
efforts is then to determine the equilibrium effect of these
interactions on helix propagation.8,9 In the case of helix-capping
interactions, side chains such as Ser and Glu near the N termini
of helices and the Gly residue at the C terminus can interact
with NH or CO groups of the main chain, stabilizing helical
structure.5 However, since most chains that have been studied
experimentally contain between 11 and 22 residues, detailed
information concerning the nucleation of helical structure is
sparse, relative to that for the propagation reaction. The process
of nucleating R-helix formation is of fundamental importance
in developing a detailed understanding of the kinetics and
mechanism of helix formation. In this study, we investigate
high molecular weight Ala-rich polypeptide chains containing
Orn or Lys side chains for solubility. The chains are pseudo-
random copolymers containing different ratios of Ala and Orn
or Lys. Measurements of the CD spectra of these polypeptides
allow determination of the helix nucleation constant, assuming
a value for the propagation constant of alanine.
Studies of a large number of short helical model peptides in
aqueous solution have defined many of the dominant factors
that govern R-helix stabilization in aqueous solution.1 These
include the H-bonding of the backbone NH and CO groups
originally postulated by Pauling,2 electrostatic3 and van der
Waals interactions4 between appropriately spaced side chains,
capping of residues at the ends of short chains,5 and interactions
between charged or polar side chains and the helix dipole.6 Data
on model peptides have been interpreted by means of helix-
coil transition models7 that include contributions from each of
the above interactions.8 Much of the information available has
resulted from analysis of short helical peptide models or
(1) Kallenbach, N. R.; Lyu, P. C.; Zhou, H. X. Circular Dichroism and
the Conformational Analysis of Biomolecules; Plenum Press: New York,
1996; pp 201-259.
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1951, 37, 205-211.
(3) (a) Lyu, P. C.; Gans, P. J.; Kallenbach, N. R. J. Mol. Biol. 1992,
223, 343-350. (b) Scholtz, J. M.; Qian, H.; Robbins, V. H.; Baldwin, R.
L. Biochemistry 1993, 32, 9668-9676.
(4) Richards, F. M. Annu. ReV. Biophys. Bioeng. 1977, 6, 151-176.
(5) (a) Presta, L. G.; Rose, G. D. Science 1988, 240, 1632-1641. (b)
Lyu, P. C.; Zhou, H. X.; Jelveh, N.; Wemmer, D. E.; Kallenbach, N. R. J.
Am. Chem. Soc. 1992, 114, 6560-6562. (d) Lyu, P. C.; Wemmer, D. E.;
Zhou, H. X.; Pinker, R. J.; Kallenbach, N. R. Biochemistry 1993, 32, 421-
425. (e) Aurora, R.; Srinivasan, R.; Rose, G. D. Science 1994, 264, 1126-
1130.(f) Doig, A. J.; Chakrabartty, A.; Klinger, T. M.; Baldwin, R. L.
Biochemistry 1994, 33, 3396-3403.
(8) (a) Rohl, C. A.; Chakrabartty, A.; Baldwin, R. L. Protein Sci. 1996,
5, 2623-2637; (b) Mun˜oz, V.; Serrano, L. Nat. Struct. Biol. 1994, 1, 399-
409. (c) Andersen, N. H.; Tong, H. Protein Sci. 1997, 6, 1920-1936. (d)
Yang, J.; Spek, E. J.; Gong, Y.; Zhou, H. X.; Kallenbach, N. R. Protein
Sci. 1997, 6, 1264-1272.
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Lockhart, D. J.; Kim, P. S. Science 1993, 260, 198-202.
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(b) Lifson, S.; Roig, A. J. Chem. Phys. 1961, 34, 1963-1974.
(9) Finkelstein, A. V.; Ptitsyn, O. B. J. Mol. Biol. 1976, 103, 15-24.
10.1021/ja982319d CCC: $15.00 © 1998 American Chemical Society
Published on Web 10/01/1998

R-Helix Nucleation Constant
J. Am. Chem. Soc., Vol. 120, No. 41, 1998 10647
We apply a statistical-mechanical analysis to describe the
helix-coil transition in long chains composed of two types of
residues.12 It is assumed that the corresponding sequences are
random. Therefore, to simulate the properties of polypeptides
with specific average Ala/Orn or Ala/Lys composition, we
generated a large population of random sequences with corre-
sponding composition and calculated the average properties of
the ensemble, including the helix content. The value(s) of the
model parameters, σ, sAla, and sOrn or sLys which give the best
fit to the measured helix content values were determined. The
value of sAla alone is held fixed since this has been accurately
determined using both hydrogen exchange11 and CD experi-
ments on short peptides.1 Values for sOrn and sLys have been
determined in an alanine-rich environment by Baldwin’s
group;13 these values can be specified as well. In practice, the
given values are slightly different from the ones that give
minimal residuals in our calculations.
Figure 1. Nucleation process in an R-helix. The figure shows that six
dihedral angles are fixed to form the first hydrogen bond, while two
are needed to form a bond adjacent to an existing one. Curved arrows
represent the dihedral angles, and dotted lines represent the hydrogen
bond (adapted from Cantor, C. R. and Schimmel, P. R. Biophysical
Chemistry III; W. H. Freeman: New York, 1980; p 1049.
Results
Synthesis of Poly(Ala-Orn) and Poly(Ala-Lys) Polypep-
tides. The preparation of monomers and their polymerization
are illustrated in Figure 2. Experimental properties of the two
sets of polypeptides we synthesized, one containing Ala and
Orn side chains and the second containing Ala and Lys side
chains, are summarized in Table 1. The composition of the
polypeptides does not match the input NCA ratios. Thus, for
an input reaction ratio of Ala/Orn ) 2/1, the polymer contains
1.84/1, determined using NMR analysis. For a reaction ratio
of Ala/Orn ) 5/1, the resulting polymer contains 4.59/1. The
ratio (output/input) varies between 0.89 and 0.92 for the Ala/
Orn copolymers. For polypeptides consisting of alanine and
lysine, the ratio varies between 0.86 and 1.01. We did not obtain
a product with reaction ratio of Ala/Lys ) 5/1, possibly due to
its limited solubility in water.
CD Measurements. The CD spectra of all polypeptides
showed R-helix signals (minima at 222 and 208 nm, maximum
at 195 nm) characteristic of a mixture of R-helix and coil (Figure
3). The isodichroic point at around 203 nm is consistent with
a two-state description for each residue in the polypeptides.14
Taking the mean residue molecular weights (see Experimental
Section) as the theoretical molecular weight and the limiting
CD of an infinitely long helix to be [θ]222 ) -41 000 which
was measured using a synthetic poly(Ala) linked to PEG for
water solubility (U. Skarpidis, unpublished results), we can
estimate apparent helicity from the molar residue ellipticities
for all polypeptides at 222 nm (Table 1). The helix content of
the chains ranges from 50-80%, depending on the composition.
As expected if Ala is helix-stabilizing, the helix content from
the CD signal of the Ala/Orn polypeptides becomes progres-
sively greater as the alanine content increases. By contrast, in
the Ala/Lys series, the effect is much weaker, despite the
difference between the s values for Lys and Ala that have been
determined in short-chain peptide models (see Table 1 and
Figure 3).13,15
Figure 1 illustrates the process of nucleating an R-helix, with
the successive addition of a helical residue to the nucleated helix.
As shown, the process of nucleation mandates a set of three
adjacent residues in helical conformation, that is, having values
of the φ and ψ dihedral angles within the right-handed R-helix
domain, φ ) -64° ( 6° and ψ ) -40° ( 8°. Following an
argument due to Zimm and Bragg,7a if each of two dihedral
angles per segment (in the nucleation of a homopolypeptide) is
restricted by a fraction r of the phase space available to random
coil, then the propagation constant would be proportional to
r2h, where h is the equilibrium constant for H-bonding in the
backbone at the expense of solvent H-bonds. Forming the first
H-bond would then correspond to r6h, since six restricted angles
are involved, so that the nucleation constant, σ in Zimm and
Bragg’s7a notation or V2 according to Lifson and Roig,7b should
be roughly proportional to r.4 Thus, if the restriction on each
dihedral angle compatible with nucleation is 0.1, σ will be 10-4
,
leading to highly cooperative formation of helical structure. If
the restriction is less severe, for example, 0.3, helix formation
becomes less cooperative, and values of σ around 10-2 result.
Reported values are within these limits, as discussed below.
An equivalent view of helix cooperativity is that it reflects the
loss of favorable bonding interactions in four residues at each
end of a helix segment relative to that in residues in the middle.10
The extent of fraying at the ends has been used directly to
evaluate s in short, artificially nucleated chains,11b but this does
not allow precise determination of the nucleation constant.
Since helix initiation may well include transient 310 helix
formation in addition to that of the R-helix and conceivably
other conformations as well, helix initiation may not be an all-
or-none process in the sense just described and may, in fact,
vary with the number and kind of residues present. In the
context of a high molecular weight polypeptide, the nucleation
process can be approximated as all-or-none so that a chain of
50% helix consists of alternating and fluctuating sequences of
helix and coil residues with equal numbers of residues on
average. The mean length of each sequence depends both on
the nucleation constant and the composition of the side chains
in the molecule.
The effects of temperature and peptide concentration on the
CD signal of the polypeptides are illustrated in Figure 4. There
(12) Vedenov, A. A.; Dykhne, A. M.; Frank-Kamenetskii, M. D. SoV.
Phys. Usp. 1972, 14, 715-736.
(13) Chakrabartty, A.; Kortemme, T.; Baldwin, R. L. Protein Sci. 1994,
3, 843-852.
(14) (a) Yang, J. T.; Wu, C.-S. C.; Martinez, H. M. Methods in Enzymol.
1986, 130, 208-269. (b) Manning, M. C.; Woody, R. W. Biopolymers 1991,
31, 569-586. (c) Gans, P. L.; Lyu, P. C.; Manning, M. C.; Woody, R. W.;
Kallenbach, N. R. Biopolymers 1991, 31, 1605-1614.
(15) Padmanabhan, S.; York, E. J.; Stewart, J. M.; Baldwin, R. L. J.
Mol. Biol. 1996, 257, 726-734.
(10) Schellman, J. A. C. R. Lab. Carlsberg Ser. Chim. 1955, 29, 230-
259.
(11) (a) Rohl, C. A.; Baldwin, R. L. Biochemistry 1994, 33, 7760-7764.
(b) Zhou, H. X.; Hull, L. A.; Kallenbach, N. R.; Mayne, L.; Bai, Y.-W.;
Englander, S. W. J. Am. Chem. Soc. 1994, 116, 6482-6483.

10648 J. Am. Chem. Soc., Vol. 120, No. 41, 1998
Yang et al.
Figure 2. Synthetic scheme for the polypeptides of this study.
Table 1. Experimental Properties of Polypeptides
molecular weightsa
Ala/X Ratio
observedb
[θ]222
xAla
helicity(%)e
c
d
polypeptide
average
mean residue
DP
input
X ) Orn [Poly(Ala-Orn)]
55-04
55-13
23200
18200
25500
17600
114.6
103.1
98.2
202
176
260
189
2/1
3/1
4/1
5/1
1.84/1
2.84/1
3.56/1
4.59/1
-21400
-27800
-30100
-31900
0.650
0.740
0.780
0.820
0.528
0.688
0.741
0.788
55-23
55-33
93.2
X ) Lys [Poly(Ala-Lys)]
62-04
31000
18700
17400
116.8
108.0
102.0
265
173
171
2/1
3/1
4/1
2.01/1
2.73/1
3.45/1
-30800
-31700
-32400
0.670
0.730
0.775
0.758
0.785
0.802
62-13
62-23
a Average molecular weights were estimated by size exclusion chromatography and represented as number average molecular weight Mn.30 Mean
residue molecular weights were calculated from the ratio of Ala/Orn(Lys) determined by NMR. b Calculated from the integrals of NMR spectra.
c CD spectra were measured in 1 M NaCl/20 mM Na/PO4, pH 7, 4 °C in a 1-mm path-length cell. The polypeptide concentrations were 50 µg/mL.
The ellipticities ([θ]222 (deg‚cm2/dmol) in this table) were calculated by taking the mean residue molecular weights as the molecular weights used
in calculation. d The molar fraction of alanine in polypeptides. e The helicities were calculated by dividing -41000(n - x)/n, where x ) 2.5, from
[θ]222 of all polypeptides.
is significant residual ellipticity at 85 °C (Figure 4, panel A)
for polypeptides with higher alanine ratio (such as 55-33).
Moreover, the peptide concentration has no effect over the
concentration range of 12.5 µg/mL to 200 µg/mL (Figure 4,
panel B).
By contrast, the deconvolution of CD values using eq 2
reveals that the σ value is sensitive to the value of the cutoff
constant, x, in the Yang equation.29 This effect is shown in
Table 2, where it can be seen that σ varies from 0.02 if x ) 0
(16) (a) Barskaya, T. V.; Ptitsyn, O. B. Biopolymers 1971, 10, 2181-
2197. (b) Bychkova, V. E.; Ptitsyn, O. B.; Barskaya, T. V. Biopolymers
1971, 11, 2161-2179.
Determination of the Nucleation Constant of Alanine.
Determining the nucleation constant σ requires specification of
the propagation constants sAla, sLys, and sOrn together with the
compositions and length distributions of the polypeptides.
Values for the former parameters have been determined in short
Ala-rich peptides by Baldwin’s group, who reported s values
of 1.4-1.6 for Ala, 0.90 for Lys, and 0.56 for Orn in an aqueous
buffer with 1 M NaCl and at 0 °C.15 Other estimates of sAla
have been published; hydrogen exchange rate measurements on
(17) (a) Wojcik, J.; Altmann, K.-H.; Scheraga, H. A. Biopolymers 1990,
30, 121-134. (b) Scholtz, J. M.; Qian, H.; York, E. J.; Stewart, J. M.;
Baldwin, R. L. Biopolymers 1991, 31, 1463-1470.
(18) Padmanabhan, S.; York, E. J.; Gera, L.; Stewart, J. M.; Baldwin,
R. L. Biochemistry 1994, 33, 8604-9809.
(19) von Dreele, P. H.; Lotan, N.; Ananthanarayanan, V. S.; Scheraga,
H. A. Macromolecules 1971, 4, 408-417.
(20) Creamer, T. P.; Rose, G. D. Proc. Natl. Acad. Sci. U.S.A. 1992, 89,
5937-5941.
(21) (a) Blaber, M.; Zhang, X.-J.; Matthews, B. W. Science 1993, 260,
1637-1640. (b) Blaber, M.; Zhang, X.-J.; Matthews, B. W. Science 1993,
262, 917-918. (c) Myers, J. K.; Pace, C. N.; Scholtz, J. M. Proc. Natl.
Acad. Sci. U.S.A. 1997, 94, 2833-2837.
a prenucleated helical peptide, for example, give a value sAla
)
1.7 at 4 °C in good agreement with the preceding estimates.
However, the differences prove to have a negligible effect on
the σ value determined in this study: using sAla ) 1.4-1.7, the
σ values change only by 10%. Similarly, it can be seen that
the residuals are lower for sOrn ) 0.45 and sLys ) 0.80 than for
the values determined by Baldwin or in our previous work.15
The effect on the value of σ is not large, that is, less than 10%.
We have also investigated the effect of the chain-length
distribution on the σ value. This again proves to be weak, so
that the value of σ is not affected by assuming forms for the
chain-length distribution different from the experimentally
measured one.
(22) (a) Vasquez, M.; Scheraga, H. A. Biopolymers 1988, 32, 41-58.
(b) Ingwall, R. T.; Scheraga, H. A.; Lotan, N.; Berger, A.; Katchalski, E.
Biopolymers 1968, 6, 331-368; (c) Groebke, K.; Renold, P.; Tsang, K.
Y.; Allen, T. J.; MaClure, K. F.; Kemp, D. S. Proc. Natl. Acad. Sci. U.S.A.
1996, 93, 4025-4029. (d) Kemp, D. S.; Oslick, S. L.; Allen, T. J. J. Am.
Chem. Soc. 1996, 118, 4249-4255.
(23) Bierzynski, A.; Kim, P. S.; Baldwin, R. L. Proc. Natl. Acad. Sci.
U.S.A. 1982, 79, 2470-2474.
(24) Waley, S. G.; Watson, J. Proc. R. Soc. 1949, A199, 499-517.
(25) (a)Katchalski, E.; Spitnik, P. J. Am. Chem. Soc, 1951, 73, 3992-
3995. (b) Blout, E. R.; Karlson, R. H. J. Am. Chem. Soc. 1956, 78, 941-
946.
(26) (a) Ben-Ishai, D.; Berger, A. J. Org. Chem. 1952, 17, 1564-1570.
(b) Ben-Ishai, D. J. Org. Chem. 1954, 19, 62-66.

R-Helix Nucleation Constant
J. Am. Chem. Soc., Vol. 120, No. 41, 1998 10649
Figure 3. CD spectra of polypeptides. (A) Poly(Ala-Orn). The curves
correspond to the samples 55-04, 55-13, 55-23, 55-33, respectively, in
descending order near 222 nm. (B) Poly(Ala-Lys). The curves are 62-
04, 62-13, 62-23, respectively, in descending order near 222 nm. CD
spectra were measured in 1 M NaCl/20 mM Na/PO4, pH 7, 4 °C in a
1-mm path length cell. The polypeptide concentrations were 50 µg/
mL.
Figure 4. The temperature and concentration dependence of polypep-
tides 55-04 and 55-33. (A) Temperature measurement points were 4
°C, 25 °C, 50 °C, 75 °C, and 85 °C. (B) The concentration range of
polypeptide 55-33 was from 12.5 µg/mL to 200 µg/mL in 10 mM KF/1
mM phosphate and 1 M NaCl/20 mM Na/PO4.
to 0.004 for x ) 4, holding the s values constant. If we assume
that the cutoff is close to 3, the value of σ minimizes the residual,
and an uncertainty of a factor of 2 is introduced. The reason
for this behavior can be understood in terms of the variation of
the mean helix length in each polypeptide as a function of x;
for x ) 0, these range from 8 to 13 residues, while for x ) 4,
the mean helix length is significantly greater, 17-36 residues.
The mean helix lengths in these polypeptides are short enough
for the correction imposed by the length dependence of the CD
signal to be significant.
Table 2. Relation Between σ Value and Cut-Off Constanta
cut-off (x)
sigma
residual
0
2
3
4
0.016
0.008
0.004
0.004
0.0040
0.0026
0.0015
0.0032
a Value of σ is sensitive to the value of the cutoff constant, x. It can
be seen that σ varies from 0.02 if x ) 0 to 0.004 for x ) 4.
determine whether the values of σ for this system of host
polypeptides are sensitive to the value of x, we recalculated the
CD data of von Dreele et al.19 on copolymers of HBG and HPG,
the hydroxy-butyl and hydroxy-propyl glutamine residues. With
x ) 2.5 and s values close to those specified by von Dreele et
al.,19 we find a good fit to the data for σ ) 0.0002, suggesting
higher cooperativity than we find in the Ala-based polypeptides
of the present study. If the s values are allowed to vary, σ and
the s values for HBG and HPG cannot all be specified uniquely
from the data we used.
The Helix Nucleation and Helix-Coil Transition Models.
A variety of model helical peptides, polypeptides, and proteins
have been investigated in the effort to define the determinants
of R-helix stability. Short oligopeptide models tend to provide
evidence that consistent scales of helix propagation constants
(s values in Zimm-Bragg7a notation, or w values in Lifson-
Roig7b notation) for individual amino acids can be determined
experimentally, provided a sufficient set of side-chain-side-
chain interactions can be calibrated and included to allow for
the numerous potential modulating effects of sequence.8 Thus,
a matrix of side-chain-side-chain interactions,9 together with
Discussion
Polypeptide Design. Various polypeptide models have
previously been used to estimate σ; values have been proposed
that vary from below 10-4 to about 10-2, depending on the
polypeptide used and the solution conditions.16,17a In short,
synthetic peptides of variable chain length, up to a 50mer, fitting
the temperature-dependent CD spectra or HX rates to s values,
including an enthalpy term for the propagation constant, led to
an estimate of σ ) 0.002 for the nucleation constant,17b,11a which
agrees closely with our determination here.
The large variation in σ values obtained from Scheraga’s17
host-guest polypeptide models seems puzzling in the light of
our results. A possible reason may be the particular helix-
forming properties of the derivatized (hydroxybutyl- or hydroxy-
propyl)-L-glutamine side chains used as the host residue in the
host-guest copolymer series.18 The values of s (and potentially
σ as well) determined for guest residues in host-guest experi-
ments might be strongly influenced by helix-stabilizing (side
chain-side chain) interactions between the host residues. To

10650 J. Am. Chem. Soc., Vol. 120, No. 41, 1998
Yang et al.
N- and C-terminal capping effects,5 must be supplied in order
to predict the helix content of oligopeptides regardless of
context.1,8d Alanine-rich peptide models have played a notable
role in these studies, since Ala proves to be strongly helix-
stabilizing in many peptide13 and protein21 systems. This is
attributed to the fact that its methyl side chain minimizes the
unfavorable entropic effect required to confine bulkier and
longer side chains into the helical geometry.20 A roughly
consistent set of s values for each of the standard side chains
has been determined, using both peptide and protein mod-
els.8,13,20
Figure 5. Structures of NCAs of alanine, ornithine, and lysine.
of the CD signal on helix length (eq 2), indicating that the mean
helix lengths in these molecules is low. This proves to be true
also in the case of copolypeptides of HBG and HPG, the host
residues used in experiments by the Scheraga group.17a Ques-
tions that remain to be addressed include (i) whether the value
of the nucleation constant is independent of the side chain, as
appears to be the case from comparison of the available results,
(ii) whether the nucleation constant is temperature-dependent,
as it arguably should be,10 and (iii) if different values for the N
and C nucleation events may need to be introduced, rather than
the symmetric process implied by use of σ or V2 in the standard
Lifson-Roig formalism.7,23 It is clear that the presence of short,
capping sequences such as SxxE at the N terminus can strongly
influence the nucleation probability for R-helical structure.5 The
nucleation process in the absence of specific signals establishes
a baseline for assessing such effects relative to the intrinsic
nucleation process in peptides, polypeptides, or nascent proteins.
The results of the above studies are at striking variance with
substitution data on the HBG or HPG polypeptides from
Scheraga’s laboratory,17a block oligopeptide data from Schera-
ga’s group,22b and data on a series of short, prenucleated peptides
studied by Kemp’s group.22c,d In these dissenting reports, Ala
is found to be helix-indifferent rather than helix-stabilizing. The
helix-stabilizing effect of Ala found in other model systems is
attributed instead to different effects exerted by neighboring side
chains, in particular, the charged side chains needed to maintain
solubility. According to Scheraga,22a solvation effects due to
the presence of charged side chains such as Lys or Arg confer
an apparent helix-stabilizing effect on neighboring alanines. A
different mechanism is invoked by Kemp’s group; the presence
of three or more adjacent Ala side chains allows a long, charged,
side chain such as Lys to interact favorably with the helix
backbone via a charge-dipole interaction.22c,d In these experi-
ments, Lys interacts strongly via its CH2 groups, while the
shorter Orn side chain is much less effective.
Experimental Section
The picture derived from nucleated short chains by Kemp’s
group is inconsistent with the results of the present study. The
difficulty is that sAla ) 1.03, the unperturbed propagation
constant determined by Kemp’s group, does not lead to a
satisfactory fit to the CD data for the series of Ala/Orn
copolymers; the values of the residuals are more than 100 times
greater than those obtained with sAla )1.6, regardless of the σ
value or sOrn value chosen. In experiments on short prenucleated
helices, the presence of Lys was found to stabilize Ala neighbors
more effectively than that of either Orn or Ala itself.22c This
means that in the Ala/Lys series, the effective s value for Ala
should be larger than that in the Orn series. In fact, the two
are indistinguishable, as shown by fitting the data for each series
independently. While we cannot exclude an effect of Lys on
the propagation constant of adjacent Ala residues in the Ala/
Lys series, the low value of sAla seen in HPG or HBG
polypeptides or short Ala-containing blocks22 is inconsistent with
our CD data. Moreover, if the helix propensity of Ala is low
but stimulated by neighboring Lys side chains, the dependence
of the CD signal on Lys composition should be greater than in
the Orn copolymer series, but it is not (Table 1).
Materials and Reagent Purification. t-Boc-L-alanine was pur-
chased from Bachem, CA and used after drying on vacuum line
overnight. All other reagents were from Aldrich, WI. Acetophenone
was purified according to the procedure of Waley and Watson.24
Triethylamine was dried over CaH2. L-Ornithine and L-lysine mono-
hydrochloride were used without further purification. Dichloromethane
(DCM), N,N-dimethylformamide (DMF), hexane, petroleum ether (PE),
and ethyl acetate (EtOAc) were all anhydrous form and used without
further purification. All glassware was thoroughly cleaned and dried
in an oven at 200 °C before use.
Peptide Synthesis and Purification. NCA polymerization has been
widely used for the synthesis of polypeptides with high molecular
weights.19,25,28b A series of Ala-Orn and Ala-Lys polypeptides were
synthesized by the copolymerization of NCAs of alanine, ornithine,
and/or lysine (Figure 5). After polymerization, the side-chain protection
groups on ornithine and lysine residues were removed by treatment
with hydrogen bromide.22b,26 The final purification was achieved by
dialysis against 0.5 M NaBr and distilled water and then lyophilization.
The polypeptides were stored at -80 °C until use. Figure 2 illustrates
the synthetic scheme used in this study.
Synthesis of NCAs of Alanine, Ornithine, and Lysine. To
synthesize Ala-NCA, we modified the procedure developed by Johnson’s
group.27 A typical synthesis is as follows: To 6 g of t-Boc-Ala (31.8
mmol) in 20 mL anhydrous CH2Cl2 was added oxalyl chloride (3.6
mL, 41.5 mmol) at 0 °C under argon atmosphere, followed by 2 drops
of DMF. The reaction mixture was allowed to warm to room
temperature and additional DMF (2-3 drops) was added dropwise until
no further gas evolved (approximately 1 h). After the reaction was
complete, the solvent was evaporated in vacuo, and the residue was
purified by column chromatography on predried silica gel. Pure Ala-
NCA was obtained by several recrystallizations in a DCM/hexane
system in 26% yield (940 mg): 1H NMR (200 MHz, acetone-d6) δ
1.50 (d, 1H, J ) 7 Hz), 4.59 (dq, 1H, J ) 1, 7 Hz), 7.84 (b, 1H); 13C
NMR δ 18.0, 54.5, 152.9, 172.9.
In summary, we have used two series of high molecular
weight copolypeptides containing Ala and Orn or Lys to
determine the helix nucleation constant. Our result, σ ) 0.004
( 0.002 at 4 °C and 1 M salt, agrees well with several values
determined by earlier studies, based on poly(Lys),27 poly(Glu),28
and a series of peptides with varying chain lengths, containing
repeats of Ala and Lys.30 Our results show that a key parameter
is the value of the cutoff constant x expressing the dependence
(27) Mobashery, S.; Johnston, M. J. Org. Chem. 1985, 50, 2200-2202.
(28) (a) Bergmann, M.; Zervas, L.; Ross, W. F. J. Biol. Chem. 1935,
111, 245-260. (b) Bodanszky, M.; Bodanszky, A. The practice of peptide
synthesis, Springer-Verlag: New York, 1994.
(29) Chen, G. C.; Yang, J. T. Anal. Lett. 1977, 10, 1195-1207.
(30) Cowie, J. M. G. Polymers: Chemistry and Physics of Modern
Materials. Chapman and Hall: New York, 1991; pp 8-10.
The synthesis of Orn-NCA and Lys-NCA was achieved by the
method of Bergmann et al. with slight modification.28a A typical run
was as follows: To 5.3 g of dibenzyloxycarbonyl-L-ornithine (12.8
mmol28a in 18 mL anhydrous CH2Cl2 was added PCl5 (4.0 g, 19.2 mmol)

R-Helix Nucleation Constant
J. Am. Chem. Soc., Vol. 120, No. 41, 1998 10651
at 10 °C under argon atmosphere, and the reaction mixture was stirred
1
for /2 h at 10 °C. After the reaction was complete, the solvent was
evaporated in vacuo, and the residue was purified by column chroma-
tography on predried silica gel. Pure Orn-NCA was obtained after
several recrystallizations in a DCM/PE system with 29% yield (1.09
g): 1H NMR (200 MHz, DMSO-d6) δ 1.49 (m, 1H), 1.69 (m, 1H),
3.03 (m, 1H), 4.46 (m, 1H), 5.03 (s, 1H), 7.36 (m, 6H), 9.10 (b, 1H);
13C NMR δ 25.4, 28.9, 40.0, 57.2, 65.5, 127.9, 128.0 (2C), 128.6 (2C),
137.5, 152.1, 156.4, 171.7. Lys-NCA was synthesized in a similar
way: 1H NMR (200 MHz, DMSO-d6) δ 1.39 (m, 2H), 1.70 (m, 1H),
3.01 (m, 1H), 4.45 (m, 1H), 5.04 (s, 1H), 7.35 (m, 6H), 9.10 (b, 1H);
13C NMR δ 22.0, 29.2, 31.0, 40.3, 57.4, 65.5, 128.0 (3C), 128.6 (2C),
137.5, 152.2, 156.3, 171.8.
Polymerization and Purification of Polypeptides. Polymerization
reactions were carried out in acetophenone with triethylamine as
initiator, with molar ratios of Ala to Orn or Lys in the range of 2/1,
3/1, 4/1, and 5/1. The ratio of amino acids to initiator (A/I ratio) was
15/1.25 After polymerization, the side-chain protecting groups of
ornithine/lysine were removed using 30% HBr in glacial acetic acid.26
A typical run for polyAla-Orn is described below.
In a round-bottom flask protected by argon and sealed by septa, a
mixture of 2 mmol NCAs (with appropriate molar ratio of 2/1, 3/1,
4/1, or 5/1 of Ala-NCA/Orn-NCA) and 18.6 µL triethylamine (0.133
mmol, A/I ratio ) 15/1) were added, respectively. The flask was
incubated at room temperature for 4-6 days until no increasing of
viscosity was observed.
After polymerization, the viscous product was dropped into a large
volume of MeOH to produce a gelatinous material, which was washed
several times with MeOH, dissolved in 20 mL 30% HBr/AcOH, and
stirred at room temperature for about 1 h. The mixture was washed
with PE and EtOAc several times, and the resulting precipitates were
dried on a vacuum line. The white precipitate was dissolved in 15
mL D2O then dialyzed overnight in dialysis tubing with a cutoff
molecular weight of 12 500 against 0.5 M NaBr and finally pure D2O,
respectively. After lyophilization, the polypeptide was obtained as a
loose, white, fibrous solid.
1
Figure 6. The H NMR of polypeptide 55-13. The spectrum shows
no peak in the range of 6-8 ppm, indicating completion of HBr
cleavage of side-chain protection groups of poly(Ala-Orn) and poly-
(Ala-Lys). Peaks A and B are used to calculate the residue ratio in
polypeptides. Peak A is assigned to be the R-CH of Ala and the peak
B the δ/ꢀ-CH2 of Orn/Lys.
Yang.29 About 5 mg of each polypeptide sample was accurately
weighed and added in D2O to make a 5 mg/mL first stock solution.
Samples for measurements were prepared by diluting the first stock
solutions with 100 mM KF, 10 mM phosphate buffer, pH 7, to a final
polypeptide concentration of 50 µg/mL and a buffer concentration of
10 mM KF, 1 mM phosphate buffer (containing 1 M NaCl/20 mM
Na/PO4 when needed) using a 1-mm path length cell. Three scans
were averaged with a 0.5-nm step in each case. Three to six
measurements were performed on each polypeptide sample.
Polypeptides of Ala-Lys were synthesized according to the same
procedure as that for polypeptides of Ala-Orn. The successful synthesis
of poly(Ala-Orn) and poly(Ala-Lys) polypeptides was confirmed by
1H NMR (Figure 6), CD spectroscopy (Figure 3), and their solubility
in water.
Helix-Coil Transition and the Determination of Nucleation
Constant. The standard Zimm-Bragg model of the helix-coil
transition was used to calculate circular dichroism values for the
copolypeptides. According to the model, each residue can adopt one
of two states which correspond to helix or coil conformations. Thus,
to define a state of a polypeptide one needs to specify the states of
each residue. The statistical weight of a polypeptide state with k helical
regions at specific locations would be written as
Determination of Residue Ratio in Synthetic Polypeptides. The
1
residue ratio in each polypeptide was determined by H NMR.32 The
NMR samples were prepared by dissolving about 5 mg of polypeptide
into 0.6 mL D2O with 0.1% TSP. The NMR resonances used for
composition determination were at 3.1 ppm (assigned to be δ/ꢀ-CH2
of Orn/Lys residues) and at 4.15 ppm (assigned to the R-CH of Ala
and Orn/Lys residues). The integrals of these two peaks were used to
determine the residue ratio, giving the results in Table 1.
Determination of Average Molecular Weight and Mean Residue
Molecular Weight of Polypeptides. The molecular weight distribution
in each of the copolypeptides was determined by size exclusion
chromatography under denaturing conditions, using a calibrated column
system that detects polypeptide by absorbance at 219 nm. (Michigan
Molecular Institute, Midland, MI); average and mean residue molecular
weights are listed in Table 1. The weight average data were
deconvoluted to yield the chain-length distribution, from which the
values of Mn and Mz were calculated. The mean residue molecular
weights used to calculate molar residue ellipticities in CD spectra were
determined from the chemical composition measured by NMR spec-
troscopy. The polypeptides are treated as repeats of a unit consisting
of x residues Ala:1 residue Orn/Lys, where x is the experimental ratio
of Ala/Orn(Lys). For example, the unit in polypeptide 55-04 consists
of 1.84 + 1 ) 2.84 residues with molar mass 195 × 1 + 1.84 × 71 )
325.6. The mean residue molecular weight is then 325.6 g/2.84 mol
) 114.6 g/mol. Mean residue molecular weights of the other
polypeptides were determined similarly and are listed in Table 1.
Circular Dichroism (CD) Measurements. CD spectra were
recorded on an Aviv DS60 spectropolarimeter equipped with a
thermoelectric temperature control. The wavelength was calibrated with
(+)-10-camphorsulfonic acid according to the method of Chen and
σk si
(1)
∏
i
where the product is taken over all H-bonded groups in the helical
state, σ is the helix nucleation constant, and si are the different
equilibrium constants for helix propagation.7a,12 The values of si depend
on the type of amino acid residues, and thus, only two different values
of si in our polypeptide system are required for a copolypeptide in a
particular solution condition, provided neighbor interactions are absent.
A chain of n residues assumes a large number of possible states
according to this model, and special algorithms are required for efficient
calculation of different chain characteristics for sufficiently large n
values. We used an iterative algorithm developed by Vedenov et al.12
and the procedure described below to calculate the average fraction of
residues in helix state, f, and the average number of helix regions, m,
for a heterogeneous polypeptide of particular sequence.
CD values were computed from the statistical mechanical analysis
using the set of helix-coil transition parameters, σ, sAla, sOrn, and sLys
The CD signal can be calculated from the mean helix length according
to the formula described by Yang et al.,14a a helix of n residues has a
CD signal at 222 nm given by
.

10652 J. Am. Chem. Soc., Vol. 120, No. 41, 1998
Yang et al.
of sAla and sOrn or sAla and sLys, the mean and standard deviation of the
chain-length distribution, and the composition of each copolymer are
specified. A trial value of σ is assumed. A population of chains
conforming to the experimental composition and chain length is
generated, and the helix content, number of helical regions and mean
length of helix regions in each simulated chain are computed
recursively.12 This is essentially the Zimm-Bragg next-neighbor
interaction model7a adapted to heteropolymers allowing calculation of
the helix and coil probabilities of residue i from those of the preceding
sequence of residues in the chain. The CD is then calculated using eq
2 above, for several values of x. The residual between the sum of
squares of the calculated and measured CD values is computed and
stored. Values of this residual are tabulated for different trial values
of σ and/or x, and the process is continued until the residuals reach a
minimum.
n - x
n
[θ]222(n) ) -41000
(2)
where x is a cutoff constant representing the effect of nonhelical amide
and carbonyl groups at the ends of peptide chains. The value x ) 2.5
was suggested by Yang et al.;14a theory suggests a slightly larger
number, x ) 4.0.14b The limiting value of [θ]222 ) -41 000 is that for
a long helix containing only Ala residues, which was measured using
a synthetic poly(Ala) linked to PEG for solubility (U. Skarpidis,
unpublished results).
To model the copolypeptides used in the experiments, we generated
1000 random sequences of two kinds of residues with appropriate
composition. Each sample population was taken to have a Gaussian
distribution of lengths with known mean value and variance. This
analysis of the helix-coil transition in long chains of two types of
residues assumes that the corresponding sequences are random. To
simulate the properties of polypeptides with specific average Ala/Orn
or Ala/Lys composition, we generated a large set of random sequences
with appropriate composition and calculated the average properties of
these. The value(s) of the model parameters, σ, sAla, and sOrn or sLys
which give the best fit to the measured values, that is, which minimize
the residual between theoretical and experimental CD values, were then
identified. This procedure is quite similar to the one used by Scheraga’s
group in evaluating helix-coil parameters for the natural amino acids
in the HBG or HPG copolypeptides.19
Acknowledgment. Drs. Yuejun Xiang and Hung-Jang Gi
contributed helpful advice on the synthesis of NCA’s. We are
grateful to Mr. Andrew H. Wood of the Michigan Molecular
Institute for determining the molecular weight distributions of
the polypeptides of this study. This work was supported by grant
GM 40746 from the NIH and a grant to N.R.K. from the Human
Frontiers of Science Program.
Helix-coil transition parameters were fit to experimental data as
follows. The CD values of each of the series of Ala-Orn and Ala-Lys
copolymers represent the set of observables. For a series, given values
JA982319D