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Triangular matrix representation of dimensionless helical hydrophobic moment ratios
Triangular matrix representation of dimensionless helical hydrophobic moment ratios Rachid C. Maroun, Robert W. McCord and Wayne L. Mattice* Department of Chemistry*, Louisiana State University, Baton Rouge, Louisana 70803 and Department of Internal Medicine, Tulane University Medical Center, New Orleans, Louisiana 70112, USA
(Received 2 May 1985; revised 3 October 1985) I f the hydrophobicity of the ith residue in an ~-helix is denoted by Hi, one can (following Eisenberg) define a correspondin9 vector, hi = aiH i. Here ai is a unit vector directed radially from the helix axis through C~. The vector sum of the hi for the N residues in an ~t-helix is denoted by h, and h2 is the square of the magnitude of h. In the absence of any correlation in the hi, we obtain h 2 = ~ Hi2, where the sum extends over all N residues in the helix. The dimensionless ratio h2/~ H 2 has the value 1 when the hi are uncorrelated. However, if hydrophobic residues occur on the opposite surface of a helix from the hydrophilic residues, h2/~ H 2 > 1. The h2/~ H 2 for the n(n-1)/2 helices that might occur in a chain of n residues are conveniently displayed as the elements in a symmetric n x n matrix. The jkth and kjth elements are h2/~ H~ for the helix that initiates at residue j and terminates at residue k. All of the h2/~ H 2 are retained in either of the trianoular matrices that together constitute the symmetric matrix. The largest element in the triangular matrix for 91ucagon is the entry for a helix that is nearly identical with the major helix found by Wiithrich when the peptide is bound to a zwitterionic micelle. Three related hormonal peptides have their maximum h2/~ H 2 in the same region of their respective triangular matrices. The triangular matrix for ~-tropomyosin shows that the h2/~. H~ are larger in the portion of the chain that forms the more stable helix in the in-register dimer. Keywords: Amphiphilichelices;glucagon; hydrophobicmoment;tropomyosin
Introduction Eisenberg and coworkers 1 define the helical hydrophobic moment, h, as ~ aiH i, where Hi and al are, respectively, a scalar representation of the hydrophobicity of amino acid residue i and a radial unit vector from the axis of the cthelix in the direction of C~.. Amphiphilic helices in crystalline proteins can be identified by their large Ihl/N, where Ihl denotes the magnitude of h for a helix comprised of N residues 1. Alternatively, one could focus attention on the dimensionless ratio h2/~, H 2, where h 2 is the square of the magnitude of h and the sum extends over all N residues 2. If there is no correlation whatsoever in the hi, h2 = ~ H 2 and the dimensionless ratio has the value of 1. The dimensionless ratio is greater than 1 if hydrophobic and hydrophilic residues tend to occur on opposite sides of a helix. A chain comprised of n residues can form n ( n - 1)/2 different helices of two or more residues. A suitable averaging scheme must be devised to obtain a single number that reflects the average amphiphilic character of these helices. One approach 2 views the helical hydrophobic moment in a manner closely related to the usual treatment of the dipole moment in flexible macromolecules 3. Polymer scientists use a dimensionless ratio, ( #2) 0 / ~ m 2, where (#2) 0 denotes the mean square unperturbed dipole moment and ~ m] is the sum of the squared magnitudes of the dipole moments for all polar groups in the chain. The dimensionless ratio is exactly 1 in the absence of any correlation in the dipole moments for 0141-8130/86/020073-06503.00 ,', 1986 Butterworth& Co. (Publishers) Ltd
the constituent groups. For most polymers, (#2) o / Z m~ is somewhat smaller than 1, signifying a preference for conformations in which there is partial cancellation of the group dipole moments. A dimensionless helical hydrophobic moment ratio can be defined as ( h 2 ) / ( H 2) 2. The mean square hydrophobic moment for all helices is denoted by (h2), and ( H 2) is the average of y' H/2 for those helices. The dimensionless ratio is exactly 1 in the absence of any correlation in the aiHi 2. If helical segments are weighted using the a, s determined for amino acid residues in 'host-guest' copolymers in water 4, ( h 2) / ( H 2) for 40 proteins ranges from 0.56 to 3.58 5.6. The average is 1.24, which signifies a slight preference for helices that are amphiphilic, i.e. helices in which residues with Hi < 0 prefer one side of the helix while residues with Hi> 0 occur preferentially on the other side. Rather than seek a single number that is the result of an averaging over all possible helices, one may retain all n ( n - I)/2 of the h2/2 H 2 for a chain of n residues. These h 2 / 2 H2iare conveniently displayed as the elements in an n × n symmetric matrix. Thejkth and kith elements are h2/ H 2 for the helix that initiates at residuej and terminates at residue k. All of the h2/Z H2i are retained in either of the triangular matrices that constitute the symmetric matrix. Space is utilized more efficiently if only one of the triangular matrices is presented. The information contained in these triangular matrices is illustrated here for three types of polypeptides: two melittins, four homologous hormonal peptides, and ~t-tropomyosin. In
Int. J. Biol. Macromol., 1986, Vol 8, April
73
Trianqular helical hydrophobic moment matrices: R. C. Maroun et al.
some cases it is helpful to also have available triangular matrices that show the probability for observation of a helix that initiates at residuej and terminates at residue k.
Calculations
U=
With Janin's hydrophobicities 7, ~ H 2 is simply calculated
w
0
0
0
0
0
0
0
w
0
0
0
0
0
0
0
0
w
0
0
0
0
0
0
0
0
0
0
0
0
o
o
o o o o
0
0
0
0
0
0
0
Ioo '0
as
H2i = H j 2 + H j2+ 1 + . . . + H k 2
1 0
0
0
0
0
0
0
_
w
0
0
0
0
0
0
~
w
0
0
0
0
00~
0
0
0
0
0
0
0
0
0
0
0
0
0
0'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t4,
0
0
0
0
0
0
0
0
(5)
~
0
0
0
0
0
0
0
'0
0
0
0
0
0
0
0
i0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
w
0
0
0
0
0
0
(1)
The geometry assumed for the a-helix is that reported for poly(L-alanine) in the solid state s. The unit twist, t, is 99.57 degrees. Therefore h is h = a j H j + T a j + ~H~+ 1 +T2aj+2Hj+2+...+Tk-JakHk
(2) U=
where T=[ c°st l sin t
-sint 1 cos t
(3)
and
h 2 = h" h
The a priori probability for a helix that initiates at residue j and terminates at residue k is denoted by Pjk. It was computed via equations (6) and (7),
Z=[10]U,U2
... U,,
1 . . . U n ~]O i
(7)
where Z denotes the configuration partition function, 0 is a null row or column of the dimension required so that matrices are conformable for multiplication, and the Ui are 8 x 8 statistical weight matrices in which the elements are I, O, a ~ %, s, or w 9. Using x for a ~ %. the statistical weight matrix for all residues except Pro is
U=
[~
(9)
:,
(10)
w 0 0 0 0 0 0 -
Ill)
The effect of these statistical weight matrices is to require that Pro occur in a non-helical region or at one of the first m positions in a helix, where m = 3 if the sequence is Gly-Pro, and m = 1 otherwise. The statistical weight for Pro is w if it is one of the first m residues in a helix. The estimate for w is 10 -z'3 (Ref. 9). All other residues contribute a statistical weight o f a ~'6 s if they are one of the initial three or final three residues in a helix. Intervening non-prolyl helical residues contribute a statistical weight of s. The only non-zero element in Vjk is the statistical weight for the helix that initiates at residue j and terminates at residue k. This statistical weight is (aft)+ ~aj+ 2ak_za k_ 10"k)lj6 sjsj+ 1 "'" Sk" It occurs in the last column of the first row of Vjk.The a, s for Cys are taken to be identical with those for Ser. Statistical weights for the remaining 18 residues are those determined for 'hostguest' copolypeptides in water at 25°C 4.
1
x
0
0
0
0
0
O;
0
0
x
0
0
0
0
0 !
0
0
0
x
0
0
0
0
0
0
0
0
s
.\
0
0[
0
0
0
0
s
.\
0
0
0
0
0
0
0
x
0
Melittins
0
0
0
0
0
0
0
x
1
x
0
0
0
0
0
Figure 1 depicts h2/E H 2 for the 325 helices of two or more residues that can be formed by each of two melittins. Each small square denotes a helix that initiates at residuej and terminates at residue k. Every element along the main diagonal has the value one because h z = H z for any 'helix' comprised of only one residue. The lower left triangular portion depicts the h 2 / ~ H 2 for the melittins from
(8)
oj
Equations (9), (10) and (11) are used for Pro when the preceding residue is Gly, Pro, or anything else, respectively.
74
U=
(6)
O]UIU2...Uj_IVjkUk+
pjk=Z-l[1
0
Int. J. Biol. Macromol., 1986, Vol 8, April
Triangular helical hydrophobic moment matrices: R. C. Maroun et al.
k--
I
Melittins (A florea) II
P
J
91
"1
-II ,-.p
problems when situated in the interior of an undistorted ~-helix. Fioure 2 depicts Pjk in the form of triangular matrices. When the statistical weights used are those dictated by short-range interactions for the various amino acid residues in water, the most probable helices (those with P~k> 0.005) include several that initiate at Pro 14, but none that propagates through Pro 14. If attention were restricted to helices that do not include Pro as an internal residue, the upper right and lower left quadrants of Fiyure 1 would be ignored. This deletion eliminates helices with h2/2 H 2 > 3, but most of the helices with h2/~ H 2 <1 survive. For this reason, ( h 2 ) / ( H 2 ) for either melittins, evaluated using the a, s for amino acid residues in water, is actually quite small 5. H o r m o n a l peptides related to g l u c a g o n
Figure 3 presents amino acid sequences for four
j--. I'
II' pI Melittins (A mellifero)
21'
\
[--)NNI I
homologous hormonal peptides: glucagon, vasoactive intestinal peptide, secretin, and residues 1-29 of growth hormone releasing factor. Pro does not occur in these peptides. Triangular matrices depicting the h2/Z H 2 are depicted in Figures 4 and 5. Reflection across the main diagonal produces more changes in these figures than in Figure 1 because the homology of the hormonal peptides is not as high as that of the melittins. Nevertheless, the patterns presented by the four hormonal peptides have several features in common. The upper right and lower left quadrants in Fiyures 4 and 5 are dominated by helices
Figure I Each element off the main diagonal of the 26 × 26 grid depicts h2/~ H~ for a helix that can be formed by either of two melittins. Both peptides contain 26 residues. The helix initiates at residuej and terminates at residue k. For the melittins from A. mellifera, j is plotted horizontally along the bottom, and k is plotted vertically along the left margin. The h2/~ H~ for this peptide occupy the triangular matrix to the left of the main diagonal. To the right of the main diagonal are the h2/~ H~ for the melittins from A. florea. For this peptide, j is plotted vertically along the right margin, and k is plotted horizontally at the top
I
21
KI
A. mellifera. Here j is plotted horizontally along the bottom, and k is plotted vertically along the left margin. The upper right triangular portion is the h2/~H~ for the melittins from A.florea. For this peptide, j is plotted vertically along the right margin, and k is plotted horizontally at the top. Figure I would be unchanged upon reflection across the main diagonal if both triangular fields were for melittins from the same species. The actual figure would show little change upon this reflection because the two melittins differ in sequence at only 5 of the 26 positions. The helix formed by residues 1-22 has the largest h2/~, H~, 4.6, in both melittins. Several helices that initiate in the vicinity of residues 1-5 and terminate at residues 20--22 have h2/ H~ greater than 4, signifying helices of exceptional amphiphilic character. Attention has previously been drawn to the amphiphilic character of melittins 1°, including the helix formed by residues 1-20 ~ The Pro at position 14 is denoted by 'P' along the margins of Figure 1. Helices with h2/~ H 2 > 4 require that residue 14 occupy a position in the helix interior. Melittins forms a bent helix, but even after distortion there is a large helical hydrophobic moment TM. If the helices did not bend, the helices with large h2/~",H 2 would be expected to have little stability because Pro presents severe steric
Melittins (A floreo) II P
I1-1
\
~-II
P-"
~
-P
21-
~
• 21
I
II I~ Melittins (A. mellifera)
<5
21
5-10 10-20 20-50
Figure 2 Triangular matrices equivalent to those in Figure 1,
except that each element is 1000 Pik instead of h2/~ H~. The Pjk for the melittins from A. mellilera and A..[loreaare found to the left and right, respectively, of the main diagonal
Int. J. Biol. Macromoi., 1986, Vol 8, April
75
Triangular helical hydrophobic moment matrices: R. C. Maroun et al.
HSQGTFTSDYSKYLDSRRAQDFVQWLMN HS D A V F T D N Y T R L R K Q M A V K K Y L N S
I LN
HSDGTFTSELSRLRDSARLQRLLQGLV YADA I FTNSYRKVLGQLSARKLLQD
I MSR
Figure 3 Amino acid sequences for (from top to bottom) glucagon, vasoactive intestinal peptide, secretin, and the first 29 residues of growth hormone releasing factor. The underlined portion denotes the segment with the largest h2/Z H~. The oneletter code used is A, Ala; D, Asp; E, Glu; F, Phe; G, Gly; H, His; I, lie; K, Lys; L, Leu; M, Met: N, Asn; Q, Gin; R, Arg; S, Ser; T, Thr; W, Trp; Y, Tyr
Glucogon i
I
II
I
I
range interactions (Fioures 6 and 7), and the helices with the largest hZ/~'H 4 and 5). This /l-a z2. (Figures correspondence is best illustrated by the locations of the broad stripes in the triangular matrices for glucagon, as well as the broad stripe and darkened square in the triangular matrices for growth hormone releasing factor (1-29). The cross-hatched area in the triangular matrix for secretin in Figure 7 corresponds to a cross-hatched region in Figure 5. The weakest correspondence is seen with vasoactive intestinal peptide. However, even in the case of vasoactive intestinal peptide, there is a much greater correlation between Pjk and hZ/Z H 2 than was the case with the melittins. In general, helices with the largest h2/ Y' H 2 in the hormonal peptides happen to be the helices that are the most probable when weighted by ~ and s. The glucagon helix with the highest h2/~ H~, residues 19-28, is nearly the same as the segment, residues 17 29, that forms a helix when bound to perdeuterated dodecyl
21 I
GRF (I- 29)
-I
I
il
21
-II
21
I
ii
2
~_1
-21
I
II
VlP
L
21
{~--I~1 ~ I~ <1
I-2
2-3
3-4
Figure 4 Triangular h2/~ H~ matrices for vasoactive intestinal peptide (left of the main diagonal) and glucagon (right of the main diagonal) with h2/~ H 2 < 1, in marked contrast to the pattern seen with the melittins in Figure 1. Most of the helices with large h2/~ H 2 are located near the carboxyl terminus. The hZ/~H } for these helices occur in the lower right quadrants of Figures 4 and 5. The helices with the largest h2/ ~ H2~ are listed in Table I and underlined in Figure 3. A detailed comparison of Figures 4 and 5 shows that the two triangular matrices with the most features in c o m m o n are those for secretin and the first 29 residues of growth hormone releasing factor. Figures 6 and 7 depict Pjk for glucagon, vasoactive intestinal peptide, secretin, and residues 1-29 of growth hormone releasing factor. The most probable helix is found in the carboxyl terminal half of all four hormonal peptides. There is a close correspondence between the location of the most probable helices, based on short-
76
II
Int. J. Biol. Macromol., 1986, Vol 8, April
I-2
2-3
3-4
Figure 5 Triangular 112/2H 2 matrices for secretin (left of the main diagonal) and the first 29 residues of growth hormone releasing factor (right of the main diagonal) 1 Selected helices with large homologous hormonal peptides
Table
h2/~H~
in
four
Residues in helix Peptide
21-28
19-26
19- 28
Vasoactive intestinal peptide Growth hormone releasing factor (1-29) Secretin Glucagon
2.9"
2.0
2.4
3.1"
2.8 3.3" 3.6
2.9 2.9b 3.9"
2.3 h 3.4
° Denotes largest h2/~ H2~for each peptide b Fragment ends at residue 27 because secretin contains 27 residues
Triangular helical hydrophobic moment matrices: R. C. Maroun et al.
Glucagon II
21
!
I
-I
II
IK'XI
[]
21
21
phosphocholine micelles ~3. The location of the latter helix was deduced by two-dimensional n.m.r, measurements and distance geometry calculations ~3. Circular dichroism spectra show a significant helix content is induced in glucagon and secretin, but not vasoactive intestinal peptide, upon interaction with lysophosphatidyl choline (palmitolyl) 14. Figures 4 and 5 show that glucagon and secretin have available a greater variety of helices with large h2/~H 2 than does vasoactive intestinal peptide. These helices may be responsible for the circular dichroism changes induced in glucagon and secretin. A much different set of circular dichroism spectra is seen when the lipid used for complex formation is anionic instead ofzwitterionic. Vasoactive intestinal peptide then shows the greatest amount of helix formation, presumably as a consequence of its higher content of amino acid residues with cationic side chains ~5.
~-Tropomyosin
!
!
II
21
VIP
<5 5-10 10-20 2 0 - 3 0 Figure 6 Triangularmatrices depicting lOOOpik for vasoactive intestinal peptide (leftof the main diagonal)and glucagon (right of the main diagonal)
GRF (I- 29)
I I~1~.
% N
II o
21 I
IS]
II
[]~
21
II
21
1
I
I
I
II
21
The ~-tropomyosin chain contains 284 residues, none of which is Pro 16. Figure 8 depicts h2/~ H 2 for the 40186 helices that might be formed by ~-tropomyosin. The amino terminal half of the chain contains more helices with large h2/~ H 2 than does the carboxyl terminal half, as shown by the extensive cross-hatched region in the upper left portion of the triangular matrix. The profile for (h2>/(H2> for tropomyosin fragments also shows 6, although in more rudimentary fashion, that the helices in the amino terminal half of the chain have greater amphiphilic character than do those in the carboxyl terminal half. The conformation adopted by tropomyosin in physiological media is a coiled-coil 17, parallel is, in register 19-2~ dimer with an exceptionally high helix content 22'23. The large helix content is a consequence of favourable helix-helix interaction in the dimer 24-26. Thermal denaturation of dimeric tropomyosin fragments demonstrates that the interacting helices are more stable in the amino terminal 133 residues than in the carboxy terminal 151 residues 26'27. In physiological media, favourable helix-helix interaction is a major factor
Secrefin
<5 5-10 10-20 2 0 - 3 0 3 0 - 4 0 Figure 7 Triangular matrices depicting 1000 Pjk for secretin (left of the main diagonal) and the first 29 residues of growth hormone releasing factor (right of the main diagonal)
I00
200
,oo
z6o
Figure 8 Triangular h2/~ H 2 matrices for ct-tropomyosin
Int. J. Biol. Macromol., 1986, Vol 8, April
77
Triangular helical hydrophobic m o m e n t matrices: R. C. M a r o u n et al.
responsible for the high helix c o n t e n t of native dimeric t r o p o m y o s i n a n d of the dimeric f r a g m e n t s / 4 27. A m p h i p h i l i c helices have the p o t e n t i a l for f a v o u r a b l e helix-helix interaction. This p o t e n t i a l is realized in the melittins tetramer, which has the h y d r o p h o b i c g r o u p s in the interior a n d therefore p r o d u c e s a near c a n c e l l a t i o n of the large h c o n t r i b u t e d by the four molecules ~°. If the h y d r o p h o b i c surfaces of two a m p h i p h i l i c helices in t r o p o m y o s i n are in c o n t a c t in the dimer, the dimeric helices s h o u l d be m o r e stable t h a n the n o n i n t e r a c t i n g m o n o m e r i c helices. Therefore the p a t t e r n in Figure 8 is consistent with the o b s e r v a t i o n that the helical d i m e r formed by residues 1-133 is m o r e stable t h a n the d i m e r formed by residues 134 284
References I 2 3 4 5 6 7 8 9 10 11
Conclusion The t r i a n g u l a r m a t r i x r e p r e s e n t a t i o n of h 2 / 2 H 2 for the n ( n - 1)/2 possible helices in a chain of n residues can easily identify h o m o l o g o u s peptides, as shown by the results for two melittins a n d four h o m o l o g o u s h o r m o n a l peptides. These matrices also are of assistance in understanding the p r o p e r t i e s of systems where a m p h i p h i l i c helices are i m p o r t a n t . T h e region in gtucagon that becomes helical when this p e p t i d e is b o u n d to a p e r d e u t e r a t e d d o d e c y l p h o s p h o c h o l i n e micelle is a region with a large II2/Z H 2. T h r e e o t h e r h o r m o n a l peptides have their highest h 2 / ~ H 2 in very nearly the same p o r t i o n of the chain as does glucagon. The m o r e stable half of the t r o p o m y o s i n d i m e r is that half with the higher
Acknowledgement This research was s u p p o r t e d by N a t i o n a l F o u n d a t i o n Research G r a n t P C M 81-18197.
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Int. J. Biol. M a c r o m o l . , 1986, Vol 8, April
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299, 371
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Science 27
Hamed, M. M. and Mattice, W. L. Biopolymers 1984, 23, 201 Flory, P. J. Macromolecules 1974, 7, 381 Sueki, M., Lee, S., Powers, S. P., Denton, J. B., Konishi, Y. and Scheraga, H. A. Maeromolecules 1984, 17, 148 Hamed, M. M. and Mattice, W. L. Biopolymers 1984, 23, 1057 Hamed, M. M. and Manice, W. L./nt. J. Biol. Maeromol. 1985, 7, 15 Janin, J. Nature 1979, 277, 491 Arnott, S. and Dover, S. D. J. Mol. Biol. 1967, 30, 209 Maroun, R. C. PhD Dissertation 1983, Louisiana State University, Baton Rouge, LO, USA, Chapter 2 Eisenberg, D., Weiss, R. M., Terwilliger, T. C. and Wilcox. W. J. Chem. Soc. Faraday Syrnp. 1982, 17, 109 De Grado, W. F., Kezdy, F. J. and Kaiser, E. T. J. Am. Chem. Soc. 1981, 103, 679 Terwilliger, T.C. andEisenberg, D.J. BioI. Chem. 1982,257,6010 Braun,W., Wider, G., Lee, K. H. and Wiithrich, K. J. Mol. Biol.
1983, 169, 921 Hamed, M. M., Robinson, R. M. and Mattice, W. L. Biopolymers 1983, 22, 1003 Robinson, R. M., Blakeney, E. W. and Mattice, W. L. Biopolymers 1982, 21, 1217 Sodek, J., Hodges, R. S. and Smillie, L. B. d. Biol. Chem. 1978,253, 1129 Crick. F. H. C. Aeta Crystalloqr. 1953, 6, 689 Caspar, D. L. D., Cohen, C. and Longley, W. d. Mol. Biol. 1969, 41, 87 Stewart, M. FEBS Lett. 1975, 53, 5 Johnson, P. and Smillie, L. B. Biochem. Biophys. Res. Commtm. 1975, 64, 1316 Lehrer, S. S. Proc. Nail Acad. Sci. USA 1975, 72, 3377 Cohen, C., Szent-Gyorgyi, A. G. d. Am. Chem. Soc. 1957, 79, 248 Holtzer, A., Clark, R. and Lowey, S. Biochemistry 1965, 4, 2401 Hodges, R., Sodek, J., Smillie, L. and Jurasek, L. Cold Sprin~ Harbor Syrup. Quam. Biol. 1972, 37, 299 McLachlan, A. and Stewart, M. J. Mol. Biol. 1975, 98, 293 Pato, M.D.,Mak, A.S. andSmillie, L.B.J. BioI. Chem. 1981,256,
593 Skolnick, J. and Holtzer, A. Maeromolecules 1983, 16, 1548
(Received 2 May 1985; revised 3 October 1985) I f the hydrophobicity of the ith residue in an ~-helix is denoted by Hi, one can (following Eisenberg) define a correspondin9 vector, hi = aiH i. Here ai is a unit vector directed radially from the helix axis through C~. The vector sum of the hi for the N residues in an ~t-helix is denoted by h, and h2 is the square of the magnitude of h. In the absence of any correlation in the hi, we obtain h 2 = ~ Hi2, where the sum extends over all N residues in the helix. The dimensionless ratio h2/~ H 2 has the value 1 when the hi are uncorrelated. However, if hydrophobic residues occur on the opposite surface of a helix from the hydrophilic residues, h2/~ H 2 > 1. The h2/~ H 2 for the n(n-1)/2 helices that might occur in a chain of n residues are conveniently displayed as the elements in a symmetric n x n matrix. The jkth and kjth elements are h2/~ H~ for the helix that initiates at residue j and terminates at residue k. All of the h2/~ H 2 are retained in either of the trianoular matrices that together constitute the symmetric matrix. The largest element in the triangular matrix for 91ucagon is the entry for a helix that is nearly identical with the major helix found by Wiithrich when the peptide is bound to a zwitterionic micelle. Three related hormonal peptides have their maximum h2/~ H 2 in the same region of their respective triangular matrices. The triangular matrix for ~-tropomyosin shows that the h2/~. H~ are larger in the portion of the chain that forms the more stable helix in the in-register dimer. Keywords: Amphiphilichelices;glucagon; hydrophobicmoment;tropomyosin
Introduction Eisenberg and coworkers 1 define the helical hydrophobic moment, h, as ~ aiH i, where Hi and al are, respectively, a scalar representation of the hydrophobicity of amino acid residue i and a radial unit vector from the axis of the cthelix in the direction of C~.. Amphiphilic helices in crystalline proteins can be identified by their large Ihl/N, where Ihl denotes the magnitude of h for a helix comprised of N residues 1. Alternatively, one could focus attention on the dimensionless ratio h2/~, H 2, where h 2 is the square of the magnitude of h and the sum extends over all N residues 2. If there is no correlation whatsoever in the hi, h2 = ~ H 2 and the dimensionless ratio has the value of 1. The dimensionless ratio is greater than 1 if hydrophobic and hydrophilic residues tend to occur on opposite sides of a helix. A chain comprised of n residues can form n ( n - 1)/2 different helices of two or more residues. A suitable averaging scheme must be devised to obtain a single number that reflects the average amphiphilic character of these helices. One approach 2 views the helical hydrophobic moment in a manner closely related to the usual treatment of the dipole moment in flexible macromolecules 3. Polymer scientists use a dimensionless ratio, ( #2) 0 / ~ m 2, where (#2) 0 denotes the mean square unperturbed dipole moment and ~ m] is the sum of the squared magnitudes of the dipole moments for all polar groups in the chain. The dimensionless ratio is exactly 1 in the absence of any correlation in the dipole moments for 0141-8130/86/020073-06503.00 ,', 1986 Butterworth& Co. (Publishers) Ltd
the constituent groups. For most polymers, (#2) o / Z m~ is somewhat smaller than 1, signifying a preference for conformations in which there is partial cancellation of the group dipole moments. A dimensionless helical hydrophobic moment ratio can be defined as ( h 2 ) / ( H 2) 2. The mean square hydrophobic moment for all helices is denoted by (h2), and ( H 2) is the average of y' H/2 for those helices. The dimensionless ratio is exactly 1 in the absence of any correlation in the aiHi 2. If helical segments are weighted using the a, s determined for amino acid residues in 'host-guest' copolymers in water 4, ( h 2) / ( H 2) for 40 proteins ranges from 0.56 to 3.58 5.6. The average is 1.24, which signifies a slight preference for helices that are amphiphilic, i.e. helices in which residues with Hi < 0 prefer one side of the helix while residues with Hi> 0 occur preferentially on the other side. Rather than seek a single number that is the result of an averaging over all possible helices, one may retain all n ( n - I)/2 of the h2/2 H 2 for a chain of n residues. These h 2 / 2 H2iare conveniently displayed as the elements in an n × n symmetric matrix. Thejkth and kith elements are h2/ H 2 for the helix that initiates at residuej and terminates at residue k. All of the h2/Z H2i are retained in either of the triangular matrices that constitute the symmetric matrix. Space is utilized more efficiently if only one of the triangular matrices is presented. The information contained in these triangular matrices is illustrated here for three types of polypeptides: two melittins, four homologous hormonal peptides, and ~t-tropomyosin. In
Int. J. Biol. Macromol., 1986, Vol 8, April
73
Trianqular helical hydrophobic moment matrices: R. C. Maroun et al.
some cases it is helpful to also have available triangular matrices that show the probability for observation of a helix that initiates at residuej and terminates at residue k.
Calculations
U=
With Janin's hydrophobicities 7, ~ H 2 is simply calculated
w
0
0
0
0
0
0
0
w
0
0
0
0
0
0
0
0
w
0
0
0
0
0
0
0
0
0
0
0
0
o
o
o o o o
0
0
0
0
0
0
0
Ioo '0
as
H2i = H j 2 + H j2+ 1 + . . . + H k 2
1 0
0
0
0
0
0
0
_
w
0
0
0
0
0
0
~
w
0
0
0
0
00~
0
0
0
0
0
0
0
0
0
0
0
0
0
0'
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t4,
0
0
0
0
0
0
0
0
(5)
~
0
0
0
0
0
0
0
'0
0
0
0
0
0
0
0
i0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
w
0
0
0
0
0
0
(1)
The geometry assumed for the a-helix is that reported for poly(L-alanine) in the solid state s. The unit twist, t, is 99.57 degrees. Therefore h is h = a j H j + T a j + ~H~+ 1 +T2aj+2Hj+2+...+Tk-JakHk
(2) U=
where T=[ c°st l sin t
-sint 1 cos t
(3)
and
h 2 = h" h
The a priori probability for a helix that initiates at residue j and terminates at residue k is denoted by Pjk. It was computed via equations (6) and (7),
Z=[10]U,U2
... U,,
1 . . . U n ~]O i
(7)
where Z denotes the configuration partition function, 0 is a null row or column of the dimension required so that matrices are conformable for multiplication, and the Ui are 8 x 8 statistical weight matrices in which the elements are I, O, a ~ %, s, or w 9. Using x for a ~ %. the statistical weight matrix for all residues except Pro is
U=
[~
(9)
:,
(10)
w 0 0 0 0 0 0 -
Ill)
The effect of these statistical weight matrices is to require that Pro occur in a non-helical region or at one of the first m positions in a helix, where m = 3 if the sequence is Gly-Pro, and m = 1 otherwise. The statistical weight for Pro is w if it is one of the first m residues in a helix. The estimate for w is 10 -z'3 (Ref. 9). All other residues contribute a statistical weight o f a ~'6 s if they are one of the initial three or final three residues in a helix. Intervening non-prolyl helical residues contribute a statistical weight of s. The only non-zero element in Vjk is the statistical weight for the helix that initiates at residue j and terminates at residue k. This statistical weight is (aft)+ ~aj+ 2ak_za k_ 10"k)lj6 sjsj+ 1 "'" Sk" It occurs in the last column of the first row of Vjk.The a, s for Cys are taken to be identical with those for Ser. Statistical weights for the remaining 18 residues are those determined for 'hostguest' copolypeptides in water at 25°C 4.
1
x
0
0
0
0
0
O;
0
0
x
0
0
0
0
0 !
0
0
0
x
0
0
0
0
0
0
0
0
s
.\
0
0[
0
0
0
0
s
.\
0
0
0
0
0
0
0
x
0
Melittins
0
0
0
0
0
0
0
x
1
x
0
0
0
0
0
Figure 1 depicts h2/E H 2 for the 325 helices of two or more residues that can be formed by each of two melittins. Each small square denotes a helix that initiates at residuej and terminates at residue k. Every element along the main diagonal has the value one because h z = H z for any 'helix' comprised of only one residue. The lower left triangular portion depicts the h 2 / ~ H 2 for the melittins from
(8)
oj
Equations (9), (10) and (11) are used for Pro when the preceding residue is Gly, Pro, or anything else, respectively.
74
U=
(6)
O]UIU2...Uj_IVjkUk+
pjk=Z-l[1
0
Int. J. Biol. Macromol., 1986, Vol 8, April
Triangular helical hydrophobic moment matrices: R. C. Maroun et al.
k--
I
Melittins (A florea) II
P
J
91
"1
-II ,-.p
problems when situated in the interior of an undistorted ~-helix. Fioure 2 depicts Pjk in the form of triangular matrices. When the statistical weights used are those dictated by short-range interactions for the various amino acid residues in water, the most probable helices (those with P~k> 0.005) include several that initiate at Pro 14, but none that propagates through Pro 14. If attention were restricted to helices that do not include Pro as an internal residue, the upper right and lower left quadrants of Fiyure 1 would be ignored. This deletion eliminates helices with h2/2 H 2 > 3, but most of the helices with h2/~ H 2 <1 survive. For this reason, ( h 2 ) / ( H 2 ) for either melittins, evaluated using the a, s for amino acid residues in water, is actually quite small 5. H o r m o n a l peptides related to g l u c a g o n
Figure 3 presents amino acid sequences for four
j--. I'
II' pI Melittins (A mellifero)
21'
\
[--)NNI I
homologous hormonal peptides: glucagon, vasoactive intestinal peptide, secretin, and residues 1-29 of growth hormone releasing factor. Pro does not occur in these peptides. Triangular matrices depicting the h2/Z H 2 are depicted in Figures 4 and 5. Reflection across the main diagonal produces more changes in these figures than in Figure 1 because the homology of the hormonal peptides is not as high as that of the melittins. Nevertheless, the patterns presented by the four hormonal peptides have several features in common. The upper right and lower left quadrants in Fiyures 4 and 5 are dominated by helices
Figure I Each element off the main diagonal of the 26 × 26 grid depicts h2/~ H~ for a helix that can be formed by either of two melittins. Both peptides contain 26 residues. The helix initiates at residuej and terminates at residue k. For the melittins from A. mellifera, j is plotted horizontally along the bottom, and k is plotted vertically along the left margin. The h2/~ H~ for this peptide occupy the triangular matrix to the left of the main diagonal. To the right of the main diagonal are the h2/~ H~ for the melittins from A. florea. For this peptide, j is plotted vertically along the right margin, and k is plotted horizontally at the top
I
21
KI
A. mellifera. Here j is plotted horizontally along the bottom, and k is plotted vertically along the left margin. The upper right triangular portion is the h2/~H~ for the melittins from A.florea. For this peptide, j is plotted vertically along the right margin, and k is plotted horizontally at the top. Figure I would be unchanged upon reflection across the main diagonal if both triangular fields were for melittins from the same species. The actual figure would show little change upon this reflection because the two melittins differ in sequence at only 5 of the 26 positions. The helix formed by residues 1-22 has the largest h2/~, H~, 4.6, in both melittins. Several helices that initiate in the vicinity of residues 1-5 and terminate at residues 20--22 have h2/ H~ greater than 4, signifying helices of exceptional amphiphilic character. Attention has previously been drawn to the amphiphilic character of melittins 1°, including the helix formed by residues 1-20 ~ The Pro at position 14 is denoted by 'P' along the margins of Figure 1. Helices with h2/~ H 2 > 4 require that residue 14 occupy a position in the helix interior. Melittins forms a bent helix, but even after distortion there is a large helical hydrophobic moment TM. If the helices did not bend, the helices with large h2/~",H 2 would be expected to have little stability because Pro presents severe steric
Melittins (A floreo) II P
I1-1
\
~-II
P-"
~
-P
21-
~
• 21
I
II I~ Melittins (A. mellifera)
<5
21
5-10 10-20 20-50
Figure 2 Triangular matrices equivalent to those in Figure 1,
except that each element is 1000 Pik instead of h2/~ H~. The Pjk for the melittins from A. mellilera and A..[loreaare found to the left and right, respectively, of the main diagonal
Int. J. Biol. Macromoi., 1986, Vol 8, April
75
Triangular helical hydrophobic moment matrices: R. C. Maroun et al.
HSQGTFTSDYSKYLDSRRAQDFVQWLMN HS D A V F T D N Y T R L R K Q M A V K K Y L N S
I LN
HSDGTFTSELSRLRDSARLQRLLQGLV YADA I FTNSYRKVLGQLSARKLLQD
I MSR
Figure 3 Amino acid sequences for (from top to bottom) glucagon, vasoactive intestinal peptide, secretin, and the first 29 residues of growth hormone releasing factor. The underlined portion denotes the segment with the largest h2/Z H~. The oneletter code used is A, Ala; D, Asp; E, Glu; F, Phe; G, Gly; H, His; I, lie; K, Lys; L, Leu; M, Met: N, Asn; Q, Gin; R, Arg; S, Ser; T, Thr; W, Trp; Y, Tyr
Glucogon i
I
II
I
I
range interactions (Fioures 6 and 7), and the helices with the largest hZ/~'H 4 and 5). This /l-a z2. (Figures correspondence is best illustrated by the locations of the broad stripes in the triangular matrices for glucagon, as well as the broad stripe and darkened square in the triangular matrices for growth hormone releasing factor (1-29). The cross-hatched area in the triangular matrix for secretin in Figure 7 corresponds to a cross-hatched region in Figure 5. The weakest correspondence is seen with vasoactive intestinal peptide. However, even in the case of vasoactive intestinal peptide, there is a much greater correlation between Pjk and hZ/Z H 2 than was the case with the melittins. In general, helices with the largest h2/ Y' H 2 in the hormonal peptides happen to be the helices that are the most probable when weighted by ~ and s. The glucagon helix with the highest h2/~ H~, residues 19-28, is nearly the same as the segment, residues 17 29, that forms a helix when bound to perdeuterated dodecyl
21 I
GRF (I- 29)
-I
I
il
21
-II
21
I
ii
2
~_1
-21
I
II
VlP
L
21
{~--I~1 ~ I~ <1
I-2
2-3
3-4
Figure 4 Triangular h2/~ H~ matrices for vasoactive intestinal peptide (left of the main diagonal) and glucagon (right of the main diagonal) with h2/~ H 2 < 1, in marked contrast to the pattern seen with the melittins in Figure 1. Most of the helices with large h2/~ H 2 are located near the carboxyl terminus. The hZ/~H } for these helices occur in the lower right quadrants of Figures 4 and 5. The helices with the largest h2/ ~ H2~ are listed in Table I and underlined in Figure 3. A detailed comparison of Figures 4 and 5 shows that the two triangular matrices with the most features in c o m m o n are those for secretin and the first 29 residues of growth hormone releasing factor. Figures 6 and 7 depict Pjk for glucagon, vasoactive intestinal peptide, secretin, and residues 1-29 of growth hormone releasing factor. The most probable helix is found in the carboxyl terminal half of all four hormonal peptides. There is a close correspondence between the location of the most probable helices, based on short-
76
II
Int. J. Biol. Macromol., 1986, Vol 8, April
I-2
2-3
3-4
Figure 5 Triangular 112/2H 2 matrices for secretin (left of the main diagonal) and the first 29 residues of growth hormone releasing factor (right of the main diagonal) 1 Selected helices with large homologous hormonal peptides
Table
h2/~H~
in
four
Residues in helix Peptide
21-28
19-26
19- 28
Vasoactive intestinal peptide Growth hormone releasing factor (1-29) Secretin Glucagon
2.9"
2.0
2.4
3.1"
2.8 3.3" 3.6
2.9 2.9b 3.9"
2.3 h 3.4
° Denotes largest h2/~ H2~for each peptide b Fragment ends at residue 27 because secretin contains 27 residues
Triangular helical hydrophobic moment matrices: R. C. Maroun et al.
Glucagon II
21
!
I
-I
II
IK'XI
[]
21
21
phosphocholine micelles ~3. The location of the latter helix was deduced by two-dimensional n.m.r, measurements and distance geometry calculations ~3. Circular dichroism spectra show a significant helix content is induced in glucagon and secretin, but not vasoactive intestinal peptide, upon interaction with lysophosphatidyl choline (palmitolyl) 14. Figures 4 and 5 show that glucagon and secretin have available a greater variety of helices with large h2/~H 2 than does vasoactive intestinal peptide. These helices may be responsible for the circular dichroism changes induced in glucagon and secretin. A much different set of circular dichroism spectra is seen when the lipid used for complex formation is anionic instead ofzwitterionic. Vasoactive intestinal peptide then shows the greatest amount of helix formation, presumably as a consequence of its higher content of amino acid residues with cationic side chains ~5.
~-Tropomyosin
!
!
II
21
VIP
<5 5-10 10-20 2 0 - 3 0 Figure 6 Triangularmatrices depicting lOOOpik for vasoactive intestinal peptide (leftof the main diagonal)and glucagon (right of the main diagonal)
GRF (I- 29)
I I~1~.
% N
II o
21 I
IS]
II
[]~
21
II
21
1
I
I
I
II
21
The ~-tropomyosin chain contains 284 residues, none of which is Pro 16. Figure 8 depicts h2/~ H 2 for the 40186 helices that might be formed by ~-tropomyosin. The amino terminal half of the chain contains more helices with large h2/~ H 2 than does the carboxyl terminal half, as shown by the extensive cross-hatched region in the upper left portion of the triangular matrix. The profile for (h2>/(H2> for tropomyosin fragments also shows 6, although in more rudimentary fashion, that the helices in the amino terminal half of the chain have greater amphiphilic character than do those in the carboxyl terminal half. The conformation adopted by tropomyosin in physiological media is a coiled-coil 17, parallel is, in register 19-2~ dimer with an exceptionally high helix content 22'23. The large helix content is a consequence of favourable helix-helix interaction in the dimer 24-26. Thermal denaturation of dimeric tropomyosin fragments demonstrates that the interacting helices are more stable in the amino terminal 133 residues than in the carboxy terminal 151 residues 26'27. In physiological media, favourable helix-helix interaction is a major factor
Secrefin
<5 5-10 10-20 2 0 - 3 0 3 0 - 4 0 Figure 7 Triangular matrices depicting 1000 Pjk for secretin (left of the main diagonal) and the first 29 residues of growth hormone releasing factor (right of the main diagonal)
I00
200
,oo
z6o
Figure 8 Triangular h2/~ H 2 matrices for ct-tropomyosin
Int. J. Biol. Macromol., 1986, Vol 8, April
77
Triangular helical hydrophobic m o m e n t matrices: R. C. M a r o u n et al.
responsible for the high helix c o n t e n t of native dimeric t r o p o m y o s i n a n d of the dimeric f r a g m e n t s / 4 27. A m p h i p h i l i c helices have the p o t e n t i a l for f a v o u r a b l e helix-helix interaction. This p o t e n t i a l is realized in the melittins tetramer, which has the h y d r o p h o b i c g r o u p s in the interior a n d therefore p r o d u c e s a near c a n c e l l a t i o n of the large h c o n t r i b u t e d by the four molecules ~°. If the h y d r o p h o b i c surfaces of two a m p h i p h i l i c helices in t r o p o m y o s i n are in c o n t a c t in the dimer, the dimeric helices s h o u l d be m o r e stable t h a n the n o n i n t e r a c t i n g m o n o m e r i c helices. Therefore the p a t t e r n in Figure 8 is consistent with the o b s e r v a t i o n that the helical d i m e r formed by residues 1-133 is m o r e stable t h a n the d i m e r formed by residues 134 284
References I 2 3 4 5 6 7 8 9 10 11
Conclusion The t r i a n g u l a r m a t r i x r e p r e s e n t a t i o n of h 2 / 2 H 2 for the n ( n - 1)/2 possible helices in a chain of n residues can easily identify h o m o l o g o u s peptides, as shown by the results for two melittins a n d four h o m o l o g o u s h o r m o n a l peptides. These matrices also are of assistance in understanding the p r o p e r t i e s of systems where a m p h i p h i l i c helices are i m p o r t a n t . T h e region in gtucagon that becomes helical when this p e p t i d e is b o u n d to a p e r d e u t e r a t e d d o d e c y l p h o s p h o c h o l i n e micelle is a region with a large II2/Z H 2. T h r e e o t h e r h o r m o n a l peptides have their highest h 2 / ~ H 2 in very nearly the same p o r t i o n of the chain as does glucagon. The m o r e stable half of the t r o p o m y o s i n d i m e r is that half with the higher
Acknowledgement This research was s u p p o r t e d by N a t i o n a l F o u n d a t i o n Research G r a n t P C M 81-18197.
78
Int. J. Biol. M a c r o m o l . , 1986, Vol 8, April
Eisenberg, D., Weiss, R. M. and Terwilliger, R. C. Nature 1982.
299, 371
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Science 27
Hamed, M. M. and Mattice, W. L. Biopolymers 1984, 23, 201 Flory, P. J. Macromolecules 1974, 7, 381 Sueki, M., Lee, S., Powers, S. P., Denton, J. B., Konishi, Y. and Scheraga, H. A. Maeromolecules 1984, 17, 148 Hamed, M. M. and Mattice, W. L. Biopolymers 1984, 23, 1057 Hamed, M. M. and Manice, W. L./nt. J. Biol. Maeromol. 1985, 7, 15 Janin, J. Nature 1979, 277, 491 Arnott, S. and Dover, S. D. J. Mol. Biol. 1967, 30, 209 Maroun, R. C. PhD Dissertation 1983, Louisiana State University, Baton Rouge, LO, USA, Chapter 2 Eisenberg, D., Weiss, R. M., Terwilliger, T. C. and Wilcox. W. J. Chem. Soc. Faraday Syrnp. 1982, 17, 109 De Grado, W. F., Kezdy, F. J. and Kaiser, E. T. J. Am. Chem. Soc. 1981, 103, 679 Terwilliger, T.C. andEisenberg, D.J. BioI. Chem. 1982,257,6010 Braun,W., Wider, G., Lee, K. H. and Wiithrich, K. J. Mol. Biol.
1983, 169, 921 Hamed, M. M., Robinson, R. M. and Mattice, W. L. Biopolymers 1983, 22, 1003 Robinson, R. M., Blakeney, E. W. and Mattice, W. L. Biopolymers 1982, 21, 1217 Sodek, J., Hodges, R. S. and Smillie, L. B. d. Biol. Chem. 1978,253, 1129 Crick. F. H. C. Aeta Crystalloqr. 1953, 6, 689 Caspar, D. L. D., Cohen, C. and Longley, W. d. Mol. Biol. 1969, 41, 87 Stewart, M. FEBS Lett. 1975, 53, 5 Johnson, P. and Smillie, L. B. Biochem. Biophys. Res. Commtm. 1975, 64, 1316 Lehrer, S. S. Proc. Nail Acad. Sci. USA 1975, 72, 3377 Cohen, C., Szent-Gyorgyi, A. G. d. Am. Chem. Soc. 1957, 79, 248 Holtzer, A., Clark, R. and Lowey, S. Biochemistry 1965, 4, 2401 Hodges, R., Sodek, J., Smillie, L. and Jurasek, L. Cold Sprin~ Harbor Syrup. Quam. Biol. 1972, 37, 299 McLachlan, A. and Stewart, M. J. Mol. Biol. 1975, 98, 293 Pato, M.D.,Mak, A.S. andSmillie, L.B.J. BioI. Chem. 1981,256,
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