- Email: [email protected]
Conformational study of the human immunoglobulin G1 hinge peptide
J. Mol. Biol. (1972) 64,221-236
Conformational Human linmunoglobulin
Study of the Gl Hinge Peptide
c. RENNEBOOGSQUILBINt
La&rat&urn
voor Algemene Biologic, Vrije Universiteit Bru-ssel,Belgium
(Received20 July 1971, and in revisedform 18 October1971) The IgGl
conformational energy of the central double pentapeptide of the human hinge
region
Cys-Pro-Prc+Cys-Pro has been calculated with the aid of S S S S Cys-Pro-Pro-@w-Pro semi-empirical potential functions. As a first approximation, the stereochemical code of Liquori (1969) has been used. It was found that a small number of families of similar backbone conformations is allowed for the chains of the cycle. But for moat backbone conformations, more than one cysteine side-chain conformation is compatible with the realization of the cycle, so that several different tertiary structures are possible for the hinge peptide. This result is very interesting for the discussion of the hinge mechanism.
1. Introduction Immunoglobulins consist of two identical light polypeptide chains (molecular weight 22,506) and two identical heavy polypeptide chains held together by diaulphide bonds and non-covalent interactions (Edelman, 1959; Edelman $ Poulik, 1961; Fleischman, Pain & Porter, 1962). Five different classesof immunoglobulins (IgG, IgA, IgM, IgD and IgE) have been defined according to the classof their heavy chains (Bull. World Health Organization, 1964). IgG has been the most thoroughly investigated. Its heavy chain ha9 a molecular weight of 53,990. The digestion of this globulin with papain releasestwo antigenbinding fragments (Fab) and one Fc fragment (Porter, 1969). The Fab fragments are made up of the amino-terminal half of the heavy chain and the whole light chain. The Fc fragment is a dimer of the remaining portions of heavy chains and is involved in complement fixation (Cohen & Porter, 1964). When pepsin is used, a fragment F(ab’)z is obtained which corresponds to the two Fab fragments joined by a disulphide bond (Nisonoff, Wissler, Lipman t Woernley, 1960). Within the classIgG, subclasseshave been distinguished by their antigenic determinants. For instance, there are four subclassesof human IgG: IgGl, IgG2, IgG3 and IgG4 (Grey L Kunkel, 1964; Terry & Fahey, 1964). A great number of amino-acid sequencesof IgG light chains (Dayhoff, 1969) and even the complete amino-acid sequenceof a heavy chain (Edelman et al., 1969) are now available. Little is known of the tertiary structure of these molecules; however, preliminary data have been obtained from crystallographic analysis of an entire IgGl myeloma protein (Terry, Matthews $ Davies, 1968) and of a human crystalline t Present Onderzoek,
Address: Belgium.
Aangesteld
Navorser
van 221
het
Nationaal
Fonda
voor
Wetenaohappelijk
222
C.
RENNEBOOC
- SQUILBIN
IgGl Fc fragment (Goldstein, Humphrey & Poljak, 1968). In these two papers, the evidence for the presence of a two-fold exis of symmetry is given. The most direct observations have been done by electron mioroscopy (Fenstein & Rowe, 1965; Valentine & Green, 1967) end have enabled the authors to postulate a Y shape model for the antihapten antibody with the hapten binding near the ends of the Fab segments. The data from hydrodynamic measurements and fluorescence polarization experiments have recently been reviewed in detail by Dorrington & Tanford (1970). These data, plus the results of electron microscopic studies would seem to suggest that the molecule consists of three domains connected by a hinge region which allows a limited flexibility of the molecule in solution and which is the most sensitive to enzymic cleavage. Furthermore, each domain would be composed of compact segments connected by a relatively exposed region which is less accessible to enzymes than the hinge region in the centre of the molecule. In Figure 1, the model for IgG proposed by Edelman & Gall (1969) and adapted by Dorrington & Tanford (1970) is shown. Considering the fundamental role of the hinge region in the flexibility of the molecule, and consequently in the molecule’s possibilities of physiological activity (combination with antigen), it would be interesting to obtain additional information about the three-dimensional structure of this region. The particular amino-acid sequence of the hinge peptides (Fig. 2) facilitates a theoretical calculation of the allowed conformations. The central double pentapeptide of the IgGl hinge region has been chosen for this study because the only X-ray diffraction data presently available concern this protein (Terry et al., 1968; Goldstein et al., 1968). Thus, there is a certain chance that its tertiary structure will be known soon and comparison with the models proposed in this paper will be possible. Moreover, it has been demonstrated that, for this protein, there exists a two-fold axis which passes through the middle of each S-S bond and which is perpendicular to them. This fact will greatly simplify the calculations in strongly reducing the number of possible conformations. Thus, the aim of this paper is to look for the possible tertiary structures of the human IgGl A
Enrymlc
cleavage
Fa
FIQ.
1. Yodel
for IgG
(from
Dorrington
& Tanford,
1970).
STUDY
OF THE
Species Human tIgG1 IgG2 Iga3 Igc4 Rabbit fIgG
HUMAN
IgG1
HINGE
PEPTIDE
223
Thr-His-Thr-C?gs-Pro-Pro-Cys-Pro-Ala-Pro-GluCys-Pro-Pro-Cys-Pro-Ala-(Pro,Glu), Glu Pro-Pro-Pro-Cys-Pro-Arg-Cys-Pro-Ala-Pro-GluGly-Pro-Pro-Cys-Pro-Pro-Cys-Pro-Ala-(Ser,Glu) -Pro-GluPro-Thr-Cys-Pro-Pro t See Frengione, Milstein & Pink, 1969. $ See Smith & Utsumi, 1967.
FIG. 2. Amino-&d
sequence of IgG hinge regions.
hinge peptide which result from local interactions. It must, of course, not be forgotten that its structure will also be influenced by long-range interactions with the rest of the polypeptide chains.
2. Calculation Procedure Computations of polypeptide conformation energiesdepend on the values of bond angles and bond lengths. The parameters used for the backbone are those of Corey t Pauling (1963). The N-H length is taken equal to 1.01 A and the C-H length to 1.08 A. The parameters for the cyst&e side chain are those of Mitchell (1958). The geometry of the proline proposed by Leung $ Marsh (1958) is used with someadjustments of the side-chain angles in order to close the ring. The proline imide group is assumedto be in the planar tram configuration. The conformation of an amino-acid residue in a polypeptide chain is defined by two dihedral anglesfor the backbone (4 around the N-C’ bond, # around the (2-C bond), and a certain number of dihedral angles x for the side chain (Fig. 3). The conventions of the IUPAC-IUB Commission on biochemical nomenclature (1970) are followed in this paper except that the x angles are ascribed zero values for the so-called &-conformation but are measuredin the range of 0 to 360”.
FIQ. 3. Cp _ r-C$‘+ I segment of a polypeptide chain. The segment is shown in B fully extended oonformation (4 = Q = 0”). The errows indicate the positive sense of rot&ion of the engles (IUPAC-IUB Commission on bioohemioal nomenolature, 1970).
224
C.
RENNEBOOG-
SQUILBIN
Two contributions to the internal energy were considered in the calculations: the electrostatic interactions and the Van der Waals interactions including a torsional potential (3 kcal.) around the c”-C/f single bond of the side chains. This torsional potential has minima at the staggered positions (De Coen, Elefante, Liquori & Damiani, 1967). The Van der Waals interactions are the sum over all pairwise interactions between atoms i and j of the molecule. Buckingham functions E(r,,) = A exp (--B T*,) C rllm6 with the parameters previously used by Liquori, Damiani & De Coen (1968) were chosen to express those interactions which depend on the values of the dihedral angles $,# and x. The electrostatic interaction energy is the sum of all pairwise electrostatic interaction energies between atoms carrying a partial charge. The data of Brant, Miller & Flory (1967) were used for the peptide group. In the present calculation, the nitrogen of the proline is assumed to be uncharged. The electrostatic energy is calculated separately to facilitate any future studies of the effect of a change in the dielectric constant on the conformational energies. The present calculations were carried out with a dielectric constant equal to 1.0. The energy map (z/ as a function of 4) for the backbone of a c _ 1 - c+ 1 polypeptide chain segment is characterized by regions of lower energy. Liquori (1969) called the most typical conformations in these regions, a, 6, c, d and a* although b, c, d for instance are not clear-cut minima. These five backbone low energy states were taken into account for the cysteine residues with one additional conformation, state e which is a low energy state when the electrostatic energy is added to the Van der Waals energy. The use of such a code (Table 1) is merely a convenient way of simplifying the calculation and reducing computer time by choosing the most typical conformations in the low energy regions. Steps of 60” were chosen for the side chain. TABLE
1
The stereochemical code
; : a* e
- 63” -166” -160” - 76” + 62” - 80”
- 49” +1iw + IO0 + 165” + 60” + looa
3. Results The study of the hinge peptide Cys-Pro-Pro-Cys-Pro S S $s-Pr o-I+ o-Czs-Pr 0 was carried out in four steps. (1) The C;t-l-q+, segments (Fig. 3) of proline and cysteiue were considered. It was confirmed that the only low energy states for the proline are a and d (Leach, Nemethy & Scheraga, 1966; Liquori, 1969) (Table 2).
STUDY
OF
THE
HUMAN
IgGl
HINGE
PEPTIDE
226
TABLE 2 Energies of the low energy states ojproline St&e
Van
5;
(kcul./mole)
Eleotrost&io
der W&s -0.8 -1.0
Total
-0.32.6
-1.11.6
A search was made for the side-chain conformations of the cysteine compatible with every backbone conformation taken into account. All conformations corresponding to Van der Waals energies greater than 20 kcal./mole were rejected. The results are given in Table 3. TABLE 3 Cysteine: number of xz values corrc.spon4&g tc a Van der Wd energy lower than 20 kc&/mole. 1800
a
6
b Ii
6( 66(
a* e
240’
6
3oo”
0”
6
-
6 6
6( 65(
6( 6( -
6
6
6
6
6
6
0’)
0”) 0”)
60”
0”) 0’)
120°
Total
4(6;:)
4(30;:)
26
6 6
5(
0”)
32 28
6;
0’)
0’)
6( 60’)
-
22 23 169
The
x1 values
of the rejected
conform&ions
are in brmkets.
(2) The dipeptides cysteylproline, prolyloyateine and prolylproline were analysed in order to see the influence of a proline on a carboxy- or ammo-terminal cysteine or proline. The criterion of 20 kcal./mole was also applied to the Van der Waals energy of the dipeptides cysteylproline and prolyloysteine. A proline does not change the number of “allowed” side-chain conformations for the cysteine when it precedes it but it diminishes this number by 1’7% when it follows the oysteine (Tables 4 and 5). Only the 132 allowed conformations of Table 4 were further used for both cysteines (see point 4). From the study of the dipeptide prolylproline, it appears that the conformations where the N-terminal proline is in state a, are less favourable for the Van der Waals as well as for the electrostatic energy (Table 6). As a first approach, and in order to reduce computer time, only the words with the N-terminal proline in cl were considered. (3) The peptide Cys-Pro-Pro-+ was then studied with a carbon (cd) replacing the hydrogen of the C-terminal peptide bond because a prolyl residue follows the cysteine (Pig. 4). The oysteine side chains were fixed in the conformation x1=240’, xz=1800 because it is the only x1 value which is allowed for any backbone conformations. Six backbone conformations (a, b, c, d, a*, e) were taken into account for the cysteyl 15
226
C. RENNEBOOG-
SQUILBIN TABLE
4
Cysteylproline: number of x2 values correspondingto a Van der Wads energy lower than 20 kcul./~~~le Xl HO0 \ state
240"
300"
0"
60"
1200
\ a
6
b
-
6 6
6 5(
i a*
66
6 6
65( 0") 6
e
6
6
6
5(
0")
0')
5( - 0")
6
-
6 60°) 5(
-
Total allowed conformations
22 22 27 18 22 21 132
The
x2 values
of the rejected
conformations
TABLE
are in brackets.
5
Lowest Van der Weals energy valuesfound for cysteylproline (ikal./mole). The proline is in d Side chain mgle
State a
b
c
d
a*
e
\
Xl
1800
X2
180"
60" 3.9
180° -0.6 180°
0.6
180"
TABLE
300"
300" -1.1
180"
180°
-0.6 300"
6
Energies of the dipeptide prolylproline (kcal.lmole) stat0s a a d
a d a
d d
Van
der Waals
3.5 4.1 -2.1 -1.8
Electrostatic
4.9 2.8 1.9 -1.7
Total
8.4 7.0 -0.2 -3.5
6.1 60"
STUDY
OF
THE
HUMAN
IgGl
HINGE
227
PEPTIDE
Proline 5
P $4 XLC4 2 I
Cysteine 4
X.
c:
4
%r
N.
I rP
C,P k
Y H4
03% c3 CO Proline 3
Proline 2
FIQ. through
4. Projection the cyst&e
of the central Hr atoms.
pentapeptide
of the human
IgGl
hinge
region
on a plane
passing
residues and two (a, d) for proline 3. Proline 2 was fixed in d. 72 “words” were thus considered. The results are summarized in Tables 7 and 8. It is interesting to compare the words with proline 3 in d which are more extended and those with proline 3 in a which are more compact. It can be seen that the change of proline 3 from d to a is accompanied by a decrease of the Van der Waals energy by an average of 0.9 koal./mole (with a maximum of 1.3 koal./mole) except when the C-terminal cyst&m has the a conformation. In this case, short-range interactions TABLE
7
Van der Wads and electrostaticenergiesof the words with Pro-Pro in d d (ikaE./mole) cys cys
\
1
Van
4 a
der Waals b c
energy d
a*
e
a
b
Electrostatic c
energy d
a*
e
b
1.0 0.5
0.8 0.3
2.4 1.9
1.0 0.6
2.5 2.2
2.3 1.8
-0.3 -4.7
-3.6 -8.5
-0.5 -5.2
-2.5 -7.2
-1.0 -5.1
-2.9 -7.6
: a* e
0.6 1.8 3.2 8.9
0.3 1.5 2.9 8.7
3.2 1.9 4.6 10.3
0.6 1.7 3.1 8.9
3.6 2.2 4.9 10.6
3.1 1.8 4.6 10.2
-1.3 -3.3 -1.7 -3.9
-6.0 -7.5 -6.2 -7.6
-1.7 -4.3 -2.1 -4.4
-3.7 -6.1 -3.9 -6.3
-1.7 -4.1 -2.1 -4.2
-4.1 -6.6 -4.4 -6.7
a
228
C.
RENNEBOOQ-
SQUILBIN TABLE
8
Van der Waals and electrostatic energies of the words with Pro-Pro d a (kc&./mole) ,-- * cys
\
Van
cys4 1
der Waals d
energy a*
e
-0.9 -0.4
1.8 1.3
0.5 1.0
1.6 2.8
-0430.4
2.6 1.4
4.2 10.0
1.8 7.6
4.0 9.8
a
b
;
>60.0 x50.0
-0.7 -0.1
2.0 1.5
ii
>lio*o >50*0
-0.60.6
a* e
>60*0 >60*0
2.0 7.8
G
f Not
Electrost&io
energy
G
d
-6.8 -0-l
-1.93.7
-3.22.5
-0.75.0
-4.70.6
1.8 0.6
-2.0 -4.9
-1.2l-9
-2.40.7
-0.13.2
-0.9 -3.9
3.2 9.0
-2.4 -6.0
1.4 -1.3
0.2 -2.2
2.5 -0.1
-1.6 -3.9
at
b
in
a*
e
oomputed.
(more than 50 kcal./mole) arise between the cd atom of proline 5 and the side chain of proline 2. Consequently, all the words containing both proline 3 and cysteine 4 in a were rejected. It is observed that in the dipeptide prolylproline, the difference in energy between dd and da is only O-3 kcal./mole. That means that a certain number of favourable interactions due to the London dispersion forces arises between pairs of atoms in the tetrapeptide when it has a more compact structure. The electrostatic energy of the tetrapeptide increases by an average of 3.6 kca1.l mole, which is just the difference between the electrostatic energies of the dipeptide prolylproline in dd and da. It should be noted that the results given in Tables 7 and 8 correspond to the energies of the words for the chosen side-chain conformations. Other side-chain arrangements could give lower energies. For instance, a rotation of x1 from 240 to 180” for a cysteine in c would represent an energy decrease of about 2 kcal./mole. (4) The following method was developed for computing all possible conformations of the hinge peptide in the stereochemical code approximation : the hydrogen attached to the sulphur of the cysteine aide chains was replaced by a false atom M at a distance of 1.02A from the sulphur (corresponding to half the length of the S-S bridge, Mitchell, 1958) in order to construct the two-fold axis. The perpendicularity of this axis will be tested with respect to the S-M segments of cyst&es 1 and 4. A given conformation was generated for one chain (Cys-Pro-Pro-Cys with a d). If it corresponded to one of the rejected conformations (see points 2 and 3), the next conformation was generated by rotating one of the angles; if not, the co-ordinates of the atoms were computed and the perpendicularity of both bonds M,S and MJ with respect to the dyad axis M1M4 was tested. If both angles did not deviate from 90” by more than 11*5”, the entire molecule was generated by a rotation of 180’ around the two&fold axis. The conformation was registered as allowed and its energy was computed. The preliminary study of the local interactions (points 1,2,3) allowed the reduction of the number of conformations to be examined from 62 x 362 x 22=186, 624 to 32,076. When the geometrical criterion was applied, this number fell to 1193. Only 33 among those geometrically allowed conformations have a negative Van der Waals energy. They can be denoted by 16 words. This means that for a certain number of words more than one side-chain conformation can give rise to a low energy cycle.
STUDY
OF
THE
HUMAN
IgGl
HINGE
PEPTIDE
229
The 16 words were classified in 7 families (Table 9) for the following reason: the geometry of the cycle depends only on the # angle of cysteine 1, the # rtngles of the prolines and the + angle of cysteine 4 but not on the 4 angle of cysteine 1 and the # angle of cysteine 4. Therefore, roughly the same cycles can be realized with different words when the side chains are disposed on the same manner. For instance, it is obvious that cysteine 1 in b or d will give the same cycle because both 4 angles are equal to 155”. Likewise, there is not a great change when cysteine 1 is in a* (&=SO’) or c ($=70”), or when cysteine 4 is in b ($*= -155”) or c (&= -GO”), or when it is in e (9&=-SO’), d (#,=-75”) or a (#*=-63’). TAEZE 9
Pam&es of w07+as of negative Van der Wads energy and number of cyclescorrespondingto eachuxnd I
clam*
II
2
a*daa* 2 cdaa+ 2
III
V
Iv
ddac
1
bdac
1
&de
2 2
d&la
1
dddd
VII
VI
cd&l
4
a+ddd cdda a*dda
1 5 1
cd&
4
dddo
3
cadc a%&
1 1
As expected, cysteine 1 never appears in a or e in the words of low energy because of the proline at its C-terminal end. For this reason, the words ending on a or e were also rejected as very improbable since a.proline follows cysteine 4 but is not explicitly considered in the calculation. There remain 11 words and 20 cycles. Table 10 gives the side-chain angle values (column 2), the energies (column 4) of these cycles, and the cosine of the angles between the dyad axis and the S-M segments(seecolumn 5).
4. Discussion Considering the approach which has been used, a choice between all the remaining words will not be attempted, but attempts will be made to obtain someinformation about the hinge mechanism of this peptide by more thoroughly studying the tertiary structure of the cycles generated from these words. The first thing to be done is to obtain more real structures, i.e. more linear disulphide bridges. It must not be forgotten that in s,first selection of the cycles, a minimum angle of 78.5” was tolerated between the dyad axis passing through the middle (M) of the S-S bridges and the S-M segments.These structures were taken as departure points of a refinement procedure. Rotations by steps of 10” around the initial conformation up to a maximum of 30” were carried out for the angles of the side chains in order to improve the perpendicularity of the two-fold axis with respect to the S-M segments, a maximum deviation of 3” being allowed. The best Van der Waals energy conformations of each family were improved on this manner (seecolumn 3 of Table 10). However, family II was disregarded because of its very unfavourable electrostatic energy. It can be concluded that slight rotations around the x1 and xa angles may improve the geometry of the cycle and most often give better energy values (seecolumn 4 of Table 10).
2. Conf%rms,tions Cl P2 P3 Xl xa xi
c4 x2
3. Improved conformations
Column 1: families. Column 5: cosine of the angle formed chain and the cysteine Cfl of t,he other chain. The approximative the CT-N1 bonds of both cysteines 1.
V
1
by
the two-fold value of the
-5.7 -8.2 -6.3 -10.3 -5.4 -3.6: -3.2 -1.2 -4.6 0.7 -4.2 -9.7 -9.8 -9.1 -10.5 -7.4 -6.9 -5.8 -7.5 -4.8 -9.2 -1.5 -1.8 -6.1 -8.4 -5.0 -4.3 -8.6 -4.1 -4.9 -7.2
10
- 6-9 -9.7 -6.3 -11.6 -4.4 -0.2 2.0 5.4 -6.4 -1.4 -8-3 -21.5 -21.8 -21.2 -22.6 - 14.8 -12.6 -13.0 -14.8 -12.0 -16.5 -8.6 -9.4 -13.7 -16.1 - 12-8 -12.4 - 16.7 -6.9 -9.1 -11.3
Total
0.080 0.022 0.112 O-016 0123 0.017 0,022 0.116 0.104 0.024 0.104 O-182 0.018 0.103 0.039 0.026 0.024 0.122 0.002 0.061 0.042 0.136 0.099 0.118 0.050 0.049 O-091 0.048 0.169 0.189 0.023
Cysl
energy 5
0.163 0.006 0.048 0.052 0.049 0,073 0.048 0.090 0.198 0.045 0198 0.158 0.034 0.106 0.041 0161 0.014 0.002 0.044 0.119 0026 0,172 0.157 0.135 oaO2 0.015 0.126 0.010 0.016 0.062 0.025
cys4
and the S-M segments. Column bridge x3 dihedral angle ie given
-1.2 -1.4 -1.0 -1.3 1.0 3.3 6.2 6.5 -1.8 -2.1 -4.1 -11.8 -12.0 -12.1 -12.1 - 7.3 -6.7 -7.2 -7.3 -7.2 -7.3 -7.2 -7.6 -7.6 -7.7 -7.8 -8.1 -8.2 -2-8 -4.1 -4.1
Elec.
(kcal/mob)
Vun deer Wads
axis S-S
4. Energies Van der WE&B
Cycles with a neptive
TAB&E
3.64
3.94
3.84 3.64
3-72
3.65
3.66
3.68
3.6
4.08
3.80
3-77
cys4
(A)
(75”)
(say
CS of formed
121V
116’
88” 98’
(8W (76”)
64”
65O
58”
14cY
loo0
(819
(76”)
(77O)
(73?
(73?
74”
74O
P3w
(105Q)
76O
7
(84”)
between the cysteine Column 7: angle
(9EP)
3.94 6: distance in braakets.
@So)
3.83
(103”)
4.07
(SO’) (83O)
(70°)
3.56
3.71 3.75
(70’)
3.66
(68O)
(78’)
3.68
3-53
(106’)
(79O)
3.69
4.1
(75’)
distance
3.64
Cysl
6. CI’-CL’
OILY by
STUDY
OF
THE
HUMAN
(a) Orthogonality
IgGl
HINGE
of the d&&hide
PEPTIDE
231
bridges
Since the S-S bridges in the improved cycles may be considered as roughly linear, their conformation may be studied in greater detail. It is known that the value of the x8 cysteine dihedral angle lies between 67 and 106” in proteins (Perahia & Pullman, 1971). The retied structures (see column 3 of Table 10) were thus selected following this criterion, the x3 absolute value being deduced from the distance between the two Cp’s (column 6 of Table 10). It is observed that no cycles of negative Van der Waals energy and with satisfactory S-S bridges were found around the conformation dso lEo d a PO lao. All cycles of negative Van der Weals energy had both x3 dihedral angles (Cys 1 and Cys 4) greater than 106”. That means that family III is not very probable unless some refinement of the backbone angles were to give better S-S bridge conformations.
V4 Energy It is interesting to discuss the Van der Waals energy and the electrostatic energy separately. On the basis of the Van der Waals energy alone, it is difficult to say which family is the most favoured after the refinement has been carried out. Even conformations with a not very negative Van der Waals energy can transform into a neighbouring conformation which has a quite favourable energy. For example, d300 Ia0 d a a*l*O Ia0 (-5.3 kcal./mole) transforms into dzQo lEo d a a*l*O eo, the Van der Waals energy (-10.3 kcal./mole) of which nearly reaches the minimum observed value (- 10.5 kcal./mole). On the contrary, the electrostatic energy remains very constant during the refinement. As can be expected from local considerations, the helical conformation d d d d is the most favoured. Consequently, family IV includes the cycles of lowest total energy so that the energy calculations con&m the supposition of Yguerabide, Epstein & Stryer (1970) that a structure resembling a poly-L-proline helix might be possible for the hinge region and “kept apart the Fab and Fc segments, thereby facilitating rotation of Fab about a bond near one end of the helix”. On the other hand, it is evident that the change of a cyst&e from d to c will increase the electrostatic energy and that the cycles with proline 3 in a will be the most unfavourable, especially since cysteine 4 is in a*. (c) Stereochemical code One might ask whether or not a greater flexibility of the backbone would lead to conclusions other than those deduced from the strict application of the stereochemical code. To test this possibility, an additional state (4 = 180“ called 0) was chosen for the prolines and considered as an approximation of the d state. Table 11 gives the words which are represented in each family. Additional words arise in some families and the number of ways of realizing the cycles increases for eaoh word because new side-chain conformations now fuhil the condition of perpendicularity with respect to the dyad axis. The energies of the words with a proline in d or 0 are of the same order of magnitude. However, one conformation (d300 3oo 0 a a*3oo a40) is striking by its low Van der Weals energy (-14.1 kcal./mole) which becomes equal to -15.1 kcal./mole after refinement of the side-chain angles (d300 2Qo0 a a*31o a40). A neighbouring low energy conformation was sought with proline 2 in d. d300 3oo d a a*aeo 210 (- 11.4 kcal./mole)
232
C. RENNEBOOQ-
SQUILBIN
TABLE
11
Number of worn% of negative Van der Wads energy in each family with the prolinee in d M 0 I
II
III
cl
Iv
dad ((0 od6
V
c;;d13 ((
VI
d d dcll (( 00
b
VII dd cooc4 (( a* d dc 1 (( 00
was found but it did not satisfy the criterion of orthogonal&y of the S-S bridges. It must be recalled that family III was disregarded for the same reason. Here, we have an example where a slight change in the backbone geometry can improve the oonformation of the S-S bridges. The notion of conformational entropy becomes more apparent with this additional state of the prolines because a greater number of structures is available. It seems logical to assume that the number of distinct ways of closing the cycle is a crude measure of the probability of the existence of the word in the protein. Following this last criterion, families V and VI are particularly favoured. Thus, the conclusion is intuitively evident: the greater the backbone flexibility, the easier the geometrical criterion of perpendicularity of the a-fold axis, with respect to the half S-S bridge, can be fulfilled. However, the conclusions concerning the number of low-energy families and, hence, the rough secondary structure of one chain of the hinge peptide do not change. (d) Hydrogen bon& It is also interesting to search for hydrogen bonds, although the number of groups susceptible of giving them is not very high owing to the presence of so many prolines. The cycles of very negative electrostatic energy were considered in greater detail in order to search for hydrogen atoms located at short distances (about 1.8 A, Pauling, 1960) from oxygen or nitrogen atoms, thereby removing the repulsive Van der Waals potential between this pair of atoms. This is indeed a very easy method of simulating the effect of hydrogen bonds. No low energy structures were found to give rise to hydrogen bonds. Nevertheless, one high energy conformation de0 6o 0 0 bs40 lBo is very interesting from this point of view. The H, atom of one chain is located at a distance of l-4 d from the O1 atom of the other chain and the peptide bonds before cysteine 1 of both chains are parailel. Unfortunately, short-range interactions arise between the cysteine 1 sulphur of one chain and backbone atoms of the other chain. However, it might be hoped that angle adjustments could diminish the energy. (e) Tertiary structure of the hinge peptide and hinge mechanism Since several cycles of about the same energy are available, their spatial structures can be studied with the aid of molecular models. The structures with proline 3 in a are found to be relatively compact, the cyclic side chains of prolines 3 and 5 and of
STUDY
OF
THE
HUMAN
IgUl
HINGE
233
PEPTIDE
both prolines 2 being respectively parallel to each other. On the other hand, the structures with proline 3 in d are found to be more extended. A characteristic feature of the IgG molecule is that a wide range of angles is observed in the electron microscope between the two Fab fragments (Feinstein & Rowe, 1965; Valentine & Green, 1967). As Green (1969) points out in his review on electron microscopy of immunoglobulins, this can be due to a flexible hinge region with low energy barriers between the various alternative conformations or to a population of stable isomers with high energy barriers between the various conformations. But he does not accept this last hypothesis as probable because a unique sequence would be unlikely to fold into a large number of different stable conformations. Considering the present energy calculations, however, it seems that the assumption of a population of stable isomers might not be so easily rejected becauseit has been proved that the same word can give rise to cycles of different tertiary structures by closing the bridges in different manners. To illustrate this fact, the cycles dzgoa5od d dzgo270(A) and dzEo130d d d2go27o(B) were considered. They are equally probable sincetheir energiesare of the sameorder of magnitude and the orthogonal&y of the S-S bridges is in both casesrespected (in other words, the x3 angles lie in the range of 67 to 106”, Perahia & Pullman, 1971). However, it can be seen in the molecular models that, although the initial single chains have the same helical structure, the resulting double-strand structures are rather different becauseof the different position of the cysteine 1 side chain and thus of the two-fold axis. If the left chains of the peptides A and B are placed contiguously, the N-terminal end of the B right chain comes toward the observer with respect to the A right chain. Figures 5 and 6 give the projection of moleculesA and B on a plane passingthrough the two-fold axis and the Hz atoms. The change in tertiary structure
Fra. 5. Projection of cycle axis and the Ha atoms.
daoa a6o d cl d29o 270 on & plane
passing
through
the M,M4
two-fold
234
Fra. 6. Projeotion of cycle axis and the Hz atom.
C. RENNEBOOG-
SQUILBIN
daso I30 cl d daao aro on a plane
passing
through
the M,J&
two-fold
between both cycles is also reflected by the wide difference of orientation of the cysteine 1 e--N bonds. A partial information about this orientation difference is given by the angle formed by both C--N bonds (100” in caseA and 145” in caseB, column 7 of Table 10). The following question now arises. Is the value of this angle of some significance with respect to the angle shown by the Fab fragments on the electron micrographs Z The answer would seemto be yes. If the Fab fragments are really independent rigid units (this hypothesis is supported by many observations, seefor example Dorrington $ Tanford, 1970), it seemslogical to conclude that their orientation in spacewill be influenced by the direction of the bonds which bind them to the hinge region. The computed values vary from 58 to 145”, the d d d d conformation being the more “open” one. This doesnot mean that smaller or larger angle values are excluded, since the number of structures studied in great detail is limited. It is, at the moment, difficult to make a choice between the two hypotheses cited above. The first one supposedthe existence of low energy conformations which can transform int.0 each other by rotation of the free angles without encountering high energy barriers. In this case, one could imagine that the mechanism of the hinge is that of a pair of scissorsthe arms of which are not necessarilycoplanar. Rotations of the cysteine side ohain x angles from one favourable conformation to another one (certainly with someadjustments of the backbone angles)would changethe orientation of the two polypeptide chains with respect to each other and would give the opening of the scissorarms. The second hypothesis supposedthe existence of a population of stable isomers. It must, then, be concluded that during the polypeptide chain synthesis, the random manner of closing the bridges will give a diversity of tertiary structures. In this case,
STUDY
OF THE
HUMAN
IgGl
HINGE
PEPTIDE
235
the binge region would be perfectly rigid. Its apparent flexibility would be due to the numerous
ways of realizing
the cycle and the mobility
of the Fab fragments
a&&d
by the fluorescencedepolarization experiments would be essentially due to rotations around
the axis joining
each Fab fragment
to the Fc fragment
(Yguerabide
et al.,
1970). The question arises, if the same conception of hinge mechanism is valid for a hinge peptide containing ouly one disulphide bridge like the rabbit one ? The great difference lies iu the fact that the twoifold axis, if it exists, may have an infiuite number of different orientations in the plane perpendicular to the S-S bridge. That means that a siugle chain iu a certain conformation (say, for instance c d d d if only 4 amino acids are considered) could give rise to different double-strand structures by a rotation of 180” around the two-fold axis. The structures would follow from the
choice of the two-fold axis direction. However, such a hypothesis should be tested in further calculations. The author wishes to thank Professor R. Hamers and Dr J-L. De Coen for useful discussion and valuable criticism and Dr C. Cherton and Mr R. Devillers for their help in preparing the computer program. The calculations of this work were carried out on the CDC 6400 computer at the Vrije Universiteit, Brussels.
REFERENCES Brent, D. E., Miller, W. G. & Flory, P. J. (1967). J. Mol. Biol. 23, 47. Bulletin World Health Organization (1964). 30, 447. Cohen, S. & Porter, R. R. (1964). Advanc. Inwwunol. 4, 287. Corey, R. B. & Pauling, L. (1953). Proc. Roy. Sot. (London) B141, 10. Dayhoff, M. 0. (1969). Atlas of protein sequences and structure, 4, D73. De Coen, J. L., Elefente, G., Liquori, A. M. & Damiani, A. (1967). Nature, 216, 910. Dorrington, K. J. & Tanford, C. (1970). Advanc. Immunol. 12, 333. Edelman, G. M. (1969). J. Amer. Chem. Sot. 81, 3155. Edelman, G. M., Cunningham, B. A., Gall, W. E., Gottlieb, P. D., Rutishauser, U. & Waxdal, M. J. (1969). Proc. Nat. Acud. Sci., Wash. 63, 78. Edelman, G. M. & Gall, W. E. (1969). Ann. Rev. Biochem. 38, 415. Edehnan, G. M. & Ponlik, M. D. (1961). J. Es@. Med. 113, 861. Feinstein, A. & Rowe, A. J. (1965). Nature, 205, 147. Fleischman, J. B., Pain, R. H. & Porter, R. R. (1962). Arch. Biochem. Biophys. SuppI. 1, 174. Frangione, B., Milstein, C. & Pink, J. R. L. (1969). Nature, 221, 145. Goldstein, D. J., Humphrey, R. L. & Poljak, R. J. (1968). J. Mol. BioZ. 35, 247. Green, N. M. (1969). Advanc. Immunol. 11, 1. Grey, H. M. & Kunkel, H. G. (1964). J. Exp. Med. 120, 253. IUPAC-TUB Commission on biochemical nomenclature (1970). J. Mol. Biol. 52, 1. Leach, S. J., Nemethy, G. & Scheraga, H. A. (1966). Biopolymers, 4, 369. Leung, Y. C. t Marsh, R. E. (1968). Acta Cry&. 11, 17. Liquori, A. M. (1969). Quart. Rev. Biophys. 2, I, 65. Liquori, A. M., Damiani, A. & De Coen, J. L. (1968). J. Mol. Biol. 33, 446. Mitchell, A. (1968). Tables of interatomic distances and configuration in molecules and ions. The Chemical Society, Burlington House, London + supplement (1959). Nisonoff, A., Wissler, F. C., Lipman, L. N. & Woernley, D. L. (1960). Arch. Biochem. Biophy.9. 89, 230. Panling, L. (1960). The n&we of the chemkal hod. Cornell University Press. Perahia, D. L Pullman, B. (1971). Biochem. Biqhys. Rea. Comm. 43, 65. Porter, R. R. (1969). Biochem. J. 73, 119.
236
C.
RENNEBOOG-SQUILBIN
Smith, D. S. & Utmmi, S. (1967). Nature, 216, 332. Terry, W. D. & Fahey, J. L. (1964). Science, 146, 400. Terry, W. D., Matthews, B. W. & Davies, D. R. (1968). Nature, 220, 239. Valentine, R. C. 81 Green, N. M. (1967). J. Mol. Biol. 27, 616. Yguerabide, J., Epstein, H. F. & Stryer, L. (1970). J. Mol. Biol. 51, 573.
Conformational Human linmunoglobulin
Study of the Gl Hinge Peptide
c. RENNEBOOGSQUILBINt
La&rat&urn
voor Algemene Biologic, Vrije Universiteit Bru-ssel,Belgium
(Received20 July 1971, and in revisedform 18 October1971) The IgGl
conformational energy of the central double pentapeptide of the human hinge
region
Cys-Pro-Prc+Cys-Pro has been calculated with the aid of S S S S Cys-Pro-Pro-@w-Pro semi-empirical potential functions. As a first approximation, the stereochemical code of Liquori (1969) has been used. It was found that a small number of families of similar backbone conformations is allowed for the chains of the cycle. But for moat backbone conformations, more than one cysteine side-chain conformation is compatible with the realization of the cycle, so that several different tertiary structures are possible for the hinge peptide. This result is very interesting for the discussion of the hinge mechanism.
1. Introduction Immunoglobulins consist of two identical light polypeptide chains (molecular weight 22,506) and two identical heavy polypeptide chains held together by diaulphide bonds and non-covalent interactions (Edelman, 1959; Edelman $ Poulik, 1961; Fleischman, Pain & Porter, 1962). Five different classesof immunoglobulins (IgG, IgA, IgM, IgD and IgE) have been defined according to the classof their heavy chains (Bull. World Health Organization, 1964). IgG has been the most thoroughly investigated. Its heavy chain ha9 a molecular weight of 53,990. The digestion of this globulin with papain releasestwo antigenbinding fragments (Fab) and one Fc fragment (Porter, 1969). The Fab fragments are made up of the amino-terminal half of the heavy chain and the whole light chain. The Fc fragment is a dimer of the remaining portions of heavy chains and is involved in complement fixation (Cohen & Porter, 1964). When pepsin is used, a fragment F(ab’)z is obtained which corresponds to the two Fab fragments joined by a disulphide bond (Nisonoff, Wissler, Lipman t Woernley, 1960). Within the classIgG, subclasseshave been distinguished by their antigenic determinants. For instance, there are four subclassesof human IgG: IgGl, IgG2, IgG3 and IgG4 (Grey L Kunkel, 1964; Terry & Fahey, 1964). A great number of amino-acid sequencesof IgG light chains (Dayhoff, 1969) and even the complete amino-acid sequenceof a heavy chain (Edelman et al., 1969) are now available. Little is known of the tertiary structure of these molecules; however, preliminary data have been obtained from crystallographic analysis of an entire IgGl myeloma protein (Terry, Matthews $ Davies, 1968) and of a human crystalline t Present Onderzoek,
Address: Belgium.
Aangesteld
Navorser
van 221
het
Nationaal
Fonda
voor
Wetenaohappelijk
222
C.
RENNEBOOC
- SQUILBIN
IgGl Fc fragment (Goldstein, Humphrey & Poljak, 1968). In these two papers, the evidence for the presence of a two-fold exis of symmetry is given. The most direct observations have been done by electron mioroscopy (Fenstein & Rowe, 1965; Valentine & Green, 1967) end have enabled the authors to postulate a Y shape model for the antihapten antibody with the hapten binding near the ends of the Fab segments. The data from hydrodynamic measurements and fluorescence polarization experiments have recently been reviewed in detail by Dorrington & Tanford (1970). These data, plus the results of electron microscopic studies would seem to suggest that the molecule consists of three domains connected by a hinge region which allows a limited flexibility of the molecule in solution and which is the most sensitive to enzymic cleavage. Furthermore, each domain would be composed of compact segments connected by a relatively exposed region which is less accessible to enzymes than the hinge region in the centre of the molecule. In Figure 1, the model for IgG proposed by Edelman & Gall (1969) and adapted by Dorrington & Tanford (1970) is shown. Considering the fundamental role of the hinge region in the flexibility of the molecule, and consequently in the molecule’s possibilities of physiological activity (combination with antigen), it would be interesting to obtain additional information about the three-dimensional structure of this region. The particular amino-acid sequence of the hinge peptides (Fig. 2) facilitates a theoretical calculation of the allowed conformations. The central double pentapeptide of the IgGl hinge region has been chosen for this study because the only X-ray diffraction data presently available concern this protein (Terry et al., 1968; Goldstein et al., 1968). Thus, there is a certain chance that its tertiary structure will be known soon and comparison with the models proposed in this paper will be possible. Moreover, it has been demonstrated that, for this protein, there exists a two-fold axis which passes through the middle of each S-S bond and which is perpendicular to them. This fact will greatly simplify the calculations in strongly reducing the number of possible conformations. Thus, the aim of this paper is to look for the possible tertiary structures of the human IgGl A
Enrymlc
cleavage
Fa
FIQ.
1. Yodel
for IgG
(from
Dorrington
& Tanford,
1970).
STUDY
OF THE
Species Human tIgG1 IgG2 Iga3 Igc4 Rabbit fIgG
HUMAN
IgG1
HINGE
PEPTIDE
223
Thr-His-Thr-C?gs-Pro-Pro-Cys-Pro-Ala-Pro-GluCys-Pro-Pro-Cys-Pro-Ala-(Pro,Glu), Glu Pro-Pro-Pro-Cys-Pro-Arg-Cys-Pro-Ala-Pro-GluGly-Pro-Pro-Cys-Pro-Pro-Cys-Pro-Ala-(Ser,Glu) -Pro-GluPro-Thr-Cys-Pro-Pro t See Frengione, Milstein & Pink, 1969. $ See Smith & Utsumi, 1967.
FIG. 2. Amino-&d
sequence of IgG hinge regions.
hinge peptide which result from local interactions. It must, of course, not be forgotten that its structure will also be influenced by long-range interactions with the rest of the polypeptide chains.
2. Calculation Procedure Computations of polypeptide conformation energiesdepend on the values of bond angles and bond lengths. The parameters used for the backbone are those of Corey t Pauling (1963). The N-H length is taken equal to 1.01 A and the C-H length to 1.08 A. The parameters for the cyst&e side chain are those of Mitchell (1958). The geometry of the proline proposed by Leung $ Marsh (1958) is used with someadjustments of the side-chain angles in order to close the ring. The proline imide group is assumedto be in the planar tram configuration. The conformation of an amino-acid residue in a polypeptide chain is defined by two dihedral anglesfor the backbone (4 around the N-C’ bond, # around the (2-C bond), and a certain number of dihedral angles x for the side chain (Fig. 3). The conventions of the IUPAC-IUB Commission on biochemical nomenclature (1970) are followed in this paper except that the x angles are ascribed zero values for the so-called &-conformation but are measuredin the range of 0 to 360”.
FIQ. 3. Cp _ r-C$‘+ I segment of a polypeptide chain. The segment is shown in B fully extended oonformation (4 = Q = 0”). The errows indicate the positive sense of rot&ion of the engles (IUPAC-IUB Commission on bioohemioal nomenolature, 1970).
224
C.
RENNEBOOG-
SQUILBIN
Two contributions to the internal energy were considered in the calculations: the electrostatic interactions and the Van der Waals interactions including a torsional potential (3 kcal.) around the c”-C/f single bond of the side chains. This torsional potential has minima at the staggered positions (De Coen, Elefante, Liquori & Damiani, 1967). The Van der Waals interactions are the sum over all pairwise interactions between atoms i and j of the molecule. Buckingham functions E(r,,) = A exp (--B T*,) C rllm6 with the parameters previously used by Liquori, Damiani & De Coen (1968) were chosen to express those interactions which depend on the values of the dihedral angles $,# and x. The electrostatic interaction energy is the sum of all pairwise electrostatic interaction energies between atoms carrying a partial charge. The data of Brant, Miller & Flory (1967) were used for the peptide group. In the present calculation, the nitrogen of the proline is assumed to be uncharged. The electrostatic energy is calculated separately to facilitate any future studies of the effect of a change in the dielectric constant on the conformational energies. The present calculations were carried out with a dielectric constant equal to 1.0. The energy map (z/ as a function of 4) for the backbone of a c _ 1 - c+ 1 polypeptide chain segment is characterized by regions of lower energy. Liquori (1969) called the most typical conformations in these regions, a, 6, c, d and a* although b, c, d for instance are not clear-cut minima. These five backbone low energy states were taken into account for the cysteine residues with one additional conformation, state e which is a low energy state when the electrostatic energy is added to the Van der Waals energy. The use of such a code (Table 1) is merely a convenient way of simplifying the calculation and reducing computer time by choosing the most typical conformations in the low energy regions. Steps of 60” were chosen for the side chain. TABLE
1
The stereochemical code
; : a* e
- 63” -166” -160” - 76” + 62” - 80”
- 49” +1iw + IO0 + 165” + 60” + looa
3. Results The study of the hinge peptide Cys-Pro-Pro-Cys-Pro S S $s-Pr o-I+ o-Czs-Pr 0 was carried out in four steps. (1) The C;t-l-q+, segments (Fig. 3) of proline and cysteiue were considered. It was confirmed that the only low energy states for the proline are a and d (Leach, Nemethy & Scheraga, 1966; Liquori, 1969) (Table 2).
STUDY
OF
THE
HUMAN
IgGl
HINGE
PEPTIDE
226
TABLE 2 Energies of the low energy states ojproline St&e
Van
5;
(kcul./mole)
Eleotrost&io
der W&s -0.8 -1.0
Total
-0.32.6
-1.11.6
A search was made for the side-chain conformations of the cysteine compatible with every backbone conformation taken into account. All conformations corresponding to Van der Waals energies greater than 20 kcal./mole were rejected. The results are given in Table 3. TABLE 3 Cysteine: number of xz values corrc.spon4&g tc a Van der Wd energy lower than 20 kc&/mole. 1800
a
6
b Ii
6( 66(
a* e
240’
6
3oo”
0”
6
-
6 6
6( 65(
6( 6( -
6
6
6
6
6
6
0’)
0”) 0”)
60”
0”) 0’)
120°
Total
4(6;:)
4(30;:)
26
6 6
5(
0”)
32 28
6;
0’)
0’)
6( 60’)
-
22 23 169
The
x1 values
of the rejected
conform&ions
are in brmkets.
(2) The dipeptides cysteylproline, prolyloyateine and prolylproline were analysed in order to see the influence of a proline on a carboxy- or ammo-terminal cysteine or proline. The criterion of 20 kcal./mole was also applied to the Van der Waals energy of the dipeptides cysteylproline and prolyloysteine. A proline does not change the number of “allowed” side-chain conformations for the cysteine when it precedes it but it diminishes this number by 1’7% when it follows the oysteine (Tables 4 and 5). Only the 132 allowed conformations of Table 4 were further used for both cysteines (see point 4). From the study of the dipeptide prolylproline, it appears that the conformations where the N-terminal proline is in state a, are less favourable for the Van der Waals as well as for the electrostatic energy (Table 6). As a first approach, and in order to reduce computer time, only the words with the N-terminal proline in cl were considered. (3) The peptide Cys-Pro-Pro-+ was then studied with a carbon (cd) replacing the hydrogen of the C-terminal peptide bond because a prolyl residue follows the cysteine (Pig. 4). The oysteine side chains were fixed in the conformation x1=240’, xz=1800 because it is the only x1 value which is allowed for any backbone conformations. Six backbone conformations (a, b, c, d, a*, e) were taken into account for the cysteyl 15
226
C. RENNEBOOG-
SQUILBIN TABLE
4
Cysteylproline: number of x2 values correspondingto a Van der Wads energy lower than 20 kcul./~~~le Xl HO0 \ state
240"
300"
0"
60"
1200
\ a
6
b
-
6 6
6 5(
i a*
66
6 6
65( 0") 6
e
6
6
6
5(
0")
0')
5( - 0")
6
-
6 60°) 5(
-
Total allowed conformations
22 22 27 18 22 21 132
The
x2 values
of the rejected
conformations
TABLE
are in brackets.
5
Lowest Van der Weals energy valuesfound for cysteylproline (ikal./mole). The proline is in d Side chain mgle
State a
b
c
d
a*
e
\
Xl
1800
X2
180"
60" 3.9
180° -0.6 180°
0.6
180"
TABLE
300"
300" -1.1
180"
180°
-0.6 300"
6
Energies of the dipeptide prolylproline (kcal.lmole) stat0s a a d
a d a
d d
Van
der Waals
3.5 4.1 -2.1 -1.8
Electrostatic
4.9 2.8 1.9 -1.7
Total
8.4 7.0 -0.2 -3.5
6.1 60"
STUDY
OF
THE
HUMAN
IgGl
HINGE
227
PEPTIDE
Proline 5
P $4 XLC4 2 I
Cysteine 4
X.
c:
4
%r
N.
I rP
C,P k
Y H4
03% c3 CO Proline 3
Proline 2
FIQ. through
4. Projection the cyst&e
of the central Hr atoms.
pentapeptide
of the human
IgGl
hinge
region
on a plane
passing
residues and two (a, d) for proline 3. Proline 2 was fixed in d. 72 “words” were thus considered. The results are summarized in Tables 7 and 8. It is interesting to compare the words with proline 3 in d which are more extended and those with proline 3 in a which are more compact. It can be seen that the change of proline 3 from d to a is accompanied by a decrease of the Van der Waals energy by an average of 0.9 koal./mole (with a maximum of 1.3 koal./mole) except when the C-terminal cyst&m has the a conformation. In this case, short-range interactions TABLE
7
Van der Wads and electrostaticenergiesof the words with Pro-Pro in d d (ikaE./mole) cys cys
\
1
Van
4 a
der Waals b c
energy d
a*
e
a
b
Electrostatic c
energy d
a*
e
b
1.0 0.5
0.8 0.3
2.4 1.9
1.0 0.6
2.5 2.2
2.3 1.8
-0.3 -4.7
-3.6 -8.5
-0.5 -5.2
-2.5 -7.2
-1.0 -5.1
-2.9 -7.6
: a* e
0.6 1.8 3.2 8.9
0.3 1.5 2.9 8.7
3.2 1.9 4.6 10.3
0.6 1.7 3.1 8.9
3.6 2.2 4.9 10.6
3.1 1.8 4.6 10.2
-1.3 -3.3 -1.7 -3.9
-6.0 -7.5 -6.2 -7.6
-1.7 -4.3 -2.1 -4.4
-3.7 -6.1 -3.9 -6.3
-1.7 -4.1 -2.1 -4.2
-4.1 -6.6 -4.4 -6.7
a
228
C.
RENNEBOOQ-
SQUILBIN TABLE
8
Van der Waals and electrostatic energies of the words with Pro-Pro d a (kc&./mole) ,-- * cys
\
Van
cys4 1
der Waals d
energy a*
e
-0.9 -0.4
1.8 1.3
0.5 1.0
1.6 2.8
-0430.4
2.6 1.4
4.2 10.0
1.8 7.6
4.0 9.8
a
b
;
>60.0 x50.0
-0.7 -0.1
2.0 1.5
ii
>lio*o >50*0
-0.60.6
a* e
>60*0 >60*0
2.0 7.8
G
f Not
Electrost&io
energy
G
d
-6.8 -0-l
-1.93.7
-3.22.5
-0.75.0
-4.70.6
1.8 0.6
-2.0 -4.9
-1.2l-9
-2.40.7
-0.13.2
-0.9 -3.9
3.2 9.0
-2.4 -6.0
1.4 -1.3
0.2 -2.2
2.5 -0.1
-1.6 -3.9
at
b
in
a*
e
oomputed.
(more than 50 kcal./mole) arise between the cd atom of proline 5 and the side chain of proline 2. Consequently, all the words containing both proline 3 and cysteine 4 in a were rejected. It is observed that in the dipeptide prolylproline, the difference in energy between dd and da is only O-3 kcal./mole. That means that a certain number of favourable interactions due to the London dispersion forces arises between pairs of atoms in the tetrapeptide when it has a more compact structure. The electrostatic energy of the tetrapeptide increases by an average of 3.6 kca1.l mole, which is just the difference between the electrostatic energies of the dipeptide prolylproline in dd and da. It should be noted that the results given in Tables 7 and 8 correspond to the energies of the words for the chosen side-chain conformations. Other side-chain arrangements could give lower energies. For instance, a rotation of x1 from 240 to 180” for a cysteine in c would represent an energy decrease of about 2 kcal./mole. (4) The following method was developed for computing all possible conformations of the hinge peptide in the stereochemical code approximation : the hydrogen attached to the sulphur of the cysteine aide chains was replaced by a false atom M at a distance of 1.02A from the sulphur (corresponding to half the length of the S-S bridge, Mitchell, 1958) in order to construct the two-fold axis. The perpendicularity of this axis will be tested with respect to the S-M segments of cyst&es 1 and 4. A given conformation was generated for one chain (Cys-Pro-Pro-Cys with a d). If it corresponded to one of the rejected conformations (see points 2 and 3), the next conformation was generated by rotating one of the angles; if not, the co-ordinates of the atoms were computed and the perpendicularity of both bonds M,S and MJ with respect to the dyad axis M1M4 was tested. If both angles did not deviate from 90” by more than 11*5”, the entire molecule was generated by a rotation of 180’ around the two&fold axis. The conformation was registered as allowed and its energy was computed. The preliminary study of the local interactions (points 1,2,3) allowed the reduction of the number of conformations to be examined from 62 x 362 x 22=186, 624 to 32,076. When the geometrical criterion was applied, this number fell to 1193. Only 33 among those geometrically allowed conformations have a negative Van der Waals energy. They can be denoted by 16 words. This means that for a certain number of words more than one side-chain conformation can give rise to a low energy cycle.
STUDY
OF
THE
HUMAN
IgGl
HINGE
PEPTIDE
229
The 16 words were classified in 7 families (Table 9) for the following reason: the geometry of the cycle depends only on the # angle of cysteine 1, the # rtngles of the prolines and the + angle of cysteine 4 but not on the 4 angle of cysteine 1 and the # angle of cysteine 4. Therefore, roughly the same cycles can be realized with different words when the side chains are disposed on the same manner. For instance, it is obvious that cysteine 1 in b or d will give the same cycle because both 4 angles are equal to 155”. Likewise, there is not a great change when cysteine 1 is in a* (&=SO’) or c ($=70”), or when cysteine 4 is in b ($*= -155”) or c (&= -GO”), or when it is in e (9&=-SO’), d (#,=-75”) or a (#*=-63’). TAEZE 9
Pam&es of w07+as of negative Van der Wads energy and number of cyclescorrespondingto eachuxnd I
clam*
II
2
a*daa* 2 cdaa+ 2
III
V
Iv
ddac
1
bdac
1
&de
2 2
d&la
1
dddd
VII
VI
cd&l
4
a+ddd cdda a*dda
1 5 1
cd&
4
dddo
3
cadc a%&
1 1
As expected, cysteine 1 never appears in a or e in the words of low energy because of the proline at its C-terminal end. For this reason, the words ending on a or e were also rejected as very improbable since a.proline follows cysteine 4 but is not explicitly considered in the calculation. There remain 11 words and 20 cycles. Table 10 gives the side-chain angle values (column 2), the energies (column 4) of these cycles, and the cosine of the angles between the dyad axis and the S-M segments(seecolumn 5).
4. Discussion Considering the approach which has been used, a choice between all the remaining words will not be attempted, but attempts will be made to obtain someinformation about the hinge mechanism of this peptide by more thoroughly studying the tertiary structure of the cycles generated from these words. The first thing to be done is to obtain more real structures, i.e. more linear disulphide bridges. It must not be forgotten that in s,first selection of the cycles, a minimum angle of 78.5” was tolerated between the dyad axis passing through the middle (M) of the S-S bridges and the S-M segments.These structures were taken as departure points of a refinement procedure. Rotations by steps of 10” around the initial conformation up to a maximum of 30” were carried out for the angles of the side chains in order to improve the perpendicularity of the two-fold axis with respect to the S-M segments, a maximum deviation of 3” being allowed. The best Van der Waals energy conformations of each family were improved on this manner (seecolumn 3 of Table 10). However, family II was disregarded because of its very unfavourable electrostatic energy. It can be concluded that slight rotations around the x1 and xa angles may improve the geometry of the cycle and most often give better energy values (seecolumn 4 of Table 10).
2. Conf%rms,tions Cl P2 P3 Xl xa xi
c4 x2
3. Improved conformations
Column 1: families. Column 5: cosine of the angle formed chain and the cysteine Cfl of t,he other chain. The approximative the CT-N1 bonds of both cysteines 1.
V
1
by
the two-fold value of the
-5.7 -8.2 -6.3 -10.3 -5.4 -3.6: -3.2 -1.2 -4.6 0.7 -4.2 -9.7 -9.8 -9.1 -10.5 -7.4 -6.9 -5.8 -7.5 -4.8 -9.2 -1.5 -1.8 -6.1 -8.4 -5.0 -4.3 -8.6 -4.1 -4.9 -7.2
10
- 6-9 -9.7 -6.3 -11.6 -4.4 -0.2 2.0 5.4 -6.4 -1.4 -8-3 -21.5 -21.8 -21.2 -22.6 - 14.8 -12.6 -13.0 -14.8 -12.0 -16.5 -8.6 -9.4 -13.7 -16.1 - 12-8 -12.4 - 16.7 -6.9 -9.1 -11.3
Total
0.080 0.022 0.112 O-016 0123 0.017 0,022 0.116 0.104 0.024 0.104 O-182 0.018 0.103 0.039 0.026 0.024 0.122 0.002 0.061 0.042 0.136 0.099 0.118 0.050 0.049 O-091 0.048 0.169 0.189 0.023
Cysl
energy 5
0.163 0.006 0.048 0.052 0.049 0,073 0.048 0.090 0.198 0.045 0198 0.158 0.034 0.106 0.041 0161 0.014 0.002 0.044 0.119 0026 0,172 0.157 0.135 oaO2 0.015 0.126 0.010 0.016 0.062 0.025
cys4
and the S-M segments. Column bridge x3 dihedral angle ie given
-1.2 -1.4 -1.0 -1.3 1.0 3.3 6.2 6.5 -1.8 -2.1 -4.1 -11.8 -12.0 -12.1 -12.1 - 7.3 -6.7 -7.2 -7.3 -7.2 -7.3 -7.2 -7.6 -7.6 -7.7 -7.8 -8.1 -8.2 -2-8 -4.1 -4.1
Elec.
(kcal/mob)
Vun deer Wads
axis S-S
4. Energies Van der WE&B
Cycles with a neptive
TAB&E
3.64
3.94
3.84 3.64
3-72
3.65
3.66
3.68
3.6
4.08
3.80
3-77
cys4
(A)
(75”)
(say
CS of formed
121V
116’
88” 98’
(8W (76”)
64”
65O
58”
14cY
loo0
(819
(76”)
(77O)
(73?
(73?
74”
74O
P3w
(105Q)
76O
7
(84”)
between the cysteine Column 7: angle
(9EP)
3.94 6: distance in braakets.
@So)
3.83
(103”)
4.07
(SO’) (83O)
(70°)
3.56
3.71 3.75
(70’)
3.66
(68O)
(78’)
3.68
3-53
(106’)
(79O)
3.69
4.1
(75’)
distance
3.64
Cysl
6. CI’-CL’
OILY by
STUDY
OF
THE
HUMAN
(a) Orthogonality
IgGl
HINGE
of the d&&hide
PEPTIDE
231
bridges
Since the S-S bridges in the improved cycles may be considered as roughly linear, their conformation may be studied in greater detail. It is known that the value of the x8 cysteine dihedral angle lies between 67 and 106” in proteins (Perahia & Pullman, 1971). The retied structures (see column 3 of Table 10) were thus selected following this criterion, the x3 absolute value being deduced from the distance between the two Cp’s (column 6 of Table 10). It is observed that no cycles of negative Van der Waals energy and with satisfactory S-S bridges were found around the conformation dso lEo d a PO lao. All cycles of negative Van der Weals energy had both x3 dihedral angles (Cys 1 and Cys 4) greater than 106”. That means that family III is not very probable unless some refinement of the backbone angles were to give better S-S bridge conformations.
V4 Energy It is interesting to discuss the Van der Waals energy and the electrostatic energy separately. On the basis of the Van der Waals energy alone, it is difficult to say which family is the most favoured after the refinement has been carried out. Even conformations with a not very negative Van der Waals energy can transform into a neighbouring conformation which has a quite favourable energy. For example, d300 Ia0 d a a*l*O Ia0 (-5.3 kcal./mole) transforms into dzQo lEo d a a*l*O eo, the Van der Waals energy (-10.3 kcal./mole) of which nearly reaches the minimum observed value (- 10.5 kcal./mole). On the contrary, the electrostatic energy remains very constant during the refinement. As can be expected from local considerations, the helical conformation d d d d is the most favoured. Consequently, family IV includes the cycles of lowest total energy so that the energy calculations con&m the supposition of Yguerabide, Epstein & Stryer (1970) that a structure resembling a poly-L-proline helix might be possible for the hinge region and “kept apart the Fab and Fc segments, thereby facilitating rotation of Fab about a bond near one end of the helix”. On the other hand, it is evident that the change of a cyst&e from d to c will increase the electrostatic energy and that the cycles with proline 3 in a will be the most unfavourable, especially since cysteine 4 is in a*. (c) Stereochemical code One might ask whether or not a greater flexibility of the backbone would lead to conclusions other than those deduced from the strict application of the stereochemical code. To test this possibility, an additional state (4 = 180“ called 0) was chosen for the prolines and considered as an approximation of the d state. Table 11 gives the words which are represented in each family. Additional words arise in some families and the number of ways of realizing the cycles increases for eaoh word because new side-chain conformations now fuhil the condition of perpendicularity with respect to the dyad axis. The energies of the words with a proline in d or 0 are of the same order of magnitude. However, one conformation (d300 3oo 0 a a*3oo a40) is striking by its low Van der Weals energy (-14.1 kcal./mole) which becomes equal to -15.1 kcal./mole after refinement of the side-chain angles (d300 2Qo0 a a*31o a40). A neighbouring low energy conformation was sought with proline 2 in d. d300 3oo d a a*aeo 210 (- 11.4 kcal./mole)
232
C. RENNEBOOQ-
SQUILBIN
TABLE
11
Number of worn% of negative Van der Wads energy in each family with the prolinee in d M 0 I
II
III
cl
Iv
dad ((0 od6
V
c;;d13 ((
VI
d d dcll (( 00
b
VII dd cooc4 (( a* d dc 1 (( 00
was found but it did not satisfy the criterion of orthogonal&y of the S-S bridges. It must be recalled that family III was disregarded for the same reason. Here, we have an example where a slight change in the backbone geometry can improve the oonformation of the S-S bridges. The notion of conformational entropy becomes more apparent with this additional state of the prolines because a greater number of structures is available. It seems logical to assume that the number of distinct ways of closing the cycle is a crude measure of the probability of the existence of the word in the protein. Following this last criterion, families V and VI are particularly favoured. Thus, the conclusion is intuitively evident: the greater the backbone flexibility, the easier the geometrical criterion of perpendicularity of the a-fold axis, with respect to the half S-S bridge, can be fulfilled. However, the conclusions concerning the number of low-energy families and, hence, the rough secondary structure of one chain of the hinge peptide do not change. (d) Hydrogen bon& It is also interesting to search for hydrogen bonds, although the number of groups susceptible of giving them is not very high owing to the presence of so many prolines. The cycles of very negative electrostatic energy were considered in greater detail in order to search for hydrogen atoms located at short distances (about 1.8 A, Pauling, 1960) from oxygen or nitrogen atoms, thereby removing the repulsive Van der Waals potential between this pair of atoms. This is indeed a very easy method of simulating the effect of hydrogen bonds. No low energy structures were found to give rise to hydrogen bonds. Nevertheless, one high energy conformation de0 6o 0 0 bs40 lBo is very interesting from this point of view. The H, atom of one chain is located at a distance of l-4 d from the O1 atom of the other chain and the peptide bonds before cysteine 1 of both chains are parailel. Unfortunately, short-range interactions arise between the cysteine 1 sulphur of one chain and backbone atoms of the other chain. However, it might be hoped that angle adjustments could diminish the energy. (e) Tertiary structure of the hinge peptide and hinge mechanism Since several cycles of about the same energy are available, their spatial structures can be studied with the aid of molecular models. The structures with proline 3 in a are found to be relatively compact, the cyclic side chains of prolines 3 and 5 and of
STUDY
OF
THE
HUMAN
IgUl
HINGE
233
PEPTIDE
both prolines 2 being respectively parallel to each other. On the other hand, the structures with proline 3 in d are found to be more extended. A characteristic feature of the IgG molecule is that a wide range of angles is observed in the electron microscope between the two Fab fragments (Feinstein & Rowe, 1965; Valentine & Green, 1967). As Green (1969) points out in his review on electron microscopy of immunoglobulins, this can be due to a flexible hinge region with low energy barriers between the various alternative conformations or to a population of stable isomers with high energy barriers between the various conformations. But he does not accept this last hypothesis as probable because a unique sequence would be unlikely to fold into a large number of different stable conformations. Considering the present energy calculations, however, it seems that the assumption of a population of stable isomers might not be so easily rejected becauseit has been proved that the same word can give rise to cycles of different tertiary structures by closing the bridges in different manners. To illustrate this fact, the cycles dzgoa5od d dzgo270(A) and dzEo130d d d2go27o(B) were considered. They are equally probable sincetheir energiesare of the sameorder of magnitude and the orthogonal&y of the S-S bridges is in both casesrespected (in other words, the x3 angles lie in the range of 67 to 106”, Perahia & Pullman, 1971). However, it can be seen in the molecular models that, although the initial single chains have the same helical structure, the resulting double-strand structures are rather different becauseof the different position of the cysteine 1 side chain and thus of the two-fold axis. If the left chains of the peptides A and B are placed contiguously, the N-terminal end of the B right chain comes toward the observer with respect to the A right chain. Figures 5 and 6 give the projection of moleculesA and B on a plane passingthrough the two-fold axis and the Hz atoms. The change in tertiary structure
Fra. 5. Projection of cycle axis and the Ha atoms.
daoa a6o d cl d29o 270 on & plane
passing
through
the M,M4
two-fold
234
Fra. 6. Projeotion of cycle axis and the Hz atom.
C. RENNEBOOG-
SQUILBIN
daso I30 cl d daao aro on a plane
passing
through
the M,J&
two-fold
between both cycles is also reflected by the wide difference of orientation of the cysteine 1 e--N bonds. A partial information about this orientation difference is given by the angle formed by both C--N bonds (100” in caseA and 145” in caseB, column 7 of Table 10). The following question now arises. Is the value of this angle of some significance with respect to the angle shown by the Fab fragments on the electron micrographs Z The answer would seemto be yes. If the Fab fragments are really independent rigid units (this hypothesis is supported by many observations, seefor example Dorrington $ Tanford, 1970), it seemslogical to conclude that their orientation in spacewill be influenced by the direction of the bonds which bind them to the hinge region. The computed values vary from 58 to 145”, the d d d d conformation being the more “open” one. This doesnot mean that smaller or larger angle values are excluded, since the number of structures studied in great detail is limited. It is, at the moment, difficult to make a choice between the two hypotheses cited above. The first one supposedthe existence of low energy conformations which can transform int.0 each other by rotation of the free angles without encountering high energy barriers. In this case, one could imagine that the mechanism of the hinge is that of a pair of scissorsthe arms of which are not necessarilycoplanar. Rotations of the cysteine side ohain x angles from one favourable conformation to another one (certainly with someadjustments of the backbone angles)would changethe orientation of the two polypeptide chains with respect to each other and would give the opening of the scissorarms. The second hypothesis supposedthe existence of a population of stable isomers. It must, then, be concluded that during the polypeptide chain synthesis, the random manner of closing the bridges will give a diversity of tertiary structures. In this case,
STUDY
OF THE
HUMAN
IgGl
HINGE
PEPTIDE
235
the binge region would be perfectly rigid. Its apparent flexibility would be due to the numerous
ways of realizing
the cycle and the mobility
of the Fab fragments
a&&d
by the fluorescencedepolarization experiments would be essentially due to rotations around
the axis joining
each Fab fragment
to the Fc fragment
(Yguerabide
et al.,
1970). The question arises, if the same conception of hinge mechanism is valid for a hinge peptide containing ouly one disulphide bridge like the rabbit one ? The great difference lies iu the fact that the twoifold axis, if it exists, may have an infiuite number of different orientations in the plane perpendicular to the S-S bridge. That means that a siugle chain iu a certain conformation (say, for instance c d d d if only 4 amino acids are considered) could give rise to different double-strand structures by a rotation of 180” around the two-fold axis. The structures would follow from the
choice of the two-fold axis direction. However, such a hypothesis should be tested in further calculations. The author wishes to thank Professor R. Hamers and Dr J-L. De Coen for useful discussion and valuable criticism and Dr C. Cherton and Mr R. Devillers for their help in preparing the computer program. The calculations of this work were carried out on the CDC 6400 computer at the Vrije Universiteit, Brussels.
REFERENCES Brent, D. E., Miller, W. G. & Flory, P. J. (1967). J. Mol. Biol. 23, 47. Bulletin World Health Organization (1964). 30, 447. Cohen, S. & Porter, R. R. (1964). Advanc. Inwwunol. 4, 287. Corey, R. B. & Pauling, L. (1953). Proc. Roy. Sot. (London) B141, 10. Dayhoff, M. 0. (1969). Atlas of protein sequences and structure, 4, D73. De Coen, J. L., Elefente, G., Liquori, A. M. & Damiani, A. (1967). Nature, 216, 910. Dorrington, K. J. & Tanford, C. (1970). Advanc. Immunol. 12, 333. Edelman, G. M. (1969). J. Amer. Chem. Sot. 81, 3155. Edelman, G. M., Cunningham, B. A., Gall, W. E., Gottlieb, P. D., Rutishauser, U. & Waxdal, M. J. (1969). Proc. Nat. Acud. Sci., Wash. 63, 78. Edelman, G. M. & Gall, W. E. (1969). Ann. Rev. Biochem. 38, 415. Edehnan, G. M. & Ponlik, M. D. (1961). J. Es@. Med. 113, 861. Feinstein, A. & Rowe, A. J. (1965). Nature, 205, 147. Fleischman, J. B., Pain, R. H. & Porter, R. R. (1962). Arch. Biochem. Biophys. SuppI. 1, 174. Frangione, B., Milstein, C. & Pink, J. R. L. (1969). Nature, 221, 145. Goldstein, D. J., Humphrey, R. L. & Poljak, R. J. (1968). J. Mol. BioZ. 35, 247. Green, N. M. (1969). Advanc. Immunol. 11, 1. Grey, H. M. & Kunkel, H. G. (1964). J. Exp. Med. 120, 253. IUPAC-TUB Commission on biochemical nomenclature (1970). J. Mol. Biol. 52, 1. Leach, S. J., Nemethy, G. & Scheraga, H. A. (1966). Biopolymers, 4, 369. Leung, Y. C. t Marsh, R. E. (1968). Acta Cry&. 11, 17. Liquori, A. M. (1969). Quart. Rev. Biophys. 2, I, 65. Liquori, A. M., Damiani, A. & De Coen, J. L. (1968). J. Mol. Biol. 33, 446. Mitchell, A. (1968). Tables of interatomic distances and configuration in molecules and ions. The Chemical Society, Burlington House, London + supplement (1959). Nisonoff, A., Wissler, F. C., Lipman, L. N. & Woernley, D. L. (1960). Arch. Biochem. Biophy.9. 89, 230. Panling, L. (1960). The n&we of the chemkal hod. Cornell University Press. Perahia, D. L Pullman, B. (1971). Biochem. Biqhys. Rea. Comm. 43, 65. Porter, R. R. (1969). Biochem. J. 73, 119.
236
C.
RENNEBOOG-SQUILBIN
Smith, D. S. & Utmmi, S. (1967). Nature, 216, 332. Terry, W. D. & Fahey, J. L. (1964). Science, 146, 400. Terry, W. D., Matthews, B. W. & Davies, D. R. (1968). Nature, 220, 239. Valentine, R. C. 81 Green, N. M. (1967). J. Mol. Biol. 27, 616. Yguerabide, J., Epstein, H. F. & Stryer, L. (1970). J. Mol. Biol. 51, 573.