H. J. G. Hayman The Hebrew University Jerusalem, Israel
Models Illustrating the Helix-coil Transition in Polypeptides
T h e usual atom models of the Stuart type1 are not suitable for demonstrating the transition of a polypeptide molecule from a random chain to the a-helix conliguration.2 The comparatively free rotation about single bonds in most of these models makes it difficult to build a satisfactory model of the a-helix unless some method is adopted for giving this configuration some inherent stability. I n the Courtauld atom modelsa this difficulty is overcome by representing the hydrogen bonds in the molecule by elastic bands connecting the appropriate oxygen and hydrogen atom models; these models, as also those described by Corey and Pauling,4 are quite satisfactory for illustrating the a-helix configuration but are unsuitable for demonstrating the helix-coil transition. We describe here some modifications of the Fisher=rschfelder-Taylor atom models5whereby a model of a polypeptide molecule in the form of a random chain can easily be rolled up to give the a-helix configuration and then unrolled again to give once more a random chrtm. This model of the a-helix configuration is stabilized by an extension of the method we described recently6 for stabilizing the staggered configurations of aliphatic chains. This method of stabilizing the a-helix configuration n7assuggested by the mathematicalmodelused by Lifson and Roig' for treating the helixcoil transition in polypeptides. According to Pauling, Corey, and B r a n ~ o nthe , ~ bond between the carbon and nitrogen atoms in a peptide linkage has a pronounced douhle bond character so that the amide group 0
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C
face of the triangular oxime coordination type nitrogen atom of the NH group.8 This pin fits into a hole (1.65 mm diameter and 5 mnl deep) drilled into one of the single bond faces of the triangular carbon atom of the CO group. (This hole can he seen in the face of the carbon atom model on the extreme right of Fig. 4.) We provide our nlodels with a certain an~ountof inherent stability when in the a-helix configuration by modifying them so that they have additional stability whenever the angles of rotation about the single bonds 1 and 2 in the above structural formula correspond to those in the a-helix. This is achieved, without sacrificing the flexibility of the random-chain form of the models, by drilling nine holes (0.9 mm diameter and 4-5 mm deep) in the appropriate single bond faces of the triangular carbon and nitrogen atom models, as shown in Figures 1 and 2. The polar coordinates of the centers of these holes are given in Tables 1 and 2. If we intend constructing both left-handed and righthanded helices, the final stage in the modification of these triangular carbon and nitrogen models is the insertion of three pins, whose shanks have been cut down to a total length of 4 mm, into the holes marked B so that only their rounded heads (2.3 mm diameter and 0.7 mm high) project above the surface of the atom model face. If, however, we are interested only in left-handed helices, confusion can be avoided by inserting three more such pins into the holes marked L;
C 2/
C~pi \H
will be essentially planar. We obtain this planarity in our model by utilizing the pin of the douhle hond
STLTLRT, H. A_,Z. physik. Chem. (Leipzig), B27,350 (1934). PAFLING, L.,COREY,R. B., AND B R ~ N S OH. N ,R., PTOC.Nat. A d . Sci., US.,37, 205 (1951). Ohtitinable from Griffin & George (Sales) Ltd., Ealing Road, Alperton, Wemhley, Middleaex, England. ' COREY.R. R.. AND PAI:LIXG. . L.,. Rev. Sci. Instr., 24, 621 (1953). 6 Oht~inahle from Fisher Scientific Co.. 633 Greenwich St.. New York 14, N . Y . HAYMAN, H. J. G.,J. CHEM.EDUC., 40, 208 (1963). LIFSON, S., AND ROIG, A,, J . Chem. Phys., 34, 1963 (1961). A triangular nitro group type of nitrogen atom model has also been used successfully by removing the pin from one of the two douhle hond faces so that it can be connected to a hydrogen stom model. ~
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Figure I . atom.
Arrangement of holes for plnr in face of a carbonyl carbon
Table 1 . Polar Coordinates ( r , 9 ) o f Holes for Pins in Face of Triangular Carbon Atom Models (Fig. 1 ) -
( 6 mm, 0') ( 7 . 5 m m , 225') ( 9 m m , 135")
Volume
( 6 m m , 112.5') ( 7 . 5 mm, 3 3 7 . 5 " ) ( 9 m m , 247.5')
(6 m m , 247.5") ( 7 . 5 mm, 112.5") ( 9 mm, 22.5")
41,Number 10, October 1964 / 561
the triangular nitrogen atom model is equiangular and that the valence angle between the two single bonds of the triangular carbon atom model is equal to 112'. The above modifications to the standard FisherHirschfelder-Taylor atom models were carried out with the help of suitable templates. Details of the construction of a typical template and its accessories can be seen in Figure 5.
Figure 2. -tom.
Arrangement of holes for pins in face of a peptide nitrogen
Table 2.
Polar Coordinates (r, 0) of Holes for Pins in Face of Nitrogen Atom Models (Fig. 2)
(6 mm, 0") ( 7 . 5 mm, 240') (9 mm, 120')
(6 mm, 94.6O) ( 7 . 5 mm, 334.6O) (9 mm, 214.6')
mm, 265.4' ( 7 . 5 mm, 145.4' (9 mm, 25.4' (6
these additional pins serve to eliminate the inherent stability of the right-handed helix but not that of the left-handed helix. Similarly, if we wish to build models of right-handed helices only, we insert the three additional pins into the holes marked R. When our models are arranged in the appropriate a-helix configuration, the heads of these pins fit into a series of conical depressions (2.3 mm diameter) drilled into two of the four faces of each atom model representing the a-carbon atom of the amino acid. Details are shown in Figures 3 and 4, and in Table 3 which gives the polar coordinates of the centers of these depressions for an a-helix consisting of 3.6 amino acid residues per turn. These coordinates have been calculated on the assumption that
Figure 5. a. Arrangement whereby the nitrogen atom model can b e mmpped onto the template and kept a t the correct angle b y being pressed between two rollen. b. The templote osembly, ready for use.
In the actual molecule, the stability of the a-helix is due to hydrogen bonding between the hydrogen atom of each NH group and the oxygen atom of the CO group in a n adjacent turn of the helix. Unfortunately, these two atoms are too close together in the a-helix to be represented satisfactorily by the standard FisherHirschfelder-Taylor atom models; we overcame this difficulty by using henlispherical hydrogen atom models made of flexible orange-colored foam plastic glued to a brass base as shown in Figure 6. These hydrogen
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Figure 6. Detoilr of the flexible hydrogen atom model used for hydrogen bonds; dimensions ore given in mm. Figure 3. Arrangement of conical depresgions in that foce of the tetmhedral carbon atom whhh will b e in contoct with the corbonyl carbon otom.
Table 3.
Polar Ceodinates ( r , 0) of Conical Depressions in Faces of Tetrahedral Carbon Atom Models
Face in contact with carbonyl carbon atom (Fix. - 3) (6 mm, (6 mm, ( 7 . 5 mm, ( 7 . 5 mm, (9 mm, (9 mm,
562
/
Figure 4. Arrangement of conirol depressions in that face of the tetrahedral carbon atom which will be in contact with the peptide nitmgen atom.
56.2') 303.8") 78.8") 191.2") 168.8") 281.2")
Face in contact with peptide nitrogen atom (Fie. 4) (6 mm, 47.3") (6 mm, 312.7") ( 7 . 5 mm, 72.7') (7.5mm, 167.3") (9 mm, 192.7") (9 mm, 287.3")
Journal of Chemiml Education
choin and portly in the form of o left-handed a helix. The eighteen giycine residues in this helix form exactly five complete ?urn%
atom models are readiiy compressed when forming the m-helix configuration, but regain their hemispherical shape when the model is converted back to a random
cham; this can he seen clearly in Figure 7 which shows a model of a polyglycine molecule partly in the form of an a-helix and partly as a random chain.
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