Studies on helical structures for polypeptides of the nonplanar peptide unit

Abstract

The calculations reported in this chapter show that the torsional potential functions for and developed by Kolaskar and Prashanth (1979) are superior to the generally used ones, since the trans dipeptide energy map obtained by them is closer to the equivalent energy map obtained from an analysis of protein structures. This study also shows that for a dipeptide, a distortion of the angle is energetically more favorable than that of the angle . Thus, the global minimum energy obtained by minimizing the energy at each grid point of the ( , ) map with respect to and occurs for a conformation with = 113.4°. On the other hand, in this conformation, the peptide unit is practically undistorted ( = +0.7°). However, it is seen that distortions of the peptide unit are readily feasible since a distortion by as much as 10° raises the energy by only 0.6 kcal/mole. The above observation, that the minimum energy conformation has a value of greater than 110°, is in contrast to the result obtained by Balasubramanian and Ramakrishnan (1972), who obtained a value of 105° for their minimum energy conformation. These differing results are not surprising in view of the fact that the global minimum energy conformations in the two cases are in different regions of the map. Since in their calculations the potential functions for and are those given in Table 2.3, the global energy minimum occurs in the -structure region, whereas it occurs in the -region when the new torsional potential functions are used, as has been already mentioned. If the -region alone is considered, it is found that in their calculations too, the local minimum energy is lowest for a value of larger than 110°, viz., 115°. Similarly, the energetically allowed regions of the ( , ) map are affected more by a distortion of the angle than of . The effect of increasing from 110° is to marginally expand the allowed regions of both the - and -regions in the direction, while shrinking the L-region in the direction. Decreasing produces the opposite effect. It is seen that the L-region becomes even more unfavorable than for = 110°, with the result that the positions of the left-handed forms of the - and 3 -helices lie outside the 5 kcal/mole contours for = 105°. For this value of , however, a different left-handed structure, called the S-helix, can occur in the L-region. It will be seen in a later chapter that this structure is stereochemically possible only when is close to this value and the peptide unit is also distorted ( , 10°). The helical parameters (n = -4.2, h = 1.2 Å) are such that this structure is not possible for = 110°, = 180°. This is evident from the (n,h) map given in Fig. 3.5. However, for = 105° and = 170°, it becomes possible and lies within the 3 kcal/mole contour, as can be seen from Figs. 3.8d and 3.9. The present investigations also show that the distortion of plays a greater role in the stability of structures in the -region than in the -region. While minimizing the energy with respect to and , it was found that the low-energy conformations in the -region have values of and close to 110° and 180°, respectively. The local minimum energy conformation of this region has values = 110° and = -0.3°. Only very few conformations in the neighborhood of this minimum, which lie within the 2 kcal/mole contour, have values of and differing from their standard values by more than 1.5°. In the -region, the situation is different. The energy minimum (-70°, -20°) occurs for a conformation with distorted (113.5°), making its energy lower than the minimum of the -region. In this region, the conformations with undistorted and lie in the neighborhood of the point (-100°, -70°), which lies only within the 3 kcal/mole contour. For larger values of , the value of of the minimum energy conformation of each grid point steadily increases and becomes very large as the (0°, 0°) conformation is reached. For example, the conformation (-40°, -20°), which lies within the 2 kcal/mole contour, has the value of as high as 118°. A look at the = 110°, = 180° map shows that this point does not lie within even the 5 kcal/mole contour, whereas it lies within the 3 kcal/mole contour of the map for = 115°, = 180°. Nonplanarity of the peptide unit is far less in evidence, and the absolute value of of any conformation lying within the outermost energy contour rarely has a value greater than 1.0°. All the above dipeptide energy calculations have been done with L-alanine as the sidechain. However, all amino acids, with the exception of glycine, have sidechains longer than alanine, so that the allowed regions for these residues would be expected to be more restricted. Dipeptide energy calculations for amino acids with longer sidechains have been done by the classical (Ponnuswamy and Sasisekharan, 1971; Sasisekharan and Ponnuswamy, 1971) and the quantum chemical (Pullman and Pullman, 1974) approach. The work of Sasisekharan’s group shows that the allowed regions of the L-alanyl dipeptide map get further reduced by the presence of a C H group but not so much by an OH group. They also found that the presence of the C atom and atoms beyond has little further effect on the dipeptide map. However, branching of the chain at the C atom restricts the allowed regions of the map. Nevertheless, the positions as well as the relative energies of the local minimum energy conformations were found to be very similar to those obtained for the L-alanyl sidechain. Therefore, the results of the energy calculations at the dipeptide level reported in this chapter can be considered, in general, valid for any amino acid. Dipeptide energy calculations with different peptide geometry (Ramachandran et al., 1974) yielded results which are not significantly different. It was found that for = 110°, = 180°, the positions and values of the energy minima, as well as the shapes of the contours, are very similar. This result implies that individual residues in proteins and polypeptides can undergo small fluctuations in geometry without becoming energetically unfavorable. Investigations carried out on the cis dipeptide showed that the positions of the local energy minima, as well as the shapes of the contours, are quite similar to those of the trans dipeptide. The global energy minimum (-4.0 kcal/mole) is only 0.6 kcal/mole higher than that of the trans dipeptide map. However, the areas enclosed by successive contours are smaller, and the - and L-regions are not bridged by even the 3 kcal/mole energy contour. These results, therefore, show that although at the dipeptide level the cis peptide unit is energetically less favorable than the trans peptide unit, this difference is very small so that it should still be expected to occur in proteins and polypeptides. However, it is found that cis peptide units occur only where proline residues are involved. The work of Ramachandran and Mitra (1976) suggests that to explain this, a larger number of residues must be considered. The energetics of structures with a larger number of cis peptide units is therefore dealt with in a subsequent chapter. The investigations carried out and reported in this chapter show that distortions of the peptide bond, and of the bond angle (N-C -C), considerably increase the conformational flexibility of polypeptides. Although the global minimum energy corresponds to a right-handed structure with the 5 1 hydrogen bonding scheme and with helical parameters n = 3.54, h = 1.47 Å, variations of this structure with different helical parameters are also energetically favorable, as is shown below. From Fig. 5.5, it is evident that the 5 1 class of structures can occur with a pitch ranging from about 4.75 Å to 5.7 Å, having energies which are only 1-2 kcal/mole above the global minimum. The 5 1 helix is the most stable structure up to a pitch of 5.85 Å, but beyond this value of pitch, the 4 1 helix becomes more favorable. Thus, a structure with a pitch in the region of 6 Å need not necessarily have a 3 -helical conformation, as has previously been believed. For this value of pitch, a 4 1 structure with n 4 and h 1.5 Å is only slightly less favorable than a 4 1 structure with n 3 and h 2.0 Å. In fact, if the alanyl sidechain is substituted by -aminoisobutyric acid, the 5 1 structure becomes even more favorable (Venkataram Prasad and Sasisekharan, 1979). As in the case of the helical pitch, the value of n also varies quite widely for the various structures. In the case of the 5 1 structure, it ranges from about 3.4 to 3.8 (Table 5.3). For these conformations, varies by about 10° and by as much as 20°. Thus, the characterization of a regular structure should be done not on the basis of the ( , ) values or on the helical parameters, but rather on the hydrogen bonding scheme and on the “virtual” torsion angle . The present study indicates that this angle is quite characteristic for each type of helix (Table 5.4). By analogy with the right-handed helices, the left-handed -helix would be expected to be the most stable of all left-handed structures. However, the present investigations on all the possible types of left-handed structures show that this is not so. Instead, a structure with the reverse type of hydrogen bonding scheme (1 4), called the S-helix, is the most stable left-handed helix. It was interesting to find that in this structure, good hydrogen bonds can be formed only when and are both distorted from their standard values. Because of this, the conformational freedom of this structure is less than that of the 4 1 helices, as can be seen from the smaller range of pitch that it can adopt (Fig. 5.5). However, it was interesting to observe that the minimum of the curve occurs at a value of very close to the minimum of the right-handed 5 1 helix. Therefore, these energy calculations show that if a polypeptide is constrained to take up a left-handed structure, the S-helical structure is most likely. The above result is important in view of the fact that experimental studies have shown that under certain conditions, some polypeptides prefer left-handed structures to the right-handed -helix. It appears very likely that in these cases, it is the S-helical structure that is taken up, and not the -helix or its modification, the -helix, as has been previously believed. The possibility of the S-helical model for these different polypeptides is, therefore, investigated, and this is reported in the next chapter. As already mentioned in the previous chapter, the S-helix has also been implicated in the structure of the N-terminal segment of the repressor. The investigations on helices with cis peptide units show that the reason for their rare occurrence is chiefly due to the non-feasibility of formation of intrachain hydrogen bonds. It was found that in terms of only nonbonded energy, a helix with all cis peptide units is more favorable than the -helix, but overall the structure is about 4 kcal/mole higher in energy. The calculations reported in this Chapter on isolated single helices, without considering the packing forces, show that the S-helical structure is energetically more favorable than the left-handed structures that have been proposed for PBA and PPEA. For PBA, the S- and -helical structures all have comparable energy. The existence of this compound in the form of -helices is, therefore, not surprising. Among the left-handed structures, the S- and -helices are far more stable (by about 17 kcal/mole) than the -helix, which had earlier been proposed for this compound. Since this difference is too large to be compensated by packing forces, the -helix can be ruled out as the structure taken up by PBA. The -helix is also unlikely since the values of h (1.16 Å) and P (-4.91°) are very different from the experimentally observed values. Although, in these calculations, the helical parameters of the S-helix (n = -4.2, h = 1.28 Å) were not exactly equal to the experimentally observed values for PBA (n = -4.0, h = 1.325 Å), it is possible to obtain a structure with the exact values by distortions in the peptide geometry. The calculations on poly(L-alanine) with a different peptide geometry, reported in the previous chapter, show that the above results are unlikely to be affected by it. It is, therefore, proposed that the left-handed structure taken up by PBA is the S-helix. For PPEA, too, the S-helical structure is more stable than the -helical structure. In fact, the difference in energy (5.5 kcal/mole) is more than that for PBA (1 kcal/mole). Unlike for PBA, the experimentally observed helical parameters of the left-handed structure of PPEA are close to those of the -helix, so that it can be considered as a possible model. However, the large difference in energy between the two structures (5.5 kcal/mole) suggests that the structure taken up by PPEA is the S-helix and not the -helix, as has been reported by Sasaki et al., (1981). It can be seen that the sidechain arrangements of the -structure and conformation III of the S-structure are similar, so that this result is unlikely to be reversed even if packing energy is also taken into account. The energy calculations carried out on poly(L-Phe) for the different helical structures show that although the benzene rings can stack better in the S-helical structure as compared to the -helical structure, the latter is more stable by 5.68 kcal/mole. This result is interesting, since it was seen in the previous chapter that for larger sidechains which contain benzene rings, as in PBA and PPEA, the situation is reversed, and the S-helical structure becomes slightly more favorable. The larger length of the sidechain and the interaction of the sidechain ester group may, therefore, play a part in stabilizing the S-helical structure of the polymers of esters of aspartic acid as compared to the -helix. The results of the present calculations are in agreement with the solution and fiber diffraction studies, which show that poly(L-Phe) exists in the -helical form. Since the handedness of the helices of poly(L-Phe) in the solid state has not been established, it is not possible to determine the type of helix which coexists with the -helix. These calculations show that among the left-handed structures considered, the S-helix is energetically the most stable. However, the helical pitch of all these structures is different from the value reported by Yamashita et al., viz. 5.59 Å, so that if left-handed helices are indeed present, they must be in a highly distorted form. On the other hand, if they are of the right-handed variety, they may be in the form of 4 1 hydrogen-bonded helices with distorted peptide units ( -10°), although its energy is higher than the S-helix by 2.4 kcal/mole. No definite conclusion can, therefore, be drawn until further experimental work is carried out. Conformational studies on the polymers of the acidic amino acid serine and the basic amino acid , -diaminopropionic acid show that for both compounds, the structures which facilitate sidechain-mainchain hydrogen bonding are the - and S-helices. The nature of hydrogen bonding in the -helical structure is, however, different for the two compounds. The sidechain -OH group forms a hydrogen bond with the carbonyl oxygen of the previous peptide unit in poly(L-Ser), while in PDPA the -NH group forms a hydrogen bond with the oxygen of the same peptide unit. Energy calculations performed on PDPA suggest that the left-handed structure taken up by this compound in NaDodSO is the S-helix, since its helical energy is lower than that of the -helix by 4.0 kcal/mole. The reason for PDPA not taking up the same structure may be due to the fact that the longer sidechain (an extra -CH group) favors hydrogen bonding with the ionic medium rather than with the main chain, thus destabilizing the S-helical structure. For poly(L-Ser) it was found that the most stable structure is the -helix. However, investigations have shown that in solution, poly(L-Ser) does not take up a helical structure, preferring rather the -structure or the random coil. It is also well-known that many silks which contain a large proportion of serine also adopt the -structure. Since energy calculations on the -structure were not carried out, it is not possible to compare its stability with the -helix. Nevertheless, it can be stated that if poly(L-Ser) takes up a helical structure, it would be the -helix. The serine residue can be accommodated into such a helix without breaking it. Thus, it is not surprising that X-ray crystallography has revealed the presence of serine residues in helical regions of proteins. It had been mentioned (Fraser and Mac Rae, 1973) that in myoglobin, the torsion angle of a serine residue in an -helical segment has a value of +60° so that the sidechain-mainchain O -H…O hydrogen bond can be formed. However, calculations show that this O…O distance is too large (3.44 Å) for hydrogen bond formation, and there is also a short contact distance of 2.1 Å between the O and O atoms. The serine residue can, on the other hand, be readily accommodated if has a value of -55° (Table 7.2).