Spare parts for helix–helix interaction

R. Preissner, A. Goede and C. Frömmel1

Institute of Biochemistry, Charité, Medical Faculty of the Humboldt University, Monbijoustr 2, 10117 Berlin, Germany


    Abstract
 Top
 Abstract
 Introduction
 Materials and methods
 Results and discussion
 Conclusions
 References
 
About 6000 contact regions (patches) of helix-to-helix packing from 300 well-resolved non-homologous protein structures were considered. The patches were defined by the spatial helical neighbors and were estimated in atomic detail using a variable distance criterion. The following questions are addressed. (1) Are the amino acid preferences and atomic composition of distinct types of helical patches indicative for the type of their neighbor? Distributions of size, atomic composition and packing density are compared for different types of helical interfaces. Thereby contact preferences are derived for parts of secondary structures adjoining each other or pointing towards the solvent. (2) Is it possible to cluster helical patches according to their structural similarity? For these purposes the patches were classified with an automatic sequence-independent superposition procedure which yields a distinctively reduced set of representative interfaces. On this basis, the methodology for finding exchangeable patches in different proteins is demonstrated.

Keywords: classification/helix packing/mimicry/similarity


    Introduction
 Top
 Abstract
 Introduction
 Materials and methods
 Results and discussion
 Conclusions
 References
 
For various proteins the appearance of secondary structures at early stages of folding has been experimentally proved (Peng et al., 1995Go). The following steps can be considered as docking of preformed elements. In this sense the interfaces between the secondary structures are of outstanding importance. Especially helix–helix interactions have been examined extensively from the beginning of protein structure research (knobs into holes model; Crick, 1953). This was the first approach considering {alpha}-helices as cylinders which can be unrolled into a plane. The lattices resulting from this projection of the C{alpha}-atoms were the basis for the majority of later studies. The helix–helix packing in coiled coils as considered by Crick (1953) and confirmed by Kendrew et al. (1960) was accessible to molecular simulations in the course of which the packing of single side chains in core positions appears very important for oligomerization (DeLano and Brünger, 1994Go). A packing analysis emphasizing the importance of the individual side chains in coiled coils was presented by Offer and Sessions (1995).

Because of their aesthetics, graphs of {alpha}-helices in biochemical textbooks outlined an idealized picture of this structurally diverse secondary structural element and of its packing. Considerable work has been done in the last two decades to draw a more realistic portrait of the complex helical arrangements. Approaches exploring the propensities of charged amino acids at helix termini (Chou and Fassman, 1978) focused on the helical dipole (Hol et al., 1978Go), providing explanations for enzymatic functions (Hol, 1985Go). Analysis of typical helical sequence patterns exhibiting clear (heptad) periodicity of hydrophobicity (Eisenberg et al., 1982Go) not only revealed the helical wheel model but also allowed the prediction of helices from their sequence including the relative arrangement (Cohen and Kuntz, 1987Go) or special types of termini (Bork and Preissner, 1990Go). A review of the work concerning {alpha}-helix-forming amino acid propensities was given by Creamer and Rose (1994).

Along with the growing number of highly resolved protein structures, it became obvious that {alpha}-helices are not just ideal cylinders fixed by linear hydrogen bonds but they are actually often curved (60%) or even kinked (Barlow and Thornton, 1988Go) and 90% of the hydrogen bonds are bifurcated (Preissner et al., 1990Go).

The packing of helices has been subjected to a number of detailed studies for particular proteins. Richmond and Richards (1978) examined helix packing in myoglobin in terms of interface size and Voronoi volumes. They pointed out the meaning of the size of the contact surface area which was emphasized in correlation with packing angle preferences (Bowie, 1997Go).

Efimov (1979) analyzed five proteins and found correlations between side chain rotamers of hydrophobic residues and helix packing (polar/apolar packing model). From a set of 10 proteins the `ridges into grooves' model was developed by Chothia et al. (1981). About 700 pairs of helices from well resolved proteins allowed a statistical analysis of interhelical angles and distances (Reddy and Blundell, 1993Go). Walther et al. (1996) continued the studies of helices from 220 proteins as lattices in a rigorous mathematical manner. Bowie (1997) found that different packing models do not adequately explain the distribution of the interhelical torsion angle, although Chothia et al. (1981) stated that a simple model would predict parallel helical axes as the most probable.

Experimental approaches to helix transplants between different proteins were made a decade ago (Du Bose and Hartl, 1989Go), but methods permitting the rational selection of candidates are missing.

The analysis given here concentrates on the molecular surface patches between {alpha}-helices as defined in Preissner et al. (1998). The idea is the use of such interfaces within proteins as a learning set for intermolecular recognition processes and for the prediction of contacts occurring during protein folding and association. Their extent is directly governed by the atomic contacts between the secondary structural elements.

Our approach was guided by a number of questions, as follows:

  1. Are there amino acid preferences for helix–helix interfaces different from other patches of the helix surface (contact preference)? This rule would be valuable for the prediction of packing regions on the surface of helices and might be combined with successful prediction procedures for packing of ideal helices (Mumenthaler and Braun, 1995Go).
  2. Are the local atomic packing densities equally distributed between the different types of helix patches (helix–helix, helix–coil, helix-extended)? For this purpose, a new error-avoiding method for volume computation was used (Goede et al., 1997Go) to achieve a better understanding of energetic constraints during folding (Gogonea and Osawa, 1994Go).
  3. Is it possible to sort helical patches according to their structural similarity like building blocks or parts of a jigsaw puzzle? This problem is tackled with an automatic sequence-independent alignment procedure (A.Goede, R.Preissner and C.Frömmel, in preparation). A successful classification of helix patches (according to r.m.s. values) could yield a model kit suitable for protein engineering.


    Materials and methods
 Top
 Abstract
 Introduction
 Materials and methods
 Results and discussion
 Conclusions
 References
 
Interface database (DIP)

This work is based on the Databank of Interfaces in Proteins (DIP); for details, see Preissner et al. (1998). A subset of 300 well-resolved protein structures from the Brookhaven Protein Data Bank (Bernstein et al., 1977Go) was selected to avoid redundancy. A database of about 150 000 surfaces was created, analyzing the inter-secondary contacts within proteins and their contact with solvent. A retrieval system allows fast scans for different criteria such as origin (helix, coil, sheet), extent (length, width, depth, number of atoms), shape or density.

Definition of secondary structures

The protein structure was dissected into structural elements on the basis of secondary structure. There is a variety of methods to assign the location of structural elements of proteins on the basis of hydrogen bond patterns, {phi}-, {Psi}-angles or backbone curvature (Colloc'h et al., 1993Go). In principle, the assessment of secondary structure is an unambiguous procedure, but known algorithms are not free of artifacts (Colloc'h et al., 1993Go). To be comparable to other studies we chose the common method of the DSSP program written by Kabsch and Sander (1983) to assign helical segments `H' (4-helix = {alpha}-helix) and extended ß-strands participating in ß-ladder `E'. All other segments are summarized under coil `C'. The most significant artifact of the Kabsch–Sander algorithm is the high frequency of short helices assigned in other methods as coil (Colloc'h et al., 1993Go). Therefore, only helices with more than four residues were taken into account in this analysis.

Calculation of atomic neighbors

To avoid artifacts in the interface definition resulting e.g. from different refinement methods during structure determination, not only a singular distance criterion was used but for any calculated atomic contact in a distance range from –0.5 to 2.5 Å the corresponding distance between the van der Waals surfaces was stored.

We used the atomic radii of Stouten et al. (1983). Contacts at negative distances (meaning overlapping van der Waals spheres) are predominantly found for hydrogen-bonded atoms. The compositional data presented here (Tables I and IIGoGo) refer to the strict criterion of cut-off = 0.0 Å. For larger cut-off values the atomic composition becomes more similar (for details, see Preissner et al., 1998).


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Table I. Amino acid propensities for particular patches of helices
 

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Table II. Atomic composition of about 25 000 helical patches (percentage)
 
Interface definitions

Interior interfaces. An interface is built by two patches from neighboring secondary structural elements. The patches are constituted by those atoms fulfilling the above-mentioned contact criterion. This analysis is focused on patches of the following type: helix–helix (HH), helix-extended (HE), helix–coil (HC), helix–solvent (Hout).

Exterior patches. For the external surface and the surface of larger holes in proteins the positions of neighboring atoms, e.g. the water molecules, are mostly unknown. In our approach the distance of protein atoms to a continuous solvent is defined using the molecular surface according to Connolly (1983a). This exterior surface is generated by the closest possible van der Waals surfaces of virtual solvent atoms and can be used as a neighbor for superficial structural elements. The distance of an atom to the solvent is defined as the minimal distance between the van der Waals and Connolly surfaces.

To verify that the different approaches for interior and exterior patches give similar results, largely inaccessible elements were stripped from their protein environment (e.g. the helix 161–177 from aldolase; PDB code 1ALD) and the cut-off dependence of atomic contacts was compared between the `original protein surrounded' and `virtual solvated' case. Three-quarters of the atoms are found to come into contact at equal cut-off values, some at 0.5 Å lower in the case of virtual solvent because of the assumed perfect atomic packing of the solvent around the protein (mean difference of cut-off values, 0.11 Å; standard deviation, 0.33 Å).

Computation of the Connolly surface

The molecular surface, called here the Connolly surface, serves as a basis for the reasonable handling of solvent patches compared with inter-secondary patches. The first part of the Connolly surface is made up of those parts of the van der Waals surface that are accessible to a solvent probe sphere (radius 1.4 Å) which is rolled over the molecule. Second, to generate a smooth and analytical describable outer-surface contour, parts of the (rolling) probe and tori are joined at circular arcs (Connolly, 1983bGo). For patches exposed to solvent the Connolly surface is used as a close virtual neighbor. The membership of the particular atoms to the solvent patch is estimated by their smallest distance to the Connolly surface (for details, see Preissner et al., 1998).

Amino acid propensities for molecular surface patches

The generally used (helix) propensity e.g. for Ala (<P>HA = 1.52) is calculated according to

while the contact preference for helix–helix regions for Ala (<P>HA = 0.95) is calculated as follows:

where

Variable Explanation of the variable Total number

HA number of Ala residues in helices 3197

Htotal number of residues in helices 24 694

AAtotal number of amino acids in the entire database 87 707

Atotal number of Ala residues in the entire database 7425

HHA number of Ala residues in helix–helix patches 2099

HHtotal number of residues in helix–helix patches in the entire database 17 050

Residues in patches are counted if at least one of their atoms is in contact with the neighboring secondary structure or solvent. In this respect one residue may occur in several patches. Therefore, given values are not propensities in a strict sense, but deviating effects for particular interfaces will be indicated.

Atomic packing density

Volume and density calculations were carried out following the algorithm of Goede et al. (1997). Computing the volume occupied by the atoms and the local packing density in proteins, one is faced with the problem of intersecting spheres. To estimate both, the space between the atoms has to be divided according to the location of the atoms relative to each other. Various methods have been proposed for this purpose which are based on Voronoi's idea of approximating the atomic space by polyhedra. Comparing the known procedures concerned with the allocation of all space amongst distinct atoms, we observed different partitioning of space with deviations up to 60% for particular atoms. Instead of dividing planes between the atoms, we use curved surfaces defined as set of those geometrical loci with equal orthogonal distance to the surfaces of the considered van der Waals spheres. The proposed dividing surface meets not only the intersection circle of the two van der Waals spheres but also the intersection circle of the two spheres enlarged by an arbitrary value (e.g. radius of water). This hyperbolic surface, enveloping the Voronoi cell. can be easily constructed and offers a number of advantages (Goede et al., 1997Go). The local packing density is estimated as the ratio of van der Waals volume and those of the corresponding Voronoi cell.

Structural alignments

An automatic procedure was created to search in a given database (DIP) of interfaces for similar regions. The search can be restricted to patches of comparable size. This superposition approach is based on a normalization of the atomic sets according to the directions of least and largest dimension. These directions are independent of transformations of the coordinate system and stable for small alterations of the atomic positions. The normalization of the atomic sets is unique except for four possible rotations (original arrangement and rotations of 180° around the x-, y- or z-axis). Therefore, the degrees of freedom are drastically reduced and the assignment of pairs of atoms is straightforward for identical and slightly modified atomic sets.

In a first step the centers of mass of the two atomic sets are determined and superimposed followed by a rotation of one of them, such that the major directions (least and largest expansions) coincide. All four normalizations are used in a further step to determine the pairs of atoms between the two patches. Two atoms only form a pair if they are mutually the nearest atoms and their distance is smaller than a given cut-off value. For further calculations the normalization with the largest number of atomic pairs is chosen. For these pairs the root mean square deviation was calculated. This normalization is used in a further step for improvements of the alignment.

In its recent implementation, the alignment procedure gives reliable results for patches of similar size. Thus, for similarity screening of the 24 HH patches constituted by 25 atoms the size was restricted to a range from 20 to 30 atoms (128 patches). In this manner the number of structural alignments required can be reduced from 3.6x107 (6000x6000) to 0.72x107 (6000x1200) for an all-against-all analysis.


    Results and discussion
 Top
 Abstract
 Introduction
 Materials and methods
 Results and discussion
 Conclusions
 References
 
General features of the database

In the database, 2176 helices, 3822 extended strands and 6477 coils were included. Because of the different mean element lengths (LH = 11.4, LE = 6.5, LC = 5.3), this results in the relationship H:E:C = 1:1:2 for the participating amino acid residues. This relationship corresponds to the number of particular helix patches: between helices (HH) 5551, between helix and ß-sheet (HE) 5548, helix and coil (HC) 11245. The number of neighboring secondary structural elements (about 10 for a helix of 11 residues length) increases with increase in the size of the helix. The size distribution of the interfaces depends on the type of interacting patches (see Figure 1Go). Small solvent-directed patches (less than 20 constituting atoms for Hout) rarely occur. While the number of HE and HC patches clearly falls off for larger sizes, HH patches are broadly distributed up to a size of more than 60 atoms.



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Fig. 1. Size distribution of interfaces between particular secondary structures (HH, HE, HC, Hout).

 
Contact preferences

According to the definition in the Materials and methods section, the propensities of amino acid residues for the helix <P>H should not be directly compared with the contact preferences for particular helical patches like <P>HH as given in Table IGo. The contact preferences express predilections additional to those of the particular secondary structural element, which means that the value 1.00 is scaled to the helix propensity of a given residue type. Thus for overall predictions the product of the two values is relevant: the contact preference for prolyl residues to occur in helix-extended patches would be below 0.3 (see Table IGo: <P>Hx<P>HE = 0.43x0.66). The helix-propensities <P>H given in the first row are very similar (correlation coefficient 0.975) to those from redundancy-excluding studies (Swindells et al., 1995Go). The standard deviation of the helix–helix contact preferences <P>HH from the mean (1.00) is clearly smaller (0.14) than that of the helix propensities itself (0.31), but the following trends can be recognized. Charged residues occur less frequently (D, E, K, R) (mean 0.875), while aromatic residues are preferred (F, H, W, Y) (mean 1.14). Generally, the predilection of hydrophobic residues for this type of interface can be confirmed and is found to be even more pronounced for helix-extended interfaces.

A rough comparison of the atomic composition as given in Table IIGo would group each two types of patches together concerning the content of main chain atoms as well as the number of polar atoms: HH and HE against HC and Hout. The equally high content of main chain atoms in the latter results from a somewhat different main chain orientation, which is expressed in an appreciable accessibility of the C{alpha}-atom for the helix–solvent patch and on the other hand by a pronounced dominance of the hydrogen bonding atoms in the helix–coil patch. In Tables I and IIGoGo clear deviations between different parts of the helical surfaces are noticeable in terms of atomic and amino acid preferences. The broadening of the range of amino acid preferences (0.28–1.92 instead of 0.43–1.52) indicates their value for structure predictions.

Similarity screening

The results of the similarity screening are outlined exemplarily for helix–helix patches consisting of 45 atoms (see Figure 2Go). Plotting the number of aligned atoms against the r.m.s. values gives clearly bimodal distributions, which can be fitted by two Gaussians (Figure 2Go). The distribution with its mean value above 1.0 Å can be interpreted as noise, but the other distribution mainly contains reasonable superpositions.



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Fig. 2. Similarity distribution for HH patches (45 atoms). The screening was carried out for 20 patches against 195 patches of similar size (40–50 atoms). The distribution can be fitted by a superposition of normal distributions (shown in the lower part). The mean of the well-aligned patches is 0.56 Å with a standard deviation of 0.14 Å. Taking into account 90% of these cases results in a risk of taking 1% of the neighboring distribution (randomly aligned patches).

 
Such examinations were carried out for patches of different sizes (15–75 atoms). The separation of the distributions depends on the size of the aligned patches. For larger patches (>25 atoms) they are well separated. The criterion for 90% quantile is therefore size dependent (data not shown). For 20 patches with 45 atoms, 4000 alignments were carried out (against 200 patches of similar size). About 200 of them indicate significant structural similarity, which results, on average, in groups of 10 similar patches. Such a cluster of six similar HH patches is illustrated in Figure 3aGo and a pair of similar patches in Figure 3bGo. Two general approaches for clustering were tested. In a first procedure, all patches were grouped into a cluster if they exhibit similarity to at least one of its members. In a second, stricter algorithm only those patches are put together that resemble each other. These two approaches give very different results because of the non-transitivity of similarity (two patches resembling a third do not necessarily resemble each other). With the first approach the clustering of 780 patches consisting of 20–30 atoms above an empirical similarity threshold (r.m.s. value <1.0 Å, >60% superimposed atoms) results in 20 clusters, while the second rigorous method ends up with 325 clusters. The desired reduction in the number of clusters (leading to a representative for each) would be in between. Therefore, a combination of both algorithms with size-dependent thresholds (scoring) has to be developed.





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Fig. 3. (a) A cluster of six similar helix–helix patches from non-homologous proteins. The proteins and the considered helices are given in the first three columns of the accompanying table. The sequences of the helices (in one-letter code) as determined by DSSP (Kabsch and Sander, 1983Go) were arranged such that the structurally superimposed residues (underlined letters) were aligned. Mandelate racemase was chosen as reference structure and patches with more than 80% of the atoms superimposed at an r.m.s. value below 0.5 Å are clustered in this group. The helices are sketched as red cylinders in all three parts of this figure.

Protein     PDB code     Helix residues     Sequence     No. of aligned atoms     R.m.s. value    

Mandelate racemase     1mns     252–260     PEEMFKALS     (Max.)25     Reference

Cytochrome c2     1c2r     B69–B75     EEDIATY     22     0.36    

Hemoglobin     1ith     B101–B108     PKHFGQL     23     0.34    

Actinidin (sulfhydryl proteinase)      2act     50–56     EQELIDC     20     0.48    

Citrate synthase     2cts     122–130     SHVVTMLDN     20     0.23    

Relaxin     6rlx     13–17     KRSLA     22     0.27    

(b) Pair of similar HH patches. Another patch from the above-mentioned helix of mandelate racemase was considered (PDB code 1mns; residues 252–260; underlined residues were aligned: PEEMFKALS). The patch considered in (a) was established with the helix 229–237, while this helix-patch is built through contact with helix 276–290. It was aligned with one from citrate synthase (PDB code 1csc; residues 89–98; PEGLFWLLV) (39 of 45 atoms; r.m.s. value 0.35 Å). (c) Replacement of an H patch in mandelate racemase by a similar one from citrate synthase. The similar patches to those in (b) are the basis for this replacement. In this case the complete helices were exchangeable. The Connolly surface of mandelate racemase is colored blue, and the original helix (right) and its substitute (left) are colored yellow.

 
Considering the interhelical torsion angles (defined via normals to their axes or their extension; see e.g. Bowie, 1997), we found for smaller superimposed patches (<25 atoms) significant deviations between helix axes (Figure 3aGo), while they are almost parallel for larger HH patches (e.g. Figure 3bGo). The reason for this is the involvement of more than two helix windings which defines the helix axis. These types of structural similarity will hardly be detected by sequence-oriented approaches because the sequence similarity between the entire helices is below the significance threshold. Nevertheless, the question arose of which expression the structural similarity finds in terms of atomic or amino acid composition of the considered patches.

Exchangeability of patches

The question remained as to whether detected similar patches could be exchanged between different proteins, which would be of interest for the construction of proteins with maintained function but different antigenic properties. This problem was considered using the similar patches from different proteins given in Figure 3bGo. First the helix 252–260 was removed from the structure of mandelate racemase (see Figure 3cGo, left). Then the corresponding residues (89–97) from citrate synthase were inserted according to the superposition of the two patches without consideration of the environment (see Figure 3cGo, right). This patch fits nearly perfectly into this artificial pocket which is expressed by a high local packing density. It is shifted only slightly from 0.62 to 0.60, which are typical values for helix–helix packing (see Figure 4aGo). Visual inspection showed that minor deviations in chi-angles could compensate for small deviations from ideal non-bonded distances. Summing up a rational selection of candidates for replacement becomes possible.



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Fig. 4. Distribution of the local packing density for helical patches (HH, HE, HC). The atomic density values for the helical patches are plotted against those in their partner patches (helix, extended, coil).

 
Packing density

We found that the mean packing density is absolutely independent of the size (5–85 atoms) of the helical interface and might serve as a quality criterion for an atomic fit.

Even the distribution of the local packing density between helices peaks sharply around the mean (mean 0.67; standard deviation 0.07; see Figure 4aGo). This distribution resembles those between helices and extended (mean 0.72; standard deviation 0.07; see Figure 4bGo), while the packing density between helices and coils is somewhat lower (mean 0.64; standard deviation 0.08; see Figure 4cGo). An explanation for this finding can be given by the separation of helix–coil interfaces that are adjacent in sequence, so-called helix caps. For these 4300 patches a pronounced lower packing density was observed (mean 0.62).


    Conclusions
 Top
 Abstract
 Introduction
 Materials and methods
 Results and discussion
 Conclusions
 References
 
Based on the analysis given here, a number of conclusions concerning helix packing can be drawn.

  1. The clear deviations in atomic (up to 200%, see Table IIGo) and amino acid composition (up to 100%, see Table IGo) of the different helical patches result in contact preferences with a broader range (0.28–1.92) than commonly used propensities (0.43–1.52). Thereby the chances increase that the prediction of interacting regions and probable partners will be possible on this basis.
  2. The mean local packing density between distinct types of secondary structures differs by more than 10% and its optimization could serve as a criterion during folding simulation.
  3. The unbiased search for recurring molecular arrangements in different proteins becomes possible. Resembling exterior patches partly reflect similar binding properties (Preissner et al., 1999Go).
  4. The promising results towards a classification of interfaces between secondary structural elements based on geometric resemblance show that parts of proteins could be exchanged using a model kit. In the case of helix–helix interfaces on average 10 similar patches can be grouped together. It depends on the similarity criterion (the softness of the bricks), but the result is a box containing less than 103 distinct bricks.

The interface files for the proteins considered and a viewer including the superposition procedure are deposited at http://www.charite.de/ch/biochem/dip.


    Notes
 
1 To whom correspondence should be addressed Back


    References
 Top
 Abstract
 Introduction
 Materials and methods
 Results and discussion
 Conclusions
 References
 
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Received February 10, 1999; accepted July 6, 1999.





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