QHELIX: A Computational Tool for the Improved Measurement of Inter-Helical Angles in Proteins
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DOI: 10.1007/s10930-007-9097-9
- Cite this article as:
- Lee, H.S., Choi, J. & Yoon, S. Protein J (2007) 26: 556. doi:10.1007/s10930-007-9097-9
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Abstract
Knowledge about the assembled structures of the secondary elements in proteins is essential to understanding protein folding and functionality. In particular, the analysis of helix geometry is required to study helix packing with the rest of the protein and formation of super secondary structures, such as, coiled coils and helix bundles, formed by packing of two or more helices. Here we present an improved computational method, QHELIX, for the calculation of the orientation angles between helices. Since a large number of helices are known to be in curved shapes, an appropriate definition of helical axes is a prerequisite for calculating the orientation angle between helices. The present method provides a quantitative measure on the irregularity of helical shape, resulting in discriminating irregular-shaped helices from helices with an ideal geometry in a large-scale analysis of helix geometry. It is also capable of straightforwardly assigning the direction of orientation angles in a consistent way. These improvements will find applications in finding a new insight on the assembly of protein secondary structure.
Keywords
Helical axisInter-helical angleProtein structureQHELIX, computational toolAbbreviations
- PDB
Protein data bank
- NMR
Nuclear magnetic resonance
- SpA
Staphylococcal protein A
1 Introductiion
The purpose of our present study was to develop a method to define helical angels with a quantitative consideration of shape irregularity of helices in determining helical axes. Using a unique algorithm proposed by Kahn [10], we attempted to quantify the deviation of the fitting line from the non-linear axis of an irregularly curved helix. Several other programs, using Kahn algorithm or similar approach, have been reported for analyzing helix structures. HELANAL [5] provided a detailed analysis of structural and position dependent characteristic features of each helix using successive local helix axes along a window of four Cα atoms. TRAJELIX calculates helix axes using Kahn’s algorithm [6]. It has been used in monitoring relative local distortions in helices between sampled and reference structures during molecular dynamics simulations of a single protein. Here, we report an automated computer program, QHELIX, which permits fast determination of inter-helical orientation and unique quantification of the irregularity of helix shape, thus distinguish between irregularly curved helices and helices with an ideal geometry in the angle calculation. Since the algorithm only takes Cα coordinates for the calculation of geometric axes, it is independent of the type of amino acids and can be applied to the geometric analysis of any kinds of secondary structure elements.
An additional critical point in the comparison of inter-helical orientation of proteins in a large scale is that the direction of orientation between two helices should be considered over the range of (−180, 180°). In the case where a reference helix is not given, determining the sign of the angle between two helices is not trivial. In the previous report, the reference helix is selected based on the relative distance to the origin of coordinate [7]. This method does not provide a consistency in selecting the reference helix during the rotational or transitional movement of the protein. The better way is determining the sign only based upon the geometric relationship between two helices that are used in the angle calculation. Here, we propose a simple but unique method for the consistent determination of the sign of inter-helical orientation without the consideration of the origin of coordinates or surrounding tertiary context.
2 Methods
3 Results and Discussion
Comparison of inter-helical angles in the Z domain, B domain, F_{c}-bound B domain and E domain of staphylococcal protein A
θ_{12} | θ_{13} | θ_{23} | |||||||
---|---|---|---|---|---|---|---|---|---|
Tashiro | Qhelix-1 | Qhelix-2 | Tashiro | Qhelix-1 | Qhelix-2 | Tashiro | Qhelix-1 | Qhelix-2 | |
Z domain | −170 | −167 | −169 | +16 | +19 | +12 | +173 | +171 | + 173 |
B domain | −148 | −149 | −143 | +48 | +46 | +51 | −168 | −161 | −163 |
E domain | +175 | +166 | +166 | +16 | +12 | +15 | −177 | −168 | −168 |
F_{c} bound B domain | −171 | −171 | −173 |
Comparison of inter-helical angle, θ_{16–19}, and the helix irregularity, h_{ir} between an irregularly curved helix (helix 16) and a helix with an ideal geometry (helix 19)
θ_{16–19} | Average displacement, h_{ir} (Å) | |||
---|---|---|---|---|
Helix 16 | Helix 19 | Δh_{ir} | ||
Qhelix-1 | −35.25 | 2.90 | 2.36 | 0.54 |
Qhelix-2 | −36.15 | 1.72 | 0.23 | 1.49 |
Orientational preferences between interacting helices within proteins have been studied extensively over the years [9, 17]. However the influence of helical irregularity on angle calculation has not been considered quantitatively so far. Angles between irregular helices can be defined in various ways, and are qualitatively different from those between regular helices. Therefore, for more accurate evaluation of the orientation preferences between helices on a large scale, the problem of non-linear helical axes should be appropriately considered in the angle calculation. What are the qualitative differences between inter-helix pairs with similar inter-helical angles and those with a different helical shape? What residue ranges should be used to define the helix axes and to calculate the inter-helical angle? While the two optional methods that our Qhelix program provides, produce similar inter-helical angles, the unique estimation of h_{ir} by the Kahn method provides a further insight into the orientation between interacting helices. It is expected that QHELIX will find useful applications in proteom-wide analysis of helical geometry in proteins. Particularly, in the problems of protein folding, the relationship of secondary structure elements should be understood in terms of surrounding tertiary context. QHELIX, which provides an improved method for the analysis of various helical shapes and their special relationship, will contribute to elucidating relationships between tertiary interaction and local secondary structure formation in the protein folding.
4 Software Availability
QHELIX was developed in C language and compiled using the GNU C compiler (gcc). The source code of the program is added as supplement 1. In addition to the source code, all the math library components and instruction for the compilation are freely available on our web site, http://compbio.sookmyung.ac.kr/∼qhelix/.
Acknowledgment
This research was supported by Sookmyung Women’s University Research Grants 1-0603-0149.