What is Self Rotation?
Self-rotation, particularly as embodied in the Self-Rotation Function (SRF), is a crucial computational technique primarily utilized in structural biology and crystallography to unravel the inherent internal symmetries within a molecule or its crystal lattice. It achieves this by comparing the molecule's Patterson function against itself, a process that ultimately highlights symmetry axes as distinct peaks.
Understanding the Self-Rotation Function
The Self-Rotation Function (SRF) serves as a powerful analytical tool for determining the intrinsic symmetry elements present within a crystal structure. Unlike other methods that focus on the symmetry of the crystal lattice itself, the SRF specifically allows determining the internal symmetry of the native data by comparison the native Patterson function against itself. This internal symmetry can relate different subunits of a macromolecule or multiple copies of the same molecule within the asymmetric unit of a crystal. This comparison is fundamental, as it bypasses the need for phase information, which is often difficult to obtain directly from diffraction data.
The core principle is that if a molecule or a group of molecules possesses internal rotational symmetry, rotating its electron density (or, more practically, its Patterson function) against itself will reveal this symmetry. This comparison results in showing up symmetry axes as peaks on a "rotation map," indicating the orientation of these internal symmetry elements.
How Self-Rotation Works
The process of self-rotation involves several key steps:
- Patterson Function Generation: First, the Patterson function of the crystal is calculated from the experimentally measured diffraction data. The Patterson function is a map of interatomic vectors, representing all possible vector differences between atom pairs in the crystal. It has the same symmetry as the crystal's electron density but with a center of symmetry.
- Self-Comparison: A copy of the calculated Patterson function is then rotated against itself. The goal is to find rotational operations (angles and axes) where the rotated Patterson map best overlaps with the original unrotated Patterson map.
- Overlap Identification: When a rotational symmetry element is present, rotating the Patterson function by the corresponding angle around the symmetry axis will cause significant overlap between the original and rotated functions.
- Rotation Map Construction: The degree of overlap (correlation) for each tested rotation is calculated and plotted onto a three-dimensional rotation map (e.g., an Euler angle map or a spherical polar angle map).
- Symmetry Axes Identification: The positions of maximum correlation on this rotation map directly correspond to the presence and orientation of internal symmetry axes within the molecular structure. These peaks indicate operations that bring the molecule (or its parts) into self-equivalent positions.
Importance and Applications
Identifying internal symmetry through self-rotation is invaluable in various fields, particularly structural biology:
- Molecular Replacement: In molecular replacement, a common method for solving new crystal structures, the self-rotation function helps determine the orientation of a known homologous structure (search model) within the unit cell of the target crystal. This is often the first step in solving the crystal structure of a new protein.
- Non-Crystallographic Symmetry (NCS) Detection: Many biological macromolecules form oligomers (e.g., dimers, trimers, tetramers) that possess internal symmetry independent of the crystal lattice symmetry. The SRF can detect and determine the parameters of this non-crystallographic symmetry (NCS), which can then be used to average electron density and improve the quality of experimental maps.
- Ab Initio Phasing: While primarily used in molecular replacement, insights from self-rotation can also inform and assist in certain ab initio phasing strategies by providing initial clues about molecular arrangements.
- Understanding Molecular Architecture: Ultimately, self-rotation helps researchers understand the fundamental architecture and organization of complex biological molecules and their assemblies.
Key Concepts in Self-Rotation
| Concept | Explanation |
|---|---|
| Patterson Function | A mathematical transformation of diffraction data that represents a map of interatomic vectors within a crystal. It is derived from the squared amplitudes of structure factors, thus losing phase information. |
| Internal Symmetry | Rotational or translational symmetry elements inherent to the molecule itself or to the arrangement of multiple identical molecules within a crystal's asymmetric unit, distinct from the crystal lattice symmetry. |
| Symmetry Axes | Imaginary lines about which a molecule or a part of a molecule can be rotated by a specific angle (e.g., 180°, 120°, 90°) to bring it into an identical or indistinguishable orientation. |
| Rotation Map | A graphical representation (often 3D) where peaks indicate the presence and orientation of rotational symmetry axes detected by the self-rotation function. |
