However, as the probe radius increases, the surface features are filled in (as in Figure 2A, left). When a probe of zero size is used, the van der Waals radius is obtained. Figure 2A shows the surfaces of the macromolecule at the different probe radii for both the hammerhead ribozyme ( 29) and lysozyme ( 30) structures. When using the rolling probe method, the size of the probe has a profound effect on the shape of the resulting surface. Figure adapted from Richards, 1977 ( 26). The excluded surface is the surface defined by the exterior of the each sphere (dashed line) as they roll across the array of atoms By subtracting the enclosed volume of the smaller sphere ( R 1) from the enclosed volume of the larger sphere ( R 2) the solvent volume (blue) is obtained. Two sphere of radius R 1 and R 2 are shown rolling across the surface of a macromolecule defined by the 12 atoms. The discrete volume method for the rolling probe allows for volumes to be subtracted and large macromolecules to be efficiently analyzed. Thus, macromolecules containing a large number of atoms can be computed with only small effect on the calculation time relative to smaller macromolecules for a given probe and grid size. The time complexity of the discrete volume method is linear, O(n), with the number of particles, but it increases as the cube, O(r 3), of the probe radius (in grid units) and the inverse cube of the 3D grid resolution, O(g − 3). This subtraction is required to obtain the channel information. The discrete method is scalable to structures of any size and complexity, and readily lends itself for subtracting any two volumes created using this method. a 3D grid of voxels, rather than the analytical one. The 3V web server uses the discrete volume method, i.e. There are two approaches of the rolling probe method to determine the volume of an enclosed surface: discrete and analytical. This method essentially works by rolling a virtual probe or ball of a given radius around the van der Waals surface of a macromolecule ( Figure 1). In order to calculate macromolecular volumes, the web server uses the rolling probe method ( 25–27). The 3V method requires no starting point and the probe radii are adaptable to the size of any structure and its channels, which is ideal for investigations relating to drug-binding sites. The Voss Volume Voxelator (3V) web server provides similar functionality, but using a different technique that can provide the overall shape of the channel.
The output of these tools is the trajectory of the channel and the maximal radius at each point along the path. These tools determine the trajectory of channels from a starting location in protein structures. More recently, a few methods have been published to traverse known channels in structures ( 21–24).
However, these programs and web servers are typically designed for small proteins, and are not necessarily useful for large macromolecular complexes. There are several programs involved in finding potential binding sites in macromolecules ( 7–18) and pores in membrane proteins ( 19, 20). While it is interesting to study these channels, extracting them from a structure is not straightforward. Additionally, large cavities are utilized as isolation chambers for protein folding chaperones, such as GroEL (∼500 000 � 3) ( 6). Channels also play an important role in many membrane proteins, including ion channels (∼8000 � 3) ( 4) and mechanosensitive channels (∼10 000 � 3) ( 5). One example is the ribosomal exit tunnel, a large protruding channel (∼22 000 � 3 in channel volume) ( 2) in the 50S ribosomal subunit that all naturally synthesized proteins must pass through ( 3). There are several examples of biologically relevant channels in the Protein Data Bank ( 1). The number of large macromolecular structures available is increasing and these new structures contain internal features with biological relevance.
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