This module introduces students to a family of algorithms for assessing molecular shape, volume, surface area, and negative space (i.e., pockets and cavities).
Topics in this module
Introduction
Representing Shape
Alpha-Shapes
Delaunay Triangulation
Weighted Alpha-Shapes
Calculating Molecular Volume Using Alpha-Shapes
Related Software
Introduction
Many problems in structural biology, require a researcher to understand the shape of a protein. At first glance, this may seem obvious. By opening a molecular visualizer, one can easily see the shape of a protein. But what about calculating the surface area or volume of the protein? What about performing analyses of the surface, such as looking for concave pockets in a protein that might be binding sites for other molecules? What about calculating the volume and shape of those empty binding pockets, in order to find molecules that might fit in them? What about determining whether a particular small molecule can fit in a binding pocket?
All of these problems require some formal notion of the shape of a protein. A protein structure file usually provides no more information than a list of atom locations in space and their types. It will be assumed that for any given application, a radius may be defined for each atom type. This leads to the space filling representation of a protein, in which each atom is treated as an impenetrable sphere.
Hiv-1 protease
A space filling representation of HIV-1 protease (yellow) with an inhibitory drug (red) blocking its binding site. This representation allows for visualization, but it brings us no closer to being able to computationally decide which parts of which atoms are on the surface of the protein and which are buried inside the structure. Some additional tool is needed to capture notions of interior and exterior and spatial adjacency.
Representing shape
Using the sphere model for atoms, one way to define the shape of a molecule is as
the union of (possibly overlapping) balls in
.
Space filling diagram
The space filling diagram models each atom as a sphere in 3D. Since proteins inside our cells are in an aqueous environment, considering
a protein's interactions with solvent molecules, particularly water, is very important forappropriately modeling them. Recall that one of the phenomena that determines the structure of a protein is the hydrophobic effect: some amino acid residues are stabilized by the presence of water, and others are repelled.
The extent of the interaction of a protein with the surrounding waterdepends on the surface area of the protein that can be reached by water molecules. Therefore, quantitave
modeling of the strength of interaction with solvent often involves computing the
solvent accessible surface area (SASA) . Computing SASA can be done by
regarding each solvent molecule as a sphere of set radius. This is of course a simplification, since water molecules are not spherical. When thissphere rolls about the molecule, its center delineates the SASA. One can
think of the SASA of a molecule as the result of growing each atom sphere bythe radius of the solvent sphere. Instead, by taking what is swept out by the
front of the solvent sphere, we obtain the
molecular surface (MS) model of
the molecule. Alternatively, the MS can be obtained by removing a layer ofsolvent radius depth from the SASA model.
Representations of molecular shape
Vdw representation
Each atom can be modeled as a Van der Waals sphere in three dimensions. The union of the
spheres gives the molecular surface.
Accessible surface area
Not all molecular surface is accessible to solvent due to the
existence of small cavities. Rolling a solvent ball over the Van der Waalsspheres traces out the surface area experienced by the solvent. Solvent
accessible surface area (SASA) is a very important measure forquantitatively determining the behavior and interaction tendencies of a protein.Two different notions and representations of the surface of a molecule. The surface determined by SASA analysis depends on the size of a typical solvent molecule. The larger the solvent, the less contoured the resulting surface will appear, because a larger probe molecules would not be able to fit into some of the interatomic spaces that a smaller one would.
Solvent accessible surface area
Probing the surface area with a solvent ball of radius 1.4 å
Typically, solvent is modeled as a ball of radius 1.4 Å. This
delineates the solvent accessible surface shown.
Probing the surface area with a solvent ball of radius 1.5 å
Increasing the radius of the solvent ball reduces the
solvent accessible surface area because there are more cavitiesthat a bulkier ball cannot penetrate.Solvent-accessible surface area (SASA) for two different solvent radii.
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Source:
OpenStax, Geometric methods in structural computational biology. OpenStax CNX. Jun 11, 2007 Download for free at http://cnx.org/content/col10344/1.6
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