Adepth: New Representation and its implications for atomic depths of macromolecules

Abstract

We applied the signed distance function (SDF) for representing the depths of atoms in a macromolecule. The calculations of SDF values were performed on grid points in a rectangular box that accommodates the macromolecule. The depth for an atom inside the molecule was then obtained as a result of tri-linear interpolation of SDF values at the nearest grid points surrounding the atom. For testing the performance of present program Adepth, we have constructed an artificial molecule whose atomic depths are known as the gold standard for accuracy assessments. On average, our results showed that Adepth reached an accuracy of 1.6% at 0.5 Å of grid spacing, whereas the current reference server DEPTH reached 7.5%. The Adepth program provides both depth and height representations; it is capable of computing iso-surfaces for atomic depths and presenting graphical view of macromolecular shape at some distance away from the surface. Web interface is available at http://biodev.cea.fr/adepth.

Figure 1.

Representation of the 3D structure of the standard molecule drawn by the vdw method in VMD (13). Each atom was scaled down to 20% of its original size. The Cartesian co-ordinates of atoms in the molecule can be expressed as (Rcosφsinθ, Rsinφsinθ, Rcosθ), where R is the radius of sphere, 0 ≤ θ ≤ π and 0 ≤ φ < 2π; totally there are 25 sampling points along the θ coordinate and 50 for the φ coordinate. Atomic depth is colour-coded as follows: cyan = 0 Å, green = 3 Å, orange = 6 Å, yellow = 9 Å and red = 12 Å.

Figure 2.

(A) Relationship of computational cost and molecular size. The CPU time was plotted against the number of atoms (N_atom) of the standard molecule for Δr = 0.5, 0.6, 0.8 and 1.0 Å. The four sets of data values were fitted with linear regression, resulting in a slope of 0.2, 0.1, 0.07 and 0.05 msec/atom for Δr = 0.5, 0.6, 0.8 and 1.0 Å, respectively. (B) Validation of Adepth and DEPTH on atomic depth calculations for the standard molecule using a probe radius of 1.5 Å. In the plot, the horizontal dashed lines represent the distances of spherical layers from the surface. Data points with open symbols represent the values of averaged atomic depth versus Δr from Adepth, whereas that with filled symbols located along the vertical axis are referred to the DEPTH server. Bars around the open symbols represent the standard deviation; when it is <1%, bars are not drawn.

Figure 3.

Implications of new representation for atomic depths. (A) Cartoon representation of the extruded crystal structure of a Fab domain of antibody protein using a probe radius of 1.5 Å, Δr = 1 Å, and depth selection threshold <3.5 Å. Of 3291 atoms, 805 are found within the given threshold. (B) Iso-surface representation for an expanded surface of an antibody molecule. The crystal structure of the antibody is represented by 1IGT (26) with vdw spheres and coloured atomic types: cyan for carbon, red for oxygen, blue for nitrogen and yellow for sulphur atoms. The atomic depths of 1IGT and the associated SDF values at grid points were computed using a probe radius of 1.5 Å at Δr = 1 Å. The iso-surface in orange wireframe was located 50 Å away from the antibody surface. (C) Clipped core structure of the serine protease domain of FVIIa (27). The orange wireframe represents the iso-surface of the SDF value at a threshold of 7.5 Å using VMD. The main-chain conformation is displayed in a ribbon of red-to-white-to-blue spectrum, where red and blue are for buried and solvent-exposed regions, respectively. The deepest atom in FVIIa is 13.5 Å inwards from the protein surface. The mutated glycines with almost no solvent-accessible surface areas are represented by coloured CPK spheres. The residue depth was calculated as 10.0 Å for Gly343 and 4.8 Å for Gly391; thus, only Gly343 is enclosed in the orange wireframe.