Abstract
Three-dimensional objects can be represented using Cartesian, spherical or cylindrical coordinate systems, among many others. Currently all protein 3D structures in the PDB are in Cartesian coordinates. We wanted to explore the possibility that protein 3D structures, especially the globular type (spheroproteins), when represented in spherical coordinates might find useful novel applications. A Fortran program was written to transform protein 3D structure files in Cartesian coordinates (x,y,z) to spherical coordinates (ρ, ϕ, θ), with the centroid of the protein molecule as origin. We present here two applications, namely, (1) separation of the protein outer layer (OL) from the inner core (IC); and (2) identifying protrusions and invaginations on the protein surface. In the first application, ϕ and θ were partitioned into suitable intervals and the point with maximum ρ in each such ‘ϕ-θ bin’ was determined. A suitable cutoff value for ρ is adopted, and for each ϕ-θ bin, all points with ρ values less than the cutoff are considered part of the IC, and those with ρ values equal to or greater than the cutoff are considered part of the OL. We show that this separation procedure is successful as it gives rise to an OL that is significantly more enriched in hydrophilic amino acid residues, and an IC that is significantly more enriched in hydrophobic amino acid residues, as expected. In the second application, the point with maximum ρ in each ϕ-θ bin are sequestered and their frequency distribution constructed (i.e., maximum ρ’s sorted from lowest to highest, collected into 1.50Å-intervals, and the frequency in each interval plotted). We show in such plots that invaginations on the protein surface give rise to subpeaks or shoulders on the lagging side of the main peak, while protrusions give rise to similar subpeaks or shoulders, but on the leading side of the main peak. We used the dataset of Laskowski et al. (1996) to demonstrate both applications.
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Abbreviations
- OL:
-
outer layer
- IC:
-
inner core
- AAR:
-
all-atom representation
- DCRR:
-
double-centroid reduced representation
- LBS:
-
ligand binding site
- fb:
-
fine binning (method)
- cb:
-
coarse binning (method)
- ϕθb:
-
phi-theta bin
- A ϕθb :
-
area of a ϕ-θ bin, referring to the area of the spherical rectangle bounded by two ϕ and two θ limits
- FD:
-
frequency distribution
- FDMR:
-
frequency distribution of maximum rho’s
- CSA:
-
catalytic site atlas
References
Anderson, C.M., Stenkamp, R.E., Steitz, T.A. 1978. Sequencing a protein by x-ray crystallography. II. Refinement of yeast hexokinase B co-ordinates and sequence at 2.1 Å resolution. J Mol Biol 25, 15–33.
Campbell, R.L., Rose, D.R., Wakarchuk, W.W., To, R.J., Sung, W., Yaguchi, M. 1994. High-resolution structures of xylanases from B. Circulans and T. Harzianum identify a new folding pattern and implications for the atomic basis of the catalysis. http://www.rcsb.org/pdb/explore/explore.do?structureId=1XNB.
Fujinaga, M., Delbaere, L.T., Brayer, G.D., James, M.N. 1985. Refined structure of alpha-lytic protease at 1.7 Å resolution. Analysis of hydrogen bonding and solvent structure. J Mol Biol 184, 479–502.
Gershoni, J.M., Roitburd-Berman, A., Siman-Tov, D.D., Tarnovitski, N., Freund N., Weiss, Y. 2007. Epitope mapping: The first step in developing epitopebased vaccines. BioDrugs 21, 145–156.
Kim, H., Lipscomb, W.N. 1993. X-ray crystallographic determination of the structure of bovine lens leucine aminopeptidase complexed with amastatin: Formulation of a catalytic mechanism featuring a gem-diolate transition state. Biochemistry 32, 8465–8478.
Landro, J.A., Gerlt, J.A., Kozarich, J.W., Koo, C.W., Shah, V.J., Kenyon, G.L., Neidhart, D.J., Fujita, S., Petsko, G.A. 1994. The role of lysine 166 in the mechanism of mandelate racemase from Pseudomonas putida: Mechanistic and crystallographic evidence for stereospecific alkylation by (R)-alpha-phenylglycidate. Biochemistry 33, 635–643.
Laskowski, R.A., Luscombe, N.M., Swindells, M.B., Thornton, J.M. 1996. Protein clefts in recognition and function. Prot Sci 5, 2438–2452.
Lisgarten, J.N., Gupta, V., Maes, D., Wyns, L., Zegers, I., Palmer, R.A., Dealwis, C.G., Aguilar, C.F., Hemmings, A.M. 1993. Structure of the crystalline complex of cytidylic acid (2′-CMP) with ribonuclease at 1.6 Å resolution. Conservation of solvent sites in RNase-A high-resolution structures. Acta Crystallogr D Biol Crystallogr 49, 541–547.
Loll, P.J., Lattman, E.E. 1989. The crystal structure of the ternary complex of staphylococcal nuclease, Ca2+, and the inhibitor pdTp, refined at 1.65 Å. Proteins 5, 183–201.
Lu, G., Lindqvist, Y., Schneider, G., Dwivedi, U., Campbell, W. 1995. Structural studies on corn nitrate reductase: Refined structure of the cytochrome b reductase fragment at 2.5 A, its ADP complex and an active-site mutant and modeling of the cytochrome b domain. J Mol Biol 248, 931–948.
Martinez, C., Nicolas, A., van Tilbeurgh, H., Egloff, M.P., Cudrey, C., Verger, R., Cambillau, C. 1994. Cutinase, a lipolytic enzyme with a preformed oxyanion hole. Biochemistry 33, 83–89.
Mosimann, S.C., Ardelt, W., James, M.N. 1994. Refined 1.7 Å X-ray crystallographic structure of P-30 protein, an amphibian ribonuclease with anti-tumor activity. J Mol Biol 236, 1141–1153.
Mumey, B., Angel, T., Kirkpatrick, B., Bailey, B., Hargrave, P., Jesaitis, A., Dratz, E. 2003. Mapping discontinuous antibody epitopes to reveal protein structure and changes in structure related to function. IEEE Computer Society Bioinformatics Conference (CSB′03), Stanford, CA, USA, 585–586.
Navia, M.A., McKeever, B.M., Springer, J.P., Lin, T.Y., Williams, H.R., Fluder, E.M., Dorn, C.P., Hoogsteen, K. 1989. Structure of human neutrophil elastase in complex with a peptide chloromethyl ketone inhibitor at 1.84-A resolution. Proc Natl Acad Sci USA 86, 7–11.
Porter, C.T., Bartlett, G.J., Thornton, J.M. 2004. The Catalytic Site Atlas: A resource of catalytic sites and residues identified in enzymes using structural data. Nucl Acids Res 32, D129–D133.
Reyes, V.M., Sheth V.N. 2011. Visualization of protein 3D structures in ‘double-centroid’ reduced representation: Application to ligand binding site modeling and screening. In: Liu, L.A., Wei, D., Li, Y. (Eds.) Handbook of Research on Computational and Systems Biology: Interdisciplinary Applications, Springer, Shanghai, 583–598.
Sheth, V.N. 2009. Visualization of Protein 3D Structures in Reduced Representation with Simultaneous Display of Intra- and Intermolecular Interactions. Thesis, Master of Science in Bioinformatics, School of Biological and Medical Sciences, College of Science, Rochester Institute of Technology, Rochester, NY 14623-5603, USA.
Smith, G.M., Alexander, R.S., Christianson, D.W., McKeever, B.M., Ponticello, G.S., Springer, J.P., Randall, W.C., Baldwin, J.J., Habecker, C.N. 1994. Positions of His-64 and a bound water in human carbonic anhydrase II upon binding three structurally related inhibitors. Protein Sci 3, 118–1125.
Tarnovitski, N., Matthews, L.J., Sui, J., Gershoni, J.M., Marasco, W.A. 2006. Mapping a neutralizing epitope on the SARS coronavirus spike protein: Computational prediction based on affinity-selected peptides. J Mol Biol 359, 190–201.
Thayer, M.M., Ahern, H., Xing, D., Cunningham, R.P., Tainer, J.A. 1995. Novel DNA binding motifs in the DNA repair enzyme endonuclease III crystal structure. EMBO J 14, 4108–4120.
Trieschmann, M.D., Pattus, F., Tadros, M.H. 1996. Molecular characterization and organization of porin from Rhodobacter capsulatus strain 37B4. Gene 12, 61–68.
Tronrud, D.E., Wen, J., Gay, L., Blankenship, R.E. 2009. The structural basis for the difference in absorbance spectra for the FMO antenna protein from various green sulfur bacteria. Photosynth. Res 100, 79–87.
Vita, R., Zarebski, L., Greenbaum, J.A., Emami, H., Hoof, I., Salimi, N., Damle, R., Sette, A., Peters, B. 2010. The immune epitope database 2.0. Nucleic Acids Res 38 (Database issue), D854–D862.
Ward, M.R., Grimes, H.D., Huffaker, R.C. 1989. Latent nitrate reductase activity is associated with the plasma membrane of corn roots. Planta 177, 470–475.
Weiss, M.S., Schulz, G.E. 1992. Structure of porin refined at 1.8 Å resolution. J Mol Biol 227, 493–509.
Winn, S.I., Watson, H.C., Harkins, R.N., Fothergill, L.A. 1981. Structure and activity of phosphoglycerate mutase. Philos Trans R Soc Lond B Biol Sci 293, 121–130.
Yang, W., Hendrickson, W.A., Crouch, R.J., Satow, Y. 1990. Structure of ribonuclease H phased at 2 Å resolution by MAD analysis of the selenomethionyl protein. Science 249, 1398–1405.
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Reyes, V.M. Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications. Interdiscip Sci Comput Life Sci 3, 161–174 (2011). https://doi.org/10.1007/s12539-011-0099-0
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DOI: https://doi.org/10.1007/s12539-011-0099-0