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Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications
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 (sp...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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International Association of Scientists in the Interdisciplinary Areas
2011
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7091412/ https://www.ncbi.nlm.nih.gov/pubmed/21956738 http://dx.doi.org/10.1007/s12539-011-0099-0 |
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author | Reyes, Vicente M. |
author_facet | Reyes, Vicente M. |
author_sort | Reyes, Vicente M. |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-7091412 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2011 |
publisher | International Association of Scientists in the Interdisciplinary Areas |
record_format | MEDLINE/PubMed |
spelling | pubmed-70914122020-03-24 Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications Reyes, Vicente M. Interdiscip Sci Article 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. International Association of Scientists in the Interdisciplinary Areas 2011-09-29 2011 /pmc/articles/PMC7091412/ /pubmed/21956738 http://dx.doi.org/10.1007/s12539-011-0099-0 Text en © International Association of Scientists in the Interdisciplinary Areas and Springer-Verlag Berlin Heidelberg 2011 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Reyes, Vicente M. Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications |
title | Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications |
title_full | Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications |
title_fullStr | Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications |
title_full_unstemmed | Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications |
title_short | Representation of protein 3D structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications |
title_sort | representation of protein 3d structures in spherical (ρ, ϕ, θ) coordinates and two of its potential applications |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7091412/ https://www.ncbi.nlm.nih.gov/pubmed/21956738 http://dx.doi.org/10.1007/s12539-011-0099-0 |
work_keys_str_mv | AT reyesvicentem representationofprotein3dstructuresinsphericalrphthcoordinatesandtwoofitspotentialapplications |