Implementation of the Spherical Coordinate Representation of Protein 3D Structures and its Applications Using FORTRAN 77/90 Language

TL;DR

This paper presents a FORTRAN implementation of spherical coordinate methods for analyzing protein 3D structures, including applications for separating outer layers from the core and predicting surface protrusions and invaginations.

Contribution

It introduces nine FORTRAN programs for converting, binning, and analyzing protein structures in spherical coordinates, demonstrating their effectiveness on real and theoretical models.

Findings

Successful separation of protein outer layer and inner core.

Effective prediction of surface protrusions and invaginations.

Validation of methods using real protein datasets and theoretical models.

Abstract

We previously described the representation of protein 3D structures in spherical coordinates (rho, phi, theta) and two of its applications: separation of the outer layer (OL) from the inner core (IC) of proteins, and assessment of protein surface protrusions and invaginations (Reyes, V.M., 2011& 2009). Here we present results demonstrating the performance success of the FORTRAN 77 and 90 programs used in the implementation of the two said applications, and how to implement both applications. In particular, we show here data that demonstrate the success of our OL-IC separation procedure using a subset of the Laskowski et al. (1996) dataset. Using a theoretical model protein in the form of a scalene ellipsoid grid of points with and without an artificially constructed protrusion or invagination, we also show results demonstrating that protrusions and invaginations on the protein surface maybe predicted. The nine programs we present here and their respective functions are: find_molec_centr.f: finds the x-, y- and z-coordinates of the protein molecular geometric centroid, cart2sphere_degrees.f90: converts PDB protein coordinates to spherical, with phi and theta in degrees, cart2sphere_radians.f90: does the same thing as the second program, but with phi and theta in radians, spher2cart_degrees.f90: converts the coordinates from spherical back to PDB, where input phi and theta are in degrees, spher2cart_radians.f90: does the same thing as the fourth program, but with phi and theta in radians, find_rho_cutoff.f: determines the rho cut-off for finding the boundary between OL and IC, phi6_theta8_binning.f90: performs the binning of phi in six- and theta in eight-degree increments, phi10_theta10_binning.f90: performs the binning of phi and theta both in ten-degree increments, and bin_rho.f90: performs the binning of rho values for plotting the frequency distribution of maximum rho values.