Book of Abstracts: Albany 2011

category image Albany 2011
Conversation 17
June 14-18 2011
©Adenine Press (2010)

Using Cartographic Techniques to Project Protein 3D Surfaces onto the 2D Plane: Potential Applications and Implications

Study of protein surfaces is quite important in protein science since the biological properties of proteins are largely (but not solely) determined by their surface properties. Meanwhile, it is estimated that a significant majority of all proteins fold into compact globular structures (‘spheroproteins’), and as such may be likened to the earth. For centuries, the surface of the earth has been represented and analyzed using cartographic spherical projection methods, such as the Mercator, Eckert, Lambert, Werner and Aitoff projections. We have recently developed a program that transforms protein 3D structure coordinates from Cartesian (x,y,z) to spherical (ρ,φ,θ) coordinates, whose origin is the geometric centroid of the protein (1). In this system, rho (ρ) plays the role of the earth’s radius from its center to an entity in the protein structure, phi (φ), the latitudes, and theta (θ), the longitudes. 2D projection of the surface of this sphere, with elevations from the “sea level” (ESLs), may be achieved using the transformation equations for the particular projection method. The ESLs, on the other hand, can be determined by choosing a reference “sea level” ρ0 (e.g., distance from center of sphere to the smallest nonzero ρ value) and using the “heights” of surface points above ρ0 as the z-coordinates (elevations along the z-axis). Established methods in geography/cartography may then be used to analyze such projections with elevations. Plots of these 2D raise-relief maps (a.k.a. terrain models) may be easily rendered using MATLAB. These 2D projection methods present a number of benefits for protein surface analysis over 3D-based methods, among which are (a) simplicity of presentation (i.e., 2D vs. 3D), (b) entire protein surface may be viewed all at once, (c) simpler and more direct protein surface comparisons (e.g., between similar but non-identical proteins, or between identical proteins in different conformations or liganded states), and (d) applicability of the myriad well-established cartographic techniques for analysis and comparison of protein surfaces. Thus far, we have written/implemented FORTRAN 77/90 programs for the following map projections: 1.) Mercator, 2.) Miller, 3.) Mollweide, 4.) Robinson and 5.) Gall-Peters. We are currently expanding this list and comparing the methods with each other in both all-atom and reduced protein representations (2) to determine which best represents the proteins’ surface properties by correlation with the proteins’ bioactivity.


  1. V. M. Reyes, Interdiscipl Sci: Comp Life Sci (2011, in press).
  2. V. M. Reyes and V. N. Sheth, In: Handbook of Research in Computational and Systems Biology: Interdisciplinary Approaches, L. A. Liu, D. Wei and Y. Qing (Eds.), Chap. 26 (2011, in press).

Vicente M. Reyes

Biological Sciences Dept.
Sch. of Medical & Biological Sciences
College of Science, Rochester Institute of Technology
Rochester, NY 14623-5603 USA

Ph: (585) 475-4115