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Spherical Harmonic Molecular Surfaces
July/August 1988 (vol. 8 no. 4)
pp. 42-50

Starlike surfaces can be defined in spherical coordinates by a function r( theta , phi ) on the unit sphere, which can be expanded in spherical harmonics to give a consequence of smooth approximations to the surface. This method has been used to approximate the solvent-accessible surface of a molecule. The coefficients in the expansion provide a small collection of numbers that characterize the molecular shape. The resulting smooth surfaces can be rendered with random dots or smooth shading. These spherical harmonic surfaces have advantages for modeling overall molecular shape, particularly time-averaged shapes relevant to electrostatic and other intermolecular interactions.

1. N. Max, "Computer Representation of Molecular Surfaces,"CG&A, Aug. 1983, pp. 21-29.
2. F. Richards, "Areas, Volume, Packing, and Protein Structure,"Ann. Reviews of Biophysics and Bioengineering, Vol. 6, 1977, pp. 151-176.
3. M. Connolly, "Solvent-Accessible Surfaces of Proteins and Nucleic Acids,"Science, Aug. 1983, pp. 709-713.
4. M. Connolly, "Analytical Molecular Surface Calculation,"J. Applied Crystallography, Oct. 1983, pp. 548-558.
5. J.F. Blinn, "A Generalization of Algebraic Surface Drawing,"ACM Trans. Graphics, Vol. 1, No. 3, July 1982, pp. 235-256.
6. W.R. Taylor, J.M. Thorton, and W.G. Turnell, "An Ellipsoidal Approximation of Protein Shape,"J. Molecular Graphics, June 1983, pp. 30-38.
7. M. Connolly, "Molecular Surface Triangulation,"J. Applied Crystallography, Dec. 1985, pp. 499-505.
8. J.J. Pangarra et al.,Linpack User's Guide, Soc. for Industrial and Applied Mathematics, Philadelphia, 1979, Chap. 9.
9. N. Max, "Polynomial Molecular Surfaces," abstract inJ. Molecular Graphics, Dec. 1986, p. 223.
10. R. Courant and D. Hilbert,Methods of Mathematical Physics, Interscience Publishers, New York, 1983.
11. M. Connolly, MS (molecular surface), 1981 (program available from the Quantum Chemistry Program Exchange, Dept. of Chemistry, Indiana Univ., Bloomington, Ind.); PPMS (piecewise polynomial molecular surface), 1986, TRB (triangulation by recursive bisection), 1986 (programs available from M. Connolly, 4 Washington Square Village, #15N, New York, NY 10012).
12. N.W. Isaacs and R.C. Agarwal, "Experience with Fast Fourier Least Squares in the Refinement of the Crystal Structure of Rhombohedral-Zinc Insulin at 1.5ÅResolution,"Acta Crystallographica, Vol. A34, 1978, pp. 782-791.
13. F.C. Bernstein et al., "The Protein Data Bank: A Computer-Based Archival File for Macromolecular Structures,"J. Molecular Biology, May 1977, pp. 535-542.
14. N. Max, "Atmospheric Illumination and Shadows,"Computer Graphics(Proc. SIGGRAPH), Aug. 1986, pp. 117-124.
15. Y. Satow et al., "Phosphocholine Binding Immunoglobulin Fab McPC603. An X-Ray Diffraction Study at 2.7Å,"J. Molecular Biology, Aug. 1986, pp. 593-604.
16. B. T. Phong, "Illumination for computer generated pictures,"Commun. Ass. Comput. Mach., vol. 18, no. 6, June 1975.
17. N. Max, "Smooth Appearance for Polygonal Surfaces," Submitted toThe Visual Computer.

Citation:
Nelson L. Max, Elizabeth D. Getzoff, "Spherical Harmonic Molecular Surfaces," IEEE Computer Graphics and Applications, vol. 8, no. 4, pp. 42-50, July-Aug. 1988, doi:10.1109/38.7748
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