Abstract
The importance of molecular shape in many areas of biochemistry and biomolecular interactions is well recognised. In spite of this a rigorous and widely applicable means of defining and quantifying molecular shape has not been available. This paper, the first of a series of papers, presents a new method of quantifying molecular “surface” shape. The development of the technique, based on Fourier shape descriptors is discussed in some depth including the computer programs written to implement and test the method. A subsequent paper will present results obtained from the application of the new quantitative molecular shape descriptors.
Similar content being viewed by others
References
P.G. Mezey, J. Comp. Chem. 8 (1987) 462.
A. Verloop, W. Hoogenstraaten and J. Tipker, Drug Design 7 (1976) 165.
G.A. Arteca and P.G. Mezey, J. Comp. Chem. 9 (1988) 554.
S.E. Leicester, Quantitative molecular surface shape analysis using spherical harmonic Fourier shape descriptors, Ph.D. Thesis, University of London (1989).
S.E. Leicester, J.L. Finney and R.P. Bywater, J. Mol. Graph. 6 (1988) 104.
N.L. Max and E.D. Getzoff, IEEE Camp. Graphics Appl. 8 (1988) 42.
T. Wallace and P.A. Wintz, Fourier descriptors for extraction of shape information, in:Image Understanding and Information Extraction, eds. T.S. Huang and K.S. Fu, School of Electrical Engineering, Purdue University, Indiana, USA TR-EE 77-35 (1977).
F. Etsami and J.J. Uicker, Comp. Vision, Graphics Image Process. 29 (1985) 216.
D.L. Fritzsche,A systematic method for character recognition, Ohio State Univ. Res. Found., Columbus, Rep. 12224 ASTIA AD 268-360 (1961).
K. Gotoh and J.L. Finney, Powder Tech. 12 (1975) 125.
R.L. Cosgriff, Identification of shape, Ohio State Univ. Res. Found., Columbus, Rep. 820-11, ASTIA AD 254 792 (1960).
C.T. Zahn and R.Z. Roskies, IEEE Trans. Comp. C21 (1972) 269–271.
P. Dennery and A. Krzywicki, Mathematics for Physicists (Harper & Row, New York, 1967).
O.R. Mitchell, P. Soc. Photo. 442 (1983) 38.
T. Wallace and P.A. Wintz, Comp. Graphics Image Process. 13 (1980) 99.
B. Shridhar and A. Baldredin, Pattern Recognition 17 (1984) 515.
K.S. Park and N.S. Lee, Comp. Biomed. Res. 20 (1987) 125–140.
R.A. Crowther, The fast rotation function in the molecular replacement method, in:The Molecular Replacement Method: A Collection of Papers on the Use of Non-crystallographic Symmetry, ed. M.G. Rossman (Gordon & Breach, New York, 1972).
E.W. Hobson,Spherical & Ellipsoidal Harmonics (Cambridge University Press, 1931).
J.P. Elliot and P.G. Dawber,Symmetry in Physics, Vol. l (Macmillan, London, 1979).
A.W. Joshi,Elements of Group Theory for Physicists (Wiley Eastern, New Delhi, 1973).
J.D. Davis and P. Rabinowitz,Methods of Numerical Integration (Academic Press, London, 1987).
R.A. Wiggins and S. Masanori, Bull. Seismolog. Soc. Am. 61 (1971) 357.
W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling,Numerical Recipes — The Art of Scientific Programming (Cambridge University Press, 1987).
F.C. Bernstein, T.F. Koetzle, G.J.B. Williams, E.F. Meyer, M.D. Bryce, J.R. Rodgers, O. Kennard, T. Shikanouchi and M. Tasumi, J. Mal. Biol. 112 (1977) 535.
Dewar Research Group and J.P.P. Stewart, AMPAC 2.0, QCPE Bull. 6 (1986) 24 (QCPE No.: 506).
M.L. Connolly, Molecular Surface Program, QCPE Bull. l (1981) 74 (QCPE No. 429).
F.M. Richards, Ann. Rev. Biophys. Bioeng. 6 (1977) 151.
E. Persoon and F. King-Sun, IEEE Trans. Syst., Man & Cybern. SMC 7 (3) (1977) 170.
C. Chatfield and A.J. Collins,Introduction to Multivariate Analysis (Chapman & Hall, London, 1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Leicester, S., Finney, J. & Bywater, R. A quantitative representation of molecular surface shape. I: Theory and development of the method. J Math Chem 16, 315–341 (1994). https://doi.org/10.1007/BF01169216
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01169216