Summary
The wavelet method offers possibilities for display, editing, and topological comparison of proteins at a user-specified level of detail. Wavelets are a mathematical tool that first found application in signal processing. The multiresolution analysis of a signal via wavelets provides a hierarchical series of ‘best’ lower-resolution approximations. B-spline ribbons model the protein fold, with one control point per residue. Wavelet analysis sets limits on the information required to define the winding of the backbone through space, suggesting a recognizable fold is generated from a number of points equal to 1/4 or less the number of residues. Wavelets applied to surfaces and volumes show promise in structure-based drug design.
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References
FinkelsteinA. and SalesinD.H., SIGGRAPH Proc., 28 (1994) 261.
ShoichetB.K. and KuntzI.D., Protein Eng., 6 (1993) 723.
DaubechiesI., Commun. Pure Appl. Math., 1 (1988) 909.
MallatS., IEEE Trans. Pattern Anal. Machine Intell., 11 (1989) 674.
PressW.H., TeukolskyS.A., VetterlingW.T. and FlanneryB.P., Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press, New York, NY, 1992.
StollnitzE.J., DeRoseT.D. and SalesinD.H., IEEE Comput. Graph. Appl., 15 (1995) 76.
StollnitzE.J., DeRoseT.D. and SalesinD.H., IEEE Comput. Graph. Appl., 15 (1995) 75.
CarsonM. and BuggC.E., J. Mol. Graph., 4 (1986) 121.
CarsonM., J. Mol. Graph., 5 (1987) 103.
CarsonM., J. Appl. Crystallogr., 24 (1991) 958.
RichardsonJ.S., Adv. Protein Chem., 34 (1981) 167.
HobohmU., ScharfM., SchneiderR. and SanderC., Protein Sci., 1 (1992) 409.
RaoS.T. and RossmannM.G., J. Mol. Biol., 76 (1973) 241.
GreerJ., Proteins, 7 (1990) 317.
JonesT.A. and ThirupS., EMBO J., 5 (1986) 819.
JonesT.A., ZouJ.-Y., CowanS.W. and KjeldgaardM., Acta Crystallogr., A 47 (1991) 110.
McReeD.E., Practical Protein Crystallography, Academic Press, San Diego, CA, 1993.
SurlesM.C., RichardsonJ.S., RichardsonD.C. and BrooksJr.F.P., Protein Sci., 3 (1994) 198.
LeeB. and RichardsF.M., J. Mol. Biol., 55 (1971) 379.
GreerJ. and BushB.L., Proc. Natl. Acad. Sci. USA, 75 (1978) 303.
ConnollyM.L., Science, 221 (1983) 709.
KleinT.E., HuangC.C., PettersenE.F., CoughG.S., FerrinT.E. and LangridgeR., J. Mol. Graph., 8 (1990) 16.
Colloc'hN. and MornonJ.-P., J. Mol. Graph., 8 (1990) 133.
CarsonM. and YangZ., J. Mol. Graph., 12 (1994) 116.
MaxN.L. and GetzoffE.D., IEEE Comput. Graph. Appl., 8 (1988) 42.
ConnollyM.L., J. Mol. Graph., 11 (1993) 139.
EckM., DuchampT., LounsberyM., DeRoseT., HoppeH. and StuetzleW., SIGGRAPH Proc., 29 (1995) 173.
MurakiS., IEEE Comput. Graph. Appl., 13 (1993) 50.
BabuY.S., SackJ.S., GreenhoughT.J., BuggC.E., MeansA.R. and CookW.J., Nature, 315 (1985) 37.
Bossart-WhitakerP., CarsonM., BabuY.S., SmithC.D., LaverW.G. and AirG.M., J. Mol. Biol., 232 (1993) 1069.
EalickS.E., CookW.J., Vijay-KumarS., CarsonM., NagabhushanT.L., TrottaP.P. and BuggC.E., Science, 252 (1991) 698.
El-KabbaniO., GreenN.C., LinG., CarsonM., NarayanaS.V.L., MooreK.M., FlynnR.G. and DeLucasL.J., Acta Crystallogr., D 50 (1994) 859.
CarsonM., BuggC.E., DeLucasL.J. and NarayanaS.V.L., Acta Crystallogr., D 50 (1994) 889.
NarayanaS.V.L., CarsonM., El-KabbaniO., KilpatrickJ.M., MooreD., ChenX., BuggC.E., VolanakisJ.E. and DeLucasL.J., J. Mol. Biol., 235 (1994) 695.
StynadkaN.C.J. and JamesM.N.G., Proteins Struct. Funct. Genet., 3 (1988) 1.
CrippenG.M. and MaiorovV.N., J. Mol. Biol., 252 (1995) 144.
IllertC. and PickoverC., IEEE Comput. Graph. Appl., 15 (1995) 89.
VriendG. and SanderC., Proteins Struct. Funct. Genet., 11 (1991) 52.
SaliA. and BlundellT.L., J. Mol. Biol., 212 (1990) 403.
HermansJ. and McQueenJ.E., Acta Crystallogr., A 30 (1974) 730.
DuncanB.S. and OlsonA.J., J. Mol. Graph., 13 (1995) 258.
JiangF. and KimS.-H., J. Mol. Biol., 219 (1991) 79.
GoodsellD.S. and OlsonA.J., Proteins, 8 (1990) 195.
GersteinM., Acta Crystallogr., A 48 (1992) 271.
LeicesterS.E., FinneyJ.L. and BywaterR.P., J. Mol. Graph., 6 (1988) 104.
Gross, M.H., Gatti, R. and Staadt, O., IEEE Visualization Proceedings, Institute of Electrical and Electronics Engineers Inc., New York, NY, 1996, pp. 135–142.
Vijay-KumarS., BuggC.E., WilkinsonK.D. and CookW.J., Proc. Natl. Acad. Sci. USA, 82 (1985) 3582.
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This paper is based on a presentation given at the 14th Molecular Graphics and Modelling Society Conference, held in Cairns, Australia, August 27–September 1, 1995.
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Carson, M. Wavelets and molecular structure. J Computer-Aided Mol Des 10, 273–283 (1996). https://doi.org/10.1007/BF00124497
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DOI: https://doi.org/10.1007/BF00124497