Parametric protein shape recognition.

Declaration I declare that this thesis has been composed by myself, that it describes my own work, that it has not been accepted in any previous application for a degree, that all verbatim extracts are distinguished by quotation marks, and that all sources of information have been speciically acknowledged. i Acknowledgements I would like to thank my supervisors Dr. They made this project possible. They also made it a pleasure to work on. Graham in particular has been an unfailing source of encouragement. Without his interest, and many stimulating lunchtime discussions, this thesis would have been a very lonely endeavour indeed. I am also grateful to the BBSRC for funding this work (and for awarding further funding to continue this research). I would also like to acknowledge Professors Peter Gray and Derek Sleeman for their support. In a Department that is mostly dominated by database and machine learning experts, they seemed to sense that my tinkerings with spherical harmonics and the like might just lead to something useful. I'd like to think that they were right. Probably the most important person during this period has been my girlfriend Terry. She tolerated long hours and even days of isolation; and yet still she seemed interested when all I wanted to talk about was proteins. We get married this October. Apart from everything else, I would like to thank Terry and my parents for proofreading this manuscript so thoroughly. They have an uncanny ability, amongst many other qualities, to instantly detect split innnitives and spelling mistakes (they didn't see this part!). Any errors that remain are entirely my own later additions. Finally, I must acknowledge several greater men than I: Fourier, Laguerre, Legendre, Schrr odinger and Wigner. If they had had computers, little of what follows would have been necessary; without Knuth's beautiful typesetting system, T E X, nothing of what follows would have been legible. ii Summary The salient points of this thesis are as follows: A two-dimensional parametric representation of protein surface shape may be used to superpose pairs of similar protein surfaces rapidly and accurately. A three-dimensional parametric surface shape representation provides an eecient and accurate way to nd complementary arrangements of a pair of surfaces, hence allowing two proteins to be \docked". Both the two-dimensional and the three-dimensional shape parameterisations are based on expansions of real spherical harmonic functions. In the 3D case, the spherical harmonic functions are …