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キーワード:
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要旨:
Since the beginning of macromolecular structure determination by high resolution nuclear magnetic resonance (NMR) spectroscopy, the quality of NMR structures has been the source of some concern: experimental data are noisy and incomplete, NMR parameters depend on physical effects for which theory makes no or only approximate predictions. In this thesis I am addressing the question, how errors in the data and approximations in the theory quantitatively affect the reliability with which the atom positions of a macromolecule can be
reconstructed. I find that the estimation of structural uncertainty needs to be considered an integral part of structure determination itself; the conventional approach to structure calculation, however, is inappropriate for answering this question in an objective way. The methods being developed in this thesis are based on the principle of inferential structure determination (ISD), a new approach to structure determination using Bayesian probability theory. I present a method that allows an objective judgement of structural uncertainty in terms
of a statistical error bar. The calculated atomic uncertainties are uniquely determined by the experimental data and background assumptions that are necessary to describe the data. The method is based on a probabilistic density model that is estimated from the data using Markov chain Monte Carlo techniques. Example calculations for two proteins using data from nuclear Overhauser effect spectroscopy (NOESY) experiments demonstrate the performance of the algorithm. The data quality is one of the factors that influence structural uncertainty. A measure for the quality of a data set follows directly
from the statistical description of the measurements. Unlike conventional, "external" quality scores, its calculation does not require additional numerical effort. Properties of the quality measure and the impact of errors in the data on the structural uncertainty are analysed by numerous calculations. Internal dynamics of a macromolecule can lead to inconsistent NOESY data that result in
systematic errors in the atomic positions. In order to reduce structural errors, I have developed a model that explicitly accounts for such inconsistencies. The degree of inconsistency is modelled separately for each measurement. Thus, the total number of unknown parameters of the model always exceeds the number of
data. Calculations show that an probabilistic approach allows one to reliably estimate even complex models; this permits some flexibility in modelling experimental observables. Compared to a model that does not account for systematic errors, the presented approach leads to both a gain in structural quality and a decrease in structural uncertainty.
