Statistical modelling in chemistry - applications to nuclear magnetic resonance and polymerase chain reaction

This thesis consists of two parts with the common theme of statistical modelling in chemistry. The first part is concerned with applications in nuclear magnetic resonance (NMR) spectroscopy, while the second part deals with applications in polymerase chain reaction (PCR). The problems considered in the first part all have their origin in protein NMR spectroscopy, although they are treated mainly from a statistical perspective in the thesis. The interpretation of complex and crowded protein NMR spectra contaminated by noise is a challenging task where the method of maximum likelihood based on the Gaussian distribution has been used with good results. In Paper A it is investigated under what conditions on the processing of the NMR signal the distributional assumptions usually made concerning the noise in the sampled signal may be appropriate. In Paper B some properties of the inverse Fisher information matrix pertaining to the model for a one-dimensional NMR signal are studied with respect to the influence of correlated noise and the problem of parameter resolution. In Paper C the combined effects of filtering and sampling are investigated in terms of their influence on the Cramér-Rao bounds for the estimated parameters of a one-dimensional NMR signal model. Finally, in Paper D a new algorithm, M-RELAX, for estimation of the parameters of several consecutive time series with amplitude decay is proposed. Such problems arise for instance in certain screening experiments in medical drug discovery. In the second part of the thesis some problems encountered in connection with diagnostic PCR analysis and detection of pathogenic bacteria in the food-chain are considered. The focus is on design of pre-PCR strategies for future routine analysis to get a reliable and robust detection of pathogenic Yersinia enterocolitica and Salmonella in complex samples from the food-chain. In Paper A a logistic regression model for the reliability of PCR detection of Yersinia enterocolitica is presented, whereby it is possible to define a practical operating range, determined by the model and a pre-specified detection probability. The development, through a statistical approach using screening, factorial design experiments and confirmatory tests, of a new medium specifically optimised for PCR is described in Paper B. A combined linear and logistic regression model for real-time PCR amplification and detection is presented in Paper C

A statistical analysis of NMR spectrometer noise.

Estimation of NMR spectral parameters, using e.g. maximum likelihood methods, is commonly based on the assumption of white complex Gaussian noise in the signal obtained by quadrature detection. Here we present a statistical analysis with the purpose of discussing and testing the validity of this fundamental assumption. Theoretical expressions are derived for the correlation structure of the noise under various conditions, showing that in general the noise in the sampled signal is not strictly white, even if the thermal noise in the receiver steps prior to digitisation can be characterised as white Gaussian noise. It is shown that the noise correlation properties depend on the ratio between the sampling frequency and the filter cut-off frequency, as well as the filter characteristics. The theoretical analysis identifies conditions that are expected to yield non-white noise in the sampled signal. Extensive statistical characterisation of experimental noise confirms the theoretical predictions. The statistical methods outlined here are also useful for residual analysis in connection with validation of the model and the parameter estimates

Development of a PCR-compatible enrichment medium for Yersinia enterocolitica: amplification precision and dynamic detection range during cultivation

A Yersinia PCR-Compatible Enrichment (YPCE) medium was developed, which removes the necessity for sample pretreatment before PCR-based detection of Yersinia enterocolitica. The medium was designed through a sequence of independent screening and factorial design experiments to study the PCR inhibition and growth characteristics of medium components. The compatibility of the YPCE medium was evaluated using real-time PCR. The real-time PCR assay, based on the fluorescent double-stranded DNA binding dye SYBR green, generated approximately a 4-log linear range of amplification and in the range of 10(5)-10(8) (CFU/ml), the coefficient of variation <5%. When a background flora was present at concentrations greater than or equal to10(6) (CFU/ml), the DNA amplification was influenced and a change in the log-linear slope leading to a lower amplification efficiency was observed. To study the dynamic detection range and relative amplification precision during enrichment, Y. enterocolitica and background flora were inoculated at various concentrations. It was possible to detect inoculation concentrations of 10(1) (CFU/ml) Y enterocolitica in the presence of at least an inoculation concentration of 10(3) (CFU/ml) of an undefined background flora and the optimal conditions for sample withdrawal was in the range of 9 to 18 h enrichment. The YPCE medium can, especially for swab samples, form part of a simple analysis procedure allowing high throughput PCR. (C) 2002 Elsevier Science B.V. All rights reserved

Level crossing prediction with neural networks

A level crossing predictor or alarm system with prediction horizon k is said to be optimal if it, at time t detects that an upcrossing will occur at time t + k, with a certain high probability and simultaneously gives a minimum number of false alarms. For a Gaussian stationary process, the optimal level crossing predictor can be explicitly specified in terms of the predicted value of the process itself and of its derivative. To the authors knowledge this simple optimal solution has not been used to any substantial degree. In this paper it is shown how a neural network can be trained to approximate an optimal alarm system arbitrarily well. As in other methods of parametrization, the choice of model structure, as well as an appropriate representation of data, are crucial for a good result. Comparative studies are presented for two Gaussian ARMA-processes, for which the optimal predictor can be derived theoretically. These studies confirm that a properly trained neural network can indeed approximate an optimal alarm system quite well – with due attention paid to the problems of model structure and representation of data. The technique is also tested on a strongly non-Gaussian Duffing process with satisfactory results

Environmental influences on exopolysaccharide formation in Lactobacillus reuteri ATCC 55730.

Lactobacillus reuteri is known to produce exopolysaccharides (EPS), which have the potential to be used as an alternative biothickener in the food industry. In this study, the effect of several environmental conditions on the growth and EPS production in the L. reuteri strain ATCC 55730 was determined. The expression of the corresponding reuteransucrase gene, gtfO, was investigated over time and the results indicated that the expression increased with growth during the exponential phase and subsequently decreased in the stationary phase. Fermentation with glucose and/or sucrose as carbon and energy source revealed that gtfO was constitutively expressed and that the activity profile was independent of the sugar source. In the applied ranges of parameter values, temperature and pH were the most important factors for EPS formation and only temperature for growth. The best EPS yield, 1.4 g g(-1) CDW, was obtained at the conditions 37 degrees C, pH 4.5 and 100 g l(-1) sucrose, which were close to the estimated optimal conditions: pH 4.56 and 100 g l(-1) sucrose. No EPS formation could be detected with glucose. In addition, no direct connection between the expression and the activity of reuteransucrase could be established. Finally, the strain ATCC 55730 was benchmarked against 14 other L. reuteri strains with respect to EPS production from sucrose and abilities to metabolise sucrose, glucose and fructose. Eight strains were able to produce glucan and a corresponding glucansucrase gene was confirmed for each of them. (c) 2007 Elsevier B.V. All rights reserved