Data methods in optometry. Part 10: non-linear regression analysis

1. The techniques associated with regression, whether linear or non-linear, are some of the most useful statistical procedures that can be applied in clinical studies in optometry. 2. In some cases, there may be no scientific model of the relationship between X and Y that can be specified in advance and the objective may be to provide a ‘curve of best fit’ for predictive purposes. In such cases, the fitting of a general polynomial type curve may be the best approach. 3. An investigator may have a specific model in mind that relates Y to X and the data may provide a test of this hypothesis. Some of these curves can be reduced to a linear regression by transformation, e.g., the exponential and negative exponential decay curves. 4. In some circumstances, e.g., the asymptotic curve or logistic growth law, a more complex process of curve fitting involving non-linear estimation will be required.

A simple, sensitive and selective quantum-dot-based western blot method for the simultaneous detection of multiple targets from cell lysates

Quantum dots (Qdots) are fluorescent nanoparticles that have great potential as detection agents in biological applications. Their optical properties, including photostability and narrow, symmetrical emission bands with large Stokes shifts, and the potential for multiplexing of many different colours, give them significant advantages over traditionally used fluorescent dyes. Here, we report the straightforward generation of stable, covalent quantum dot-protein A/G bioconjugates that will be able to bind to almost any IgG antibody, and therefore can be used in many applications. An additional advantage is that the requirement for a secondary antibody is removed, simplifying experimental design. To demonstrate their use, we show their application in multiplexed western blotting. The sensitivity of Qdot conjugates is found to be superior to fluorescent dyes, and comparable to, or potentially better than, enhanced chemiluminescence. We show a true biological validation using a four-colour multiplexed western blot against a complex cell lysate background, and have significantly improved previously reported non-specific binding of the Qdots to cellular proteins.

Combinatorial approach to multi-substituted 1,4-Benzodiazepines as novel non-peptide CCK-antagonists

For the drug discovery process, a library of 168 multisubstituted 1,4-benzodiazepines were prepared by a 5-step solid phase combinatorial approach. Substituents were varied in the 3,5, 7 and 8-position on the benzodiazepine scaffold. The combinatorial library was evaluated in a CCK radiolabelled binding assay and CCKA (alimentary) and CCKB (brain) selective lead structures were discovered. The template of CCKA selective 1,4-benzodiazepin-2-ones bearing the tryptophan moiety was chemically modified by selective alkylation and acylation reactions. These studies provided a series of Asperlicin naturally analogues. The fully optimised Asperlicin related compound possessed a similar CCKA activity as the natural occuring compound. 3-Alkylated 1,4-benzodiazepines with selectivity towards the CCKB receptor subtype were optimised on A) the lipophilic side chain and B) the 2-aminophenyl-ketone moiety, together with some stereochemical changes. A C3 unit in the 3-position of 1,4-benzodiazepines possessed a CCKB activity within the nanomolar range. Further SAR optimisation on the N1-position by selective alkylation resulted in an improved CCKB binding with potentially decreased activity on the GABAA/benzodiazepine receptor complex. The in vivo studies revealed two N1-alkylated compounds containing unsaturated alkyl groups with anxiolytic properties. Alternative chemical approaches have been developed, including a route that is suitable for scale up of the desired target molecule in order to provide sufficient quantities for further in vivo evaluation.

Neural network enhanced self tuning adaptive control application for non-linear control of dynamic systems

The main theme of research of this project concerns the study of neutral networks to control uncertain and non-linear control systems. This involves the control of continuous time, discrete time, hybrid and stochastic systems with input, state or output constraints by ensuring good performances. A great part of this project is devoted to the opening of frontiers between several mathematical and engineering approaches in order to tackle complex but very common non-linear control problems. The objectives are: 1. Design and develop procedures for neutral network enhanced self-tuning adaptive non-linear control systems; 2. To design, as a general procedure, neural network generalised minimum variance self-tuning controller for non-linear dynamic plants (Integration of neural network mapping with generalised minimum variance self-tuning controller strategies); 3. To develop a software package to evaluate control system performances using Matlab, Simulink and Neural Network toolbox. An adaptive control algorithm utilising a recurrent network as a model of a partial unknown non-linear plant with unmeasurable state is proposed. Appropriately, it appears that structured recurrent neural networks can provide conveniently parameterised dynamic models for many non-linear systems for use in adaptive control. Properties of static neural networks, which enabled successful design of stable adaptive control in the state feedback case, are also identified. A survey of the existing results is presented which puts them in a systematic framework showing their relation to classical self-tuning adaptive control application of neural control to a SISO/MIMO control. Simulation results demonstrate that the self-tuning design methods may be practically applicable to a reasonably large class of unknown linear and non-linear dynamic control systems.

Non-linear hierarchical visualisation

This thesis applies a hierarchical latent trait model system to a large quantity of data. The motivation for it was lack of viable approaches to analyse High Throughput Screening datasets which maybe include thousands of data points with high dimensions. High Throughput Screening (HTS) is an important tool in the pharmaceutical industry for discovering leads which can be optimised and further developed into candidate drugs. Since the development of new robotic technologies, the ability to test the activities of compounds has considerably increased in recent years. Traditional methods, looking at tables and graphical plots for analysing relationships between measured activities and the structure of compounds, have not been feasible when facing a large HTS dataset. Instead, data visualisation provides a method for analysing such large datasets, especially with high dimensions. So far, a few visualisation techniques for drug design have been developed, but most of them just cope with several properties of compounds at one time. We believe that a latent variable model (LTM) with a non-linear mapping from the latent space to the data space is a preferred choice for visualising a complex high-dimensional data set. As a type of latent variable model, the latent trait model can deal with either continuous data or discrete data, which makes it particularly useful in this domain. In addition, with the aid of differential geometry, we can imagine the distribution of data from magnification factor and curvature plots. Rather than obtaining the useful information just from a single plot, a hierarchical LTM arranges a set of LTMs and their corresponding plots in a tree structure. We model the whole data set with a LTM at the top level, which is broken down into clusters at deeper levels of t.he hierarchy. In this manner, the refined visualisation plots can be displayed in deeper levels and sub-clusters may be found. Hierarchy of LTMs is trained using expectation-maximisation (EM) algorithm to maximise its likelihood with respect to the data sample. Training proceeds interactively in a recursive fashion (top-down). The user subjectively identifies interesting regions on the visualisation plot that they would like to model in a greater detail. At each stage of hierarchical LTM construction, the EM algorithm alternates between the E- and M-step. Another problem that can occur when visualising a large data set is that there may be significant overlaps of data clusters. It is very difficult for the user to judge where centres of regions of interest should be put. We address this problem by employing the minimum message length technique, which can help the user to decide the optimal structure of the model. In this thesis we also demonstrate the applicability of the hierarchy of latent trait models in the field of document data mining.

Contrast sensitivity for complex and random gratings

This thesis studied the effect of (i) the number of grating components and (ii) parameter randomisation on root-mean-square (r.m.s.) contrast sensitivity and spatial integration. The effectiveness of spatial integration without external spatial noise depended on the number of equally spaced orientation components in the sum of gratings. The critical area marking the saturation of spatial integration was found to decrease when the number of components increased from 1 to 5-6 but increased again at 8-16 components. The critical area behaved similarly as a function of the number of grating components when stimuli consisted of 3, 6 or 16 components with different orientations and/or phases embedded in spatial noise. Spatial integration seemed to depend on the global Fourier structure of the stimulus. Spatial integration was similar for sums of two vertical cosine or sine gratings with various Michelson contrasts in noise. The critical area for a grating sum was found to be a sum of logarithmic critical areas for the component gratings weighted by their relative Michelson contrasts. The human visual system was modelled as a simple image processor where the visual stimuli is first low-pass filtered by the optical modulation transfer function of the human eye and secondly high-pass filtered, up to the spatial cut-off frequency determined by the lowest neural sampling density, by the neural modulation transfer function of the visual pathways. The internal noise is then added before signal interpretation occurs in the brain. The detection is mediated by a local spatially windowed matched filter. The model was extended to include complex stimuli and its applicability to the data was found to be successful. The shape of spatial integration function was similar for non-randomised and randomised simple and complex gratings. However, orientation and/or phase randomised reduced r.m.s contrast sensitivity by a factor of 2. The effect of parameter randomisation on spatial integration was modelled under the assumption that human observers change the observer strategy from cross-correlation (i.e., a matched filter) to auto-correlation detection when uncertainty is introduced to the task. The model described the data accurately.

Discriminating antigen and non-antigen using proteome dissimilarity III:tumour and parasite antigens

Computational genome analysis enables systematic identification of potential immunogenic proteins within a pathogen. Immunogenicity is a system property that arises through the interaction of host and pathogen as mediated through the medium of a immunogenic protein. The overt dissimilarity of pathogenic proteins when compared to the host proteome is conjectured by some to be the determining principal of immunogenicity. Previously, we explored this idea in the context of Bacterial, Viral, and Fungal antigen. In this paper, we broaden and extend our analysis to include complex antigens of eukaryotic origin, arising from tumours and from parasite pathogens. For both types of antigen, known antigenic and non-antigenic protein sequences were compared to human and mouse proteomes. In contrast to our previous results, both visual inspection and statistical evaluation indicate a much wider range of homologues and a significant level of discrimination; but, as before, we could not determine a viable threshold capable of properly separating non-antigen from antigen. In concert with our previous work, we conclude that global proteome dissimilarity is not a useful metric for immunogenicity for presently available antigens arising from Bacteria, viruses, fungi, parasites, and tumours. While we see some signal for certain antigen types, using dissimilarity is not a useful approach to identifying antigenic molecules within pathogen genomes.

Exploratory data analysis with non-linear and missing data in geochemistry

Exploratory analysis of data seeks to find common patterns to gain insights into the structure and distribution of the data. In geochemistry it is a valuable means to gain insights into the complicated processes making up a petroleum system. Typically linear visualisation methods like principal components analysis, linked plots, or brushing are used. These methods can not directly be employed when dealing with missing data and they struggle to capture global non-linear structures in the data, however they can do so locally. This thesis discusses a complementary approach based on a non-linear probabilistic model. The generative topographic mapping (GTM) enables the visualisation of the effects of very many variables on a single plot, which is able to incorporate more structure than a two dimensional principal components plot. The model can deal with uncertainty, missing data and allows for the exploration of the non-linear structure in the data. In this thesis a novel approach to initialise the GTM with arbitrary projections is developed. This makes it possible to combine GTM with algorithms like Isomap and fit complex non-linear structure like the Swiss-roll. Another novel extension is the incorporation of prior knowledge about the structure of the covariance matrix. This extension greatly enhances the modelling capabilities of the algorithm resulting in better fit to the data and better imputation capabilities for missing data. Additionally an extensive benchmark study of the missing data imputation capabilities of GTM is performed. Further a novel approach, based on missing data, will be introduced to benchmark the fit of probabilistic visualisation algorithms on unlabelled data. Finally the work is complemented by evaluating the algorithms on real-life datasets from geochemical projects.

Addressing missing data in geochemistry: a non-linear approach

Exploratory analysis of petroleum geochemical data seeks to find common patterns to help distinguish between different source rocks, oils and gases, and to explain their source, maturity and any intra-reservoir alteration. However, at the outset, one is typically faced with (a) a large matrix of samples, each with a range of molecular and isotopic properties, (b) a spatially and temporally unrepresentative sampling pattern, (c) noisy data and (d) often, a large number of missing values. This inhibits analysis using conventional statistical methods. Typically, visualisation methods like principal components analysis are used, but these methods are not easily able to deal with missing data nor can they capture non-linear structure in the data. One approach to discovering complex, non-linear structure in the data is through the use of linked plots, or brushing, while ignoring the missing data. In this paper we introduce a complementary approach based on a non-linear probabilistic model. Generative topographic mapping enables the visualisation of the effects of very many variables on a single plot, while also dealing with missing data. We show how using generative topographic mapping also provides an optimal method with which to replace missing values in two geochemical datasets, particularly where a large proportion of the data is missing.

Reporter ion-based mass spectrometry approaches for the detection of non-enzymatic protein modifications in biological samples

Development of mass spectrometry techniques to detect protein oxidation, which contributes to signalling and inflammation, is important. Label-free approaches have the advantage of reduced sample manipulation, but are challenging in complex samples owing to undirected analysis of large data sets using statistical search engines. To identify oxidised proteins in biological samples, we previously developed a targeted approach involving precursor ion scanning for diagnostic MS3 ions from oxidised residues. Here, we tested this approach for other oxidations, and compared it with an alternative approach involving the use of extracted ion chromatograms (XICs) generated from high-resolution MSMS data using very narrow mass windows. This accurate mass XIC data methodology was effective at identifying nitrotyrosine, chlorotyrosine, and oxidative deamination of lysine, and for tyrosine oxidations highlighted more modified peptide species than precursor ion scanning or statistical database searches. Although some false positive peaks still occurred in the XICs, these could be identified by comparative assessment of the peak intensities. The method has the advantage that a number of different modifications can be analysed simultaneously in a single LC-MSMS run. This article is part of a Special Issue entitled: Posttranslational Protein modifications in biology and Medicine. Biological significance: The use of accurate mass extracted product ion chromatograms to detect oxidised peptides could improve the identification of oxidatively damaged proteins in inflammatory conditions. © 2013 Elsevier B.V.

Non-peptidic antagonists of the CGRP receptor, BIBN4096BS and MK-0974, interact with the calcitonin receptor-like receptor via methionine-42 and RAMP1 via tryptophan-74

The receptor for calcitonin gene-related peptide (CGRP) has been the target for the development of novel small molecule antagonists for the treatment of migraine. Two such antagonists, BIBN4096BS and MK-0974, have shown great promise in clinical trials and hence a deeper understanding of the mechanism of their interaction with the receptor is now required. The structure of the CGRP receptor is unusual since it is comprised of a hetero-oligomeric complex between the calcitonin receptor-like receptor (CRL) and an accessory protein (RAMP1). Both the CLR and RAMP1 components have extracellular domains which interact with each other and together form part of the peptide-binding site. It seems likely that the antagonist binding site will also be located on the extracellular domains and indeed Trp-74 of RAMP1 has been shown to form part of the binding site for BIBN4096BS. However, despite a chimeric study demonstrating the role of the N-terminal domain of CLR in antagonist binding, no specific residues have been identified. Here we carry out a mutagenic screen of the extreme N-terminal domain of CLR (residues 23-63) and identify a mutant, Met-42-Ala, which displays 48-fold lower affinity for BIBN4096BS and almost 900-fold lower affinity for MK-0974. In addition, we confirm that the Trp-74-Lys mutation at human RAMP1 reduces BIBN4096BS affinity by over 300-fold and show for the first time a similar effect for MK-0974 affinity. The data suggest that the non-peptide antagonists occupy a binding site close to the interface of the N-terminal domains of CLR and RAMP1.

The N-terminus of CD14 acts to bind apoptotic cells and confers rapid-tethering capabilities on non-myeloid cells:CD14 and rapid tethering of apoptotic cells

Cell death and removal of cell corpses in a timely manner is a key event in both physiological and pathological situations including tissue homeostasis and the resolution of inflammation. Phagocytic clearance of cells dying by apoptosis is a complex sequential process comprising attraction, recognition, tethering, signalling and ultimately phagocytosis and degradation of cell corpses. A wide range of molecules acting as apoptotic cell-associated ligands, phagocyte-associated receptors or soluble bridging molecules have been implicated within this process. The role of myeloid cell CD14 in mediating apoptotic cell interactions with macrophages has long been known though key molecules and residues involved have not been defined. Here we sought to further dissect the function of CD14 in apoptotic cell clearance. A novel panel of THP-1 cell-derived phagocytes was employed to demonstrate that CD14 mediates effective apoptotic cell interactions with macrophages in the absence of detectable TLR4 whilst binding and responsiveness to LPS requires TLR4. Using a targeted series of CD14 point mutants expressed in non-myeloid cells we reveal CD14 residue 11 as key in the binding of apoptotic cells whilst other residues are reported as key for LPS binding. Importantly we note that expression of CD14 in non-myeloid cells confers the ability to bind rapidly to apoptotic cells. Analysis of a panel of epithelial cells reveals that a number naturally express CD14 and that this is competent to mediate apoptotic cell clearance. Taken together these data suggest that CD14 relies on residue 11 for apoptotic cell tethering and it may be an important tethering molecule on so called 'non-professional' phagocytes thus contributing to apoptotic cell clearance in a non-myeloid setting. Furthermore these data establish CD14 as a rapid-acting tethering molecule, expressed in monocytes, which may thus confer responsiveness of circulating monocytes to apoptotic cell derived material. © 2013 Thomas et al.

MEG and complex systems

MEG beamformer algorithms work by making the assumption that correlated and spatially distinct local field potentials do not develop in the human brain. Despite this assumption, images produced by such algorithms concur with those from other non-invasive and invasive estimates of brain function. In this paper we set out to develop a method that could be applied to raw MEG data to explicitly test his assumption. We show that a promax rotation of MEG channel data can be used as an approximate estimator of the number of spatially distinct correlated sources in any frequency band.

Covalent attachment of chiral manganese(III) salen complexes onto functionalised hexagonal mesoporous silica and application to the asymmetric epoxidation of alkenes

Two modified Jacobsen-type catalysts were anchored onto an amine functionalised hexagonal mesoporous silica (HMS) using two distinct anchoring procedures: (i) one was anchored directly through the carboxylic acid functionalised diimine bridge fragment of the complex (CAT1) and (ii) the other through the hydroxyl group on the aldehyde fragment of the complex (CAT2), mediated by cyanuric chloride. The new heterogeneous catalyst, as well as the precedent materials, were characterised by elemental analyses, DRIFT, UV-vis, porosimetry and XPS which showed that the complexes were successfully anchored onto the hexagonal mesoporous silica. These materials acted as active heterogeneous catalysts in the epoxidation of styrene, using m-CPBA as oxidant, and α-methylstyrene, using NaOCl as oxidant. Under the latter conditions they acted also as enantioselective heterogeneous catalysts. Furthermore, when compared to the reaction run in homogeneous phase under similar experimental conditions, an increase in asymmetric induction was observed for the heterogenised CAT1, while the opposite effect was observed for the heterogenised CAT2, despite of CAT2 being more enantioselective than CAT1 in homogeneous phase. These results indicate that the covalent attachment of the Jacobsen catalyst through the diimine bridge leads to improved enantiomeric excess (%ee), whereas covalent attachment through one of the aldehyde fragments results in a negative effect in the %ee. Using α-methylstyrene and NaOCl as oxidant, heterogeneous catalyst reuse led to no significant loss of catalytic activity and enantioselectivity. © 2005 Elsevier Inc. All rights reserved.

The role of pinning and instability in a class of non-equilibrium growth models

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the "perturbative" limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behaviour. Possibilities of controlling this instability by introducing statistically "irrelevant" (in the sense of renormalisation groups) higher ordered nonlinearities have also been discussed.