Estimation of expression levels in spotted microarrays with saturated pixels.

Digital images obtained by the laser scanning of spotted microarrays often include saturated pixel values. These arise when the scan settings are sufficiently high and some pixels exceed the limit L=65535 and are instead set to L. Failure to adjust for this censoring leads to biased estimates of gene expression levels. To impute censored values, we propose a linear model based on the principal components of uncensored spots on the same array. This is computationally fast, flexible to adapt to distinctive spot shapes and profiles on different arrays, and is shown to be more effective than the polynomial-hyperbolic model in correcting for the bias. The application to biological data demonstrates the potential for enhancing the dynamic range of detection. Fortran90 subroutines implementing these methods are available at http://www.bioss.ac.uk/~chris.

A comparison of parametric and nonparametric methods for normalising cDNA microarray data.

Normalisation is an essential first step in the analysis of most cDNA microarray data, to correct for effects arising from imperfections in the technology. Loess smoothing is commonly used to correct for trends in log-ratio data. However, parametric models, such as the additive plus multiplicative variance model, have been preferred for scale normalisation, though the variance structure of microarray data may be of a more complex nature than can be accommodated by a parametric model. We propose a new nonparametric approach that incorporates location and scale normalisation simultaneously using a Generalised Additive Model for Location, Scale and Shape (GAMLSS, Rigby and Stasinopoulos, 2005, Applied Statistics, 54, 507-554). We compare its performance in inferring differential expression with Huber et al.'s (2002, Bioinformatics, 18, 96-104) arsinh variance stabilising transformation (AVST) using real and simulated data. We show GAMLSS to be as powerful as AVST when the parametric model is correct, and more powerful when the model is wrong.

The responses of growing pigs to a chronic-intermittent stress treatment.

Many of the stressor treatments used in animal models of depression have parallels in the normal experiences of domestic pigs. The experiment described here aimed to assess whether a chronic-intermittent stress regime caused behavioural or physiological changes, indicative of depression, in domestic pigs. Ten juvenile male pigs were exposed to a social and environmental stress regime. Over the stressor period, weight gain was significantly lower in test pigs than in control pigs. Stress treatment had a significant effect on salivary cortisol levels, with test pigs having a higher salivary cortisol concentration than control pigs after the stress treatment but not before. Test pigs showed less ventral lying than control pigs in the post-stress observation. A detrended fluctuation analysis (DFA) of postural behavioural organisation showed that test pigs had a more structured pattern of activity than controls in the post-stress observation and a tendency towards a more structured pattern in the pre-stress observation. There were no major behavioural differences between the two groups during three repeated open field tests. The results suggest that the stressor treatment did create a mild chronic stress, as indicated by the hypercortisolaemia and lower weight gain in the test pigs. However, no unambiguous behavioural indicators of depression were seen. The behavioural analysis did show that fractal techniques, such as DFA, could be applied to pig behaviour and that they can reveal extra novel information about the structure of an individual's behavioural organisation and how it changes in response to complex environmental stressors.

Automated estimation of leaf area development in sweet pepper plants from image analysis.

High-throughput automated plant phenotyping has recently received a lot of attention. Leaf area is an important characteristic in understanding plant performance, but time-consuming and destructive to measure accurately. In this research, we describe a method to use a histogram of image intensities to automatically measure plant leaf area of tall pepper (Capsicum annuum L.) plants in the greenhouse. With a device equipped with several cameras, images of plants were recorded at 5-cm intervals over a height of 3m, at a recording distance of less than 60cm. The images were reduced to a small set of principal components that defined the design matrix in a regression model for predicting manually measured leaf area as obtained from destructive harvesting. These regression calibrations were performed for six different developmental times. In addition, development of leaf area was investigated by fitting linear relations between predicted leaf area and time, with special attention given to the genotype by time interaction and its genetic basis in the form of quantitative trait loci (QTLs). The experiment comprised parents, F1 progeny and eight genotypes of a recombinant inbred population of pepper. Although the current trial contained a limited number of genotypes, an earlier identified QTL related to leaf area growth could be confirmed. Therefore, image analysis, as presented in this paper, provides a powerful and efficient way to study and identify the genetic basis of growth and developmental processes in plants.

The importance of 'memory' in statistical models for animal feeding behaviour.

We investigate models for animal feeding behaviour, with the aim of improving understanding of how animals organise their behaviour in the short term. We consider three classes of model: hidden Markov, latent Gaussian and semi-Markov. Each can predict the typical 'clustered' feeding behaviour that is generally observed, however they differ in the extent to which 'memory' of previous behaviour is allowed to affect future behaviour. The hidden Markov model has 'lack of memory', the current behavioural state being dependent on the previous state only. The latent Gaussian model assumes feeding/non-feeding periods to occur by the thresholding of an underlying continuous variable, thereby incorporating some 'short-term memory'. The semi-Markov model, by taking into account the duration of time spent in the previous state, can be said to incorporate 'longer-term memory'. We fit each of these models to a dataset of cow feeding behaviour. We find the semi-Markov model (longer-term memory) to have the best fit to the data and the hidden Markov model (lack of memory) the worst. We argue that in view of effects of satiety on short-term feeding behaviour of animal species in general, biologically suitable models should allow 'memory' to play a role. We conclude that our findings are equally relevant for the analysis of other types of short-term behaviour that are governed by satiety-like principles.

SPICY: towards automated phenotyping of large pepper plants in the greenhouse.

Most high-throughput systems for automated plant phenotyping involve a fixed recording cabinet to which plants are transported. However, important greenhouse plants like pepper are too tall to be transported. In this research we developed a system to automatically measure plant characteristics of tall pepper plants in the greenhouse. With a device equipped with multiple cameras, images of plants are recorded at a 5cm interval over a height of 3m. Two types of features are extracted: (1) features from a 3D reconstruction of the plant canopy; and (2) statistical features derived directly from RGB images. The experiment comprised 151 genotypes of a recombinant inbred population of pepper, to examine the heritability and quantitative trait loci (QTL) of the features. Features extracted from the 3D reconstruction of the canopy were leaf size and leaf angle, with heritabilities of 0.70 and 0.56 respectively. Three QTL were found for leaf size, and one for leaf angle. From the statistical features, plant height showed a good correlation (0.93) with manual measurements, and QTL were in accordance with QTL of manual measurements. For total leaf area, the heritability was 0.55, and two of the three QTL found by manual measurement were found by image analysis.

Estimation of centres and radial intensity profiles of spherical nano-particles in digital microscopy.

Control of the microscopic characteristics of colloidal systems is critical in a wealth of application areas, ranging from food to pharmaceuticals. To assist in estimating these characteristics, we present a method for estimating the positions of spherical nano-particles in digital microscopy images. The radial intensity profiles of particles, which depend on the distances of the particles from the focal plane of the light microscope and have no closed functional form, are modelled using a local quadratic kernel estimate. We also allow for the case where pixel values are censored at an upper limit of 255. Standard errors of centre estimates are obtained using a sandwich estimator which takes into account spatial autocorrelation in the errors. The approach is validated by a simulation study.

Statistical estimation of gene expression using multiple laser scans of microarrays.

UNLABELLED: We propose a statistical model for estimating gene expression using data from multiple laser scans at different settings of hybridized microarrays. A functional regression model is used, based on a non-linear relationship with both additive and multiplicative error terms. The function is derived as the expected value of a pixel, given that values are censored at 65 535, the maximum detectable intensity for double precision scanning software. Maximum likelihood estimation based on a Cauchy distribution is used to fit the model, which is able to estimate gene expressions taking account of outliers and the systematic bias caused by signal censoring of highly expressed genes. We have applied the method to experimental data. Simulation studies suggest that the model can estimate the true gene expression with negligible bias. AVAILABILITY: FORTRAN 90 code for implementing the method can be obtained from the authors.

A statistical model for unwarping of 1-D electrophoresis gels.

A statistical model is proposed which relates density profiles in 1-D electrophoresis gels, such as those produced by pulsed-field gel electrophoresis (PFGE), to databases of profiles of known genotypes. The warp in each gel lane is described by a trend that is linear in its parameters plus a first-order autoregressive process, and density differences are modelled by a mixture of two normal distributions. Maximum likelihood estimates are computed efficiently by a recursive algorithm that alternates between dynamic time warping to align individual lanes and generalised-least-squares regression to ensure that the warp is smooth between lanes. The method, illustrated using PFGE of Escherichia coli O157 strains, automatically unwarps and classifies gel lanes, and facilitates manual identification of new genotypes.

Statistical exploration of variation in quantitative two-dimensional gel electrophoresis data.

Two-dimensional gel electrophoresis is a major technique in global analysis at the protein level. This paper presents an examination of spot volume data from three gel sets with radioactively labeled yeast Saccharomyces cerevisiae proteins. A strong variance versus mean dependence in data was found to be stabilized by applying a shifted logarithmic transformation. However, transformed data showed a remaining substantial variance heterogeneity for different proteins. Furthermore, examination of studentized residuals revealed that transformed data were approximately normally distributed and that there were spatial correlations among the measurement errors in the gel.