Practical implementation of the planar and spatial rotator in a complex tissue: the brain.

In neuroscience, application of widely used stereological local volume estimators, including the planar rotator, is challenged by the combination of a complex tissue organisation and an estimator requirement of either isotropic or vertical sections, i.e. randomly oriented tissue. The spatial rotator is applicable with any tissue orientation but is sensitive to projection artefacts. The challenge is thus to select the most appropriate method for individual analyses. In this study, agreement between estimates of mean cell volume acquired with the vertical planar and the spatial rotator is assessed for two brain regions with different types of cytoarchitecture (motor cortex and hippocampal cornu ammonis 1). The possibility of using the planar rotator in tissues cut in an arbitrary direction is explored and requirements for a theoretically unbiased result as well as histological considerations are provided. LAY DESCRIPTION: Cells may change volume both during disease and with advancing age. Assessment of the volume of individual cells can therefore serve as a useful indicator of general tissue state. Most available methods to estimate cell volume in tissue sections, however, require that the tissue analysed has random orientation. Particularly for complex tissues such as the brain this is a challenge as identification, delineation and subdivision of many brain areas rely heavily on the use of anatomical atlases where illustrations depict the tissue in a few well-known orientations. In this study, the practical application of two different methods for estimating mean cell volumes in tissues cut in a preferred orientation is evaluated. Requirements for the feasibility of cell volume estimation without random tissue orientation as well as histological considerations are provided.

Stereological estimation of particle shape and orientation from volume tensors.

In the present paper, we describe new robust methods of estimating cell shape and orientation in 3D from sections. The descriptors of 3D cell shape and orientation are based on volume tensors which are used to construct an ellipsoid, the Miles ellipsoid, approximating the average cell shape and orientation in 3D. The estimators of volume tensors are based on observations in several optical planes through sampled cells. This type of geometric sampling design is known as the optical rotator. The statistical behaviour of the estimator of the Miles ellipsoid is studied under a flexible model for 3D cell shape and orientation. In a simulation study, the lengths of the axes of the Miles ellipsoid can be estimated with coefficients of variation of about 2% if 100 cells are sampled. Finally, we illustrate the use of the developed methods in an example, involving neurons in the medial prefrontal cortex of rat.

The spatial rotator.

This paper presents a new local volume estimator, the spatial rotator, which is based on measurements on a virtual 3D probe, using computer assisted microscopy. The basic design of the probe builds upon the rotator principle which requires only a few manual intersection markings, thus making the spatial rotator fast to use. Since a 3D probe is involved, it is expected that the spatial rotator will be more efficient than the the nucleator and the planar rotator, which are based on measurements in a single plane. An extensive simulation study shows that the spatial rotator may be more efficient than the traditional local volume estimators. Furthermore, the spatial rotator can be seen as a further development of the Cavalieri estimator, which does not require randomization of sectioning or viewing direction. The tissue may thus be sectioned in any arbitrary direction, making it easy to identify the specific tissue region under study. In order to use the spatial rotator in practice, however, it is necessary to be able to identify intersection points between cell boundaries and test rays in a series of parallel focal planes, also at the peripheral parts of the cell boundaries. In cases where over- and underprojection phenomena are not negligible, they should therefore be corrected for if the spatial rotator is to be applied. If such a correction is not possible, it is needed to avoid these phenomena by using microscopy with increased resolution in the focal plane.

On semiautomatic estimation of surface area.

In this paper, we propose a semiautomatic procedure for estimation of particle surface area. It uses automatic segmentation of the boundaries of the particle sections and applies different estimators depending on whether the segmentation was judged by a supervising expert to be satisfactory. If the segmentation is correct the estimate is computed automatically, otherwise the expert performs the necessary measurements manually. In case of convex particles we suggest to base the semiautomatic estimation on the so-called flower estimator, a new local stereological estimator of particle surface area. For convex particles, the estimator is equal to four times the area of the support set (flower set) of the particle transect. We study the statistical properties of the flower estimator and compare its performance to that of two discretizations of the flower estimator, namely the pivotal estimator and the surfactor. For ellipsoidal particles, it is shown that the flower estimator is equal to the pivotal estimator based on support function measurements along four perpendicular rays. This result makes the pivotal estimator a powerful approximation to the flower estimator. In a simulation study of prolate and oblate ellipsoidal particles, the surfactor also performs well for particles which are not extremely elongated. In particular, the surfactor is not very much affected by the singularity in the surfactor formula or by possible inaccuracies in the necessary angle measurements. We also assess the performance of the semiautomatic procedure in a study of somatostatin positive inhibitory interneurons from mice hippocampi. Only 35% of the cells needed to be analysed manually and an important decrease in workload was obtained by using the semiautomatic approach.

The semi-automatic nucleator.

The nucleator is a well-established manual stereological method of estimating mean cell volume from observations on random cell transects through reference points of the cells. In this paper, we present an automated version of the nucleator that uses automatic segmentation of the boundaries of the cell transects. An expert supervises the process. If the segmentation is judged to be satisfactory, an estimate of the cell volume is calculated automatically on the basis of the whole cell transect. In the remaining cases, the expert intervenes and uses the classical nucleator. The resulting estimator is called the semi-automatic nucleator. In this paper, we study the statistical properties of the semi-automatic nucleator. Formulae for the bias and mean square error are derived. The semi-automatic nucleator may have a small bias but will still in most cases be more efficient than the classical nucleator. Procedures for estimating bias and mean square error from a pilot study are provided. The application of the semi-automatic nucleator is illustrated in a study of somatostatin positive inhibitory interneurons which were genetically labelled with green fluorescent protein (GFP). The cells were sampled with an optical disector. The centre of mass in a central cell transect was used as reference point. It is found in this study that the number of cells needed for obtaining, for instance, a 5% precision of the estimate of mean cell volume is 150 and 189 for the semi-automatic and the classical nucleator, respectively. Taking into account that the time spent analysing one cell is shorter for the semi-automatic nucleator than for the classical nucleator, the semi-automatic nucleator is superior to the classical nucleator.

A note on the stereological implications of irregular spacing of sections.

Stereological methods for serial sections traditionally assume that the sections are exactly equally spaced. In reality, the spacing and thickness of sections can be quite irregular. This may affect the validity and accuracy of stereological techniques, especially the Cavalieri estimator of volume. We present a new formula for the accuracy of the Cavalieri estimator that includes the effect of random variability in section spacing. A modest amount of variability in section spacing can cause a substantial increase in estimator variance.

On error prediction in circular systematic sampling.

An extended covariogram model is discussed for estimating the precision of circular systematic sampling. The extension is motivated by recent developments in shape analysis of featureless planar objects. Preliminary simulation results indicate that it is important to consider the extended covariogram model.

Shape discrimination by total curvature, with a view to cancer diagnostics.

This paper investigates the use of total curvature for shape discrimination of objects via profiles of their planar sections (not assumed to be star shaped). Methods of estimating total curvature from observation of a finite number of points on the boundary of the object are investigated, including a simple discrete approximation method and various interpolation methods. Total curvature is capable of revealing shape differences on a local scale, as demonstrated by the analysis of two data sets of malignant and normal or benign tumour cell nuclear profiles.

Directional analysis of digitized three-dimensional images by configuration counts.

A method for estimating the orientated rose of normal directions of a three-dimensional (3D) set Z from a digitization of Z, i.e. a voxel image, is presented. It is based on counts of informative configurations in n x n x n voxel cubes. An algorithm for finding all informative configurations is proposed and an estimation procedure is described in detail for the case n= 2. The presented method is a 3D version of a method of estimating the orientated rose of binary planar images using n x n configurations. A new feature is the design-based approach, being more appropriate for biomedical image analysis than the formerly applied model-based approach.

Volume estimation from projections.

We describe a new estimator of the volume of axially convex objects from total vertical projections with known position of the vertical axis. The estimator combines the Cavalieri method with the known formula for area in terms of the support function of a convex body. We examine the accuracy of the proposed estimator for ellipsoidal objects having exactly known support function and volume. In addition, we illustrate practical problems of accuracy by implementing the method for some biological products.

Shape modelling of spatial particles from planar central sections -- a case study.

In this paper we develop statistical tools for shape modelling of spatial particles from central sections through the particles. The particles are assumed to be star-shaped with respect to a reference point inside the particles and are modelled as stochastic deformations of spheres centred at the reference points. The resulting particles are rotation invariant with respect to the reference point. As an illustration, the model is applied to study shape differences between neurons in the Granular and CA1 layer in the human hippocampus.

Directional analysis of digitized planar sets by configuration counts.

The oriented rose of normal directions of a random set Z can be used to quantify its anisotropy. A method for estimating this quantity from a digitization of Z in a sampling window, i.e. its pixel image, is presented. The image is analysed locally by considering pixel squares of size n x n. This allows us to count the number of different types of n x n configurations in the pixel image. We show that it suffices to restrict attention to the so-called informative configurations. The number of informative configurations increases only polynomially in n. An algorithm to find these informative configurations is presented. Furthermore, estimators of the oriented rose based on counts of observed informative configurations are derived. The procedure is illustrated by a simulated example and an analysis of a microscopic image of steel.

On the orientational analysis of planar fibre systems from digital images.

The orientational characteristics of fibres in digital images are studied. The fibres are modelled by a planar Boolean model whose typical grain is a thick (coloured) fibre. The aim is to make stereological inference on the rose of directions of the unobservable central fibres from observations made on a digital image of the thick fibres. For central fibres, the relation between the rose of directions and the point intensity, observed on a sampling line, is known. We derive, under regularity conditions, the relation between the unobservable point intensity and the scaled variogram observed on the line in a binary and a greyscale image. Using such a relation, it is possible to draw inference about the rose of directions from the scaled variogram, which is easy and quick to determine in a digital image.

Non-uniform systematic sampling in stereology.

Non-uniform systematic sampling designs in stereology are studied. Various methods of constructing non-uniform systematic sampling points from prior knowledge of the measurement function are presented. As an example, we consider area estimation from lengths of linear intercepts. The efficiency of two area estimators, based on non-uniform sampling of parallel lines, is compared to that of the classical 2D Cavalieri estimator, based on uniform sampling, in a sample of planar profiles from transverse sections of 41 small myelinated axons. The comparison is based on simulations. It is concluded that for profiles of this type one of the non-uniform sampling schemes is more efficient than the traditional uniform sampling scheme. Other examples where non-uniform systematic sampling may be used are in area estimation from lines emanating from a fixed point, area estimation from concentric circles or spirals and curve length estimation from sweeping lines. It is shown that proportional-to-size sampling is a special case of non-uniform systematic sampling. Finally, the effect of noise in the observations is discussed.

Activation of AMP-activated protein kinase increases mitochondrial enzymes in skeletal muscle.

Muscle contraction causes an increase in activity of 5'-AMP-activated protein kinase (AMPK). This study was designed to determine whether chronic chemical activation of AMPK will increase mitochondrial enzymes, GLUT-4, and hexokinase in different types of skeletal muscle of resting rats. In acute studies, rats were subcutaneously injected with either 5-aminoimidazole-4-carboxamide-1-beta-D-ribofuranoside (AICAR; 1 mg/g body wt) in 0.9% NaCl or with 0.9% NaCl alone and were then anesthetized for collection and freezing of tissues. AMPK activity increased in the superficial, white region of the quadriceps and in soleus muscles but not in the deep, red region of the quadriceps muscle. Acetyl-CoA carboxylase (ACC) activity, a target for AMPK, decreased in all three muscle types in response to AICAR injection but was lowest in the white quadriceps. In rats given daily, 1 mg/g body wt, subcutaneous injections of AICAR for 4 wk, activities of citrate synthase, succinate dehydrogenase, and malate dehydrogenase were increased in white quadriceps and soleus but not in red quadriceps. Cytochrome c and delta-aminolevulinic acid synthase levels were increased in white, but not red, quadriceps. Carnitine palmitoyl-transferase and hydroxy-acyl-CoA dehydrogenase were not significantly increased. Hexokinase was markedly increased in all three muscles, and GLUT-4 was increased in red and white quadriceps. These results suggest that chronic AMPK activation may mediate the effects of muscle contraction on some, but not all, biochemical adaptations of muscle to endurance exercise training.

The efficiency of systematic sampling in stereology--reconsidered.

In the present paper, we summarize and further develop recent reseach in the estimation of the variance of sterelogical estimators based on systematic sampling. In particular, it is emphasized that the relevant estimation procedure depends on the sampling density. The validity of the variance estimation is examined in a collection of data sets, obtained by systematic sampling. Practical recommendations are also provided in a separate section.

The optical rotator.

The optical rotator is an unbiased, local stereological principle for estimation of cell volume and cell surface area in thick, transparent slabs. The underlying principle was first described in 1993 by Kiêu & Jensen (J. Microsc. 170, 45-51) who also derived an estimator of length. In this study we further discuss the methods derived from this principle and present two new local volume estimators. The optical rotator benefits from information obtained in all three dimensions in thick sections but avoids over-/ underprojection problems at the extremes of the cell. Using computer-assisted microscopes the extra measurements demand minimal extra effort and make this estimator even more efficient when it comes to estimation of individual cell size than many of the previous local estimators. We demonstrate the principle of the optical rotator in an example (the cells in the dorsal root ganglion of the rat), evaluate its efficiency and compare it with other unbiased, local stereological principles available for estimation of cell volume and surface area.

Fusarium graminearum A 3/5 as a novel host for heterologous protein production.

We describe a novel fungal expression system which utilizes the Quorn myco-protein fungus Fusarium graminearum A 3/5. A transformation system was developed for F. graminearum and was used to introduce the coding and regulatory regions of a trypsin gene from Fusarium oxysporum. The protein was efficiently expressed, processed and secreted by the recombinant host strain. In addition, the promoter and terminator of the F. oxysporum trypsin gene have been successfully utilized to drive the expression of a cellulase gene from Scytalidium thermophilum and a lipase gene from Thermomyces lanuginosus in F. graminearum.

Characterization of tertiary interactions in a folded protein by NMR methods: studies of pH-induced structural changes in human growth hormone.

The pH-induced conformational changes in human growth hormone (hGH) have been studied, using a new quantitative NMR approach that combines 13C labeling of specific backbone carbonyl carbons with a complete spectral analysis of the corresponding 13C resonances. Thus, a complete analysis of the carbonyl resonances of the 26 Leu residues of hGH and their variation with pH provided detailed information about the equilibrium folding processes of the protein, including information about the kinetics of the folding. By combining this information with the pH dependence of readily identifiable 1H resonances, the pH-induced changes observed in the carbonyl carbon spectra can be associated with specific regions in the protein and can be ascribed to a series of localized adjustments in the tertiary structure, brought about by changes in the hydrogen bond interactions or electrostatic interactions between different residues in the globular folded protein. The preexchange lifetimes of these adjustments range from a fraction of a millisecond to a few milliseconds.

Specific carbon-13 labelling of leucine residues in human growth hormone.

Biosynthetic human growth hormone specifically 13C-labelled in the carbonyl positions of all 26 leucine residues has been obtained by recombinant DNA techniques using 13C-labelled leucine and an E. coli strain that requires leucine. It is shown that, on the whole, the labelling is specific with no significant mislabelling as would have been the case had the 13C-labelled leucine been metabolized.