The relative merits of direct morphometry of reconstructions of whole cells,and statistical morphometry by stereology of random sections of cells

Stereology, or the derivation of quantitative, three-dimensional (3-D) data about cells by statistical analysis of the structures of random sections, is widely used in cytology and pathology. However, there are situations where this approach is inadequate, and only an analysis of a homogeneous population of whole cells will give the required results. This involved 3-D reconstruction from physical or optical sections, or tomography or photogrammetry of whole-cell mounts. Use of stereo views of individual sections or projections adds considerably to the information available for both contouring and reconstruction. Recent image-processing advances in clinical radiography have shown, for the first time, that rapid, high-resolution digitization and contrast enhancement enable nearly all structural details to be routinely extracted from the micrographs and adequately portrayed. Three-D whole-cell reconstructions provide the digital data for many kinds of morphometric measurements on both whole cells and their individual organelles and membranes. Rapid fixation or freezing allows improved quantitative structure/function correlations of organelles with disturbances in cell metabolism or gene expression.     

Shape, size, and distribution of cell structures by 3-D graphics reconstruction and stereology. I. The regulatory volume decrease of astroglial cells

This report discusses fundamental limitations in attempting to derive cell size, shape, or distribution from the two-dimensional images provided by conventional electron microscopy. Morphometric or stereologic measurement of random thin sections is a convenient way to obtain some information of this type. However, it cannot provide complete, objective information about real size, shape, or connectivity of cells containing irregular or unevenly distributed structures or nonuniform populations of cells. Anisotropic structures require analysis of a complete set of serial sections. The analysis may utilize either stereo, mono, or tilted optical slices, and subsequent integration of this information into a single 3-D computer data set. In this study, we analyze stereo pairs of high-voltage electron micrographs of serial thick sections (0.5 micron) and critical-point-dried whole-cell mounts of rat brain astroglial cell cultures. The Z-axis resolution is increased by digitizing contours at discrete levels within each stereo view. This is accomplished with a new type of stereoscopic contouring device. We calculated area and volume changes accompanying hypo-osmolar swelling and spontaneous reversal of the swelling. (Regulatory Volume Decrease-RVD). An understanding of the mechanism of swelling of astroglial cells is important for improving the treatment of brain injury. The total cell-volume results are comparable with results previously obtained using nonmetabolized, radioactively tagged compounds that diffuse into various cell compartments. Our serial-section and whole-cell data also provide new information about the relative swelling of nucleus, cytoplasm, and individual organelles such as mitochondria. The basic biological problem being approached is whether homeostasis of cell function is accompanied by surface area and volume regulation of enzyme-rich membranes and organelles. Conversely, it is proposed to explore the possibility that abnormal organelle areas and volumes are indicators of perturbations of cell division, metabolism, or gene expression.     

Shape,size, and distribution of cell structures by 3-D graphics reconstruction and stereology

This report discusses fundamental limitations in attempting to derive cell size, shape, or distribution from the two-dimensional images provided by conventional electron microscopy. Morphometric or stereologic measurement of random thin sections is a convenient way to obtain some information of this type. However, it cannot provide complete, objective information about real size, shape, or connectivity of cells containing irregular or unevenly distributed structures or nonuniform populations of cells. Anisotropic structures require analysis of a complete set of serial sections. The analysis may utilize either stereo, mono, or tilted optical slices, and subsequent integration of this information into a single 3-D computer data set. In this study, we analyze stereo pairs of high-voltage electron micrographs of serial thick sections (0.5 μm) and critical-point-dried whole-cell mounts of rat brain astroglial cell cultures. The Z-axis resolution is increased by digitizing contours at discrete levels within each stereo view. This is accomplished with a new type of stereoscopic contouring device. We calculated area and volume changes accompanying hypo-osmolar swelling and spontaneous reversal of the swelling. (Regulatory Volume Decrease-RVD). An understanding of the mechanism of swelling of astroglial cells is important for improving the treatment of brain injury. The total cell-volume results are comparable with results previously obtained using nonmetabolized, radioactively tagged compounds that diffuse into various cell compartments. Our serial-section and whole-cell data also provide new information about the relative swelling of nucleus, cytoplasm, and individual organelles such as mitochondria. The basic biological problem being approached is whether homeo-stasis of cell function is accompanied by surface area and volume regulation of enzyme-rich membranes and organelles. Conversely, it is proposed to explore the possibility that abnormal organelle areas and volumes are indicators of perturbations of cell division, metabolism, or gene expression.     

A microcomputer based system for three-dimensional reconstructions from tomographic or histologic sections

The reconstructions of three-dimensional (3-D) objects from serial two-dimensional (2-D) images can contribute to the understanding of many biologic structures, from organelles to organs and tissues. The 3-D reconstruction of sections can be divided into several major tasks: image acquisition, alignment of slices, internal object definition, object reconstruction and rotation of the completed image. A fast, versatile, interactive system was devised for the reconstruction of 3-D objects from serial 2-D images using a low-cost microcomputer, original programs and commercial software. The system allows reconstruction from any serial images, e.g., electron micrographs, histologic sections or computed tomograms. A photographic image or a microscopic field is acquired into the computer memory using a video digitizer. Slices are superimposed and aligned to each other using an operator-interactive program. A contour-(edge-) finding algorithm isolates an object of interest from the background image by "subtraction" of the image from an overlaid, slightly shifted identical image. Contours for each slice are input to a reconstruction procedure, which calculates the x, y and z coordinates of every point in a slice and the thickness and number of slices. It then calculates the illumination for every point using a given point source of light and an intensity-fading coefficient. Finally, the points are represented by cubes to provide dimension and reflective surfaces. A cube of appropriate shade and color represents in 2-D the equivalent of a 3-D object; this results in a very effective 3-D image. The reconstruction is rotated by recalculating the positions of every point defining the object and rebuilding the image.(ABSTRACT TRUNCATED AT 250 WORDS)     

Volumetric morphometry reveals spindle width as the best predictor of mammalian spindle scaling

The function of cellular structures at the mesoscale is dependent on their geometry and proportionality to cell size. The mitotic spindle is a good example why length and shape of intracellular organelles matter. Spindle length determines the distance over which chromosomes will segregate, and spindle shape ensures bipolarity. While we still lack a systematic and quantitative understanding of subcellular morphology, new imaging techniques and volumetric data analysis promise novel insights into scaling relations across different species. Here, we introduce Spindle3D, an open-source plug-in that allows for the quantitative, consistent, and automated analysis of 3D fluorescent data of spindles and chromatin. We systematically analyze different mammalian cell types, including somatic cells, stem cells, and one- and two-cell embryos, to derive volumetric relations of spindle, chromatin, and the cell. Taken together, our data indicate that mitotic spindle width is a robust indicator of spindle volume, which correlates linearly with chromatin and cell volume both within single cell types and across mammalian species.     

Three-dimensional evaluation of the spinal local neural network revealed by the high-voltage electron microscopy: a double immunohistochemical study

Three-dimensional (3-D) analysis of anatomical ultrastructures is important in biological research. However, 3-D image analysis on exact serial sets of ultra-thin sections from biological specimens is very difficult to achieve, and limited information can be obtained by 3-D reconstruction from these sections due to the small area that can be reconstructed. On the other hand, the high-penetration power of electrons by an ultra-high accelerating voltage enables thick sections of biological specimens to be examined. High-voltage electron microscopy (HVEM) is particularly useful for 3-D analysis of the central nervous system because considerably thick sections can be observed at the ultrastructure level. Here, we applied HVEM tomography assisted by light microscopy to a study of the 3-D chemical neuroanatomy of the rat lower spinal cord annotated by double-labeling immunohistochemistry. This powerful methodology is useful for studying molecular and/or chemical neuroanatomy at the 3-D ultrastructural level.     

Shape changes and polarization of cells migrating through tissue. A high-voltage electron microscope and computer graphics study of serial thick sections

Structural changes of carcinoma cells and fibroblasts migrating through small spaces in the elastic-collagen reticulum of mouse peritoneum have been studied by high-voltage electron microscopy of serial thick sections and by computer graphics reconstruction of cell profiles. The change of shape profile of an individual cell, between serial sections is large and the distribution of organelles is very non-uniform and changes markedly between sections. Conclusions about adhesion, intercell contact, cell shape and polarization of cytoplasmic organelles could only be reached by assessing a complete set of serial sections. Our preliminary results suggest that interesting structural changes occur in both carcinoma cells and fibroblasts when migrating through this tissue.     

Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L(2,3) edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell's nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Three-dimensional reconstruction and quantitative analysis of rat lung type II cells: a computer-based study

The three-dimensional structure of alveolar epithelial type II cells was imaged using a computer-based system designed for reconstruction and quantitative analysis of serially sectioned specimens. Six type II cells were reconstructed from serial ultrathin sections of lungs from two Sprague Dawley male rats and the results were compared to standard morphometric estimates of type II cell composition from five other Sprague Dawley male rats. A minor portion of the type II cell surface was in contact with the alveolar airspace while most of the cell surface was embedded in the alveolar septal interstitium. The type II cells contained multiple Golgi regions located close to the nucleus. Mitochondria formed a few branching filamentous networks extending throughout the cell. The reconstructed cells appeared to represent a homogeneous population having fractional volumes of intracellular organelles very similar to those found by morphometric techniques. The spatial distribution of secretory organelle volume suggests that the organization of this cell type reflects an ordered progression of secretory particle maturation which is consistent with earlier hypotheses of lamellar body assembly.     

Fine structural quantification of drought-stressed Picea abies (L.) organelles based on 3D reconstructions

Ultrastructural investigations of cells and organelles by transmission electron microscopy (TEM) usually lead to two-dimensional information of cell structures without supplying exact quantitative data due to the limited number of investigated ultrathin sections. This can lead to misinterpretation of observed structures especially in context of their three-dimensional (3D) assembly. 3D investigations and quantitative morphometric analysis are therefore essential to get detailed information about the arrangement and the amount of subcellular structures inside a cell or organelle, respectively, especially when the plant sample was exposed to environmental stress. In the present research, serial sectioned chloroplasts, mitochondria, and peroxisomes from first year spruce needles (Picea abies (L.) Karst.) were 3D reconstructed and digitally measured using a computer-supported image analysis system in order to obtain a detailed quantitative characterization of complete cell organelles including precise morphological data of drought-induced fine structural changes. In control plants, chloroplast volume was composed of 56% stroma, 15% starch, 27% thylakoids, and 2% plastoglobules. In drought-stressed chloroplasts, the relative volume of both the thylakoids and the plastoglobules significantly increased to 37% and 12%, respectively. Chloroplasts of stressed plants differed from control plants not only in the mean thylakoid and plastoglobules content but also in the complete lack of starch grains. Mitochondria occurred in variable forms in both control and stressed samples. In stressed plants, mitochondria showed a significant smaller mean volume which was only 81% when compared with the control organelles. Peroxisomes were inconspicuous in both samples and their volume did not differ between control and drought-stressed samples. The present study shows that specific subcellular structures are subject to significant quantitative changes during drought stress of spruce needles giving a detailed insight in adaptation processes of the investigated cell organelles.     

Electron tomographic analysis of frozen-hydrated tissue sections

Electron tomography of frozen-hydrated tissue sections enables analysis of the 3-D structure of cell organelles in situ and in a near-native state. In this study, 160-200-nm-thick sections were cut from high-pressure frozen rat liver, and improved methods were used for handling and mounting the sections. Automated data collection facilitated tilt-series recording at low electron dose (approximately 4000 e(-)/nm(2) at 400 keV). Higher doses (up to 10,000 e(-)/nm(2)) were found to increase contrast and smooth out surface defects, but caused section distortion and movement, with likely loss of high-resolution information. Tomographic reconstruction showed that knife marks were 10-40 nm deep and located on the "knife face" of the section, while crevices were 20-50 nm deep and found on the "block face." The interior of the section was normally free of defects, except for compression, and contained useful structural information. For example, the topology of mitochondrial membranes in tissue was found to be very similar to that in frozen-hydrated whole mounts of isolated mitochondria. In rare cases, a 15-nm banding pattern perpendicular to the cutting direction was observed in the interior of the section, most evident in the uniformly dense, protein-rich material of the mitochondrial matrix.     

3-D image analysis system and megakaryocyte quantitation

A quasi-automatic computer image analysis system has been developed for 3-D reconstruction of stained serial sections and implemented on an IBAS system. Some new automatic image analysis techniques have been designed and incorporated into the system. For image segmentation, a transition region determination based thresholding method is introduced. Neither histogram calculation nor empirical parameters are needed in the automatic threshold selection. A two step 3-D reconstruction procedure--symbolic and pictorial reconstructions--is designed to improve the flexibility and the computational capability of the system. The global level registration and local level registration are separated. The former consists of establishing the relationship among a large numbers of profile pairs dispersed in adjacent sections. A pattern matching method based on pattern recognition principles is devised to exploit the information about the statistical character of mismatch caused by deformation of sections and about the relationship of nearby objects. For the latter, an equivalent elliptical approximation method based on the physical theory of the rotation of rigid bodies is proposed. The system has been used for 3-D reconstruction and quantitation of megakaryocytes in human bone marrow tissue. Features about individual 3-D megakaryocyte cell and the spatial distribution of megakaryocytes are determined. The latter is a new contribution to megakaryocyte quantitation and is not possible by using conventional stereologic techniques. These experimental results have demonstrated the ability of the system to perform quantitative analysis.     

Reprint of "Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)" [J. Struct. Biol. 160 (2007) 35-48

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L_2,3 edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell’s nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Sperm cells in pollen tubes ofNicotians tabacum L.: three-dimensional reconstruction,cytoplasmic diminution,and quantitative cytology

Summary The organization of the sperm cells and vegetative nucleus (male germ unit) ofNicotiana tabacum was examined 18 h after semivivo pollination using transmission electron microscopy, computerassisted serial section reconstruction and quantitative cytology. Based on a measurement of 11 cellular parameters in nine reconstructed sperm cell pairs, there are no statistically significant differences between the two cells. The S_vn is characterized by a strapshaped cytoplasmic extension that is physically associated with the surface of the vegetative nucleus. The nucleus is located adjacent to the sperm crosswall, with sperm organelles being distributed between the nucleus and the extension. The S_ua is a tapered cell with cytoplasmic areas at both poles and deep axial invaginations near the crosswall. This cell has a centrally-located nucleus and a largely polar distribution of organelles. Three mechanisms for cytoplasmic diminution were observed that appear to contribute actively to the loss of cytoplasmic volume and organelles: (1) enucleated cytoplasmic body production in the S_ua; (2) vesiculation at the tip of the cytoplasmic projection of the S_vn; and (3) vesicle-containing body accumulation in the periplasm of both the S_vn and S_ua.Abbreviations 3-D three-dimensional - ECB enucleated cytoplasmic body - MGU male germ unit - S_vn leading sperm cell - S_ua trailing sperm cell - TEM transmission electron microscopy - VCB vesicle-containing body     

Application of the serial sectioning and tridimensional reconstruction techniques to the morphological study of the Plasmodium falciparum mitochondrion

The use of serial sectioning followed by tridimensional reconstruction is a convenient way to study the spatial morphology of any structure (cell or organelle). This method was applied to the study of organelles of Plasmodium falciparum (FCR3) and enabled clarification of morphological features of the mitochondrion. The mitochondrion is polymorphic; in single sections it may be rounded, elongated or branched in shape. Its matrix may be dense or transparent, and it may or may not possess cristae. The 3-D reconstruction indicated that the mitochondrion is single in P. falciparum. Its form varies according to the age of the trophozoite. It becomes branched, and each lobe of the mitochondrion follows a daughter nucleus during the formation of merozoites.     

Three-dimensional reconstruction of glycosomes in trypanosomatids of the genus Phytomonas

Computer aided three dimensional (3-D) reconstruction of cells from two isolates of protozoa of the genus Phytomonas, trypanosomatids found in plants, were made from 0.3 mum thick sections, imaged on a Zeiss 902 electron microscope with a energy filter for inellastically scattered electrons, in order to obtain information about glycosomal shape diversity. Direct counts of peroxisomes (glycosomes) from Phytomonas sp. from Chamaesyce thymifolia indicated that there were fewer glycosomes per cell than the simple count of ultrathin section profiles would suggest and that these organelles could be long and branched. On the other hand, the stacked glycosomes observed in the isolate from Euphorbia characias were small individual structures and no connection was seen between them.     

Use of X-ray computed microtomography for non-invasive determination of wood anatomical characteristics

Quantitative analysis of wood anatomical characteristics is usually performed using classical microtomy yielding optical micrographs of stained thin sections. It is time-consuming to obtain high quality cross-sections from microtomy, and sections can be damaged. This approach, therefore, is often impractical for those who need quick acquisition of quantitative data on vessel characteristics in wood. This paper reports results of a novel approach using X-ray computed microtomography (microCT) for non-invasive determination of wood anatomy. As a case study, stem wood samples of a 2-year-old beech (Fagus sylvatica L.) and a 3-year-old oak (Quercus robur L.) tree were investigated with this technique, beech being a diffuse-porous and oak a ring-porous tree species. MicroCT allowed non-invasive mapping of 2-D transverse cross-sections of both wood samples with micrometer resolution. Self-developed software 'microCTanalysis' was used for image processing of the 2-D cross-sections in order to automatically determine the inner vessel diameters, the transverse cross-sectional surface area of the vessels, the vessel density and the porosity with computer assistance. Performance of this new software was compared with manual analysis of the same micrographs. The automatically obtained results showed no significant statistical differences compared to the manual measurements. Visual inspection of the microCT slices revealed very good correspondence with the optical micrographs. Statistical analysis confirmed this observation in a more quantitative way, and it was, therefore, argued that anatomical analysis of optical micrographs can be readily substituted by automated use of microCT, and this without loss of accuracy. Furthermore, as an additional application of microCT, the 3-D renderings of the internal microstructure of the xylem vessels for both the beech and the oak sample could be reconstructed, clearly showing the complex nature of vessel networks. It can be concluded that the use of microCT in wood science offers an interesting potential for all those who need quantitative data of wood anatomical characteristics in either the 2-D or the 3-D space.     

计算机三维重建华虻复眼性特异小网膜细胞结构

本文在计算机三维重建的基础上讨论了华虻复眼小网膜性特异结构与功能的关系,三维模型展示了中央小网膜细胞和部分外周小网膜细胞的空间构型及相互关系.在生物组织连续切片三维重建的对位技术方面,摸索了一套方法.保证了在Cromemco微机系统上实现对华虻复眼小网膜细胞的三维重建.证实了复眼光感受器性特化区R_7和R_8为并行排列的形式,并与非性特化区的R_7、R_8进行了比较.     

Accelerated Optical Projection Tomography Applied to In Vivo Imaging of Zebrafish

Optical projection tomography (OPT) provides a non-invasive 3-D imaging modality that can be applied to longitudinal studies of live disease models, including in zebrafish. Current limitations include the requirement of a minimum number of angular projections for reconstruction of reasonable OPT images using filtered back projection (FBP), which is typically several hundred, leading to acquisition times of several minutes. It is highly desirable to decrease the number of required angular projections to decrease both the total acquisition time and the light dose to the sample. This is particularly important to enable longitudinal studies, which involve measurements of the same fish at different time points. In this work, we demonstrate that the use of an iterative algorithm to reconstruct sparsely sampled OPT data sets can provide useful 3-D images with 50 or fewer projections, thereby significantly decreasing the minimum acquisition time and light dose while maintaining image quality. A transgenic zebrafish embryo with fluorescent labelling of the vasculature was imaged to acquire densely sampled (800 projections) and under-sampled data sets of transmitted and fluorescence projection images. The under-sampled OPT data sets were reconstructed using an iterative total variation-based image reconstruction algorithm and compared against FBP reconstructions of the densely sampled data sets. To illustrate the potential for quantitative analysis following rapid OPT data acquisition, a Hessian-based method was applied to automatically segment the reconstructed images to select the vasculature network. Results showed that 3-D images of the zebrafish embryo and its vasculature of sufficient visual quality for quantitative analysis can be reconstructed using the iterative algorithm from only 32 projections—achieving up to 28 times improvement in imaging speed and leading to total acquisition times of a few seconds.     

Quantitative imaging of intact cells and tissues by multi-dimensional confocal fluorescence microscopy

Confocal fluorescence microscopy enables visualisation and quantitation of fluorescent probes at high resolution deep within intact tissues, with minimal disturbance both of cell–cell interactions and the mechanical, ionic and physiological effects of the extracellular matrix. We illustrate the principles of multiple-parameter 3-D (x,y,z) imaging using reconstruction of nuclear channels in mammalian cells. Repeated sampling in time generates 4-D (x,y,z,t) images which can be used to follow dynamic changes, such as blue-light-dependent chloroplast re-orientation, in intact tissues. Quantitative measurements from multi-dimensional images require calibration of the spatial dimensions of the image and the fluorescence intensity response. This must be determined throughout the volume, which must be sampled to correct for geometric distortion as well as photometric errors arising from the complete optical system, including the specimen. The effects of specimen calibration are illustrated for morphological analysis of stomatal closing responses to abscisic acid in Commelina from 4-D images. Calibrated 4-D imaging allows direct volume measurements and we have followed volume regulation of chondrocytes in cartilage explants during osmotic perturbation. In intact cartilage, unlike in isolated cells, the chondrocytes exhibit volume regulatory mechanisms. In other cases, the fluorescence intensity of the probe may be related to a physiological parameter of interest and changes in its distribution within the cell. Optical sectioning permits discrimination of signal in separate compartments within the cell and can be used to follow transport events between different organelles. We illustrate 3-D (x,y,t) measurements of vacuolar glutathione conjugate pump activity in intact roots of Arabidopsis by following the sequestration of a fluorescent conjugate between glutathione and monochlorobimane. Dynamic measurements of protein localisation are now possible following the introduction of chimeric fusion proteins with green fluorescent protein (GFP) from Aequoria victoria. We have analysed the disposition of heterochromatin in nuclei of living Schizosaccharomyces pombe cells expressing a chimeric construct between Swi6 and GFP. Heterochromatin dynamics can be followed throughout mitosis in 4-D (x,y,z,t) images. Statistical analysis of the fluorescence histograms from each nucleus over time provides quantitative support for aggregation and dispersion of Swi6-GFP clusters during mitosis, rather than dissociation of Swi6 from the heterochromatin. A wide range of single-wavelength and ratio probes are available for imaging different ion activities. We compare 3-D (x,y,t) measurements of ion activities made using single-wavelength (Fluo-3 for calcium) and ratio (BCECF for pH) measurements, using stomatal responses in Vicia faba to peptides from the auxin-binding protein of maize and tip growth in pollen tubes of Lilium longiflorum as examples. Ratioing techniques have many advantages for quantitative fluorescence measurements and we conclude with a discussion of techniques to develop ratioing of single-wavelength probes against alternative references, such as DNA, protein or cell wall material.Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.