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Use of Image Analysis to Study Growth and Division of Yeast Cells
Abstract
Studies of biological objects like yeast cells are usually complicated due to seemingly unpredictable changes in various properties of the living organisms. This study represents an attempt to show how various time dependent properties of yeast can be captured and precisely quantified by modern image analysis methods. During the course of this study, various complications which had been anticipated were encountered and resolved. As each strain differs by various properties like average size, shape, and cellular membrane thickness, the necessary adjustments to data capture and processing for automated data analysis were the biggest complication encountered. The study successfully shows the applicability of the chosen method of image analysis to various shapes of yeast, with cell shapes varying from elliptical, cylindrical citrical, tube-shaped, to oblong. The yeast properties' quantification was based on calculated fractal dimension and fractal measure of the studied strains. The information about speed of growth of the colony as well as about the changes occurring within individual cells was correlated to the change of the fractal parameters in the captured images of the yeast. The studied parameters were: growth of the cells, changes in the thickness of the cellular wall, number of cells present in the sample, and changes in the shape of the cells. Samples were probed with a Nikon Eclipse E400 optical microscope and a Nikon Eclipse E200 optical microscope with phase contrast. HarFA 5.1 (Harmonic and Fractal Image Analyzer) (HarFA) software was used for processing the obtained images. Custom developed HarFA software is designed to facilitate fractal image analysis.
... Box counting method (Fig. 11, right) Fractal measures can be used for determining areas of white (K W ), black (K B ), and of borderline of both regions (K BW ) [14,15]. Wavelet method is based on using two-dimensional Haar transformation [14,15]. ...
... Box counting method (Fig. 11, right) Fractal measures can be used for determining areas of white (K W ), black (K B ), and of borderline of both regions (K BW ) [14,15]. Wavelet method is based on using two-dimensional Haar transformation [14,15]. It is an integral transformation with the base of ''square-shaped'' functions (called Haar wavelet, see Fig. 12 up left). ...
... (11). Fractal measures can be used for determining the volume below the surface (K B ), volume under the surface (K W ), and volume of surface (K BW ) [14,15]. ...
The Kolmogorov K- entropy [1, 2] is important characteristic which describes a degree of chaoticity of the systems. It gives the average rate of information loss about a position of the phase point on the attractor. It is well-known that K q = 0 in an ordered system, K q → ∞ is infinite in a random system, and 0 K q q is order of entropy. Numerically, the Kolmogorov entropy can be estimated as the Renyi entropy S q [3]. A special case of Renyi entropy for the q = 1 is in information theory the Shanon entropy S 1 [4]. By multiplying of Shanon entropy by Boltzmann constant k B we will get the thermodynamic entropy S.
... The fractal measure is a commonly used parameter in fractal theory. It describes the number of isochromatic pixels of a specific segment in the fractal system and tells how much of the area is filled by the fractal segments under investigation (Tomankova et al 2006). ...
More precise measurements of the complexity of leaf shapes can open new pathways to understanding plant adaptation and resilience in the face of global changes. We present a method to measure the complexity of plant leaf shapes by relating their fractal dimension to topological entropy. Our method relies on 'segmental fractal complexity' and stems from a fractal-thermodynamic system analogy. The complexity of plant leaf shapes is an algebraic combination of the fractal dimension of the components, leaf lamina, background, and leaf edge. We applied this method to leaf forms of 42 tropical plant species. Topological entropy is an improvement over the leaf dissection index because of its ability to capture the spatial positioning of a leaf's lamina, edge, and background. It is also an advancement over conventional geometric and fractal dimension-based measures of leaf complexity because it does not entail information loss due to the pre-processing and is perceptibly simple.
... Computer models have been developed to mimic the fungal colonies, which are studied for the nature of hyphal branching tips, growth and next neighborhood characteristics, growth parameters have been studied with respect to fractal dimension (Obert, 1993). Single yeast cells quantified with fractal dimension for their diameter and division (Tomankova, 2006, Vesela, 2001. Woriax (2009) studied biochemical and physiochemical changes and responded to environment changes in bacterial colonies com-pared with the help of fractal dimension of bacterial colony. ...
In Iron ore mining areas of Goa, water resources are polluted due to high turbidity and mineral colloids. For bioclarification of the turbidity, we need to identify some promising property of strains by which the strains of freshwater yeasts can be screened. This work presents a screening of freshwater yeast cultures, based on the complexity of colony margins. We performed screening of the wild aquatic yeasts isolated from different fresh water bodies of Goa on 2nd, 4th and 6th day of incubation respectively. Colony margins of sixteen different strains were studied for their fractality indexes and on comparison significant differences were observed among them. We report comparative analysis of five representative strains in this paper. Particularly strain Bchlm-1-2 showed high fractality index approximately 1410 on 6th day of incubation. This work provides quantitative scoring system of the morphological behavior of large number of strains. Our approach has the potential to improve the accuracy and speed to quantify and compare large number of isolates on the basis of their colony margins.
... Con la finalidad de corroborar los resultados anteriores se procedió a analizar la imagen seleccionada (ver figura 5A) con otra aplicación llamada HarFA V.5.438 (Tomankova et al., 2006) que nos permitió realizar de modo manual el análisis. Se analizó la imagen con el algoritmo del umbral (automático) empleado en el análisis espectral, el cual funciona con una prestación de conteo de cajas como la expuesta arriba, para esta prestación se empleó el método de análisis de pendiente (slope analysis) y se basa en una forma de estimación fractal similar al análisis multifractal. ...
The cities exhibit a principle of fractal ordering –fractal and self-affinity or independent self-similar patterns of scale– which was demonstrated as a morphological characteristic of urban complexity for several decades. This study explores and develops a complex approach to the cycle path of the city of Bogotá D.C (Colombia) through fractal estimates and densities of its different spaces. Complementary methodologies such as geographic information systems (GIS) for the processing of data were used. As a result, the sites of greater and lesser density in the structure of the Bogota´s bikeway are shown as an indicator of evolution and planning. It was concluded that the set of sizes of the fractal dimensions has a power law distribution -represented by a dashed line- which reaffirms its fractal nature. As an innovative aspect, this work proposes to establish a possible connection between the social sciences and the complexity sciences, among which are the fractal geometry, from a transdisciplinary exploration that contributes to the recent studies on urban complexity from Latin America.
... In fact "computer vision" (or generally image processing) o en requires, sometimes real time, processing of a very large and heterogeneous data sets (including shape, spatial orientation, color, tex-ture, motion, etc.). Extensive image fi les or series of images are processed e.g. in medicine (Söhn et al., 2005;Zagrodsky et al., 2005;Li et al., 2006), biological studies (Tománková et al., 2006;Klotz et al., 2007), but also in agricultural sciences (Yahya et al., 2009;Zadravec and Žalik, 2009;Zhong et al., 2009) or food sciences (Havlíček et al., 2008;Severa, 2007;Severa, 2008). In spite of increasing hardware performance, large or sometimes huge data sets o en cause problems and certain data reduction, regularization and/or modifi cation is needed. ...
The paper presents the software procedure (using MAPLE 11) intended for considerable reduction of digital image data set to more easily treatable extent. The example with image of peach stone is presented. Peach stone, displayed on the digital photo, was represented as a polygon described by the coordinates of the pixels creating its perimeter. The photos taken in high resolution (and corresponding data sets) contain coordinates of thousands of pixels - polygon's Vertexes. Presented approach substitutes this polygon by the new one, where smaller number of Vertexes is used. The task is solved by use of adapted least squares method. The presented algorithm enables reduction of number of Vertexes to 10% of its original extent with acceptable accuracy+/- one pixel (distance between initial and final polygon). The procedure can be used for processing of similar types of 2D images and acceleration of following computations.
... The process of image analysis is based on the detection of fluid boundaries in shadowgraph pictures. As discussed above, the identification of features in images is nowadays a common function in image processing programs; among many examples, Matlab has a built-in routine called "bwtraceboundary" to outline object boundaries in black and white images, Labview has the "Threshold" tool on the NI Vision Assistant and HarFA and PEJET have a thresholding process for colour images, [13,14,4] and [15]. In this work, both HarFA and PEJET were used to analyze colour RGB shadowgraph images. ...
The shadowgraph technique is discussed in terms of some modern application to fluid visualization and the characterization of freesurface flows. A brief description of shadowgraph photography is presented which emphasizes the parameters which need to be controlled to obtain useful images for digital processing and analysis. Several examples of shadowgraph images are presented together with their analysis to exemplify the variety of quantitative measurements that are possible with modern imaging tools. Three experimental setups were developed for different novel applications at different length scales: centimeterlong jets, millimetersize sprays and micrometersize droplets. The components used for these shadowgraph imaging systems range from standard photographic flash sources to specialized spark flash lamps and from single lens reflex (SLR) camera lenses to purposebuilt systems with researchgrade optical elements. Image analysis was developed and used to derive various types of information from the different systems. For jets it was used to determine the dynamic surface tension of the jetted fluid, for sprays it was employed to determine the ligamentdroplet size distribution along the jetting axis and in inkjet printing it was used to determine the angular deviation and terminal speed of the jets and droplets.
... The resulting images (300 × 300 dpi) were captured by means of HarFA (Harmonic and Fractal image Analyzer) software (http://www.fch.vutbr. cz/lectures/imagesci) (Zmeškal et al. 2001), which was previously shown to be suitable for the evaluation of images from biological experiments (Tománková et al. 2006) and neuroscience (Wu et al. 2010). The scanned images were saved as bitmaps and subjected to 2D Wavelet Analysis. ...
The positive effect of humic acids on the growth of plant roots is well known, however, the mechanisms and role of their physical structure in these processes have not been fully explained yet. In this work, South-Moravian lignite was oxidized by means of nitric acid and hydrogen peroxide to produce a set of regenerated humic acids. The elemental composition, solid state stability and solution characteristics were determined and correlated in vitro with their biological activity. A modified hydroponic method was applied to determine the effects of their potassium salts on Zea mays seedlings roots with respect to the plant weight, root length, root division, and starch and protein content. The relations between the determined parameters were evaluated through Principal Component Analysis and Pearson's correlation coefficients. The results indicated that the most important factor determining the biological activity of South-Moravian lignite potassium humates is related to the nature of self-assemblies, while the chemical composition had no direct connection with the root growth of Zea mays seedlings. It was demonstrated a controlled processing that provided humic substances with different chemical and physicochemical properties and variable biological activity.
A new method that combines fractal theory and red, green and blue (RGB) colour intensity was developed to sort dried jujube fruits by using support vector machine (SVM). Our result shows that the new method is fast and accurate in dried jujube fruits classification. The SVM models based on fractal parameters only achieved 85.18–92.73% total accuracy rate. The total classification accuracy of SVM based on RGB intensity values was 94.44%. However, the SVM models based on combining fractal parameters with RGB intensity values achieved 94.44–98.15% total accuracy rate. The best classification accuracy (98.15%) was found when using SVM model based on combining fractal measures (FM) with RGB intensity values (C = 512, γ = 0.0078125). Therefore, the SVM model based on combining FMs with RGB intensity is recommended in dried jujube fruits classification.
This paper compares chromatic white light (CWL) and interference microscope measurements aiming to find a proper non-contact method for a thickness determination of thin soft organic films. Standard samples with vacuum deposited aluminum films of different thicknesses in the range of 50-1000 nm were prepared and measured by both methods. It was found that the CWL technique is proper for a measurement of thin soft organic films with higher than 40-50 nm film thicknesses. As a complementary feature of the method 2D and 3D surface morphology imaging of the films could be recorded and the surface film roughness could be calculated. In a case of optical inhomogeneity the method requires covering with a uniform high reflective coating. The interference microscopy method results in a relatively lower film thickness with a higher standard deviation and a higher standard relative error. It could be connected with the resolution of the interferograms measured.
This article describes a new method of determining fractal dimension and fractal measure using integral (e.g. wavelet – Haar) transformations. The main advantage of the new method is the ability to analyse both, black & white and grey scale (or colour) images. The fractal dimension (box counting fractal dimension) evaluated using the Haar transformation offers in difference to the classic box counting method much wider range of usability. It can be also used to determine the fractal parameters of surfaces or volume of three-dimensional structures e.g. distribution of the mass or electrical charge in the surface or space. The theory of the fractal structures in E-dimensional Euclidean space is described more closely in our previous work.
This article describes the basic concept of fractal analysis with relation to printed structures and introduces "intensity fractal function" as a tool of practical factor analysis of printed images. The properties of the "intensity fractal function" are demonstrated on samples of printed images.
J.R. Partington and B. Ünalmış consider in their 2001 paper [J.R. Partington, B. Ünalmış, Appl. Comput. Harmon. Anal. 10 (1) (2001) 45–60] the windowed Fourier transform and wavelet transform as tools for analyzing almost periodic signals. They establish Parseval-type identities and consider discretized versions of these transforms in order to construct generalized frame decompositions. We have found a gap in the construction of generalized frames in the windowed Fourier transform case; we comment on this gap and give an alternative proof. As for the wavelet transform case, in [J.R. Partington, B. Ünalmış, Appl. Comput. Harmon. Anal. 10 (1) (2001) 45–60] the generalized frame decomposition is done only for the simplest wavelet, the Haar wavelet; we show how to construct generalized frame decompositions for a wide family of wavelets.
Deconvolution is one of the most frequently used mathematical operations in the evaluation of data in many branches of science and engineering. Analytical chemistry is no exception: deconvolution is part of routine methodologies in major instrumental techniques such as many modalities of spectroscopy and chromatography. The need for proper deconvolution, however, is often overlooked in the emerging field of bio-analytical chemistry as applied to live tissue in vivo, or cells in vitro. It is in this context that some of the major problems inherent to deconvolution, and to one of its most commonly used methodologies, deconvolution via discrete Fourier transform (DFT), are explored in this work. To illustrate the nature and severity of the difficulties involved and the resulting errors and potential for misinterpretation, the problem of assessing cellular processes with different microsensors is chosen as an example here. In particular, cancer multidrug resistance (MDR) modulated doxorubicin (DOX) efflux from drug sensitive cells derived from Chinese hamster ovary cancer, and their MDR subline, are discussed. DOX concentration monitored with a carbon fiber microelectrode at close proximity to a monolayer of these cells can be perceived as the result of convolution of cellular efflux with extracellular diffusion. Deconvolution via DFT to reconstruct the efflux process, however, leads to patterns that are very far from realistic. The observations and conclusions made using this example are relevant to other areas of analytical chemistry, and science and engineering in general that use deconvolution methods in processing experimental results of many types.
Two methods for defining Fourier power spectra for DNA sequences or other biological sequences are compared. The first method
uses indicator sequences for each letter. The second method by Silverman and Linsker assigns to each letter a vertex of a
regular tetrahedron in space, and this can be generalized to any dimension. While giving different Fourier transforms, it
is shown that the power spectra of the two methods are essentially the same. This is also true if one replaces the Fourier
transform in both methods with another linear transform, such as the Walsh transform.
Yeasts are unicellular eukaryotes, and are used widely as a model system in basic and applied field of life science, medicine, and biotechnology. The ultrastructure of yeast cells was first studied in 1957 and the techniques used have advanced greatly in the 40 years since then; an overview of these methods is first presented in this review. The ultrastructure of budding and dimorphic yeast cells observed with a scanning electron microscope (SEM) and a transmission electron microscope (TEM) after thin sectioning and freeze-etching are then described, followed by discussion of the regeneration of the cell wall ofCandida albicans protoplasts detected by cryosectioning.C. albicans protoplasts are regenerated to synthesize microfibrils on their surface. They are aggregated into thicker bundles which are intermeshed, forming a wide-meshed network of long fibrils. These microfibrillar structures are chains of β-1,3-glucan which are broken down after treatment with β-1,3-glucanase. Morphologically identical microfibrils are synthesizedin vitro by a cell-free system in which the active cell membrane fraction as a source of β-1,3-glucan synthetase and UDP glucose as the sole substrate are used. The diameter of an elemental fibril of β-glucan is estimated to be 2.8 nm from the pattern of autocorrelation of the image obtained by computer processing. In contrast, in the presence of aculeacin A the formation of normal fibrillar nets or bundles is significantly inhibited, resulting in the occurrence of short fibrils. These electron microscopic data suggest that aculeacin A inhibits not only the synthesis of β-1,3-glucan but the aggregation of microfibrils of this polysaccharide, allowing formation of the crystalline structure. On the basis of the cumulative data obtained from the electron microscopic studies, we are led to the assumption thatde novo synthesized β-glucan chains might initially form fine particles which are then transformed into thin fibrils with single to multiple strands which appear to be oriented parallel to each other so that they develop into fibrillar structures. This process of assembly of β-glucan molecules leads to the development of a fibrous network within the regeneratingCandida cell wall. Third, the mechanism of cell wall formation is shown by low-voltage (LV) SEM and TEM, using various techniques and computer graphics, of the regeneration system ofSchizosaccharomyces pombe protoplasts: after 10 min of regeneration, the protoplasts begin to grow fibrillar substances of a β-glucan nature, and a fibrillar network covers the surface of all protoplasts. The network is originally formed as fine particles on the protoplasts surface and these are subsequently lengthened to microfibrils 2 nm thick. The microfibrils twist around each other and develop into 8 nm thick fibrils forming flat bundles 16 nm thick. Interfibrillar spaces are gradually filled with amorphous particles of an α-galactomannan nature and, finally, the complete cell wall is formed after 12 h. Treatment of reverting protoplasts with RuO4 provided clear TEM images of glucan fibrils with high electron density. The relationship between cell wall regeneration and intracellular organelles was examined by using serial thin sections stained with PATAg and computer-aided three-dimensional reconstruction. The secretory vesicles in a protoplast had increased markedly by 1.4, 3.4, and 5.8 times at 1.5, 3.0, and 5 h, respectively. Three-dimensional analysis indicates that Golgi apparatus are located close together in the nucleus of the protoplast and are dispersed into the cytoplasm during the progress of cell wall formation.
Image analysis is now a well established complement to optical microscopy, allowing routine quantification of microscopic observations. Recent method developments include location and enumeration of bacteria in solid foods, in situ microscopy and image analysis for on-line monitoring of yeast fermentations, and texture analysis of fungal colonies for subsequent transfer. Notable recent applications include studies on the pulsatile growth of hyphal apices, biochemical differentiation of fungal colonies, and simple structural differentiation of mycelia from submerged fungal cultures.
The development of a complex multicellular organism requires a coordination of growth and cell division under the control of patterning mechanisms. Studies in yeast have pioneered our understanding of the relationship between growth and cell division. In recent years, many of the pathways that regulate growth in multicellular eukaryotes have been identified. This work has revealed interesting and unexpected relationships between mechanisms that regulate growth and the cell cycle machinery.
To remain viable, cells have to coordinate cell growth with cell division. In yeast, this occurs at two control points: the boundaries between G1 and S phases, also known as Start, and between G2 and M phases. Theoretically, coordination can be achieved by independent regulation of growth and division, or by participation of surveillance mechanisms in which cell size feeds back into cell-cycle control. This article discusses recent advances in the identification of sizing mechanisms in budding and in fission yeast, and how these mechanisms integrate with environmental stimuli. A comparison of the G1-S and G2-M size-control modules in the two species reveals a degree of conservation higher than previously thought. This reinforces the notion that internal sizing could be a conserved feature of cell-cycle control throughout eukaryotes.