New method of estimation of the relative area of perforations on valves of centric diatoms using SEM images on the example of Minidisus vodyanitskiyi Lyakh et Bedoshvili

The diatoms interact with the environment through the siliceous frustule. The total area of frustule perforations determines the ability of diatom to exchange nutrients, gases and other matters. The aim of the present study was to estimate the area of perforations on the valve surface of a centric diatom. In the paper we describe a method for the estimation of the area of perforations on a diatom valve using SEM images. The method is tested on valves of centric diatom Minidiscus vodyanitskiyi Lyakh et Bedoshvili. The results show that the total area of cribral pores is less than 5% of the total valve area. This value is consistent with the relative perforation of land plants leaves, which is less than 3%. We hypothesize that such small valve area occupied by perforations is usual for many other centric diatom species. To verify this hypothesis additional researches are necessary.


Introduction
The diatoms interact with the outer environment through the siliceous frustule. The architecture of frustule determines the ability of a diatom to exchange the nutrients and the products of vital function (Bukhtiyarova 2009;Hale & Mitchel 2001;Pahlow et al. 1997;Pickett-Heaps et al. 1990). The area of a cell cover outlines individual contact space, where "physical, maximum energy and informative interaction, high interchange of substances are accomplished between individual and environment" (Bukhtiyarova 2013). The frustule surface area-to-volume ratio characterizes the intensity of those processes (Hein et al. 1995;Pahlow et al. 1997). However when researchers estimate the surface area of microalgae, they do not take into account that unicellular organisms exchange matter only through the pores in their cell wall. The other parts of a cell wall are impenetrable for material fluxes. Therefore if we examine the fluxes of material through the cell wall relying on the area of pores rather than the total surface area, we can improve understanding of relationships between characteristics of material fluxes and organism morphometry or discover new ones.
The relative area of perforations on a diatom frustule is the total area of the pores divided by the total area of the frustule. It is expressed as a percent. Later Losic et al. (2007) used term porosity to designate relative areas occupied by cribral pores and foramens on diatom valves. However porosity usually designate the fraction of void within the layer. The alternative term widelly used in a metal industry is an open area, but we suppose that the relative area will be better understood by biologists than the open area.
The goal of the paper is: (i) to present a method for the estimation of the relative area of perforation of diatom frustule using SEM images, and (ii) to apply the method for the estimation of the relative area of cribral pores on the valves of centric diatom Minidisus vodyanitskiyi Lyakh et Bedoshvili.

Materials and methods
Minidiscus vodyanitskiyi ( Fig. 1-3) have been recently described from the Sea of Azov (Lyakh & Bedoshvili 2018). High abundance of specimens allow collecting a set of SEM images where valve areolae and cribral pores are well distinguished. The valves of these specimens have tiny sizes and are covered by relatively small number of locular areolae. That helped us to estimate their relative area of perforations using image processing technique and manually selecting areolae on SEM images. Microscopic technique. Samples with diatom specimens were washed in water once, treated with 30% hydrogen peroxide (OOO Reaktiv, Russia) for 1 h, washed three times in ethyl alcohol, treated with concentrated hydrochloric acid for 24 h and washed at least five times in distilled water. After each step, the material was pelleted by centrifugation at 1000 g for 10 min.
The resulting preparations of the diatom frustules were mounted on stubs for SEM, dried, sputtercoated with gold in an SCD 004 sputter coater (Balzers, Liechtenstein) and analyzed under a Quanta 200 (FEI Company, United States) microscope.

Morphology of a valve and areolae.
The detailed morphology of M. vodyanitskiy frustule and valve are thorough described in the previous paper (Lyakh & Bedoshvili 2018). Here we give the morphological details that are necessary to better understand the used method.
The specimens of M. vodyanitskiy have circular valves of diameter 2.7-7.8 µm (Lyakh & Bedoshvili 2018: Figs 5-6, 15). Valve face is flat. Valve mantle is convex and narrow. Areolae shape varies from the large, rounded-elliptic openings in the valve center to the smaller, elongated polygonal ones near the valve margin. On the valve margin, the areolae are elongated and do not have outer tangential ribs. Areolae loculate with external foramina and internal cribra. Cribra are perforated by equally located cribral pores (Figs 9-10). Tiny filiform siliceous growth are presented on the areola ribs of some specimens (Figs 2-3, 6). The density and length of the filiform growth are varied (Lyakh & Bedoshvili 2018: Figs 12-13, 15).
The method overview. The relative area of perforations uses the total area of all cribral pores, A all-pores, and the valve total area. The valve total area was calculated from the valve image. To find A all-pores , we estimated their total number. We assumed that the number of pores on a cribrum was proportional to the area of the cribrum, which is equal to the area of areola foramen. The area of every areola foramen was proportional to the number of pixels occupied by the foramen on a valve image. So image processing techniques were used to find those areas. Additional software helps to convert all found values into the relative area of perforations. The details of the method are described below.
Step 1. Finding of the elliptical distortion of a valve. On SEM images some circular valves have the shape of an ellipse which is sometimes rotated, because those valves do not lie in the image plane (Figs 1-3). The images of such valves are elliptically distorted.
The ratio between minor and major diameters of the ellipse, that outlines valves margin, determines the coefficient of distortion, k ell = D major / D minor . If we multiply the area of the ellipse on k ell , we obtain the area of the original circular valve.
To find k ell , it is necessary to draw an ellipse along a valve border. It is known from the analytical geometry that any five points, every three of which are not lied on a straight line, define an unique ellipse. Therefore, to construct those ellipses, we loaded every image of a valve into Inkscape, put five points on valve margin using "Draw Bezier curves and straight lines" tool, and used "Ellipse by 5 points" Inkscape extension (Pernsteiner 2019), which turns a path with five control points into an ellipse passing through them (Fig. 4).
The constructed ellipse consists of four control points such that pairs of opposite points define the main ellipse diameters. That allows easily finding those diameters (Fig. 4) and calculating coefficient of distortion. This technique allow restoring borders of any valves including particularly visible.
Step 2. Selecting areola foramens on the valve image. To select regions of images occupied by areola foramens on images, we applied two segmentation algorithms of ImageJ software: thresholding and watershed segmentation. Unfortunately, they could not identify all areolae on every studied valve due to a low contrast between foramens and hyaline areas between them and the presence of inorganic material on a valve surface (Fig. 4). Because of that we manually selected other foramens in GIMP using "Fuzzy Select (Magic Wand)" tool.
Selected foramens were painted in yellow or blue color depending on their position and connection with neighboring foramens. Areolae of M. vodyanitskiy that are located on valve margin are incomplete. They do not separated from the valve margin, that is why their foramens are open towards the margin (Lyakh & Bedoshvili 2018: Figs 5, 15). On SEM images the foramens of marginal areolae appears merged. To indicate such regions with visually merged foramens, we paint them in blue color. All other foramens are painted in yellow color (Fig. 5).
Step 3. Restoring a convex shape of areola foramens. Areola foramens on some valves are closed by filiform siliceous growths (Figs 2-3, 6). Because of that those image regions do not represent real shape of foramens. On the masked image that regions have the shape of concave polygons (Fig. 7). To restore a real shape of foramens, we used original auxiliary software. It makes the images of foramens convex constructing a convex hull around them. That allows removing the images of filiform growths from the images of foramens (Fig. 8). The program makes convex only those regions that are painted in yellow color and ignores regions of other colors.
Step 4. Identifying inorganic flakes on valve image. The surface of many valves were covered by inorganic material (Figs 2-4). The area of that regions is excluded from total area of the valve.
To highlight those parts of valve images, we manually outlined them by vector polygons in Inkscape and painted in purple color (Fig. 5). This color indicates to our program that area of those regions should be extracted from the area of a valve. As we did not exactly know the proportion of pores and hyaline parts in extracted area, we assumed that in average this proportion corresponded to the proportion of pores and hyaline parts on a whole valve.
Step 5. Calculating the surface areas of a valve and area of areola foramens. The area of a valve surface, A valve , is equal to the area of a circle with the diameter D major , which is the major diameter of the bounding ellipse (Fig. 4).
The total areas of areola foramens, A foramens , and inorganic flakes, A inorganic , are determined as the total areas of colored spots on a valve image. The spots areas are equal to the number of pixels painted in the predefined colors. Yellow and blue colors correspond to foramnes, pink color denotes inorganic flakes. The numbers of pixels of each color are counted by the developed program. These numbers were converted to square micrometers using the ratio of the length of a scale bar in micrometers and in pixels.
To remove elliptic distortion, all calculated areas were multiplied to k ell . The area of a valve that is free from inorganic flakes, A free-valve , and relative area of a valve occupied by areola formanes, A foramens-relative , were calculated as follow: (1) Step 6. Estimating an approximate number and the total area of cribral pores. Studied specimens have locular areolae that are covered from the inner side by a siliceous plate named cribrum. The area of a cribrum is equal to the area of a foramen. The cribrum is equally perforated by small cribral pores (Fig. 9, 10) (Lyakh & Bedoshvili 2018: fig. 7), which facilitate matter exchange between protoplast and the environment. We assumed that all cribral pores were circles of equal diameters located on the same distances from each other. Using SEM images of the inner parts of valves, we estimated the average diameters of cribral pores, D pore , and the area of one pore, A pore = π D pore 2 / 4. To estimate the number of pores on a valve, N pores , we measure average distance between them, D interpore . SEM images show that cribral pores are located in a triangular grid (Fig. 9). We assumed that this grid is regular that allow replacing part of a cribrum by a right hexagon with a pore in the middle (Fig. 10). The area of the hexagon is (2) The number of hexagons, that can fit into the given area of areola, gives the approximate number of pores perforated that area. The task of finding the exact number of regular hexagons fit the give area does not have unambiguous solution. The approximate solution is to divided the given area on the area of one hexagon, and take the integer part of the resulting value. After that we can estimate the total area of all pores, A all-pores : N pores = A foramen / A hex , A all-pores = N pores ·A pore . (3) Step 7. Estimating the relative area of perforations on a valve.
The relative area of perforations on a valve, Y valve , is the ratio of the total area of all cribral pores to the total area of a valve that is free of inorganic flackes:

Used software
Inkscape vector editor (inkscape.org) is used to outline the valve borders and regions on valve surfaces covered by inorganic flackes. GIMP image editor (gimp.org) is used to select areola foramens on SEM images. ImageJ image processing software (imagej.nih.gov/ij) is used to make image segmentation using thresholding and watershed segmentation techniques and to estimate the average diameter and distance between cribral pores.
The auxiliary software developed by the first author helps to find total number and total area of all cribral pores and to estimate the relative area of perforations.

Results
The measured morphometric characteristics of M. vodyanitskiyi specimens and other centric diatom species are presented in Table 1.
The calculated number and total area of cribral pores is bigger than real ones, because pores do not perforate full cribra area but only a part of it (Figs 9-10). Because of that we consider that the relative area of perforations of M. vodyanitskiyi valves is smaller than 5 %.

Figures 4-10.
Steps used to measure the relative area of perforations on valve SEM images. 4. The bounded ellipse is constructed using five points, and ellipse main diameters were determined. 5. Areola foramens (yellow and blue) and inorganic flakes (pink) were manually selected. 6-8. The real convex shape of areola foramens covered by filiform siliceous growth was restored using convex hull algorithm. 9. Average diameter and distance between cribral pores were measured. 10. Cribral pores were represented by hexagons and the number of those hexagons was estimated.
The obtained result were compared with the data of Losic et al. (2007), who measured the relative area of perforations of two valves of centric diatoms, T. eccentrica and Coscinodiscus sp., using AFM (Table  1). Also De Stefano et al. (2008) estimated the relative area of perforations of the valve of C. wailesii using thresholding of SEM image, and obtained the value 0.57. As this value differs from all previously results and the authors did not provide a clear algorithm by which their data were obtained, we consider that this value is incorrect and do not include it into table. 1) These values are calculated as the product of the relative area of perforations of an areola on the relative area of areola foramens.

Discussion
The described method helps to study the relative area of perforations of diatoms using SEM images where areola foramens and cribral pores are well visible. It is a good alternative to the studying of valve topography using AFM (Luis et al. 2017), because presented method does not require the cultivation of diatoms and gives the comparable results. Moreover presented method allows fulfilling retrospective analysis of the relative area of perforations from published images. The described method is similar to the morphometric method of Sicko-Goad et al. (1977), who were estimated the volumes of the organelles of planktonic algae on electron microscope micrographs.
Manual selection of frustule (valve) components on an image is time consuming and appropriate for tiny diatoms with small number of areolae as those we consider. For a large diatoms with numerous areolae it is necessary to combine manual and automatic segmentation algorithms. Besides this it is possible to simulate the valve patterns and estimate the area of frustule components perforations with the help of geometric models (Lyakh 2013).
The area of perforations is a component of the functional morphology of a diatom frustule (Bukhtiyarova 2009(Bukhtiyarova , 2015. It can be used as a quantitative character in diatoms taxonomy, and as a potential indicator of the influence of the environmental factors on microalgae. The results obtained show that a very low valve arealess than 5 % of the total areais sufficient for the providing a protoplast with nutrients and dissolved gases. It is interesting that this value is consistent with the relative perforation of land plants leaves, which is less than 3% (Lawson & Blatt 2014).
The correspondence between the relative area of perforations of valves of M. vodyanitskiyi, T. eccentrica, Coscinodiscus sp., and leaves of land plants allow hypothesising that such small values of the relative area of perforations are usual for many other centric diatom species. To verify this hypothesis it is necessary to continue these researches.