The spatial organization of epithelia (pseudostratified or stratified) actually remains unknown so far because of the methodical complexity of the 3-D cell sheets architectonics reconstruction as well as the lack of a sufficiently developed formalized theory of the biologic tissue structure (Lewis 1946, Smolyaninov 1980, Dormer 1980, Maresin 1990 et al). The currently available theory can describe only one topological variant for each regular model (constructed from either hexahedral or 14-hedral cells) of simple and/or stratified epithelia. Thus, other tissue organization variants (the structure of pseudostratified epithelia, in particular) as well as the tissue structure transformation in normal development or pathology fail to be taken into theoretical consideration.
Therefore the widespread technique of the 3-D epithelia reconstruction by use of serial sections in fact can't be theory-based and remains rather empirical yielding poor results. The resolution of this technique remains low as well, in spite of use of modern technique for analyzing images (Russ 1955, Carragher and Smith 1996). The technique can only expose some metric peculiarities of tissues, but is unable to reveal any regularity of the epithelial topology. As the result, the lack of knowledge on the 3-D epithelia organization complicates understanding those morphogenesis in norm and does not allow to investigate their reorganization principles in metaplasy, displasy and/or malignant growth.
To overcome this difficulty, we have developed a new theory of the spatial organization of cell sheets. It is based on theoretical development of the tissue modular structure concept, wherein the module is a morphofunctional tissue unit that arises as a result of division of labour between cells. The concept considers the cell sheet as a polymerized module. Such consideration enables one to create the theory of monomeric modules evolution and to build a natural tissue modules classification in the form of a periodic table (Savostyanov 1976, 1977, 1989a, Savostyanov 2005, Savostyanov 2011). It was shown that the table parameters (variables) have a biological sense and are suitable for quantitative evaluating of the multicellular organisms evolution.
Being based on general properties of epithelia, we have formulated the set of rules for tissue modules polimerization. Such consideration allows us to understand the fundamental principles of epithelia spatial organization. The new theory is capable of estimating and synthesizing families of 1-D, 2-D tissue models (Savostyanov 1989 b, 1991, 2001 a) and 3-D ones (Savostyanov 1994, 1998, 2001 b, 2005, 2007). Recently the cpecial computer program "Gistoarch" was created to build the family of 3-D models of cell sheets histoarchitectures (Savostyanova et al. 2007). Thus, it makes easy the prediction and oriented search of earlier unknown topologies of epithelial sheet histoarchitectonics.
In this way more than 50 new variants of spatial organization of epithelia are revealed by present time (and their amount continues to enlarge). A new high performance approach for research of spatial organization of epithelial sheets was developed on this basis. The synthesis of 2D and 3D models and their experimental verification is the matter of approach presented.
Below the basic difference of this approach from empirical ones is described. Use of models allows to predict the changes of cell shape and contiguity at various levels of sheets. So the analysis of tissue sections becomes oriented at this point. As a result it becomes possible to carry out exact restoration of internal epithelia topology and geometry of their cells instead labour-consuming and rather approximate empirical reconstruction of structures with many serial sections. It could be done comparing the small number of tissue sections with a set of theoretical model sections and subsequent choice of that of these models, which corresponds to a reality in the greatest degree.
New approach sharply raises the productivity of sections study, makes unnecessary their exact overlapping and allows to manage their smaller number. As a result the technique of three-dimensional tissues reconstruction is considerably simplified. Simultaneously for the first time it radically raises the technique resolution power up to a level, which is necessary to study not only the external form, but also internal frame of epithelial sheets. So the new approach appears to be suitable for study of three-dimensional organization of various epithelia structure, even in cases of embryo tissue quick growth embryo tissues, where the structure order is significantly "noised" by cells prolipheration and death.
Within the framework of this approach the spatial organization of simple, pseudostratified and stratified epithelia of various animals is considered in their normal and pathological development and the evidence of their histoarchitectonic topological variants, which were unknown before, is received. Besides it, some new properties, such as color translation symmetry and stoichiometry of structure, are described. A complex of new informative attributes for diagnostics is offered.
The next results could serve as an example of the elaborated approach efficiency. For the first time it becomes possible to show, that known for a long time family of Kepler`s correct regular parquets can be interpeted as the mathematical models of cell sheets (Savostyanov 1991, 2001a, 2005). It means, that it is possible for the simple epithelia to realize at least 11 topological variants of spatial organization rather than one (as it was considered so far). Nine of predicted variants have already been found in the real epithelia of the various animals, the detection of other two is predicted (fig. 1).
It was shown that stoichiometry is typical for the models
(fig. 2) (Savostyanov & Grefner 1993).
Besides it, a new class of 2-d models, characterized by the
various cell structure or, formally, by the chromatic number
(fig. 3) is offered. Formally these
models are the variants of the solution known in the graph theory as a
Hivudís problem of the map colouring.
Thus, such properties of tissues as color translation symmetry and stoichiometry of a structure, which were unknown before, are described first time.
The family of 2-D models obtained has allowed to find out, that all of them are capable to convert one to another. On this basis the method of the 3-d models synthesis for the pseudostratified and stratified epithelia is worked out and it is shown that the sheet topology is also varied and can be deduced (Savostyanov, 1994, 1998, 2001b, 2005, Savostyanova et al. 2007, Magnitskaya et al. 2009). For example, more than 30 variants of three-dimensional tissue structures are constructed by now, more than half of them is confirmed experimentally.
Some examples of three-dimensional architecture of epithelia with various numerical ratio of cells in the layers and rows are given in drawings below. So, in drawings (fig 4) and (fig. 5), the epidermal structures are shown (Savostyanov & Grefner 1998). In drawings (fig. 6), (fig. 7) and (fig. 8, fig. 9, fig. 10), the sensory epithelium of birds papilla are presented. The model in the (fig. 9) demonstrate the type of an epithelium organization whith reserv cells.
In drawings (fig. 11) and (fig. 12), the appositional and superpositional eye of insects are shown (Savostyanov 2001 c).
For the first time the concept about direct and inverted orientation of models is introduced and it is shown, that depending on orientation the same model design can simulate a stratified or pseudostratified epithelia..
The drawing (fig. 13) is show that one of the possible way to develop the initial models is to introduce into them a new cell population.
Use of the models has also allowed us to find out, that the epithelial sheets are constructed of the original histoarchitectonical blocks or slices. Such slices can either exist independently (as models of primitive layers), or to be combined with each other, derivating the calculated family of 3-d structure models of the pseudostratified and stratified sheets (fig. 14). It is possible to see also, that the model on (fig. 12) is constructed by repettition of the same slice (made between levels a - c and a - e) in various orientation (direct and inverted).
The slices combination can generate a multitude variant of tissue architectures and this multitude basically can be limited and computable. It speaks about an opportunity of a computing histology creations, that capable to find the set of all possible epithelia architecture variants and, thus, to predict the ways of tissue development.
In addition, it is possible to construct a family of models basing on a curved surface such as hemisphere or cylinder (either externally or internally). The models (fig. 15) can correspond to actual glandular structures.
It is important to emphasize, that inasmach as the models created are formal, they can be used to study the various type of real epithelia wiht similar cell ratio in the layers and rows.
The models described above reflect both topology of epithelial sheets, and (schematically) geometry of their cells. To take into account the real cell shape, the geometrical parameters of models can be easily modified. For example, the steepness of an inclination of cell sides can vary. Besides it, some cells can swell and become convex, whereas the ones, which are situated adjacent to them, become concave. Such updating will make the models more realistic.
The tissue models can promote comprehension of a short of their changes in normal development and pathology. For example, these changes can be reduced to transformation of one organization variant to another one like phase transitions (fig. 16).
We have known that all described designs of epithelia should turn into each other. It enables to assume, that the transformation of epithelia in a carcinogenesis also can occur similarly (Grefner, Savostyanov and Khudoley 1997). The study of these transformations can promote comprehension of mechanisms of tumour morphogenesis and search of new informative attributes for their early diagnostics and can form the basis for forecasting of their changes in normal and pathological development.
The further synthesis of three-dimensional models and their verification will enable us to discover the laws of tissue structures completely. It facilitates the development of the theory of biological tissue structure, which is able to describe a real tissue more precisely. It makes easy to create not only isolated collections of tissue models, but to deduce from uniform positions every possible variant of tissue spatial organization, giving their compact and evident description (just as it has been made in crystallography). The cells of models can be "transparent" to show their internal structure depending of tissue topology.
The correct and full description of three-dimensional organization of tissues will allow us to predict their structure changes during normal and pathological development in 4-D space. With respect to the biomedical research presented in this work, 3-D reconstruction is applied in order to reveal the spatial distribution of gene expression in embryonic organs during both normal and abnormal development.
The new theory will make possible the computer synthesis of tissue models and allow us to describe an extensive histological material compactly and evidently. Due to their evidence these results may successfully be used in the educational process.
The results obtained can form the basis to create the intelligent (smart) automated system of diagnostics.
This work was supported by RFBR grant N 95-04-12049a.
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