The relatively thick primary walls of epidermal and collenchyma cells often form waviness on the surface that faces the protoplast when they are released from the tensile in-plane stress that operates in situ. This waviness is a manifestation of buckling that results from the heterogeneity of the elastic strain across the wall. In this study, this heterogeneity was confirmed by the spontaneous bending of isolated wall fragments that were initially flat. We combined the empirical data on the formation of waviness in growing cell walls with computations of the buckled wall shapes. We chose cylindrical-shaped organs with a high degree of longitudinal tissue stress because in such organs the surface deformation that accompanies the removal of the stress is strongly anisotropic and leads to the formation of waviness in which wrinkles on the inner wall surface are always transverse to the organ axis. The computations showed that the strain heterogeneity results from individual or overlaid gradients of pre-stress and stiffness across the wall. The computed wall shapes depend on the assumed wall thickness and mechanical gradients. Thus, a quantitative analysis of the wall waviness that forms after stress removal can be used to assess the mechanical heterogeneity of the cell wall.

The development of cell pattern in the surface cell layer of the shoot apex can be investigated in vivo by use of a time-lapse confocal images, showing naked meristem in 3D in successive times. However, how this layer is originated from apical initials and develops as a result of growth and divisions of their descendants, remains unknown. This is an open area for computer modelling. A method to generate the surface cell layer is presented on the example of the 3D paraboloidal shoot apical dome. In the used model the layer originates from three apical initials that meet at the dome summit and develops through growth and cell divisions under the isotropic surface growth, defined by the growth tensor. The cells, which are described by polyhedrons, divide anticlinally with the smallest division plane that passes depending on the used mode through the cell center, or the point found randomly near this center. The formation of the surface cell pattern is described with the attention being paid to activity of the apical initials and fates of their descendants. The computer generated surface layer that included about 350 cells required about 1200 divisions of the apical initials and their derivatives. The derivatives were arranged into three more or less equal clonal sectors composed of cellular clones at different age. Each apical initial renewed itself 7–8 times to produce the sector. In the shape and location and the cellular clones the following divisions of the initial were manifested. The application of the random factor resulted in more realistic cell pattern in comparison to the pure mode. The cell divisions were analyzed statistically on the top view. When all of the division walls were considered, their angular distribution was uniform, whereas in the distribution that was limited to apical initials only, some preferences related to their arrangement at the dome summit were observed. The realistic surface cell pattern was obtained. The present method is a useful tool to generate surface cell layer, study activity of initial cells and their derivatives, and how cell expansion and division are coordinated during growth. We expect its further application to clarify the question of a number and permanence or impermanence of initial cells, and possible relationship between their shape and oriented divisions, both on the ground of the growth tensor approach.

The topology of a cellular pattern, which means the spatial arrangement of cells, directly corresponds with cell packing, which is crucial for tissue and organ functioning. The topological features of cells that are typically analyzed are the number of their neighbors and the cell area. To date, the objects of most topological studies have been the growing cells of the surface tissues of plant and animal organs. Some of these researches also provide verification of Lewis’s Law concerning the linear correlation between the number of neighboring cells and the cell area. Our aim was to analyze the cellular topology and applicability of Lewis’s Law to an anisotropically growing plant organ. The object of our study was the root apex of radish. Based on the tensor description of plant organ growth, we specified the level of anisotropy in specific zones (the root proper, the columella of the cap and the lateral parts of the cap) and in specific types of both external (epidermis) and internal tissues (stele and ground tissue) of the apex. The strongest anisotropy occurred in the root proper, while both zones of the cap showed an intermediate level of anisotropy of growth. Some differences in the topology of the cellular pattern in the zones were also detected; in the root proper, six-sided cells predominated, while in the root cap columella and in the lateral parts of the cap, most cells had five neighbors. The correlation coefficient r_L between the number of neighboring cells and the cell area was high in the apex as a whole as well as in all of the zones except the root proper and in all of the tissue types except the ground tissue. In general, Lewis’s Law was fulfilled in the anisotropically growing radish root apex. However, the level of the applicability (r_L value) of Lewis’s Law was negatively correlated with the level of the anisotropy of growth, which may suggest that in plant organs in the regions of anisotropic growth, the number of neighboring cells is less dependent on the cell size.

This study examines historical water management practices as a means of addressing climate change, focusing on the Tyski Stream catchment in Upper Silesia, Poland, a region marked by extensive urbanization and industrial evolution. It investigates the effectiveness of historical hydrotechnical systems, such as bead-like ponds from the 15th to 18th centuries, in enhancing water retention, reducing flood risks, and supporting ecosystem services. In a critical period, over 54 years (1827–1881), the number of reservoirs decreased from 142 to 31 (the area of ponds decreased from 161 to 32 ha). Throughout the entire period, between 1748 and 2017, the surface area of the analyzed reservoirs decreased from 163 ha to 16.8 ha. This was related to progressive industrialization, urban sprawl, and changes in legal frameworks, such as land ownership laws, leading to ecosystem degradation, loss of biodiversity, and altered hydrological processes. The research emphasizes the potential of reviving historical water management systems on natural processes to mitigate the impacts of climate change. By analyzing historical cartographic resources, this study assesses the feasibility of reconstructing lake systems in areas with similar topographic and hydrological features. It also stresses the necessity of community engagement and securing widespread social and political support to ensure public acceptance and the success of renaturation initiatives. The findings indicate that restoring these systems can offer diverse benefits, including improved water management, enhanced biodiversity, and greater urban resilience, while addressing the socio-political complexities of implementing large-scale environmental restoration projects. The aim of this study is to utilize archival materials for engineering solutions to prevent flooding and enhance water retention.