On the Possible Spatial Structures of the β – Amyloid.

Spatial models of the β - structures of protein molecules, forming layers of amino acids, in principle, of unlimited length for both antiparallel and parallel conformation have been constructed. It is shown that the simplified flat Pauling models do not reflect the spatial structure of these layers. Using the recently developed theory of higher-dimensional polytopic prismahedrons, models of the volumetric filling of space with amino acid molecules are constructed. The constructed models for the first time mathematically describe the native structures of globular proteins.

Spatial Structures of Fibrillar Proteins

The protein molecules are considerate in the space of the highest dimension with a change in dimension with demand at the conformation of the molecules. It was shown that the widespread quasi-plane model of the Pouling protein structure do not reflect and even contradict the spatial structures of the protein in various conformations. It was found that the linear structures and folded structures of the protein in space of the highest dimension have translational symmetry. The elementary elements of protein translational symmetry were determined, their dimensions were calculated (9 for the linear structures and 23 for folded structures).

Urban Spatial Structures From Human Flow By Hodge-Kodaira Decomposition

Human flow in cities indicates social activity and can reveal urban spatial structures based on human behaviours for relevant applications. Scalar potential is a mathematical concept, and if successfully introduced, it can provide an intuitive perspective of human flow. However, the definition of such a potential to the origin-destination flow matrix and determination of its plausibility remain unsolved. Here, we apply Hodge-Kodaira decomposition, in which a matrix is uniquely decomposed into a potential-driven (gradient) flow and a curl flow. We depict the potential landscapes in cities due to commuting flow and reveal how the landscapes have been changed or unchanged by years or transport methods. We then determine how well the commuting flow is described by the potential, by evaluating the percentage of the gradient component for metropolitan areas in the USA and show that the gradient component is almost 100% in several areas; in other areas, however, the curl component is dominant, indicating the importance of circular flow along triangles of places. The potential landscape provides an easy-to-use visualisation tool to show the attractive places of human flow and will aid in various applications in commerce, urban design, and epidemic spreading.

Spatial structure governs the mode of tumour evolution

Characterizing the mode—the way, manner or pattern—of evolution in tumours is important for clinical forecasting and optimizing cancer treatment. Sequencing studies have inferred various modes, including branching, punctuated and neutral evolution, but it is unclear why a particular pattern predominates in any given tumour. Here we propose that tumour architecture is key to explaining the variety of observed genetic patterns. We examine this hypothesis using spatially explicit population genetics models and demonstrate that, within biologically relevant parameter ranges, different spatial structures can generate four tumour evolutionary modes: rapid clonal expansion, progressive diversification, branching evolution and effectively almost neutral evolution. Quantitative indices for describing and classifying these evolutionary modes are presented. Using these indices, we show that our model predictions are consistent with empirical observations for cancer types with corresponding spatial structures. The manner of cell dispersal and the range of cell–cell interactions are found to be essential factors in accurately characterizing, forecasting and controlling tumour evolution.

Differences in Airborne Particulate Matter Concentration in Urban Green Spaces with Different Spatial Structures in Xi’an, China

With the acceleration of urbanization and industrialization, air pollution is becoming one of the most serious problems in cities. Urban green spaces, as “green infrastructure”, are an important part of urban ecosystems for air purification. Therefore, 10 typical green spaces of urban parks in the city of Xi’an, China, were selected as study areas according to vegetation structure and species composition. Considering meteorological factors and time changes, the effects of the selected green spaces with different vegetation structures of different heights on the reduction in airborne particulate matter concentration were explored. The results showed that the following: (1) Temperature, relative humidity, wind speed, and air pressure had significant correlation with the concentration of airborne particulate matter at the different heights, and the correlations were the same at 1.5 and 5 m. (2) After heating in winter, the concentration of airborne particulate matter with different particle sizes increased significantly. The concentration of airborne particulate matter showed different trends throughout the day, and the small particles (PM1 and PM2.5) had a trend of “lower in the morning and evening, and higher at noon”, while the large particles (PM10 and TSP) gradually decreased over time. (3) In the selected green spaces with different vegetation structure types, the concentration of airborne particulate matter below the canopy (1.5 m) was generally higher than that in the middle of the canopy (5 m), but the effects of reducing the concentration of airborne particulate matter were consistent at the different heights. (4) The adsorption capacity of PM1 and PM2.5 concentration was strong in the partially closed broad-leaved one-layered forest (PBO), and poor in the partially closed broad-leaved multi-layered forest (PBM). Partially closed broad-leaved multi-layered forest (PBM) and partially closed coniferous and broad-leaved mixed multi-layered forest (PMM) also had strong dust-retention effect on PM10 and TSP, while closed broad-leaved one-layered forest (CBO) had a poor dust-retention effect. The results showed that the reduction effects of urban green spaces with different spatial structures on air particles were different, and were restricted by various environmental factors, which could provide a theoretical basis for the optimization of urban green space structure and the improvement of urban air quality.

Heterogeneous Diffusion, Stability Analysis, and Solution Profiles for a MHD Darcy–Forchheimer Model

In the presented analysis, a heterogeneous diffusion is introduced to a magnetohydrodynamics (MHD) Darcy–Forchheimer flow, leading to an extended Darcy–Forchheimer model. The introduction of a generalized diffusion was proposed by Cohen and Murray to study the energy gradients in spatial structures. In addition, Peletier and Troy, on one side, and Rottschäfer and Doelman, on the other side, have introduced a general diffusion (of a fourth-order spatial derivative) to study the oscillatory patterns close the critical points induced by the reaction term. In the presented study, analytical conceptions to a proposed problem with heterogeneous diffusions are introduced. First, the existence and uniqueness of solutions are provided. Afterwards, a stability study is presented aiming to characterize the asymptotic convergent condition for oscillatory patterns. Dedicated solution profiles are explored, making use of a Hamilton–Jacobi type of equation. The existence of oscillatory patterns may induce solutions to be negative, close to the null equilibrium; hence, a precise inner region of positive solutions is obtained.

Mental Map of Hryhoriy Galagan: Territorial and Ethnonational Structuring in Ukrainian Nobleman’s World View (mid-1830s — mid-1860s)

The article examines the spatial structures and related images of ethno-national communities in the world view of Hryhoriy Pavlovych Galagan (1819–1888), a representative of the Ukrainian local nobility and a prominent public figure. The research methodology includes the achievements of modern humanitarian geography, first of all the method of mental mapping, which allows to study the spatial structures in the world view of the individual, taking into account his socio-cultural environment. The research is based on ego-documents — diaries and correspondence from the Galagan family archive. Special attention is paid to toponymes and ethnonymes in these texts. It is shown that the spatial representations of Hryhoriy Galagan were a complex system that developed under the influence of the socio-cultural sphere in which he lived. Thus, humanitarian geography is represented as a discursive practice due to social and political interests. The article deals, in particular, with such spatial constructs as “Little Russia”, “Ukraine”, “Russia”, “Rus”, “Europe”, as well as related communities — “Little Russia people”, “Russian people”, “Europeans”. Galagan’s spatial and ethno-national ideas are shown as a very dynamic system that was constantly changing under the influence of socio-political and ideological movements, such as the Polish uprisings of 1830–1831 and 1863–1864, the rise of Slavophilia and Ukrainophilia. Attention is paid to the importance of travel for the development of the system of spatial and ethno-national structures. In addition, the conditionality of this system with ideas about history is proved. The issues raised in this article will contribute to further in-depth research in cultural anthropology, as well as be useful to historians working in the biographical genre.

A New Response Surface Stochastic Analysis Method for Spatial Structure Stability—The Reticulated Shell Structure as an Example

For a long time, spatial structures have been widely used. However, compared with the high strength of their material, their stability is weak, and especially sensitive to damage and defects. This feature has increased the engineering industry’s high requirements for their stability analysis. As we all know, this problem is more prominent for the reticulated shell structure, which is a classic representative of the spatial structure. However, in the current analysis methods for the stability of reticulated shells, the deterministic analysis method cannot consider the random characteristics of defects. Other random methods, such as the random defect modal method, and many improved methods, require more samples and calculation time. This unfavorable situation makes its engineering application greatly restricted. In addition, the random modal superposition method and derivation method based on Monte Carlo has not fundamentally changed this limitation. In order to fundamentally overcome this traditional shortcoming, this paper comprehensively studies the advantages of the high accuracy of the random defect modal method and the improved method, and at the same time, investigates the speed advantage of the response surface method, and then creates a new stochastic analysis method based on the response surface method. Finally, the analysis results of the calculation examples in this paper prove that it successfully balances and satisfies the dual requirements of accuracy and speed required for calculating the stability of the reticulated shell structure. Moreover, it has universal applicability to different forms of reticulated shells, such as classic 6-point flat domes, traditional reticulated shell structures, and bionic reticulated shell structures, and even other types of spatial structures.

Screening of Self-Assembling of Collagen IV Fragments into Stable Structures Potentially Useful in Regenerative Medicine

The aim of the research was to check whether it is possible to use fragments of type IV collagen to obtain, as a result of self-assembling, stable spatial structures that could be used to prepare new materials useful in regenerative medicine. Collagen IV fragments were obtained by using DMT/NMM/TosO− as a coupling reagent. The ability to self-organize and form stable spatial structures was tested by the CD method and microscopic techniques. Biological studies covered: resazurin assay (cytotoxicity assessment) on BJ, BJ-5TA and C2C12 cell lines; an alkaline version of the comet assay (genotoxicity), Biolegend Legendplex human inflammation panel 1 assay (SC cell lines, assessment of the inflammation activity) and MTT test to determine the cytotoxicity of the porous materials based on collagen IV fragments. It was found that out of the pool of 37 fragments (peptides 1–33 and 2.1–2.4) reconstructing the outer sphere of collagen IV, nine fragments (peptides: 2, 4, 5, 6, 14, 15, 25, 26 and 30), as a result of self-assembling, form structures mimicking the structure of the triple helix of native collagens. The stability of spatial structures formed as a result of self-organization at temperatures of 4 °C, 20 °C, and 40 °C was found. The application of the MST method allowed us to determine the Kd of binding of selected fragments of collagen IV to ITGα1β1. The stability of the spatial structures of selected peptides made it possible to obtain porous materials based on their equimolar mixture. The formation of the porous materials was found for cross-linked structures and the material stabilized only by weak interactions. All tested peptides are non-cytotoxic against all tested cell lines. Selected peptides also showed no genotoxicity and no induction of immune system responses. Research on the use of porous materials based on fragments of type IV collagen, able to form stable spatial structures as scaffolds useful in regenerative medicine, will be continued.