Capillary network formation and structure in a modified discrete mathematical model of angiogenesis

Angiogenesis, as part of cancer development, involves hierarchical complicated events and processes. Multiple studies have revealed the significance of the formation and structure of tumor-induced capillary networks. In this study, a discrete mathematical model of angiogenesis is studied and modified to capture the realistic physics of capillary network formation. Modifications are performed on the mathematical foundations of an existing discrete model of angiogenesis. The main modifications are the imposition of the matrix density effect, implementation of realistic boundary and initial conditions, and improvement of the method of governing equations based on physical observation. Results show that endothelial cells accelerate angiogenesis and capillary formation as they migrate toward the tumor and clearly exhibit the physical concept of haptotactic movement. On the other hand, consideration of blood flow-induced stress leads to a dynamic adaptive vascular network of capillaries which intelligibly reflects the brush border effect . The present modified model of capillary network formation is based on the physical rationale that defines a clear mathematical and physical interpretation of angiogenesis, which is likely to be used in cancer development modeling and anti-angiogenic therapies.

Effects of SO2 Pollution on Household Insurance Purchasing in China: A Cross-Sectional Study

There have been considerable concerns regarding the effects of air pollution on health and economy over the past decades across the world. As insurance coverage has been closely related to household welfare, we aim to investigate the influence of air pollution, in particular, the sulfur dioxide (SO₂) pollution on household purchases of commercial health insurance using data from the 2017 China Household Financial Survey (CHFS). The results show that the rise in SO₂ emission has a significant positive association with tendency of residents to participate in commercial health insurance. The possibility of household commercial health insurance purchasing increases by 4% per 1,000 tons of SO₂ emission. In addition, the proportion of commercial health insurance expenditure in household annual income increases by 29% per 1,000 tons of SO₂ emission. The effects are also found to differ among resident groups. Residents in eastern parts of China are more likely to buy commercial health insurance facing SO₂ pollution compared to those in western parts of China; people with higher income are more likely to be affected compared to those with lower income; families with the household head being female are more likely to be affected compared to those with the household head being male. This research provides baseline information on the formulation and implementation of future operation strategy in commercial health insurance companies of China.

The role of mechanical interactions in EMT

The detachment of cells from the boundary of an epithelial tissue and the subsequent invasion of these cells into surrounding tissues is important for cancer development and wound healing, and is strongly associated with the epithelial-mesenchymal transition (EMT). Chemical signals, such as TGF-β, produced by surrounding tissue can be uptaken by cells and induce EMT. In this work, we present a novel cell-based discrete mathematical model of mechanical cellular relaxation, cell proliferation, and cell detachment driven by chemically-dependent EMT in an epithelial tissue. A continuum description of the model is then derived in the form of a novel nonlinear free boundary problem. Using the discrete and continuum models we explore how the coupling of chemical transport and mechanical interactions influences EMT, and postulate how this could be used to help control EMT in pathological situations.

On a Non-Discrete Concept of Prokaryotic Species

The taxonomic concept of species has received continuous attention. A microbial species as a discrete box contains a limited number of highly similar microorganisms assigned to that taxon, following a polyphasic approach. In the 21st Century, with the advancements of sequencing technologies and genomics, the existence of a huge prokaryotic diversity has become well known. At present, the prokaryotic species might no longer have to be understood as discrete values (such as 1 or 2, by homology to Natural numbers); rather, it is expected that some microorganisms could be potentially distributed (according to their genome features and phenotypes) in between others (such as decimal numbers between 1 and 2; real numbers). We propose a continuous species concept for microorganisms, which adapts to the current knowledge on the huge diversity, variability and heterogeneity existing among bacteria and archaea. Likely, this concept could be extended to eukaryotic microorganisms. The continuous species concept considers a species to be delimited by the distance between a range of variable features following a Gaussian-type distribution around a reference organism (i.e., its type strain). Some potential pros and cons of a continuous concept are commented on, offering novel perspectives on our understanding of the highly diversified prokaryotic world, thus promoting discussion and further investigation in the field.

A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation

Mechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty, we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an individual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the individual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. We discuss applications of the model, such as determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.

Modeling small cell lung cancer (SCLC) biology through deterministic and stochastic mathematical models

Mathematical cancer models are immensely powerful tools that are based in part on the fractal nature of biological structures, such as the geometry of the lung. Cancers of the lung provide an opportune model to develop and apply algorithms that capture changes and disease phenotypes. We reviewed mathematical models that have been developed for biological sciences and applied them in the context of small cell lung cancer (SCLC) growth, mutational heterogeneity, and mechanisms of metastasis. The ultimate goal is to develop the stochastic and deterministic nature of this disease, to link this comprehensive set of tools back to its fractalness and to provide a platform for accurate biomarker development. These techniques may be particularly useful in the context of drug development research, such as combination with existing omics approaches. The integration of these tools will be important to further understand the biology of SCLC and ultimately develop novel therapeutics.

Boundary Layer Effect on Behavior of Discrete Models

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson’s ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis.

Stochastic modeling for dynamics of HIV-1 infection using cellular automata: A review

Recently, the description of immune response by discrete models has emerged to play an important role to study the problems in the area of human immunodeficiency virus type 1 (HIV-1) infection, leading to AIDS. As infection of target immune cells by HIV-1 mainly takes place in the lymphoid tissue, cellular automata (CA) models thus represent a significant step in understanding when the infected population is dispersed. Motivated by these, the studies of the dynamics of HIV-1 infection using CA in memory have been presented to recognize how CA have been developed for HIV-1 dynamics, which issues have been studied already and which issues still are objectives in future studies.

Phylogenetic analysis and positive-selection site detecting of vascular endothelial growth factor family in vertebrates

Vascular endothelial growth factor (VEGF), known to play an important role in vascular homeostasis, vascular integrity and angiogenesis, is little known about the evolutionary relationship of its five members especially the role of gene duplication and natural selection in the evolution of the VEGF family. In this study, seventy-five full-length cDNA sequences from 33 vertebrate species were extracted from the NCBI's GenBank, UniProt protein database and the Ensembl database. By phylogenetic analyses, we investigated the origin, conservation, and evolution of the VEGFs. Five VEGF family members in vertebrates might be formed by gene duplication. The inferred evolutionary transitions that separate members which belong to different gene clusters correlated with changes in functional properties. Selection analysis and protein structure analysis were combined to explain the relationship of the site-specific evolution in the vertebrate VEGF family. Eleven positive selection sites, one transmembrane region and the active sites were detected in this process.

Dynamic thermal time model of cold hardiness for dormant grapevine buds

BACKGROUND AND AIMS

Grapevine (Vitis spp.) cold hardiness varies dynamically throughout the dormant season, primarily in response to changes in temperature. The development and possible uses of a discrete-dynamic model of bud cold hardiness for three Vitis genotypes are described.

METHODS

Iterative methods were used to optimize and evaluate model parameters by minimizing the root mean square error between observed and predicted bud hardiness, using up to 22 years of low-temperature exotherm data. Three grape cultivars were studied: Cabernet Sauvignon, Chardonnay (both V. vinifera) and Concord (V. labruscana). The model uses time steps of 1 d along with the measured daily mean air temperature to calculate the change in bud hardiness, which is then added to the hardiness from the previous day. Cultivar-dependent thermal time thresholds determine whether buds acclimate (gain hardiness) or deacclimate (lose hardiness).

KEY RESULTS

The parameterized model predicted bud hardiness for Cabernet Sauvignon and Chardonnay with an r(2) = 0·89 and for Concord with an r(2) = 0·82. Thermal time thresholds and (de-)acclimation rates changed between the early and late dormant season and were cultivar dependent but independent of each other. The timing of these changes was also unique for each cultivar. Concord achieved the greatest mid-winter hardiness but had the highest deacclimation rate, which resulted in rapid loss of hardiness in spring. Cabernet Sauvignon was least hardy, yet maintained its hardiness latest as a result of late transition to eco-dormancy, a high threshold temperature required to induce deacclimation and a low deacclimation rate.

CONCLUSIONS

A robust model of grapevine bud cold hardiness was developed that will aid in the anticipation of and response to potential injury from fluctuations in winter temperature and from extreme cold events. The model parameters that produce the best fit also permit insight into dynamic differences in hardiness among genotypes.