Tetsuji Tokihiro

Abstract We introduce a three-dimensional mathematical model for the dynamics of vascular endothelial cells during sprouting angiogenesis. Angiogenesis is the biological process by which new blood vessels form from existing ones. It has been the subject of numerous theoretical models. These models have successfully replicated various aspects of angiogenesis. Recent studies using particle-based models have highlighted the significant influence of cell shape on network formation, with elongated cells contributing to the formation of branching structures. While most mathematical models are two-dimensional, we aim to investigate whether ellipsoids also form branch-like structures and how their shape affects the pattern. In our model, the shape of a vascular endothelial cell is represented as a spheroid, and a discrete dynamical system is constructed based on the simple assumption of two-body interactions. Numerical simulations demonstrate that our model reproduces the patterns of elongation and branching observed in the early stages of angiogenesis. We show that the pattern formation of the cell population is strongly dependent on the cell shape. Finally, we demonstrate that our current mathematical model reproduces the cell behaviours, specifically cell-mixing, observed in sprouts.

We discuss the characteristics of the patterns of the vascular networks in a mathematical model for angiogenesis. Based on recent in vitro experiments, this mathematical model assumes that the elongation and bifurcation of blood vessels during angiogenesis are determined by the density of endothelial cells at the tip of the vascular network, and describes the dynamical changes in vascular network formation using a system of simultaneous ordinary differential equations. The pattern of formation strongly depends on the supply rate of endothelial cells by cell division, the branching angle, and also on the connectivity of vessels. By introducing reconnection of blood vessels, the statistical distribution of the size of islands in the network is discussed with respect to bifurcation angles and elongation factor distributions. The characteristics of the obtained patterns are analysed using multifractal dimension and other techniques.

Recent studies have suggested that thaw-aging can improve sensory attributes of freeze-thawed meat. Acceleration of proteolysis is expected to promote tenderisation and improve taste; however, the details of protein degradation, including substrate proteins and cleavage sites, remain unclear. Here, we report a time course overview of the peptidome of beef short plates during thaw-aging. The accelerated degradation of key proteins for meat tenderisation, such as troponin T and desmin, was confirmed. Additionally, 11 cleavage sites in troponin T related to taste-active peptide generation were identified. Terminome analysis showed that the contribution of each protease varies depending on the substrate proteins and the thaw-aging period. Based on our results; proteases, not only calpains, but also others contributed to the degradation of myofibrillar proteins. The techniques employed indicate that meat proteolysis during thaw-aging is not constant but dynamic.