A three-dimensional model with two-body interactions for endothelial cells in angiogenesis.

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.

Coordinated linear and rotational movements of endothelial cells compartmentalized by VE-cadherin drive angiogenic sprouting.

Angiogenesis is a sequential process to extend new blood vessels from preexisting ones by sprouting and branching. During angiogenesis, endothelial cells (ECs) exhibit inhomogeneous multicellular behaviors referred to as "cell mixing," in which ECs repetitively exchange their relative positions, but the underlying mechanism remains elusive. Here we identified the coordinated linear and rotational movements potentiated by cell-cell contact as drivers of sprouting angiogenesis using in vitro and in silico approaches. VE-cadherin confers the coordinated linear motility that facilitated forward sprout elongation, although it is dispensable for rotational movement, which was synchronous without VE-cadherin. Mathematical modeling recapitulated the EC motility in the two-cell state and angiogenic morphogenesis with the effects of VE-cadherin-knockout. Finally, we found that VE-cadherin-dependent EC compartmentalization potentiated branch elongations, and confirmed this by mathematical simulation. Collectively, we propose a way to understand angiogenesis, based on unique EC behavioral properties that are partially dependent on VE-cadherin function.

Pattern formation of elliptic particles by two-body interactions: A model for dynamics of endothelial cells in angiogenesis.

A two-dimensional mathematical model for dynamics of endothelial cells in angiogenesis is investigated. Angiogenesis is a morphogenic process in which new blood vessels emerge from an existing vascular network. Recently a one-dimensional discrete dynamical model has been proposed to reproduce elongation, bifurcation, and cell motility such as cell-mixing during angiogenesis on the assumption of a simple two-body interaction between endothelial cells. The present model is its two-dimensional extension, where endothelial cells are represented as the ellipses with the two-body interactions: repulsive interaction due to excluded volume effect, attractive interaction through pseudopodia and rotation by contact. We show that the oblateness of ellipses and the magnitude of contact rotation significantly affect the shape of created vascular patterns and elongation of branches.

Peptidomic analysis characterising proteolysis in thaw-aging of beef short plate.

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.

Cohesive and anisotropic vascular endothelial cell motility driving angiogenic morphogenesis.

Vascular endothelial cells (ECs) in angiogenesis exhibit inhomogeneous collective migration called "cell mixing", in which cells change their relative positions by overtaking each other. However, how such complex EC dynamics lead to the formation of highly ordered branching structures remains largely unknown. To uncover hidden laws of integration driving angiogenic morphogenesis, we analyzed EC behaviors in an in vitro angiogenic sprouting assay using mouse aortic explants in combination with mathematical modeling. Time-lapse imaging of sprouts extended from EC sheets around tissue explants showed directional cohesive EC movements with frequent U-turns, which often coupled with tip cell overtaking. Imaging of isolated branches deprived of basal cell sheets revealed a requirement of a constant supply of immigrating cells for ECs to branch forward. Anisotropic attractive forces between neighboring cells passing each other were likely to underlie these EC motility patterns, as evidenced by an experimentally validated mathematical model. These results suggest that cohesive movements with anisotropic cell-to-cell interactions characterize the EC motility, which may drive branch elongation depending on a constant cell supply. The present findings provide novel insights into a cell motility-based understanding of angiogenic morphogenesis.

A Novel Analysis of the Peptide Terminome Characterizes Dynamics of Proteolytic Regulation in Vertebrate Skeletal Muscle Under Severe Stress.

In healthy cells, proteolysis is orderly executed to maintain basal homeostasis and normal physiology. Dyscontrol in proteolysis under severe stress condition induces cell death, but the dynamics of proteolytic regulation towards the critical phase remain unclear. Teleosts have been suggested an alternative model for the study of proteolysis under severe stress. In this study, horse mackerel (Trachurus japonicus) was used and exacerbated under severe stress conditions due to air exposure. Although the complete genome for T. japonicus is not available, a transcriptomic analysis was performed to construct a reference protein database, and the expression of 72 proteases were confirmed. Quantitative peptidomic analysis revealed that proteins related to glycolysis and muscle contraction systems were highly cleaved into peptides immediately under the severe stress. Novel analysis of the peptide terminome using a multiple linear regression model demonstrated profiles of proteolysis under severe stress. The results indicated a phase transition towards dyscontrol in proteolysis in T. japonicus skeletal muscle during air exposure. Our novel approach will aid in investigating the dynamics of proteolytic regulation in skeletal muscle of non-model vertebrates.

Integrate and fire model with refractory period for synchronization of two cardiomyocytes.

We investigate an integrate and fire model for two cardiomyocytes interacting with each other. A feature of the model is to incorporate the refractory periods of the cardiomyocytes as well as the influence of firing of adjacent cells. The present model predicts that, if refractory periods of the two cells are nearly equal, the beating rhythms of the two cells always synchronize and their beating rate is tuned to the faster rate between the two cells. On the other hand, if their refractory periods significantly differ, they exhibit various kinds of harmonious beating rhythms. These results successfully explain the well known characteristics of synchronized beating of cultured cardiomyocytes. We also discuss effects of a delay time of cell-to-cell interaction, that gives further complicated phase diagrams for the beating rhythms.

Community effect of cardiomyocytes in beating rhythms is determined by stable cells.

The community effect of cardiomyocytes was investigated in silico by the change in number and features of cells, as well as configurations of networks. The theoretical model was based on experimental data and accurately reproduced recently published experimental results regarding coupled cultured cardiomyocytes. We showed that the synchronised beating of two coupled cells was tuned not to the cell with a faster beating rate, but to the cell with a more stable rhythm. In a network of cardiomyocytes, a cell with low fluctuation, but not a hight frequency, became a pacemaker and stabilised the beating rhythm. Fluctuation in beating rapidly decreased with an increase in the number of cells (N), almost irrespective of the configuration of the network, and a cell comes to have natural and stable beating rhythms, even for N of approximately 10. The universality of this community effect lies in the fluctuation-dissipation theorem in statistical mechanics.

Path-preference cellular-automaton model for traffic flow through transit points and its application to the transcription process in human cells.

We all use path routing everyday as we take shortcuts to avoid traffic jams, or by using faster traffic means. Previous models of traffic flow of RNA polymerase II (RNAPII) during transcription, however, were restricted to one dimension along the DNA template. Here we report the modeling and application of traffic flow in transcription that allows preferential paths of different dimensions only restricted to visit some transit points, as previously introduced between the 5' and 3' end of the gene. According to its position, an RNAPII protein molecule prefers paths obeying two types of time-evolution rules. One is an asymmetric simple exclusion process (ASEP) along DNA, and the other is a three-dimensional jump between transit points in DNA where RNAPIIs are staying. Simulations based on our model, and comparison experimental results, reveal how RNAPII molecules are distributed at the DNA-loop-formation-related protein binding sites as well as CTCF insulator proteins (or exons). As time passes after the stimulation, the RNAPII density at these sites becomes higher. Apparent far-distance jumps in one dimension are realized by short-range three-dimensional jumps between DNA loops. We confirm the above conjecture by applying our model calculation to the SAMD4A gene by comparing the experimental results. Our probabilistic model provides possible scenarios for assembling RNAPII molecules into transcription factories, where RNAPII and related proteins cooperatively transcribe DNA.

Ultradiscrete optimal velocity model: a cellular-automaton model for traffic flow and linear instability of high-flux traffic.

In this paper, we propose the ultradiscrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultradiscrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the modified Korteweg-de Vries (mkdV) equation, a soliton equation. Meanwhile, the ultradiscrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.

Stochastic optimal velocity model and its long-lived metastability.

In this paper, we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models, i.e., the asymmetric simple exclusion process and the zero range process. Moreover, it is regarded as a stochastic extension of the optimal velocity model. In the fundamental diagram (flux-density diagram), our model exhibits several regions of density where more than one stable state coexists at the same density in spite of the stochastic nature of its dynamical rule. Moreover, we observe that two long-lived metastable states appear for a transitional period, and that the dynamical phase transition from a metastable state to another metastable/stable state occurs sharply and spontaneously.