Zero Poynting vector E∥H Beltrami field cylindrical cavity resonators

In this paper, we present novel cylindrical cavity resonators accommodating spatially and temporally zero Poynting vector Beltrami standing waves with the parallel electric and magnetic fields (E∥H). We introduce the special boundary conditions, i.e., longitudinal electromagnetic conductor (LEMC) on which zero longitudinal electromagnetic components are enforced and circumferential electromagnetic conductor (CEMC) on which zero circumference electromagnetic components are enforced in an axisymmetric waveguide system, and show that the zero Poynting vector E∥H Beltrami standing wave is generated as a superposition of dual degenerated axisymmetric TM and TE standing waves in a cylindrical resonator using the LEMC and CEMC boundary conditions. We present physical implementation methods of the LEMC and CEMC boundary conditions composed of the circumferentially arranged corrugations and the concentrically aligned cylindrical thin fins, respectively. In addition, we numerically demonstrate the Beltrami standing field generation and reveal its peculiar electromagnetic properties: the spatially and temporally E∥H with zero Poynting vector distribution, identical electric and magnetic energy density distributions, and zero local reactive energy flow

Quarter-wavelength E‖H Beltrami cavity resonators

In this paper, we present the design and implementation methods of quarter-wavelength resonators accommodating Beltrami standing waves with parallel electric and magnetic (E‖H) fields. The resonator is bounded by the quarter-wavelength longitudinal electromagnetic conductor (LEMC), the circumferential electromagnetic conductor (CMEC), and the radial electromagnetic conductor (REMC). The LEMC, CEMC, and REMC boundaries are artificially implemented by the circumferentially aligned corrugation, concentrically aligned circular fins, and axisymmetrically aligned radial fins, respectively. The coupling control methods by introducing slots in the CEMC and REMC with the external TM01 and TE01 circular waveguides are presented. We design the quarter-wavelength resonators with the implemented LEMC, CEMC, and REMC boundaries with controlled external couplings and numerically demonstrate their E‖H properties, which confirms the validity of the proposed design method

A mass conserved reaction-diffusion system captures properties of cell polarity

Various molecules exclusively accumulate at the front or back of migrating eukaryotic cells in response to a shallow gradient of extracellular signals. Directional sensing and signal amplification highlight the essential properties in the migrating cells, known as cell polarity. In addition to these, such properties of cell polarity involve unique determination of migrating direction (uniqueness of axis) and localized gradient sensing at the front edge (localization of sensitivity), both of which may be required for smooth migration. Here we provide the mass conservation system based on the reaction-diffusion system with two components, where the mass of the two components is always conserved. Using two models belonging to this mass conservation system, we demonstrate through both numerical simulation and analytical approximations that the spatial pattern with a single peak (uniqueness of axis) can be generally observed and that the existent peak senses a gradient of parameters at the peak position, which guides the movement of the peak. We extended this system with multiple components, and we developed a multiple-component model in which cross-talk between members of the Rho family of small GTPases is involved. This model also exhibits the essential properties of the two models with two components. Thus, the mass conservation system shows properties similar to those of cell polarity, such as uniqueness of axis and localization of sensitivity, in addition to directional sensing and signal amplification.Comment: PDF onl

Live imaging of whole mouse embryos during gastrulation : migration analyses of epiblast and mesodermal cells

During gastrulation in the mouse embryo, dynamic cell movements including epiblast invagination and mesodermal layer expansion lead to the establishment of the three-layered body plan. The precise details of these movements, however, are sometimes elusive, because of the limitations in live imaging. To overcome this problem, we developed techniques to enable observation of living mouse embryos with digital scanned light sheet microscope (DSLM). The achieved deep and high time-resolution images of GFP-expressing nuclei and following 3D tracking analysis revealed the following findings: (i) Interkinetic nuclear migration (INM) occurs in the epiblast at embryonic day (E)6 and 6.5. (ii) INM-like migration occurs in the E5.5 embryo, when the epiblast is a monolayer and not yet pseudostratified. (iii) Primary driving force for INM at E6.5 is not pressure from neighboring nuclei. (iv) Mesodermal cells migrate not as a sheet but as individual cells without coordination

The gene regulatory system for specifying germ layers in early embryos of the simple chordate

動物胚の遺伝子発現を数式で表現 --動物の胚葉形成システムをまるごと理解--.京都大学プレスリリース. 2021-06-10.In animal embryos, gene regulatory networks control the dynamics of gene expression in cells and coordinate such dynamics among cells. In ascidian embryos, gene expression dynamics have been dissected at the single-cell resolution. Here, we revealed mathematical functions that represent the regulatory logics of all regulatory genes expressed at the 32-cell stage when the germ layers are largely specified. These functions collectively explain the entire mechanism by which gene expression dynamics are controlled coordinately in early embryos. We found that regulatory functions for genes expressed in each of the specific lineages contain a common core regulatory mechanism. Last, we showed that the expression of the regulatory genes became reproducible by calculation and controllable by experimental manipulations. Thus, these regulatory functions represent an architectural design for the germ layer specification of this chordate and provide a platform for simulations and experiments to understand the operating principles of gene regulatory networks

Origin of diverse phosphorylation patterns in the ERBB system

シグナル伝達による多様な細胞応答の起源 --実験と理論の融合による反応特性の決定. 京都大学プレスリリース. 2022-01-21.Intercellular signals induce various cellular responses, including growth, proliferation, and differentiation, via the dynamic processes of signal transduction pathways. For cell fate decisions, ligand-binding induces the phosphorylation of ERBB receptors, which in turn activate downstream molecules. The ERBB family includes four subtypes, which diverged through two gene duplications from a common ancestor. Differences in the expression patterns of the subtypes have been reported between different organs in the human body. However, how these different expression properties influence the diverse phosphorylation levels of ERBB proteins is not well understood. Here we study the origin of the phosphorylation responses by experimental and mathematical analyses. The experimental measurements clarified that the phosphorylation levels heavily depend on the ERBB expression profiles. We developed a mathematical model consisting of the four subtypes as monomers, homodimers, and heterodimers and estimated the rate constants governing the phosphorylation responses from the experimental data. To understand the origin of the diversity, we analyzed the effects of the expression levels and reaction rates of the ERBB subtypes on the diversity. The difference in phosphorylation rates between ERBB subtypes showed a much greater contribution to the diversity than did the dimerization rates. This result implies that divergent evolution in phosphorylation reactions rather than in dimerization reactions after whole genome duplications was essential for increasing the diversity of the phosphorylation responses

Self-organizing Mechanism for Development of Space-filling Neuronal Dendrites

Neurons develop distinctive dendritic morphologies to receive and process information. Previous experiments showed that competitive dendro-dendritic interactions play critical roles in shaping dendrites of the space-filling type, which uniformly cover their receptive field. We incorporated this finding in constructing a new mathematical model, in which reaction dynamics of two chemicals (activator and suppressor) are coupled to neuronal dendrite growth. Our numerical analysis determined the conditions for dendritic branching and suggested that the self-organizing property of the proposed system can underlie dendritogenesis. Furthermore, we found a clear correlation between dendrite shape and the distribution of the activator, thus providing a morphological criterion to predict the in vivo distribution of the hypothetical molecular complexes responsible for dendrite elongation and branching