Papers - Ei Shin-Ichiro
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Bifurcation of co-existing traveling wave solutions in a three-component competition–diffusion system
Shin-Ichiro Ei, Hideo Ikeda, Toshiyuki Ogawa
Physica D: Nonlinear Phenomena 448 133703 - 133703 2023.06
Publishing type:Research paper (scientific journal) Publisher:Elsevier BV
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Alien invasion into the buffer zone between two competing species
Shin-Ichiro Ei, Hideo Ikeda, Toshiyuki Ogawa
Discrete and Continuous Dynamical Systems - B 2023
Publishing type:Research paper (scientific journal) Publisher:American Institute of Mathematical Sciences (AIMS)
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Method of fundamental solutions for Neumann problems of the modified Helmholtz equation in disk domains
Shin-Ichiro Ei, Hiroyuki Ochiai, Yoshitaro Tanaka
Journal of Computational and Applied Mathematics 402 113795 - 113795 2022.03
Publishing type:Research paper (scientific journal) Publisher:Elsevier BV
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Oscillations and bifurcation structure of reaction–diffusion model for cell polarity formation
Masataka Kuwamura, HirofumiIzuhara, Shin-ichiro Ei
Journal of Mathematical Biology 84 ( 4 ) 2022.02
Language:English Publishing type:Research paper (scientific journal) Publisher:Springer Science and Business Media LLC
DOI: 10.1007/s00285-022-01723-5
Other Link: https://link.springer.com/article/10.1007/s00285-022-01723-5/fulltext.html
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Intracellular trafficking of Notch orchestrates temporal dynamics of Notch activity in the fly brain
Miaoxing Wang, Xujun Han, Chuyan Liu, Rie Takayama, Tetsuo Yasugi, Shin-Ichiro Ei, Masaharu Nagayama, Yoshitaro Tanaka, Makoto Sato
Nature Communications 12 ( 1 ) 2021.12
Publishing type:Research paper (scientific journal) Publisher:Springer Science and Business Media LLC
<title>Abstract</title>While Delta non-autonomously activates Notch in neighboring cells, it autonomously inactivates Notch through <italic>cis</italic>-inhibition, the molecular mechanism and biological roles of which remain elusive. The wave of differentiation in the <italic>Drosophila</italic> brain, the ‘proneural wave’, is an excellent model for studying Notch signaling in vivo. Here, we show that strong nonlinearity in <italic>cis</italic>-inhibition reproduces the second peak of Notch activity behind the proneural wave in silico. Based on this, we demonstrate that Delta expression induces a quick degradation of Notch in late endosomes and the formation of the twin peaks of Notch activity in vivo. Indeed, the amount of Notch is upregulated and the twin peaks are fused forming a single peak when the function of Delta or late endosomes is compromised. Additionally, we show that the second Notch peak behind the wavefront controls neurogenesis. Thus, intracellular trafficking of Notch orchestrates the temporal dynamics of Notch activity and the temporal patterning of neurogenesis.
DOI: 10.1038/s41467-021-22442-3
Other Link: http://www.nature.com/articles/s41467-021-22442-3
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Corrigendum to “Interaction of non-radially symmetric camphor particles” [Physica D 366 (2018) 10–26] (Physica D: Nonlinear Phenomena (2018) 366 (10–26), (S0167278917303603), (10.1016/j.physd.2017.11.004))
Shin Ichiro Ei, Hiroyuki Kitahata, Yuki Koyano, Masaharu Nagayama
Physica D: Nonlinear Phenomena 422 2021.08
Publishing type:Research paper (scientific journal)
The authors regret that the experimental condition was wrongly described in Section 4 in page 20 and the caption of Fig. 5 in page 21. The concentration of camphor methanol solution was 3 mol/L, not 0.3 mol/L. The authors would like to apologise for any inconvenience caused.
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Correction to: A continuation method for spatially discretized models with nonlocal interactions conserving size and shape of cells and lattices International journal
Shin-Ichiro Ei, Hiroshi Ishii, Makoto Sato, Yoshitaro Tanaka, Miaoxing Wang, Tetsuo Yasugi
Journal of Mathematical Biology 82 ( 6 ) 57 2021.05
Language:English Publishing type:Research paper (scientific journal) Publisher:Springer Science and Business Media LLC
In this paper, we introduce a continuation method for the spatially discretized models, while conserving the size and shape of the cells and lattices. This proposed method is realized using the shift operators and nonlocal operators of convolution types. Through this method and using the shift operator, the nonlinear spatially discretized model on the uniform and nonuniform lattices can be systematically converted into a spatially continuous model; this renders both models point-wisely equivalent. Moreover, by the convolution with suitable kernels, we mollify the shift operator and approximate the spatially discretized models using the nonlocal evolution equations, rendering suitable for the application in both experimental and mathematical analyses. We also demonstrate that this approximation is supported by the singular limit analysis, and that the information of the lattice and cells is expressed in the shift and nonlocal operators. The continuous models designed using our method can successfully replicate the patterns corresponding to those of the original spatially discretized models obtained from the numerical simulations. Furthermore, from the observations of the isotropy of the Delta-Notch signaling system in a developing real fly brain, we propose a radially symmetric kernel for averaging the cell shape using our continuation method. We also apply our method for cell division and proliferation to spatially discretized models of the differentiation wave and describe the discrete models on the sphere surface. Finally, we demonstrate an application of our method in the linear stability analysis of the planar cell polarity model.
DOI: 10.1007/s00285-021-01610-5
Other Link: https://link.springer.com/article/10.1007/s00285-021-01610-5/fulltext.html
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Effective nonlocal kernels on reaction–diffusion networks
Shin-Ichiro Ei, Hiroshi Ishii, Shigeru Kondo, Takashi Miura, Yoshitaro Tanaka
Journal of Theoretical Biology 509 110496 - 110496 2021.01
Publishing type:Research paper (scientific journal) Publisher:Elsevier BV
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Noise-induced scaling in skull suture interdigitation
Yuto Naroda, Yoshie Endo, Kenji Yoshimura, Hiroshi Ishii, Shin-Ichiro Ei, Takashi Miura
PLOS ONE 15 ( 12 ) e0235802 - e0235802 2020.12
Publishing type:Research paper (scientific journal) Publisher:Public Library of Science (PLoS)
Sutures, the thin, soft tissue between skull bones, serve as the major craniofacial growth centers during postnatal development. In a newborn skull, the sutures are straight; however, as the skull develops, the sutures wind dynamically to form an interdigitation pattern. Moreover, the final winding pattern had been shown to have fractal characteristics. Although various molecules involved in suture development have been identified, the mechanism underlying the pattern formation remains unknown. In a previous study, we reproduced the formation of the interdigitation pattern in a mathematical model combining an interface equation and a convolution kernel. However, the generated pattern had a specific characteristic length, and the model was unable to produce a fractal structure with the model. In the present study, we focused on the anterior part of the sagittal suture and formulated a new mathematical model with time–space-dependent noise that was able to generate the fractal structure. We reduced our previous model to represent the linear dynamics of the centerline of the suture tissue and included a time–space-dependent noise term. We showed theoretically that the final pattern from the model follows a scaling law due to the scaling of the dispersion relation in the full model, which we confirmed numerically. Furthermore, we observed experimentally that stochastic fluctuation of the osteogenic signal exists in the developing skull, and found that actual suture patterns followed a scaling law similar to that of the theoretical prediction.
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Shin-Ichiro Ei, Hiroshi Ishii, Makoto Sato, Yoshitaro Tanaka, Miaoxing Wang, Tetsuo Yasugi
Journal of Mathematical Biology 81 ( 4-5 ) 981 - 1028 2020.11
Publishing type:Research paper (scientific journal) Publisher:Springer Science and Business Media LLC
Abstract
In this paper, we introduce a continuation method for the spatially discretized models, while conserving the size and shape of the cells and lattices. This proposed method is realized using the shift operators and nonlocal operators of convolution types. Through this method and using the shift operator, the nonlinear spatially discretized model on the uniform and nonuniform lattices can be systematically converted into a spatially continuous model; this renders both models point-wisely equivalent. Moreover, by the convolution with suitable kernels, we mollify the shift operator and approximate the spatially discretized models using the nonlocal evolution equations, rendering suitable for the application in both experimental and mathematical analyses. We also demonstrate that this approximation is supported by the singular limit analysis, and that the information of the lattice and cells is expressed in the shift and nonlocal operators. The continuous models designed using our method can successfully replicate the patterns corresponding to those of the original spatially discretized models obtained from the numerical simulations. Furthermore, from the observations of the isotropy of the Delta–Notch signaling system in a developing real fly brain, we propose a radially symmetric kernel for averaging the cell shape using our continuation method. We also apply our method for cell division and proliferation to spatially discretized models of the differentiation wave and describe the discrete models on the sphere surface. Finally, we demonstrate an application of our method in the linear stability analysis of the planar cell polarity model.DOI: 10.1007/s00285-020-01534-6
Other Link: https://link.springer.com/article/10.1007/s00285-020-01534-6/fulltext.html
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Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel
Shin-Ichiro Ei, Jong-Shenq Guo, Hiroshi Ishii, Chin-Chin Wu
Journal of Mathematical Analysis and Applications 487 ( 2 ) 124007 - 124007 2020.07
Publishing type:Research paper (scientific journal) Publisher:Elsevier BV
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Center Manifold Theory for the Motions of Camphor Boats with Delta Function Reviewed
Kota Ikeda, Shin-Ichiro Ei
Journal of Dynamics and Differential Equations - 37 2020.01
Language:English Publishing type:Research paper (scientific journal)
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JAK/STAT guarantees robust neural stem cell differentiation by shutting off biological noise. Reviewed
Tanaka Y, Yasugi T, Nagayama M, Sato M, Ei SI
Scientific reports 8 ( 1 ) 12484 2018.08
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Heterogeneity-induced effects for pulse dynamics Reviewed
Chao-Nien Chen, Shin-Ichiro Ei, Shyuh-yaur Tzeng
PHYSICA D-NONLINEAR PHENOMENA 2018.07
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Interaction of non-radially symmetric camphor particles Reviewed
Shin-Ichiro Ei, Hiroyuki Kitahata, Yuki Koyano, Masaharu Nagayama
Physica D: Nonlinear Phenomena 366 10 - 26 2018.03
Language:English Publishing type:Research paper (scientific journal) Publisher:Elsevier B.V.
In this study, the interaction between two non-radially symmetric camphor particles is theoretically investigated and the equation describing the motion is derived as an ordinary differential system for the locations and the rotations. In particular, slightly modified non-radially symmetric cases from radial symmetry are extensively investigated and explicit motions are obtained. For example, it is theoretically shown that elliptically deformed camphor particles interact so as to be parallel with major axes. Such predicted motions are also checked by real experiments and numerical simulations.
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Masataka Kuwamura, Sungrim Seirin-Lee, Shin-ichiro Ei
SIAM Journal on Applied Mathematics 78 ( 6 ) 3238 - 3257 2018.01
Publishing type:Research paper (scientific journal) Publisher:Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/18m1163749
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JAK/STAT guarantees robust differentiation of neural stem cells by shutting off biological noises in the developing fly brain Reviewed
Makoto Sato, Tetsuo Yasugi, Yoshitaro Tanaka, Masaharu Nagayama, Shin-Ichiro Ei
CYTOKINE 100 127 - 127 2017.12
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Mathematical modeling for meshwork formation of endothelial cells in fibrin gels Reviewed
Daiki Sasaki, Hitomi Nakajima, Yoshimi Yamaguchi, Ryuji Yokokawa, Shin-Ichiro Ei, Takashi Miura
JOURNAL OF THEORETICAL BIOLOGY 429 95 - 104 2017.09
Language:English Publishing type:Research paper (scientific journal) Publisher:ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
Vasculogenesis is the earliest process in development for spontaneous formation of a primitive capillary network from endothelial progenitor cells. When human umbilical vein endothelial cells (HUVECs) are cultured on Matrigel, they spontaneously form a network structure which is widely used as an in vitro model of vasculogenesis. Previous studies indicated that chemotaxis or gel deformation was involved in spontaneous pattern formation. In our study, we analyzed the mechanism of vascular pattern formation using a different system, meshwork formation by HUVECs embedded in fibrin gels. Unlike the others, this experimental system resulted in a perfusable endothelial network in vitro. We quantitatively observed the dynamics of endothelial cell protrusion and developed a mathematical model for one-dimensional dynamics. We then extended the one-dimensional model to two-dimensions. The model showed that random searching by endothelial cells was sufficient to generate the observed network structure in fibrin gels. (C) 2017 Elsevier Ltd. All rights reserved.
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ANNIHILATION OF TWO INTERFACES IN A HYBRID SYSTEM Reviewed
Shin-Ichiro Ei, Kei Nishi, Yasumasa Nishiura, Takashi Teramoto
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S 8 ( 5 ) 857 - 869 2015.10
Language:English Publishing type:Research paper (scientific journal) Publisher:AMER INST MATHEMATICAL SCIENCES-AIMS
We consider the mixed ODE-PDE system called a hybrid system, in which the two interfaces interact with each other through a continuous medium and their equations of motion are derived in a weak interaction framework. We study the bifurcation property of the resulting hybrid system and construct an unstable standing pulse solution, which plays the role of a separator for dynamic transition from standing breather to annihilation behavior between two interfaces.
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INSTABILITY OF MULTI-SPOT PATTERNS IN SHADOW SYSTEMS OF REACTION-DIFFUSION EQUATIONS Reviewed
Shin-Ichiro Ei, Kota Ikeda, Eiji Yanagida
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 14 ( 2 ) 717 - 736 2015.03
Language:English Publishing type:Research paper (scientific journal) Publisher:AMER INST MATHEMATICAL SCIENCES
Our aim in this paper is to prove the instability of multi-spot patterns in a shadow system, which is obtained as a limiting system of a reaction-diffusion model as one of the diffusion coefficients goes to infinity. Instead of investigating each eigenfunction for a linearized operator, we characterize the eigenspace spanned by unstable eigenfunctions.