九州大学 研究者情報
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基本情報 研究活動 教育活動
村川 秀樹(むらかわ ひでき) データ更新日:2018.06.13



主な研究テーマ
応用数学,数値解析学
キーワード:非線形拡散問題,反応拡散系,自由境界問題,細胞接着, 数理モデル
2006.04~2018.03.
研究業績
主要原著論文
1. H. Murakawa, An efficient linear scheme to approximate nonlinear diffusion problems, Jpn. J. Ind. Appl. Math., 35, 1, 71-101, 2018.03.
2. E. Mainini, H. Murakawa, P. Piovano and U. Stefanelli, Carbon-nanotube geometries as optimal configurations, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 15, 4, 1448-1471, 2017.10.
3. M. Iida, H. Monobe, H. Murakawa and H. Ninomiya, Immovable, moving and vanishing interfaces in fast reaction limit, J. Differential Equations, 263, 5, 2715-2735, 2017.09.
4. H. Murakawa, A linear finite volume method for nonlinear cross-diffusion systems, Numer. Math., 136, 1, 1-26, 2017.05.
5. E. Mainini, H. Murakawa, P. Piovano and U. Stefanelli, Carbon-nanotube geometries: analytical and numerical results, Discrete Contin. Dyn. Syst. S, 10, 141-160, 2017.02.
6. Y. Matsunaga, M. Noda, H. Murakawa, K. Hayashi, A. Nagasaka, S. Inoue, T. Miyata, T. Miura, K. Kubo and K. Nakajima, Reelin transiently promotes N-cadherin-dependent neuronal adhesion during mouse cortical development, Proc. Natl. Acad. Sci. USA, 114, 8, 2048-2053, 2017.02, Reelin is an essential glycoprotein for the establishment of the
highly organized six-layered structure of neurons of the mammalian
neocortex. Although the role of Reelin in the control of
neuronal migration has been extensively studied at the molecular
level, the mechanisms underlying Reelin-dependent neuronal layer
organization are not yet fully understood. In this study, we directly
showed that Reelin promotes adhesion among dissociated neocortical
neurons in culture. The Reelin-mediated neuronal aggregation
occurs in an N-cadherin–dependent manner, both in vivo and
in vitro. Unexpectedly, however, in a rotation culture of dissociated
neocortical cells that gradually reaggregated over time, we found
that it was the neural progenitor cells [radial glial cells (RGCs)],
rather than the neurons, that tended to form clusters in the presence
of Reelin. Mathematical modeling suggested that this clustering
of RGCs could be recapitulated if the Reelin-dependent
promotion of neuronal adhesion were to occur only transiently.
Thus, we directly measured the adhesive force between neurons
and N-cadherin by atomic force microscopy, and found
that Reelin indeed enhanced the adhesiveness of neurons to
N-cadherin; this enhanced adhesiveness began to be observed
at 30 min after Reelin stimulation, but declined by 3 h. These
results suggest that Reelin transiently (and not persistently)
promotes N-cadherin–mediated neuronal aggregation. When
N-cadherin and stabilized β-catenin were overexpressed in the
migrating neurons, the transfected neurons were abnormally
distributed in the superficial region of the neocortex, suggesting
that appropriate regulation of N-cadherin–mediated adhesion is important
for correct positioning of the neurons during neocortical
development..
7. H. Murakawa and H. Togashi, Continuous models for cell-cell adhesion, J. Theor. Biol., 2015.06, Cell adhesionisthebindingofacelltoanothercellortoanextracellularmatrixcomponent.Thisprocess
is essentialinorganformationduringembryonicdevelopmentandinmaintainingmulticellular
structure. Armstrongetal.(2006)[J.Theor.Biol.243,pp.98–113]proposedanonlocaladvection–
diffusion systemasapossiblecontinuousmathematicalmodelforcell–cell adhesion.Althoughthe
systemisattractiveandchallenging,itgivesbiologicallyunrealisticnumericalsolutionsunder
certain situations.Weidentifytheproblemsandchangeunderlyingideaofcellmovementfrom “cells
moverandomly” to “cells movefromhightolowpressureregions”. Thenweprovideamodified
continuous modelforcell–cell adhesion.Numericalexperimentsillustratethatthemodified modelis
able toreplicatenotonlySteinberg'scellsortingexperimentsbutalsosomephenomenawhichcannot
be capturedatallbyArmstrong–Painter–Sherratt model..
8. D. Hilhorst and H. Murakawa, Singular limit analysis of a reaction-diffusion system with precipitation and dissolution in a porous medium, Networks and Heterogeneous Media, 2014.12.
9. H. Murakawa, Error estimates for discrete-time approximations of nonlinear cross-diffusion systems, SIAM J. Numer. Anal., 2014.04.
10. H. Murakawa, A relation between cross-diffusion and reaction-diffusion, Discrete Contin. Dyn. Syst. S, 5, 147-158, 2012.02.
11. H. Murakawa, A linear scheme to approximate nonlinear cross-diffusionsystems, Math. Mod. Numer. Anal., 45, 1141-1161, 2011.11.
12. H. Murakawa and H. Ninomiya, Fast reaction limit of a three-componentreaction-diffusion system, J. Math. Anal. Appl., 379, 150-170, 2011.07.
13. A. Ducrot, F. Le Foll, P. Magal, H. Murakawa, J. Pasquier and G. Webb, An in vitro cell population dynamics model incorporating cellsize, quiescence, and contact inhibition, Math. Models Methods Appl. Sci., 21, 871-892, 2011.04.
14. R. Eymard, D. Hilhorst, H. Murakawa and M. Olech, Numerical approximation of a reaction-diffusion system with fast reversible reaction, Chinese Annals of Mathematics B, 31, 631-654, 2010.09.
主要学会発表等
1. H. Murakawa, Spatial patterns in a population model structured by cell size, quiescence and sensing radius, Everything disperses to Miami, the role of movement and dispersal in spatial ecology, epidemiology and environmental science, 2012.12.
2. H. Murakawa, Instantaneous limit of a reaction-diffusion system with a fast precipitation and dissolution reaction, Singularities arising in Nonlinear Problems 2012, 2012.11.
3. H. Murakawa, A free boundary problem with triple-junctions and a linear numerical method for capturing the interfaces, ALGORITMY 2012 Conference on Scientific Computing, 2012.09.
4. H. Murakawa, Triple-junctions in a strong interaction limit of a three-component system, The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 2012.07.
5. 村川秀樹, 非線形交差拡散系の線形数値解法, 日本数学会2012年度年会, 2012.03.
6. H. Murakawa, Singular limit of a three-component reaction-diffusion system, Workshop on Nonlinear Partial Differential Equations--China-Japan Joint Project for Young Mathematician, 2011.11.
7. H. Murakawa, Fast reaction limit and nonlinear diffusion, Modeling and Analysis in the Life Sciences : A ReaDiLab Conference in Tokyo, 2011.11.
8. 村川秀樹, 反応拡散系近似:理論と応用, 日本数学会2011年度秋季総合分科会, 2011.09.
9. H. Murakawa, Numerical solution of nonlinear cross-diffusion systems by a linear scheme, The 4th MSJ-SI,Mathematical Society of Japan,Seasonal Institute,Nonlinear Dynamics in Partial Differential Equations, 2011.09.
10. H. Murakawa, A free boundary problem in the limit of a fast reaction system, Mathematical and numerical analysis for interface motion arising in nonlinear phenomena, 2011.07.
11. H. Murakawa, Reaction-diffusion system approximation to nonlinear diffusion problems and its applications, Seminaires de Mathematiques du vivant, 2010.11.
12. H. Murakawa, Reaction-diffusion system approximation to nonlinear diffusion problems and its applications, Seminaires de Mathematiques du vivant, 2010.11.
13. 村川秀樹, ある3成分反応拡散系の急速反応極限に現れる自由境界問題, 日本数学会2010年度秋季総合分科会, 2010.09.
14. H. Murakawa, A relation between reaction-diffusion interaction and nonlinear diffusion, The 8th AIMS Conference on Dynamical Systems Differential Equations and Applications, 2010.05.
学会活動
所属学会名
日本応用数理学会
日本発生生物学会
日本数学会
学協会役員等への就任
2017.09~2019.08, 日本数学会, 応用数学分科会分科会委員.
学会誌・雑誌・著書の編集への参加状況
2010.04~2012.03, 数学, 国内, 編集委員.
学術論文等の審査
年度 外国語雑誌査読論文数 日本語雑誌査読論文数 国際会議録査読論文数 国内会議録査読論文数 合計
2017年度      
2015年度      
2014年度    
2013年度    
2012年度    
2011年度      
2010年度  
2009年度    
その他の研究活動
外国人研究者等の受入れ状況
2017.07~2017.11, 1ヶ月以上, National University of Lesotho, Kingdom of Lesotho, 民間・財団.
受賞
応用数学研究奨励賞, 日本数学会, 2016.03.
研究資金
科学研究費補助金の採択状況(文部科学省、日本学術振興会)
2018年度~2021年度, 基盤研究(B), 分担, 生命科学におけるパターン形成の新しいモデルと数学的解析手法の確立.
2017年度~2020年度, 基盤研究(C), 代表, 細胞接着の数理:理論と応用.
2014年度~2016年度, 基盤研究(C), 代表, 細胞接着の数理:実験、モデリング、解析.
2010年度~2012年度, 若手研究(B), 代表, 反応拡散系近似理論の発展と応用.
2007年度~2009年度, 若手研究(B), 代表, 反応拡散系近似理論の新展開.
日本学術振興会への採択状況(科学研究費補助金以外)
2010年度~2010年度, 国際学会等派遣事業, 代表, A relation between reaction-diffusion interaction and nonlinear diffusion.
競争的資金(受託研究を含む)の採択状況
2014年度~2020年度, 戦略的創造研究推進事業 (文部科学省), 分担, 生命現象における時空間パターンを支配する普遍的数理モデル導出に向けた数学理論の構築.

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