Convergence rate of solutions toward stationary solutions to the compressible Navier–Stokes equation in a half line

AbstractWe study a large time behavior of a solution to the initial boundary value problem for an isentropic and compressible viscous fluid in a one-dimensional half space. The unique existence and the asymptotic stability of a stationary solution are proved by S. Kawashima, S. Nishibata and P. Zhu for an outflow problem where the fluid blows out through the boundary. The main concern of the present paper is to investigate a convergence rate of a solution toward the stationary solution. For the supersonic flow at spatial infinity, we obtain an algebraic or an exponential decay rate. Precisely, if an initial perturbation decays with the algebraic or the exponential rate in the spatial asymptotic point, the solution converges to the corresponding stationary solution with the same rate in time as time tends to infinity. An algebraic convergence rate is also obtained for the transonic flow. These results are proved by the weighted energy method

The role of astrocytes during repair of cerebral infarction in mdx mice

様々な大きさのジストロフィンアイソフォーム(427kDa, 260kDa, 140kDa, 116kDa, 71-75kDa)が広く体内に存在していることはよく知られている.中枢神経系においては71-75kDaのDp71が著明に多く,毛細血管の内皮の基底膜に接しているアストロサイトの細胞質に局在することが報告されている.しかしながらDp71の機能についてはよくわかっていないことが多い.そこで今回,脳組織におけるDp71の役割を調べるために,コントロールマウス(wild-typeマウス)およびデュシャンヌ型筋ジストロフィーモデル動物であるmdxマウスを用いて実験的脳梗塞を作成し,その治癒過程を形態学的に観察した.また,GFAPおよびDp71に関して生化学的に分析をおこなった.HE染色およびGFAP免疫組織学的染色の結果から,形態学的にはmdxマウスとコントロールマウスの脳に違いは認められなかった.しかしながら,mdxマウスの脳において,Dp71の発現量がコントロールマウスよりも少ないことがわかった.またmdxマウスにおいて,脳梗塞の修復過程におけるアストロサイトの反応がコントロールマウスよりも弱いことがわかった.これらの結果から,mdxマウスの脳において,アストロサイトの機能,アストロサイトの血管新生に関わる機能の障害されていることが示唆された.It is now well known that dystrophin isoforms (427kDa, 260kDa, 140kDa, 116kDa, 71-75kDa) are widely distributed throughout our body. In the central nervous system a considerable amount of Dp71 (71-75kDa) is found in the perivascular cytoplasm of the astrocytes. However, the function of this dystrophin is still unknown. To investigate the role of Dp71 in the brain tissue, cerebral infarction was induced in the control (wide-type) mouse and mdx mouse which is known as an animal model of human muscle dystrophy (Duchenne type), and morphological changes of the infarcted area were observed during repair of the infarction. In addition, biochemical analysis of GFAP and Dp71 was carried out in the brain of the control and mdx mouse. In our present study, there were no differences in brain morphology between mdx and control mouse as revealed in H-E stain and GFAP immunohistochemistry. However, the Dp71 were smaller in quantity in the brain of the mdx mouse than that of the control mouse. The reaction of astrocytes during repair of serebral infarction was distinctly delayed in the mdx mouse compared with that of the control mouse. These findings suggest that the astrocytes in the brain of the mdx mouse are functionally impaired including perivascular cytoplasmic processes with relation to neo-vascularization

Expression of myogenin, MyoD and MHC isoforms in regenerating skeletal muscle.

骨格筋再生過程におけるミオシン重鎖(MHC)アイソフォーム発現とmyogenin，MyoDタンパクの発現様式との関連性を検討するために，塩酸ブピバカインを用いてマウスヒラメ筋損傷モデルを作成し，損傷筋の再生過程を組織形態学的に確認すると同時に，再生各段階におけるMHCアイソフォームと，myogeninおよびMyoDタンパク発現を経時的に検索した．本研究における筋損傷は塩酸ブピバカインをマウス(C57BL/10SnSlc)のヒラメ筋に注入することで作成した．組織学的には，塩酸ブピバカイン投与後3日目で筋線維はほとんど消失し，処置後6日目で中心核を有する再生筋線維がかなり出現し，処置後28日目では対照群のものと同程度まで回復した．生化学的分析では，対照群ヒラメ筋はMHCⅠ(34．3±1．7%)とMHCⅡa(65．7±1．7%)で構成されていた．実験群ヒラメ筋ではMHCⅠは処置後14日目まで減少し，その後増加傾向を示し，処置後90日目では36．3±2．9%となった．また，正常ヒラメ筋では検出されない速筋型MHC(MHC Ⅱd，MHC Ⅱb)が処置後3日目から28日目まで検出された．Western blotを用いた分析では，myogeninタンパク正常ヒラメ筋（遅筋）で検出された一方，前脛骨筋（速筋）においては検出できなかった．実験群ヒラメ筋では，myogeninは対照群と比較して処置後３日目より増加し（3．1±0．5），処置後６日目でピークに達した（5．8±0．8）．それからmyogeninタンパクは徐々に減少していったが，処置後90日目においてもなお対照群ヒラメ筋の1．8倍の発現を維持し続けた．一方，MyoDタンパクは正常前脛骨筋において正常ヒラメ筋の3．3倍の発現が認められた．MyoDは処置後３日目で対照群ヒラメ筋と比較して5．4倍になりピークに達した．その後は徐々に減少し始めた．しかし処置後90日目においても2．2倍の発現があった．これらのことから筋の再生過程においては速筋タイプの筋細胞が出現するmyogeninとMyoDは衛星細胞の分化と筋の再生に密接に関係していることが示唆された．To investigate the precise mechanism of skeletal muscle cell regeneration, the changing pattern ofmyosin heavy chain(MHC)isoforms during the regenerating process was observed with relation to theactivation of myogenin and MyoD. In addition, histopathological observation of the damaged muscles wasperformed throughout the experiment.In this study, muscle damage was induced by intramuscular injection of bupivacaine hydrochloride in thesoleus muscle of mice (C57BL/10SnSc). In the light microscopic observation, muscle cells had almost disappeared at 3 days after bupivacainetreatment with severe inflammatory cell infiltration. At 6 days after treatment, a considerable number ofregenerating muscle cells containing centrally located nuclei appeared in the damaged soleus muscle. At28 days, these regenerating muscle cells showed almost the same appearance as the control muscle cellscontaining subsarcolemmal nuclei, although a small number of muscle cells with central nuclei were stillrecognized.In the biochemical analysis, control soleus muscles contained only MHC I (34.3±1.7 %)and MHC IIa(65.7±1.7 %). In the damaged muscles, MHC I was decreased toward 14 days after treatment, and thengradually increased. At 90 days, the contents of MHC I was finally recovered to 36.3±2.9 %.0 In addition,MHC IId and MHC IIb appeared in the damaged muscle from 3 to 28 days after treatment. However, theyhad disappeared at 90 days.Using western blot analysis, myogenin protein was recognized in the control soleus muscles (slow typemuscle), while the myogenin could not be found in the first type muscle of the anterior tibial muscle. Themyogenin contents increased to about three fold (3.1±0.5)at 3 days after treatment compared withthose of control muscles and reached the maximum level (5.8±0.8)at 6 days after treatment. Then, myogenin contents gradually decreased,although they still remained high (1.8 times)at the end of experiment (90 days after treatment). Incontrast to the myogenin protein, a high level (3.3 times)of MyoD protein was detected in the anteriortibial muscle compared with that of control soleus muscles. In the damaged soleus muscles, MyoDcontents reached a maximum level (5.4 times)at 3 days after treatment compared with that of controlsoleus muscles, and then gradually decreased toward the end of experiment. However, MyoD protein stillremained 2.2 times compared with that of control soleus muscles. These findings described above indicate that, 1)a property of fast type muscle cells appeared in theregenerating muscle cells during the regenerating process, and 2)myogenin and MyoD are closelyrelated to the differentiation of the satellite cells and regeneration of the skeletal muscle cells

Function of skeletal muscle sarcoplasmic reticulum and expression of sarcoplasmic reticulum Ca2+-ATPase in right congestive heart failure rats

右心不全に伴って,速筋および遅筋の筋小胞体Ca2+取り込み能が減少するという仮説を検証した.右心不全は,モノクロタリン(30 ㎎/㎏)を投与することにより引き起こし,投与後4週で,長指伸筋およびヒラメ筋を両後肢から採取した.筋の疲労耐性は,連続的な強縮刺激を行うことにより測定した.長指伸筋では刺激開始1分後,ヒラメ筋では4分後の張力を測定し,初期値に対するそれらの割合を疲労の指標とした.長指伸筋およびヒラメ筋の疲労耐性は,右心不全群で有意に低下した.筋小胞体Ca2+取り込み速度は,Indo-Ⅰを付加したホモジネートで測定した.その結果,Ca2+取り込み速度は,長指伸筋で25.4%(p<0.01),ヒラメ筋で30.4%(p<0.05)低下した.このCa2+取り込み速度の低下は,筋小胞体Ca2+-ATPaseタンパク量の低下と一致した.筋小胞体Ca2+取り込み能の低下は,筋張力の低下を引き起こし,このCa2+ handlingの低下は,少なくとも右心不全による運動耐容能の低下の一因であろう.In this study, we investigated the hypothesis that right congestive heart failure (CHF) would impair sarcoplasmic reticulum (SR) Ca2+ uptake in skeletal fast- and slow-twitch muscles. To induce CHF, the rats were injected with monocrotalin (30 ㎎/㎏). After 4 weeks of injection, extensor digitorum longus (EDL) and soleus (SOL) muscles were sampled from both hind limbs. Muscle fatigue resistance was measured in vitro as the relative decline in force production of tetanic contraction induced by electrical stimulation over 1 and 4 min in EDL and SOL, respectively. Evaluation of fatigue characteristics showed that CHF significantly reduced fatigue resistance in both muscles under study.SR Ca2+uptake rate wasmeasured in vitro with Indo-I on muscle homogenates. As hypothesized, Ca2+uptake rate was decreasedby 25.4%(P < 0.01) and 30.4%(P < 0.05) in EDL and SOL, respectively. This decline in Ca22+uptake ratewas accompanied by an immunochemically determined decrease in SR Ca2+-ATPase protein. Taking intoaccount previous findings that the depressed SR Ca2+uptake leads to the reduce in muscle forceproduction, these results suggest that impaired SR Ca2+handling capacity in skeletal muscle may accountat least partly for deteriorations in exercise tolerance resulting from right CHF

Evaluation of a tranfected HEK293 cell line overexpressing the gc-c receptor [abstract]

Guanylate cyclase C (GC-C) is typically highly expressed in the brush border of the intestinal epithelium and in human colorectal adenocarcinomas, but is minimally expressed in extraintestinal tissues. Many studies have demonstrated that GC-C is a useful target for imaging and treatment of colorectal cancers using GC-C ligands. In this study, we have established a transfected Hek293 cell line overexpressing the human GC-C receptor and tested its ligand binding, proliferation, biodistribution and imaging properties. A pcDNA3.1(+)/GC-C plasmid was constructed and used to stably transfect Hek293 cells. A Hek293/GC-C cell line was successfully selected and confirmed by receptor binding studies, western blot and RT-PCR. Transfection did not significantly influence the in vitro cell growth rate compared with Hek293/control. Scatchard assay, immunoblot, and RT-PCR analyses all demonstrated significant overexpression of GC-C in the transfected cell line, and the functionality of the expressed protein was demonstrated by a > 150-fold increase in generation of cGMP upon ligand stimulation relative to the control cell line. Further, treatment of Hek293/GC-C with GC-C ligands resulted in decreased cell proliferation measured by MTT assay, as has been previously observed for other GC-C- expressing colorectal cancer cell lines. Biodistribution and in vivo imaging studies carried out in nude mice bearing Hek293/GC-C xenografts also demonstrated high specific uptake of an Indium-111-labeled GC-C agonist. The Hek293/GC-C cell line described here will provide a useful model for the development of GC-C agonists as diagnostic and therapeutic agents for colorectal cancer

Accurate estimation of a phase diagram from a single STM image

We propose a new approach to constructing a phase diagram using the effective Hamiltonian derived only from a single real-space image produced by scanning tunneling microscopy (STM). Currently, there have been two main methods to construct phase diagrams in material science: ab initio calculations and CALPHAD with thermodynamic information obtained by experiments and/or theoretical calculations. Although the two methods have successfully revealed a number of unsettled phase diagrams, their results sometimes contradicted when it is difficult to construct an appropriate Hamiltonian that captures the characteristics of materials, e.g., for a system consisting of multiple-scale objects whose interactions are essential to the system’s characteristics. Meanwhile, the advantage of our approach over existing methods is that it can directly and uniquely determine the effective Hamiltonian without any thermodynamic information. The validity of our approach is demonstrated through an Mg–Zn–Y long-period stacking-ordered structure, which is a challenging system for existing methods, leading to contradictory results. Our result successfully reproduces the ordering tendency seen in STM images that previous theoretical study failed to reproduce and clarifies its previously unknown phase diagram. Thus, our approach can be used to clear up contradictions shown by existing methods