Matrine Inhibits Disturbed Flow–Enhanced Migration via Downregulation of ERK12–MLCK Signaling VSMC

Matrine Inhibits Disturbed Flow e Enhanced Migration via Downregulation of ERK1/2e MLCK Signaling Vascular Smooth Muscle Cells

Ping Zhu,1Ji-Mei Chen,1Hui-Ming Guo,1Xiao-Ping Fan,1Xiao-Shen Zhang,1Rui-Xin Fan,1Shao-Yi Zheng,1Ruo-Bin Wu,1Xue-Jun Xiao,1Huan-Lei Huang,1Xiao-Lan Zhu,1Huai-Pu Liu,1Guang Long,2Yan-Fang Chen,3and Jian Zhuang,1Guangzhou and Hengyang,People’s Republic of China and Dayton,Ohio

Background:To investigate the effects of matrine on the vascular smooth muscle cell (VSMC)migration modulated by disturbed ?ow and their underlying molecular mechanisms in vitro.Methods:Isolated rat aortic VSMCs were grown to con?uence on 20-?80-mm ?bronectin-coated glass cover slides,and then,denuded zones were made at the position calculated to be the oscillating ?ow-reattachment zone and also in the downstream laminar ?ow region.VSMCs were treated with different doses of matrine (0,10,20,30,and 40mg/L),or PD98059(30m M),ML-7(10m M)combined with matrine (40mg/L)for 30minutes before and during the experiments.Then,the wounded monolayers were kept under static conditions or were subjected to laminar or disturbed ?ow for 21hours or 10hours.The VSMC migration was assessed by microscopic images.The extracellular signal-regulated kinase 1/2(ERK1/2)and myosin light chain kinase (MLCK)proteins were determined by Western blot.

Results:Disturbed ?ow signi?cantly increased phosphorylation of ERK1/2.Selective inhibition of ERK1/2phosphorylation by inhibitor PD98059and matrine signi?cantly suppressed VSMC migration under disturbed ?ow.Disturbed ?ow signi?cantly enhanced phosphorylation of MLCK,whereas both matrine and PD98059inhibited the phosphorylation of MLCK under disturbed ?ow.The complete inhibition of MLCK phosphorylation using the selective MLCK inhibitor ML-7signi?cantly inhibited VSMC migration under disturbed ?ow.

Conclusion:Matrine inhibits VSMC migration under disturbed ?ow,in part,by downregulation of ERK1/2e MLCK signaling pathway.

INTRODUCTION

The development of atherosclerosis and vascular restenosis after angioplasty has been attributed to hemodynamic changes at the site of injury.In particular,the progression of atherosclerosis and vascular restenosis was attenuated in areas where shear stress in the blood ?ow is high and was exac-erbated in areas with low shear stress.1,2Abnormal migration and proliferation of vascular smooth muscle cells (VSMCs)are considered the hallmarks for the development of vascular restenosis.Previous study showed that in animal models of balloon cath-eter injury,intimal thickening was accelerated by low shear stress in the absence of the inner endothe-lial cell (EC)lining,suggesting that VSMCs could

P.Z.,J-.M.C.,H-.M.G.authors have equal contribution to this work.

1

Cardiovascular Surgery Department,Guangdong Cardiovascular Institute,Guangdong General Hospital,Guangdong Academic of Medical Sciences,Guangzhou,People’s Republic of China.

2Medical School,Nan Hua University,Hengyang,People’s Republic of China.

3Department of Pharmacology and Toxicology,Boonshoft School of Medicine,Wright State University,Dayton,OH.

Correspondence to:Jian Zhuang,MD,PhD,Guangdong Cardiovas-cular Institute,Guangdong General Hospital,Guangdong Academic of Medical Sciences,96Dongchuan Road,Guangzhou 510100,Guang-dong,People’s Republic of China;E-mail:zhuangjianzggd@https://www.wendangku.net/doc/3c5134567.html, Ann Vasc Surg 2012;26:268–275DOI:10.1016/j.avsg.2011.10.006óAnnals of Vascular Surgery Inc.

268

respond directly to changes in blood?ow.Further-

more,in that study,2the intimal thickening that

occurred in response to decreased?ow levels was

a result of increased VSMC migration.Thus,dysre-

gulation of blood?ow may play an important role

in the development of pathophysiological states in

blood vessels.

In vitro studies investigating the effects of shear

stress on vascular cells have been focused primarily

on ECs because they are directly exposed to the

shear stress of?owing blood under normal physio-

logical conditions.3It had long been thought that

the underlying VSMCs were shielded from blood

?ow and were only subjected to shear stress when

the EC layer was removed,as occurs in balloon

angioplasty.However,recent studies have shown

that even in the presence of an intact endothelium,

VSMCs are subjected to shear stress through their

exposure to interstitial?ow driven by the transmu-

ral pressure gradient.4,5Although it has been shown

that disturbed?ow with altered?uid shear stress

gradients modulates VSMC migration and neointi-

mal hyperplasia in vivo,6data on differences in

VSMC migration between laminar and disturbed

?ows in vitro are scarce.Furthermore,the molec-

ular mechanisms by which blood?ow modulates

VSMCs migration have not been clearly de?ned.

Radix Sophorae Flavescentis is a commonly used

drug in traditional Chinese medicine for many

diseases,including hepatitis B7and cancer.8Matrine

is one of the major components of Radix Sophorae

Flavescentis.Unpublished data from our lab have

shown that matrine inhibited rat VSMC growth in

a dose-dependent manner.As many drugs that

inhibit cell cycle progression normally also inhibit

migration,9we hypothesized that matrine may

also inhibit rat VSMC migration.

This study aimed to elucidate the underlying

molecular mechanisms by which disturbed?ow

modulates VSMC migration in a modi?ed parallel-

plate?ow chamber,and to investigate the role of

matrine in VSMC migration under different laminar

and disturbed?uid?ows.

MATERIALS AND METHODS

Chemicals

Matrine was obtained from the National Institute

for the Control of Pharmaceutical and Biological

Products(Beijing,China),and its purity was >99%.Matrine stock solution was prepared in PBS with10mM4-(2-hydroxyethyl)piperazine-1-

ethanesulfonic acid(HEPES).Flow System and Chamber Design

The perfusion medium for all experiments consisted of Dulbecco’s modi?ed Eagle’s medium(GIBCO) supplemented with2%fetal bovine serum(GIBCO) and0.5U/mL penicillin.The?ow chambers and accompanying apparatuses were maintained at 37 C throughout the experiment.Time-matched controls consisted of slides mounted on?ow cham-bers without?ow and were performed for all exper-imental groups.

A vertical-step?ow(VSF)chamber was used as previously described.10,11Brie?y,in the test section of the VSF,the channel width(w)was80mm,the entrance height(h)was0.75mm,and the main channel height(h)was1.5mm(Fig.1).The total and entrance lengths were150mm and50mm, respectively.The Reynolds number used in the experiment was1,300,based on?ow rate and channel geometry.The disturbed?ow pattern is shown schematically in Figure1.Wall shear stress and distance to the reattachment points were predicted using Computational Fluid Dynamics package FLUENT(version6.1,Fluent Inc.,Lebanon, NH).Position‘‘a’’represents the stagnation?ow area;‘‘b’’is the area below the center of

the Fig.1.Diagram of denudation procedure under disturbed and laminar?ows.Strips of con?uent vascular smooth muscle cell(VSMC)monolayer were denuded with a cell scraper at the positions of(a)oscillating?ow-reattachment zone and(b)pulsatile laminar?ow area and were then subjected to?ow.The microscopic images were taken every7hours.The?ow direction was from left to right.The size of the vortex excursion in the oscillating ?ow-reattachment zone was w22.5mm.The size of the denuded zone was w400m m.

Vol.26,No.2,February2012Matrine inhibits disturbed?ow e enhanced migration269

recirculation eddy;‘‘c’’is the reattachment?ow area;and‘‘d’’is the area where laminar?ow has been redeveloped.The locations of areas a,b,c, and d were calculated to be about3.2,9.6,16.1, and22.5mm from the step,respectively.All exper-iments were performed at a mean?ow rate of2,700 mL/min,corresponding to a downstream laminar shear stress of10dyne/cm2.

Cell Culture

VSMCs were isolated from rat aorta.12Cells were grown in DMEM(GIBCO)containing10%calf serum(GIBCO)at37 C in a5%CO2-humidi?ed chamber.The purity of VSMC population was deter-mined by immunostaining with a-smooth muscle actin antibody.Experiments were performed on cells cultured for less than10passages.

Analysis of Migration

VSMCs were grown to con?uence on20-?80-mm ?bronectin-coated glass cover slides.A strip of VSMCs perpendicular to?ow direction was removed from the con?uent VSMC monolayer by using a cell scraper.Such denuded zones,which had a width of400±20m m(mean±standard devi-ation),were made at the position calculated to be the oscillating?ow-reattachment zone and also in the downstream laminar?ow region(Fig.1).The wounded VSMC monolayer was subjected to?ow in the step chamber for various periods.Because the width of the denuded zone(400m m)under disturbed?ow was smaller than that of the vortex excursion,the cells on both sides of the denuded zone were within the zone of oscillating disturbed ?ow.Shear stress experiments that measured migration were performed in the presence of2% FBS after incubation in serum-free media for24 hours and in the presence or absence of the selective ERK1/2pathway inhibitor PD98059(30m M) (Sigma Chemical Company,St.Louis,MO),the MLCK inhibitor ML-7(10m M)(Sigma),or at different concentrations of matrine for30minutes before and during the?ow stimulation.

Western Blot

The same cells used for aforementioned experi-ments were also used for Western blot analysis. Cells were lysed in lysis buffer containing20mM Tris-HCl(pH7.4),0.4M KCl,2mM dithiothreitol, and10%glycerol.Protein concentrations in the cell lysates were determined with bicinchoninic acid kit(Sigma Chemical Company,St.Louis, MO).Total protein lysates were separated using a sodium dodecyl sulfate polyacrylamide gel and transferred to polyvinylidene di?uoride membrane (Bio-Rad Laboratories,Hercules,CA).The blot was subsequently incubated with a primary antibody against ERK1/2(1:1,000,Santa Cruz Biotechnology,Santa Cruz,CA),phospho-ERK1/2 (1:1,000,Santa Cruz,CA),MLCK(1:1,000,Santa Cruz,CA),phospho-MLCK(1:1,000,Santa Cruz, CA),and then,a horseradish peroxidase e conju-gated secondary antibody(1:2,000,Santa Cruz, CA).The proteins were visualized using the enhanced chemiluminescence detection reagents (Roche Applied Science,Basel,Switzerland)and subsequent X-ray radiography.The densities of bands on the?lm were scanned and quanti?ed through densitometry.The results are expressed as the ratio of band intensities of cell cycle e related proteins to b-actin.All Western blot experiments were repeated at least thrice with a different cell preparation.

Statistical Analysis

The data are expressed as mean±standard deviation and analyzed using the statistical software package SPSS12.0(SPSS Inc,Chicago,IL).1-way analysis of variance was performed,and P<0.05was consid-ered to be statistically signi?cant.

RESULTS

Disturbed Flow e Promoted VSMC

Migration

To determine the effects of different?ow patterns on VSMC migration,a strip of con?uent VSMCs was removed(w400m m in width)and subjected to disturbed and laminar?ows or kept under static ?ow(control).Microscopic images were taken every7hours.The disturbed?ow enhanced VSMC migration into the denuded area,whereas laminar?ow inhibited VSMC migration as compared with the VSMCs receiving static?ow. The direction of?ow was from left to right (Fig.2A);therefore,the left side of the denuded zone is the upstream side and the right side is the downstream https://www.wendangku.net/doc/3c5134567.html,ing the DIAS software,the centroids of the cells were determined at7-hour intervals,and the net migration distance was calcu-lated from the positions of centroids.In all cases,the net migration distance increased linearly with time (Fig.2B).In the static controls and under disturbed ?ow,the migration of cells occurred from both sides, but the rate of migration of the cells was signi?-cantly increased under disturbed?ow as compared with that under static conditions.Under laminar

270Zhu et al.Annals of Vascular Surgery

?ow,the average net migration distance of the cells at the upstream edge (along the ?ow direction)was signi?cantly larger than that of the cells at the downstream edge (against the ?ow direction).

Matrine-Inhibited VSMC Migration and ERK1/2Phosphorylation

Treatment with matrine-inhibited VSMC migration under laminar ?ow,disturbed ?ow,and static condi-tions in a dose-dependent manner (Fig.3A,B).Treat-ment with the MEK1pharmacological inhibitor

PD98059(30m M)signi?cantly suppressed VSMC migration in all ?ow patterns (Fig.4A,B)as well.Disturbed ?ow signi?cantly enhanced the phos-phorylation of ERK1/2protein,whereas laminar ?ow signi?cantly inhibited phosphorylation of ERK1/2in VSMCs,as compared with the static control (Fig.4C,D).Treatment with the MEK1pharmacological inhibitor PD98059(30m M)completely inhibited the phosphorylation of ERK1/2(Fig.4C,D),and the phosphorylation of ERK1/2was also signi?cantly suppressed by matrine under disturbed ?ow,laminar ?ow and static condition (Fig.4C,

D).

Fig.2.Disturbed ?ow promoted VSMC migration.The wounded VSMC monolayers were kept under static conditions or subjected to laminar or disturbed ?ow,and the VSMC migration process was recorded at 7-hour intervals.The direction of laminar ?ow was from left to right.The left-hand side of the zone is denoted as ‘‘upstream’’side,and the right-hand side,as ‘‘downstream.’’(A )Phase-contrast images of the VSMC migration over the 21-hour period.Black vertical lines indicate the locations of wound edges at the beginning of the experiment.(B )The net migration distance as a function of time for the cells in the ?rst row at wound

edges.The centroids of the cells at the wound edges were determined,and the net migration distance into the denuded zone was calculated from the positions of the centroids.The values represent mean ±standard devia-tion (SD)from three experiments.All statistical compar-isons were made on the same side of the denuded zone with the same cell numbers.*denotes P <0.05when compared with the migration distance at the beginning of the experiment under the same ?ow condition.y denotes P <0.05when compared with static condition at the same moment.

Vol.26,No.2,February 2012Matrine inhibits disturbed ?ow e enhanced migration 271

Matrine-Inhibited Disturbed Flow e Induced Phosphorylation of MLCK in VSMCs

The phosphorylation of MLCK in VSMCs was signif-icantly increased by disturbed ?ow,but was signi?-cantly inhibited by laminar ?ow,in comparison with static control (Fig.4E,F).Complete inhibition of MLCK phosphorylation with ML-7(an inhibitor for MLCK)signi?cantly decreased VSMC migration under disturbed ?ow,laminar ?ow,and static

condition (Fig.4A,B).Treatment with PD-98059(30m M)or matrine (40mg/L)signi?cantly decreased the enhanced phosphorylation of MLCK under disturbed ?ow (Fig.4E,F).However,no synergistic inhibitory effect was observed on phos-phorylation of MLCK under different ?ow condi-tions by cotreatment with matrine (40mg/L)and PD-98059(30m M)(Fig.4E,F),only the increased inhibitory effect of matrine on VSMCs migration was shown (Fig.4A,

B).

Fig. 3.VSMCs were treated with different doses of matrine (0,10,20,30,and 40mg/L)for 30minutes before and during the experiments.Then,the wounded monolayers were kept under static conditions or were subjected to laminar or disturbed ?ow for 21hours.The direction of laminar ?ow was from left to right.(A )Phase-contrast images of the VSMC migration over the 21-hour period.Black vertical lines indicate the loca-tions of wound edges at the beginning of the experiment.(B )The net migration distance as a function of time for the cells in the ?rst row at wound edges.The centroids

of the cells at the wound edges were determined,and the net migration distance into the denuded zone was calculated from the positions of the centroids.The values represent mean ±SD from three experiments.All statis-tical comparisons were made between the same cell row number and on the same side of the denuded zone.y denotes P <0.05when compared with static condition under the same treatment.*denotes P <0.05when compared with untreated controls under the same ?ow condition.

272Zhu et al.Annals of Vascular Surgery

Vol.26,No.2,February2012Matrine inhibits disturbed?ow e enhanced migration273

DISCUSSION

The results of this study demonstrated that VSMC migration into the denuded area was modulated by different ?ow patterns.The VSMC migration rate was signi?cantly increased under disturbed ?ow compared with static conditions,but signi?-cantly decreased under laminar ?ow.The regenera-tion of the denuded VSMC monolayer may be involved in both VSMC proliferation and migration.Our data showed no signi?cant increase in VSMC proliferation during the 21-hour procedure.Thus,cell spreading and migration appeared to be the major mechanism for the in vitro VSMC wound closure in our present study.Treatment with matrine markedly inhibited VSMC migration in all ?ow patterns.

The ERK1/2signaling cascade has been shown to be a critical regulator of cell function,and its blockade could inhibit rat VSMC migration.13,14Furthermore,ERK1/2may also regulate shear stress e dependent VSMC migration in a modi?ed vein graft model.6In a three-dimensional ?ow study,interstitial ?ow induces VSMC migration in collagen I gels via an ERK1/2-dependent mecha-nism.15To verify whether ERK1/2is modulated in our model,we determined the phosphorylation levels of ERK1/2in migrated VSMCs under different ?ow conditions.Our data showed that compared with static conditions,disturbed ?ow signi?cantly increased the phosphorylation levels of ERK1/2,whereas laminar ?ow signi?cantly decreased ERK1/2phosphorylation levels.Furthermore,treat-ment with the pharmacological inhibitor PD-98059completely inhibited the activity of ERK1/2and signi?cantly suppressed VSMC migration under disturbed ?ow.Additionally,matrine could mark-edly decrease phosphorylation of ERK1/2under disturbed ?ow,an effect similar to that of PD-98059.Taken together,these data suggest that

disturbed shear stress regulates VSMC migration,at least in part,via modulation of ERK1/2activity and that matrine acts upstream of this pathway.Although the exact mechanism by which ERK1/2regulates cell migration is not fully understood,it is thought that MLCK-mediated regulation of ERK1/2signaling may be involved.A previous study showed that ERK1/2in cultured carcinoma cells can phos-phorylate MLCK,which in turn phosphorylates myosin light chain and induces actin e myosin II interactions,thereby enhancing cell migration.16To verify whether MLCK is involved in our experi-ment model,we examined the effect of MLCK inhi-bition on VSMC migration by using ML-7(an inhibitor for MLCK)and determined the effect of ERK1/2inhibition on the activity of MLCK.Our results showed that MLCK inhibition markedly sup-pressed VSMC migration under different ?ows and that inhibition of ERK1/2inhibited MLCK activity,suggesting that ERK1/2may regulate VSMC migra-tion,in part,by the modulation of MLCK in the present model.Our results also demonstrated that treatment with matrine markedly inhibited MLCK phosphorylation under different ?ows.However,the inhibitory effect of matrine on MLCK activity may be independent of ERK1/2activity,as cotreat-ment with matrine and PD-98059did not enhance the inhibitory effect of PD-98059on phosphoryla-tion of MLCK under different ?ows.After PD-98059or ML-7treatment,VSMC migration could still be observed,albeit to a much lower extent.These results suggest that factors other than ERK1/2and MLCK may also be involved in the regulation of VSMC migration.

Recently,p38mitogen-activated protein kinase (MAPK)signaling has been demonstrated to be involved in migration of VSMCs.17However,it seems that p38MAPK does not play a major role in ?ow-induced VSMC migration in a three-dimensional ?ow ?eld.15Thus,it deserves further

Fig.4.VSMCs were treated with PD98059(30m M),ML-7(10m M),or matrine (40mg/L)for 30minutes before and during the experiments.Then,the wounded monolayers were kept under static conditions or were subjected to laminar or disturbed ?ow for 10hours.The direction of laminar ?ow was from left to right.(A )Phase-contrast images of the VSMC migration over the 10-hour period.Black vertical lines indicate the locations of wound edges at the beginning of the experiment.(B )The net migration distance as a function of time for the cells in the ?rst row at wound edges.The centroids of the cells at the wound edges were determined,and the net migration distance into the denuded zone was calculated from the positions of the centroids.(C )Western blot analysis (the protein samples were collected from total cells in the ?ow chamber)of extracellular signal-regulated kinase 1/2(ERK1/2)expression (top )and phosphorylation (bottom )of ERK1/2.(D )Relative phosphorylation activity of ERK1/2.(E )Western blot analysis (the protein samples were collected from total cells in the ?ow chamber)of expression (top )and phosphorylation (bottom )of myosin light chain kinase.(F )Relative phosphorylation activity of myosin light chain kinase.The values represent mean ±SD from three experiments.All migration analyses were made on the same side of the denuded zone with the same cell numbers.y denotes P <0.05when compared with static condition under the same treatment.*denotes P <0.05when compared with untreated controls under the same ?ow condition.

=

274Zhu et al.Annals of Vascular Surgery

study whether p38MAPK plays a major role in VSMC migration in our model.

The migration of VSMCs between upstream and downstream is very different in the laminar?ow in our model;one possible reason is that the?uid ?ow impeded VSMCs in downstream from migrating towards the center.Certainly,we do not distinguish difference of phosphorylation levels of ERK1/2and MLCK of VSMCs between upstream and downstream,thus we cannot rule out that impact of direction of water?ow causes different phosphorylation levels of ERK1/2and MLCK of VSMCs between upstream and downstream. CONCLUSION

In summary,our data demonstrated that matrine ERK1/2e MLCK signaling is involved in disturbed ?ow e mediated VSMC migration.Matrine could inhibit VSMC migration under all?ow conditions, in part,by downregulation of ERK1/2e MLCK signaling,indicating a potential treatment of vascular restenosis related to shear stress.

This work was supported by the Major International(Regional) Joint Research Project(2008DFA31140,2010DFA32660) and the Guangdong Natural Science Foundation Project(10251008002000002,S2011010005836).

J.Z.,designed the study;X.P.F.,X.S.Z.,R.X.F.,S.Y.Z., R.B.W.,X.J.X.,H.L.H.,X.L.Z.,H.P.L.,and G.L.,performed research;J.M.C.and H.M.G.,analyzed data;P.Z.,wrote the manuscript;Y.F.C.,revised the manuscript. REFERENCES

1.Asakura T,Karino T.Flow patterns and spatial distribution

of atherosclerotic lesions in human coronary arteries.Circ Res1990;66:1045e66.

2.Kohler TR,Jawien A.Flow affects development of intimal

hyperplasia after arterial injury in rats.Arterioscler Thromb 1992;12:963e71.

3.Lipowsky H.Shear stress in the circulation.In:Bevan JA,

Kaley G,Rubanyi GM eds.Flow-dependent regulation of vascular function.Bethesda,MD:American Physical Society,1995.pp28e45.

4.Tada S,Tarbell JM.Interstitial?ow through the internal elastic

lamina affects shear stress on arterial smooth muscle cells.Am J Physiol Heart Circ Physiol2000;278:H1589e97.

5.Wang DM,Tarbell JM.Modeling interstitial?ow in an

artery wall allows estimation of wall shear stress on smooth muscle cells.J Biomech Eng1995;117:358e63.

6.Goldman J,Zhong L,Liu SQ.Negative regulation of vascular

smooth muscle cell migration by blood shear stress.Am J Physiol Heart Circ Physiol2007;292:H928e38.

7.Li Y,Yang Y,Fang L,et al.Anti-hepatitis activities in the

broth of Ganoderma lucidum supplemented with a Chinese herbal medicine.Am J Chin Med2006;34:341e9.

https://www.wendangku.net/doc/3c5134567.html,u FY,Chui CH,Gambari R,et al.Antiproliferative and

apoptosis-inducing activity of Brucea javanica extract on human carcinoma cells.Int J Mol Med2005;16:1157e62.

9.Gerthoffer WT.Mechanisms of vascular smooth muscle cell

migration.Circ Res2007;100:607e21.

10.Chiu JJ,Chen CN,Lee PL,et al.Analysis of the effect of

disturbed?ow on monocytic adhesion to endothelial cells.

J Biomech2003;36:1883e95.

11.Chiu JJ,Wang DL,Chien S,et al.Effects of disturbed?ow

on endothelial cells.J Biomech Eng1998;120:2e8.

12.Ross R,Glomset J,Kariva B,et al.A platelet-dependent

serum factor that stimulates the proliferation of arterial smooth muscle cells in vitro.Proc Natl Acad Sci USA 1974;7:1207e10.

13.Graf K,Xi XP,Yang D,et al.Mitogen-activated protein

kinase activation is involved in platelet-derived growth factor-directed migration by vascular smooth muscle cells.

Hypertension1997;29:334e9.

14.Shi ZD,Tarbell JM.Fluid?ow mechanotransduction in

vascular smooth muscle cells and?broblasts.Ann Biomed Eng2011;39:1608e19.

15.Shi ZD,Ji XY,Berardi DE,et al.Interstitial?ow induces MMP-

1expression and vascular SMC migration in collagen I gels via an ERK1/2-dependent and c-Jun-mediated mechanism.Am J Physiol Heart Circ Physiol2010;298:H127e35.

16.Klemke RL,Cai S,Giannini AL,et al.Regulation of cell

motility by mitogen-activated protein kinase.J Cell Biol 1997;137:481e92.

17.Mugabe BE,Yaghini FA,Song CY,et al.Angiotensin

II-induced migration of vascular smooth muscle cells is mediated by p38mitogen-activated protein kinase-activated c-Src through spleen tyrosine kinase and epidermal growth factor receptor transactivation.J Pharma-col Exp Ther2010;332:116e24.

Vol.26,No.2,February2012Matrine inhibits disturbed?ow e enhanced migration275

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Tensorflow笔记：第七讲 卷积神经网络 本节目标：学会使用CNN实现对手写数字的识别。 7.1 √全连接NN：每个神经元与前后相邻层的每一个神经元都有连接关系，输入是特征，输出为预测的结果。 参数个数：∑（前层×后层+后层） 一张分辨率仅仅是28x28的黑白图像，就有近40万个待优化的参数。现实生活中高分辨率的彩色图像，像素点更多，且为红绿蓝三通道信息。 待优化的参数过多，容易导致模型过拟合。为避免这种现象，实际应用中一般不会将原始图片直接喂入全连接网络。 √在实际应用中，会先对原始图像进行特征提取，把提取到的特征喂给全连接网络，再让全连接网络计算出分类评估值。

例：先将此图进行多次特征提取，再把提取后的计算机可读特征喂给全连接网络。 √卷积Convolutional 卷积是一种有效提取图片特征的方法。一般用一个正方形卷积核，遍历图片上的每一个像素点。图片与卷积核重合区域内相对应的每一个像素值乘卷积核内相对应点的权重，然后求和，再加上偏置后，最后得到输出图片中的一个像素值。 例：上面是5x5x1的灰度图片，1表示单通道，5x5表示分辨率，共有5行5列个灰度值。若用一个3x3x1的卷积核对此5x5x1的灰度图片进行卷积，偏置项

b=1，则求卷积的计算是：(-1)x1+0x0+1x2+(-1)x5+0x4+1x2+(-1)x3+0x4+1x5+1=1（注意不要忘记加偏置1）。 输出图片边长=（输入图片边长–卷积核长+1）/步长，此图为：（5 – 3 + 1）/ 1 = 3，输出图片是3x3的分辨率，用了1个卷积核，输出深度是1，最后输出的是3x3x1的图片。 √全零填充Padding 有时会在输入图片周围进行全零填充，这样可以保证输出图片的尺寸和输入图片一致。 例：在前面5x5x1的图片周围进行全零填充，可使输出图片仍保持5x5x1的维度。这个全零填充的过程叫做padding。 输出数据体的尺寸=(W?F+2P)/S+1 W：输入数据体尺寸，F：卷积层中神经元感知域，S：步长，P：零填充的数量。 例：输入是7×7，滤波器是3×3，步长为1，填充为0，那么就能得到一个5×5的输出。如果步长为2，输出就是3×3。 如果输入量是32x32x3，核是5x5x3，不用全零填充，输出是（32-5+1）/1=28，如果要让输出量保持在32x32x3，可以对该层加一个大小为2的零填充。可以根据需求计算出需要填充几层零。32=（32-5+2P）/1 +1，计算出P=2，即需填充2

常用函数 类参考

全局函数1、common.func.php 公用函数 获得当前的脚本网址 function GetCurUrl() 返回格林威治标准时间 function MyDate($format='Y-m-d H:i:s',$timest=0) 把全角数字转为半角 function GetAlabNum($fnum) 把含HTML的内容转为纯text function Html2Text($str,$r=0) 把文本转HTML function Text2Html($txt) 输出Ajax头 function AjaxHead() 中文截取2，单字节截取模式 function cn_substr($str,$slen,$startdd=0) 把标准时间转为Unix时间戳 function GetMkTime($dtime) 获得一个0000-00-00 00:00:00 标准格式的时间 function GetDateTimeMk($mktime) 获得一个0000-00-00 标准格式的日期 function GetDateMk($mktime) 获得用户IP function GetIP() 获取拼音以gbk编码为准 function GetPinyin($str,$ishead=0,$isclose=1)

dedecms通用消息提示框 function ShowMsg($msg,$gourl,$onlymsg=0,$limittime=0) 保存一个cookie function PutCookie($key,$value,$kptime=0,$pa="/") 删除一个cookie function DropCookie($key) 获取cookie function GetCookie($key) 获取验证码 function GetCkVdValue() 过滤前台用户输入的文本内容 // $rptype = 0 表示仅替换html标记 // $rptype = 1 表示替换html标记同时去除连续空白字符// $rptype = 2 表示替换html标记同时去除所有空白字符// $rptype = -1 表示仅替换html危险的标记 function HtmlReplace($str,$rptype=0) 获得某文档的所有tag function GetTags($aid) 过滤用于搜索的字符串 function FilterSearch($keyword) 处理禁用HTML但允许换行的内容 function TrimMsg($msg) 获取单篇文档信息 function GetOneArchive($aid)

有限元网格划分

有限元网格划分 摘要:总结近十年有限元网格划分技术发展状况。首先,研究和分析有限元网格划分的基本原则；其次,对当前典型网格划分方法进行科学地分类,结合实例,系统地分析各种网格划分方法的机理、特点及其适用范围,如映射法、基于栅格法、节点连元法、拓扑分解法、几何分解法和扫描法等；再次,阐述当前网格划分的研究热点,综述六面体网格和曲面网格划分技术；最后,展望有限元网格划分的发展趋势。 关键词:有限元网格划分；映射法；节点连元法;拓扑分解法；几何分解法；扫描法；六面体网格 1 引言 有限元网格划分是进行有限元数值模拟分析至关重要的一步，它直接影响着后续数值计算分析结果的精确性。网格划分涉及单元的形状及其拓扑类型、单元类型、网格生成器的选择、网格的密度、单元的编号以及几何体素。在有限元数值求解中，单元的等效节点力、刚度矩阵、质量矩阵等均用数值积分生成，连续体单元以及壳、板、梁单元的面内均采用高斯（Gauss）积分，而壳、板、梁单元的厚度方向采用辛普生（Simpson）积分。 2 有限元网格划分的基本原则 有限元方法的基本思想是将结构离散化,即对连续体进行离散化,利用简化几何单元来近似逼近连续体,然后根据变形协调条件综合求解。所以有限元网格的划分一方面要考虑对各物体几何形状的准确描述,另一方面也要考虑变形梯度的准确描述。为正确、合理地建立有限元模型,这里介绍划分网格时应考虑的一些基本原则。 2.1 网格数量 网格数量直接影响计算精度和计算时耗,网格数量增加会提高计

算精度,但同时计算时耗也会增加。当网格数量较少时增加网格，计算精度可明显提高,但计算时耗不会有明显增加;当网格数量增加到一定程度后,再继续增加网格时精度提高就很小,而计算时耗却大幅度增加。所以在确定网格数量时应权衡这两个因素综合考虑。 2.2 网格密度 为了适应应力等计算数据的分布特点,在结构不同部位需要采用大小不同的网格。在孔的附近有集中应力,因此网格需要加密;周边应力梯度相对较小,网格划分较稀。由此反映了疏密不同的网格划分原则:在计算数据变化梯度较大的部位,为了较好地反映数据变化规律,需要采用比较密集的网格;而在计算数据变化梯度较小的部位,为减小模型规模,网格则应相对稀疏。 2.3 单元阶次 单元阶次与有限元的计算精度有着密切的关联,单元一般具有线性、二次和三次等形式,其中二次和三次形式的单元称为高阶单元。高阶单元的曲线或曲面边界能够更好地逼近结构的曲线和曲面边界,且高次插值函数可更高精度地逼近复杂场函数,所以增加单元阶次可提高计算精度。但增加单元阶次的同时网格的节点数也会随之增加,在网格数量相同的情况下由高阶单元组成的模型规模相对较大,因此在使用时应权衡考虑计算精度和时耗。 2.4 单元形状 网格单元形状的好坏对计算精度有着很大的影响,单元形状太差的网格甚至会中止计算。单元形状评价一般有以下几个指标: (1)单元的边长比、面积比或体积比以正三角形、正四面体、正六面体为参考基准。 (2)扭曲度:单元面内的扭转和面外的翘曲程度。 (3)节点编号:节点编号对于求解过程中总刚矩阵的带宽和波前因数有较大的影响,从而影响计算时耗和存储容量的大小 2.5 单元协调性 单元协调是指单元上的力和力矩能够通过节点传递给相邻单元。为保证单元协调,必须满足的条件是: (1)一个单元的节点必须同时也是相邻点,而不应是内点或边界

人工智能实践：Tensorflow笔记 北京大学 4 第四讲神经网络优化 (4.6.1) 助教的Tenso

Tensorflow笔记：第四讲 神经网络优化 4.1 √神经元模型：用数学公式表示为：f(∑i x i w i+b)，f为激活函数。神经网络是以神经元为基本单元构成的。 √激活函数：引入非线性激活因素，提高模型的表达力。 常用的激活函数有relu、sigmoid、tanh等。 ①激活函数relu: 在Tensorflow中，用tf.nn.relu()表示 r elu()数学表达式 relu()数学图形 ②激活函数sigmoid：在Tensorflow中，用tf.nn.sigmoid()表示 sigmoid ()数学表达式 sigmoid()数学图形 ③激活函数tanh：在Tensorflow中，用tf.nn.tanh()表示 tanh()数学表达式 tanh()数学图形 √神经网络的复杂度：可用神经网络的层数和神经网络中待优化参数个数表示 √神经网路的层数：一般不计入输入层，层数 = n个隐藏层 + 1个输出层

√神经网路待优化的参数：神经网络中所有参数w 的个数 + 所有参数b 的个数 例如： 输入层 隐藏层 输出层 在该神经网络中，包含1个输入层、1个隐藏层和1个输出层，该神经网络的层数为2层。 在该神经网络中，参数的个数是所有参数w 的个数加上所有参数b 的总数，第一层参数用三行四列的二阶张量表示（即12个线上的权重w ）再加上4个偏置b ；第二层参数是四行两列的二阶张量（）即8个线上的权重w ）再加上2个偏置b 。总参数 = 3*4+4 + 4*2+2 = 26。 √损失函数（loss ）：用来表示预测值（y ）与已知答案（y_）的差距。在训练神经网络时，通过不断改变神经网络中所有参数，使损失函数不断减小，从而训练出更高准确率的神经网络模型。 √常用的损失函数有均方误差、自定义和交叉熵等。 √均方误差mse ：n 个样本的预测值y 与已知答案y_之差的平方和，再求平均值。 MSE(y_, y) = ?i=1n (y?y_) 2n 在Tensorflow 中用loss_mse = tf.reduce_mean(tf.square(y_ - y)) 例如： 预测酸奶日销量y ，x1和x2是影响日销量的两个因素。 应提前采集的数据有：一段时间内，每日的x1因素、x2因素和销量y_。采集的数据尽量多。 在本例中用销量预测产量，最优的产量应该等于销量。由于目前没有数据集，所以拟造了一套数据集。利用Tensorflow 中函数随机生成 x1、 x2，制造标准答案y_ = x1 + x2，为了更真实，求和后还加了正负0.05的随机噪声。 我们把这套自制的数据集喂入神经网络，构建一个一层的神经网络，拟合预测酸奶日销量的函数。

有限元网格划分和收敛性

一、基本有限元网格概念 1．单元概述?几何体划分网格之前需要确定单元类型.单元类型的选择应该根据分析类型、形状特征、计算数据特点、精度要求和计算的硬件条件等因素综合考虑。为适应特殊的分析对象和边界条件,一些问题需要采用多种单元进行组合建模。? 2.单元分类选择单元首先需要明确单元的类型，在结构有限元分析中主要有以下一些单元类型：平面应力单元、平面应变单元、轴对称实体单元、空间实体单元、板单元、壳单元、轴对称壳单元、杆单元、梁单元、弹簧单元、间隙单元、质量单元、摩擦单元、刚体单元和约束单元等。根据不同的分类方法,上述单元可以分成以下不同的形式。?3。按照维度进行单元分类 根据单元的维数特征，单元可以分为一维单元、二维单元和三维单元。?一维单元的网格为一条直线或者曲线。直线表示由两个节点确定的线性单元。曲线代表由两个以上的节点确定的高次单元,或者由具有确定形状的线性单元。杆单元、梁单元和轴对称壳单元属于一维单元,如图1~图3所示。 ?二维单元的网 格是一个平面或者曲面，它没有厚度方向的尺寸.这类单元包括平面单元、轴对称实体单元、板单元、壳单元和复合材料壳单元等,如图4所示。二维单元的形状通常具有三角形和四边形两种，在使用自动网格剖分时,这类单元要求的几何形状是表面模型或者实体模型的边界面。采用薄壳单元通常具有相当好的计算效率。

??三维单元的网格具有空间三个方向的尺寸，其形状具有四面体、五面体和六面体,这类单元包括空间实体单元和厚壳单元，如图5所示．在自动网格划分时，它要求的是几何模型是实体模型(厚壳单元是曲面也可以）。 ? 4.按照插值函数进行单元分类 根据单元插值函数多项式的最高阶数多少，单元可以分为线性单元、二次单元、三次单元和更高次的单元。 线性单元具有线性形式的插值函数,其网格通常只具有角节点而无边节点，网格边界为直线或者平面.这类单元的优点是节点数量少，在精度要求不高或者结果数据梯度不太大的情况下，采用线性单元可以得到较小的模型规模.但是由于单元位移函数是线性的，单元内的位移呈线性变化,而应力是常数,因此会造成单元间的应力不连续,单元边界上存在着应力突变，如图6所示。

比较PageRank算法和HITS算法的优缺点

题目：请比较PageRank算法和HITS算法的优缺点，除此之外，请再介绍2种用于搜索引擎检索结果的排序算法，并举例说明。 答： 1998年，Sergey Brin和Lawrence Page[1]提出了PageRank算法。该算法基于“从许多优质的网页链接过来的网页，必定还是优质网页”的回归关系，来判定网页的重要性。该算法认为从网页A导向网页B的链接可以看作是页面A对页面B的支持投票，根据这个投票数来判断页面的重要性。当然，不仅仅只看投票数，还要对投票的页面进行重要性分析，越是重要的页面所投票的评价也就越高。根据这样的分析，得到了高评价的重要页面会被给予较高的PageRank值，在检索结果内的名次也会提高。PageRank是基于对“使用复杂的算法而得到的链接构造”的分析，从而得出的各网页本身的特性。 HITS 算法是由康奈尔大学( Cornell University ) 的JonKleinberg 博士于1998 年首先提出。Kleinberg认为既然搜索是开始于用户的检索提问，那么每个页面的重要性也就依赖于用户的检索提问。他将用户检索提问分为如下三种：特指主题检索提问（specific queries，也称窄主题检索提问）、泛指主题检索提问（Broad-topic queries，也称宽主题检索提问）和相似网页检索提问（Similar-page queries）。HITS 算法专注于改善泛指主题检索的结果。 Kleinberg将网页（或网站）分为两类，即hubs和authorities，而且每个页面也有两个级别，即hubs（中心级别）和authorities（权威级别）。Authorities 是具有较高价值的网页，依赖于指向它的页面；hubs为指向较多authorities的网页，依赖于它指向的页面。HITS算法的目标就是通过迭代计算得到针对某个检索提问的排名最高的authority的网页。 通常HITS算法是作用在一定范围的，例如一个以程序开发为主题的网页，指向另一个以程序开发为主题的网页，则另一个网页的重要性就可能比较高，但是指向另一个购物类的网页则不一定。在限定范围之后根据网页的出度和入度建立一个矩阵，通过矩阵的迭代运算和定义收敛的阈值不断对两个向量authority 和hub值进行更新直至收敛。 从上面的分析可见，PageRank算法和HITS算法都是基于链接分析的搜索引擎排序算法，并且在算法中两者都利用了特征向量作为理论基础和收敛性依据。

数据库常用函数

数据库常用函数

一、基础 1、说明：创建数据库 CREATE DATABASE database-name 2、说明：删除数据库 drop database dbname 3、说明：备份和还原 备份：exp dsscount/sa@dsscount owner=dsscount file=C:\dsscount_data_backup\dsscount.dmp log=C:\dsscount_data_backup\outputa.log 还原：imp dsscount/sa@dsscount file=C:\dsscount_data_backup\dsscount.dmp full=y ignore=y log=C:\dsscount_data_backup\dsscount.log statistics=none 4、说明：创建新表 create table tabname(col1 type1 [not null] [primary key],col2 type2 [not null],..) CREATE TABLE ceshi(id INT not null identity(1,1) PRIMARY KEY,NAME VARCHAR(50),age INT) id为主键，不为空，自增长 根据已有的表创建新表： A：create table tab_new like tab_old (使用旧表创建新表) B：create table tab_new as select col1,col2… from tab_old definition only 5、说明：删除新表 drop table tabname 6、说明：增加一个列 Alter table tabname add column col type 注：列增加后将不能删除。DB2中列加上后数据类型也不能改变，唯一能改变的是增加varchar类型的长度。 7、说明：添加主键： Alter table tabname add primary key(col) 说明：删除主键： Alter table tabname drop primary key(col) 8、说明：创建索引：create [unique] index idxname on tabname(col….) 删除索引：drop index idxname 注：索引是不可更改的，想更改必须删除重新建。 9、说明：创建视图：create view viewname as select statement 删除视图：drop view viewname 10、说明：几个简单的基本的sql语句 选择：select * from table1 where 范围 插入：insert into table1(field1,field2) values(value1,value2) 删除：delete from table1 where 范围 更新：update table1 set field1=value1 where 范围

ANSYS有限元网格划分的基本要点

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