An Exploration of Dynamics of the Moving Mechanism of the Growth Cone

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1 Molecules olecules ISSN hp:// Invie Lecue An Eploion of Dnics of he Movin Mechnis of he owh Cone Ruin Wn Hsuo Hshi 3 Zhin Zhn 4 n un-bo Dun 5 School of Science Donhu Univesi 88 Wes n-an Ro Shnhi 5 Chin Insiue fo Copuionl Science n Enineein Ocen Univesi of Chin Shnon 663 Chin 3 Depen of Bin Science n Enineein ue School of Life Science n Sses Enineein Kushu Insiue of Technolo Wsu-Ku Kiushu Jpn 4 Shnhi Telecounicion Copoion Shnhi 9 Chin 5 Depen of hsics n Asono The Univesi of Biish Colui Vncouve BC V6T Z Cn Asc: A sochsic nonline nic oel is popose o eplin he owh cone he ip of cell pocess such s owin on o enie of neuon. The oel eplins he ouw oion of he ip s n eension of he eleon u he cin-o sse s olecul oo. The ineic ene is supplie he fo AT holsis in he fo of no oion of we olecules eein he cin-o. The echnicl sucue is povie he -cin coolecules foin spil filen. The o hes fo sochsic isiuion of sll sphees. The e che elsic spins o he spil os of he o filens. Une hel iion he sse sus oscillion which is iece he inecion eween he o hes n he cin filen. As he ene of oscillion is issipe he cin filen is ove ow he cene of he owh cone. The join poili ensi of oveen of he cin filen is oine solvin non-sion vesion of he K equion. B incopoin poili isiuion of cin filens povie he eoe of he ip he iece oion of he ip is epline.

2 Molecules Kewos: Acin-o sse he owh cone no noise n issipion sochsic elsic collision he join poili ensi he non-sion K equion.. Inoucion I is ipon o unesn he echnis of oion of he owh cone he ip of n on in oe o eplin how i is ccuel iece o is es in he foion of funcionl neul newos. The vious echniss of oveen of he owh cone hve een iscusse [-6 which incopoe he heo of olecul cluch n slie in he cin-o sse [ Howeve he souce of he ineic ene fo oion eins unepline. In his epo novel heo is popose which he equie ene is povie hel ene fo he holsis of AT. The popose oel incopoes he well ocuene oel of he cin-o sse [9. The cin n o olecules uneo no oen we olecules. Owin o he elsic popeies of he helicl connecions of he o olecules he sse vies. The isiuion of he iecion of oscillo oion is uie he newo of cin filens une he enclo ene of he on ip [ 3. The hel ene seves o epn he cene of he owh cone. I follows h he cin-o echnis is issipive non-equiliiu sse feein on hel ene n h he join poili ensi is funcion of he isiuions of isplceen n veloci of he olecules. The iecion en he owh cone cn e oine solvin he oe-lnc equion [9.. This oel eplins he ouw hus of he on ip n he consicion in he iee of he shf. Secion suizes he cin-o oel. Secion 3 escies he echnis fo hnes hel ene o viions n escies he echnis o focus he oion ino he hus of he pe of he owh cone. Secion 4 ives he conclusions n iscusses he poles clifie he oel fo fuue su.. Mechnicl oel of he cin-o sse In his ppe ccoin o he heo of olecul chines of he livin cell we pesen new ie n new nonline echnicl oel h cn e use o escie wh he owh cone cn inuc he ech of neuonl slience in poilisic sense. In ohe wos wh foces n coniions cn occu he en of on n he enie o pefo oveen. In he olecul ioloicl sense he oel oiines fo he cin-o sse s clss of olecul oos n he ene of oion of he sse is supplie fo he no noise of we olecules enee houh he ene of AT holsis. The sucue of he oel is copose of he elsic colliin spheicl shpes se posses spil sucue h is of he cin filen he o hes n he spins nec se posses elsic pope h is of hes of he AT

3 Molecules enze n he -helicl os of he o. The oel pesene in he ppe is suppoe - iffcion pens [9. In n open n non-equiliiu sse ue o he inecion n he no collision on he cin olecules n he o olecules une no hel noise ll he cin filens possess ovin enenc lone he iecion of he owh cone in sense of he poilisic sisics. In his poceue he o sses cn wo fo olecules of he cin houh consuin he pil ene of viion n he esul ouses he cin filen is ove n is epn o he ne of cene of owh cone. I is follows h he cin-o sse is jus in of issipive non-equiliiu sse. The ehvio poceue inuces he nsfoion of he ineolecul ene of viion o he ineolecul ene of nslionl oion in i insnnei ue o he specil locion of newo of he cin filen foe une eeio ene of he on [3. In oe o unesn he echnis of oveen of he owh cone echnicl oel on he cin-o sse une he no noise of we olecules enee houh he ene of AT holsis is iven in he iue. Noe h his iinive fiue is ploe in cconce wih he olecul sucue of he cin-o sse. -cin Mo he -o of helicl iue. The iin of he cin-o sse. In iue we onl escie he le sie of he echnicl oel of he olecul sses ue o he cin-o sse o e seicl sucue. Alhouh he ssuin of he soe of oin isplceen of he o fo he cin filen is hee oele o he sochsic elsic collie foce h inuce he oveen of he cin filen u he echnicl effec oine in his oel is in coplee cconce wih he soe of oion of he -helicl o pesene in efeences [9-. As e no evience cn eonse isiuion of he o he in efeence [9. Hence we cn no ive n epolion which poin ou he foce of collision pouce on he o hes n he cin filen o e counec ech ohe ecuse of he sochsic isiuion of he o hes whees - cslloph eonse h he clic nle eween he

4 Molecules o he n he cin filen is ou 45 nle iven in iue n he clic nle is pefoe sll flucue oun ou 45 nle even if he clic nle cn in he sochsic iffusion une he no noise. The foce of collision pouce lon wih he iecion ou 45 nle cuse he oveen of he cin filen. This poin is h we eslish he ses of he ove echnicl oel. In he elow hee is fiue on - cslloph wih espec of clic nle eween he o he n he cin filen iven in efeences [9. iue. A oel of he coo cople illuses how he specopic esuls escie Be e l [. Copih 998 Nionl Ace of Sciences U.S.A." In his fiue he cin filen is shownin puple on he lef. The clic oin of he o he shown in e ches iil o he cin filen wih is lih chin oin eenin own ou 45 nle. The wo lih chins h help fo his oin e shown in whie n cn wih he specopic lel of Be e l. che o he le. The lih chin oin is lso shown in secon oienion in lue oe upw ppoiel 36 o siule he einnin of he powe soe suese he esuls ofbe e l.. The powe soe woul consis of oion of his oin fo he uppe posiion o he lowe. This oion woul pull he ehe h connecs he o he o he hic filen own ou 5 n. The posiion of he ehe is epice scheicll he hic lc veicl lines [9. Hee is cie in he inepeion in efeence [9 on he cin-o sse. The inecion of he -cin n o hes is coonl oseve in hee ses: In io-i.e. io ois-he se oine in he sence of AT ll o hes e oun iil o cin in confiuion houh o esele h foun he en of he powe soe; In elion o hes e

5 Molecules lel eche fo cin n e oun in helicl oun he hic filen o e isoee n no oun o eihe filen; 3 In uscle he o hes e uneoin cclic inecion wih cin poucin foce. Copin iues n he echnicl oel eslishe in iue cn e eee o e copleel coec. 3. The echnis of viion n he hus of he pe of he owh cone o he se of convenience he cin-o sses e en ino ccoun s wo lls posses ech he cene of ss oele in he iue 3. In his fiue in ino ccoun he oienion is of in collision s fiucil is lon he oienion of his fiucil is pefoin he pllel nsfoion he is of cooine in espec wih he o n he -cin cn e oine une he se of locion of equiliiu. Oienion is The locion of collision The iecion of coposiion of foces of o he The iecion of coposiion of foces of -cin θ ξ The nlsis foce on he -cin efoe collision The nlsis foce on he o he efoe collision iue 3. The nlsis foce in he cin-o sse.

6 Molecules icull he oion equion on he cene of ss of he cin filen is concene wih sep oveen of he cin filen une he cion of collision of he o he. In ohe wos he cene of ss o f he cin filen is coninuousl pefoe in w of he oveen of sep sep une he join cion of he sochsic n he coposiion foces. In sho ccoin o he ioloicl sense he cin filen n o he cn e lws collie lhouh he e siplifie o ech cenes of he ss. This inepeion is ve ipon fo unesnin of he iue 3 siplifie he iue. o he se of siplici he oion occue in he cin h is collie he o he is no consiee in he ove echnicl oel. In ohe wos on he nlsis of foce in iue 3 we onl show he collision eween he wo sses in he sse. Accoin o iue 3 we ive he oion equions efoe collision n cion ie of collision fo he wo sses. In hee he oion equion of he cene of ss of he ll o hes efoe collision is iven θ θ θ θ whee sols n enoe he viscous coefficien n he spin consn especivel. An e he ol ss of he o hes n he cin filen especivel. n e he consn of viion n he viionl cceleion θ enoes he nle eween he iecion of oion of he o he n he viion n is he nle eween he vi of he o he n is n enoes he cive isn eween cenes of wo sses i is funcion of ie. In iue 3 he ve. The equion of oion of he cene of ss of o hes in he cion ie of collision is iven 3 4 whee enoes he sochsic foces h is oele he us whie noise which is el-coele wih zeo en vlue [6: 5 τ δ 6 τ Sol enoes he coefficien of he sochsic foce. The oion equion of he cene of ss of he cin filen efoe collision is iven θ θ 7 θ θ 8

7 Molecules whee is he sochsic foce which is oele he us whie noise which is el-coele wih zeo en vlue [6: 9 τ τ δ Noe h n e wo uul inepenen sochsic foces so. The equion of oion of he cene of ss of he cin filen in he cion ie of collision is iven whee θ {[ R R } θ 3 R 4 whee sol R enoes he isn fo he lncele locion of he o he o he cene of ss of he cin filen n is he isn eween cenes of he wo sses he insnneous of collision. Accoin o he ove oion equions we oin he followin he Io s sochsic iffeenil equion on he cin-filen sse D B 5 whee enoes Winne pocess. In hee he fo of i of ech vico in equion 5 in collision is iven B D 6 Susiuin equion 6 ino equion 5 iels

8 Molecules Le he join poili ensi of collision is 8 Then he K equion coesponin o equion 7 is iven [ { [ [ } [ [ 9 We cn no oin he soluion of close fo of he join poili ensi fo non-sion K equion. Howeve when he pees e eeine one cn solve he K equion ens of nueicl eho. This wo will pefo in he fuue. The soluion of he K equion 9 shows he poili ensi of chne of ovin se on he -cin une he sochsic elsic collision. In iue 4 we cn fil see he chne of he ovin iecion of he -cin in collision. The oion lon he iecion of coposiion of foce is shown in e line on he -cin. The nle eween he e line n he hoizonl line is jus he clic nle eween he -cin n he o he in soe shown iue 4. In ohe wos he nle of collision is ou 45 nle n he clic nle is los pefoe sll flucuin oun ou 45 nle ue o he influence of he sochsic noise. The ovin chnes of pouce lon his iecion of coposiion of foce cuses he oveen of he cin filen. This esul shows h he echnicl oel ssue in iue n iue 3 s well s he echnicl nlsis pefoe is

9 Molecules ve effecive. The iecion of coposiion of foce of he o hes The iecion of coposiion of foce of he -cin efoe collision The ovin iecion of he -cin in collision θ θ iue 4. The se of collision on he cin-o sse. The fo of i of ech vico in equion 5 efoe collision is iven B 4 3 D n whee θ θ θ θ

10 Molecules θ θ 3 θ θ 4 Susiuin equion ino equion 5 iels 4 3 Le he join poili ensi efoe collision is Then he K equion coesponin o equion is iven [ { 3 [ [ [ 4 [ } 3 Siill he soluion of he close fo cn e no oine fo equion 3 when he pees e eeine we cn solve he K equion 3 ens of nueicl eho. This wo will lso pefo in he fuue. The soluion of he K equion 3 shows he poili ensi of ovin en on he -cin efoe collision o fe collision. This soluion is he coniion of iniilizion of equion 9 in ohe wos he soluion of equion 9 is he coniion of iniilizion of equion 3 nel soluions of equions 9 n 3 e ech ohe s he coniion of iniilizion. Thee eis n -cins he lellipoi of he owh cone he inecion on he -cin n he o in he lellipoi n filopoi cn pouces echnicl foce h pushe he

11 Molecules cin ino he ne of cene of he owh cone ccoin o he ove nlsis we now h his echnicl foce is jus he foce of sochsic collision in he sisic sense. Une cion of he foce of sochsic collision he owh cone possesses oivi of he epnse o he consicion. 4. Concluin es In his ppe new nonline echnicl oel hs een popose fo he echnis of oveen of he cin-o sse. This oel cn e use o inepeion he nic echnis of he cin-o sse. Due o he oveen of he cin-o o e pefoe in suounin of he no hel noise we use he poili ensi funcion o escie ehviol poceue of he nic sse o e oe esonle. The soluions of he join poili ensi funcion of he K equion 9 cn e use o escie he chne of ovin se on he -cin une he sochsic elsic collision. The soluions of he join poili ensi funcion of he K equion cn e use escie he ovin enenc on he -cin efoe collision o fe collision. Alhouh he nueicl esuls on he K equions hve een no pefoe u he clic nle oine une coniion of collision ees sicll wih he esul oseve - iffcion pens. Theefoe he echnicl oel pesene in his ppe is sisfco. Due o he oion of he -cin o eeine he oveen of he owh cone in le oun n he lellipoi of he owh cone eiss he newo foe n -cin so he oion of he owh cone n he oveen of he -cin is uul honious ecepion he ehviol poceue of he cin epoleizion n he cin poleizion. The echnicl echnis of ovin honious is he sochsic collie foce n he no foce fo hel noise. I follows h we cn oin he conclusion h he ech n consicion of he owh cone possess noness. Acnowleens This wo ws suppoe he Nionl Nul Science ounion of Chin NSC Nue: Refeences. Levin I. B.; Kcze L.KThe Neuon Cell n Molecul Biolo. Ofo Univesi ess Inc.: New o997.. Nicholls J..; Min A. R.; Wllce B.. o Neuon n Bin. A Cellul n Molecul Appoch o he uncion of he Nevous Sse. SINAUER Chen. Z. Molecul Neuonl Biolo The Sueon ulishe of Deos McAllise A. KConseve cues fo on n enie owh in he evelopin coe. Neuon 33-4.

12 Molecules u T. W.; Bnn C.I. Dnic eulion of on uince. N Neuosci. Nov 4 Suppl Acees A.; uus A. Cellul n olecul feues of on collels n enies. Tens Neuosci. Nov Hule A..; Sions R.M. Nue VnBuen.; Wlle. S.; His D. E.; Tus K. M.: Wshw D. M.; Lowe S. The essenil lih chin is equie fo full foce poucion selel uscle o. oc. Nl. Ac. Sci. USA Roe Cooe. New nle on o. oc. Nl. Ac. Sci.. USA ni T. ; Iwne A.H. A le sep fo o. oc. Nl. Ac. Sci. USA Be J.E.; Bus-Msche I.; Rchnn S.; Lcone L. E. W.; Thos D. D. oc. Nl. Ac. Sci USA Seffen W.; Sih D.; Sions R.; Sleep J. Mppin he cin filen wih o. oc. Nl. Ac. Sci. USA MDI hp:// Repoucion is peie fo noncoecil puposes.