Theory of coupled electromagnetic circuits, the connection to quantum mechanical resonance interactions and relevance to chronobiology

Transcription

1 Theo of coupled elecogec ccus he coeco o uu echcl esoce ecos d elevce o choobolog W. Ule Gee Coelsse Fz Hlbeg d Ohld Schwzopff Klu üche-psg ep. of Rdo Ocolog d PI of Phscs Göge Uves of eso epols N US bsc The esece of specfc bohhs d he ole of geogec do sol gec cves e well-esblshed b ppope coelos choobolog. Fo phscl vewpo hee e wo dffee ccesses o bohhs o se up coecos o olecul pocesses:. ffuso of chged olecules gec felds.. uu echcl peubo heoecl ehods d he esoce doos o chceze specfc ecos bewee cosues. The ehods of po pe he ee of olecul pocesses b ccus wh chcesc esoces d befeueces whch esul fo he pl fs phscl pocesses. s eples he uelg pocesses bewee N bse ps H bods d he TP decoposo e cosdeed.. Ioduco The descpo of olecul pocesses d he eegchge spo bewee olecules s echcl d oe posg eleccl oscllos hs log hso H d Süe 95 Ule 98. Thus olecule o ecg olecules v H bod copog echge of poos c be egded s ce chge dsbuo of pope cpcces whees ce olecul chges of he cofguos e coeced b cues. I he el uu echcs Hesebeg used clculos of cues o e sos bewee goud d eced ses of os o epl specl popees of he. These sos usull e ve fs pocesses he lfee of eced sgle ses ous o -7 sec; ol he lfee of eced ple ses ves fo - sec o ues d hous. The oscllos of bewee olecule ses IR spec e uch slowe usull fco - -4 coped o sgle ecos bu sll he fs coped o soe bohhs cells. I ppes h he bsc pcple of coupled elecc oscllos s lso useful o sud phsologcl pocesses fo esos: I s possble o egd cells s cople sses of chged lessucues d ll boolecules e usull hghl chged os.e. ulpoles. The s coseuece o cosde cellul sses s vous dffee chge dsbuos cpcces d cues duced b chge sfe v H bods o ohe olecul defoos. Ths coeco dces h he og of bochecl esoces s of uu echcl ue sce ol hs ool c deee olecul popees d esoce ecos. I ece e he develope of olecul elecocs

2 ppes o be ve ousdg devse Ce 98 Cpbell d Pe 98 Rdhw e l. fuhe eesg feue s he sud of bohhs. I s oe gol of hs sud o show h bohhs esul fo ve coplced couplgs of elecogec oscllos d b splg of esoce feueces. h we ob fs oscllos d ddo oe o wo feueces whch e ve slow. I ce sese hs esul be egded s supeposo of bes o fs oscllo feueces. led wo coupled elecc oscllos e suffce o sud such odel.. ehods Theoecl p.. eoos bbevos d bsc euos I he followg we e use of he defos: : ducvce; C: cpcce; : uul ducvce bewee wo soleods; U: volge; : elecc chge he cpcce; dd: elecc cue he soleod; : secod e devve; dces efe o he eled oscllo ube. The bsc euo of ll elecogec pocesses s he followg euo: U ducvce U cpcce fuhe bsc euo s he cosdeo of oe elecc oscllo wh d C Fgue. Fo euo d Fgue follows: C Fgue : Oe sgle oscllo : ducvce d C: cpcce.

3 Fgue : Two decl oscllos ccodg o Fgue wh uul couplg of he cues gec couplg. The soluo of euo s spl gve b he sz : cos C I s he s of he followg secos o educe coupled elecogec ccus o euo d s soluo v he cocep of ol odes. Replcg cos b s o b fog ehe le cobo of se d cose o ep euo s lso ssfed... Couplg of wohee decl elecc oscllos: gec couplg v couplg cos d he bsc pcple of choobolog Thus fo splc we fs cosde Fgues d. The bsc euos pplcble o boh Fgues e: C C C 4 Whou esco euo 4 efes o Fgue whees Fgue s descbed f he coeco of oscllos d o oscllo s ueched b pug. The oscllo s copleel depede d s eed b euos. Fo hs cse he ol odes e edl obed b he subsuos d 5

4 4 Fgue : Thee decl oscllos ccodg o Fgues d wh couplg bewee ech oscllo: wh wh d wh. The soluos esulg fo euo 5 e decl wh hose of euo f he ol odes d e seed: cos cos s s C C 6 7 The b pludes c be fed b pope l codos. g he coeco bewee he oscllos s eoved d s vld. The ol odes of coupled oscllos Fgue e obed b he subsuos: ; ; 8 The soluos es of ol odes e: cos cos cos s s s C 9 C C Obvousl he soluos 9 - gee wh he soluo f s ced ou... Pedul ovees - he plcos o bohhs d choobolog

5 5 ue o he couplg he esoce feuec ccodg o euos 6-7 d 9 - he feueces esulg fo o he deoo c be educed whees ccodg o 7 whee he dffeece - ees he deoo; becoe ve hgh f ous ppoel o. Eple: We choose C such us h d T π ds c. 6.8 ds. Plese oe h he defo π T holds. The f.9.9 foul 7 povdes T c. 8.5 ds d 6 T. π c. ds. Howeve f.99 he hee s o sgfc chge foul 6.e. T c. 8.5 ds bu foul 7b povdes T.6 ds. sudde chge of o C pl sgfc chges he eled esoce feueces. I pcul he deoo of foul 7 whee he dffeece hs o be used led o sevee chges of he egefeuec d T. I follows h he esoce feueces e degeee d ol s chged; he deoo s cesed. Ths povdes decese of he egefeuec d coespodg pologo of he esoce e T. Usg g he bove vlues C d.99 he T ous o c. ds. I ohe wods: ssue h he upeubed oscllo shows ccse-sep peod he he feedsdewd coupled oscllos ech oscllo couples wh ohe oscllos led o ccsep peod f he feed-sdewd couplg s sog s ssued he bove cse. Sce he soluos 6-7 esul fo wo coupled oscllos d boh chge pludes d lel deped o d. We pefo le cobos of ehe soluo 6 o 7 ode o vew he ou of foo cog coupled oscllos. We show hs ou he cse of soluo 6-7.We e use of gooec heoe d of he subsuos s α β s α β s α cos β cos α β cos α β cos α cos β α β ; α β The euos 6-7 c be ewe he fo: ol s cos cos cos s cos Euo povdes he foo h he supeposo plude ol cos he bsc pludes whch e he dffeeces d espl. d he feuec ve fs oscllo feuec he secose d ve slow oscllo

6 6 feuec - he cose o πt. If d he secod es of euo 9 vshes d he cose s efeed o s ce pludefeuec copog bes bewee he wo coupled oscllos. Howeve f he pludes d d cosdebl dffe fo ech ohe he bes e sll pese bu he do o pl he ole. I ppes h choobolog we hve o del wh sl suos whee fs oscllos suleousl ppe besdes ve slow oscllg copoes. Sce he sg po of euo e wo decl oscllos wh oe couplg bewee he hs s he odel h ve elsc cse s evde h supeposo of oe cople codos led o fs oscllos d oe h oe be plude... Two oscllos wh C C coo delecc edu ε d he couplg λε I ppes h Fgue 4 epeses lso sgfc foo wh espec o cellul pocesses sce delecc edu bewee boolecules e.g. we s he elsc. The pesece of delecc edu cpcce C lso chge s gude. The bsc euos ccodg o Fgue 4 e: C ; λ λ C 4 C C Fgue 4: gec couplg bewee dffee oscllos The soluo pocedue s he se s led used:

7 7 ep 5 Ths sz povdes he euo: λ λ 6 The peubed egefeueces of he eleccll coupled oscllos e gve b: ± 4 λ 7 If he coeco v pope delecc edu s vshg λ we ob wo soled sses. I should be eoed h wh he help of he feueces d we e ble o fo g wo dffee le cobos es of cosese d pedul ovees ccodg o he soluo follow fo hs behvo. Ths poble wll be dscussed coeco wh he e seco..4. gec couplg bewee dffee oscllos The poble s solved sl o euo 4. Ised of uue pees C we ow cosde he cse Fgue 5 C C C : C C C 8

8 8 C C C Fgue 5: Coupled elecc oscllos ccodg o euo 7 The egefeueces of he ucoupled oscllos e: C C ; C ; 9 Euo 8 s solved he se e s pevousl used: ep.. Ths sz eues he soluo of he followg euo of whch he dee hs o vsh: If we pefo he subsuo we hve o solve he followg polol euo p. The soluo pocedue s descbed he eboo of bowz d Segu 97. ll es esulg fo euo e:

9 9 { } ; ; ; 7.5 ; ; ; p p p b b b b p p b p dv dv dv p dv p Res: The subsuo p leds he euo b. The clculo pocedue fo b es of p d e gve bove euo. If oe hs clculed es of b he he oos e edl copued. Wh espec o he oos he followg cses hve o be egded: ; 7 4. ; 7 4. < > ueul d el b decl wo el b cople cojuge wo el oe b The soluo of he euo povdes ol odes le cobo of cose d se: 5 ] s cos [ I s g possble o cosuc pedul ovees s pevousl ced ou. The fold ceses cosdebl. We e use of he followg defos: 6 ' ; ' ; ' ; The coespodg ovell soluo s:

10 ol [cos [s cos ' cos ' cos s cos s cos ' cos ' cos s cos s cos ' cos ' ] ] 7 h we ob ve slow dffeece feueces pedul ovees o bes d 6 fs o ve fs feueces. The dffee bes be coeced wh ccd ccse-sep d ccsep whees he fs oscllos gh hve ve sho e peods secods ues o soe hous..5. Soe Geelzos The pecedg seco eled o Fgue 5 be geelzed b wo eesos:. I ddo o he gec couplgs d s lso possble o oduce coecg delecc ed bewee he cpcces. The we hve o eed ll es cog ecep he dgol elees euo b cpcve couplgs. The clculo pocedue of he egefeueces s he se ol he pees p d coseuel b euo wll co fuhe es.. I s lso possble o oduce fouh oscllo; he couplg o ohe oscllos be ehe gec do elecc d euo hs o be eeded o fou dffee chges 4 : ep..4 8 eve cse we hve o solve polol euo of fouh ode f we pefo he subsuo : 4 p s 9 I he eboo of bowz d Segu 97 he pocedue s descbed how o fd he oos of hs euo. escve codo s h bu egve vlues hve o be ecluded. I es of ol odes he geel soluo s gve b: cos s...4

11 The fold of pedul ovees of he chges bewee he oscllos s oe eesg. O he ohe sde he dffcules o ob suble d lso cese. The pedul ovees e gve b: ol 4 l 4 cos cos ' l cos l 4 Fgues 6 6b e eples of such geelzo. s l cos ' l l 4 s C C C Fgue 6: Eeso of he coupled ccus o sse wh cesed cople coped o Fgue 6.

12 C C C Fgue 6b: Two dffee oscllos C C wh eleccl C couplg b ppope delecc edu. We should eo h he hecl ee of 5 o oe coupled oscllos ples uecl evluos of he coespodg polol euos fo he egefeueces..6. specs of pedul ovees be feueces of coupled ccus I felds of ppled phscs he sgl lss pls do ole. I pcul we eebe s sgfcce foo do cool heo d he eled echologes. I hs cse oe cosdes les wo coupled elecogec ccus; he pludes of he ol odes ssf f oe h wo coupled ccus e ppled he ec should lso be vld. Ths suo esebles echcl logue el wo peduls wh dffee sses d coeced b spg. I hs cse copoes he eeel slow oscllg goud geuec d s ve fs odulo. The ol eeg eeds s log e o vel fo oe pedulu o he ohe oe d o eu. The pedul ovee s heefoe efeed o s be feuec bes. The l codos hve o be chooses such h he ve slow goud feuec epeses he ce sgl.e.. I coscopc sses s lws possble o ssf such l codos. Wh egd o oleculcellul bolog whee chge dsbuos of boolecules o eve cells e cosdeed s cpcces d chge sfe pocesses bove ll H bods o ecg ellc os s cues we do o ow hese l codos. Ths es h

13 fs oscllos gh be do d ol fuhe copoes show bes.e. ccd ccsesep do ccsep peods. We hve pefoed lss of be feueces.e. πτ. I s ve soshg h eve fo cses whee d efe o fs oscllos T d T ou o c. bewee secods d oe ue we e ble o ob ueous ccd ccsesep d ccsep peods. The ol po pope s h o T T. Fgues 7 7d show he eld of ccd ccsesep ccsep d ccg eples hve bee suded b Hlbeg e l 96. Fgue 7: Fou coupled oscllo cee esoces he ccd cc-sesep ccsep ccg peod. The e se ous o ± %.

14 4 Fgue 7b: s Fgue 7 ol he possble e se evl educed o ±. %. Fgue 7c: Suleous occuece of esoces of 4 coupled oscllos peods ± % 4 dffee peods ± %.

15 5 Fgue 7d: s Fgue 7c he e evl fo he occuece s educed o. %. Fgues 7-7d show he eld of ccd cc-sesep ccsep d c. ccg peod τ depedece of T d T. Those cses whee ccd o ccsesep ec e obed e sgfcl cesed; heefoe we do o show hese coecos. If we hve hs plce loo o spo pheoe d eco pocesses phscs he he followg fcs e o vef: Tsos fo sgle o ple ses hve lfe es he ode of secods o ues o loge. If eced olecules e coupled o ses of log olecul chs he he eced se vels due o he pope couplg b ducg olecul defoos d eede chges of he elecc chge. Ths s oe o less he slow pocess; solos behve hs e. Pue sgle ecos pl lfees of bou -8 secods. I olecul chs hese ecos e efeed o s ecos whch e dped b esso of lgh. Theefoe he ueso ses wh e he pcpl pocesses ledg o e peods wh log duos bohhs suded choobolog. Sce τ ssf ueous dffee ds of peods f s popel gve he choobologcl fdgs e o e fouded ssfco e. I ohe wods we do o e ow he coducos fo he pefeeces of soe bohhs ledg o be e. Oe w s o sud coelos s pefoed b he Hlbeg goup Hlbeg e l d o lze e sees Schwege e l 986. Howeve we shll eu o hs ueso he followg secos..7. Peodc oscllos d he so o he couu

16 6 We coue Fgue b oducg fuhe oscllos whee lws he dec eghbos e coupled v. The we hve o lze he followg sse of euos C: ep C Euo leds o he followg euo Fo euo follows h he hs ol dgol elees of he fo d decs eghbos wh he elees. I chpe 9 we lso egd he peodc elecc couplg bewee eghbos. I he couu l hs ples wve euo. Wh egd o he gec couplg ccodg o euo 4 such wve euo co be obed. O he ohe sde peodc oscllos wh gec couplg gh hve esced bologcl poce sce he peodc s lcg such sses. I s eesg o oe h fo sses wh peodc elecc couplg we c deve wve euo sl o h cosdeed couu phscs obed b peodc echcl couplg. The logue o Fgue 4 s he cse of elecc couplg: 4 C λ I he couu l.e. he dsce bewee he chges d - becoes fel sll euo 4 ssues he shpe: 5 l ] [ C λ The e - epeses he secod devve wh egd o spce f l s ced ou. The we ob wve euo he chge spce: 6 v

17 7 I should be eoed h he vcuu cse he veloc v s eul o he veloc of lgh c. u v be cosdebl slle he pesece of delecc edu ε.e. v c. Wh egd o he pesupo of euos 6 el peodc sse he se coes e vld s pevousl poed ou: I bologcl sses he ssupo of peodc boud codos be he delsc cos o phscs of csls whee polzo wves of olecul csls e suded. Theefoe he sud of soe coupled oscllos be oe helpful. The cluso of Oh s essce R o be we of dpg dped wves s sghfowd d euo 6 ssues he shpe: R v 7 The echcl logue of euo 6 s sse of coupled oscllos wh ss d he foce cos f. The euo of oo eds: d d f 8 oducg he couu l he fsho s euo 6 we ob he wve euo of sg wh egd o he plude o elogo.e. v 9 I hs cse v s he veloc of soud he sg. I cos o eleccl couplgs he sg soluos of euo 9 ssf well-ow coss e.g. odes d. Ths cos povdes dscee specu of odes: λ ;... } 4 I euo 4 λ efes o he wvelegh d o he dsce of he sg bewee he wo odes wh d. The couu so of coupled elecogec oscllos wh ccodg o euos - c edl be ced ou bu we ob geelzed wve euo: C C 4

18 8 I he couu l we ob fo euo 4 c l [ l c ; ] C 4 I s possble o epess es of C whch povdes: C 4 Euo 4 s edl be solved b ple wves Foue epso. Wg he -veco he fo lc we ob: [ C ] 44 coseuece of he soluo 44 s h spe of C gh pl fs oscllo of sgle ccu he couplg bewee he oscllos ch wh us led o ve slow oscllo feueces due o foul 5. Ths s pcul ue fo >>. The supeposo of goud wve wh ve slow peodc d fse odulo s lso possble. Ths spec gh be eesg choobolog..8. Sdg wves The ueso ses whch w sdg wve soluos becoe esoble. Fo hs pupose we ssue h he gec couplg s euped posos d. The pope wve ode eced wh hs evl co popge o he dos < d > d logous boud codos hold s fo he sg. These boud codos c be ssfed fo pue se odes.e. ep s π π Cobg hs esul wh euo 44 we ob π lc [ π l... c C ] 46

19 9 ue o he le of euo 4 he supeposo of he odes elds he followg soluo: s π cos 47 The ueso ses whee bolog such soluo s pplcble. Sdg wves esulg fo gec couplg esul whe he ed-pos d he couplg v s euped b eleccll eul olecules. The he eced wve pludes hve o e wh hs evl d he fo odes wh he goud feuec ve slow d fse odulos. Such so se bedow f oe edpo fuhe olecule chges he odl codos d he couplg o he eghbog evoe s esblshed. The wve he escpes o ech ph o do whch could o be eched befoe due o he lcg couplg eco. Ths gh be possble echs d effec of euoses ce spse. The escped sdg wve be eplced b ew oe whe he coespodg codo s eesblshed d he wve s eced b fuhe sgls..9. Theoecl cosdeos of esoce ecos bewee boolecules d he uu echcl bse The ueso ses whch w we c sfe uu echcl pcples d esuls o pobles of ccus whch epese chge dsbuos d cues flueced b gec felds..9.. Soe bsc specs of pheoeologcl coelos d olecul popees I gh ppe h uu heo co povde foo o he poble ude cosdeo el esoces ecg olecules. ccodg o pevous sud Ule 98b he eco bewee olecules c descbe he checl ff whch s pheoeologcl descbed b he heus euo b he cosdeo of suble e schees d so pobbles. Ths heo cludes besdes he specfc ff he so o eced ple ses b vsble lgh o b eco bewee pope olecules whch c be chcezed b he log lfe-e d supeposo of spo pheoe sl o dffuso pocesses. oeove he cluso of gec felds d cue s ue ul d bsed o oe fudel heo s dffuso. The esoces c be vewed lgh of ccus s pevousl cosdeed. lhough he pevous sud ws l esced o

20 esoce eco bewee dugs d N ode o epl ve dffee coelos bewee cceogec olecules d ugec c edl eeded o ohe specs such s us-degeee ple esoces of coupled oscllos whch e he ees hs vesgo. Theefoe he ueso ses wh s coeco bewee checl ff of boolecules d he e schees wh bohhs. fs we cosde he clssfco of dugs wh egd o he ugec d b h o he ccogec effecv. Ths poble hs log hso d he polcclc oc hdocbos PHC hve bee vesged b uhos wh he help of uu checl es. sed o clculos of ecv dces of goud se popees. d. Pull 96 hve developed he fous K- d - ego odel o epl d pedc he ccogec cv of soe PHCs. Howeve b cluso of oe vlble PHCs h he Pulls hd ogll vlble ueous ecepos could be vefed. Theefoe hs odel dd o co he whole uh wh egd o he coeco bewee checl sucueecv d ccogec d fuhe ue dffee odels hve bee poposed. We pcull eo he coelo of low eced ses of PHCs so 958 chge sfe echss esoces of PHCs d N Hoff d d 96 d he coeco bewee he dpole-dpole esoce eco of PHCs d eced ses of he o cd poph s 97 d he double esoce ses of PHCs wh bsopo of bophoos Popp e l 979. Sce ech of he eoed coelos ol bes ecepos Sug 977 hs pefoed ulegesso lss ode o bg oe lgh hs shocog of ehodolog.

21 Sgle ses ev Fgue 8: Te schee of double esoces of ccogec PHCs. The sold ow epeses peed so fo he goud se o hghe eced se whees he dshes efe o fobdde so of he lowe eced se o he goud se he lfee s sgfcl cesed. The eeg dffeece bewee hese wo eced ses ous o c.. ev Popp e l 979. Sgle se ev Tple se Fgue 8b: Ths e schee copoes he se effec s Fgue 8 he eco of he eced ple se fo goud se s fobdde. Sp-ob couplg pes doless sos fo he eced sgle se o he us-degeee ple se. The lfee of hs se be ve log ode of secods o ues.

22 Sgle ses ev Tple ses Fgue 8c: Te schee of he cosc dug cclophosphde d s eboles Ule The eeg levels of he eboles e ol slghl chged bu he so pobbl c dscll dffe due o chges of sp-ob couplg. ccodg o Ule 98b 98 Fgues 8-8c epese e schees whch e chcesc fo hose olecules wh specfc eco wh N o he o cd poph; he ogl esco o PHCs s supefluous. Wh he help of he so pobbles of he eled olecule ses he d of eco c be specfed checl eco dpole-dpole esoce eco chge sfe ec.. I should lso be poed ou h he e schees ude cosdeo co be esced o he ogl olecules bu he eboles poduced b epodo hdolo cbolo ec. usull show he se e schee wh chged so pobbles. Thus olecules chcezed b he e schee 8c he checl eco echs c be clssfed b bdclc ecos H 964 Fuu e l 969. If fo ugec subse o dug he bse ps of N o RN copoe he boecepos oe of he bove e schees should be pplcble d he ozo eeg should lso be copble wh he boecepo.e. c. 6.9 ev 7.7 ev. Howeve s evde h he peseed fdgs lso be ppled o ohe esoce eco e.g. wh poe hooes ec. The e schee ehe be sl s s he cse fo poph d devves o he dffee f boecepos wh ohe specfc popees

23 hve o be ccoued fo. I eve cse he checl ff bewee olecules ccodg o he heus euos sds close coeco o esoce ecos deved b uu echcs. Ths s he subjec of he e chpe..9.. uu echcl specs d peubo heo ccodg o he ehodolog of uu echcsuu ches hee e wo ppoches o descbe he eco bewee wo olecules d :. We ssue he Hlo H of he ol sse s of he fo H H H H 48 Fo he se of splc we suppose h he ol sse s well s he subsses d shll e he sgle goud se. The we hve o clcule e.g. Hee-Foc des fucol Fe popgos o se-epcl ehods he goud se eeges of he subsses d d of he ol sse depedece o ll ucle co-odes elsc clculos esced. The Hlo H s ssued s usul Coulob ecos bewee elecos ucle d bewee elecos og heselves. gec ecos of chged pcles sp-sp d sp-ob couplgs e eed s peubos d wll be oduced sepel. lhough he ol sse shll e he sgle goud se coecos b eced cobuos v CI ehods becoe he ve essel whe d udego ecos sce boh olecules hve o be soge defoed d dsoed. Ths fc s led ue fo seped olecules whou he eco e H d he vld of he o-cossg ule s dco fo he elevce of eced cofguos.. We ssue h he Schödge euo fo H d H s eclppoel solved: H H ψ ψ E E ψ ψ 49 Fo he followg cosdeos he possbl of he fs cse s o elev s we c esue d clssf he egeses d so pobbles bewee he ses ude vous codos. Now we epd he egefucos of H ccodg o euo es of he egefucos of H d H :

24 4 ψ C ψ 5 We e use of he peubo heo o clssf he degee of he ppoo he pplcbl of he usul peubo heo s ssued sce he ses e o degeee le sole H os. The fs ode ppoo s deeed b he well-ow elos fo he coeffces: C H E E d H ψ H ψ 5 The secod-ode ppoo does o povde ew pcpl sgh sce ol udc es ddoll ppe: C [ H H E E E E H H E E H E E C ] 5 Wh e he plcos of hese esuls? We c vef h peubo heo hs dvges bochecl pobles. The dsdvges of he ppoch po s es o see: I s he hopeless o copue he ol sses dug-boecepo o booleculeboolecule d boecepo c be ssoced wh lge boolecule N RN poe hooe. Ths ppoch s led hopeless f oe wshes o defe he Hlo of such boecepo oe h of he ve coplced geoe of he double-sded N cludg he H bods bewee he bse ps ecg wh cho. Theefoe we hve o esc ouselves o heoecl es ccodg o po whch lso pe o use epeel popees e.g. esuees of he ozo eeg eced ses d so pobbles clusve esse cossgs due o sp-ob d sp-sp couplg. Wh espec o such sg-po he ehods of peubo heo ppes o be ppope. We hve led eoed he coelo of s dpole-dpole eco bewee poph d ccoge d he ole of he eced ses of he PHCs he do. ev.5 ev Fgues 8 8c. Ths o be cogec sce he lowes eced ses of he uclec cds lso le hs do: gue G:. ev dee :

25 5.5 ev he T:.5 ev cose C:.45 ev d ucl U:.7 ev. I s ow h he ple ses e uffeced b he eo-eol uoes d N o RN we he obseve eeg bd of ple ses wh he bove eoed evl h sepe eeg levels ple coduco bd ebo e l 969. The fs eced sgle ses e oe flueced b he uoec eulbu duced b he H bods bewee ce bse ps. Theefoe hese eced ses le he lge do bewee.7 ev d 4.7 ev. I should be eoed h poph possess wo eced ses bewee 4 ev d 4. ev d he lowes ple se s he se evl s he ple ses of he uclec cds. Ths pope s lso ue fo he deves elo d seoo bu he ohe o cds clusve phelle ol possess sgle d ple ses beod 4.7 ev d.6 ev especvel. hs poso should be poed ou h b ccoug fo he elees of goud se d eced ses ecos d so pobbles we e ble o epl he checl ff bewee eel olecule d boecepos such s N. The Hlo fo chged pcle e.g. eleco poo eel gec feld d fo sp-obsp-sp couplgs hs he fo dels e gve b He 96 96b 965 Ule d H 978: H gec µ h e c 5 5b H I sp σ gd µ 4 h c I V p he µ c v σ II l T l σ σ III l l 54 The coseueces of euos 5 5b 54 e eedous sce ll gec ecos e ccoued fo d he eeg levels obed b he Hlos H d H e ddoll spled up. I cos o usul pplcos he ss µ euo 5 s eled o poo ss. Wh z - z he soluo fuco of he Schödge euo 5 fo fee pcles sc gec feld ehbs he fo He 965:

26 6 ψ β E f α ep α β z ep.5 ξ H e µ c e h µ c o ; feuec... ; ξ 55 c ξ hαc e µ h b The fuco fα epeses b fuco; H efes o Hee polols of he degee wh he eeg egevlue E ccodg o euo 55b. Plese oe h fo elecogec wves euo 5 s he bss fo elecc dpole sos. The epessos I III hve he followg egs: I efes o sp-ob couplgs of elecos olecules cses o be eplcl eoed I lso efe o poos. Epesso II epeses he sp-pul effec.e. he sll eco eeg of he sp eel gec feld. Wh egd o ddol elecogec wves II s esposble fo sos bewee dffee sp ses duced b he wves. Epesso III efes o sp-sp couplg eleco sp ucle sp; s usull ve sll d ples coespodgl sll splgs of he eeg levels. Sce ll cobuos I III descbed b euo 54 cel epese peubos d splgs of dscee eeg levels esul fo hese popees we se ow he os po elees he Hlo of sp-ob couplg s deoed b H SO : e c e c l ψ ψ l H so H ψ so ψ ψ ψ X ψ l X ψ [ ε l ε ] [ ε ε ] 56 If we loo he deoos of euo 56 we g fd he sl pope s vld fo he elecoc ecos epessed b H el he eeg dffeece hs o be ve sll o ecod sgfc cobuos of sgle-ple sos. The elevce of he e schees 8b d 8c d he poce fo he checl ecv e epled b hese popees of he deoos. I cos o he ve fs pue sgle sos he lfee

27 7 of ple ses hs pcul eg log olecul chs sce chge d eeg spo echss e eced whch c led o solo spo chs e.g. uscles vdov 979 o cve H bods. The secod cobuo II epese he eco eeg of he sp gec oe eel gec feld.e. gve eeg level E s spled up o eld: E E ± µ g 57 µ g γ s h The gec oe µ g ehe efe o he poo o eleco oe γ s he gogec o. Cobuo II lso becoes elev wh egd o sos bewee dffee sp ses duced b elecogec wves; eple s NR. The poce he cse of he uch wee geogec feld wll be dscussed le. The hd cobuo III efes o he couplg of sp wh evoel sp sses d epeses spo echs wh eeel low eeg..9.. Coseueces of he esoce deoos ecos wh gec felds d couplgs o sp sses o pobles of checl ff H bods d ccus I s geel feue h ll cobuos I III c be eed b well elboed peubo clculos whee eve ode he eeg dffeeces ppe he deoos. The bsc sg-po s copoed b he Hlo H d s cosues H H H. Thus hese cosues belog o -pcle Schödge euos he c be foud eboos of uu echcs see e.g. He 965 do oleolocl Schödge euos wh el sucue Ule 98. The le ehod lso offes he possbl o clcule v chge deses d cues he popees of elecc ccus es e. Fuheoe hs ppoch copoes ue ul w he des fucol fols whch hs bee pu fowd fo he clculo of -pcle pobles boches d olecul bolog e.g. he clculo of uelg of poos bewee N bse ps Péez e l. The bss seleo of he followg clculos copoes Fgues 9 d. The bd sucue sgle d ple ses of N s deeed b he π elecos of he bses d he d-

28 8 elecos of he phosphe ese Ule These d-elecos ehb lge couplg ge of c..5 Å whch eches besdes eghbog π elecos of he se sd lso d-elecos of he coplee sd clusve π elecos of he eled ucleodes. coseuece of hese popees s h he uppe zoe of he ple bd cog huge ube of dscee ples d he lowe edge of he sgle eco bd ovelp; fuhe essel pope s he sp-ob couplg of he d-elecos whch llows sos fo sgle o ples d evese. The ows sold les Fgue 9 e lso vld evese deco whees he dshed ows dced pocesses wh he lle pobbl. Owg o he splg up of he ple levels of d-elecos we ob ddol cscde of ple ses whch c seve s pupg echs of eeg whch hve s og TP GTP ec. Eced ses Ε Ε Goud se Fgue 9: Ths fgue cludes he coes of he pecedg fgues 8 8c sgles: lef ples: gh; he pesece of oe o oe fuhe ple ses below he double esoce ope ew phs fo ecos e.g. popgo of ple ses. I s well-ow pope h he H bods bewee he bse ps T d G C odfes he locl cofoo of he N bses ccodg o he poso of he echge poos eo-eol uoes. I pcul he eced sgle ses e ffeced b he uoezo bu wh egd o ple ses he fluece o bd s less oewoh ebo e l 969. coseuece of he dffeece he locl chge dsbuo of he eo d eol uoe s sec poel of he H bod whch s loweed he eo cofoo. ssug locl epeue of o K he poo uelg veloc fo

29 9 he gh-hd sde eol uoe of Fgue o he lef-hd eo uoe s fs whees fo he evese pocess he coespodg veloc s eeel sll fco. Sce he chged uelg poos copoe sp ½ d cue bewee he coespodg bse ps we c e he eegec pocesses s peubos. The fluece of he geogec feld ode.5-5 Tesl s he dffcul bu ve posg due o he helcl sucue of N:. If he deco of uel cue bewee wo bse ps s pepedcul o he deco of he geogec feld he we hve u effec of he supeposed ool oo duced b he oez foce hghes o feuec.. If he deco of uel cue bewee wo bse ps s ppoel pllel o he deco of he geogec feld he we hve u effec of he supeposed scew duced b he oez foce lowes o feuec. Geogec d sol gec felds hve ow bou he se ode of segh.. Thee e fuhe cofguos of H bods bewee bse ps whee he pojeco of he gec duco les bewee he eee cses d. The ool oo of he poos duces ddol sp-ob couplgs d sp-sp couplgs wh eghbog H bods d d-elecos. The eeel sll eeg dffeeces he eled doos of he peubo epso of he wve fucos eld sesve esoces b eel elecogec wves wh ogs fo he eh o he su. The possble eeg levels sgles ples of N suffe vous fuhe splg whch c be eced b ppope esoce codos. I he lguge of elecogec ccus spob d sp-sp couplgs c be epeed s uul ducce cses I d III of euo 54. The eco eeg of he poo sp he geogec feld s epeseed b he cobuo II of hs euo sp-pul effec. The oez foce eco of he chged poo wh he geogec feld s epessed b he Hlo 5. Ths oo s uzed d leds o dscee eeg levels epessed b he o feuec goud feuec. Ecos of he goud se c ol occu b dsopo of elecogec wves wh ve low eeg d pope egefeuec. The se of he poel bewee N bse ps ccodg o he dshed le of Fgue ehbs ddol eesg coseuece. ue o he log pobbl of bdce he eo cofoo coped o he bdce he eol cofoo he

30 helcl N ssues ddol sbl wh egd o ugec flueces. If poel ccodg o odel would be vld he hs pope would o es d he oo of poo bewee he wo due o uu echcl uelg would be decl. T G C C G H bods Fgue : Seco of he double-sded N hel d he H bods poos bewee he bse ps T d G C. The ddol ccul oo of poos bewee bse ps sees o pl lso po ole N eplco d scpo sce epeses e fo he oo specfc ps of he N sds. Soe coseueces of clculos efeg o hs seco wll be dscussed seco. The ddol ccul oo of poos bewee bse ps sees o pl lso po ole N eplco d scpo sce epeses e fo he oo specfc ps of he N sds. Soe coseueces of clculos efeg o hs seco wll be dscussed seco. Fgue s obed b oleolocl feld wh el sucue d sp Ule 98: 57 ' ' ' ' ' ' ep ' ' ' ' ' ]] [ [ ε ε ε ε ε ε ψ σψ ψ σ λ ψ ψ σ ψ ε ε ε π µ z z H H H P z z K d K H l l l so c e h h

31 I lowes ode he soluo fucos c be ppoed b he poduc wve fucos ψ φeleccl p Φgec 57 Icluso of hghe ode cobuos of gec peubos o he ledg eleccl p of he Hlo φ g ples esoce doos s led poed ou fo H. eleccl p The ecess ego pocedue hs led bee woed ou Ule 98; gec ecos b eel felds d ecos wh sp e eed s sll peubos. The elsc poel fo uelg poos bewee N bse ps s es o hdle b he geelzed Guss covoluo eel K whch cos ulpole epsos b ode ccoued fo es of wo-po Hee polols H. Fgue : ouble u poel bewee he bse ps T. ef u: Keo-uoe of dshed le odel. odel epeses he sec ppoo s vld fo H bods we... Coeco o dffuso heo of chged pcles gec felds I hs seco we dscuss he poble of he eco of chged pcles fo dffee vewpo el he eco-dffuso heo whch s lso vluble s copleo of he

32 pecedg secos.... Fc s lw of dffuso d he Kologoov fowd euo ffuso.e. ow oo hs he geel pope h coceos of pclesolecules ed o dsbue eve vlble spce f hee e o coss. Fc s lw of dffuso pls e ole lo of phsologcl pocesses sce he esco o pue bochecl ecs eues spl eulbu of coceos whch does o es. Fc s lw s well-ow d shows he se sucue s ohe spo euos.e. spo of he: 58 s he dffuso coeffce he plce opeo d he pcle des. Ths euo esuls fo he pope h coceo gde ples cue d blce euo cosevo of he ovell pcle ube us be ssfed he bsece of checl poels: j dv j dv j v 59 If he pcles e os wh elecc chge he he pesece of gec felds descbed b he veco poel ddol oeu due o gec feld oez foce hs o be ccoued fo: p v dv p c c 6 : pcle ss whch lso be effecve ss c: veloc of lgh p: oeu. Iseg 6 euo 59 we ob followg euos:

33 6 j dv j C C Fo euo 6 follows he Kologoov fowd euo: 6 v dv The e dvv esuls fo he co of gec feld d s egded s decol foce whees pue dffuso hs o pefeece deco. I bove euos we hve ol odfed he dffuso cue b he gec eco bu o e he blce euo due o he pesece of poel. I ode o ech full guge vce we hve o we: 6 ] [ c c C c Ths euo shows pcul poce sce c be sfoed o Schödge euo wh gec feld 5. The Kologoov fowd euo 6 s specl cse of euo Eel gec feld wh z-deco fs we cosde he cse z cul we choose s follows: 64 ; z Iseg euo 64 euo 6 d usg he subsuo c we ob: 65 Y Euo 66 s solved b he followg pocedue: 66 ep ep ep γ α γ α ϕ z z The cobuo fo he z-deco leds o pue dffuso whees he -deco s lso

34 4 coeced o he -deco due o he e euo 57. Theefoe φ s deeed b he euo: 67 ϕ ϕ α ϕ The followg subsuos e pefoed: 68 ; s s ξ α η η Ths povdes he desoless bsc euo 69 ϕ ξ δ ξ ϕ The soluo fucos e cople Guss ulpled wh Hee polols he cople spce: 7...; ep H α δ ξ ξ ϕ Wh egd o elos 69 d 7 soe coes e jusfed. The soluo fuco φ foll gees wh h of uu echcs oscllo gec feld : o feuec bu ξ s o el see 68. ccodg o gooec heoes he cople spce s lso possble o epese φ b cobos of se d cose fucos. Theefoe he soluo fuco of euo 55 s copleed b he pocedue: 7 ep ep z α α ϕ Φ The soluo fuco φ ssfg euo 67 c be decl obed b su of se - d cose fuco f.e. ep ξ s sfoed o pll el fucos. 7 cos s P P P P ϕ I he cse of > we hve o ulpl d wh polols of d o deee he coeffces v euo 67. Iseg euo 7 o euo 67 we ob:

35 5 P ± P ± α 7 ; So he se d cose sll co cople gue. The gude of d N depeds of boudl codos bu coplced sses le olecul bolog he e hdl o deee. Thee e bscll wo escos gve b euos :. α. α 74 Fo he geel cse wh polols of d foul 74 hs o be odfed:. α α 75 The deoo of euos sees o be oewoh sce vsh o les ve huge. Ths behvo coespods o esoce codo. We shll eu o hs spec fe lss of he geogec d sol gec feld. ccodg o pevous esuls Φ z obed b cg ou he egl Φ ep γ z ep γ f γ dγ 76 If f γ he Φ z s gve b he well-ow Guss.e.: Φ z ep z 4 4 π 77 If f γ s gve b polol epso he we ob Guss ulpled wh ce polols P l Ule 98: Φl z Pl z ep z 4 4 π 78 The clculo of P l s developed he ced efeece. O he ohe sde f he spce vlble fo dffuso hs coss d boudes he Φ z s deeed b soe eo fucos ef. The spl boudes be gve b z γ d z γ d we ow ob:

36 6 Φ U ep z 4 [ ef s ef s] z z U 8 s z z ; s z z 79 I c be see h due o he cople vlues of s d s he dffuso of he chged pcles dops oscllo behvo esulg fo he cos boudes. I eve cse he behvo -deco s deeed b he gec feld sce α s led fed b euo 7. Ths fc ples h boh ep α d ep- α ehb cople vlues.e. we c ob ehe dped oscllos o ehced oscllos depedece of he cul coceos d coecos wh possble pools. We po ou hose supeposos wh dffee vlues of e lso llowed. I s sghfowd s o eed he bsc euo 6 b eco poel he ghhd sde whch s gve b ehe. λ dec of he coceo due o he couplg o fuhe copoe.. λ foo of he coceo due o he dec-couplg of fuhe copoe. The geel soluo 79 hs o be geelzed decfoo eco: Φ z ϕ ep α ep α dec Φ z ϕ ep α ep α foo ep λ ep λ 8 Ths esul s of ees wh egd o he -s cobuo.e. ep α ep α sce boh epoel fucos ehb oscllo behvo d ehe ehcee o pohbo b dpg e possble coseueces. Ths s lso eple of he decol popees of gec felds checl ecos. We shll ow sess ou ees o he geogec d sol gec feld. Sce he geogec feld depeds o he loclzo o he eh sufce sepo of boh copoes es ol sese f we cosde h pojeco of he sol gec feld whch s pepedcul o he geogec deco sol gec feld: z ; geogec feld:

37 7. s he geogec feld segh s bou 4 sol gec feld segh he pojeco of he sol feld deco o he geogec feld s copleel eglgble. Sce he blood flow lso ces os he gec feld segh of hs cue duces gec feld of he ode of he sol gec feld d he pojeco of h copoe whch hs he se oeo s he sol gec feld slghl ehce he sol gec feld segh. Wh egd o he vecos veco poel d gec duco we use he followg defos: 8 d 8 Now euo 6 ssues he shpe: 8 ; c c z We odf foul 66 o solve bove euo 8 el ec: 84 ep ep γ γ Φ z Thus we ob: 85 Φ Φ Φ Φ γ I ode o e use of euos 68 7 wh espec o he -coode we hve fs o eglec he e Φ sce >> >>. I secod sep we shll ccou fo hs e whch copoes coelo bewee boh copoes. Theefoe we ob: 86 ; s s ξ γ η η Ths elds foll he hoc oscllo euo of uu echcs:

38 ; ep H γ δ ξ ξ ϕ ϕ ξ δ ξ ϕ Fll we hve o cosde φ f ; f esuls fo he poduc dd of euo 85. I fs ode we e ccou of he ed poduc b he fuco 88 ep f The we hve o solve he euo 89 ep ϕ ϕ d d Ths foul c be evel solved o eld: 9 cos s ± p p p ϕ I he e sep we hve o ccou fo he ed poduc epoel fuco whch phscs s efeed o s peubo epso: 9 ] [ h ϕ ϕ Repeg hs pocedue we ob: 9 cos ] [ h h ϕ ϕ The ol soluo s gve b he poducs 9 ep ep z ϕ ϕ γ γ Thee s o oe degee of feedo fo pue dffuso sce eve z-deco he soluos deped o hose of he -deco. Fuheoe boh d deco e oduled b h. I s evde h deco whee he ve slow s do due o he sochsc oo of os s supeposed b coespodg slow oscllos. O he

39 9 ohe hd he fs oscllos deco e oduled b he feuec d powes of. Sce we co swch off gec felds cells d ll boolecules e oe o less chged besdes he ellc os hee e vous plcos of hs fc: We pcul h of he ogzo of boolecules d opholog whee he decol foces hve pled sgfc ole he evoluo... Soe pplcos I hs seco we cosde pobles of eegchge sfe pocesses of N d he hdolc decoposo of TP... Popees of N Fgue clel shows h he H-bods bewee N bse ps eded b he poos epese cue. Sce he cue poduced b ech poo duces gec feld hee ess gec couplg. The segh of hs couplg depeds o phse popees e.g. whehe eghbog poos suleousl u pllel o oppose bewee he bse ps. O he ohe sde he chge dsbuos he N-bss coupled v deobophosphes hve o be egded s coupled cpcces. The poo cue bewee bse ps hve bee clculed wh he help of euo 57. Ths cue s pefebl ffeced b he geogec feld Fgues d b. Sce he N ess s double hel depeds o he locl oeo of he H bod eled o he eel feld whehe geogec s full o l suo ve we pese due o he oez foce. Theefoe he poo cue co ol occu log he slles dsce sgh-le of he bse ps bu he coespodg oo epeses ddol scew. The ool feuec s chcezed b he o feuec. I he l cse of ve sll pojeco gle fuhe cew oged b he eeel sll sol gec feld lso fluece he poo oo. Theefoe he ovell oo leds o fuhe couplgs log he H bods of he double hel: sp-ob couplg ccodg o he ool oo d sp-sp couplg bewee he ovg poos d bewee poos d d-elecos of he phosphes of he ucleodes. Sce he N bses of he sds uull chge cofguos ecos ue of sgles d ples wh espec o eo-eol uoes he whole sse of boh sds epeses esoos wh delecc couplg.

40 4 Wh egd o he gec ecos log he double hel we hve o ccou fo he we couplgs sp-ob d sp-sp. Howeve due o he H bods eded b uel cues bewee bse ps he wvele oos elecc couplgs bewee he bses of he eled N sds d gec ecos e o b; he cocde he phses. The popees of Fgues d b coeco wh Fgue e os po fo bohhs. Thus he poel ccodg o Fgue s wh slgh odfcos vld fo ll H bods of N. If hs poel would hve he fo of fl u bewee he eled bse ps he poos would osclle wh hs u ccodg o he locl epeue H bod would be possble bewee he bse ps d eo-eol uoezo would o es. Ths es h he whole double-sded hel could o es he el fo. Sce he eco eded b H bods s coeced wh uu echcl uelg he feueces of he poos vellg bewee bse ps e sgfcl loweed coped o hel oscllos poel u. Fgue geogec G poo C φ Fgue b geogec G poo φ C Fgues d b: ecos of he geogec feld eled o H bod bewee he bse ps G d C. I Fgue φ s eeel sll H bod d geogec e el pllel; Fgue b he pojeco of geogec pepedcul o he s bewee G d C s sgfcl hghe. fs le us cosde he H bod bewee d T G d C coeco wh Fgue.

41 4 Thus he poos osclle copbl fs wh he coespodg poel u befoe successful uelg c hppe. Ths gves se fo oscllg cue epessed b ducvce he duo of hl pobbl he bses s coeced o he cpcce C. I fs ode we c epese he H bods G C b decl oscllos Fgue o Fgue 6 sce he e o posoed copl w d he H bods T b Fgue o Fgue 4. Tble peses he esuls whwhou gec couplgs whch hve bee deeed v clculos of he chges he bse ps d cues bewee he. Tble : Resoce feueces of he H bods of N whwhou couplg bewee he coespodg bse ps T d G C. T πτ sec - G C πτ sec E-. E- 8.7 E- 6.4 E- 4.9 E-. E- 9.8 E- The e sep ccous fo he gec eco of poos of he H bods he geogec feld Fgues b ledg o o feueces. ue o he double hel we c ob ll possbles.e. l effec f poo oo d gec feld e pepedcul d u fluece f boh e pllel. I he le cse he sol gec feld c c wh ve slow feuec. The e of esoces v bewee 9 sec d hous f ol he sol gec feld s pese ude he pcul cofguo of he double hel. Sce hs oo ehbs lws he fo of ccles oud he s bewee he bse ps he geogec feld s peel chgg whch fll leds o uul couplgs bewee he poos vellg hough d bc d o sp-obsp-sp couplgs. coseuece of ll hese uul couplgs s h we ob besdes he fs oscllos be feueces of he ode: τ.5 d; τ.95 d; τ.4 ds; τ 6.7 ds. I he couu l whch povdes g sdg wves we hve lso o ccou fo hese couplg. ccodg o pevous seco he eled wve euo wh secolocl gec couplg eds:

42 4 94 ] l [ c Tes l v Tes c The secolocl cobuos esuls fo we couplgs of loge ge. Thus he coeffces d 4 e gve b: 94 4 ; 4 4 Cobuos of hghe ode c be egleced bu he dce he cople suo of N. I sl fsho he N bses log he sds e lso coeced olocl w l due o he couplg v d elecos of he phosphe goups. Euo 6 ow becoes: 95 ; v b v b b b v The sdg wve soluos of euos co hold euos due o he coeco es. Thus we ob es up o ode 4 whch ow eseble he soluos of esoos cossg of 4 couplg es. ue o sp-sp couplg we hve lso o dd he esece of sp wves of whch he sp oeo s gve b he deco of he geogec feld so f ohe gec of soge ode e bse. If we eplce euo 47 chge b sp S euvle euo holds see He 965. I fs ode euo 94 povdes he led sed soluos: s ep c π π The dffeece o euo 45 s ol he wegh fco c he egevlues e sll uchged: 96 ] [... C l l c c π π I fuhe odes we ccou fo he couplgs. h we odf euo 96 b ddg he es

43 4 oe h c c c : 97 9 [ '' 4 [ ' [... '' ; ' ; '' s '' ep ' cos ' s ' ep s ep C l C l C l c c c c c c π π π π π π π The soluo 97 s b o es coplee. We should le o ecll h C d C e eled o esoce feueces esulg fo odfcos of he bss feuec. The soluo 97 povdes be feueces wh slow oos hough d bc log he N sds.e. he whole sse s o gd. These be feueces e eled o he bove vlues of τ τ τ τ bu fuhe uecl vlues he evls of elevce es. The popgo of he chges of he cofguo of he N bses obes he lowes ode he soluo 47 bu we hve lso dd coeco es 98 '' cos s ' cos cos s cos s b b b π π π π The soluos ccodg o euos e o depede sce he vlues fo hve o gee. I soe odel clculos we hve obed he uecl vlues: c.89 c.9 c. b.87 b. c.. s led eoed hs euo lso ehbs sdg wves. specfc ecos soe N-ses d eeg suppl he double sded N s opeed wve-le fsho e.g. v H bod of we o poe.

44 44 Fgue : Peodc sse of esoos wh gec couplg. The gec couplg c be eplced b eleccl couplg C. Ths leds o sl pe of wve euo. Fuhe es esul fo couplgs bewee odjce eghbos.. Hdolc dec of TP-g-Poe coplees Fgue 4 shows TP-g-poe cople whch oe c fd e.g. he fles of uscle cells. The eeg of.5 ev s soed s cofed solo vdov 979. The solo c cel be cosdeed s sdg wve of sse of oscllos wh eleccl couplg. The pesece of C os we opoos d opo led o he hdolss of TP d he couplg codo fo sdg wves.e. ode he edpos bes dow. The soed eeg escpes o becoe vlble fo soe ohe boolecules such s echcl wo of uscles he uscle of he he ve po o shess of poes N eplco d scpo ec. I ppes o o be pobble h he soed solo eeg hs ve low feueces. Howeve f C os show 7-ds-peod due o he sol gec feld he becoes evde h TP hdolss lso occus wh 7-ds-peod Ule e l 995 Ule. The effec of he geogec feld leds o copbl fs oscllos c. ue. The fs d slow oscllos occu suleousl. Fgue 4 peses he hdolc pocess schec w. Howeve cosdeg he gec eco hs pocess s he coplced. ccodg o he esuls seco.. we hve o ccou fo he deco of he geogec feld d fo he pepedcul copoe of he sol gec feld. The cobuo of he le feld s he sll leds l o

45 45 ovell effec d c be coped wh bee-hve whch ces ou eeel slow pedul ovee whees he bees e he fs ovg vous decos. The effecve ss of he g hs bou gude s C whch ples el he se peod ccsep s C. The whole cople ccodg o Fgue 4 ehbs degees of feedo. Oe of he s he ccul oo of he ol cople he geogec feld whch povdes ccse-sep peod bu hs be dffee depedece of he ss ube of he poe.e. he peod could lso be boh loge d shoe. Fuhe degees e he lge ube of locl oscllos of he posve d egve cosues of he phosphe goups d of he chged poe ses. These ool oscllos e he fs ode: soe secods. So he whole suo c be copoed b coupled ccus wh 4 o oe esoos s pevousl show. Whe we hve loo o Fgues 7 7d we c vef h he whole oo cossg of degees of feedo povdes befeueces fo oe d up o ds. The copoes of ccse-sep d ccsep wll becoe suppo b ehcee whch leds o ddol sblzo. C OH - H poe g P P TP Fgue 4: g-tp-poe cople schec epeseo d hdolo b C H O. The dec of TP wh elese of dphosphe goup P Fgue 4 s fouded b H bod.e. oe poo of he we olecule hs o fulfll uel pocess o ech oge of TP; heefoe he sec poel fo uu echcl uelg s pplcble Fgue. ue o he ool oscllos duced b he geogec feld he ovell oo s he cople. Thus we hve les o be we of sp-ob d sp-sp couplg whch ehce he pobbl of uu echcl uelg. ue o he geogec eco he soed eeg of.5 ev he poe hs o be sdg ccul wve whch cofs he ssupos of vdov bsed o he ole Schödge euo ced bove.

46 46 4. Soe coclusos Ths seco eds o develop shess of he peseed esuls wh fdgs of soe ohe uhos. fs we eebe he fdgs of Pgoge e l 997. ccodg o hese uhos ole eco-dffuso euos wh feedbc d feed-sdewd couplgs epese sses f fo hel eulbu d show ddoll he pope of checlbologcl clocs he usselo o he Oegoo e specfc eples see lso Ule. The flueces of gec felds geogec d sol gec hve o bee ccoued fo b Pgoge e l. These flueces c coopeve w.e. he c led o ehcee o f he gec esoces do o cocde wh checl clocs o hbo co. I eve cse feedbc d feed-sdewd couplgs of checl ecos bewee specfc olecules fd he foudos uu echcl esoce deoos lzed hs couco. The e schees d so pobbles of wo olecules hve o be ve sl o eld checl ff of he. The esoce doos duced b gec ecos led o fuhe splg of he e schees fe sucue splg d due o sp-ob d sp-sp couplgs esse cossg wll be de possble. Fuhe po specs e fdgs of Evsfev 9 Yosh e l 9 d ow wh egd o lgh-depede fluece of cpochoe d geosesv of ccd cloc d he fluece of sol cv o olecul pocesses o eh. The couco of Yosh e l s pll bsed o esuls of ow ced bove. Thus ve po Zegebe o eh s he lgh-d ccle. Ths pocess gh hve bee he og of he ccd evoluo bolog bu couse of he evoluo he hh hs becoe depede s show vous epees.e. behves s sc eco pocess of specfc boolecules. Fo he vewpo of e schees s evde h cpochoe d cochoe olecules cog F NP NPH d ecg wh poph d s devves elo d seoo e edl eced b eel lgh he d hh o duce eced sgle d ple ses see e schee 9. Sce vsble lgh s bsobed he s spo echss ledg o logge ecos e eued o ffec fuhe olecul pocesses. The dscussed gec popees ow becoe he sgfc sce ol esse cossg c led o spo of eeg. I log olecul chs pue sgle ecossos pl ol locl ecos whch e dped b sce of lgh d he poduco. po spo echs s epeseed b ch of H bods we Fgues 5 5b sce we olecules e lws pese

47 47 cellul ssue. Fgue 5: Poo echge bewee wo we olecules lef: l se gh: fl se. Fgue 5b: H bod wh echge of poos ch of we olecul: possble echs of eeg sfe cells d ecellul edu. The esuls obed b ced bove l del wh he ole of sp-ob couplg sgle-ple sos d sp wves sses f fo hel eulbu whee he T ule s voled due o phse sos d ccl pos. pcul sess e feuec bds fo Hz og: eh ccd hh Egel e l 996 d he Hz do Evsfev whch hs sol og. The ssoced eeg les below he eeg T hel eulbu d c ol ffec d schoze hose pocesses coeced wh gec popees ccl pos o peve hel eulbu whch would be deh of lvg sses. Sce he coeco of elecogec popees o bohhs s pove fc he vewpo of he gude of he eeg c cel o be vld. s fl eple we pese ow esuee esuls of he

48 48 TP ebols gowh d so phse obed v -P NR specoscop uo spheods. The esuee codos hve bee publshed elsewhee. These esuees show ddo o he fs pocesses pcl ccles of whch he ccsep ccse-sepe e ve poe. The ccd peod s lso pese bu ppes o o pl he do ole. The esuees hve bee ced ou coplee dess; heefoe s esued h he lgh-d hh c be ecluded. Thee hve bee pu fowd ew esuee ehods o uf TP cellul pocesses whch vod he sog gec felds of NR specoscop ud e l 975 sso e l 8 Webe e l. Fgue 6: TP coceo uo spheods gowh d pleu phse of CH l cells. These ehods ppe o be uch close o he cellul phsolog d seve o eld bee opzo of cce dohep Ule. Refeeces. bowz d I. Segu 97 Hdboo of hecl Fucos wh Fouls Gphs d hecl Tbles Nul ueu of Sdds G.. ebo. N. os d K. K. Tueov 969 uescece of bopoles d cells Pleu Pess odo New Yo J.. s 97 Phoo phscs of oc olecules Wle-Iescece odo F.. ow 96 Cold Spg Hbo Sposu uu olog F.. ow 976 o Sses K. Cpbell d. Pe 98 Phscs 9 F.. Ce 98 I olecul Elecocs evces cel ee New Yo.S. vdov 979 Ieol Joul of uu Ches 6 5 W. Egel W. Hellug d. Johso 996 oelecogecs 7 V. K. Evsfev 9 The Ope olog Joul 8 4

49 49 K. Fuu d H. Fujoo 969 ull. Che. Soc. Jp 4 99 F. Hlbeg. Egel C. Hbuge d. Hll 965 c edocol Kbh 5 Suppl 5-54 F. Hlbeg d G. Coélsse 99 Choobolog 8 4 H. F. He 96 Joul of Checl Phscs 7 8 H. F. He 96b Joul of Checl Phscs 7 9 H. F. He 965 dvced uu Ches ddso-wele Publshg Cop Ic. sschuses H. H d W. Süe 95 Z. Nufoschug 6 75 H. H 964 Theoe de chesche dug Spge Hedelbeg T.. Hoff d J. d 96 Cce Resech 474. O. vo lefeld d. Tcheo J. Che. Phs ud d. Thoe 975 l. oches R. so 958 Nue J. F. sso C. Kz. zoff d E.. Gud 8 l. Che Péez. Tuce H. Hjlso d O.. vo lefeld JCS 5 55 F.. Popp G. ece H.Kög d W. Pesch 979 Elecogec o-ifoo Ub & Schwzebeg ücheweloe I. Pgoge d I. Seges 997 The Ed of Ce Te Chos d he New ws of Nue The Fee Pess New Yo. Pull d. Pull 96 Nue 9 8. K. Rdhw.. Ku d.. Sgh I. Jou. Copue pplcos 7 8 H. Schwege S. ege H. Kesche. öle E. Hlbeg R. Sohe d F. Hlbeg 986 Poc. N. cd. Scece US P. Schuse G. Zudel d C. Sdof 976 The Hdoge od Rece eveopes Theo d Epees Noh-Holld Publshg Cop sed d New Yo S. S. Sug 977 Ieol Joul uu Ches XII Supplee I 87 W. Ule d H. H 978 Nuovo Ceo W. Ule 98 Theoec Chc c W. Ule 98b Theoec Chc c W. Ule 979 Z. Nufoschug 4c W. Ule 98 I. Jou. uu Ches W. Ule 98 I. Jou. uu Ches W. Ule G. Coélsse d F. Hlbeg 995 I vvo W. Ule I vvo 6 6 C. Webe E. Gud E. Hech. zoff d C. Kz IFE Poceedgs Spge Hedelbeg T. Yosh. hd d C. H. Helfch-Föse 9 Joul Plosbolog 7 e86