Stochastic dynamics of ion channels in sensory cilia: regulation by feedback

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Hugo Golden
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1 Sohai dynai of ion hannel in enoy ilia: egulaion by feedbak Manoj Gopalakihnan MPI-PKS Pee Boowki Main Zapooky Fank Jülihe 4/9/5 MPI-PKS, -4-5

2 `Duing he pa deade, he olfaoy ye ha eeged fo elaive obuiy a an idioynai enoy ye o i uen plae a a odel ye fo oleula deeion he olfaoy ye i lealy ipe wih oppouniie fo he iaginaive inveigao. S. Fieein, `How he olfaoy ye ake ene of en, Naue 43, /9/5 MPI-PKS, -4-5

3 Peview feedbak fluuaion Olfaoy Signal anduion adapaion Infoaion anfe 4/9/5 MPI-PKS,

In huan being, nealy diffeen ype of O have been idenified.

4 he olfaoy ye: fo he odoan o he bain Eah olfaoy eepo neuon ON expee a ingle ype of odoan eepo O poein. In huan being, nealy diffeen ype of O have been idenified. he ON ae hoogeneouly diibued a he enoy ogan, bu he axon fo all ON expeing he ae O onvege o a ingle egion a he olfaoy bulb. 4/9/5 MPI-PKS,

5 he iliu he ilia ae long hin uue, onued fo ioubule, peen in any diffeen ype of ell. he ilia and loely elaed flagella help loooion in baeia and pe. In epiaoy a, he ilia help weep away du paile. he olfaoy ilia ae uh lowe oving, and ay he olfaoy eepo. 4/9/5 MPI-PKS,

Signal anduion in olfaoy eepo neuon he wheel and gea he O belong o he faily of G- poein-oupled eepo GPC. he odoan-aivaed O eleae G- poein, whih aivae he enzye adenylyl ylae.

6 Signal anduion in olfaoy eepo neuon he wheel and gea he O belong o he faily of G- poein-oupled eepo GPC. he odoan-aivaed O eleae G- poein, whih aivae he enzye adenylyl ylae. Adenylyl ylae eleae aged yli AMP AMP, whih bind o CNG hannel fo Ca and Na, and aue he o open. he influx of Ca ineae he elei poenial of he ebane noally a -65V, and when he poenial eahe a hehold of -4V, an aion poenial i iggeed, whih popagae along he axon. 4/9/5 MPI-PKS,

7 Caliu: he wo-faed eenge Ca aplifie he olfaoy epone by opening Clhannel.. bu inhibi i own influx by foing Ca-alodulin oplex and loing he hannel, heeby egulaing he epone. 4/9/5 MPI-PKS,

8 Adapaion due o feedbak Adapaion in enoy ye: abiliy o adju eniiviy o diffeen iulu ineniie. Help he ye o peven auaion of epone, and allow i o epond o an even lage iulaion. In he olfaoy ye, adapaion i piaily aued by a negaive feedbak involving Ca. 4/9/5 MPI-PKS,

9 `Olfaoy ignal anduion i ininially noiy * Exenal iulu ye noie Noiy oupu * Lowe and Gold, PNAS 9, /9/5 MPI-PKS,

10 Adapaion and fluuaion: Sohai odel of ion hannel dynai wih feedbak A e of CNG ion hannel along he one-dienional iliu. A hannel i eihe open, o loed, and ake ohai aniion beween he ae. When he hannel i open, aliu ion ene he iliu a a onan ae i. S i, : [ i, ] he ine-ellula aliu i alo eoved by Caliu pup in he ebane, opeaing a a ae. x, D i i S i, feedbak x i 4/9/5 MPI-PKS, -4-5

11 he D lii: iolaed ingle hannel he zeo-dienional ohai hannel poble, wih ie vaying Ca onenaion. he dynai of i eniely peified by he aii of he hannel ae. [ ] i i de S d d is λ 4/9/5 MPI-PKS, -4-5

12 Wha we eek. well, uliaely Given a eain `inpu ignal/doe, Wha i he epone S o of he ye? he fluuaion : S o he oelaion in he epone 4/9/5 MPI-PKS, -4-5

13 4/9/5 MPI-PKS, he linea feedbak appoxiaion We aue ha he pobabiliy diibuion and ae govened by he ae equaion he eady ae diibuion ielf look non-ivial: i i no vey obviou how o find he oelaion. ] [ ] ; [ P ], [ ], [ P P,, ] ; [ P i J P i D P d dp

14 N-poin funion of he wo-ae poe S < < < S > P S S > [, ] P S S S > [, ] P P [, ] [, ] P [, ] P [, ] 4/9/5 MPI-PKS,

15 he elf-onien effeive feedbak heoy Do he eplaeen i a ohai field, wih he ondiion ha aiially! Uliaely, we ake he appoxiaion elf-onien wih he ubiuion and o on.. ψ < ψ > < < ψ ψ α > < > αψ 4/9/5 MPI-PKS, > { } < S > < P [, ; ψ ] > EF

16 4/9/5 MPI-PKS, Puing he heoy o wok Dienionle foulaion: he ae equaion i: wih he oluion { } ] [ ] ;, [ P P d d { } d d P θ θψ α τ τ ψ exp ] ; [,, i,,,,

17 4/9/5 MPI-PKS, Weak feedbak: peubaion heoy Aue,o ha Now we ake he ubiuion....whih give [ ] O d e d e S > < e e << O S α α

18 Define he noie e η he noie oelao, o fi ode in he feedbak: when EF S S O Fluuaion in he faion of open hannel in eady ae: EF Fluuaion and oelaion: A Channel ae e hange ign when > 4/9/5 MPI-PKS,

19 4/9/5 MPI-PKS, Fluuaion and oelaion: B Caliu We define he Ca fluuaion In he abene of feedbak, Saionay ae fluuaion: O e e O

20 Validiy of EF: Geneal aguen In vey geneal e, he EF i expeed o wok if he epoal pofile of Ca i no ignifianly affeed by he hannel noie. Moe peifially, we would need. Fo weak feedbak <<, hi ondiion equie ha >> λ EF i valid in he lii and. 4/9/5 MPI-PKS, -4-5

21 Nueial iulaion 4/9/5 MPI-PKS, -4-5

22 . ie evoluion of <S>.,.,. 4/9/5 MPI-PKS, -4-5

23 . Doe-epone uve: adapaion λ 4/9/5 MPI-PKS,

24 Siulaion veu EF 5. λ 4/9/5 MPI-PKS,

25 3. Channel fluuaion in eady ae 4/9/5 MPI-PKS,

26 4. Ca fluuaion in eady ae 4/9/5 MPI-PKS,

27 5. Auo-oelaion in aionay ae I: hannel 4/9/5 MPI-PKS,

28 6. he effe of feedbak: opaion wih heoy 4/9/5 MPI-PKS,

29 7. Auo-oelaion in aionay ae II: Ca 4/9/5 MPI-PKS,

30 Whihe nex? he feedbak bing in a ong hioy dependene in he dynai of he hannel, and a bee ehod need o be eployed in ode o ea he feedbak in a igoou anne, aenable o yeai ipoveen. PAH INEGAL MEHODS! 4/9/5 MPI-PKS,

31 Pah-inegal foulaion of he poble S τ τ τ τ Chaaeize he hioy of he poe in e of { } he e of flip-ie, o equivalenly, he e of ie ineval i and i. i { } { } 4/9/5 MPI-PKS,

32 he `fee paile : wo-ae poe wih onan ae S Φ, ;,,..., e e... e he pobabiliy funional fo a given hioy of ae-flip, wih he inegaion eaue ˆ d d... d d [ ] 4/9/5 MPI-PKS,

33 he pobabiliy of eun o zeo i wien a a u of hioie. P Φ, ;,,..., [, ] wih he `fee paile aion... d d... d e F F [{, }; ; ] i i i 4/9/5 MPI-PKS,

34 ewie P, e I I d d e... d d e In Laplae anfo, P I 4/9/5 MPI-PKS,

35 4/9/5 MPI-PKS, A ueful `heoe g d f d g d f d G k k g f G g f d G Conide a geneal ie-odeed inegal of he fo I Laplae anfo i iply Poof: ju ue he onvoluion heoe! If hen, g f G

36 4/9/5 MPI-PKS, Finally Uing he heoe, we find ha And, afe ubiuion, Afe inveion, I ] [ P e P P

37 4/9/5 MPI-PKS, Inluding feedbak S [ ] i j i F j j d e exp,,..., ;, τ O d e i j i F j j

38 4/9/5 MPI-PKS, Calulaing he oeion o he eady ae he Laplae anfo of he eun-o-zeo pobabiliy i { } O J I P J [ ] λ λ λ λ λ y y J < y

39 he fi ode oeion We deeine he eady ae fo he Laplae anfo ielf uing he elaion { P } S li S Fo opaion, he effeive feedbak appoah give S EF 3 O O he eul ah when and when 4/9/5 MPI-PKS,

40 Copaion beween EF and pah inegal alulaion 5. λ 4/9/5 MPI-PKS,

41 Conluion and oulook wo appoahe o udy ohai ignal anduion wih feedbak: effeive feedbak heoy and a oe igoou pah inegal ehod. I i poible o opue all he ean and oelaion uing hee ehod, a lea in a peubaive fahion. Exenion of he wok o udy infoaion anfe, by inluding an inpu ignal, a well a genealizaion o he full one-dienional poble i uenly being udied. 4/9/5 MPI-PKS,

Consider a Binary antipodal system which produces data of δ (t)

Consider a Binary antipodal system which produces data of δ (t) Modulaion Polem PSK: (inay Phae-hi keying) Conide a inay anipodal yem whih podue daa o δ ( o + δ ( o inay and epeively. Thi daa i paed o pule haping ile and he oupu o he pule haping ile i muliplied y o(