SUPPLEMENTARY INFORMATION

Transcription

1 UPPLEENTARY INFORATION o: /naure10874 upplemenary eho Expermen: maeral an meho Proen preparaon. Inner-arm ynen ubpece c, g, f) were olae from he ouer-armle muan of Chlamyomona renhar ran oa1) eenally accorng o he meho of Kagam an Kamya 18. Crue exrac of ynen ubpece were fraconae by hgh-performance lqu chromaography HPLC) on a onoq 5/50 GL anon exchange column GE Healhcare Japan, Tokyo, Japan) by eluon wh a lnear graen from 10 o 500 m KCl n HDE oluon conanng 0.5 m PF, a a flow rae of 600 µl mn -1 wh a 115 ml graen. Fnal concenraon of ynen ubpece were µg ml -1. The poole fracon of each ubpece were furher purfe by a econ HPLC fraconaon n Q PC3./3 column, GE Healhcare Japan, Tokyo, Japan) wh a lnear graen from 10 o 400 m KCl n HDE oluon a a flow rae of 00 µl mn -1 wh a. ml graen. Pury an aggregaon of ubpece wa examne by 3% D-PAGE wh lver anng an by ucroe eny graen cenrfugaon. A knen conruc K560-H) wa prepare accorng o he prevou uy 30. Porcne bran ubuln, purfe accorng o Vallee 31, wa polymerze no mcroubule n he aembly buffer a 37C an ablze by ang 10 Taxol. Cy3-labele fluorecen mcroubule were prepare, accorng o he meho of Howar an Hyman 3 wh ome mofcaon. croubule have polymorphm; ha, a varaon n he number of prooflamen. The number of prooflamen vare wh change n compoon of he polymerzaon buffer. Deermnaon of he prooflamen number requre elecron mcrocopc obervaon. In our proceure polymerzng ubuln n he preence of DO an PIPE), ca. 7% of mcroubule ha 14 prooflamen an ca. 13 % ha 13 prooflamen. Concenraon of proen, ynen c, g, f, knen an ubuln concenraon were eermne ung he Brafor ye-bnng aay. In vro moly aay. In vro aay were performe a 0- C, bacally accorng o akakbara e al. 19. A flow cell wa mae of wo coverlp 4 mm 40 mm) cleane wh non-onc eergen an rne wh e-onze waer. The wo lver of polycarbonae flm 50 m n hckne were ue a pacer of he flow cell 10 l n volume). Fraconae ynen c g ml -1 ) wa lue, f neceary, each a varou concenraon n buffer oluon conanng 30 m HEPE/KOH ph 7.4), 5 m go 4, 1 m DTT, 1 m EGTA, an 1 mg ml -1 bovne erum albumn. The flow cell wa fluhe 1

2 REEARCH UPPLEENTARY INFORATION wh 10 l of he lue ynen oluon, ncubae for 5 mn an hen wahe by he buffer conanng no ynen. oluon 0 l) conanng 40 μg ml -1 mcroubule, 0.5 m ATP, an 1 m DTT wa nrouce no he flow cell. Wh he concenraon of mcroubule ue an urface area of a flow cell ue, number of mcroubule foun on he urface wa 5.3 ± 0.3 mcroubule per 100 m n = 4). The urface ene of ynen were calculae from he concenraon of ynen molecular wegh of ynen c wa aume o be 600 kd) an he geomery of he flow cell, an we aume ha ynen rbue evenly on he gla urface. croubule were vualze on an Olympu ep-fluorecence mcrocope BX-51, Olympu, Tokyo, Japan) ung obecve lene UPlan Apo 10, n.a.= 0.4, UPlan Apo 0, n.a.= 0.7, UPlan Apo 40, n.a. = 0.85; Olympu), he WIG fler e Olympu, Tokyo Japan) an a 100 W mercury lgh ource. The mage wa proece ono an mage-nenfe CCD camera Veo cope V4-1845; Veo cope Inernaonal L, erlng, VA, UA, CCD300T-RCX; Dage-TI, chgan Cy, IN, UA) or E-CCD camera C9100-1, Hamamau Phoonc) for fluorecence mage an procee by he conra enhancemen an offe conrol. For Image-nenfe CCD, equence of veo frame were capure ung a frame grabber car ream Px, an recore ono a compuer har c. For he E-CCD, he mage were recly recore ono a compuer har k. The poon of mcroubule were gze an analyze by a cuom auomae rackng program or crp wren n Image J hp://rb.nfo.nh.gov//). The lengh of mcroubule were meaure ung Image J apple o veo mage of mcroubule boun ghly o he coverlp urface an vewe by fluorecence mcrocopy. The mean lengh of mcroubule ue wa 15.6 ± 7.3 µm n = 57). Lengh of flamen employe n vorex formaon expermen fell n h range. For he expermen hown n Fg. 1 an n he man ex, he eny of ynen c ue wa 500 μm -. Collon expermen. To examne he effec of ynen ene on he behavor of mcroubule a her collon, he ene of ynen c ue wa vare from 750 o 500 μm -. Deny of he mcroubule wa μg ml -1 n a oluon an he eny on he urface wa aue o be 10 mcroubule per μm uable for obervaon of nvual collon. The angle mae by he wo ncomng mcroubule approach angle) wa meaure ung gze an egmene mage of mcroubule collon an crp wren n Image J. Collon were clafe no four caegore, parallel, an-parallel algnmen, parallel onng, oppng an crong-over. Approach angle were clafe no bn of wh π/10 an he frequency of each collon ype wa coune n each bn. To oban he aa hown n Fg. 3, he ene of ynen c ue wa 500 μm -.

3 UPPLEENTARY INFORATION REEARCH Long me rackng of ngle mcroubule. To examne he behavor of a mcroubule moon whou collon, we racke a hea of a mcroubule for uraon of up o 350 a n Fg. 4 n he man ex. Deny of he mcroubule wa 4.8 ng ml -1 n a oluon, an he urface eny wa abou 5 mcroubule per 1 mm uable for obervaon of ngle mcroubule moon whou collon. The urface eny of ynen c ue wa 000 μm -. The poon of he leang en of a mcroubule wa race an recore a he poon of he mcroubule. Effec of urface ene of mcroubule on he paern. The effec of he eny of mcroubule on he paern wa explore a hown n upplemenary Fg. 1. The eny of ynen c ue here wa 1500 μm -. The concenraon of mcroubule n oluon wa vare a 114.5, 57., 8.6, 14.3 μg ml -1. A he concenraon , 57. μg ml -1, he generaon of vorex wa oberve ncly, wherea he formaon of he vorex wa no obvou wh he concenraon 8.6, 14.3 μg ml -1. Effec of he eny of ynen c an knen on he collon of mcroubule. The algnng of mcroubule rven by ynen c no alway occur. The urface eny of ynen c nfluence he collon ac. upplemenary Fg. 3a llurae he probably of mcroubule algnng an an-algnng collon a a funcon of he urface eny of ynen c. For each moor eny, we examne abou nney even n whch wo mcroubule approache each oher. A emonrae, he probably of mcroubule algnng ncreae wh an ncreae n he urface eny of ynen c. The probably became aurae when he eny of ynen c reache 1500 µm -. In erm of he ype of moor proen, he hgh probably of nemac algnmen collon eem axonemal ynen-pecfc: nner arm ynen c, g, an f of Chlamyomona flagella nuce gnfcan mcroubule algnng bu no knen an cyoplamc ynen expree n Dcyoelum cell. In he knen-mcroubule yem, more han 80% of mcroubule ene o clmb over he oher mcroubule upon collon crong), rrepecve o he urface knen eny upplemenary Fg. 3b). Depe havng one moor oman per molecule, ynen c can rve a mcroubule procevely. Furhermore, ha a low uy rao he fracon of he me ha ynen pen n aache o mcroubule o he oal me of an ATPae cycle) aroun Thee reul ncae ha nner arm ynen ha a mechanm o arac mcroubule cloe o moor oman. In an axoneme, we uppoe ha uch aracon beween ynen an mcroubule relevan for mooh flagella moon 33, an reul n he collon behavor oberve n our expermen. 3

4 UPPLEENTARY INFORATION 4 REEARCH Daa analy Analy of he mcroubule raecore. A hown n Fg. 4a), he raecory of he hea of a mcroubule mooh an curve. In aon, he raecory ocllae weakly ue o he ynamc characerc of he mcroubule an he ynen. To oban he long-erm behavor of a mcroubule, we moohe he expermenally-eermne raecore an elmnae he effec of velocy flucuaon an he mall ocllaon a follow. The poon of a mcroubule wa meaure every Δ=0.68. The poon of a mcroubule a me beween hee momen of meauremen wa emae ung a hr-orer plne nerpolaon. Here, x), y)) he emae poon a. Aumng ha he velocy of a mcroubule wa no change urng he nerval beween wo conecuve meauremen, he velocy an he ance along he raecory from he arng pon were emae a y x v 1) / / ) for Δ < < +1)Δ 4) ), ) 0 v 5) repecvely. To oban he long-erm behavor of he curvaure of raecory, x an y were moohe ung he econ-orer avzky-golay moohng meho 34. nce he velocy of a mcroubule flucuae, x an y for gven ance along he raecory, Δ, were ue for moohng. The moohe x-componen of he raecory, x g, wa calculae a follow:, ), ), ), g x G x G x G x, 0 6) where he lengh of he whole raecory,,, R n L n G he coeffcen for he avzky-golay moohng meho, n L he number of earler aa ue, an n R he number of laer aa ue mlar equaon were ue for calculang y g ). Here, wa aken a Δ = 160 μm. The moohe ervave an econ ervave of x an y by, x g /, y g /, x g / an y g /, can be obane n he

5 UPPLEENTARY INFORATION REEARCH ame manner. The curvaure of he raecory, κ, wa emae a g g g g x y x x ) 7) 3 / g g x y where maller han. Fgure 4 c) gve he frequency rbuon of κ, from whch we obane he mean κ 0 = μm -1, an he anar evaon σ κ = μm -1. To evaluae he peren lengh of κ, he auocorrelaon R) of κ wa calculae a 1 R ) 8) n n 0 0 where n a non-negave neger, < > repreen he acal average for all n an all obervaon. The logarhm of R) wa fe wh a / 0 ung he arquar-levenberg meho 35,36. Fng parameer were a an 0 an R) μm) wa ue for fng. 0 peren lengh of κ) wa emae a 54± 4 μm by he fng of R). ahemacal moel Non-menonalzaon an parameer eermnaon of mahemacal moel. In orer o analyze he moel wh eq. ) an 3) n he man ex, we non-menonalyze hem a X e x co e y n T A n T N T ) ~ 1 0 ) T ) T where he um over he N ) parcle currenly whn ance 1 of parcle. The nonmenonalze varable are<ζt) ζt )> = η δt T ),<ζt)> = 0, an T = v 0 /l, Ω =ω l /v 0, X = x /l, A = αl/v 0, λ = τv 0 /l, η = σ l/v 0 ) 3. The anar evaon of Ω now expree a T ) ) / 0. The expermenal aa can be nerpree o he moel a follow. A an neracon lengh l, we pu l = 15 μm ha approxmaely correpon o he lengh of mcroubule. A he velocy of he parcle v 0, we pu v 0 = 8.75 μm -1 ha approxmaely correpon o he average velocy of he mcroubule. The rbuon of ω eermne from he expermenal aa of he rbuon of κ, by emang ω = v 0 κ 9) 5

6 REEARCH UPPLEENTARY INFORATION an σ ω = v 0 σ κ. nce we pu v 0 = 8.75 μm -1, we oban he rbuon of ω a he Gauan rbuon where he average wa ra -1 an he anar evaon wa ra/. The relaxaon me τ can be obane from τ = 0 /v 0, an 6.0. The eny of he mcroubule aken a ρ = 0.05 μm -. ubequenly, we oban he normalze parameer a, Ω 0 = 0.01, T) 0 ) 0. 07, λ = 36.1, an he eny Numercal mulaon. For our numercal calculaon Fg. 5a), we ue Ω 0 = 0.01, T) 0 ) 0.07, λ = 100, an he eny 10. The mulaon me wa e o an he me ep wa e o 1. Parameer A govern he relave mporance of algnng collon. If oo mall, parcle o no nerac ofen enough an go hrough each oher. If A oo hgh, parcle, n he abence here of any erc repulon, form unrealcally ene bunle. We foun he A = 0.1 yel realc collon ac compare o he expermenal reul) an ue h value n our mulaon. The area wa 51 51, an we hu ue N = parcle. Peroc bounary conon were ue n orer o mnmze he effec of wall o a o be cloe o expermenal conon n he bulk of he flow cell. Parcle were nally ranomly rbue an ranomly orene. For he numercal calculaon, we ue a hgher λ han he expermenal value. Through he exploraon of parameer, we foun ha he vorex paern can appear for λ > 60. We wll cu h pon n he followng econ. Phae agram of he mahemacal moel ee alo upplemenary Fgure ). To gan a eeper ngh of our mahemacal moel, we vare he relaxaon me of angular velocy λ an he mean parcle eny ρ a keepng Ω 0 = 0.01, T ) 0 ) We meaure u n)/n a upplemenary Fg. a,c) an exp ) N upplemenary Fg. b, c), where u n) he varance of he local eny an he global nemac orer parameer. The area wa Afer T = , we collece aa up o T = The followng proceure wa ue o calculae u n): 10 napho aken wh every me ep were umme up. We hen calculae he rbuon of eny ne 4 4 ze cell n he umme mage. Th wa conuce every ΔT = 100, an u n), he varance of local eny rbuon, wa obane. We ue u n)/n a, where n a he average number of parcle per cell, o quanfy eny flucuaon. The global nemac orer parameer wa me average. We foun ha u n)/n a mall when parcle 6

7 UPPLEENTARY INFORATION REEARCH poon are ranom an ake large value n he preence of bunchng/paern. non-zero when he yem poee global nemac orer. Thu, we can enfy ) ranom u n)/n a mall, zero)upplemenary Fg. )), ) vorex u n)/n a large, zero) upplemenary Fg. II)), ) nemac phae non-zero) upplemenary Fg. )). The upermpoe mage of u n)/n a an, an he phae agram of he paal paern are hown n upplemenary Fg. c an. In he low eny regon, he vorex paern are able only when he relaxaon me λ uffcenly hgh, an nemac phae able only when λ uffcenly low. The bounary beween he nemac an he vorex phae flucuae lghly epenng on he eny, bu wa almo conan an aroun λ = 60 when ρ a > 0.5. Th crcal value of λ for vorex formaon larger han he one he expermenally obane value; abou 1.6 fol. Conerng he mplcy of our mahemacal moel, we beleve ha h no really a crepancy bu ncave of ome relavely goo agreemen wh our expermenal reul. Reference 30. Cae, R. B., Perce, D. W., Hom-Booher, N., Har, C. L. & Vale, R. D. The reconal preference of knen moor pecfe by an elemen oue of he moor caalyc oman. Cell 90, ) 31. Vallee, R. B. Reverble aembly purfcaon of mcroubule whou aembly-promong agen an furher purfcaon of ubuln, mcroubule-aocae proen, an AP fragmen. eho Enzymol. 134, ). 3. Howar, J. & Hyman, A. A. Preparaon of marke mcroubule for he aay of he polary of mcroubule-bae moor by fluorecence mcrocopy. eho Cell Bol. 39, ). 33. Lnemann, C. B. Teng he geomerc cluch hypohe. Bol Cell. 96, ). 34. avzky A. an Golay. J. E. moohng an fferenaon of aa by mplfe lea quare proceure. Analy. Chem. 36, ). 35. arquar, D. W. An algorhm for lea-quare emaon of nonlnear parameer. IA J. Appl. ah. 11, ). 36. Levenberg, K. A meho for he oluon of ceran problem n lea quare. Quar. Appl. ah., ). 7

8 REEARCH UPPLEENTARY INFORATION upplemenary Fgure an Legen upplemenary Fgure 1 Deny epenence of vorex paern formaon. The concenraon of mcroubule n oluon wa vare a a, 14.3, b, 8.6, c, 57. an, μg ml -1. When he eny of mcroubule wa maller han 8 6 μg ml -1, he vorex paern coul no be oberve. 8

9 UPPLEENTARY INFORATION REEARCH upplemenary Fgure Phae agram of mahemacal moel of neracng elf-propelle parcle Eq. 6)). a, The varaon of eny, u n), ve by he average number of parcle, n a, an b, he nemac orer parameer,, ploe agan fferen ρ a an λ. c, upermpoe mage of a an b, Re an green repreen, u n)/n a an, repecvely. Yellow color how he area wh hgh u n)/n a an., Phae agram of he mahemacal moel. ) ranom, ) vorex, an ) nemac phae, he ypcal napho of each phae a T= alo hown, where only 1000 parcle are hown a re arrow. 9

10 REEARCH UPPLEENTARY INFORATION upplemenary Fgure 3 Depenence of collon behavor on ynen c an knen eny. Compare wh he cae of ynen c, mo of mcroubule u croe over n cae of knen. 10