SUBDIFFUSION SUPPORTS JOINING OF CORRECT ENDS DURING REPAIR OF

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1 SUBDIFFUSIO SUPPORTS JOIIG OF CORRECT EDS DURIG REPAIR OF DA DOUBLE-STRAD BREAKS S. Gs *, V. Hable, G.A. Dexle, C. Geubel, C. Sebenwh,. Haum, A.A. Fedl, G. Dollnge Angewande Physk und essechnk LRT, Unvesä de Bundesweh ünchen, eubbeg, Gemany. Depamen of Radaon Oncology, Unvesy of unch, 8336 unch, Gemany. Supplemenay Infomaon aeals and ehods Cell culue and adaon Geneaon of a sable ansfecan (clone F) of human oseosacoma cells (UOS) wh pegfp- DC was descbed 34. Twelve o 7 hous befoe adaon he cells wee seeded no cusommade cell conanes 35 and culvaed n HEPES-buffeed, phenol ed-fee medum supplemened wh.5 m Tolox a 37 C and 5 % CO. The adaon was pefomed a he mcobeam facly SAKE 36,37 a he unch 4 V andem acceleao wh one cabon on (43 ev, LET 37 kev/µm) o 3 poons ( ev, LET.6 kev/µm) pe pon n a 5x5 µm max, wh an accuacy of.58 µm n x and.86 µm n y 35 (see Fg. ). In some expemens, 4x4 µm o 6x6 µm maces wee used. The nal enegy of he cabon ons was 55 ev, whch was educed o 43 ev a he poson of he cells. The enegy educon s caused by he vacuum ex wndow (7.5 µm Kapon), he enance wndow of he cell conane (5 µm yla) and abou 3 µm of gowh medum ha he ons have o avese o each he cells. The enegy of he poons s no much nfluenced by hs sack of maeals. One sngle 43 ev cabon on esuls n appoxmaely double-sand beaks along s appoxmaely 7 µm ack hough he

2 nucleus 8, and he lowes numbe of poons necessay o oban obsevable foc, whch was abou 3 poons pe pon, means an aveage numbe of hee double-sand beaks ha ae dsbued andomly along he on ack acoss he cell nucleus ha has a hegh of abou (7. ±.3) µm. Dung adaon and he subsequen obsevaon he cells wee coveed by cell culue medum and he empeaue was kep consan a 37 C. Dsance ackng wh D Fluoescence coscopy coscopc D onlne obsevaon of DC foc began -4 s afe adaon as soon as he max paen of he GFP-agged epa poen foc was vsble wh a suffcenly hgh sgnal-o-nose ao n he epfluoescence mcoscope (Zess Axove, obecve Zess Plan-Apochoma 4x/.95 Ko Ph3), whch s led by 9 and s pa of he SAKE age saon. % - 4 % of he adaed cells expessed a suable amoun of GFP-agged molecules o be quanavely analyzed. Wh he Sma Expemens ool of he Zess AxoVson sofwae me sees of dffeen neval lengh (e.g. 5 s, o mnues) and oal lengh oal ( mnues up o seveal hous) wee ecoded by a Zess AxoCam Rm CCD camea, enablng he obsevaon and ackng of foc pas fo many dffeen me nevals. Images wee aken mosly a 6 s o 6 s nevals. In some expemens, also 5 s and 8 s nevals wee used. To allow long obsevaon mes wh a suffcen numbe of mages, llumnaon was pefomed by a commecally avalable LED lgh souce fo fluoescence mcoscopy (Zess Colb), whch educes phoobleachng and phoooxcy effecs sgnfcanly as compaed o a mecuy ac lamp, snce no UV lgh s emed. oon analyss was pefomed wh he open souce mage analyss sofwae ImageJ (hp://sb.nfo.nh.gov/) usng he SpoTacke plugn (hp://bgwww.ep.ch/sage/sof/spoacke/), developed by Danel Sage e al. 38 fo ackng fluoescen pacles n dynamc mage sequences wh subpxel esoluon.

3 Quanave dynamcs analyss oon analyss ncludes excan-ha fleng (called SpoEnhancngFle n he plugn), whch s opmally aloed fo he deecon of a Gaussan-lke spo n nosy mages 38, and a ackng algohm ha uses dynamc pogammng o exac he opmal (x,y,) aecoy of one pacle a a me. Ths s done by opmzng a cos funcon, whch weghs n a use-defned way he nensy of he manually chosen spo, s vaaon fom one fame o he nex and he movemen, whch can be esced o a maxmal dsplacemen (e.g. pxels, o moe fo fas-movng cells). In hs wok we se he weghng paamees nensy faco and movemen consan o %, nensy vaaon o 8 % and cene consan o %. Afe vsually vefyng ha he foc wee acked coecly, he wo-dmensonal dsance l() of all neghboung foc pas wee calculaed fom he x-y coodnaes gaheed by he SpoTacke algohm. We ake he sandad devaon σ (l()) of he changes n foc dsances l () as a measue fo he undelyng andom walk pocess nsead of he mean squaed dsance change <l ()> σ (l()) L² (eq. (S5)) as used by 8,9 and ohes, n ode o make he measuemen nsensve o a possble gowh of he cell nucleus ha conbues o an aveage dsance change L <l()> of he foc. We measued an aveage gowh of L of abou % (see below) whch means an aveage nm ncease of he nally µm damee of he cell nucle n hous. The sandad devaon σ () of he l () s wce he mean squae dsplacemen SD() by andom walk of a sngle pacle afe a me neval. Usng eq. () one obans: σ ( ) σ ( l( ) ) SD( ) 4dD Γ α α eq. (S) ( α ) wh he dmensonaly beng d fo ou case. The sandad devaon σ of he dsance changes l (cf. Fg. S), whch eveals he undelyng foc dynamcs, s ndependen of deconal moon ( df ) of foc n he nucleus (e.g. due o cell defomaon) and heefoe a bee measue fo he foc dynamcs han he mean of he squaed dsance changes l. The wo quanes ae equvalen n 3

4 he case of no addonal df and ae wce he mean squae dsplacemen SD of a sngle pacle (eq. (S)). Fo evey evaluable cell σ() was calculaed fom he l of neghboung foc (sepaaely fo vecal and hozonal pas) and hen aveaged ove all analyzed cells. Fo compason second nex neghbous dsances wee analyzed as well. Each cell sample conssed of 4 dffeen, ndependenly pefomed expemens. The vaous expemens dd no dffe whn he gven accuacy and hus he daa have been pooled. The measuemen unceany σ (esmaed o appoxmaely nm fom he pecson of he poson of each focus cene) was quadacally subaced fom he measued σ. Fg. S Dsbuon funcon p(l,) of he dsance changes l fo nomal dffuson. The mean Δ l of he Gaussan dsbuon s shfed o a posve value whch ndcaes a deced moon, e.g. a defomaon acng on he cell. The sandad devaon σ of he dsbuon s a measue fo he undelyng dffuson. 4

5 Compason of subdffuson and consaned dffuson modellng The dffuson daa obaned fom he dsance analyss afe cabon adaon was also fed wh a model of consaned dffuson as poposed by Jegou e al. 9. The equaon descbng a confned dffuson n D wh a dffuson coeffcen D c n a egon of adus c s 9 σ exp 4 ( ) c Dc c eq. (S) when boh foc dffuse wh he same D c n he same adus c. Assumng an addonal nomal dffuson of hs egon wh a dffuson consan D n leads o 9 σ 4Dc exp c 4 ( ) c D n c eq. (S3) A compason of hese wo models wh he subdffuson model s dsplayed n fg. S. The lnea (fg. Sa) and double-logahmc (fg. Sb) plos of hese fs demonsae ha he consaned dffuson models do no f he expemenal daa (R.9 and educed χ 5. fo he consaned dffuson model and R.95 and educed χ.8 fo he consaned plus nomal dffuson model). Fuhemoe, hese models yelded dffeen esuls fo he confnemen adus afe poon and cabon adaon ((346 ± 8) nm vs. (6± 9) nm), whch s bologcally mplausble. 5

6 Fg. S. Lnea (a) and double-logahmc (b) plo of he squaed sandad devaons σ (± SE) of he dsance changes l() beween neghboung DC foc n he nucle of cells adaed wh cabon ons. The daa ae fed wh he powe-law funcon fo subdffuson (eq. ()), wh eq. (S) fo consaned dffuson and wh eq. (S3) fo consaned dffuson plus nomal dffuson of he egon of consan. The confnemen adus c n he consaned dffuson model s (6± 9) nm, and (5± ) nm n he model of addonal nomal dffuson of he confnemen egon. The dffuson coeffcen D c s (.6±.) x -5 µm /s and (3.6±.3) x -5 µm /s, especvely and he nomal dffuson consan D n n he hd model s (.6±.4) x -6 µm /s. 6

7 Compason of mobly afe dffeen pos-adaon nevals In one sample, me sees wh me lag 6 s wee ecoded decly afe adaon and one hou lae (fom 6-8 mn afe adaon) (see Fg. S3), showng a slghly slowe bu no sgnfcan change n mobly. Thus egodcy s well epesened fo he undelyng subdffuson pocess. Fg. S3. Compason of mobly deemned fom me-sees ecoded decly afe adaon ( s sees, fs mn) and fom lae mes ( nd sees, 8- mn afe adaon) evaluaed n he same sample. 7

8 Cell cycle dependence As he cells had no been synchonzed accodng o he cell cycle phase, adaon ook place n all phases. Thus he σ²() values exaced ae he aveage of all cells evaluaed. Howeve, a few pecen of he cells could no be ncluded no he analyss because hey showed a vey dffeen behavou of he foc dynamcs whch dd no allow he exacon of he movemens n he same way as pesened befoe. These cells wee concdenly adaed afe he checkpon fo moss, so ha hese cells saed dvdng even despe he adaon. A sees of pcues ha ncludes one of hese cells dvdng dung he analyss and some ohes ha do no dvde and behave as usual ae shown n Fg. S4. Even hough he cell dvson pocess cean DC-foc can be obseved. The daughe cells also showed epa poen foc, ofen n a smla paen o ha adaed n he mohe cell (see Fg. S4, ::45 h afe adaon). Fg. S4. Tme sees of UOS cells adaed wh cabon ons n a 4x4 µm max. The aow ndcaes a cell undegong moss despe adaon, sang abou mnues afe adaon. The ohe cells clealy show he max paen dung he complee obsevaon me ( h). Tme ndcaon hous:mnues:seconds (hh:mm:ss). A smla foc paen as n he undvded cells can be ecognzed n he dvded cell. 8

9 Influence of changes of he nucleus sze afe adaon Analyzng he mean squaed dsance change <l ()> of IRIF pas dung a me neval afe adaon s a way of deemnng he andom walk behavou of he ndvdual IRIF. The ensembleaveaged <l ()> of IRIF pas wh an nal dsance l (a he me of he adaon) s calculaed accodng o l ( ) ( l ( ) l ) l ( ) l l( ) l l ( ) l l l( ) l l ( ) l l l( ) eq. (S4) Adapng l ( ) l SD( ) l σ ( ) eq. (S5) whch descbes he squaed dsance l afe a andom walk pocess fo a change n l due o a change n nucleus sze L() n he me neval, yelds ( ) ( l L( ) ) ( ) l σ ( ) l L( ) L( ) l σ eq. (S6) Inoducng hs no he equaon fo he mean squaed dsance change (eq. (S4)) gves l σ ( ) ( ) l σ ( ) l L( ) L( ) l l l( ) σ ( ) L( ) l L( ) l( ) ( ) L( ) eq. (S7) The las equvalence occus because he mean dsance change only due o andom appoaches fo lage values of and hus he mean of he dsance changes of all IRIF pas dung s equal o he change of he nucleus sze, <l()>l. Ths means ha measung he mean squaed dsance change <l ()> of IRIF can oveesmae he eal andom walk behavou n case of a change of nucleus sze dung he me neval. The ensemble aveage of he l () (.e. <l ()> ) fo dffeen me pons afe adaon eveals hs aveage dsance change of he foc pas L() <l()> wh me and hus whehe he cell nucle change he szes afe adaon (see eq. (S4)). We see an ncease of <l ()> ha s lage han he conbuon fom he ncease of σ () (see Fg. S5). The addonal conbuon eflecs an aveage 9

10 gowh of he foc dsances L/l ~ - % whn hous ha coesponds o a gowh of he damee of he cell nucleus of - nm fo a µm szed nucleus. Fg. S5. ean squaed dsance <l > of all foc pas wh nal dsance <l > ~ 4.9 µm (squaes) and <l > ~ 5.7 µm (ccles) as a funcon of me afe adaon. Fo each sample, he mean squaed nal dsance <l > (doed lne) and he conbuon of a andom walk wh σ (dashed lne, wh eo bas n gey)) ae gven fo compason. Eo bas fo <l > ae domnaed by he accuacy of he max applcaon.

11 Random walk of he cene of mass of DSB The me-aveaged SD of DSB (aveaged ove he me pons of a me sees) s defned as 39 ( ) ( ) ( ) [ ] SD Theefoe he me-aveaged SD of he cene of mass of DSB (a posons ) s gven by ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) ( ) ( ) [ ] ( ) ( ) [ ] ( ) ( ) [ ] ( ) ( ) ( ) ( ) ( ) ( ) SD SD SD SD k k k k k C C C,...,, snce he las em s small compaed o he fs em fo lage numbes of me pons (as he do poduc eaches andom negave and posve values). Ths means ha he SD (and hus also σ ) of he cene of mass of DSB appeas o be smalle han he andom walk behavou of a sngle DSB by a faco /.

12 Refeences (as n Acle) 8. Haupne, A. e al. Spaal Dsbuon of DA Double-Sand Beaks fom Ion Tacks, Royal Dansh Academy of Scences and Lees, Copenhagen, (6b). 9. Jegou, T. e al. Dynamcs of elomees and pomyelocyc leukema nuclea bodes n a elomease-negave human cell lne, ol. Bol. Cell, 7 8 (9). 34. Hable, V. e al. Recumen Knecs of DA epa poens dc and Rad5 bu no 53BP depend on damage complexy, PLoS OE 7, e4943 (). 35. Hable, V. e al. The lve cell adaon and obsevaon seup a SAKE, uclea Insumens and ehods n Physcs Reseach Secon B: Beam Ineacons wh aeals and Aoms 67, 9 97 (9). 36. Dazmann, G. e al. The unch mcopobe SAKE: Fs esuls usng ev poons and 9 ev sulfu ons. 7h Inenaonal Confeence on uclea copobe Technology and Applcaons, uclea Insumens and ehods n Physcs Reseach Secon B: Beam Ineacons wh aeals and Aoms 8, 6 (). 37. Haupne, A. e al. coadaon of cells wh enegec heavy ons, Rada Envon Bophys 4, (4). 38. Sage, D. eumann, F. R. Hedge, F. Gasse, S.. & Unse,. Auomac ackng of ndvdual fluoescence pacles: applcaon o he sudy of chomosome dynamcs, IEEE Tans Image Pocess 4, (5). 39. Buov, S. Jeon, J.-H. ezle, R. & Baka, E. Sngle pacle ackng n sysems showng anomalous dffuson: he ole of weak egodcy beakng, Phys Chem Chem Phys 3, 8 8 ().