Trapping metastatic cancer cells with mechanical ratchet arrays

Ac a Bioma e ialia 170 (2023) 202–214 Con en s lis s a ailable a ScienceDi ec Ac a Bioma e ialia jou nal homepage: www.else ie .com/loca e/ac bio Full leng h a icle T apping me as a ic cance cells wi h mechanical a che a ays Da id Caballe o a , b , ∗, Rui L. Reis a , b , Subhas C. Kundu a , b a 3B’s Resea ch G oup, I3Bs – Resea ch Ins i u e on Bioma e ials, Biodeg adables and Biomime ics, Uni e si y o Minho, Headqua e s o he Eu opean Ins i u e o Excellence on Tissue Enginee ing and Regene a i e Medicine, A ePa k - Pa que da Ciência e Tecnologia, 4805-017 Ba co, Guima ães, Po ugal b ICVS/3B’s-PT Go e nmen Associa e Labo a o y, B aga, Guima ães, Po ugal a i c l e i n o A icle his o y: Recei ed 16 Ma ch 2023 Re ised 26 July 2023 Accep ed 17 Augus 2023 A ailable online 23 Augus 2023 Keywo ds: Cance T aps Di ec ed mig a ion Ra che Mic o ab ica ion a b s a c Cu en ea men s o cance , such as chemo he apy, adio he apy, immuno he apy, and su ge y, ha e posi i e esul s bu a e gene ally ine ec i e agains me as a ic umo s. T ea men e ec i eness can be imp o ed by employing bioenginee ed cance aps, ypically u ilizing chemoa ac an -loaded ma e ials, o a ac infil a ing cance cells p e en ing hei uncon olled sp ead and po en ially enabling e adi- ca ion. Howe e , he encapsula ed chemical compounds can ha e ad e se e ec s on o he cells causing unwan ed esponses, and he gene a ed g adien s can e ol e unp edic ably. He e, we epo he de elop- men o a cance ap based on mechanical a che s uc u es o cap u e me as a ic cells. The aps use an a ay o asymme ic local ea u es o mechanically a ac cance cells and di ec hei mig a ion o p olonged pe iods. The apping efficiency was ound o be g ea e han iso opic o in e se aniso opic a che s uc u es on ei he dissemina ing cance cells and umo sphe oids. Impo an ly, he aps ex- hibi ed a educed e ec i eness when a ge ing non-me as a ic and non- umo igenic cells, unde sco ing hei pa icula sui abili y o cap u ing highly in asi e cance cells. O e all, his o iginal app oach may ha e he apeu ic implica ions o figh ing cance , and may also be used o con ol cell mo ili y o o he biological p ocesses. S a emen o significance Cu en cance ea men s ha e limi a ions in ea ing me as a ic umo s, whe e cance cells can in- ade dis an o gans. Bioma e ials loaded wi h chemoa ac an s can be implan ed o a ac and cap- u e me as a ic cells p e en ing uncon olled sp ead. Howe e , encapsula ed chemical compounds can ha e ad e se e ec s on o he cells, and g adien s can e ol e unp edic ably. This pape p esen s an o ig- inal concep o “cance aps” based on using mechanical a che -based s uc u es o cap u e me as a ic cance cells, wi h g ea e apping efficiency and s abili y han p e iously s udied me hods. This inno- a i e app oach has significan po en ial clinical implica ions o figh ing cance , pa icula ly in ea ing me as a ic umo s. Addi ionally, i could be applied o con ol cell mo ili y o o he biological p ocesses, opening new possibili ies o biomedicine and issue enginee ing. ©2023 The Au ho (s). Published by Else ie L d on behal o Ac a Ma e ialia Inc. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ) 1. In oduc ion The ad en o mode n nano echnologies and issue enginee - ing s a egies has enabled he de elopmen o inno a i e ools o figh cance [1–8] . Despi e he demons a ed benefi s o cu - en he apeu ic app oaches, such as su ge y, chemo he apy, adio- he apy, and immuno he apy, hey o en p esen limi a ions (e.g., accessibili y o umo s, side e ec s, o lack o e ec i i y –can- ∗Co esponding au ho . E-mail add ess: [email p o ec ed] (D. Caballe o) . ce cells migh emain a e ea men ), pa icula ly in ea ing me as a ic umo s. These issues ha e spu ed in e es in pu su- ing inno a i e issue-enginee ed app oaches o a ge highly infil- a ing cance cells. Consequen ly, cance aps ha e eme ged as a issue-enginee ed app oach o selec i ely cap u ing me as a ic cells when implan ed wi hin he body and p e en ing hei uncon- olled sp eading, as well as allowing hei analysis and/o po en- ial e adica ion [9] . These aps a e ypically made o biocompa - ible bioma e ials loaded wi h chemoa ac an s o a ac agg es- si e cance cells [ 10 , 11 ]. A my iad o chemokines and g ow h ac- o s ha e been employed o igge he mig a ion o cance cells owa ds he ap [12–14] . Howe e , he li e ime o his ype o ap h ps://doi.o g/10.1016/j.ac bio.2023.08.034 1742-7061/© 2023 The Au ho (s). Published by Else ie L d on behal o Ac a Ma e ialia Inc. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ) D. Caballe o, R.L. Reis and S.C. Kundu Ac a Bioma e ialia 170 (2023) 202–214 is limi ed due o he una oidable deg ada ion o he chemokine g adien s, and chemokines hemsel es may p oduce undesi ed e- sponses in o he cell ypes. To o e come hese issues, chemical- ee aps ha e been p oposed ha ely on opog aphical and mo - phological ea u es (e.g., fib illa y mic o/nano-s uc u es, acks, o g oo es) o guide and cap u e cance cells [ 11 , 15 ]. These aps a e mo e s able bu can s ill ace challenges in e ms o cap u ing cells efficien ly. Fo ins ance, mic o-fil e memb anes wi h size-sensi i e po es ha e been employed o selec i ely ap cance cells wi hin mic ofluidic sys ems [16–19] . Despi e hei po en ial o be im- plan ed in blood essels o nex o he umo a e su ge y o se- lec i ely cap u e ci cula ing o highly infil a ing umo cells, hei ansla ion o clinical se ings has been impeded by he possibili y o clogging, which could lead o se e e consequences. Physical en- apmen ep esen s ano he mechanical-based s a egy aimed a cap u ing me as a ic cells. This me hod in ol es igge ing a con- o ma ional change o he apping ma e ial, ypically a hyd ogel, in esponse o en i onmen al cues, such as he acidic condi ions p esen in he umo mic oen i onmen [20] . Despi e i s p omis- ing capabili ies, a significan limi a ion o physical en apmen is i s inabili y o di e en ia e be ween cance ous and heal hy cells. To add ess his challenge, i has been p oposed modi ying he hy- d ogel wi h a ecogni ion molecule ha specifically a ge s ecep- o s o e exp essed in cance cells [ 21 , 22 ]. Al hough his app oach has demons a ed success in apping specific cance cell ypes, he a iabili y in ecep o exp ession ac oss di e en ypes o cance may es ic i s applicabili y o all cance cells. Recen ly, mechanical aps based on he mig a ion concep o a che axis ha e been p oposed [ 23 , 24 ], which use a ays o aniso opic ea u es o mechanically pola ize and ein o ce he o - ganiza ion o he inne cell cy oskele on, gene a ing a di ec ional memo y [25–29] . Owing o his simplis ic mechanism o ac ion, mechanical a che -based aps o e unique ad an ages o selec- i ely cap u ing cance cells [30] , bu hei abili y o do so has no ye been ully demons a ed in p ac ice. In his wo k, we p esen he ab ica ion o mechanical a che -based annula aps ha use asymme ic ea u es o p omo e he cap u e and di ec ed mig a- ion o me as a ic cance cells. Ou analysis e eals he wo king mechanism o he aps o biasing cell mo ion and how cell dy- namics is impac ed by he ap a chi ec u e. Nex , we show ha he efficacy o he aps can be modula ed by p ope ly scaling he ap. We also showcase he diminished efficacy o he aps when aimed a non-me as a ic and non- umo igenic cells, highligh ing hei pa icula sui abili y o cap u ing in asi e cance cells. Fi- nally, we demons a e ha he aps can e ec i ely im pede he in asion o dissemina ing mul i-cellula umo sphe oids. O e all, hese esul s sugges ha mechanical a che -based cance aps ha e he po en ial o become a aluable adjunc o cu en cance ea men s. Mo eo e , hese aps could find applica ions in o he biological con ex s whe e he selec i e ec ui men o specific cell ypes, such as immune cells, s em cells, and o he s, is desi able. Fo example, he aps could be used o selec i ely isola e and collec hese cell ypes om a mul i-cellula issue, o o enhance o gan egene a ion p ocesses. 2. Ma e ials & me hods P epa a ion o he a che -based aps : The aniso opic a che - like mic os uc u es we e designed using CAD so wa e (Au oCAD, Au odesk). An O- ing (i.e. annula ) mo phology was designed o concen a e he cap u ed cells in he cen e o he ap, wi h he iangula ea u es poin ing inwa ds. Fo compa ison (con- ol), iangles poin ing ou wa ds and iso opic g oo es we e also designed. Two di e en iangle sizes we e also conside ed o scaling a gumen s (Table S1). UV-pho oli hog aphy (Mask aligne MDA-400M, SPS-Eu ope) was used o ab ica e a 10 μm hick SU8 mold (SU8 2010, Mic ochemicals GmbH) on o a Si wa e and di ec ly eplica ed wi h PDMS (Sylga d 184, Dow Co ning, 10:1 w/w p e-polyme /c oss-linke ; 70 °C o 1 h) ( Fig. 1A ). The PDMS eplica was ende ed hyd ophilic by O 2 plasma (Diene ) o 30 s a 200 W, silanized wi h ichlo o (1H,1H,2H,2H pe fluo ooc yl) silane (Sigma-Ald ich) by apo phase o 1 h a oom empe a u e, and cu ed o 1 h a 70 °C. Nex , a small olume o PDMS (50 μL) was spin-coa ed a 20 0 0 pm o 30 s on op o a glass co e slip ( hickness #1, Menzel-Gläse ) o c ea e a hin polyme ic laye . The silanized PDMS eplica was ca e ully loca ed on op and hen ac- uumed o 1 h o emo e all bubbles, ollowed by cu ing o 1 h a 70 ºC. Then, he PDMS eplica was ca e ully eleased o ob ain a hin PDMS laye wi h he mic o- a che ap s uc u es ( Fig. 1A ). Las ly, he mic o ab ica ed a che s we e ende ed hyd ophilic by O 2 plasma ea men (30 s, 200 W) and unc ionalized wi h 25 μg mL −1 fib onec in om bo ine plasma (Sigma-Ald ich) in PBS o p omo e cell adhesion. Bo h nega i e and posi i e PDMS eplicas we e cha ac e ized by whi e ligh in e e ome y o confi m he ac- cu a e eplica ion o he ea u es (see supplemen a y me hods and Fig. S1). Cell cul u e: Human MDA-MB-231 (me as a ic) and MCF-7 (non- me as a ic) b eas adenoca cinoma cells (ATCC), along wi h L929 mu ine fib oblas s, we e cul u ed using high glucose DMEM media (Sigma-Ald ich). Human non- umo igenic MCF10A b eas epi he- lial cells (ATCC) we e cul u ed in MEGM Bulle ki media (Lonza). All media was supplemen ed wi h 10% e al bo ine se um (FBS; Gibco), NaHCO 3 (3.7 g L −1 ), and 1% penicillin/s ep omycin (Al a- gene). All cell ypes we e cul u ed a low passages unde physio- logical condi ions (37 ºC and 5% CO 2 ). Cells we e ypsinized using T ypLE Exp ess Enzyme (1X) (Gibco). P epa a ion o umo sphe oids : Ul a-low adhesion U-bo omed 96 well-pla es (Co ning) we e used o o m 3D mic o-sized sphe oids by spon aneous agg ega ion. Fo his, 2500 cells we e deposi ed in each well in 100 μl o cul u e media, and he sphe oids we e g own o 4 days esul ing in sphe oids wi h an a e age diame e o 545 ±51 μm ( n = 36). Fo he expe imen s, he sphe oids we e ca e ully emo ed wi h a mic opipe e. Cell s aining: Cells we e fixed wi h 10x o malin (Sigma-Ald ich) o 20 min a oom empe a u e and washed wi h PBS o 5 min (x3). Cells we e hen pe meabilized wi h 0.5% T i on (Sigma- Ald ich) o 3 min. Nex , he cells we e washed wice o 5 min wi h PBS. Fo s aining, phalloidin– e ame hyl hodamine B iso h- iocyana e (1:250; 1 h) (Sigma-Ald ich) and DAPI (4.6-diamidino-2- phenylidole) (1:10 0 0; 20 min) (Sigma-Ald ich) we e used o imag- ing ac in filamen s and nuclei, espec i ely. The s ained samples we e washed in PBS o 5 min (x3). To e ec i ely inhibi cell p oli - e a ion in li e cell mig a ion s udies ( umo sphe oid expe imen s), cells we e ea ed wi h high DAPI concen a ions (10 μg/mL; 30 min) dilu ed in cell cul u e media, ollowed by insing wi h esh media p io o s a ing he expe imen . This app oach ha nesses DAPI’s abili y o specifically bind o DNA, p o iding s able fluo es- cence and low oxici y [ 31 , 32 ]. Finally, cell-pe mean Calcein AM (10 μM; The mo Fishe Scien ific) was employed o li e mul i- cellula (cance s. non-cance cells) expe imen s. Op ical mic oscopy: Time-lapse expe imen s we e pe o med in a Zeiss Axio Ve in e ed op ical mic oscope using 10 ×0.45 N.A. ai objec i e a a 1 image/15 min o acquisi ion a e o a minimum o 60 h. The mic oscope was equipped wi h a cha ge-coupled de- ice came a (Zeiss), an HXP 120 C fluo escence ligh uni (Zeiss) o epifluo escence expe imen s, and an in eg a ed shu e o p e- en pho o oxici y. Fo expe imen s, aps we e loca ed in a Pe i P35 dish and mechanically fixed wi h a home-made PDMS O- ing o he same ex e nal diame e as he dish. 2 mL o cell cul u e me- dia was added and a hin laye o mine al oil (Sigma-Ald ich) was ca e ully deposi ed on op co e ing he medium o minimize me- dia e apo a ion. 203 D. Caballe o, R.L. Reis and S.C. Kundu Ac a Bioma e ialia 170 (2023) 202–214 Fig. 1. Mic opa e ned cance a che aps. (A) Scheme desc ibing he s ep-by-s ep ab ica ion o he cance ap. (B) A schema ic ep esen a ion o he design and wo king mechanism o he cance ap based on in e connec ed aniso opic a che -like opog aphic s uc u es. The pa ame e s b and h co espond o he heigh and wid h o he iangula a che uni , espec i ely. MIN and MAX deno e he lowes and highes z posi ions, espec i ely. (C-D) B igh field images and magnified iews showing he di e en designs o he O- ing cance aps (IN, OUT, and NULL – con ol). (E) S aining illus a ing he ap wo king mechanism desc ibed in (A) o cells mig a ing di ec ionally om one apping mo i o he neighbo ing one (Phalloidin –F-ac in: ed; DAPI – nucleus: blue). Scale ba s: 100 μm. The bo om schemes illus a e he p ofile o he po en ial well in which he cells a e apped and unde going di ec ed mig a ion. Scale ba s: (B) 1.2 mm; (C) D) 500 μm; (D) 100 μm. T ap assay: Two di e en assays we e pe o med: seeding o in- di idual cells iso opically dis ibu ed ac oss he aps, and seeding o mul i-cellula umo sphe oids in he inne pa o he ap. A - e seeding, cells and sphe oids we e allowed o adhe e o 1–2 h be o e he s a o he expe imen . Biophysical analysis : To analyze he efficacy o he ap in p o- mo ing he di ec ed mig a ion and apping o cance cells, he ol- lowing pa ame e s we e defined: 1. La ice uni (l.u.): Leng h o he pe iodic iangula uni wi hin he a che pa e n. I se es as a undamen al measu emen o disc e izing he sys em and analyzing cell mig a ion wi hin he a che s uc u e. The la ice uni defines he spa ial scale o e which cellula mo emen and di ec ional bias a e quan i- fied and e alua ed. 2. Mean bias pe la ice uni ( p ): Ne di ec ional bias o cells mi- g a ing wi hin he a che pa e n, indica ing hei consis en mo emen in a specific di ec ion. I is quan ified by coun ing he numbe o s eps (in l.u.) ha he cells mig a e owa d he poin ed (n + ) o wide (n-) edge di ec ion [33] . This alue is a - e aged ou o all cells and condi ions. 3. Pe sis ence leng h/ ime (L pe /T pe ): Leng h and ime du ing which a cell mig a es s aigh wi hou e e sing i s mo ion, e- spec i ely. To measu e hese biophysical pa ame e s, cell a- jec o ies we e acked using he Poin ing Cell T acking Plug-in (Fiji, NIH) a 15 min in e als. The gene a ed x-y poin s we e connec ed o gene a e a se o mig a ion pa hs used o calcu- la e L pe and T pe . 4. Mean eloci y: A e age speed o cells mig a ing along he ap- ping ea u es in bo h di ec ions. 5. Confinemen ac o ( ): Ra io o he numbe o cells loca ed in he inne egion o he o al numbe o cells loca ed in all egions. 6. % inc ease: Cell en ichmen wi hin he aps compa ing he be- ginning and end o he expe imen . 7. Size a io (S ): Ra io o he cell size ela i e o he ea u e. Image p ocessing – nuclei densi y hea map: An a e age nuclei hea map was gene a ed using a Py hon code de eloped in-house (Py hon 3.11.4) wi hin Jupy e Lab ( 3.5.3). The code u ilized se - e al lib a ies, including NumPy, Ma plo lib, and sciki -image. The loaded images unde wen p ep ocessing s eps o imp o e hei quali y, including alignmen . The a e age in ensi y ac oss all im- ages was calcula ed using he np.mean() unc ion om he NumPy lib a y. The esul ing a e age in ensi y da a was isualized as a hea map using he Ma plo lib lib a y. The pl .imshow() unc ion was employed o plo he hea map, using he ’ho ’ colo map o in ensi y mapping. The in ensi y ange o he hea map was de e - mined using he np.pe cen ile() unc ion, which p o ided he lowe and uppe pe cen ile alues. The comple e code implemen a ion can be ound in he Supplemen a y Me hods. S a is ical analysis : Da a a e p o ided as he Mean ±S.E.M. S a- is ical analysis was pe o med using a one-way ANOVA wi h a Dunn ´ s pos -hoc es , and significance was accep ed a P < 0.05 (O iginP o). The da a se indica ing he numbe o expe imen al epe i ions and cells analyzed is desc ibed in he Fig. cap ions. 204 D. Caballe o, R.L. Reis and S.C. Kundu Ac a Bioma e ialia 170 (2023) 202–214 3. Resul s 3.1. De elopmen and wo king mechanism o he cance aps We designed an assay o ap me as a ic cance cells by me- chanically di ec ing hei mo ion owa ds a specific cap u ing loca- ion. The aps we e based on an a ay o mic o ab ica ed a che - like aniso opic s uc u es wi h a heigh (h) la ge han i s base, and in e connec ed h ough a na ow b idge ( Fig. 1B ). Wi h his configu a ion, he s uc u es physically pola ized he cells and ig- ge ed hei di ec ed mig a ion owa ds he inne pa o he ap (cap u e a ea). The apping e ec was enhanced by he h ee- dimensional (3D) a chi ec u e o he ea u es, which ac ed as po- en ial wells o dep h z max - z min confining he cells wi hin he a che -like a ay channels. These we e pa e ned ollowing an O- ing, o annula , dis ibu ion o concen a e he cells in he inne pa o he ap (cap u e a ea). To maximize he numbe o cells apped wi hin he s uc u es and he a che ing e ec , and min- imize hei mig a ion ou side he ea u es, we ab ica ed a che uni s uc u es ha we e la ge han he a e age cell size. Fo his, we measu ed he a e age a ea o he cells seeded on he ap’s fla su ace ob aining a alue o < A cell > = 1072 ±47 μm 2 (Fig. S2). To demons a e he a che ing e ec , we designed h ee di e en configu a ions, namely ap IN, OUT, and NULL ( Fig. 1C ). In b ie , ap IN and OUT included he a che a ays poin ing inside and ou side he O- ing, espec i ely, whe eas in he NULL – con ol – condi ion he iso opic eng a ed linea g oo es guided he mo ion o cells unidi ec ionally combining con ac guidance and confine- men ( Fig. 1D ). In his case, no p e e en ial di ec ion o mo ion was obse ed and cells could mig a e inwa ds and ou wa ds he O- ing ap wi h equal p obabili y (see below). We deposi ed highly in- asi e MDA-MB-231 b eas cance cells on op o he ap and a - e 1-2 h, mos o hem adhe ed uni o mly h oughou he su ace. Non-adhe ed cells we e emo ed by eplacing he media by esh one. We obse ed ha a e sho ime pe iods, cells we e mainly loca ed wi hin he wells, and in some cases, he ou e egions we e almos deple ed o cells (Fig. S3A). We hen ini ia ed he cell ap- ping expe imen whe e cells we e allowed o mig a e o se e al hou s wi hou in e up ion. Cells ha adhe ed di ec ly wi hin he aps we e confined and immedia ely unde wen mig a ion, ol- lowing an adhesion- unneling- apping mechanism by c ossing he na ow in e connec ion b idge be ween neighbo ing mo i s ( Fig. 1B and Fig. 1E ). In con as , cells ha adhe ed o he uppe fla egions beha ed as fluc ua ing ou -o -equilib ium pa icles and mig a ed andomly. E en ually, hey we e cap u ed by he opog aphic ea- u es ha ac ed as apping po en ial wells (Fig. S3B and Mo ie S1). Using fixed samples, we measu ed he ac ion o cells loca ed in he uppe (MAX) and lowe (MIN) z-posi ions (i.e., ou side and inside he channels), finding a pe cen age o 65%, 62%, and 59% in he IN, OUT, and NULL condi ions, espec i ely (Fig. S4A-B). Sim- ila ly, cells loca ed a he ou e egion and en ance o he ap we e engul ed by he ea u es (Fig. S3C and Mo ie S2). No e ha cance cells could e en ually escape he ea u es due o he limi ed heigh o he channels and mig a e ac oss he op o he ap un il hey we e apped again (Fig. S3D and Mo ie S3). Nex , we in es iga ed he dynamics o cells wi hin indi idual mo i s and ound ha cells exhibi ed s ochas ic mig a ion owa ds ei he he poin ed o wide edge ( ip o base o he iangula mo- i ). This mig a ion was acili a ed by he con ac guidance mecha- nism, whe e cells adhe ed o he walls o he opog aphical s uc- u e. Al hough cells had he abili y o mig a e in ei he di ec ion, he asymme y o he iangula uni a o ed cell mig a ion o- wa ds he poin ed edge. This p e e ence can be a ibu ed o he mechanical in e ac ion be ween he cell and he wall a an app ox- ima ely 80 ºangle, which inc eased he likelihood o dis up ing cell pola i y and e e sing i s di ec ion o mo ion when mig a ing o- wa ds he wide edge ( Fig. 2A and Mo ie S4). In con as , when cells mig a ed owa ds he poin ed edge o he iangula s uc- u e, he shallow angle be ween he walls o he ea u e and he b idge induced apid hopping ( unneling) owa ds he neighbo ing mo i , making i he p e e ed condi ion o guiding and apping he cells. Th oughou his p ocess, he nucleus played a pi o al ole in de e mining he di ec ion o cell mo ion by allowing o p e en - ing cell passage h ough he b idge. In doing so, he nucleus unde - wen mechanical de o ma ion ( Fig. 2B ), which did no occu when cells mo ed along he g oo es (NULL). This mechanical de o ma- ion is an ene gy-in ensi e p ocess and is mo e a o able when cells a e mo ing owa ds he poin ed edge, as indica ed by he en- e gy p ofiles depic ed in Fig. 1E . Fu he mo e, his in e ac ion also led o pauses in mo ion as cells ansi ioned om one mo i o he neighbo ing one. To alida e his obse a ion, we conduc ed an analysis o he lo- ca ion and in e ac ion o cell nuclei wi h he opog aphical walls. Ou findings confi med ha he nucleus was he p ima y o ganelle in e ac ing wi h he walls in he wide edge when cells mig a ed owa ds his di ec ion ( Fig. 2C ). As men ioned ea lie , his in e ac- ion esul ed in he loss o pola i y and p omo ed he e e sal o cell mo ili y owa ds he poin ed edge, which is he p e e ed di- ec ion o mo ion. The p e e ence o he poin ed edge was also e iden in he measu emen o cell nuclei loca ion. The densi y map o he mean nuclei posi ion on a iangula s uc u e e ealed a non-uni o m dis ibu ion, p ima ily concen a ed in he poin ed edge egion ( Fig. 2D ). This finding sugges s ha he opog aphical ap cap u es he nucleus-cell complex in a manne analogous o an ene gy po en ial well, as explained abo e. To explo e whe he he in e ac ion wi h he opog aphical wall s uc u e influenced he o ien a ion o he nuclei, we quan ified he o ien a ion angle ( α) wi h espec o he a che labo a o y amewo k axis on fixed samples. Ou analysis e ealed a peak dis- ibu ion a ound 0 º, which con as ed wi h he andom o ien a ion obse ed o cell nuclei loca ed in he uppe fla egions ( Fig. 2E ). Fu he mo e, e en when only a po ion o he cell was loca ed wi hin he a che s uc u es, he nucleus emained apped inside, he eby influencing he o e all cell locomo ion p ope ies ( Fig. 2F ). Nex , o u he demons a e he c ucial ole o he nucleus, we acked i s posi ion and o ien a ion by fi ing i o an ellipse a pe- iodic ime poin s. This analysis highligh ed he mechanical in e - ac ion be ween he nucleus and he walls, u he suppo ing i s impo ance in he a che ing mechanism ( Fig. 2G and Mo ie S5). Las ly, we quan ified he pe cen age o nuclei loca ed inside and ou side he aps, finding a clea bias o IN/OUT condi ions, sug- ges ing he key ole o he nuclei in he mechanism o apping and cell guidance ( Fig. 2H ). 3.2. Guiding he long- e m mo ion o cance cells in he a che aps The efficiency o he cance ap is di ec ly p opo ional o he abili y o cells o unde go long- e m di ec ed mig a ion, so we nex moni o ed how cance cells mig a ed along he aps. Gene ally, cells we e smalle han he a ea o an indi idual ea u e, as ea lie indica ed, and he e o e, se e al could be alloca ed wi hin a sin- gle ea u e a e seeding (Fig. S4C). Ne e heless, when he sys em eached he s eady s a e a e ew hou s, cells dis ibu ed along he a ay and mainly one o wo cells we e ound wi hin an indi id- ual mo i ( Fig. 3A ). Unde hese condi ions, cells mig a ed mainly a ached o he opog aphical walls ia a con ac guidance mecha- nism. Fig. 3B shows ime-sequence images o a cell mig a ing along he opog aphical s uc u es (Mo ie S6). Fo IN and OUT a che aps, indi idual cells mig a ed pe sis en ly o se e al hou s wi h- ou s opping o e e sing mo ion. No e ha cells we e also capa- ble o s ochas ically e e sing hei mo ion and mig a ing owa ds he di ec ion se by he base o he iangula ea u es (Fig. S5 205 D. Caballe o, R.L. Reis and S.C. Kundu Ac a Bioma e ialia 170 (2023) 202–214 Fig. 2. The ole o cell nuclei in he apping and a che ing o cance cells. (A) Re e sing he mo ion o cance cells wi hin an indi idual a che s uc u e. (Le ) Scheme illus a ing he p ocedu e o e e sing he di ec ion o mo ion: (1) Di ec ed mig a ion – owa d he base o he iangle –along he walls h ough con ac guidance; (2) Me- chanical in e ac ion wi h he wall and pola i y dis up ion; (3) Re e sal o mo ion; (4) Di ec ed mig a ion and hopping owa ds he neighbo ing s uc u e. (Righ ) Phase con as image showing a ime sequence o his e e se e en . Whi e a owheads indica e he posi ion o he cell and la ge a ows he di ec ion o cell mo ion (see also Mo ie S5. Scale ba : 100 μm. (B) Mechanical de o ma ion o he cell nucleus squeezing h ough he b idge walls. (C) Mechanical in e ac ion o he nucleus wi h he walls om he wide and poin ed edge. (D) Densi y map o cell nuclei posi ion wi hin an indi idual ea u e ( n = 231 nuclei). (E) Nuclei o ien a ion inside and ou side he a che s uc u e (n a che = 141; n fla = 227 cells; N = 3). (F) Immunos aining image depic ing he apping o he nuclei and he pa ial sp eading o he cell ou side he ap, as indi- ca ed by he whi e a owhead (in ed, F-ac in; in blue, DAPI). (G) Time-sequence images highligh ing he posi ion and in e ac ion o he nucleus wi h he a che walls. (H) Pe cen age o nuclei loca ed inside o ou side he ap o all condi ions ( N = 3; n = 227). Scale ba s: 100 μm. and Mo ie S7). In he NULL condi ion, cells spon aneously pola - ized and mig a ed di ec ionally in bo h di ec ions wi h equal p ob- abili y, displaying a fluc ua ing beha io as expec ed ( Fig. 3C and Mo ie S8). We u he in es iga ed whe he he efficacy o guid- ing and apping cance cells was a ec ed by cell densi y, ha is, wi h mul iple cells wi hin he ap. In e es ingly, we ound ha he capaci y o he ap o cap u e (and bias) he mo ion o cells was main ained, e en hough a e y high densi ies, cell jamming had a p onounced e ec on cell locomo ion capabili ies by in en- si ying cell confinemen and mechanical in e ac ions ( Fig. 3B - 3C , Mo ie S7, and Fig. S6). I is impo an o no e ha de e mining he p ecise cell densi y h eshold o jamming is challenging in such a dynamic and e ol ing sys em. Fo mode a e densi ies, cells could mig a e di ec ionally as indi idual en i ies, e en hough he physi- cal in e ac ion be ween he cells in e e ed wi h he efficacy o he ap, ansien ly delaying he a che ing e ec . This was mo e e i- den o he NULL condi ion, whe e only one cell could fi wi hin he g oo e and he in e ac ion be ween wo cells caused hem o e e se hei mo ion (Mo ie S8). Howe e , as men ioned ea lie , his ansien jamming e ec disappea ed when he s eady s a e was eco e ed in he a che ap. Al oge he , on a e age, he cells mig a ed owa ds he poin ed edge o he opog aphical ea u es in IN/OUT condi ions. We nex quan ified he p obabili y o a cell o mig a e owa ds one o he opposi e di ec ion. Fo his, we measu ed he posi ion o a cell a he beginning and he end o he expe imen and mea- su ed he o al ne mo ion owa d he poin ed o wide edge. To assess he deg ee o di ec ionali y and pe sis ence, we defined se - e al biophysical pa ame e s ( Fig. 4A and Me hods). We disc e ized ou sys em in o la ice uni s (l.u.) finding ha he IN/OUT a che ap had a biasing e ec , wi h an a e age cell mig a ion owa d he poin ed edge (60 ±5 % s 40 ±5 %) ( Fig. 4B ). In con as , he con- ol NULL condi ion did no p o ide any significan bias (52 ±10 % s 48 ±7 %), confi ming he a che ing e ec o he asymme - ic s uc u es. Nex , we measu ed he mean bias pe l.u. defined as ollows [33] (see Me hods): p = n + −n − n + + n − (1) 206 D. Caballe o, R.L. Reis and S.C. Kundu Ac a Bioma e ialia 170 (2023) 202–214 Fig. 3. Long- ange di ec ed mig a ion o cance cells along a che cance aps. (A) Cell cy oskele on s aining showing ha he majo i y o cells we e loca ed ( apped) wi hin he opog aphical ea u es. (B-C) Time-sequence illus a ing he long- e m mig a ion o indi idual and mul iple cells o IN/OUT and NULL condi ions. Whi e a owheads indica e he posi ion o he cells. Las panel shows he comple e mig a ion pa h acking o e ime. Time in hh:mm. Scale ba : 100 μm. (S a is ics: N = 4; n cells = 100). By defini ion, he a e age alue o < p > is -1 < P < 1. Fig. 4C shows he end obse ed in he o al cell bias, wi h cells p e e en ially mo ing owa ds he poin ed edge o IN and OUT condi ions. Despi e obse ing cells mig a ing long dis ances wi h- ou e e sing in he NULL g oo es, a alue o < p > ∼0 was ob- ained a e a e aging ou , indica ing a clea s ochas ic beha io as expec ed. We hen e alua ed he pe sis ence o cell locomo ion in he a che (IN/OUT condi ion), finding ha cells mig a ed mo e pe sis en ly owa ds he poin ed edge, co e ing longe dis ances and pe iods (L pe poin ed > L pe wide and T pe poin ed > T pe wide ), confi m- ing he p e e en ial di ec ion o mo ion ( Fig. 4D , 4E ). This was in con as o cells mig a ing along g oo es, whe e he e was no sig- nifican di e ence in L pe and T pe in ei he di ec ion. In e es ingly, we obse ed ha L pe NULL < L pe IN/OUT , likely due o he absence o mechanical cues in he su ounding en i onmen o NULL con- di ion ha ails o s imula e p e e en ial cell mig a ion. Addi ion- ally, we obse ed ha T pe was sligh ly la ge owa ds he poin ed edge compa ed o he wide edge, wi h T pe NULL being significan ly smalle han T pe IN/OUT . This o e all indica es a mo e s able pola - i y memo y when cells mig a e owa ds he poin ed edge. In e es - ingly, cells mig a ed wi h he same eloci y ega dless o he di ec- ion and mo phology o he aps, sugges ing ha cells mig a ed by 207 D. Caballe o, R.L. Reis and S.C. Kundu Ac a Bioma e ialia 170 (2023) 202–214 Fig. 4. Biophysical analysis o cance cell mig a ion on a che aps. (A) Scheme desc ibing he key biophysical pa ame e s used o quan i y cell bias and pe sis ence. (B) Quan ifica ion o he pe cen age (%) o cell bias. (C) Plo o < p > o each condi ion as gi en by Eq. (1) . (D-F) Analysis o he di e en biophysical pa ame e s: cell bias (B), pe sis ence leng h –L pe (C), pe sis ence ime –T pe (D), and mean pe sis ence speed –< > pe (E). ( N = 3; n cells = 229; ∗P < 0.05; ∗∗P < 0.01; ∗∗∗P < 0.001). (G) Pe cen age o inc ease o cell a ea o all he s udied condi ions as indica o o confinemen efficacy ( N = 3; n aps = 5 pe condi ion –15 in o al; ∗P < 0.05; ∗∗P < 0.01). con en ional locomo ion mechanisms – con ac guidance and con- finemen – ha a e no a ec ed by he asymme y o he sys em o de o ma ion ( Fig. 4F ). This implies ha he a che does no im- pac he capaci y o he cells o apply ac ion o ces bu only hei abili y o a o mig a ion in one specific di ec ion. Las ly, he e was no significan change in he biophysical pa ame e s o he NULL condi ion in ei he di ec ion due o he symme y o he sys em ( Fig. 4D - 4F ). The biophysical pa ame e s we e s ongly dependen on cell densi y; when he numbe o cells wi hin he a che in- c eased, he a e o di ec ional swi ching inc eased, consequen ly leading o a dec ease in pe sis ence (T pe and L pe ). Cell jamming, esul ing om he s ochas ic o ma ion o ho spo s wi h an excess o cells o as a esul o cell o e -p oli e a ion especially a e long acquisi ion imes, was ound o u he enhance cell-cell mechan- ical in e ac ions, causing a highe umbling equency, and hus, a dec eased efficacy o he a che in sho ime in e als (Fig. S6). Howe e , when he sys em was allowed o each equilib ium, he efficacy was pa ially eco e ed. Nex , o demons a e he efficiency o he ap, we quan ified cell en ichmen in he h ee dis inc egions o he ap ( Fig. 4G ). Specifically, we quan ified he cell a ea a he s a and conclusion o he expe imen , and subsequen ly de e mined he inc ease in he a ea occupied by he cells as shown in Eq.(2) : % inc ease = A −A 0 A 0 ×100 (2) Whe e A is he o al a ea occupied by cells a he end o he ex- pe imen and A 0 is he espec i e a ea a he beginning. In e es - ingly, he IN condi ion displayed a p onounced accumula ion o cells in he inne egion (1) , con as ing wi h he OUT and NULL condi ions. Addi ionally, a mode a e inc ease was also obse ed in egion (2) , albei wi hou s a is ical significance. The g ow h ob- se ed in egion (3) could be p edominan ly a ibu ed o cell p o- li e a ion, which may also impac he esul s in he o he egions. Howe e , he ob ained di e ences among he dis inc condi ions sugges he e ec i eness o he ap in confining cance cells. Nex , we es ed he specifici y o he aps o guide me as a ic cance cells by es ing hei e ec on non-in asi e cells, such as MCF-7, which display an epi helial pheno ype, non- umo igenic MCF10A mamma y epi helial cells, and L929 fib oblas s. Fo non- in asi e MCF-7, we obse ed ha in all he s udied condi ions (i.e., IN, OUT, and NULL) hese cells we e unable o unde go di ec ed mig a ion (Fig. S7 and Mo ies S9-S11). MCF-7 cells p oli e a ed and o med densely packed monolaye s, which we e no significan ly a ec ed by he apping wells. The s onge bias exhibi ed by he highly me as a ic cell line compa ed o he less agg essi e MCF7 cells sugges s ha mo e poo ly di e en ia ed cells may unde go a che axis a he han hose wi h a mo e di e en ia ed epi he- lial pheno ype. This epi helial pheno ype oge he wi h he la ge size o he colonies inac i a ed he biasing e ec o he a che s. As a esul , he di e en se o biophysical pa ame e s desc ip- i e o apping efficiency and cell bias could no be quan ified. Simila ly, o non- umo igenic MCF10A, we obse ed no significan biasing e ec , wi h cells exhibi ing limi ed mig a ion du ing he long acquisi ion imes. This ou come was again a ibu ed o hei epi helial pheno ype, which p omo ed s ong cell-cell in e ac ions and consequen ly inc eased ic ion, inhibi ing he e ec i eness o he ap (Fig. S8 and Mo ie S12). Su p isingly, L929 fib oblas s did no exhibi any ec ifica ion o hei mo ion ei he , mos p obably due o he high dynamics and p oli e a ion a e o his cell line compa ed o ha o he umo igenic MDA-MB-231 cells. This high p oli e a ion led o a apid o e c owding wi hin he sys em. As a esul , he mul iple mechanical in e ac ions among he fib oblas s caused hem o apidly escape he confinemen o he ap, he eby 208 D. Caballe o, R.L. Reis and S.C. Kundu Ac a Bioma e ialia 170 (2023) 202–214 limi ing i s e ec i eness in e aining and biasing he cell mo ion, and limi ing he ex apola ion and quan ifica ion o he biophysical pa ame e s (Fig. S9 and Mo ie S13). This apid o e c owding could be add essed by p e en ing cell p oli e a ion (e.g., an i-mi o ic d ugs o nuclea s aining). Howe e , such an app oach migh in e - e e wi h he na u al dynamics and in e ac ions among cells, which a e c ucial o unde s anding he ap’s pe o mance unde ealis- ic condi ions whe e p oli e a ion plays an impo an ole. Hence, i is an essen ial pa ame e o conside . Finally, we conduc ed an assessmen o he ap’s efficacy in so ing mixed popula ions o cells comp ising MDA-MB-231 cells and L929 fib oblas s. Ou find- ings e ealed dis inc beha io s: ini ially, cance cells we e apped wi hin he opog aphical ea u es o he ap, o ming egula and o de ed s uc u es esembling a wo-dimensional colloidal c ys al (Fig. S10A). In con as , fib oblas s exhibi ed an iso opic dis ibu- ion h oughou he ap. In e es ingly, as he sys em became mo e c owded, he p esence o fib oblas s compelled he cance cells o mig a e ou side he opog aphic wells, impac ing on he o e all e - ficacy o he ap. This was suppo ed by he quan ifica ion o he pe cen age o cell bias and < p > a ea ly ime poin s, as well as he a ia ion in he amoun o MDA-MB-231 cance cells in he ap- ping egions, which e ealed a dec ease in he ob ained alues o a mixed popula ion o cells compa ed o hose ob ained o only cance cells (Fig. S10B-D). This obse a ion highligh s how cell in- e ac ions and jamming can impac he e ec i eness o he ap, which demons a es g ea e efficacy in cap u ing isola ed and in- asi e cance cells. These findings collec i ely sugges ha he ap exhibi s limi ed e ec i eness wi h he non- umo igenic and non-me as a ic cells used and highe efficacy on he in asi e cells es ed, alida ing he selec i i y o he aps in p ima ily a ge ing me as a ic cance cells. This indica es ha he mechanisms discussed ea lie , such as pola iza ion, nuclei posi ioning, and con ac guidance, may no uni- e sally apply o all cell ypes. To u he in es iga e hese assump- ions, u u e expe imen s in ol ing a b oade ange o cell ypes would be necessa y. 3.3. Modula ing he efficacy o cance aps h ough scaling concep s We obse ed ha ela i ely la ge cells ended o mig a e o- wa ds he base o he aniso opic ea u es, which is he opposi e di ec ion om wha we had claimed p e iously, sugges ing ha cells in eg a e he ela ionship be ween cell and ea u e sizes o de e mine he di ec ion o mig a ion. Fo his eason, and o u - he explo e he ole o scaling in cell apping and guidance, we nex in es iga ed how he size ela ion influenced cell di ec ional- i y. Fo his, we adjus ed he ap size close o ypical cell dimen- sions by c ea ing aniso opic ea u es ha we e 1.2- old smalle han he o iginal ones (deno ed as ap - in Table S1; Fig. S11A-B). We fi s in es iga ed how a dec ease in size a ec ed he capabili y o he ap o cap u e cance cells and he abili y o hese cells o mig a e, since cell densi y inc eased. A e 1-2 h o seeding, mos cells we e al eady apped wi hin he wells e en hough a la ge accumula ion o cells was obse ed compa ed o he la ge ap ( ap + ) p e iously u ilized (Fig. S11C). Despi e his highe densi y o cells ha inc eased he mechanical in e ac ion be ween hem, di ec ional mig a ion was s ill obse ed once he equilib ium was eached. Ne e heless, we obse ed a sligh ly la ge pe sis ence o cells seeded in he ap + a che s uc u es, pa icula ly owa ds he poin ed edge, as indica ed by he a io o big o small alues measu ed o all he biophysical pa ame e s (Fig. S11D). No signi - ican a ia ion was obse ed o he NULL condi ion. This obse a ion sugges s ha cance aps a e mo e e ec i e a cap u ing lowe numbe s o cells, while s ill emaining e ec i e o la ge quan i ies. Indeed, we obse ed ha cells could mig a e di- ec ionally in he smalle aps ( ap -) bu hei efficacy depended, no only in he amoun o cells apped, bu mainly on he ela- i e size be ween he cell and he mo i ( Fig. 5A and Mo ies S14 – S16). To gain mo e insigh s in o his, we classified he cells based on hei size ela i e o he ea u e in oducing he size a io S ( Eq.3 ): S = A ea cell A ea ea u e (0 < S ≤1) (3) No e ha only unconfined cells smalle han he a ea o an indi idual iangula a che uni we e included o he analysis, which accoun ed o he majo i y o cells. To add ess he dy- namic na u e o cell a ea, we measu ed he p ojec ed cell a ea us- ing au oma ic h esholding (ImageJ, NIH) a di e en ime poin s o each cell wi hin an indi idual a che uni and calcula ed he mean alue. Fo con enience, we g ouped S in o h ee ca ego ies: small (S = 0 –0.35), medium (0.36 –0.7), and big (0.71 –1) ( Fig. 5B ). Using he s anda d la ge ap, he mos efficien one (see Fig. S11D), deno ed as ap + in Table S1, we measu ed S o cells belonging o each o hese ca ego ies and he espec i e bias. In e es ingly, we ound ha he scaling be ween he ea u e and he cells influenced hei final di ec ion o mig a ion ( Fig. 5C ). In b ie , smalle cells (la ge S ) mig a ed, in a e age, owa ds he poin ed edge as p e iously obse ed, whe eas bigge ones (small S ) mig a ed p e e en ially owa ds he wide edge, he eby e e s- ing hei mo ion. Medium-sized cells (a e age S ) also mig a ed owa d he poin ed edge, bu expe ienced a highe difficul y in c ossing o he neighbo ing mo i s, mos likely due o he highe mechanical in e ac ion be ween he nuclei and he in e connec - ing b idge ( Fig. 5A - mid and Mo ie S15). This esul ed in la ge cells acing mo e difficul ies in passing h ough i . As a esul , he e was an inc eased likelihood o hese cells e e sing hei di ec ion o mo ion. Howe e , he p e iously discussed a che ing mecha- nism emained alid in his scena io. Fo e y big cells (small S ), o he ac o s, such as p o usion adhesions, could syne gize wi h he nucleus and ac as c ucial de e minan s causing he e e sal o cell di ec ionali y. To confi m his hypo hesis, addi ional expe i- men s analyzing p o usion ac i i y and adhesion may be equi ed [ 24 , 32 ], Al oge he , hese scaling expe imen s ha e alida ed ou hy- po hesis and app oach, and may enable he design o mo e effi- cien aps ha a e mo e cell-specific, o e en ually, could be used o sepa a e cells based on hei ela i e size [ 30 , 34-37 ]. 3.4. Res ic ing he dissemina ion o cance cells om mul i-cellula sphe oids While he aps ha e a well-demons a ed capaci y o guide cance cells owa ds he apping egion, we nex in es iga ed hei capabili y o e ain he dissemina ion o cance cells. Fo his, we seeded mul i-cellula cance sphe oids in he cen e o he ap- ping egion and allowed hem o dissemina e o abou 60 h. To be e isualize cell sp eading and mig a ion, and o a oid bias in he quan ifica ion o ap efficacy, cell p oli e a ion was inhib- i ed by s aining li e cells wi h high concen a ions o DAPI (see Me hods). Few hou s a e seeding, cance cells s a ed o escape ou he sphe oid and dissemina e uni o mly as single cells, which mechanically in e ac ed wi h he inne edge o he ap ( Fig. 6 and Mo ie S17). Cells had a simila p obabili y o in ading bo h IN/OUT a che a ays and he non-di ec ional NULL g oo es be- cause he access o he channels (i.e., b idge) was iden ical in all cases (d in = d ou = d NULL ) in all cases ( Fig. 1 ). Once inside he channel, he cells we e exposed o he same mechanical cues dis- cussed be o e. Fo he IN/OUT condi ions, cell mo ion was biased mainly owa d he poin ed edge o he indi idual ea u es, he e- o e, con ibu ing o confine (IN) o sp ead (OUT) hei mo ili y. Despi e he enhanced confinemen , cance cells could s ill in ade 209 D. Caballe o, R.L. Reis and S.C. Kundu Ac a Bioma e ialia 170 (2023) 202–214 Fig. 5. Modula ing cell guidance h ough scaling. (A) Time-lapse sequence showing he mig a ion o cells o inc easing sizes in iden ical a che aps as highligh ed by he di e en S ac o s. Fo small and med S alues, cells mig a e on a e age owa ds he poin ed edge, whe eas o la ge S cells e e se he di ec ion o mo ion and mig a e mainly owa ds he opposi e di ec ion. The dashed ec angle highligh s a cell expe iencing difficul ies in hopping owa d he neighbo ing mo i due o he mechanical in e ac ion be ween he nuclei and he walls o he opog aphical ea u e. Time in hh:mm. Scale ba s: 100 μm. (B) Plo o S o he h ee defined scaling ca ego ies. (C) Bias plo highligh ing he di e en mig a ion o cells depending on he S alue. (S a is ics: N = 3; n cells = 96; ∗P < 0.01; ∗∗P < 0.05). he IN- a che channels, bu on a e age, hey e e sed hei mo- ion and mig a ed back o he inne apping egion. In con as , on a e age, he cance cells en e ing he OUT ap displayed longe mig a ion dis ances owa ds he ou e egion, exhibi ing high L pe and T pe alues (3.6 ±0.5 l.u. and 7.1 ±1.7 h, espec i ely) sim- ila o hose obse ed o indi idual cells in he same condi ion (see also Fig. 4D , 4E ). This demons a es he capaci y o he aps o guide cance cells owa ds he apping egion, and e ain he dis- semina ion o cance cells ou side he ap. The quali a i e efficacy o he IN ap o con aining cance cells was fi s es ablished by imaging he la ge accumula ion o cells in compa ison o he OUT a che ap (Fig. S12A). The cells ha mig a ed ou wa ds we e p i- ma ily con ained wi hin he channel. The NULL condi ion also a- cili a ed he dispe sion o cance cells, p ima ily in he ou wa d di- ec ion. In his pa icula case, a g ea e numbe o cells we e ob- se ed ou side he channels, po en ially indica ing he occu ence o jamming e ec s. To quan i y he amoun o dissemina ed cance cells o each condi ion, we measu ed he no malized a ea o DAPI- s ained cells a he beginning and end o he expe imen , showcas- ing he g ea e capaci y o he IN- a che ap o confine cance cell mig a ion (Fig. S12B). Finally, o u he suppo hese esul s, we calcula ed he confinemen ac o ( ) a he inne apping a ea a he end o he expe imen . The  ac o is he a io o he numbe o cells loca ed in he inne egion o he o al numbe o cells lo- ca ed in all egions (inside: 1; channels: 2; ou side: 3; see Fig. 6D – le ) as shown in Eq.(4) . = A 1  3 i =1 A i (4) Whe e A i (i = 1..3) is he o al nuclei a ea (p ojec ed) a = 60 h. By defini ion, is a uni less quan i y wi h a alue in he ange o 0 ≤≤1; he close o 1, he mo e confined he cells a e in he inne egion. Fo IN a che aps, we ob ained a IN = 0.90; his high  alue was in con as o OUT = 0.81 and NULL = 0.83 ( Fig. 6D – igh ). O e all, hese esul s demons a e he supe io e ec i eness o he de eloped a che aps in limi ing he sp ead o cance cells, o e ing p omising po en ial o con olling cell dis- semina ion. 4. Discussion Se e al wo ks ha e epo ed a my iad o (bio-) ma e ials (e.g., sca olds, hyd ogels, mic opa icles, e c.) o cap u ing cance cells [ 11 , 12 , 38 , 39 ]. Howe e , mos o hese cell apping app oaches em- ploy (bio-) chemical means o a ac he cells, which come wi h many d awbacks (e.g., limi ed li e- ime) and undesi ed e ec s (e.g., in e e ence wi h o he non- umo al cells). To add ess hese issues, he use o pu ely mechanical means o di ec he mo ion o can- 210