Polymer physics view of peripheral chromatin: de Gennes' self-similar carpet

A polyme -physics iew o pe iphe al ch oma in:
de Gennes’ sel -simila ca pe model
Ozan S. Sa ıye
Pˆı ˆı Reis Uni e si y, School o A s and Sciences, Tuzla 34940, Is anbul, Tu key∗
Ayku E ba¸s
UNAM Na ional Nano echnology Resea ch Cen e and
Ins i u e o Ma e ials Science & Nano echnology, Bilken Uni e si y, Anka a 06800, Tu key
Uni e si y o Silesia, Ins i u e o Physics, Ka owice, Poland†
(Da ed: Janua y 15, 2024)
Using scaling a gumen s o model pe iphe al ch oma in localized nea he inne su ace o he nu-
clea en elope (NE) as a lexible polyme chain, we discuss he s uc u al p ope ies o he pe iphe al
ch oma in composed o al e na ing lamin-associa ed domains (LADs) and in e -LADs. Modeling
he a ac ion o LADs o NE by de Gennes’ sel -simila ca pe , which ea s he ch oma in laye
as a polyme ac al, explains wo majo expe imen al obse a ions: (i) The high densi y o ch o-
ma in close o he nuclea pe iphe y decays o a cons an densi y as he dis ance o he pe iphe y
inc eases. (ii) Due o he dec easing mesh size owa ds he nuclea pe iphe y, he ch oma in ca pe
inside NE excludes molecules ( ia non-speci ic in e ac ions) abo e a h eshold size ha depends on
he dis ance om he nuclea pe iphe y.
I. INTRODUCTION
Inside he highly c owded olume o he euka yo ic
cell nucleus, ch oma in is no andomly dis ibu ed [1–
7]. While euch oma in, which allows access o lineage-
speci ic genes, is o en obse ed away om he nuclea
su aces, he e och oma in, which is commonly associa ed
wi h gene silencing, is localized nea he nuclea su -
aces [4–10]. This 3d o ganiza ion scheme is also one
o he epigene ic ac o s egula ing he biological cha -
ac e is ics and heal h o a cell [11,12]. Consis en ly,
many gene ic diso de s wi h a e minal na u e, such as
a ious ypes o laminopa hies [13–18] and in some can-
ce s [19,20], mani es hemsel es as al e a ions in pe iph-
e al ch oma in dis ibu ion. Unde s anding he o igins
o such dis o ed dis ibu ion pa e ns equi es cha ac-
e izing he s uc u al and con o ma ional p ope ies o
pe iphe al ch oma in localized nea he inne su ace o
he nuclea en elope (NE).
Recen p og ess in sequence-based ch oma in con o -
ma ion cap u e echnologies (e.g., Hi-C [21], ChIP [22],
and DamID [23]) in addi ion o de elopmen s in high-
esolu ion-mic oscopy (e.g., FISH [24]), ha e p o ided
he mos de ailed s uc u al p ope ies o pe iphe al
ch oma in so a [7,25]. These expe imen s epo
ha pe iphe al ch oma in, also e e ed o as lamina-
associa ed domains (LADs), in e ac wi h nuclea bound-
a y componen s and ha e he cha ac e is ics o gene-
inac i e he e och oma in. These domains ha e sha ply
de ined bounda ies, and hei leng hs ange be ween
0.1 Mb (mega-basepai s) o 10 Mb wi h a median leng h
o abou ∼0.5 Mb [7,26–31]. LADs a e connec ed
∗ossa iy[email p o ec ed]
†a[email p o ec ed] .edu.
by ela i ely longe s ands o in e -LADs, which o m
ch oma in loops p o uding owa ds he nuclea in e io
(Fig. 1). In e es ingly, unlike LADs, in e -LADs ex-
hibi he cha ac e is ics o gene-ac i e euch oma in [31–
34]. Consis en ly, expe imen s epo ed ha la ge mul-
ip o ein complexes main aining gene ansc ip ion (e.g.,
RNA polyme ase II) and enzymes in ol ed in DNA e-
pai machine y (e.g., DNA glycosylase) in e ac less wi h
LADs han wi h in e -LADs [7,9,26]. Rela edly, expe -
imen s p obing ch omosome s uc u es wi h nanome e -
sized dex an pa icles showed ha la ge p obe pa i-
cles could no pene a e nea he nuclea bounda y [35],
which sugges s a dense (ch oma in) en i onmen wi h
smalle mesh sizes a he nuclea pe iphe y, in compa i-
son o cen al nuclea space.
LADs a e ancho ed o he inne su ace o NE (see
Fig. 1) ia molecula in e ac ions p o ided by a zoo o
lamina-associa ed p o eins such as LBR, LAP1, LAP2β,
LEMD2, MAN1, PRR14, e c. (see, e.g., Re s. [7,17,30]
and e e ences he ein). As such, gi en he leng h o
LADs, i is in ui i e o hink ha long s ands o LADs
bind o he inne -nuclea su ace ia mul i alen molec-
ula con ac s, which can p o ide cumula i e in e ac ion
ene gies on he o de o ∼10 kBT[36,37] easily, whe e kB
is he Bol zmann cons an s and Tis he absolu e empe -
a u e. This cumula i e a ac ion s eng h can s abilize
LADs s ongly enough ha he a e age dis ibu ion o
pe iphe al ch oma in may no change d as ically du ing
he li e ime o a heal hy cell. No ably, a kine ic u no e
be ween su ace-a ached and non-a ached LAD seg-
men s can occu . This molecula pic u e can allow pe-
iphe al ch oma in o be conside ed as an adso bed poly-
me laye , which can e eal he unc ional ole o pe iph-
e al ch oma in s uc u es.
In his s udy, we conside pe iphe al ch oma in as a
lexible polyme chain adso bed on o he NE su ace by
employing de Gennes’ sel -simila ca pe model. Using
2
LAD
LAD
in e -LAD
nuclea en elope
LAD
in e -LAD
nuclea in e io
in e -LAD
in e -LAD
FIG. 1. Au ho s’ iew o pe iphe al ch oma in. A polyme
ain o al e na ing LADs (pu ple and blue) and in e -LADs
(ligh and da k g een) along a pe iphe al ch omosome. Open
ci cles indica e he sha p LAD/in e -LAD bo de s. Va ious
p o eins ancho ing LADs o he nuclea bounda y a e ep e-
sen ed wi h iangles. The eal biological en i onmen a he
euka yo ic nuclea pe iphe y may ha e a highe ch oma in
densi y han shown he e.
scaling a gumen s, we es ima e he hickness o he LAD
laye and ela e he polyme na u e o ha high-densi y
ch oma in laye o he expe imen ally obse ed s e ic
hind ance o la ge molecules om he pe iphe al egion
o he nucleus. We ela e ou esul s and p edic ions o
he a ailable expe imen al da a o nuclea ch oma in dis-
ibu ion p o iles, and las ly, discuss he implica ions and
weaknesses o ou model, oge he wi h u u e pe spec-
i es.
II. SCALING THEORY OF PERIPHERAL
CHROMATIN
Du ing in e phase o euka yo ic cells, nuclea ch o-
ma in does no unde go mic oscopic changes. A his
s age, indi idual ch omosomes occupy dis inc e i o-
ies, bu no all neighbo he nuclea bounda y [2,38].
This s udy only conside s pe iphe al ch omosomes, o m-
ing a s aigh o wa d polyme in e ace nea he NE.
A. Assump ions and jus i ica ions
In polyme physics, a Kuhn segmen o size b= 2`pis
de ined as he la ges segmen o a polyme chain below
which he polyme beha es as a igid od. The chemical
composi ion o a polyme a ec s he pe sis ence leng h
`p, and hus, he Kuhn size b. Howe e , polyme chains
wi h dis inc ly di e en chemis y can exhibi uni e sal
con o ma ional cha ac e is ics when conside ing chains
composed o a su icien ly la ge numbe o Kuhn seg-
men s (i.e.,N1).
Conside ing he pe sis ence leng h o ch oma in on he
o de o `p∼1 kb o 10 kb [39–45], e en he sho es e-
po ed LADs can co espond o NL∼101 o ∼102Kuhn
segmen s espec i ely. These alues a e much sho e
han a single ch omosome (i.e., wi h N∼106Kuhn seg-
men s) bu long enough o be s a is ically conside ed as
a lexible polyme chain adso bed on a su ace.
Ch omosomes a e o ganized in o ch oma in ibe s,
which a e p o ein-DNA complexes. One majo p o ein
complex o ganizing DNA in o ch oma in ibe is he his-
one oc ame . Because he one-dimensional packing den-
si y o his one p o eins a ies along he ibe , ch oma in is
a highly he e ogeneous polyme . Due o he a ia ions in
hei his one packing densi ies [46,47], he e och oma in
and euch oma in can be s uc u ally dis inc and possi-
bly ha e noniden ical pe sis ence leng hs [48]. Fo he
same eason, alues epo ed in he li e a u e o ch o-
ma in pe sis ence leng h a y la gely, anging be ween
`p≈30 nm and `p≈300 nm [49–51]. The e o e, i is no
s aigh o wa d o assign a clea di e ence be ween he
pe sis ence leng hs o he e och oma in and euch oma in.
Thus, we assume an iden ical Kuhn monome size on he
o de o b≃10 nm as a lowe limi o he e och oma in-
ich LADs and euch oma in- ich in e -LADs. No e ha
h oughou he a icle, ≃signs deno e scaling ela ions
wi h neglec ed p e ac o s o o de uni y. Since scaling
heo ies ocus on he o de magni udes o he e ec s bu
no exac numbe s, igno ing all p e ac o s on he o de o
uni y, assuming equal Kuhn leng hs o LADs and in e -
LADs should no a ec ou scaling analysis. He eon, by
he e m “monome ”, we e e o a “Kuhn monome ” o
size b.
We assume ha he ch oma in in i s na i e nuclea
en i onmen can be modeled as a polyme solu ion in
he concen a ed egime. Tha is, he olume ac ion
o ch oma in is φ > 0.1. Single-pa icle acking expe i-
men s epo ing Rouse- ype dynamics o he subsec ion
o ch omosomes suppo his assump ion [52,53].
We igno e he e ec s o elec os a ic in e ac ions since
a physiological sal condi ions (i.e.,cs≈100 mM), ch o-
ma in could be ea ed as a neu al polyme o scaling
pu poses [49,54]. In ou calcula ions, he e is also no se-
lec i e a ac ion be ween ch oma in segmen s ha can
lead o a phase sepa a ion.
Since he cha ac e is ic size o he ch omosome is an
o de o magni ude smalle han he cu a u e adius o
he nucleus (i.e.,∼100µm s. ∼101µm), we ea he
inne NE su ace as plana .
To dis inguish be ween a su ace-adso bed and a non-
adso bed ch oma in monome , he adso p ion o LAD
segmen s o NE is modeled unde he “weak adso p-
ion” limi . The weak adso p ion scheme also consid-
e s all weak in e ac ions such as hyd ogen bonding, ionic
in e ac ions, e c. Thus, ins ead o conside ing a sub-
se o ch oma in monome s ancho ed o NE by associ-
a ed p o eins wi h adso p ion ene gies on he o de o
−U1kBT, each ch oma in monome (whe he LAD o
in e -LAD) has an equal p obabili y o in e ac ing wi h
he su ace wi h an adso p ion ene gy o U≈ −kT ,
whe e 0 <<1. LADs will be dis inguished om in e -
LADs ia he o ma ion o an adso bed laye (see Sec. C
3
FIG. 2. Illus a ion o wo isola ed chains adso bed on a la
su ace. Bo h polyme chains ha e he same numbe NLo
Kuhn monome s o size b. The polyme on he le is adso bed
mo e s ongly (wi h a la ge ) compa ed o he polyme on
he igh . Fo he mo e s ongly adso bed polyme on he le ,
numbe o monome s in an adso p ion blob gaand adso p ion
blob (mesh) size ξaa e smalle [see Eqs. (1) and (3)], while
numbe o blobs NL/gaand end- o-end size RLa e la ge [see
Eq. (4)].
below).
All pa ame e s we conside a e he a e ages o quan i-
ies ha ha e Gaussian dis ibu ions. As a gued abo e,
an a e age numbe o Kuhn monome s pe LAD and pe
in e -LAD (NLand NI) a e bo h conside ed o be much
la ge han uni y. This egime o long polyme s p o ides
an excellen playg ound o scaling heo ies.
B. Single-chain adso p ion model o an isola ed
LAD: adso p ion blobs a he pe iphe y
We begin ou discussion by conside ing a single LAD
composed o NLmonome s. While his discussion will
p o ide insigh o only an isola ed LAD adso bed on NE,
i will help us in oduce he concep s o chain adso p ion,
which will be used in he nex sec ion o desc ibe he bio-
logically ele an scena io o mul iple independen LADs
o a ch omosome, o e lappingly adso bed on NE.
Conside an n-me segmen o a LAD, which is long
enough o be conside ed as a lexible chain, bu s ill much
sho e han he whole LAD, i.e., 1 nNL. I he
o al a ac ion ene gy ac ing on all o i s monome s is
smalle han he he mal ene gy kBT, he mal luc ua-
ions domina e he cumula i e su ace a ac ion. As a
esul , he n-me segmen has an unpe u bed con igu a-
ion; i s oo -mean-squa e size, (n)≃bnν, is he same
as ha o an unpe u bed/non-adso bed n-me . The ex-
ponen νdepends on he sol en quali y, polyme olume
ac ion, and he molecula a chi ec u e o he polyme .
In he biologically ele an concen a ed egime o ou
conce n, ν= 1/2 o linea polyme s [55] and ν < 1/2
o cyclic polyme s [56–61].
As ninc eases, he numbe o con ac s ha he n-me
segmen can o m wi h he su ace, and hence, he e ec
o su ace a ac ion on he segmen , inc eases. A a
leng h scale
ξa≃bgν
a(1)
he cumula i e adso p ion ene gy o monome s in con ac
wi h he su ace becomes on he o de o he mal ene gy
kBT. In Eq. 1,gais he numbe o monome s pe ad-
so p ion blob. The monome olume ac ion wi hin an
adso p ion blob can be w i en as φa≃b3ga/ξ3
a. Using
Eq. (1), we can w i e he olume ac ion as a unc ion
o adso p ion blob size as
φa≃(ξa/b)(−3ν+1)/ν .(2)
Thus, he numbe o monome s in con ac wi h he su -
ace inside an adso p ion blob is (φa/b3)×(ξ2
ab). He e,
φa/b3is he numbe densi y o monome s inside an ad-
so p ion blob, and ξ2
abis he con ac olume o he blob
wi hin a dis ance b o he su ace. Thus, he adso p-
ion ene gy o a blob is (kBT)×(φa/b3)×(ξ2
ab)≃
kBT(ξa/b)1/ν−1. Equa ing his ene gy o he mal en-
e gy kBT, we ob ain he size o an adso p ion blob as
ξa≃b−ν/(1−ν),(3)
o he numbe o monome s in an adso p ion blob as
ga≃−1/(1−ν).
The e a e NL/gaadso p ion blobs along a single LAD.
An isola ed single LAD chain adso bed on he nuclea
pe iphe y, he e o e, beha es as a wo-dimensional sel -
a oiding andom walk o adso p ion blobs on he su ace
(Fig. 2). Such a andom walk o NL/gas eps, each o
size ξa, has a oo -mean-squa e end- o-end size o RL≃
ξa(NL/ga)3/4[62], om which, we ob ain
RL≃b(3/4−ν)/(1−ν)N3/4
L,(4)
ia Eq. (3). As he su ace a ac ion becomes s onge
wi h inc easing , he adso p ion blob size ξash inks,
see Eq. (3), bu he numbe NL/gao adso p ion blobs
pe chain inc eases. The combined e ec inc eases he
wo-dimensional end- o-end LAD size RL.
Assuming a median alue o NL≈103 o a single
LAD, we ob ain RL≃100 nm o he size o a single LAD
a e assuming = 1. Assuming a weake a ac ion (i.e.,
 < 1 dec eases he LAD’s size since he segmen loses
con ac wi h he su ace. Ne e heless, when he dis ance
be ween neighbo ing adso bed LADs is smalle han RL,
hose LADs in e ac by s e ically epelling each o he ,
and he abo e pic u e o isola ed LADs loses alidi y.
As will be discussed nex , such a dense LAD en i onmen
al e s polyme con o ma ions and can lead o a s e ic
en i onmen o molecules di using h ough LADs.
4
(c) (d)
dis ance o NE, z
φb
φa
ch oma in olume ac ion, φ
−(3ν−1)/ν
NE
nuclea in e io
inc easing
osmo ic p essu e
ξaξb
dis ance o NE, z
ξa
ξb
mesh size, ξ
1
NE
nuclea in e io
inc easing
s e ic hinde ance
ξaξb
FIG. 3. a) and b) Illus a ion o mul i-chain adso p ion on a la su ace. Osmo ic p essu e on chain segmen s is colo -coded
om high p essu e close o he su ace (pu ple) o low p essu e away om he su ace (g een). In (b), only se e al blobs a e
indica ed by ci cles illed wi h ch oma in segmen s o g aphical simplici y. c) and d) The log-log plo s o ch oma in olume
ac ion φand mesh (i.e., blob) size ξas unc ions o dis ance z om he adso bing su ace. As he ch oma in densi y dec eases
and he mesh size app oaches i s bulk alue, he s e ic hind ance o p o eins dec eases, as depic ed by sphe es o a ying sizes
in (d).
C. Mul i-chain adso p ion model o a single
ch omosome
Conside an indi idual ch omosome in con ac wi h NE
loca ed a z= 0, whe e zde ines he dis ance om he
su ace owa d he nuclea in e io . A ce ain ac ion o
he ch omosome monome s should be in con ac wi h he
NE su ace o o m LADs, while he es o ms loops (e.g.,
in e -LADs depic ed in Fig. 1). Expe imen s show ha
only ∼30% o LADs iden i ied by sequencing echniques
a e loca ed a he nuclea pe iphe y [7,24,63]. Thus, we
can a gue ha he e is insu icien space a he pe iphe y
o adso b all LADs.
I LADs and in e -LADs a e su icien ly long, we may
ea hem as independen chains. Acco dingly, we sug-
ges a molecula pic u e in which, nea he nuclea pe-
iphe y, many LADs compe e o adso p ion o he same
limi ed su ace space and s e ically epel each o he .
The adso p ion ene gy is kBTpe monome a con ac
wi h NE. This su ace a ac ion o e comes he s e ic e-
pulsion be ween segmen s, and consequen ly, monome
concen a ion nea he su ace is a i s maximum. Con-
a ily, monome s posi ioned away om he su ace do
ha e ze o adso p ion ene gy. As a esul , he s e ic e-
pulsion be ween segmen s becomes mo e dominan , a-
o ing a less dense ch oma in en i onmen (Fig. 3a,c).
Such a mul i-chain adso p ion scheme can be desc ibed
by de Gennes’ sel -simila ca pe model [64], in which
he compe i ion be ween s e ic chain-chain epulsion and
chain-su ace a ac ion de e mines he p ope ies o he
adso bed polyme laye .
As discussed in he p e ious subsec ion, con o ma ions
o he adso bed segmen s o his mul i-chain s uc u e
a e de e mined by he adso p ion blobs o size ξa(i.e.,
Eq. (3)). The s e ic epulsion be ween chains de ines a
second leng h scale, he “co ela ion blob” size ξ, which
is he a e age dis ance be ween chain segmen s o di e -
en chains. A he leng h scale o he co ela ion blob,
he in e -chain s e ic epulsion ene gy is de ined o be on
he o de o he mal ene gy kBT. Hence, a leng h scales
below ξ, in e -chain s e ic epulsion is compensa ed by
he mal ene gy, and chain segmen s ha e con o ma ions
unpe u bed by he s e ic epulsion. Tha is o say, a
leng h scales sho e han ξ, a chain segmen and i s sub-
sec ions a e unawa e o o he segmen s and beha e as i
i is isola ed. Thus, he co ela ion blob size can be w i -
5
en as ξ≃bgν, whe e gis he numbe o monome s pe
blob.
The abo e de ini ion o co ela ion blob size, ξ, gi es
he osmo ic p essu e (s e ic epulsion ene gy densi y) as
π≃kBT/ξ3. A he su ace, since he s e ic in e ac ions
(kBTpe co ela ion blob) a e compensa ed dominan ly
by he adso p ion ene gy (kBTpe adso p ion blob), he
co ela ion blob coincides wi h he adso p ion blob (i.e.,
ξ=ξa). The high osmo ic p essu e, due o he high den-
si y o monome s close o he su ace, is elaxed g adu-
ally as he dis ance z o he NE su ace inc eases. Such
a elaxa ion inc eases co ela ion leng h ξand dec eases
olume ac ion φ. Inside he “bulk” o he nucleus, a
away om NE, he co ela ion blob size ξband he ol-
ume ac ion φba e bo h independen o he dis ance z,
and hey a e ela ed by [55]
φb≃(ξb/b)(−3ν+1)/ν and ξb≃bφν/(−3ν+1)
b.(5)
The abo e ela ions also hold a an a bi a y dis ance
z o he su ace. The olume ac ion o monome s inside
a co ela ion blob is he same as he o e all local olume
ac ion φ(z) a z,i.e.,
φ≃b3g/ξ3≃(ξ/b)(−3ν+1)/ν .(6)
Hence, de Gennes’ sel -simila ca pe can be seen as
laye s o co ela ion blobs o inc easing size ξ(z) wi h in-
c easing dis ance z om he su ace (Figs. 3b,d). The
o iginal model [64] a gues a z-dependence o he co e-
la ion blob size, namely,
ξ(z)≃z(7)
sugges ing a linea ela ion be ween co ela ion leng h
wi h he dis ance zun il i eaches he bulk alue a
z=ξb. Plugging he abo e exp ession in o Eq. (6) also
p o ides a dis ance-dependen densi y p o ile:
φ(z)≃(z/b)(−3ν+1)/ν .(8)
In summa y, de Gennes’s sel -simila ca pe model p e-
dic s he ch oma in olume ac ion and he co ela ion
blob size p o iles be ween nuclea bounda y and bulk as
ollows
φ(z)≃




φa,z < ξa
φa(z/ξa)(−3ν+1)/ν ,ξa< z < ξb
φb,ξb< z
,(9)
ξ(z)≃




ξa,z < ξa
z,ξa< z < ξb
ξb,ξb< z
,(10)
Eqs. 9and 10 a e plo ed in Figs. 3c and d in log-
log scales. No ably, he co ela ion blob size ξis p o-
po ional o mesh size (i.e., he size s e ically a ailable
o nuclea p o eins). Thus, he smalle he ξis, he
s onge he s e ic hind ance nea he nuclea bounda y
becomes. Figs. 3highligh s h ee dis inc compa men s
o ou model, each wi h a di e en ch oma in densi y and
mesh (co ela ion) size p o iles. These h ee egions can
in e p e ed as ollows:
1. In close p oximi y o he nuclea en elope
A z < ξa, he su ace is co e ed wi h a laye o ad-
so p ion blobs o size ξa. This high-densi y laye has a
hickness o ξagi en de e mined by he a e age size o
adso bed segmen s (Eq. (3) and can be in e p e ed as a
ue LAD laye . Since some LADs (o whole LADs) can-
no ind space on he su ace o ge adso bed due o he
ini e space a ailable, hey would be pushed owa ds he
nuclea in e io by he high ch oma in-osmo ic p essu e
nea he su ace. No ably, such a laye can also p o ide
ex a s eng h o NE. [33]
2. In be ween he nuclea pe iphe y and he nuclea bulk
As zinc eases along he in e ace egion o ξa< z < ξb,
he high p essu e and densi y a he nuclea pe iphe y
elaxes, and he ch oma in densi y app oaches i s bulk
alues 3c. The elaxa ion o su ace e ec s inc eases co -
ela ion leng h ξwi h inc easing z. This inc easing co -
ela ion size can allow la ge molecules o di use h ough
he dense ch oma in s uc u e. In p inciple, laye s o
blobs in his in e ace egion con ain subsec ions o bo h
LADs and in e -LADs.
3. Inside he nuclea bulk
Fa away om he nuclea pe iphe y a z > ξb, he
abo emen ioned p essu e elaxa ion is comple e. The
ch oma in sec ions in his egion do no eel he adso b-
ing su ace om his dis ance. He e, he only e ec o
NE on he ch oma in is he nuclea con inemen . Expe -
imen s iden i ied his in e io egion wi h low ch oma in
densi y and high ansc ip ional ac i i y [4,6,25,29].
This egion is mani es ed by a su ace-independen mesh
size (co ela ion leng h) ξb, which is la ge han he mesh
size nea he su ace.
III. COMPARISON TO EXPERIMENTAL DATA
FROM LITERATURE
To ob ain a quan i a i e alida ion o ou model, we
acili a e he expe imen ally a ailable da a published in
he li e a u e. Fi s , we compa e ou scaling p edic ions
wi h he ch oma in densi y p o iles o euka yo ic cell
ypes (Fig. 4and Table I).

6
(a) (b)
0.05 0.1 0.5 1.0
z / R
0.2
0.4
0.6
0.8
1.0
φ / φa
NE
(z/R)/(ξa/R)
φ / φa
NE
−1
−1/2
0.5 1.0 5.0 10.0
0.2
0.4
0.6
0.8
1.0
HT
HF
HC
MC
MG
MF
DL
FIG. 4. Log-log plo s o he dependence o ch oma in olume ac ion φon dis ance o nuclea pe iphe y z. Da a a e om
a ious euka yo ic cell ypes; Table I o abb e ia ions. In bo h panels, φda a is scaled by he maximum measu ed olume
ac ion φa o ha cell ype. In he le panel, zis scaled by cell adius R, such ha z/R = 1 is a he nuclea cen e . The
dec ease in ch oma in densi y close o he nuclea pe iphe y a small z/R, is due o a deple ion egion no conside ed in he
heo y. In he igh panel, z/R is scaled wi h ξa/R o ob ain a da a collapse in acco dance wi h Eq. (11). Fi ing pa ame e es
o ξa/R a e gi en in Table I. The dashed and do ed lines show ou p edic ions o φ/φa≃(z/ξa)−1and φ/φa≃(z/ξa)−1/2;
see Fig. 3c and Eq. (11) wi h ν= 1/2 and ν= 2/5 espec i ely. The da a poin s a e joined o guide he eye.
In li e a u e, he nuclea ch oma in densi y p o iles
we e o en epo ed in he uni s o luo escence in en-
si y o a bi a y uni s as a unc ion o nuclea adial dis-
ance. The e o e, o compa e ou esul s summa ized in
Eq. 9wi h such da a, we no malize he densi y axis by
he maximum alue o he signal o he co esponding
cell ype. The maximum alue is ma ched o he densi y
alue nea he su ace in ou model (i.e., φa). Then, we
compa e he escaled da a wi h ou no malized densi y
dis ibu ion (i.e., φ/φa) (Fig. 4a).
In gene al, as shown in Fig. 4a, dec easing ch oma in
concen a ion wi h inc easing dis ance om he nuclea
pe iphe y is a common hallma k o he densi y p o iles
in all simula ions and expe imen s [35,65–73] and ag ees
well wi h ou model, see Eq. (9) and Fig. 3c. This can be
seen mo e quan i a i ely in he mas e cu e combining
Code Re . Cell ype ξa/R
HT [65] Human T-cell 0.42
HF [66] Human ib oblas 0.11
HC [67] Human ca diomyocy e 0.26
MC [67] Mouse ca diomyocy e 0.20
MG [68] Mouse ganglion†0.12
MF [68] Mouse ib oblas †0.06
DL [69] D osophila la al muscle 0.16
TABLE I. Fi pa ame e s, ξa/R, used o collapse he ex-
pe imen al da a on a mas e cu e in Fig. 4b. (†Includes
only gene-poo he e och oma in, bu no he gene- ich eu-
ch oma in.)
all he a ailable da a by using he exp ession
φ(z)
φa
≃z/R
ξa/R(−3ν+1)/ν
(11)
o ξa< z < ξb. To ob ain he o e lap in Fig. 4b, we use
ξa/R as a ee i pa ame e in Eq. 9 o all cell ypes (see
Table I o he i alues). We obse e ha he hickness
o he LAD laye ela i e o he nuclea adius is in he
ange o abou ξa/R ≃0.1−0.2, which ag ees well wi h
high- esolu ion mic oscopy images [24,31,63]. The only
excep ion is he human T-cell, o which we p edic a
ξa/R alue o abou 40% (Table I). Also, no e ha da a
o his cell ype is singled ou om he o he collapsed
da a se s in Fig. 4b.
The da a in Fig. 4b highligh s a concen a ion decay
om he nuclea su ace o he bulk. Howe e , o he
human T-cell, his decay is s onge ; while ou model
p edic s φ/φa= (z/ξa)−1 o he human T-cell o linea
chains o ν= 1/2, all o he da a can be collapsed on o
a uni e sal line o φ/φa= (z/ξa)−1/2away om he nu-
clea cen e . This exp ession is ob ained i an exponen
o ν= 2/5 is chosen o he s a is ical con o ma ion o
he LAD and in e -LAD segmen s; see Eq. (9). While he
exponen ν= 2/5 desc ibes he da a ela i ely well, i is
la ge han some p edic ions (i.e., ν= 1/3) [56,61], bu
consis en wi h o he s [57–60]. Al e na i ely, he a e age
o size LADs da a could e lec a ansi ion egime om
aν= 2/5-con olled egime o a egime o mo e compac
polyme sizes (i.e., ν= 1/3) [74,75].
Nex , we compa e he co ela ion leng hs ha we p e-
7
dic wi h he a ailable expe imen al da a epo ing he
e ec i e po osi y o nuclea ch oma in. By mic oin-
jec ing luo escen -labeled dex an p obe molecules o
a ying molecula mass Min o in e phase HeLa nuclei,
G¨o isch e al. co ela ed he nuclea dis ibu ion o such
pa icles wi h he nuclea po osi y nea and away om
he pe iphe y [35]. While small dex an molecules (i.e.,
d/20 nm) wi h M≤77 kDa can di use close o he nu-
clea pe iphe y, la ge molecules canno . Fo hose la ge
molecules, he dex an densi y inc eases away om he
NE and le els o inside he nuclea bulk. This inding is
in quali a i e ag eemen wi h ou p edic ions o dec eas-
ing mesh size nea he su ace gi en by
This inding is in quali a i e ag eemen wi h ou p e-
dic ions o he mesh size [see Eq. (6)],
ξ(z)≃(b[φ(z)]−2,ν= 2/5
b[φ(z)]−1,ν= 1/2.(12)
No e ha he abo e p edic ions a e much s onge
han he in e se squa e oo dependence ob ained by con-
side ing ch oma in as hexagonal packed c ys als [76].
The smalles leng h scale in ou model is he Kuhn
leng h (o he pe sis ence diame e ), b= 2`p. Such a
scaling model can only make limi ed p edic ions abou
he phenomena ela ed o leng h scales smalle han b.
One such p edic ion is ha since he Kuhn leng h de-
ines he size o he smalles loops ha can be o med
by he polyme chain inside he dense ch oma in en i-
onmen , any molecule smalle han bcan ind po es o
di use along. This simple pic u e is adequa e o desc ibe
he smalles mesh size o b≈20 nm obse ed by G¨o isch
e al. close o he nuclea pe iphe y. In ac , his is on
he o de o he Kuhn size o ch oma in, which b≃10
nm.
A second s e ic ba ie in he expe imen s obse ed is
he mesh size o ξ≈60 nm, which can be in e ed as
he size ξao he adso p ion blobs o ou model [35,76].
Fo he HeLa nuclei o adius R≈1µm, his adso p ion
blob size alue leads o ξa/R ≈0.06, in acco d wi h he
ange o alues p esen ed in Table I. We no e ha by
plugging he alues ξa≈60 nm and b≈20 nm in o
Eq. (1), we ob ain he numbe o Kuhn monome s in an
adso p ion blob as ga≃10 o bo h linea (ν= 1/2)
and cyclic (ν= 2/5) chains. Recalling ha ou scaling
heo y assumes ga1, a alue o ga≃10 is a he
limi ing bounda y o he alidi y o ou model.
Finally, om his ela i e hickness ξa/R, we p edic
he ela i e nuclea olume o he LAD laye as
VLAD/V ≃ξa/R, (13)
whe e V≃R3is he nuclea olume. Fo a nuclea
adius o a ound R≈5µm, using he alues in Table I,
we ob ain a ela i e olume o he LAD laye in he ange
V/VLAD ≃10−20%, wi h an a e age LAD laye hickness
o ξa<1µm. This p edic ion ag ees well wi h high-
esolu ion mic oscopy images [24,31,63].
IV. DISSCUSSION
By e isi ing de Gennes’ sel -simila ca pe model, we
a gue ha lamina-associa ed ch oma in domains can be
conside ed as mul iple independen chain segmen s (o
a ch omosome) a ac ed o a su ace wi h an ene gy o
U=−kBTpe adso bed Kuhn monome . In ou cal-
cula ions, we assume ch oma in laye s adjacen o he
su ace wi h a hickness ξaa e all occupied by LADs.
In eali y, o sho LAD and long in e -LAD segmen s,
only a ac ion o he su ace is co e ed by isola ed LADs
ha o m adso p ion blobs o size ξa. In con as , he
es o he nuclea su ace is co e ed by in e -LADs o
co ela ion leng h ξb. Howe e , DamID and ChIP-seq
expe imen s associa e ∼40% o he genome as LADs [7,
9,77]. Fo such long LADs, he laye s close o he nuclea
pe iphe y mus be illed almos en i ely wi h adso p ion
blobs co esponding o LAD chains, pe ou assump ions.
Ou calcula ions do no dis inguish be ween ch oma in
sec ions pe manen ly e he ed o NE and hose in e ac -
ing weakly wi h he pe iphe y. Ne e heless, he s a-
is ical na u e o he scaling analyses a o s su ace lo-
caliza ion limi ed by s e ic epulsion be ween LAD seg-
men s. Thus, he de ailed na u e o he su ace local-
iza ion does no change he ou come and p o ides ela-
i ely good ch oma in dis ibu ions as compa ed o ex-
pe imen s. Howe e , dis inguishing e he ing om weak
a ac ion o a ying he chain s i ness a ec ed he con-
ac p obabili ies a ∼100 kb scale [45], bu a e aging
o e many segmen s in con ac wi h NE can p o ide a
pic u e simila o ou p edic ions. I is also in ui i e o
hink ha mo e pe manen con ac s wi h NE can gi e
LADs s uc u al p ope ies such as hose obse ed in
cyclic polyme b ushes [78–80] o a combina ion o a
b ush and de Gennes’ ca pe [81]. In ac , assuming a
cyclic a chi ec u e o he in e -LADs ha a e a ached
om bo h ends o NE and p o ude owa ds he nuclea
in e io , o ming loops, explains he ch oma in densi y
p o ile da a o a ious euka yo ic cells (Fig. 4).
In ac , an in e -LAD in be ween wo consecu i e
LADS, can be a ached o NE om bo h ends and e -
ec i ely could ha e a cyclic polyme opology. In addi-
ion, on smalle leng h scales, ch oma in loops a e o med
by he in e ac ions be ween opologically associa ed do-
mains along he ch omosome [5,6,10,25,82,83]. Hence,
he pe iphe al ch oma in could be modeled as a cyclic
polyme ha can be desc ibed by he exponen ν= 2/5.
In ha sense, he ou lie da a poin in Fig. 4b, human T-
cells, can be a ionalized by he a gumen ha he in e -
LADs in human T-cells a e e he ed o NE a dis an
posi ions, and as such, he pe iphe al ch oma in in be-
ween hese e he ing poin s canno be ea ed as a con-
cen a ed solu ion o cyclic chains bu as linea chains.
Mo eo e , he T-cell ch oma in dis ibu ion dec easing
s ongly wi h su ace sepa a ion (Fig. 4b) may also be
due o he cons ained elease o lamina-associa ed en-
hance s and genes om he nuclea en elope, as obse ed
du ing Ju ka T-cell ac i a ion [84], which changes he 3d
8
o ganiza ion o he genome.
Ou model explains he s e ic hind ance o la ge
molecules om he nuclea pe iphe y. Adso p ion o
LADs o NE gene a es a s uc u ally dis inc laye o
ch oma in wi h a mesh size smalle han in he bulk o
he nucleus (i.e.,ξ < ξb). This pic u e leads o an e ec-
i e hind ance mechanism. The smalles mesh size is ξa
a he p oximi y o NE. The same ξade ines he hick-
ness o he denses laye on he su ace, i.e., he hick-
ness o he LAD laye . As he dis ance o NE inc eases,
he mesh size g ows owa ds ha inside he nuclea bulk
(ξb). This hind ance can exclude la ge p o eins o an-
sc ip ion machine y om he LADs and ein o ce he
supp essi e en i onmen o LADs ia his non-speci ic
e ec ha does no depend on he nucleic acid sequence.
The exac mechanism can allow la ge mesh sizes, o
ins ance, nea he nuclea po e complexes a ound which
euch oma in is ela i ely spa se, allowing mo e ansc ip-
ional ac i i y nea LADs. The hind ance o e y small
molecules (smalle han he pe sis ence diame e o ch o-
ma in, ∼20 nm) canno be explained by he mechanism
o g owing mesh size ξ, bu could be due o he con e -
gence o nucleosome in o an e ec i e (dense) mel (e.g.,
polyme b ush [81]). Consis en ly, a ecen s udy [85] dis-
cusses ha su ace-a ached LADs ha e less gene ac i i y
han non-a ached LADs, which eside a he in e ace
be ween he so-called “compa men A” and “compa -
men B”. This esul suppo s he inc easing mesh size
along he in e ace egion. P o eins egula ing he ge-
ne ic machine y canno each he dense laye o su ace-
a ached LADs, while hey each he non-a ached LAD
segmen s o he la ge mesh size.
The polyme model does no sepa a e LADs and in e -
LADs. Ye , one can conclude ha ch oma in sec ions
away om he nuclea pe iphe y a e o in e -LAD na-
u e implici ly. A mo e de ailed model can sepa a e hese
wo ch oma in ypes, possibly conside ing copolyme s
wi h wo di e en pe sis ence leng hs [48]. Ne e heless,
we an icipa e ha wi hin he limi s o alid biological
pa ame e s, dec easing s e ic hind ance and dec easing
ch oma in densi y owa ds he nuclea in e io will be
p ese ed e en in a mo e complex model. This is also
e iden om he expe imen al da a in which mo e com-
pac ch omocen e egions o he genome ha e a mild
e ec on ch oma in dis ibu ion, albei hese aces cause
highe he e och oma in concen a ion nea hei su ace.
(See, e.g., MG and MF da a in Fig. 4b and he co e-
sponding Re . [68].)
O e all, ou heo e ical app oach demons a es ha
o ganizing a me e s-long genome inside a mic on-size nu-
cleus can equi e he acili a ion o a ious polyme s uc-
u es, many o which ha e been s udied ex ensi ely in he
con ex o syn he ic polyme s. Re ealing he s uc u al
complexi y o genome o ganiza ion can help us ex end
ou knowledge o he ela ionship be ween 3d ch omo-
some o ganiza ion, gene ic egula ion, and nuclea mo -
phology.
ACKNOWLEDGMENTS
We hank J. Pa u ej o he aluable discussions. This
wo k has been suppo ed by he Na ional Science Cen e ,
Poland (G an Polonez Bis No. 2021/43/P/ST3/01833)
and The Council o Science and Technology o Tu key
(TUBITAK) G an no 122F309.
[1] T. C eme and C. C eme , Na u e Re iews Gene ics 2,
292 (2001).
[2] C. Weie ich, A. B e o, S. S ein, J. on Hase, C. C eme ,
T. C eme , and I. Solo ei, Ch omosome Resea ch 11,
485 (2003).
[3] M. R. B anco and A. Pombo, TRENDS in Cell Biology
17, 127 (2007).
[4] A. Buchwal e , J. M. Kaneshi o, and M. W. He ze ,
Na u e Re iews Gene ics 20, 39 (2019).
[5] L. A. Mi ny, M. Imakae , and N. Abdennu , Cu en
Opinion in Cell Biology 58, 142 (2019).
[6] H. Zheng and W. Xie, Na u e Re iews Molecula Cell
Biology 20, 535 (2019).
[7] N. B iand and P. Collas, Genome Biology 21, 85 (2020).
[8] D. E. Olins and A. L. Olins, Na u e Re iews Molecula
Cell Biology 4, 809 (2003).
[9] D. Pe ic-Hupkes, W. Meuleman, L. Pagie, S. W. M.
B uggeman, I. Solo ei, W. B ugman, S. G ¨a , P. Flicek,
R. M. Ke kho en, M. an Lohuizen, M. Reinde s, L. Wes-
sels, and B. an S eensel, Molecula Cell 38, 603 (2010).
[10] A. Pombo and N. Dillon, Na u e Re iews Molecula Cell
Biology 16, 245 (2015).
[11] E. Wegel and P. Shaw, Ch omosoma 114, 331 (2005).
[12] F. E del, Cu en Opinion in Gene ics and De elopmen
61, 62 (2020).
[13] B. Bu ke and C. L. S ewa , Na u e Re iews Molecula
Cell Biology 3, 575 (2002).
[14] C. J. Hu chison, Na u e Re iews Molecula Cell Biology
3, 848 (2002).
[15] K. Ho mann, C. K. D ege , A. L. Olins, D. E. Olins,
L. D. Shul z, B. Lucke, H. Ka l, R. Kaps, D. M¨ulle ,
A. Vay´a, J. Azna , R. E. Wa e, N. S. C uz, T. H. Lindne ,
H. He mann, A. Reis, and K. Spe ling, Na u e Gene ics
31, 410 (2002).
[16] L. D. Shul z, B. L. Lyons, L. M. Bu zenski, B. Go ,
R. Samuels, P. A. Schwei ze , C. D ege , H. He mann,
V. Kalscheue , A. L. Olins, D. E. Olins, K. Spe ling, and
K. Ho mann, Human Molecula Gene ics 12, 61 (2003).
[17] P. Taimen, K. P leghaa , T. Shimi, D. M¨olle , K. Ben-
Ha ush, M. R. E dos, S. A. Adam, H. He mann,
O. Medalia, F. S. Collins, A. E. Goldman, and R. D.
Goldman, P oceedings o he Na ional Academy o Sci-
ences 106, 20788 (2009).
[18] K. B. P leghaa , P. Taimen, V. Bu in-Is aeli, T. Shimi,
S. Lange -F ei ag, Y. Ma kaki, A. E. Goldman, M. Wehn-
e , and R. D. Goldman, Nucleus 6, 66 (2015).
9
[19] D. Zink, A. H. Fische , and J. A. Nicke son, Na u e
Re iews Cance 4, 677 (2004).
[20] D. M. Ca one and J. B. Law ence, Semina s in Cance
Biology 23, 99 (2013).
[21] E. Liebe man-Aiden, N. L. an Be kum, L. Williams,
M. Imakae , T. Ragoczy, A. Telling, I. Ami , P. J. S.
B yan R. Lajoie, M. O. Do schne , R. Sands om,
B. Be ns ein, M. A. Bende , M. G oudine, A. Gni ke,
J. S ama oyannopoulos, L. A. Mi ny, E. S. Lande , and
J. Dekke , Science 326, 289 (2009).
[22] E. Lund, A. R. Oldenbu g, and P. Collas, Nucleic Acids
Resea ch 42, e92 (2014).
[23] B. an S eensel, J. Del ow, and S. Heniko , Na u e Ge-
ne ics 27, 304 (2001).
[24] J. Kind, L. Pagie, H. O abozkoyun, S. Boyle, S. S.
de V ies, H. Janssen, M. Amendola, L. D. Nolen, W. A.
Bickmo e, and B. an S eensel, Cell 153, 178 (2013).
[25] I. Je ko i´c and G. Ca alli, Na u e Re iews Molecula Cell
Biology 22, 511 (2021).
[26] L. Guelen, L. Pagie, E. B asse , W. Meuleman, M. B.
Faza, W. Talhou , B. H. Eussen, A. de Klein, L. Wessels,
W. de Laa , and B. an S eensel, Na u e 453, 948 (2008).
[27] W. Meuleman, D. Pe ic-Hupkes, J.-B. B. Jop Kind,
L. Pagie, M. Kellis, M. Reinde s, L. Wessels, and B. an
S eensel, Genome Resea ch 23, 270 (2013).
[28] T. Rønningen, A. Shah, A. R. Oldenbu g, K. Vek e ud,
E. Delba e, J. Ø. Moskaug, and P. Collas, Genome Re-
sea ch 25, 1825 (2015).
[29] L. Chang, M. Li, S. Shao, C. Li, S. Ai, B. Xue, Y. Hou,
Y. Zhang, R. Li, X. Fan, A. He, C. Li, and Y. Sun,
P o ein and Cell 13, 258 (2020).
[30] X. Wong, J. A. Cu le , V. E. Hoskins, M. Go don, A. K.
Madugundu, A. Pandey, and K. L. Reddy, Li e Science
Alliance 4, e202000774 (2021).
[31] B. an S eensel and A. S. Belmon , Cell 169, 780 (2017).
[32] J. C. Ha , T. R. Lupe chio, X. Wong, E. Cohen, S. J.
Wheelan, and K. L. Reddy, Jou nal o Cell Biology 208,
33 (2015).
[33] A. Janssen, S. U. Colmena es, and G. H. Ka pen, An-
nual Re iew o Cell and De elopmen al Biology 34, 265
(2018).
[34] J. Madsen-Øs e bye, A. Bellange , N. M. Galigniana,
and P. Collas, F on ie s in Cell and De elopmen al Bi-
ology 10, 913458 (2022).
[35] S. M. G¨o isch, M. Wachsmu h, K. F. T´o h, P. Lich e ,
and K. Rippe, Jou nal o Cell Science 118, 5825 (2005).
[36] Y. Le y, J. N. Onuchic, and P. G. Wolynes, Jou nal o
he Ame ican Chemical Socie y 129, 738 (2007).
[37] A. E ba¸s, D. Ho inek, and R. R. Ne z, Jou nal o he
Ame ican Chemical Socie y 134, 623 (2012).
[38] T. C eme and M. C eme , Cold Sp ing Ha bo Pe spec-
i es in Biology 2, a003889 (2010).
[39] Y. Cui and C. Bus aman e, P oceedings o he Na ional
Academy o Sciences 97, 127 (2000).
[40] J. Dekke , K. Rippe, M. Dekke , and N. Kleckne , Sci-
ence 295, 1306 (2002).
[41] S. Jun, J. He ick, A. Bensimon, and J. Bechhoe e , Cell
Cycle 3, 223 (2004).
[42] K. Bys icky, P. Heun, L. Gehlen, J. Langowski, and
S. M. Gasse , P oceedings o he Na ional Academy o
Sciences 101, 16495 (2004).
[43] K. S. Bloom, Ch omosoma 117, 103 (2008).
[44] P. R. Cook and D. Ma enduzzo, Jou nal o Cell Biology
186, 825 (2009).
[45] A. B une , N. Des ain ille, and P. Collas, Nucleus 12, 6
(2021).
[46] G. J. Tho n, C. T. Cla kson, A. Rademache , H. Ma-
mayusupo a, G. Scho a, K. Rippe, and V. B. Tei , Na-
u e Communica ions 13, 1861 (2022).
[47] M. A. Ricci, C. Manzo, M. F. Ga c´ıa-Pa ajo,
M. Lakadamyali, and M. P. Cosma, Cell 160, 1145
(2015).
[48] M. Gi a d, M. O. de la C uz, J. F. Ma ko, and A. E ba¸s,
bioRχi 12.01.403832, 1 (2020).
[49] J. Langowski, The Eu opean Physical Jou nal E 19, 241
(2006).
[50] H. Hajjoul, J. Ma hon, H. Ranchon, I. Goi on, J. Mozzi-
conacci, B. Albe , P. Ca i ain, J.-M. Vic o , O. Gadal,
K. Bys icky, and A. Bancaud, Genome Resea ch 23,
1829 (2013).
[51] D. Kolbin, B. L. Walke , C. Hul , J. D. S an on, D. Adal-
s einsson, M. G. Fo es , and K. Bloom, Genes 14, 2193
(2023).
[52] S. S. Ashwin, T. Nozaki, K. Maeshima, and M. Sasai,
P oceedings o he Na ional Academy o Sciences 116,
19939 (2019).
[53] R. Benelli and M. Weiss, Biophysical Jou nal 121, 2684
(2022).
[54] J. F. Ma ko, Jou nal o Molecula Biology 432, 621
(2020).
[55] M. Rubins ein and R. H. Colby, Polyme Physics (Ox o d
Uni e si y P ess, Ox o d, G ea B i ain, 2003).
[56] M. E. Ca es and J. M. Deu sch, Jou nal de Physique
F ance 47, 2121 (1986).
[57] S. B own and G. Szamel, The Jou nal o Chemical
Physics 109, 6184 (1998).
[58] M. M¨ulle , J. P. Wi me , and J.-L. Ba a , Eu ophysics
Le e s 52, 406 (2000).
[59] K. Hu , C. Jeong, R. G. Winkle , N. Lace ic, R. H. Gee,
and D. Y. Yoon, Mac omolecules 44, 2311 (2011).
[60] C. Jeong and J. F. Douglas, Mac omolecula Theo y and
Simula ions 26, 1700045 (2017).
[61] A. Rosa and R. E e ae s, Phys. Re . Le . 112, 118302
(2014).
[62] B. Nienhuis, Physical Re iew Le e s 49, 1062 (1982).
[63] J. Paulsen, M. Sekelja, A. R. Oldenbu g, A. Ba a eau,
N. B iand, E. Delba e, A. Shah, A. L. Sø ensen,
C. Vigou oux, B. Buendia, and P. Collas, Genome Biol-
ogy 18, 21 (2017).
[64] P. G. de Gennes, Mac omolecules 14, 1637 (1981).
[65] D. Amiad-Pa lo , D. Lo be , G. Bajpai, A. Reu eny,
F. Ronca o, R. Alon, S. Sa an, and T. Volk, Science
Ad ances 7, eab 6251 (2021).
[66] Y. Li, V. Ag awal, R. K. A. Vi k, E. Ro h, W. S. Li,
A. Eshein, J. F ede ick, K. Huang, L. Almassalha, R. Ble-
he , M. A. Ca ignano, I. Szlei e , V. P. D a id, and
V. Backman, Scien i ic Repo s 12, 12198 (2022).
[67] B. Seelbinde , S. Ghosh, S. E. Schneide , A. K. Sco ,
A. G. Be man, C. J. Goe gen, K. B. Ma gulies, K. C. B.
J ., E. Casas, A. R. Swea ingen, J. B umbaugh, S. Cal e,
and C. P. Neu, Na u e Biomedical Enginee ing 5, 1500
(2021).
[68] I. Solo ei, M. K eysing, C. Lanc ˆo , S. K¨osem, L. Peichl,
T. C eme , J. Guck, and B. Jo e, Cell 137, 356 (2009).
[69] D. Amiad-Pa lo , C. P. Unnikannan, D. Lo be , G. Ba-
jpai, T. Olende , E. S oops, A. Reu eny, S. Sa an, and
T. Volk, Cells 12, 932 (2023).