ARTICLE
Complian mechanical esponse o he ul a as
olding p o ein EnHD unde o ce
An onio Rei s1, I ene Ruiz O iz2, Amaia Ochando ena Saa 1, Jö g Schön elde 1, Da id De Sancho2,3,
Vic o Muñoz4✉& Raul Pe ez-Jimenez 1,5,6✉
Ul a as olding p o eins ha e become an impo an pa adigm in he s udy o p o ein olding
dynamics. Due o hei low ene ge ic ba ie s and as kine ics, hey a e amenable o s udy
by bo h expe imen and simula ion. Howe e , single molecule o ce spec oscopy expe i-
men s on hese sys ems a e challenging as hese p o eins do no p o ide he mechanical
finge p in s cha ac e is ic o mo e mechanically s able p o eins, which makes i di ficul o
ex ac in o ma ion abou he olding dynamics o he molecule. He e, we in es iga e he
un olding o he ul a as p o ein Eng ailed Homeodomain (EnHD) by single-molecule a omic
o ce mic oscopy expe imen s. Cons an speed expe imen s on EnHD esul in ea u eless
ansi ions ypical o complian p o eins. Howe e , in he o ce- amp mode we eco e sig-
moidal cu es ha we in e p e as a e y complian p o ein ha olds and un olds many imes
o e a ma ginal ba ie . This is suppo ed by a simple heo e ical model and coa se-g ained
molecula simula ions. Ou esul s show he abili y o o ce o modula e he un olding
dynamics o ul a as olding p o eins.
h ps://doi.o g/10.1038/s42005-022-01125-5 OPEN
1CIC nanoGUNE BRTA, Tolosa A enue 76, 20018 San Sebas ian, Spain. 2Donos ia In e na ional Physics Cen e (DIPC), Manuel La dizabal Ibilbidea 4,
20018 San Sebas ian, Spain. 3Polime o e a Ma e ial Au e a uak: Fisika, Kimika e a Teknologia, Kimika Fakul a ea, Uni e si y o he Basque Coun y (UPV/
EHU), Manuel La dizabal Ibilbidea 3, 20018 San Sebas ian, Spain. 4Depa men o Bioenginee ing, Uni e si y o Cali o nia, 95343 Me ced, CA, USA.
5Ike basque Founda ion o Science, Plaza Euskadi 5, 48009 Bilbao, Spain.
6
P esen add ess: CIC bioGUNE, Basque Resea ch Technology Alliance (BRTA),
Bizkaia Technology Pa k, 48160 De io, Spain. ✉email: [email p o ec ed];[email p o ec ed]
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1234567890():,;
Mos single-domain p o eins exhibi an all-o -none
olding beha io due o he high ene gy ba ie s ha
need o be o e come du ing he (un) olding p ocess.
The (un) olding o his ype o p o ein is highly coope a i e1, and
equilib ium and kine ic expe imen s on his ype o sys em whe e
he equilib ium is pe u bed ei he by empe a u e o a chemical
dena u an a e easily in e p e able. Fo hese p o eins, he
ensemble o s a es is mos ly dis ibu ed be ween he olded and
un olded s a e, and he e o e i is no possible o ex ac in o -
ma ion abou he olding mechanism, i.e., he my iad o con-
o ma ions ha a e isi ed as he p o ein e ol es owa ds he
na i e s a e2. This becomes possible o ul a as olding p o eins,
which lie on he o he side o he coope a i i y spec um. They
old in imescales be ween milliseconds and mic oseconds and a e
cha ac e ized by hei small size, ypically helical s uc u e, and
low (<3k
B
T) ee-ene gy ba ie s3. Fo his eason, he e is a
measu able popula ion in he in e media e s a es o he p o ein,
which could, in p inciple, be esol ed by spec oscopy and,
po en ially, e en a he single-molecule le el.
A e hei ini ial applica ions o p o ein olding h ee decades
ago, single-molecule o ce spec oscopy (smFS) echniques a e
now es ablished as a means o accessing de ails o he (un) olding
p ocess ha a e dis inc om hose de i ed om adi ional
me hods elian on ensemble a e aging4. smFS echniques ei he
using op ical o magne ic weeze s o an a omic o ce mic oscope
(AFM), allow di ec manipula ion o an (un) olding eac ion
coo dina e h oughou he applica ion o con olled mechanical
o ces5–7. Two-s a e and mul i-s a e p o eins o en ha e easily
in e p e able signals upon mechanical un olding, e.g., a saw- oo h
pa e n cha ac e ized by well-defined con ou leng hs in cons an
speed mode, o disc e e jumps o measu able ex ension in he
o ce– amp, and o ce–clamp modes8–10. Howe e , as he coop-
e a i i y o he p o ein dec eases, p o eins oppose less esis ance
o he ex e nal o ce, and hese finge p in s become less p e-
dic able o disappea al oge he . Fo example, Rie and his co-
wo ke s s udied he p o o ypical ul a as olde illin headpiece
subdomain using op ical weeze s11 They ob ained con inuous
hump-like equilib ium ansi ions a a ange o pulling speeds
and comple ely ea u eless cons an o ce aces a he midpoin .
Mo e ecen ly, Pe kins and his co-wo ke s s udied he compu-
a ionally designed, h ee-helix bundle α3D12–14, which in bulk
also olds in he mic osecond egime15.α3D u ned ou o
be ex emely labile unde o ce, esul ing in a ba ely dis in-
guishable peak o less han 12 pN. In p e ious wo k, we s udied
he e e sible olding and un olding p o ein gpW a a cons an
o ce unde he AFM16,17. We esol ed hopping ansi ions in an
ene gy landscape wi h a low ee ene gy ba ie induced by he
ex e nal o ce.
He e, we expand he ealm o ul a as olde s s udied using
smFS examining he mechanical un olding o he Eng ailed
Homeodomain (EnHD), a DNA binding domain o he an-
sc ip ion ac o eng ailed om D osophila melanogas e . EnHD is
a h ee-helix bundle o 54 esidues ha olds close o he p o ein
olding speed limi , in he ange o a ew mic oseconds, and has
been ex ensi ely cha ac e ized in bulk18–20. F om he analysis o
calo ime ic and kine ic expe imen s, i has been p edic ed o
ha e a ma ginal olding ba ie 21,22. Rema kably, EnHD did no
old in o i s con o ma ion in a se o long- ime-scale a omis ic
simula ions, bu ano he homeodomain exhibi ed a downhill ee
ene gy su ace23. Ou pulling expe imen s show ha EnHD has
weak mechanical s abili y, as expec ed o a p o ein ha olds
o e a ma ginal ee ene gy ba ie . When subjec ed o a g adu-
ally inc easing mechanical o ce (i.e., a o ce– amp) he obse ed
signa u e is no s epwise bu sigmoidal. We in e p e hese esul s
as a complian mechanical esponse compa ible wi h he simple
heo e ical adap a ion o he Bell model and molecula simula-
ions using a coa se-g ained simula ion model. The eme ging
pic u e is ha o a e y complian p o ein ha olds and un olds
many imes o e a ma ginal ba ie induced by he applied o ce.
Resul s
Single-molecule o ce-ex ension expe imen s a a cons an
speed. Fo ou AFM expe imen s, we enginee ed a polyp o ein
whe e he p o ein EnHD (PDB code:1enh, Fig. 1a) is sandwiched
be ween wo pai s o I91 domains o human ca diac i in,
esul ing in he (I91)
2
-EnHD-(I91)
2
cons uc . The I91 domains
se e as mechanical handles when he polyp o ein is subjec ed o
a mechanical o ce (Fig. 1b). Impo an ly, he mechanical p op-
e ies o I91, such as un olding o ce and con ou leng h (ΔL
c
), a e
well cha ac e ized and a e clea ly dis inguishable in o ce spec-
oscopy measu emen s24,25. Thus, I91 se es as a molecula
finge p in o an adequa e ace selec ion when he mechanical
p ope ies o he p o ein o in es iga ion a e di ficul o ecognize.
In he case o EnHD, his is pa icula ly impo an gi en i s weak
coope a i i y, which may esul in a ea u eless signal unde o ce.
Fi s ly, we conduc ed o ce-ex ension expe imen s whe e he
EnHD polyp o ein is o ced o elonga e a a cons an eloci y o
40 nm s−1. The un olding o he molecule ypically c ea es a
saw oo h pa e n in hese expe imen s because he un olding o
each domain is composed o a s age o building up o ce while he
domain emains esis an o he applied ension ollowed by a
sudden d op on he egis e ed o ce due o he igge ing o
un olding. Regis e ed measu emen s show he cha ac e is ic
saw oo h pa e n o I91 domains (Fig. 1c), and he analysis wi h
he wo m-like chain (WLC) model e eals mechanical s abili y o
app oxima ely in he ange o 181 ± 8 pN (a e age ± SEM),
250
200
150
100
50
0
Fo ce (pN)
250200150100500
Ex ension (nm)
I91 I91 I91 I91
I91
I91
Can ile e ip
ab c
Gold subs a e
EnHD
EnHD
I91
I91
Fig. 1 Single-molecule o ce-ex ension expe imen s. a Rep esen a ion o he c ys al s uc u e o he EnHD domain. bScheme o he expe imen al se up.
The EnHD is sandwiched be ween wo i in homodime s, deposi ed in solu ion o e a gold su ace, and d agged by he AFM can ile e , esul ing in he
un olding o he p o eins. cFo ce-ex ension ace including he cha ac e is ic saw oo h pa e n o he i in domains, and he ini ial ea u eless signal o
EnHD. S e ching is conduc ed a a speed o 40 nm s−1.
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al hough i depends on he un olding speed, and a ΔL
c
o
28 ± 1 nm (a e age ± SD), in ag eemen wi h wha is desc ibed in
he li e a u e26 (Supplemen a y Fig. 1). Con e sely, no clea
saw oo h pa e n is de ec ed o he un olding EnHD. This sug-
ges s ha EnHD has a e y low mechanical esis ance and un olds
a e y low o ces, so i goes i ually unde ec ed in o ce-
ex ension expe imen s.
Coa se-g ained molecula dynamics simula ions. These
expe imen al esul s a e consis en wi h coa se-g ained molecula
simula ions using a s uc u e-based all-a om simula ion model
(see Me hods). Fi s , in na i e condi ions, he p o ein exhibi s a
unimodal ee ene gy su ace de i ed om he p ojec ion on
he ele an eac ion coo dina e o olding, he ac ion o na i e
con ac s, Q(Fig. 2a). Upon he applica ion o an ex e nal o ce
ha pulls om he p o ein ends a cons an ex ension speed,
EnHD is e y complian , esul ing in a low o ce peak (Fig. 2b).
Because he uni s in he model canno be compa ed di ec ly wi h
hose in he expe imen , we show he same esul o pulling
simula ions on an immunoglobulin-like domain o i in used as a
finge p in o e e ence. The simula ions eco e he s a k di -
e ences be ween a mechanically esis an p o ein and he ea-
u eless o ce-ex ension pa e n o EnHD. We show snapsho s o
di e en con o ma ions along he un olding ajec o y in Fig. 2d.
The mechanical un olding in ol es un angling he bundle, ol-
lowed by he mel ing o he alpha helices. We ha e also un
cons an o ce simula ions using ou coa se-g ained model. As we
ound o p o ein gpW16, o ce induces a small ee ene gy ba ie
o app oxima ely ~2 k
B
T ha sepa a es wo well-defined minima
in he p o ein landscape (Fig. 2a, c). We no e ha a simila
hopping pa e n be ween he olded and un olded s a es is
obse ed in expe imen s pe o med a a cons an o ce o 8 pN
(Supplemen a y Fig. 2a, b), al hough we we e able o measu e
only a ew o hese e en s due o he complexi y o low o ce
expe imen s using ou AFM. These ansi ions in he second
imescale a e mos ly obse ed when he o ce pe u ba ion is
main ained o gi e su ficien ime o c oss he ene gy ba ie
induced by o ce. As we showed in ou s udy o p o ein gpW27,
he obse a ion o ansi ions in he second imescale is consis en
wi h he low ba ie p edic ed by he simula ions, i we conside
ha he dynamics unde cons an o ce a e mainly de e mined by
he appa a us. On he o he hand, he change in ex ension
be ween he na i e and mechanically un olded s a es obse ed in
he simula ions is sho e han in expe imen s, likely due o he
many simplifica ions in he coa se-g ained model.
Single-molecule o ce– amp expe imen s. To u he esol e
he mechanical un olding o he EnHD p o ein, we p epa ed
o ce– amp measu emen s a di e en alues o he o ce
loading a e. This app oach gi es accu a e con ol o he applied
o ce due o he in e en ion o a eedback loop ha compen-
sa es o changes a a window o ime below 1 ms. Thus, his
p o ocol pe mi s scanning a b oad ange o un olding o ces
while con olling he o ce applied. The o ce p o ocol s a s by
pushing he can ile e agains he gold subs a e wi h a 10 pN
o ce. Then, he can ile e slowly pulls om he p o ein a he
desi ed loading a e (we used alues o 1, 10, and 100 pN s−1),
p o iding enough esolu ion o de ec he un olding esponse o
ou p o ein a bo h low and high o ces. Finally, he a e is
inc eased so ha o ces high enough o un old I91 a e eached
mo e quickly. Fo wo-s a e p o eins, his ype o expe imen
ypically egis e s disc e e jumps wi h leng hs ex ensions ha
a e o ce-dependen and ha can be explained by models o
polyme elas ici y such as he wo m-like chain (WLC) o eely-
join ed chain28,29. Howe e , o EnHD we ob ained an unex-
pec ed sigmoidal un olding pa e n a o ces below 20 pN
Fig. 2 Cou se-g ained molecula dynamics simula ions. a Po en ial o mean o ce o he p ojec ion o coa se-g ained simula ions on he ac ion o na i e
con ac s, Q. The black cu e co esponds o he simula ions in na i e condi ions, and he ed cu e a he mechanical midpoin . bFo ce-ex ension cu es
om simula ions a a cons an pulling speed o 1e−3 nm/ps o EnHD ( ed) and i in (black). cF ee ene gy landscape o bo h he end- o-end ex ension, L,
and Q. Con ou lines ma k 0.5 k
B
T.dCa oon ep esen a ion o di e en con o ma ions sampled du ing he mechanical un olding, wi h imes amps ela i e
o he numbe ing in. The g een and blue beads co espond o he alpha ca bons o he N and C- e mini, espec i ely.
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(Fig. 3a and Supplemen a y Fig. 3). In he final pa o he o ce-
amp aces, we obse e he e en s co esponding o he ou
I91 i in epea s wi h a cha ac e is ic 24.5 nm leng h. P io o
he I91 un oldings, he o al change in he ex ension o he
sigmoidal pa e n ma ches he ex ension o EnHD o abou
15nmin he20pN ange o ce(Fig.3a), sugges ing ha his
beha io co esponds o he un olding o EnHD.
To disca d he possibili y o any unspecific in e ac ions be ween he
p o ein cons uc and he su ace, we epea he cycle by quenching he
o ce a e he ini ial sigmoidal inc ease ollowed by ano he o ce-
amp a he same loading a e, which esul ed in a simila sigmoidal
inc ease e y much like in he fi s e en (Fig. 3b). This ep oducibili y
in a single p o ein domain sugges s ha we a e indeed looking a he
mechanical un olding o EnHD. The sigmoidal cu es ha we epo
ha e no been obse ed in he smFS li e a u e be o e and mus be
in e p e ed wi h ca e. In Fig. 3c, we show he a e age o se e al o ce-
amp aces a 10 pN s−1, om whose de i a i e we es ima e a mid-
un olding o ce F
1/2
o his p o ein o 7.6 pN, which is close also o he
alue o he o ce a which we obse ed he hopping in o ce-clamp
expe imen s (Supplemen a y Fig. 2b). Baseline p opaga ion o F
1/2
o ce alue esul s in an ex ension o ~7.5 nm (Fig. 3c), which is
compa able o he ex ension ob ained by he WLC conside ing a
con ou leng h L
c
o 19 nm and pe sis ence leng h ρo 0.4 nm. The F
1/2
alue o 7.6 pN is also in he same ange as ha o gpW also measu ed
a ampso 10pN/s(F
1/2
=4.6 pN; see Fig. 3c, inse ) and is also
consis en wi h he alue o he mid-un olding o ce ecen ly
de e mined o α3D (F
1/2
=8.9 pN)14. These esul s sugges ha
EnHD has a mechanical esis ance ha is in e media e o hose o gpW
and α3D, demons a ing ha he mid-un olding o ce is a ea u e o
ul a as olding p o eins, bu , mo e impo an ly, shows ha
o ce– amp expe imen s a e sui able o he cha ac e iza ion o
complian un olding pa e ns and ha he un olding midpoin is
unique o each p o ein. In e es ingly, he o ce- amp pe u ba ion is
s ill su ficien ly as o EnHD o a oid slow ansi ions in he second
imescale, such as hose c ea ed by he en opic ene gy ba ie , easily
obse able in he o ce–clamp egime.
A heo e ical model o EnHD mechanical un olding. To be e
unde s and he molecula e en esponsible o he sigmoidal
signal, we ha e un s ochas ic simula ions based on he Bell
model a inc easing o ce30,31. We se he model pa ame e s using
olding and un olding a es in he o de o he expe imen ally
de i ed alues o he in bulk a 25 °C18,20, and calib a e he
posi ion o he ansi ion s a e o ma ch he a e age expe imen al
cu e (Fig. 3c). In Fig. 4, we p esen he esul o mul iple s o-
chas ic simula ions whe e olding and un olding can occu mul-
iple imes in he imescale o he expe imen . We ep esen he
dis ance o he ansi ion s a e (DTS) as a pe cen age o he o al
leng h. Using a ansi ion s a e ha is close o he un olded s a e
EnHD
gpW
25
20
15
10
5
0
Leng h (nm)
403020100-10
Fo ce (pN)
20100
100
50
0
Leng h (nm)
I91
EnHD EnHD
I91
I91
I91
150
0
Fo ce (pN)
151050
Time (s)
EnHD I91
I91
I91
I91
300
0
Fo ce (pN)
12840
Time (s)
125
100
75
50
25
0
Leng h (nm)
15
10
5
0
ab c
Fig. 3 Single-molecule o ce– amp expe imen s. a Time se ies o he measu ed ex ension ( op) and o ce (bo om) in a o ce- amp expe imen a 10 pN s−1
loading a e o EnHD. The inse highligh s he signal co esponding o EnHD un olding. bSame as a, bu now including wo consecu i e low loading- a e o ce
amps sepa a ed by a o ce-quench o ze o o ce. cA e age o ce/leng h cu e om mul iple aces o EnHD and p o ein gpW (n=29 independen aces om
mul iple expe imen s) a 10 pN s−1. Ve ical dashed lines ma k he mid-un olding o ce (F
1/2
) o EnHD ( ed) a 7.6 pN, and gpW (b own) a 4.6 pN. P opaga ing
baselines (black dashed lines) p o ide an es ima ed ex ension o abou 7.5 nm o EnHD. The inse is he fi s de i a i e o he sigmoidal fi , indica ing also mid-
un olding o ce.
DTS = 1%
Exp
Model
0
0
5
10
15
20
20 40 60 80
Ex ension (nm)
DTS = 87%
Exp
Model
0
0
5
10
15
20
20 40 60 80
Fo ce (pN)
Ex ension (nm)
DTS = 98%
Exp
Model
0
0
5
10
15
20
20 40 60 80
Fo ce (pN)
DTS = 20%
Exp
Model
0
0
5
10
15
20
20 40 60 80
Fo ce (pN)
Ex ension (nm)
0
2
4
6
8
10
12
14
16
18
-10 0 10 20 30 40 50 60 70 80
Exp
Model
ab
Fig. 4 Da a analysis using he Bell model. a Fo ce-ex ension plo om a simula ion using he nume ical Bell model wi h s ochas ic ansi ions (ligh g een).
A e age expe imen al aces we e ob ained a 1 pN/s (o ange). bSame Bell model a e shown in (g een) using di e en ansi ion s a e dis ances and he
a e age expe imen al aces a e supe imposed (o ange).
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(i.e., a 90% o he dis ance be ween olded and un olded) allows
us o ecapi ula e he sigmoidal cu es obse ed in he expe i-
men s (Fig. 4a). O he DTS a e ep esen ed in Fig. 4b o com-
pa ison. We no e ha a sho dis ance o he ansi ion s a e
would esul in s epwise ansi ions, as obse ed o mechanically
s able p o eins like he i in domains, and a longe ansi ion s a e
would esul in an almos linea un olding. In ou expe imen s,
we ha e occasionally obse ed bo h ypes o ansi ions (Sup-
plemen a y Fig. 4), sugges ing a ce ain plas ici y in he ansi ion
s a e o EnHD ha would be consis en wi h i s low ee ene gy
ba ie . Using he a omis ic coa se-g ained model, we ha e un
simula ions ha g adually inc ease he un olding o ce (see
Me hods). The imescale ha we co e in he molecula simula-
ions is sho e han ha in he expe imen s and in he s ochas ic
model. S ill, i is su ficien o ep oduce he epe i i e olding and
un olding, suppo ing ou in e p e a ion o he esul s (Supple-
men a y Fig. 5).
Discussion
In he pas decade, he s udy o p o eins by smFS has e ealed a
a ie y o aspec s in hei olding dynamics ha a e mos ly
unde ec able by adi ional ensemble a e aging me hods. How-
e e , only ecen ly ha e hese me hods been applied o p o eins
wi h low coope a i i y, which a e challenging due o hei low
un olding o ces and as olding kine ics16. He e we ha e p e-
sen ed esul s on a p o ein wi h weak coope a i i y, EnHD, using
a combina ion o expe imen s, nume ical modeling, and mole-
cula simula ions. Ou esul s show ha EnHD is a complian
p o ein ha olds, o e coming a ma ginal ee ene gy ba ie
induced by mechanical o ce. The mid-un olding o ce ob ained
om bo h cons an o ce and o ce- amp expe imen s o EnHD
is in he same ange as o he labile p o eins like gpW16 and
α3D14. F om ou o ce- amp expe imen s, we ob ain a no el
sigmoidal signa u e ha we in e p e as mul iple e en s o olding
and un olding o he p o ein, which occu epe i i ely in he
imescale o he expe imen .
In p e ious wo k, we in es iga ed he ins umen al e ec s in
cons an - o ce expe imen s on gpW16,17. Recen heo e ical
analysis indica es ha olding and un olding will be slowed down
conside ably bo h by he o ce p obe and he smFS
expe imen s32,33. Al hough a de ailed analysis o hese e ec s is
beyond he scope o he cu en wo k, ou esul s show olding
and un olding a es in he s ochas ic model up o wo o de s o
magni ude slowe han in bulk. Ou p e ious analysis o gpW
also indica ed ha despi e in oducing a slowdown in he
dynamics, he appa en olding and un olding measu ed by he
ins umen indeed ace he ue molecula olding and un olding
e en s. We find ha e en in hese condi ions, he o ce- amp
expe imen s wi h EnHD esul in a sigmoidal cu e wi h mul iple
olding and un olding e en s, ha could be ep oduced using a
simple Bell model. We ha e disco e ed ha he plas ici y o he
mechanical ansi ion s a e is a ea u e o EnHD ha defines he
low coope a i i y o his p o ein, making he un olding highly
complian . Thus, his wo k shows how o ce can be used as a ool
o in es iga e low-coope a i i y p o eins c ea ing a mechanical
signa u e ha e eals he plas ici y and compliance o he
un olding p ocess. We belie e ha wi h g ea e imp o emen s
bo h in he ime esolu ion o he ins umen s and in he design
o can ile e s12,34, we an icipa e ha smFS expe imen s o olding
and un olding will con inue e ealing molecula de ails o weakly
coope a i e p o eins.
Me hods
P o ein exp ession and pu ifica ion. Gene encoding (I91)
2
-EnHD-(I91)
2
chime ic
polyp o ein cons uc was designed and op imized o exp ession in Esche ichia coli
(Li e Technologies). He e, wo addi ional cys eine esidues we e added in he
C- e minus, which helps o sample immobiliza ion on he gold su ace. S anda d
DNA manipula ion p o ocols we e used o clone he cons uc in o he pQE80L
exp ession plasmid (Qiagen). C41 s and compe en cells o E. coli (No agen) we e
used o p o ein exp ession. T ans o med compe en cells we e g own in 1 L o LB
media a 37 °C un il an OD
600
o a ound 0.6 was eached. Then p o ein exp ession
was in oduced by 1 mM o IPTG and u he incuba ion a 37 °C o 4 h. Cells we e
hen cen i uged, and a gen le cell lysis p o ocol was used o a oid damage o he
exp essed polyp o eins. The sample was hen pu ified fi s by HisTag a fini y ch o-
ma og aphy using a g a i y column filled wi h HisPu Cobal esin (The mo Fishe
Scien ific) and second by size exclusion ch oma og aphy using a Supe dex 200 HR
column (GE Heal hca e). The final elu ion bu e was HEPES 10 mM pH 7.0, NaCl
150 mM, and EDTA 1 mM. The sample was u he concen a ed using ul afil a ion
Amicon 3k fil e s (Millipo e). The final p o ein concen a ion was es ima ed o be
a ound 1 mg mL−1using a Nanod op (The mo Scien ific). Then he samples we e
snap- ozen in liquid ni ogen and s o ed a −80 °C.
Single-molecule o ce spec oscopy (smFS). All smFS o ce ex ension, con-
s an o ce, and o ce amp expe imen s we e pe o med on an A omic Fo ce
Spec ome e AFS-1 (Luigs Neumann). Biole e can ile e s om Olympus/
B uke we e used wi h a sp ing cons an o a ound 6 pN nm−1 o all cons an
o ce and o ce amp measu emen s. The sp ing cons an was measu ed be o e
each expe imen using he equipa i ion heo em wi hin a so wa e buil -in
p ocedu e. Da a was eco ded be ween 0.5 and 4 kHz o he cons an o ce
and o ce amp measu emen s. Fo hose expe imen s ha included quenching
o o ce (Fig. 2c), he o ce was amped a 1 pN s−1un il 45 pN (s a ing om
10 pN pushing F< 0). A his poin , i was es o ed back o 10 pN pushing and
ampedwi h hesame a eun il45pNagain.Du ing hecombina iono
o ce– amp and cons an o ce expe imen s (Fig. 3), he o ce was amped a a
a e o 1 pN s−1un il eaching he 8 pN cons an o ce. Then he p o ein was
held o 20–30 s a he cons an o ce be o e he amp a 1 pN s−1was con-
inued. To educe o al expe imen al acquisi ion ime, all aces include a apid
inc ease o he o ce a e o 30 pN s−1a he end o quickly each he high
o ces equi ed o un old Ti in-I91 domains. All AFM expe imen s we e ca ied
ou a oom empe a u e (~24 °C) in HEPES bu e a pH 7.0. Typically, 40 µl
o he p o ein sample (~µM concen a ion) was le o a ound 20 min o
adso p ion on a esh gold-coa ed su ace, using gold e apo a ion (Oe likon
UNIVX350). A e he adso p ion ime, he sample was hen insed o he gold
su ace wi h he HEPES bu e o emo e he unbounded p o ein sample jus
be o e s a ing he measu emen s. Mul iple aces a e collec ed in each
expe imen and se e al samples we e used in e e y condi ion. Da a was col-
lec ed and analyzed using Igo P o 6.0 so wa e.
Theo e ical model. To in e p e he o ce amp expe imen s we use a simple model o
wo-s a e kine ics ha allows o s ochas ic jumps be ween he olded and un olded s a es
depending on he o ce-dependen a es o olding and un olding, k
(F)andk
u
(F). This
dependence is desc ibed using he Bell model30,i.e.k
(F)=k
(0)exp(-βΔx
F)and
k
u
(F)=k
u
(0)exp(βΔx
u
F), whe e k
/u
(0) a e he alues o he olding and un olding a es
in bulk, Δx
/u
is hedis ance o he omei he s a e o he ansi ions a eandβis he
in e se he mal ene gy. The ex ension o ei he he olded o he un olded s a e a a gi en
o ce a e desc ibed using he WLC model, using a con ou leng h o 19 nm and a
pe sis ence leng h o 0.4 nm. Simula ions we e un using a Gillespie algo i hm35.Igo P o
6.0 and Ma lab 9.5 so wa e we e used o calcula ions and analysis.
Coa se-g ained molecula dynamics simula ions. We un molecula simula-
ions using an a omis ic s uc u e-based model36.B iefly, he model keeps all he
hea y a oms o he p o ein and ep esen s in e ac ions ia ha monic e ms o
bonds, angles, and dihed als. Fo a om pai s ha a e in con ac in he na i e
con o ma ion, non-bonded in e ac ions a e ep esen ed by a Lenna d-Jones
po en ial. All o he pai wise in e ac ions a e epulsi e. Models we e gene a ed
using he s and-alone e sion o he SMOG so wa e package37,andsimula ions
we e pe o med using he G omacs so wa e package38, using a leap- og s o-
chas ic dynamics in eg a o wi h a imes ep o 5e−4 sandacouplingcons an
o 1 ps (we no e ha he imescales o he model do no co espond o physical
imes). We fi s un simula ions a mul iple empe a u es o es ima e he olding
empe a u e in he model. Then we un pulling simula ions a a cons an o ce
andcons an pullingspeedusing hepullcodeinG omacs.Finally,weemula e
he o ce– amp mode by conca ena ing housands o sho simula ion uns, each
o which has an inc emen ally la ge cons an pulling o ce and s a s om he
las snapsho o he p e ious un. Resul s we e analyzed using he MD aj
Py hon lib a y39.
Repo ing summa y. Fu he in o ma ion on esea ch design is a ailable in he Na u e
Po olio Repo ing Summa y linked o his a icle.
Da a a ailabili y
Da a suppo ing he findings o his s udy a e a ailable om he co esponding au ho
upon easonable eques . Codes used o analyze he da a a e a ailable upon eques .
COMMUNICATIONS PHYSICS | h ps://doi.o g/10.1038/s42005-022-01125-5 ARTICLE
COMMUNICATIONS PHYSICS | (2023) 6:7 | h ps://doi.o g/10.1038/s42005-022-01125-5 | www.na u e.com/commsphys 5
Recei ed: 8 July 2022; Accep ed: 30 Decembe 2022;
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Acknowledgemen s
This wo k has been suppo ed by g an s PID2019-109087RB-I00 o R.P.-J. and
PGC2018-099321-B-I00 and RYC-2016-19590 o D.D. om he Spanish Minis y o
Science and Inno a ion. This p ojec has ecei ed unding om he Eu opean Union’s
Ho izon 2020 esea ch and inno a ion p og am unde g an ag eemen No. 964764 o
R.P.-J. D.D. ecei es suppo om Eusko Jau la i za (Basque Go e nmen ) h ough
he p ojec IT1254-19. A.R. is he ecipien o a doc o a e ellowship om he Spanish
Minis y o Science and Inno a ion. I.R.-O. acknowledges financial suppo om
Donos ia In e na ional Physics Cen e (DIPC).
Au ho con ibu ions
R.P.-J., V.M., and D.D. concei ed he p ojec and designed he esea ch. A.R., A.O.-S.,
and J.S. cloned he p o ein and pe o med smFS expe imen s. A.R., D.D., V.M., and R.P.-
J. analyzed smFS expe imen s. I.R.-O. and D.D. conduc ed compu a ional molecula
dynamics simula ions. V.M. pe o med heo e ical analysis. All au ho s con ibu ed o
w i ing and e ising he pape .
Compe ing in e es s
The au ho s decla e no compe ing in e es .
Addi ional in o ma ion
Supplemen a y in o ma ion The online e sion con ains supplemen a y ma e ial
a ailable a h ps://doi.o g/10.1038/s42005-022-01125-5.
Co espondence and eques s o ma e ials should be add essed o Vic o Muñoz o
Raul Pe ez-Jimenez.
Pee e iew in o ma ion Communica ions Physics hanks he anonymous e iewe s o
hei con ibu ion o he pee e iew o his wo k. Pee e iewe epo s a e a ailable.
Rep in s and pe mission in o ma ion is a ailable a h p://www.na u e.com/ ep in s
Publishe ’s no e Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in
published maps and ins i u ional a filia ions.
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