RESEARCH
Func ional s eng hening h ough synap ic
scaling upon connec i i y dis up ion in
neu onal cul u es
Es e anía Es é ez-P iego1,2, Sa a Telle 1,2, Cla a G anell3,4, Alex A enas5, and Jo di So iano 1,2
1Depa amen de Física de la Ma è ia Condensada, Uni e si a de Ba celona, Ba celona, Spain
2Uni e si a de Ba celona Ins i u e o Complex Sys ems (UBICS), Ba celona, Spain
3GOTHAM Lab – Ins i u e o Biocompu a ion and Physics o Complex Sys ems (BIFI), Uni e si y o Za agoza, Za agoza, Spain
4Depa men o Condensed Ma e Physics, Uni e si y o Za agoza, Za agoza, Spain
5Depa amen d’Enginye ia In o mà ica i Ma emà iques, Uni e si a Ro i a i Vi gili, Ta agona, Spain
Keywo ds: Neu onal cul u es, Calcium imaging, CNQX, E ec i e connec i i y, Global e iciency,
Func ional o ganiza ion, Synap ic scaling
ABSTRACT
An elusi e phenomenon in ne wo k neu oscience is he ex en o neu onal ac i i y
emodeling upon damage. He e, we in es iga e he ac ion o g adual synap ic blockade on
he e ec i e connec i i y in co ical ne wo ks in i o. We use wo neu onal cul u es
con igu a ions—one o med by abou 130 neu onal agg ega es and ano he one o med by
abou 600 indi idual neu ons—and moni o hei spon aneous ac i i y upon p og essi e
weakening o exci a o y connec i i y. We epo ha he e ec i e connec i i y in all cul u es
exhibi s a i s phase o ansien s eng hening ollowed by a second phase o s eady
de e io a ion. We quan i y hese phases by measu ing GEFF, he global e iciency in
p ocessing ne wo k in o ma ion. We e m hype e iciency he sudden s eng hening o GEFF
upon ne wo k de e io a ion, which inc eases by 20–50% depending on cul u e ype. Relying
on nume ical simula ions we e eal he ole o synap ic scaling, an ac i i y–dependen
mechanism o synap ic plas ici y, in coun e ac ing he pe u ba i e ac ion, nea ly
ep oducing he obse ed hype e iciency. Ou esul s demons a e he impo ance o
synap ic scaling as esilience mechanism.
AUTHOR SUMMARY
Neu onal ci cui s exhibi homeos a ic plas ici y mechanisms o cope wi h pe u ba ions o
damage. A cen al mechanism is ‘synap ic scaling,’ a sel -o ganized esponse in which he
s eng h o neu ons’ exci a o y synapses is adjus ed o compensa e o ac i i y a ia ions.
He e we p esen expe imen s in which he exci a o y connec i i y o in i o co ical
ne wo ks is p og essi ely weakened h ough chemical ac ion. The spon aneous ac i i y and
e ec i e connec i i y o he whole ne wo k is moni o ed as deg ada ion p og esses, and he
capaci y o he ne wo k o b oad in o ma ion communica ion is quan i ied h ough he
global e iciency. We obse ed ha he ne wo k esponded o he pe u ba ion by
s eng hening he e ec i e connec i i y, eaching a hype e icien s a e o mode a e
pe u ba ions. The s udy p o es he impo ance o ‘synap ic scaling’ as a d i e o unc ional
eo ganiza ion and ne wo k-wide esilience.
a n o p e n a c c e s s j o u n a l
Ci a ion: Es é ez-P iego, E., Telle , S.,
G anell, C., A enas, A., & So iano, J.
(2020). Func ional s eng hening
h ough synap ic scaling upon
connec i i y dis up ion in neu onal
cul u es. Ne wo k Neu oscience, 4(4),
1160–1180. h ps://doi.o g/10.1162
/ne n_a_00156
DOI:
h ps://doi.o g/10.1162/ne n_a_00156
Recei ed: 16 Janua y 2020
Accep ed: 15 July 2020
Compe ing In e es s: The au ho s ha e
decla ed ha no compe ing in e es s
exis .
Co esponding Au ho :
Jo di So iano
[email p o ec ed]
Handling Edi o :
Ola Spo ns
Copy igh : ©2020
Massachuse s Ins i u e o Technology
Published unde a C ea i e Commons
A ibu ion 4.0 In e na ional
(CC BY 4.0) license
The MIT P ess
Func ional s eng hening h ough synap ic scaling
INTRODUCTION
Response o pe u ba ions o damage in li ing neu onal ci cui s is a cen al ye un esol ed
p oblem in neu oscience. A simple ne wo k desc ip ion o damage in ui i ely sugges s ha
he ailu e o connec i i y pa hways p ecipi a es a p og essi e de e io a ion o ne wo k ac i i y
ha ul ima ely comp omises he unc ionali y o he sys em. Realis ic desc ip ions o li ing neu-
onal ci cui s, howe e , expose he complex in e play be ween he physical a chi ec u e o he
ne wo k, neu onal dynamics, and plas ici y mechanisms in go e ning ci cui beha io , aming
scena ios in which esponse o damage is no only possible, bu as and ne wo kwide. This
is pa icula ly impo an in he con ex o b ain and neu ological diso de s, since adequa e
p ognosis o unc ional al e a ions may help o elucida e ac ions o s op o e e damage.
S udies in s oke, o ins ance, ha e poin ed ou he impo an ole o plas ici y in p e en -
ing a cascade o deg ada ion and os e ing eco e y (Calab esi, Cen onze, Pisani, Cupini, &
Be na di, 2003;Mu phy & Co be ,2009). Cu en mul idisciplina y app oaches o p ognosis
a e making an e o o in eg a e acqui ed expe imen al da a wi h nume ical models o cha ac-
e ize neu onal damage and subsequen ne wo k esponses (Basse & Spo ns,2017;Fo ni o,
Zalesky, & B eakspea , 2015). Thus, unde s anding he di e en ac o s a play—connec i i y,
dynamics, and plas ici y—and hei in e ela ion has become a cen al goal in medical ne wo k
neu oscience.
In he las ew yea s, subs an ial e o s ha e been in es ed in linking s uc u al cha ac e -
is ics o neu onal ne wo ks wi h hei capaci y o cope wi h pe u ba ions and damage (Ae s,
Fias, Caeyenbe ghs, & Ma inazzo, 2016;Fa ooq, Chen, Geo giou, Tannenbaum, & Lengle ,
2019;Majdandzic e al.,2013). Speci ically o b ain unc ional ne wo ks, s udies un eiled he
impo ance o modula and hie a chical o ganiza ions (Meunie , Lambio e, Fo ni o, E sche, &
Bullmo e, 2009), hubs ( an den Heu el & Spo ns,2013), and o he node s uc u al aspec s
(Basse & Spo ns,2017;Basse , Zu n, & Gold,2018;Spo ns,2014;S am,2014). Despi e he
p og ess and enligh enmen in his di ec ion, he inco po a ion o plas ici y and sel - egula o y
mechanisms as addi ional ac o s is opening new a enues o unde s anding esilience o in-
Resilience:
The capaci y o a neu onal ci cui o
main ain ac i i y and unc ional
cha ac e is ics upon loss o
weakening o neu ons o
connec ions.
sul . Indeed, he b ain and o he li ing neu onal ci cui s a e elian on di e se adap i e mech-
anisms o p ope pe o mance and s abili y ha include synap ic plas ici y and s uc u al
Synap ic plas ici y:
The s eng hening o weakening o
synapses acco ding o neu onal
ac i i y, o ins ance, o po en ia e
speci ic connec i i y pa hways.
plas ici y (Bu z, S eenbuck, & an Ooyen,2014;Fau h & Te zla ,2016;Fau h, Wö gö e , &
Te zla , 2015). These mechanisms a e cen al o egain ci cui s’ ope abili y upon se e e pe -
u ba ions o inju y (Ba al & Reyes,2016;Cos a, Mizusaki, Sjös öm, & an Rossum,2017;
Ma de ,2011;Mu phy & Co be ,2009;Telle e al.,2019). One o he mos impo an synap ic
plas ici y mechanisms is synap ic scaling, in which he s eng h o exci a o y synapses is ad-
Synap ic scaling:
A egula o y mechanism o neu onal
ci cui s by which synap ic s eng h is
adjus ed o compensa e o ch onic
changes in ac i i y.
jus ed o compensa e o a ia ions in ac i i y (Desai, Ru he o d, & Tu igiano,1999;Fong,
Newman, Po e , & Wenne , 2015;G. G. Tu igiano, Leslie, Desai, Ru he o d, & Nelson,
1998). The capaci y o synap ic scaling o egula e neu onal ac i i y was demons a ed bo h in
i o (Echegoyen, Neu, G abe , & Sol esz,2007;G. Tu igiano,2012;G. G. Tu igiano,2008)
and in i o (Ba al & Reyes,2016;Hanes e al.,2020) a a synapse le el. Al hough di e -
en in es iga ions poin ed ou he ole o synap ic scaling in co ec ing neu onal ac i i y a e
damage, o ins ance in ela ion o Alzheime ’s pa ien s cogni i e de ici s (Bo ge-Hol hoe e ,
Mo eno, & A enas, 2011) and e inal lesions (Keck e al.,2013), he e a e no s udies demon-
s a ing i s impac in he unc ional o ganiza ion o a neu onal ci cui .
Func ional o ganiza ion:
A se o global ne wo k ai s, such as
modula i y o global e iciency, ha
imp in dis inc o ganiza ional
cha ac e is ics o a ne wo k.
The aim o his s udy is o analyze he ac ion o synap ic scaling om a ne wo k neu osci-
ence pe spec i e and expose i s po en ial as a esilience mechanism. To his end, we designed
an expe imen al pipeline in which small co ical ci cui s in i o we e exposed o a mal unc ion-
like e en ha g aduallyweakened he connec i i y among in e connec ed neu onal assemblies
Ne wo k Neu oscience 1
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Func ional s eng hening h ough synap ic scaling
(clus e s), and analyzed simul aneously he ac i i y o he en i e ne wo k. The pe u ba i e ac-
ion was deli e ed h ough inc easing doses o CNQX, an AMPA-glu ama e ecep o an agonis
CNQX (6-cyano-7-ni oquinoxaline-
2,3-dione):
An agonis o AMPA-glu ama e
ecep o s in exci a o y neu ons,
equen ly used o ei he weaken
exci a o y synap ic communica ion
o block i en i ely.
in exci a o y synapses (So iano, Ma ínez, Tlus y, and Moses,2008;Tibau, Valencia, & So iano,
2013a). Al hough CNQX a ge ed synap ic connec i i y, we measu ed solely i s impac on
he spon aneous ac i i y, ha is, he spon aneous dynamic in e ac ions among clus e s. Func-
ional cha ac e is ics o he cul u ed ne wo ks we e he e o e quan i ied by measu ing he al e -
a ions in ac i i y as he blockade p og essed and by compu ing he global e iciency (La o a &
Global e iciency:
A measu e o ne wo k capaci y o
in o ma ion exchange. The highe he
o e all connec i i y among nodes,
he highe he global e iciency.
Ma chio i, 2001;Rubino & Spo ns,2010), a measu e o he in eg a ion o he low o in o ma-
ion in a ne wo ked sys em. Ou expe imen s showed ha , as CNQX was applied, he e was
an ini ial phase in which he global e iciency aised, e ealing an inc eased in o ma ion low
capaci y in he ne wo k. This hype e iciency was ep oducible among ne wo k ealiza ions,
Hype e iciency:
In he con ex o ou wo k, an ab up
inc ease o global e iciency esul ing
om a s eng hening o e ec i e
connec ions.
al hough he le el o impac depended on cul u e de ails. Beyond his phase, global e iciency
p og essi ely decayed un il ac i i y ceased. By using nume ical simula ions we showed ha
synap ic scaling, simula ed as a local s eng hening o emaining e ec i e connec ions upon
damage, was su icien o explain he expe imen al beha io . Simple models based on bond
pe cola ion (Ki kpa ick,1973), ha is, he deg ada ion o dele ion o connec ions wi hou any
Pe cola ion:
Beha io o in o ma ion o o he
measu e as nodes o connec ions a e
emo ed, ypically sepa a ing a
‘connec ed’ and a ‘disconnec ed’
phase.
scaling, ailed a cap u ing his hype e iciency phenomenon. To ou knowledge, he expe i-
men s and modeling p esen ed he e is he i s s ong e idence o he impac o synap ic scaling
in p ese ing ne wo k e iciency and whole-sys em pe o mance, hus exposing synap ic scal-
ing as an in insic mechanism o esilience in li ing neu onal ne wo ks. Ou s udy s eng hens
he ision o synap ic scaling as an eme gen and gene al p ope y o li ing neu onal ci cui s,
and pa es he way owa d a be e p edic ion o he ac ion o pe u ba ions and damage in
such ci cui s.
RESULTS
Weakening o Synap ic Communica ion Al e s Func ional O ganiza ion
We in es iga ed spon aneous ac i i y in clus e ed neu onal cul u es p epa ed in 6-mm-diame e
PDMS wells on glass, as illus a ed in Figu e 1A. These cul u es eme ged as a sel -o ganized
p ocess in which he absence o adhesi e p o eins in he glass subs a e a o ed neu onal
mobili y and agg ega ion (Sege , Ben enis e, Shapi a, & Ben-Jacob,2003;Telle e al.,2014;
Telle , Tahi begi, Mi , Sami ie , & So iano,2015). By day in i o (DIV) 7 upon p epa a ion,
agg ega ion shaped highly compac neu onal islands e med clus e s ha emained s able in
posi ion and size. In ou expe imen s, abou 130 neu onal clus e s ypically o med in he
6-mm-diame e wells (Figu e 1B). Table 1 summa izes he se o ne wo ks in es iga ed and
hei cha ac e is ics. The spon aneous ac i i y in he clus e ed ne wo ks was moni o ed a DIV
8–12 h ough calcium luo escence imaging (Figu e 1B), which allowed us o ollow he e o-
lu ion o all clus e s in he cul u e wi h high spa ial and empo al esolu ion. Ac i e clus e s
appea ed as b igh objec s whose luo escence in ensi y amped up upon ac i a ion. The ad-
an age o clus e ed neu onal cul u es is ha hey exhibi spon aneous ac i i y wi h a ich
spa io empo al s uc u e (Telle e al.,2014,2015), in which clus e s coac i a e in g oups o
a ying size and iming (Figu e 1B–C). Since he s uc u e o coac i a ion pa e ns, and in u n
ne wo k unc ional cha ac e is ics, is g ounded on he coupling among clus e s, hese cul u es
s and ou as a pa icula ly sui ed expe imen al p epa a ion o in es iga e he impac o chemi-
cal pe u ba ions o damage (Telle e al.,2014 ,2015,2019). The ichly s uc u ed dynamics o
clus e ed ne wo ks—and sis e designs in he o m o enginee ed ci cui s (Kanne e al.,2015;
Yamamo o e al.,2018)—is enligh ening since dynamics shape ne wo ks wi h a unc ional o -
ganiza ion quali a i ely simila o ha o he b ain, wi h modula ai s and hubs (Telle e al.,
2015;Yamamo o e al.,2018). Thus, ou clus e ed cul u es combine he con ollabili y and
Ne wo k Neu oscience 1162
Func ional s eng hening h ough synap ic scaling
Figu e 1. Clus e ed neu onal cul u es and expe imen al p ocedu e. (A) Schema ic p epa a ion
o clus e ed neu onal ne wo ks. Dissocia ed a co ical neu ons we e pla ed on a 6-mm-diame e
PDMS wells. The absence o adhesi e p o eins acili a ed neu onal agg ega ion, gi ing ise o an
assembly o neu onal islands (clus e s) by day in i o (DIV7). (B) Fluo escence image o a ypical
neu onal cul u e. Ci cula objec s a e neu onal clus e s. Labels highligh ou he loca ion o ou
clus e s whose luo escence aces a e shown in panel C. (C) Rep esen a i e luo escence aces o
ou clus e s o g adually highe le els o he AMPA glu ama e ecep o an agonis CNQX. Sha p
inc eases o he signal co espond o ac i i y e en s. Yellow boxes illus a e episodes o coo dina ed
ac i i y. The o e all ac i i y o he clus e s dec eases wi h CNQX as a esul o he educed exci a o y
d i e. DFF indica es no malized luo escence signal, gi en by DFF(%) = 100.(F−F0)/F−0, wi h
F0 he luo escence signal a es .
accessibili y o an in i o sys em wi h some o he dynamical ichness and unc ional com-
plexi y o na u ally o med neu onal ci cui s.
In ou expe imen s we we e in e es ed in analyzing he dynamics o a clus e ed ne wo k
as he connec i i y s eng h among clus e s, and in u n hei dynamic coupling, was educed.
The abili y o ou expe imen al sys em o simul aneously moni o he en i e ne wo k made
i unique o in es iga e he ac ion o pe u ba ions and hei impac on ne wo k unc ional
o ganiza ion. Since spon aneous coo dina ed ac i i y is mos ly media ed by he exci a o y d i e
o AMPA-glu ama e ecep o s, bo h he capaci y o he ne wo k o i e and clus e - o-clus e
synap ic coupling could be al e ed in a con olled manne h ough he blockade o AMPA
ecep o s. Thus, ollowing So iano, Rod íguez Ma ínez, Tlus y, and Moses (2008), we a ge ed
he exci a o y AMPA-glu ama e ecep o s wi h g adually highe doses o he an agonis CNQX,
causing a p og essi e educ ion o spon aneous ac i i y un il i ceased. Fo cla i y in he analysis
o he da a and i s in e p e a ion, NMDA exci a o y ecep o s (which accoun o abou 20% o
Ne wo k Neu oscience 1
163
Func ional s eng hening h ough synap ic scaling
Table 1. Summa y o he s uc u al and dynamical cha ac e is ics o he eigh clus e ed ne wo ks
in es iga ed.
Expe imen DIV Nφ(µm)d(µm)a(bu s s/min) hki hwi
1 8 157 156 ±56 406 ±16 7.10 6.0 ±3.1 2.8 ±0.5
2 8 125 170 ±55 437 ±15 2.52 5.9 ±2.8 3.2 ±0.6
3 8 116 177 ±60 455 ±14 1.47 6.3 ±2.7 2.9 ±0.5
4 9 152 137 ±34 282 ±8 5.51 5.3 ±2.1 3.0 ±0.4
5 9 144 177 ±53 411 ±15 1.71 4.4 ±1.9 3.3 ±0.7
6 9 124 160 ±52 452 ±15 7.14 5.0 ±1.7 2.9 ±0.6
7 9 118 215 ±68 469 ±18 3.85 4.9 ±1.9 3.1 ±1.1
8 12 128 193 ±70 462 ±15 2.91 5.7 ±2.2 2.9 ±0.5
No e. DIV is he day in i o o he cul u e, N he numbe o clus e s, φ hei a e age diame e ,
d he ypical clus e s’ in e dis ance, a he a e age collec i e ac i i y, hki he a e age e ec i e
connec i i y pe clus e , and hwi he a e age weigh o e ec i e connec ions. φ,d,hki, and hwi
a e epo ed as he means ±s anda d de ia ions.
he o al exci a o y d i e in co ical neu ons) and GABA inhibi o y ecep o s we e ully blocked
wi h he co esponding an agonis s.
An example o he impac o CNQX on ne wo k spon aneous ac i i y is shown in Figu e 1C.
He e, he luo escence aces o ou ep esen a i e clus e s a e depic ed o g adually highe
CNQX le els. Wi hou blockade, all ou clus e s exhibi ed a ich ac i i y wi h s ong coo di-
na ion. As CNQX was applied, he le el o ac i i y and coo dina ion swi ly dec eased, and
o ull synap ic blockade he clus e s ei he i ed weakly and independen ly o became silen .
The all o spon aneous ac i i y and he b eakdown o clus e s’ coac i a ion pa e ns o he
en i e ne wo k a e shown as as e plo s in Figu e 2A. In he plo s, he do s ma k he iming o
clus e s’ ac i a ion, da a ha a e di ec ly ob ained om he analysis o he luo escence signal.
In he sequence o as e plo s, [CNQX] =0(unpe u bed ne wo k) shapes a s ongly cohe en
dynamics in which mos o he clus e s coac i a e a unison, a ea u e ha e lec s he s ong
coupling among clus e s. The s eng h o spon aneous ac i i y was quan i ied h ough he col-
lec i e ac i i y a, de ined as he equency o ac i i y episodes (bu s s) in which a leas i e clus-
e s pa icipa ed (abou 5% o he ne wo k). Ac i i y awas high o [CNQX] =0, wi h clus e s
exhibi ing abou 7 bu s s/min. Ac i i y se e ely d opped o abou 4.4 bu s s/min o he small
pe u ba ion wi h [CNQX] =60 nM, which was accompanied by a s ong dis up ion o he
unison beha io , ende ing an o e all dynamic in which clus e s ac i a ed in g oups o a ying
size. The decay in ac i i y accen ua ed as CNQX g ew, al hough some g oups o clus e s s ill
main ained s ong coo dina ed ac i i y e en o ela i ely la ge doses o [CNQX] =600 nM.
Spon aneous ac i i y inally s opped by [CNQX] &1, 000 nM. In ou s udy we in es iga ed a
o al o eigh clus e ed ne wo ks. All o hem exhibi ed a simila quali a i e end, al hough he
s uc u e o coo dina ed ac i i y and i s changes on deg ada ion depended on he clus e - o-
clus e wi ing de ails in he cul u e (Table 1).
Ac i i y da a was nex analyzed in de ail o compu e he e ec i e connec i i y o he ne -
E ec i e connec i i y:
Causal s a is ical ela ionship among
he ac i i y pa e ns o neu ons in a
ne wo k, leading o di ec ed and
weigh ed adjacency connec i i y
ma ices.
wo ks, allowing us o quan i y whole-ne wo k al e a ions on CNQX ac ion. The e ec i e ne -
wo ks (weigh ed and di ec ed) we e ex ac ed using ans e en opy, an app oach ha we
showed app op ia e o neu onal cul u es in p e ious s udies (S e e , Ba aglia, So iano, &
Geisel, 2012;Telle e al.,2014;Tibau, Ludl, Rüdige , O landi, & So iano,2020). F om he
in e ed e ec i e ne wo ks we ex ac ed he global e iciency GEFF, which in o ms abou he
capabili y o he ne wo k o ope a e as a whole. Fo cla i y, he global e iciency was always
Ne wo k Neu oscience 1164

Func ional s eng hening h ough synap ic scaling
Figu e 2. Ne wo k ac i i y and unc ional o ganiza ion upon deg ada ion. (A) Rep esen a i e as e
plo s o spon aneous ac i i y o g adually highe exci a o y blockade. Blue do s ma k he clus e s’
ac i a ions. The concen a ion o CNQX and he a e age collec i e spon aneous ac i i y aa e in-
dica ed abo e each panel. Ras e s a e limi ed o 10 min o cla i y. (B) Co esponding e ec i e
connec i i y ma ices. The b igh e he colo , he highe he connec i i y weigh among wo clus-
e s. Ma ices a e o de ed acco ding o he unc ional communi ies a [CNQX] = 60 nM. The scaled
global e iciency GEFF inc eases a [CNQX] = 60 nM o s eadily dec ease a e wa ds. (C) E ec i e
connec i i y maps o pe u bed and con ol expe imen s. Clus e s’ and links’ colo s iden i y di e -
en unc ional communi ies. Con ol expe imen s expe ienced he same expe imen al pipeline as
pe u bed ones, bu only GABAAand NMDA ecep o s we e blocked. No signi ican al e a ions in
he e ec i e connec i i y we e obse ed. The pe u bed expe imen co esponds o he da a shown
in (A).
scaled ela i e o i s alue in he unpe u bed condi ion. We no e ha he global e iciency is
based on he calcula ion o he sho es opological pa hs among connec ed nodes in a ne -
wo k, and ha o weigh ed ne wo ks he sho e pa hs a e hose wi h s onge weigh . Thus,
an inc ease in GEFF can a ise om ei he a highe numbe o links, s onge weigh s, o bo h.
Figu e 2B p o ides an example o he in e ed e ec i e connec i i y ma ices. A summa y o
he a e age connec i i y hkiand a e age weigh hwi o he eigh s udied cul u es is p o ided
Ne wo k Neu oscience 1
165
Func ional s eng hening h ough synap ic scaling
in Table 1. Func ional communi ies we e al eady p esen o [CNQX] =0, a ea u e ha in-
dica es ha he obse ed coo dina ed ac i i y was shaped by s ongly in e ac ing g oups o
clus e s. This is clea in he co esponding connec i i y map o Figu e 2C, in which he majo -
i y o he clus e s belonged o he same communi y, as calcula ed by modula i y op imiza ion
Modula i y:
Tendency o he nodes in a ne wo k
o connec wi hin a g oup mo e
s ongly han wi h nodes in ano he
g oup.
using he Lou ain algo i hm (Blondel, Guillaume, Lambio e, & Le eb e,2008). Well-de ined
communi ies eme ged o [CNQX] =60 nM and highe concen a ions, as indica ed by he
iche s uc u e o he connec i i y maps, which show g adually smalle and mo e isola ed
communi ies. Fo [CNQX] &600 nM ac i i y p ac ically ceased and no unc ional cha ac e -
is ics could be ende ed.
The connec i i y maps o Figu e 2C also helped o pic u e he CNQX deg ada ion p ocess in
e ms o he spa ial a angemen o he clus e s. The maps showed ha he unc ional commu-
ni ies we e physically compac , ha is, hey we e cons i u ed by g oups o adjacen clus e s.
This indica es ha he clus e s ypically connec ed o hei immedia e neighbo s upon ne -
wo k o ma ion, and sugges s ha he o e all dynamics o he ne wo k a e media ed by local
in e ac ions. In his di ec ion, he maps also show ha he physical loca ion o he unc ional
communi ies was p ese ed, bu ha hey educed in size as CNQX g ew.
Eme gence o Hype e iciency in CNQX-Pe u bed Ne wo ks
The abo e g adual agmen a ion o he ne wo k wi h CNQX was no accompanied by a s eady
loss o clus e s’ in e communica ion. Su p isingly, o he mode a e CNQX concen a ion o
60 nM, he global e iciency GEFF inc eased by 8%— o he pa icula expe imen o Figu e 2—
wi h espec o he ini ial condi ion, o la e all as expec ed. We no e ha he inc ease in GEFF
s ongly con as s wi h he all o spon aneous ac i i y, which is educed by 60%. We e m
hype e iciency his ab up inc ease in GEFF and, as we elabo a e la e , i s p esence indica es
he nonlinea ela ionship be ween he s uc u al al e a ions caused by CNQX and he e ec i e
connec i i y ones ha eme ge om dynamical in e ac ions among he clus e s. In o he wo ds,
while CNQX ac ion on exci a o y synapses is s eady and ollows a pe cola ion-like silencing
p ocess (So iano, Rod íguez Ma ínez, e al., 2008), he e ec i e connec i i y obeys mo e
complex mechanisms in which swi ching dynamic in e ac ions and plas ici y-d i en adap a-
ion play a cen al ole.
Be o e in es iga ing he possible hype e iciency mechanisms, we e i ied ha his phe-
nomenon was no an expe imen al a i ac by compa ing he e olu ion o CNQX-dosed ne -
wo ks wi h con ol ones ha we e p epa ed and manipula ed iden ically. Figu e 2C compa es
he connec i i y maps o he ep esen a i e pe u bed ne wo k wi h a con ol one. Along he
expe imen , which las ed 75 min, he con ol cul u e e ained he same unc ional ai s ac oss
he ne wo k wi h small a ia ions, while he deg aded one signi ican ly changed.
The da a o he ep esen a i e expe imen o Figu e 2 was a gene al end ha consis en ly
epea ed ac oss eigh di e en cul u es, despi e hei a iabili y in numbe o clus e s, spon a-
neous ac i i y, and e ec i e connec i i y ai s. In all cases, CNQX caused a agmen a ion o
he ne wo k in o communi ies oge he wi h a sudden inc ease o GEFF o mode a e CNQX
le els.
To a e age o e cul u e ealiza ions, howe e , we obse ed ha each cul u e esponded
sligh ly di e en ly upon pe u ba ion. This esul ed in speci ic CNQX concen a ions o he
beginning o unc ional al e a ions and he end o ac i i y. Thus, o each cul u e, we consid-
e ed a e e ence alue [CNQX] e abo e which dynamic al e a ions we e de ec able, and a
maximum [CNQX]max a which ac i i y ully ceased (Figu e 3A). Da a was hen escaled ac-
co ding o hese poin s o ob ain he global e iciency as a unc ion o an adequa e con ol
Ne wo k Neu oscience 1
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Func ional s eng hening h ough synap ic scaling
Figu e 3. T ea men o expe imen al cu es and ela ionship be ween spon aneous ac i i y and global e iciency. (A) De ini ion o [CNQX] e
(concen a ion be o e any ne wo k al e a ion occu ed) and [CNQX]max (no ne wo k ac i i y). (B) Alignmen o he eigh expe imen s (g ay
cu es), hei a e age (blue), and compa ison wi h ou a e aged con ols (o ange). (C) E olu ion o GEFF as a unc ion o he a e age global
ac i i y a o e e y CNQX concen a ion. Da a is scaled ela i e o [CNQX] e o pool all expe imen s oge he and highligh de ia ions om
he unpe u bed condi ion (do ed lines). The plo shows ha hype e iciency s a es (GEFF >1) a e compa ible wi h low spon aneous ac i i y
a es (g ay box). The hick blue line is a nonlinea sca e plo smoo hing o indica e he gene al end o he da a. I s shading is he con idence
in e al se as 80%.
pa ame e ha we e m deg ada ion le el d. The deg ada ion le el d=0means ha no CNQX
is applied and he e o e he cul u e exhibi s i s na u al dynamics, while d=1co esponds o
he CNQX dose ha is able o ully silence he cul u e’s ac i i y. The esul ing GEFF(d)cu es
o he eigh expe imen s and hei a e age a e shown Figu e 3B. All analyzed cul u es exhib-
i ed hype e iciency, which anged om a minimum o 3% o a maximum o 50%, and ha on
a e age p ocu ed abou 20% GEFF inc ease. This clea peak in global e iciency was inexis en
in con ols.
An aspec ha is impo an o poin ou is he complex ela ionship be ween clus e s’
collec i e ac i i y aand global e iciency GEFF. The da a o Figu e 2A and B shows ha he
hype e iciency obse ed a [CNQX] =60 nM coincides wi h a p ominen decay in ne wo k’s
collec i e ac i i y. The eason o his appa en con adic ion is ha he global ac i i y jus
in o ms abou he equency o collec i e beha io , bu does no cap u e he local dynamic in-
e ac ion among clus e s. This in o ma ion is p o ided by he e ec i e connec i i y, om which
he global e iciency is compu ed. Thus, we hypo hesize ha he clus e s s eng hen hei cou-
pling despi e coac i a ing oge he less o en. The complex ela ionship be ween aand GEFF
is illus a ed in Figu e 3C, in which we plo ed one agains he o he o each CNQX concen-
a ion, bu scaled he alues ela i e o [CNQX] e o pool all eigh expe imen s in a single
plo . In e es ingly, se e al o he poin s co esponding o a d op in ac i i y, o example, in he
ange 0.5–1, a e associa ed o GEFF alues abo e 1 (shaded a ea). These poin s a e p ecisely
he ones ha a e behind he obse ed hype e iciency, and ha we associa e o a s eng hen-
ing o he e ec i e coupling among clus e s. This analysis hus sugges s ha a d op in global
ac i i y caused by CNQX is esponded o by an inc ease in clus e s’ e ec i e coupling.
A Deg ada ion Model wi h Synap ic Scaling Rep oduces he Hype e iciency Phenomenon
We ca ied ou nume ical simula ions o unde s and he o igin o hype e iciency in he CNQX
pe u bed expe imen s. In he simula ions we conside ed he same e ec i e ne wo ks as in
he expe imen s o [CNQX] e and applied wo connec i i y deg ada ion schemes, namely
pe cola i e deg ada ion (PD) and synap ic scaling deg ada ion (SSD). As ske ched in Figu e 4A,
on he one hand, PD co esponds o a s anda d bond pe cola ion in which links a e g adually
Ne wo k Neu oscience 1
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Func ional s eng hening h ough synap ic scaling
Figu e 4. Nume ical models and hype e iciency. (A) Ske ch o he models used o simula e he
impac o a g adual loss o e ec i e connec ions. In his example, he wo models a ge an e ec i e
connec ion wi h weigh H=2. Fo pe cola i e deg ada ion (PD, le ) he bo om connec ion is
simply emo ed upon a ack. Fo synap ic scaling deg ada ion (SSD, igh ) he same connec ion is
emo ed, bu he su i ing ou going connec ions a e upscaled o dis ibu e he los weigh p opo -
ionally among hei s. All cu es a e a e ages o e eigh ealiza ions, and shadings indica e s anda d
de ia ion. (B) Compa ison o he deg ada ion ac ion be ween expe imen s (blue) and nume ical
models (PD, pink; SSD, g een). PD po ays a as -decaying beha io and he ne wo k becomes dis-
connec ed by d≃0.4. SSD ep oduces he hype e iciency (HE) peak and he gen le decay o GEFF
wi h dup o he end o he disin eg a ion p ocess. The inse shows he dis ibu ion o maximum hy-
pe e iciency alues o expe imen s and model. Despi e he dispe sion in he da a, SSD p ocu ed
o e all simila alues.
emo ed om weake o s onge acco ding o a h eshold H. This model e lec s he si ua ion
in which clus e s’ dynamic in e ac ion p og essi ely anish as deg ada ion g ows. On he o he
hand, SSD consis s in he same link emo al bu wi h he c ucial inclusion o synap ic scaling,
which is simula ed as he s eng hening o he su i ing links’ weigh s p opo ionally o he los
link’s weigh . This model cap u es a compensa o y esponse mechanism o he loss in ac i i y.
In bo h models, he h esholds a e ecalcula ed a e he emo al p ocess o a ge he nex
weakes link, yielding a na u ally inc easing sequence o h esholds. To compa e he models
wi h he expe imen s, he h esholds Hwe e escaled in he ange [0, 1] o conco d wi h he
deg ada ion le el d.
Ne wo k Neu oscience 1
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Func ional s eng hening h ough synap ic scaling
a e o 50 ames pe second ( ps), a size o 1,024 ×1,024 pixels, and a spa ial esolu ion o
5.76 µm/pixel.
Spon aneous Ac i i y and Ne wo k Bu s s
Clus e ed cul u es we e measu ed a DIV 8–12, a de elopmen al s age in which he clus e s
exhibi ed spon aneous ac i i y wi h a leas 1 collec i e ac i a ion (bu s ) pe minu e (Table 1).
Since, as obse ed p e iously by Telle e al. (2014,2015), spon aneous ac i i y in clus e ed
cul u es is o en o a modula na u e, in which he size o collec i e ac i a ions encompasses
om ew clus e s o he en i e ne wo k, we conside ed as bu s hose ac i i y e en s in which
a leas i e clus e s coac i a ed in a window o 200 ms (Telle e al.,2014).
Homgeneous cul u es we e measu ed a DIV 12 and exhibi ed s ongly cohe en dynamics,
in which he whole ne wo k ac i a ed oge he du ing a bu s ing episode, emaining p ac-
ically silen in be ween bu s s. A e age bu s ing equency in he ou s udied cul u es was
9.6 ±4.9 bu s s/min.
Expe imen al P ocedu e and Pha macology
Bo h exci a o y and inhibi o y connec ions we e p esen in he clus e ed cul u es. To in es i-
ga e he changes in ac i i y induced solely by p og essi ely weake AMPA glu ama e exci a ion
in neu ons, NMDA exci a o y ecep o s, which accoun o 20% o exci a o y d i e in co ical
neu ons, we e blocked wi h 20 µM o he ecep o an agonis APV (Sigma A5282), and GABAA
inhibi o y ecep o s we e blocked wi h 40 µM o he an agonis bicuculline (Sigma B7561).
Bo h an agonis s we e applied simul aneously and he cul u e was le 5 min in da kness o
biochemical s abiliza ion. A 15-min eco ding was hen conduc ed and swi ly analyzed o
e alua e he ini ial s a e o he ne wo k. Cul u es exhibi ing poo o agmen ed ac i i y we e
disca ded. Fo he highly ac i e cul u es, AMPA glu ama e exci a o y connec i i y was hen
g adually weakened by applica ion o he ecep o an agonis CNQX, wi h p ese concen a-
ions o [CNQX] (nM) =30, 60, 120, 300, 600, 1,000. Fo each CNQX concen a ion, spon a-
neous ac i i y was eco ded o 15 min. Cul u es we e kep in da kness o 5 min in be ween
eco dings o he nex d ug applica ion o ake e ec .
To in es iga e whe he he neu onal cul u es we e able o eco e he ac i i y pa e ns p io
o CNQX ac ion, he s udied clus e ed cul u es we e washed o wi h esh RS a he end o he
eco ding session, APV and bicuculine applied again, and ac i i y moni o ed o addi ional
20 min.
Con ol expe imen s we e ca ied ou o e i y ha he en i e p ocedu e and du a ion o
he eco dings did no a ec he heal h o he neu ons. Con ol eco dings consis ed iden ical
manipula ions as s anda d expe imen s bu wi hou addi ion o CNQX.
A p ac ically iden ical p ocedu e was ollowed wi h homogeneous cul u es, wi h he only
di e ence ha he CNQX concen a ions we e adjus ed ollowing Tibau e al. (2020) and Tibau
e al. (2013b), and used [CNQX] (nM) =100, 200, 400, 800, 1,000, 2,000.
Da a Analysis
Fluo escence aces. Fo each expe imen , neu onal clus e s o indi idual neu ons we e man-
ually iden i ied on a highly con as ed luo escence image and asc ibed as egions o in e es
(ROIs). The a e age luo escence (g ay scale le el) wi hin each ROI was hen compu ed, and
he aw luo escence aces Fi( ) o each clus e iex ac ed. Each ace was hen co ec ed
Ne wo k Neu oscience 1
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Func ional s eng hening h ough synap ic scaling
om global d i s and a i ac s and no malized as DFFi(%)≡100 ·(Fi( )−Fi,0)/Fi,0, whe e
Fi,0 i he basal luo escence o each clus e . The onse imes o ac i a ion o clus e s o indi id-
ual neu ons we e de e mined as hose e en s in which he luo escence ace c ossed a p ese
h eshold, se as he mean + 2 imes he s anda d de ia ion o he en i e luo escence ace
(Telle e al.,2014,2015). T ains o ac i i y we e hen buil by asc ibing as ‘1’ he exis ence o
an ac i a ion a a gi en ime poin , and ‘0’ o he wise.
Ne wo k Analysis
E ec i e connec i i y. I was in e ed using a modi ied e sion o ans e en opy (TE) (Sch eibe ,
2000). TE was compu ed o each pai o nodes Xand Y(ei he clus e s o neu ons) wi h signals
xmand ymindexed by 0≤m≤mmax, whe e mmax is he o al numbe o ime s eps in he
da a, as
TEY→X=−∑
0≤n≤nmax
0≤i≤iM
pxm+1,x(i)
m,y(i)
m×log2
pxm+1

x(i)
m,y(i)
m
pxm+1

x(i)
m,(1)
whe e iis he index o he pas ime s ep conside ed, ha is, he leng h o he ec o s {x(i)
m},
and iM=2is he Ma ko o de o he model. He e, ins an aneous eedback was assumed,
meaning ha Xand Ycould in e ac wi hin a ime bin, as in gene alized ans e en opy
(O landi, S e e , So iano, Geisel, & Ba aglia,2014;S e e e al.,2012). E ec i e connec i i y
was in e ed o he 15-min-long as e plo s (mmax =45, 000 poin s wi h an acquisi ion a e o
50 ps). TE =0 o an iden ical o andom pai o signals. Since expe imen al eco dings a e
sho , i may occu ha andom ac i a ions in nea by ime bins a e aken as causal in e ac ions.
Thus, o ejec spu ious connec ions, signi icance zwas es ablished o any connec ion X o
Yby compa ing he TEY→Xes ima e wi h he join dis ibu ion o TE o all inpu sco es X′
o Yand ou pu sco es X o Y′( o any X′and Y′), as
z=TEY→X− hTEjoin i
σjoin
,(2)
whe e hTEjoin iis he a e age alue o he join dis ibu ion and σjoin is i s s anda d de ia-
ion. Signi ican connec ions we e hen se as hose wi h z≥2. This h eshold was consid-
e ed op imal since i cap u ed he low o neu onal communica ion du ing ac i i y a bo h
local and global scales. A lowe h eshold o z=1yielded ne wo ks ha excessi ely em-
phasized whole-ne wo k coo dina ed ac i i y, e ec i ely shaping andom g aphs in all s udied
cases. Th esholds z&3emphasized he s onges neu on- o-neu on in e ac ions only and o -
en yielded emp y ma ices. All esul s p esen ed he e we e consis en wi h h esholds in he
ange 1.5 ≤z≤2.5. By cons uc ion, he adjacency ma ix A={aij}o signi ican connec-
ions was di ec ed and weigh ed, concep ually cap u ing he s eng h o dynamic in e ac ions
be ween clus e s o neu ons, and wi h he weigh o he connec ion gi en in s anda d de ia ion
uni s o he join dis ibu ion.
Densi y o links D. Fo a ne wo k wi h Nnodes, i was de ined as he ac ion o o al exis ing
e ec i e links ( ega dless hei weigh ) o all possible links, ha is, D=∑ij bij/(N(N−1)),
whe e B={bij}is he bina ized adjacency ma ix o A.
Single ealiza ion global e iciency G. The analysis o he da a o each in es iga ed cul u e
p o ided a se e ec i e adjacency ma ices {aij}k, whe e kis he s ep o CNQX applica ion.
Ne wo k Neu oscience 1
176
Func ional s eng hening h ough synap ic scaling
Fo each o hese ma ices, he global e iciency Go a ne wo k wi h Nnodes was de e mined
ollowing he s anda d de ini ion (La o a & Ma chio i,2001;Rubino & Spo ns,2010)
G=1
N(N−1)∑
i6=j
1
d(i,j),(3)
whe e d(i,j)is he sho es weigh ed pa h calcula ed on he ma ix {aij}, ha is, he smalles
sum o weigh s h oughou all possible pa hs be ween iand j. In his cons uc ion, highe
connec ion weigh s co espond o sho e leng hs, and he e o e he global e iciency inc eases
wi h he weigh o he connec ions. I no pa h exis s be ween nodes iand j hen d(i,j) = ∞,
so ha he e is no con ibu ion o he summa ion in Equa ion 3. The e m N(N−1)in his
equa ion is a no maliza ion ac o ha accoun s o all possible di ec ed links ha can be
o med by he Nnodes. Global e iciency was calcula ed using he B ain Connec i i y Toolbox
in Ma lab.
Deg ada ion Le el dand Alignmen o Expe imen al Cu es
The CNQX concen a ions we e con e ed in o a well-de ined pa ame e ha cap u ed in a
ange [0, 1] he p og essi e damage o a neu onal ne wo k. Thus, o each expe imen n, he
CNQX concen a ions we e ans o med in o s eps o a deg ada ion le el dby de ining
d(n)
k=[CNQX](n)
k−[CNQX](n)
e
[CNQX](n)
max
,(4)
whe e kis he s ep o CNQX applica ion along he expe imen , [CNQX]k he co esponding
concen a ion alue, [CNQX] e he e e ence concen a ion abo e which he dynamic al e -
a ions in he ne wo k a e measu able, and [CNQX]max he concen a ion ha ully silenced he
ne wo k. Wi h his cons uc ion, he deg ada ion le el d a ied be ween 0 (no al e a ion o he
ne wo k) o 1 ( ull silencing o ac i i y and comple e e ec i e ne wo k b eakdown). Da a ou -
side hese bounds was dis ega ded. Since [CNQX] e and [CNQX]max a ied ac oss cul u es,
he use o dp o ided a obus manne o a e age among cul u es.
Scaled Global E iciency GEFF and A e aged GEFF(d)Cu es
The se o global e iciency alues o each expe imen , G(n)(d), was scaled wi h espec o i s
e e ence alue p io damage, as G(n)
EFF(d) = G(n)(d)/G(n)
e , whe e G(n)
e is he global e iciency
measu ed a d=0. The G(n)
EFF(d)cu es we e hen in e pola ed as 100 equidis an poin s by
using a cubic in e pola ion ha p ese ed he shape o he cu es, and a e aged o e n=8
expe imen al ealiza ions (clus e ed cul u es) o n=4(homogeneous cul u es).
Nume ical Models o Ne wo k Deg ada ion
Two nume ical models we e p oposed o elucida e he impac o g adual deg ada ion on ne -
wo k global e iciency. Bo h models conside ed he same ini ial e ec i e ne wo ks as in he
expe imen s o d=0, deno ed as {a(0)
ij }, and applied a se ies o ules o he dele ion o links.
Since he e ec i e connec i i y ma ices we e ob ained om ans e en opy wi h a signi i-
cance h eshold z=2, he alues {a(0)
ij }we e bounded be ween amin =2and a gi en amax
ha depended on each ne wo k.
Pe cola i e deg ada ion (PD). This model p og essi ely dele ed he e ec i e ou pu links
whose weigh s we e equal o lowe han a h eshold H, s a ing a H=amin and p og essi ely
Ne wo k Neu oscience 1
177
Func ional s eng hening h ough synap ic scaling
a ge ing s onge links (Figu e 4A, le ). Thus, a a gi en simula ion s ep, he dele ed links we e
hose ha ul illed H=aij, inc easing Ha e wa d o a ge he nex weak link in he ne wo k,
un il all links o he ne wo k we e dele ed. The global e iciency Gwas compu ed a each
h eshold, and he inal GPD( H) alues s o ed o u he analysis.
Synap ic scaling deg ada ion (SSD). This model also p og essi ely dele ed he weakes ou -
pu links, bu wi h he c ucial addi ional ule ha , upon link emo al (wi h weigh H), all
su i ing ou pu links sha ed he weigh o he emo ed one, inc easing hei s p opo ionally
(Figu e 4A, igh ). Thus, i he e we e a leas wo links and he o al ou pu s eng h be o e
dele ion was sbe
i=∑jabe
ij , he new weigh s we e gi en by aij =abe
ij ·sbe
i/(sbe
i− H). I only
one ou pu link was p esen , i was dele ed as in PD. The new global e iciency o he ne wo k
GSSD( H)was hen compu ed, he h eshold upda ed o seek o he new weakes links, and
he p ocess s a ed again. Simula ion ended when all links in he ne wo k we e emo ed, and
he inal GSSD( H) alues s o ed.
The GPD( H)and GSSD( H)da a ob ained om he models was inally ea ed as in he
expe imen s. Fi s , o each simula ed ne wo k, he H alues (which anged om amin o amax
in he PD model, and om amin o a ce ain a∗
max ≥amax o SSD) we e scaled as d∈[0, 1].
The new GPD(d)and GSSD(d)cu es we e hen scaled ela i e o hei alues a d=0and
a e aged among ealiza ions o ob ain he scaled global e iciencies GEFF(d), which could be
di ec ly compa ed wi h he expe imen s.
E hics S a emen
All p ocedu es we e app o ed by he E hical Commi ee o Animal Expe imen a ion o he
Uni e si y o Ba celona, unde o de DMAH-5461, and in acco dance o he egula ions o
he Gene ali a de Ca alunya (Spain).
AUTHOR CONTRIBUTIONS
Es e anía Es é ez-P iego: Da a cu a ion; Fo mal analysis; In es iga ion; Me hodology; So -
wa e; Visualiza ion; W i ing - O iginal D a . Sa a Telle : Da a cu a ion; Me hodology; Re-
sou ces; So wa e; Supe ision; Valida ion. Cla a G anell: Da a cu a ion; Fo mal analysis;
Me hodology; Valida ion; Visualiza ion; W i ing - Re iew & Edi ing. Alex A enas: Concep ual-
iza ion; Fo mal analysis; Funding acquisi ion; In es iga ion; P ojec adminis a ion; Resou ces;
Supe ision; W i ing - Re iew & Edi ing. Jo di So iano: Concep ualiza ion; Funding acqui-
si ion; In es iga ion; Me hodology; Resou ces; So wa e; Supe ision; Valida ion; W i ing -
O iginal D a ; W i ing - Re iew & Edi ing.
FUNDING INFORMATION
Jo di So iano, Fundació Bancà ia “La Caixa” (h p://dx.doi.o g/10.13039/100000778), Awa d
ID: LCF/PR/HR19/52160007. Jo di So iano, H2020 Fu u e and Eme ging Technologies
(h p://dx.doi.o g/10.13039/100010664), Awa d ID: 713140 MESOBRAIN. Es e anía Es é ez-
P iego, H2020 Fu u e and Eme ging Technologies (h p://dx.doi.o g/10.13039/100010664),
Awa d ID: 713140 MESOBRAIN. Jo di So iano, Sec e a ía de Es ado de In es igación,
Desa ollo e Inno ación (h p://dx.doi.o g/10.13039/501100007136), Awa d ID: FIS2013-
41144-P, FIS2016- 78507-C2-2-P, FIS2017-90782-REDT. Sa a Telle , Sec e a ía de Es ado de
In es igacíón, Desa ollo e Inno ación (h p://dx.doi.o g/10.13039/501100007136),Awa d ID:
FIS2013-41144-P, FIS2016- 78507-C2-2-P, FIS2017-90782-REDT. Jo di So iano, Depa amen
Ne wo k Neu oscience 1
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Func ional s eng hening h ough synap ic scaling
d’Inno ació, Uni e si a s i Emp esa, Gene ali a de Ca alunya (h p://dx.doi.o g/10.13039
/501100002943), Awa d ID: 2017-SGR-1061. Alex A enas, Depa amen d’Inno ació, Uni e -
si a s i Emp esa, Gene ali a de Ca alunya (h p://dx.doi.o g/10.13039/501100002943), Awa d
ID: 2017-SGR-896. Alex A enas, Sec e a ía de Es ado de In es igación, Desa ollo e Inno-
ación (h p://dx.doi.o g/10.13039/501100007136),Awa d ID: PGC2018-094754-B-C21. Alex
A enas, Uni e si a Ro i a i Vi gili (h p://dx.doi.o g/10.13039/501100007512), Awa d ID:
2017PFRURV-B2-41. Alex A enas, ICREA Academia . Alex A enas, James S. McDonnell Foun-
da ion (h p://dx.doi.o g/10.13039/100000913), Awa d ID: 220020325. Cla a G anell, James
S. McDonnell Founda ion (h p://dx.doi.o g/10.13039/100000913), Awa d ID: 220020457.
Cla a G anell, Sec e a ía de Es ado de In es igación, Desa ollo e Inno ación (h p://dx.doi.o g
/10.13039/501100007136), Awa d ID: Juan de la Cie a.
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