Deco, G., Et. Al. (2014) How Local Excitation–Inhibition Ratio Impacts the Whole Brain Dynamics

8/11/2019 Deco, G., Et. Al. (2014) How Local ExcitationInhibition Ratio Impacts the Whole Brain Dynamics

1/13

Systems/Circuits

How Local ExcitationInhibition Ratio Impacts the Whole

Brain Dynamics

Gustavo Deco,1,2* Adrian Ponce-Alvarez,1* Patric Hagmann,3,4 Gian Luca Romani,5 Dante Mantini,6,7

and Maurizio Corbetta81Center for Brain and Cognition, Computational Neuroscience Group, Department of Information and Communication Technologies, and 2Institucio

Catalana de la Recerca i Estudis Avancats (ICREA), Universitat Pompeu Fabra, Barcelona, 08010, Spain,3Department of Radiology, Lausanne University

Hospital and University of Lausanne (CHUV-UNIL), 1011 Lausanne, Switzerland, 4Signal Processing Laboratory 5, Ecole Polytechnique Federale de

Lausanne (EPFL), 1015 Lausanne, Switzerland,5Institute of Advanced Biomedical Technologies, G. dAnnunzio University Foundation, Department of

Neuroscience and Imaging, G. dAnnunzio University, Chieti, 66013, Italy, 6Department of Health Sciences and Technology, ETH Zurich, 8057, Zurich,

Switzerland,7Department of Experimental Psychology, University of Oxford, OX1 3UD, Oxford, United Kingdom, and 8Department of Neurology,

Radiology, Anatomy of Neurobiology, School of Medicine, Washington University in St Louis, St Louis, Missouri 63110

The spontaneous activity of the brain shows different features at different scales. On one hand, neuroimaging studies show that long-range correlations are highly structured in spatiotemporal patterns, known as resting-state networks, on the other hand, neurophysio-

logical reports show that short-range correlations between neighboring neurons are low, despite a large amount of shared presynapticinputs. Different dynamical mechanisms of local decorrelation have been proposed, among which is feedback inhibition. Here, we

investigated the effect of locally regulating the feedback inhibition on the global dynamics of a large-scale brain model, in which thelong-range connections aregivenby diffusionimagingdata of human subjects. We used simulations andanalytical methods to show that

locally constraining the feedback inhibitionto compensate for the excess of long-range excitatoryconnectivity, to preserve the asynchro-nous state, crucially changes the characteristics of the emergent resting and evoked activity. First, it significantly improves the models

prediction of the empirical human functional connectivity. Second, relaxing this constraint leads to an unrealistic network evoked

activity, with systematic coactivation of cortical areas which are components of the default-mode network, whereas regulation of feed-back inhibitionpreventsthis. Finally, information theoreticanalysis showsthat regulationof the localfeedback inhibitionincreasesboththe entropy and the Fisher information of the network evoked responses. Hence, it enhances the information capacity and the discrim-

ination accuracy of the global network. In conclusion, the local excitationinhibition ratio impacts the structure of the spontaneousactivity and the information transmission at the large-scale brain level.

Key words: anatomical connectivity; functional connectivity; large-scale brain model; local feedback inhibition; resting-state activity

IntroductionThe spontaneous activity of the brain, i.e., not stimulus- or task-driven, shows different features at different spatial scales. Indeed,although long-range activity correlations between brain regions

are highly and strongly structured in spatiotemporal patterns,known as resting-state networks, on one hand, short-range cor-

relations within local circuits are low or even negligible, on theother hand.

Numerous neuroimaging experiments demonstrate the exis-tence of spontaneouslong-range correlations, i.e., resting functional

connectivity (FC), by fMRI (Biswal et al., 1995; Greicius et al., 2003;Fransson, 2005; Fox and Raichle, 2007), MEG (Liu et al., 2010;Brookes et al., 2011;Luckhoo et al., 2012;de Pasquale et al., 2012),and EEG-fMRI techniques (Mantini et al., 2007). The topology ofhuman FC patterns has been studied in detail across different con-ditions of rest or cognitive tasks (Achard et al., 2006,Bassett et al.,2006). In humans, a consistent set of functional networks (default,dorsal attention, ventral attention, vision, somatomotor, auditory,frontoparietal) have been identified in the resting-state activityacross subjects and across multiple sessions using a variety of methods,which can be used to generate whole-brain functional parcellations ofthe cerebral cortex (Doucet et al., 2011;Power et al., 2011;Yeo et al.,2011; Hackeretal., 2013). Of particular interest isthedefault network: a

setof correlated brainregions that aremoreactivatedat rest than duringthe performance of cognitivegoal-directed tasks (Shulman et al., 1997;Raichle et al., 2001; FoxandRaichle, 2007).

Received Dec. 4, 2013; revised April 25, 2014; accepted April 30, 2014.

Author contributions: G.D. and A.P.-A. designed research; G.D. and A.P.-A. performed research; G.D., A.P.-A.,

P.H., G.L.R., D.M., and M.C. analyzed data; G.D. and A.P.-A. wrote the paper.

G.D. was supported by the ERC Advanced Grant: DYSTRUCTURE (no. 295129), by the Spanish Research Project

SAF2010-16085 and by the CONSOLIDER-INGENIO 2010 Program CSD2007-00012, the Foundation La Marato

(Catalonia), and the FP7-ICT BrainScales and The Human Brain Project FET-Flagship. P.H was supported by Leen-

aards Foundation. M.C. was supported by NIH Grants R01HD061117 and R01MH096482. The research reported

hereinwassupportedbytheBrainNetworkRecoveryGroupthroughtheJamesS.McDonnellFoundation.Wethank

H. Sompolinsky and M. Lechon f or critical comments and valuable discussions.

The authors declare no competing financial interests.

*G.D. and A.P.-A. contributed equally to this work.

Correspondenceshouldbeaddressedto DrAdrian Ponce-Alvarez,UniversitatPompeuFabraC/ RocBoronat,138,

08018 Barcelona, Spain. E-mail: [email protected]:10.1523/JNEUROSCI.5068-13.2014

Copyright 2014 the authors 0270-6474/14/347886-13$15.00/0

7886 The Journal of Neuroscience, June 4, 2014 34(23):7886 7898


2/13

In contrast, single-cell recordings in monkeys indicate thatshort-range spontaneous correlations between neighboring neu-rons are low (Ecker et al., 2010), despite a large amount of sharedpresynaptic inputs. Different mechanisms have been proposed toaccount for this decorrelation including chaotic dynamics(vanVreeswijk and Sompolinsky, 1996), balance of excitation and in-hibition (Renart et al., 2010), and feedback inhibition (Tetzlaff et

al., 2012). In theoretical models, these mechanisms all producethe observed low (3 Hz for excitatory neurons) and irregular(Poisson-like) cortical activity observed in vivo (Burns andWebb, 1976;Softky and Koch, 1993;Wilson et al., 1994).

The aim of this study is to investigate the effect of local deco-rrelation on both the resting and evoked activity of a large-scalebrain model. Resting-state brain models assume that long-rangefunctional correlations emerge from the embedding of local dy-namics in the underlying anatomical connectivity structure(Honey et al., 2007,2009;Ghosh et al., 2008;Deco et al., 2009,2013a,b; Deco and Hughes, 2012). In general, biophysicalresting-state models use single-area dynamical models that,whenisolated, emulate spontaneous state activity, i.e., uncorrelated

low firing rate activity. However, the long-range anatomical cou-plings break down the asynchronous state, producing intra-areacorrelations which are not consistent with the empirical findings.Here, we show that the regulation of the local feedback inhibitionprovides a mechanism for reconciling the two levels of spontane-ous correlation at different spatial scales and we evaluate its func-tional consequences for both the resting and the evoked globalbrain dynamics.

Materials and MethodsStructural connectivity matrix.Neuroanatomical structure was obtainedusing diffusion spectrum imaging (DSI) data and tractography from fivehealthy right-handed male human subjects (Hagmann et al., 2008;Honey et al., 2009). The gray matter was subdivided into 998 regions-of-

interest (ROIs) which are grouped into 33 cortical regions per hemi-sphere (66 areas in total) according to anatomical landmarks (Table 1).White matter tractography was used to estimate the fiber tract densityconnecting each pair of ROIs, averaged across subjects. Anatomical con-nectivity among the 66 cortical regions was calculated by summing allincoming fiber strengths to the corresponding ROIs of the target region,and dividing it by its region-dependent number of ROIs, resulting in anonsymmetricconnectivitymatrix. This normalizationby the numberofROIs, which have approximately the same surface on the cortex, i.e., thesame number of neurons, is required because neuronal activity is sensi-tive to the number of incoming fibers per neuron in the target region. Asthedynamical modelof oneregion already takes intoaccount theeffect ofits internal connectivity (see below), the connection of a region to itselfwas set to 0 in the connectivity matrix for the simulations.

Empirical functional connectivity.The empirical resting fMRI FC wasmeasured in 48 scanning sessions from 24 right-handed healthy youngvolunteers (15 females, age range 2031 years). Subjects were informedabout the experimental procedures and provided written informed con-sent. The study design was approved by the local Ethics Committee ofChieti University. Subjects lay in a supine position and viewed a blackscreen with a centered red fixation point of 0.3 visual degrees, through amirror tiltedby 45 degrees. Each volunteer underwenttwo scanning runsof 10min in a resting-statecondition. Specifically,theywere instructedtorelax, but to maintain fixation during scanning. The eye position wasmonitored at 120 Hz during scanning using an ISCAN eye tracker sys-tem. Scanning was performed with a 3T MR scanner (Achieva; PhilipsMedical Systems) at the Institute for Advanced Biomedical Technologiesin Chieti, Italy. Functional images were obtained using T2-weightedecho-planar imaging (EPI) with blood oxygenation level-dependent

(BOLD) contrast using SENSE imaging. EPIs (TR/TE 2000/35 ms)comprised 32 axial slices acquired continuously in ascending order cov-ering theentirebrain (voxelsize 3 3 3.5 mm3). For each scanning

run, initialfive dummy volumes allowing theMRI signal to reach steady-state were discarded. The next 300 functional volumes were used for theanalysis. A three-dimensional high-resolution T1-weighted image (TR/TE 9.6/4.6 ms, voxelsize 0.980.98 1.2mm 3) covering theentirebrain was acquired at the end of the scanning session and used for ana-tomical reference. Initial data preprocessing was performed using theSPM5software package (Wellcome Departmentof Cognitive Neurology,London, UK) running under MATLAB (MathWorks). The preprocess-ing steps involved the following: (1) correction for slice-timing differ-ences, (2) correction of head-motion across functional images, (3)coregistration of the anatomical image and the mean functional image,and(4) spatial normalizationof allimages to a standard stereotaxic space(Montreal Neurological Institute; MNI) with a voxel size of 3 3 3mm 3. Furthermore, the BOLD time series in MNI space were subjectedto spatial independent component analysis (ICA) for the identifica-tion and removal of artifacts related to blood pulsation, head move-ment and instrumental spikes and those that correlate with the whitematter and CSF patterns (Sui et al., 2009; Mantini et al., 2013). TheBOLD artifact removal procedure was performedusing the GIFTtoolbox(http://mialab.mrn.org/software/gift/index.html). No global signal re-gression was performed. For each recording session (subject and run),the BOLD time series from the 998 ROIs of the brain atlas (Hagmann etal., 2008) were averaged over the corresponding 66 brain regions. Finally,we concatenated in time the remaining sessions for each parcel and cal-culated the correlation matrix (FC).

Computational model. In this study we modeled a cortical area as acanonical local network composed of interconnected excitatory and in-

hibitory neurons coupled through NMDA, AMPA, and GABA synapses.In the large-scale brain model, we assumed that the inter-area connec-tions are constrained by the empirical anatomical matrix that expresses

Table 1. Names and abbreviations (alphabetically) of the brainregions considered

in thehuman connectome from Hagmann etal. (2008)

Brain region Abbreviation

Bank of the superior temporal sulcus BSTSCaudal anterior cingulate cortex CACCaudal middle frontal cortex CMFCuneus CUN

Entorhinal cortex ENTFrontal pole FPFusiform gyrus FUSInferior parietal cortex IP

Isthmus of the cingulate cortex ISTCInferior temporal cortex ITLingual gyrus LINGLateral occipital cortex LOCCLateral orbitofrontal cortex LOFMedial orbitofrontal cortex MOFMiddle temporal cortex MTParacentral lobule PARCParahippocampal cortex PARHPosterior cingulate cortex PCPericalcarine cortex PCAL

Precuneus PCUNPars opercularis POPEPars orbitalis PORBPrecentralgyrus PRECPostcentralgyrus PSTCPars triangularis PTRIRostral anterior cingulate cortex RACRostral middle frontal cortex RMFSuperior frontal cortex SFSupramarginalgyrus SMAR

Superior parietal cortex SPSuperior temporal cortex STTemporal pole TPTransverse temporal cortex TT

Deco, Ponce-Alvarez et al. Balanced Resting-State J. Neurosci., June 4, 2014 34(23):78867898 7887
http://mialab.mrn.org/software/gift/index.htmlhttp://mialab.mrn.org/software/gift/index.html


3/13

the density of white matter fiber tracts connecting two given brain areas.However, because the large-scale spiking model is composed of manythousands of coupled nonlinear differential equations corresponding toeach singleneuron andsynapse,some approximations need to be done tosimplify the model. For this, we used a dynamic mean field (DMF) tech-nique(Wong and Wang, 2006)that approximates the average ensemblebehavior, instead of considering the detailed interactions between indi-vidual neurons. This allow us varying the parameters and, furthermore,

to greatly simplify the system of stochastic differential equations by ex-pressing it in terms of the first and second-order statistical moments,means and covariances, of network activity. In the following we presentthe details of the model and its simplified versions.

Single area spiking model.To show the effect of feedback inhibition onthecorrelations between intra-area neurons andon thefiringrateactivitywe used a network of integrate-and-fire (IF) spiking neurons with excit-atory (AMPA and NMDA) and inhibitory (GABA-A) synaptic receptortypes (Deco andJirsa,2012).Eachlocal cortical areais modeled by a fullyconnected recurrent network of a population ofNEexcitatory pyramidalneurons and a population ofNIinhibitory neurons. The dynamical evo-lution of the IF neurons membrane potential V(t) is driven by the in-coming local excitatory and inhibitory inputs within the same corticalarea, long-range excitatory inputs from all other cortical areas, and ex-ternal inputs. The time evolution of the membrane potential of a givenneuroniobeys the following differential equation:

CmdVit

dt gmVit VL

gAMPA ,extVit VEsAMP A,extt

gAMPA ,recVit VEj1

NE

wijsjAMP A,rect,

gNMD AVit VE

1 NMD AeVit

j1

NE

wijsjNMD At

gGABAVit VI

j1

NI

wijsjGABAt (1)

if the membrane potential is below a given thresholdVthr. The neurongenerates a spike, when the membrane potential reaches the thresholdVthr. The spike is transmitted to other neurons and the membrane po-tential is instantaneously reset to Vreset andmaintained there for a refrac-tory time ref during which the neuron is unable to produce furtherspikes. In Equation 1, gmis the membrane leak conductance, Cmis thecapacity of themembrane, andVL is theresting potential. Themembranetime constant is defined bymCm/gm. The synaptic input current isgiven by the last four terms on the right hand side of Equation 1. Thespikes arriving at the synapse produce a postsynaptic excitatoryor inhib-itory potential given by a conductance-based model specified by thesynaptic receptors, corresponding to: glutamatergic AMPA external ex-citatory currents, AMPA and NMDA recurrent excitatory currents, and

GABAergic recurrent inhibitory currents. The respective synaptic con-ductances aregAMPA,ext,gAMPA,rec,gNMDA,rec, andgGABA, andVEandVIare the excitatory and inhibitory reversal potentials, respectively. Thedimensionless parameters wijof the connections are the synaptic weightsdefined as following: the recurrent self-excitation within each excitatorypopulation is given by the weight wEE w 1.4 (for both AMPA andNMDA recurrent synapses); recurrent inhibition and connections fromexcitatory to inhibitory neurons and vice versa have the weight wII,wIE,andwEI, respectively. The gating variablessj

it are the fractions of openchannels of neurons and are given by the following:

dsjIt

dt

sjIt

I

k

t tjk, forI AMPA or GABA (2)

dsjNMD At

dt

sjNMD At

NMD A,decay xj

NMD At1 sjNMD At (3)

dxjNMD At

dt

xjNMDA t

NMD A,rise

k

t tjk. (4)

Where the sums over the indexkrepresent all the spikes emitted by thepresynaptic neuronj(at timestj

k);AMPAandGABArepresent the decaytimes for AMPA andGABA synapses, andNMDA,riseand NMDA,decayare

the rise and decay times for the NMDA synapses. All neurons in thenetwork receive an AMPA-mediated external background input of un-correlated Poisson spike trains with a mean rate of0 2.4 kHz. Param-eter values of the neurons and the synapses are summarized in Table 2.

The values of the local connections were set towII wEI wIE1.With these parameter values the spiking activity of the above local net-work mimics the observed spontaneous activity, i.e., uncorrelated lowactivity with mean firing rate equal to 2.92 and 7.54 Hz for the excitatoryunits and the inhibitory units, respectively. However, when two or morelocal networks are connected through long-range excitatory connec-tions, the external excitation increases the correlations within the localnetworks (see below). To compensate for the excess of excitation, wepostulate a local regulation mechanism, called feedback inhibition con-trol (FIC), in which the connectionweights frominhibitory to excitatoryneurons within each cortical area are adjusted to clamp the firing rate at

3 Hz for each local excitatory neural population in the large-scale net-work (see below). In the FIC case, the optimized inhibitoryexcitatoryweight of cortical areaiis notedwEIJi, whereaswII wIE 1.

Large-scale cortical dynamic mean field model. As we will see below, theadjustment of the local feedback inhibition of each cortical area involvesthe recursive adaptation of the inhibitory excitatory weights. This algo-rithm requires the computation of the global dynamics during a longperiod of time, until the FIC constraint is satisfied in allareas. Therefore,weusedhere a reduced DMF (Wong andWang,2006) for computingtheglobaldynamics of thewhole cortex. TheDMF expressesconsistentlythetime evolution of the ensemble activity of the different excitatory andinhibitory neural populations building up the spiking network. In theDMF approach, each population firing rate depends on the input cur-rents into that population. On the other hand, the input currents dependon the firing rates. Hence, the population firing rate can be determinedself-consistently by a reduced system of coupled nonlinear differentialequations expressing the population firing rates and the respective inputcurrents. The large-scale model interconnects these local subnetworksaccording the structural connectivity matrix (SC) defined by the neuro-anatomical connections between those brain areas in the human, as ob-tained by DSI and describe above. The inter-area connections areestablished as long range excitatory synaptic connections either betweenexcitatory pools of different areas only or both between excitatory poolsand from excitatory pools to inhibitory the inhibitory pools of differentareas (feedforward inhibition). Inter-areal connections are weighted bythe strength specified in the neuroanatomical matrix SC, denoting thedensity of fibers between those regions, and by a global scaling factor G.The global scaling factor is a free control parameter that we vary system-atically to study the dynamics of the global cortical system.

In brief, the mean field approach considers the diffusion approxima-tion according to which sums of synaptic gating variables (Eq. 1) arereplaced by the averaged component and a Gaussian fluctuation term.

Table2. Parameters forspiking andthe DMF model

Excitatory neurons Inhibitory neurons Synapses

NE

160 neurons NI

40 neurons VE

0 mVCm

0.5 nF Cm

0.2 nF V1 70 mVg

m 25 nS g

m 20 nS AMPA 2 ms

VL

70 mV VL

70 mV NMDA,rise 2 msVthr 50 mV Vthr 50 mV NMDA,decay 100 ms

Vreset 55 mV Vreset 55 mV GABA 10 msref 2 ms ref 1 ms 0.5 kHzgAMPA,ext 3.37 nS gAMPA,ext 2.59 nS 0.062

gAMPA,rec 0.065 nS gAMPA,rec 0.051 nS NMDA 0.28

gNMDA,rec 0.20 nS gNMDA,rec 0.16 nSgGABA 10.94 nS gGABA 8.51 nS

7888 J. Neurosci., June 4, 2014 34(23):7886 7898 Deco, Ponce-Alvarez et al. Balanced Resting-State


4/13

Moreover, the first passage time equation, that gives the mean firing rateof a neuron receiving a noisy input, is approximated by a simple sigmoi-dal inputoutput function giving the firing rate as a function of theinputs (Wong and Wang, 2006). Because the synaptic gating variable ofNMDA receptors has a much longer decay time constant (100 ms) thanthe AMPA receptors, the dynamics of the NMDA gating variable domi-nates the timeevolutionof thesystem, while the AMPA synapticvariableinstantaneously reaches its steady-state. We thus have neglected contri-

butionsby theAMPA receptorsto thelocalrecurrent excitation. Alltheseapproximations greatly simplify the model without compromising itsperformance. Indeed, it has been previously shown that these approxi-mations conserve the first-order (fixed points of the mean activity) andthe second-order (correlation structure) statistics of the original large-scale spiking model (Deco et al., 2013a)which includes AMPA, NMDA,and GABA synapses. Finally, in the present study long-range AMPA-mediated connections areassumed to be instantaneous, thusconductiondelays between distant cortical areas are neglected.

The global brain dynamics are described by the following set of cou-pled nonlinear stochastic differential equations:

IiE

WEI0 wJNMDA SiE

GJNMD Aj

CijSjE

JiSiI

Iexternal,

(5)

IiI

WII0 JNMD ASiE

SiI

GJNMD Aj

CijSjE, (6)

riE

HEIiE

aEIiE

bE

1 expdEaEIiE

bE, (7)

riI

HIIiI

aIIiI

bI

1 expdIaIIiI

bI, (8)

dS iEt

dt

SiE

E 1 Si

EriE

it, (9)

dS iIt

dt

SiI

I ri

I it, (10)

where ri(E,I) denotes the population firing rate of the excitatory ( E) or

inhibitory ( I) population in the brain areai.Si(E,I) denotes the average

excitatory or inhibitory synaptic gating variable at the local area i. Theinput currents to the excitatory or inhibitory population i is given byIi(E,I). Iexternalencodes external stimulation for simulating task evoked

activity (it is zero for all pools under resting state condition, and 0.02 forthose pools excited in a task condition). Furthermore, w

1.4 is the

local excitatory recurrence, andCijis the structural connectivity matrixexpressing the neuroanatomical links between the areas i and j. Theparameter can be equal to 1 or 0 and indicates whether long-rangefeedforward inhibition (FFI) is considered ( 1) or not ( 0). Notethat in thecase of FFIthe proportionof excitatoryinhibitory long-rangeconnections and excitatoryexcitatory long-range connections is thesame. H(E) andH(I) denotes the neuronal inputoutput functions ofexcitatory pools and inhibitory pools, respectively. The inputoutputfunction converts incoming inputs into firing rates. The kinetic param-eters are 0.641/1000 (the factor 1000 is for expressing everything inms), andE NMDAandI GABA. The excitatory synaptic coupling

JNMDA 0.15 (nA) andthe local feedback inhibitory synapticcouplingJiis 1 for each brain area i in the no-FIC case, and for the FIC case it isadjusted independently, by the algorithm described below. The overalleffective external input isI0 0.382 (nA) scaled byWEandWI, for theexcitatory pools and the inhibitory pools, respectively. In Equations 9and 10iis uncorrelated standard Gaussian noise and the noise ampli-tude at each node is 0.01(nA). Equation 9 is derived from Equations3 and 4, by replacing the sum over presynaptic delta-like spikes by themean firing rate ri

(E) andnoting that theeffectivetime constant of NMDAisNMDA NMDA,riseNMDA,decay 100 ms(Wong and Wang, 2006).

Similarly,Equation 10 is derived from Equation 2.See Table 3 for param-eter values. The values ofWI,I0, andJNMDAwere chosen to obtain a lowlevel of spontaneous activity for the isolated local area model.With these

parameter values the mean spiking activity of the excitatory pool, for anisolatelocal network(G 0), is equal to 3.0631Hz. Notethatthistuningis necessary because the system of equations (510) results from a suc-cession of approximations, among them the neglect of AMPA receptors,which inclusion would otherwise highly complicate the reduced model(Wong and Wang, 2006).

The fixed points of the above dynamical system were calculated bynumerically solving the steady-state system of nonlinear equations (Eqs.510, in the absence of noise) using the MATLABs fsolve function.

For comparison to the empirical fMRI BOLD functional connectivitymatrix, we transformed the simulated excitatory synaptic activity,S (E),to BOLD signals using the BalloonWindkessel hemodynamic model(Friston et al., 2003;Deco et al., 2013a).

FIC. For an isolated node, with the intrinsic parameters described above,an input to the excitatory pool equal to Ii

E bE/aE 0.026; i.e.,

slightly inhibitory dominated, leads to a firing rate equal to 3.0631 Hz.Hence, in the large-scale model of interconnected brain areas, we aim toconstraint in each brain area (i) the local feedback inhibitory weightJisuch that Ii

E bE/aE 0.026 is fulfilled (with a tolerance of

0.005, implying an excitatory firing rate between 2.633.55 Hz). Toachieve this, we apply following procedure: we simulate during a periodof 10 s the system of stochastic differential Equations 510 and computethe averaged level of the input to the local excitatory pool of each brainarea, i.e., Ii

(E). If IiE

bE/aE 0.026 then we upregulate thecorresponding localfeedback inhibitionJiJi; otherwise, we down-regulateJiJi . We recursively repeat this procedure until the con-

straint on the input to the local excitatory pool is fulfilled in all 66 brainareas.

Analytical approximation of the activity covariance. To estimate thenetworks statistics, we approximate deterministic dynamical equationsfor statistical moments of networks gating variables. This momentsmethod avoids extensive simulations of the entire stochastic system,that otherwise would be required for estimation of the network mo-ments. For this, we express the system of stochastic differential equations(510) in terms of the first- and second-order moments of the distribu-tion of synaptic gating variables: i

(m), the expected mean gating variableof a given local neural population of typem (wheremEor I) of thecortical area i, and Pij

(mn), the covariance between gating variables ofneural populations of typemandnof local cortical areasiandj, respec-tively. The moments are defined as follows:

imt Si

mt (11)

Pijmnt Si

mt imtSj

nt jnt. (12)

Where the angular brackets . denote the average over realizations. Invector form, the system of equations writes as follows:

d

dtS

E

S I fES E,S I

fIS E,S I , (13)

whereS SE, SI S1E,, SN

E, S1I,, SN

I,fkESE, SI

SkE

E

(1 SkE)HEIk

E andfkISE, SI

SkI

I HIIk

I for k 1,..,N.

Taylor expandingSaround S; i.e.,Si(m) i

(m) Si(m), up to

the first order, we get the following:

Table 3. DMF model variables

Excitatory gating variables Inhibitory gating variables

aE 310 (nC1) a

I 615 (nC1)

bE 125 (Hz) b

I 177 (Hz)

dE 0.16 (s) d

I 0.087 (s)

E NMDA 100 (ms) I GABA 10 (ms)

WE 1 W

I 0.7



5/13

fkmS fk

m i

fkm

SiE Si

E

i

fkm

SiI Si

I.

(14)

Using thisapproximation, tacking theaverage over realizations, andnot-ing that:

Sim

t t 0, (15)

we obtain themotionequations for the means of the gating variablesandthecovariance of the fluctuations around themean.For the mean values:

diE

dt

d

dtS E

iE

E 1 i

EHEuiE (16)

diI

dt

d

dtS I

iI

I HIui

I. (17)

Whereui(m) is the mean input current to the neural population m E, I

of cortical areai, defined as follows:

uiE

WEI0 wJNMD AiE

GJNMD Aj

CijjE

JiiI

Iexternal

(18)

uiI

WII0 JNMD A iE

iI

GJNMD Aj

CijjE. (19)

For the fluctuations:

d

dtSi

mSjn

pE,I

k

fim

Sk p Sk

pSjn

pE,I

k

fim

Skp Sk

pSim 2ij. (20)

LetPbeing the covariance matrix between gating variables. Pis a blockmatrix defined as follows:

P SST PEE PEI

PIE PII , where the superscript Tis the transpose.Using Equation 20, we obtain the motion equation of the covariance

matrix:

dP

dt AP PATQn, (21)

WhereQn

is the covariance matrix of the noise (which is diagonal foruncorrelatedwhite noise) and A is theJacobian matrixof the system. A isa block matrix defined as follows:

A AEE AEI

AIE AII, whereAijmn fi

m

Sjn.

Finally, note that the above derivatives can be written as follows:

fim

Sjn 1m HEuiEEmEnij

1 1 iEEmEn

Hmuin

u Kij

mn. (22)

Where K KEE KEI

KIE KII, with KijEI Jiij, KIE JNMDAI GJNMDAC,K

II I, andKEE wJNMD AI GJNMD AC, whereI

andCare theN-by-Nidentity matrix and anatomical connectivity ma-trix, respectively.

Equations 2022 indicate that the covariance of gating variables is

determined by both theunderlying connectivity andthe dynamics.In thestationary regime, the covariance matrix of fluctuations around thespontaneous state is given by the algebraic equation:

AP PATQn 0, (23)

which can be solved using the Eigen-decomposition of the Jacobian ma-trix evaluated at the fixed points: A LDL1, where D is a diagonalmatrix containing the eigenvalues ofA, denotedi, and the columns ofmatrixL arethe eigenvectors ofA. Multiplying Equation 23 byL1 fromthe left and by L from the right (the superscript dagger being theconjugate transpose) we get the following:

P LML, (24)

Where M is given by the following: Mij Qj

/i j, and

Q L1QnL.

Thus, the covariance matrix of spontaneous fluctuations is deter-mined by theeigenvaluesof theJacobianmatrix, which, in turn, is relatedto the connectivity matrix and the dynamics. Hence, Equation 24 pro-vides a direct link between the correlation structure, the underlying con-nectivity,and dynamics. Indeed, the interpretation of Equation 24 is thatthe input covariance (M ) is propagated through the dynamical systemand is mapped to its approximated output (P).

Finally, to compare the results from the above moments method tothe empirical functional connectivity, we estimated the correlation ma-trix, notedQ, between the gating variables of the excitatory populations,

defined as follows:Qij PijEEPiiEE PjjEE.

Power spectrum of linear fluctuations.The power spectrum of fluc-tuations around the fixed points, (), can be obtained by, first,writing the equation of the fluctuations around the fixed points, givenby the following:

dSt

dt ASt t. (25)

Taking the Fourier transform of Equation 25 we get the following:

i S AS . (26)

Hence,S J i1. The power spectrum being theexpectation of the Fourier transformed autocorrelation function, we get

the following:

SS 2A i1AT i1.

(27)

Thus, the power spectrum ofSkis as follows:

k 2

l

Jkl i kl12. (28)

Model prediction of the empirical connectivity.As a measure of similar-ity between two FC matrices we used the uncenteredPearson correlationcoefficient between corresponding elements of the upper triangular partof the matrices, defined as follows:

rc

XY

SDXSDY. (29)

WhereXandYare the vectors containing the upper triangular values ofeach matrix, respectively, and SD is the standard deviation. For FC ma-trices, becausethe sampling distribution of correlationcoefficients is notnormally distributed, we used the Fishers z-transformation to convertthe matrixelements before applying any subsequent test. The uncenteredcorrelation takes intoaccount thedifference in themean valuesof theFCmatrices. Confidence intervals were obtained using bootstrap resam-pling (1000 resamples).

For comparing a structural connectivity matrix and a FC matrix weused the centered Pearson correlation defined as follows:

rc X XY Y

SDXSDY . (30)

Entropy of binary evoked patterns.The response of the large-scale net-work to different stimuli was analyzed to investigate its behavior under



6/13

hypothetical task conditions and its information capacity. Stimuli wereconstructed by imposing an external input Iexternal 0.02 (1) to theexcitatory populationof 10%of thebrainareas, randomly selected,or (2)to both the excitatory and inhibitory populations of 10% of the brainareas,randomlyselected. Theprocedure wasrepeated1000times andtheresulting steady-state evoked response of the network were stored.Evokedpatternswere binarizedby imposing a thresholdabovewhich theexcitatory firing rate of a given area was set to 1 and, otherwise, it was set

to 0 (onlythe firing rateof the excitatory pools wereused, thus the binaryevoked pattern is 66-dimensional). The threshold was defined as .SD,where SD is the standard deviation across all evoked patterns and themultiplier is a scalarparameter. In thisway we obtained binarypatternscontaining 66 entries. The entropy of the set of evoked binary patternsRis defined as follows:

HR i1

n

pi log2pi. (31)

Wherenis the number of unique patterns andpiis the probability thatpatterniis observed. Only patterns with at least one non-null entry wereanalyzed.

To removethe sampling bias, we correctedthe entropy valuesby usinga quadratic extrapolation procedure (Treves and Panzeri, 1995;Shew et

al., 2011). This procedure evaluates the entropy for random samples offractionsffrom the full set ofKpatterns to estimate the sample entropyH(f). It has been shown that the bias of the entropy can be accuratelyapproximated as second order expansions in 1/(fK); i.e.,H(f) H0k1(fK)

1 k2(fK)2, where H0is the true value of the entropy and

k1(fK)1 k2(fK)

2 is the bias (Treves and Panzeri, 1995). Fitting(least-square-error procedure) the sample entropyH(f) with a quadraticfunction of 1/(fK), provides the estimate of the unbiased entropyH0.Additionally, the fitting provides confidence intervals.

Fisher information.We quantified the encoding accuracy of the large-scale network response by calculating the Fisher information (FI). As-suming that the network response is well described by a multivariateGaussian distribution, i.e., for weak noise,FI canbe writtenas thesum oftwo terms: FI FImeanFIcov(Abbott and Dayan, 1999), where

FImeanI I

T

PI1 I (32)

FIcovI 1

2Trace([P(I)PI1]2). (33)

Where I and P(I) arethe stationary mean synaptic activity andthecovariance matrix evoked by an excitatory stimulus of intensityI, re-spectively; I andP(I) are the first derivatives with respect to thestimulus, evaluated at I. The values of I and P(I) were estimatedusing the moments equations (Eqs. 16 19, for the mean, and Eq. 24 forthe covariance),in the presence of an applied stimulus, i.e., IexternalI.Only the excitatory parts of andPwere considered for calculating theFI. In this study, the stimulus was applied to the excitatory population ofboth right and left lateral occipital cortex (LOCC), i.e., Iexternal IforrLOCC and lLOCC, and Iexternal 0 for all other cortical areas. The

intensity of the stimulus varied from I0.02 to I0.1 in steps of0.001.

Betweenness centrality.The centrality of a node within the anatomicalnetwork was quantified using the betweenness centrality measure. Thisnetwork measures expresses the number of shortest paths that passthrough a given node. For calculating the betweenness centrality we bi-narized the anatomical matrixC by imposing a threshold equal to 0.05above which the anatomical coupling was set to 1 and, otherwise, it wasset to 0.

ResultsLocal feedback inhibition controlIn the present study we investigated the effect of regulating thelocal feedback inhibition on the long-range resting correlations

between cortical areas. For this, we used a large-scale model,composed of local networks, or nodes, representing corticalareas, interconnected by the anatomical connectivity matrix, or

structural connectivity, between those cortical areas (Deco andJirsa, 2012;Deco et al., 2013a). Large-scale anatomical connec-tivity data were obtained using DSI and tractography techniques(Hagmann et al., 2008; see Materials and Methods). Isolated localbrain area models consist of 80% IF excitatory neurons and 20%inhibitory IF neurons recurrently connected (all-to-all). Intra-area connection weights were such that when isolated the net-work emulates the neurophysiological characteristics of theempirical observed spontaneous state, i.e., low correlations be-tween the spiking activity of theneurons and lowfiring rate at3Hz (see Materials and Methods for details;Deco and Jirsa, 2012).

When the different brain areas are coupled, however, the addi-tional excitatory input injected into each brain area by the long-range pathways breaks the delicate local balance of excitation andinhibition and induces both local correlations and elevated localfiring rate. To show this effect, we considered an example casecomposed of two interconnected single brain areas (Fig. 1a).Connections between the two brain areas were symmetric. Theintroduction of coupling between nodes leads to high synchro-nized activity in the excitatory pool (Fig. 1b, top). Our workinghypothesis is that local feedback inhibition compensates the ex-cess of excitation and decorrelates the activity. To test this, weused a learning algorithm to optimize the strength of the localinhibitory feedback for each brain area (see Materials and Meth-

ods) such that all excitatory pools have a low firing rate 3 Hz.This optimization, or feedback inhibition control, effectivelyreduces the intra-area correlations (the mean correlation coeffi-

Figure 1. The effect of FIC on the spontaneous spiking activity of two coupled model areas.a, Two network brain areas model with symmetric connections through their correspondingexcitatory pools.Thelocalbrainareamodels consist of 80%excitatoryneuronsand 20%inhib-itory neurons recurrently connected such that when isolated the network emulates the neuro-physiological characteristics of the empirical observed spontaneousstate, i.e.,low correlationsbetweenthespikingactivitiesoftheneuronsandlowfiringrateat3Hz.IntheFICscenario,thefeedback inhibition is adjusted to compensate the extra excitation the each excitatory poolreceivewhenthebrainareasmodelareconnected. b, c,Spikingactivityofexcitatoryunitsfrom

onebrainareawithoutFIC(b,top)andwithFIC(c,top).Duetosymmetry,thespikingactivityintheother brainareahas thesamestatistics. Theaveraged activities ofboth excitatory poolsareplotted in blue and green, for the model without FIC (b, bottom) and the model with FIC (c,bottom).d, Filled bars, Mean correlation coefficient (SEM) across all pairwise correlationswithinone excitatorypool, without and withFIC (redand blue,respectively).Open bars,Corre-lation between the mean firing rates of both excitatory pools, without and with FIC (red and

blue, respectively).



7/13

cient is 0.11 0.06 and 0.23 0.05 withand without FIC, respectively,p 1010,ttest),but, interestingly, allowsfor a mod-erate correlation between the mean firingrates of both excitatory pools (equal to0.35 and 0.63 with and without FIC, re-spectively;Fig. 1c,d). In other words, un-

der FIC, microscopic activity is partiallydecorrelated while mesoscopic (popu-lation level) quantities covary.

This is the key manipulation that westudy in thelarge-scalemodel. Beforepro-ceeding anyfurther,it is importantto notethat, in the previous example, althoughthe firing rate is maintained constant, ma-nipulation of the inhibitory feedbackchanges the eigenvalues of the local net-work, and, thus, modifies the dynamics.

Large-scale models with and without

FIC: stationary statesIn the large-scale cortical network, con-sisting on coupled cortical areas, we com-pensated the local feedback inhibitionweights (Ji), as previously, to clamp thefiring rate 3 Hz for each local excitatoryneural population i (see Materials andMethods). Because this local compensa-tion mechanism, achieved through recur-sive adjustments ofJi, is computationallyexpensive, we used a DMF to reduce thelarge-scale spiking network (Wong andWang, 2006;see Materials and Methods).The DMF ignores the interaction between

single neurons within a cortical area andinstead considers the ensemble meso-scopic dynamics. By reducing the numberof variables, theDMF model allowsfor theoptimization of feedback inhibitionweights(Fig. 2a,b).

In thefollowing we compared thefixedpoints of the model with long-range excit-atoryexcitatory connections (EE model)and the model with long-range excitatoryexcitatory connec-tions and local feedback inhibition regulation (FIC model). Wealso consider a third model in which the firing rate within eachcortical region is maintained low through long-range connections

fromthe excitatory populationsto the inhibitory populations (feed-forward inhibition,) in the same proportion as long-range excitato-ryexcitatory connections and according to the anatomicalconnectivity (see Materials and Methods).

In allmodels theinter-area coupling is scaledby a singleglobalparameter,G, that changes the network from weakly to stronglyconnected and determines the dynamical state of the system. Wefirst calculated the bifurcation diagrams characterizing the sta-tionary states of the brain system for the three models(Fig. 2c,d)as a function ofG. In all cases we plot, for the different possiblestates, the maximal firing rate activity across all excitatory popu-lations. The EE model presents a bifurcation at G 1.47 sepa-rating two qualitatively different topologies of the attractor

landscape. For small values of the global coupling G, only onestable state exists, characterized by a firing activity that increasesasGincreases (stable branch). ForGlarger than the critical value

1.47 a bifurcation occurs and a second fixed point appears whichis not stable (unstable branch). The FIC model has only onestable state of low firing activity in all cortical areas, for G 4.45. For larger values ofG, long-range interactions are toostrong to be compensated by FIC and the activity diverges. Inthe FFI model the maximum firing rate monotonically in-creases as a function ofG.

Feedback inhibition control improves the modelsFC predictionWe next investigate the structure of the emergent correlationsfrom thethreeglobal brain models. Thepredictions of themodelswere evaluated using the empirical human resting-state FC, ob-tained by averaging the results across 48 fMRI scanning sessionsfrom 24 healthy human subjects and projected to the same par-cellation adopted for the anatomical structural matrix (SC). Forcomparison with the empirical data, we considered the FC of

simulated BOLD signals which are obtained by transforming themodel synaptic activity through a hemodynamic model (see Ma-terials and Methods). We calculated the similarity between the

Figure2. TheeffectofFIConthespontaneousmean-fieldactivityofthelarge-scalebrainmodel.a,Adynamicmeanfield(DMF)reductionof themodel wasusedto studythe large-scalemodelof thebrain,composedofNnodes, eachcontaining oneexcitatoryand one inhibitory neural population. The inter-area connections are established as long range synaptic AMPA-mediated instan-taneous connections between the excitatory pools in those areas. In the case of the model with feedforward inhibition (FFI)long-rangesynaptic AMPA-mediated instantaneous connections from the excitatorypool of a givenarea to the inhibitorypool of

a different area were also considered (dashed arrows). Inter-areal connections are weighted by the strength specified in theneuroanatomical matrix SC, denoting the density of fibers between those regions, and scaled by a global factor G. The localrecurrentexcitationisNMDA-mediated.IntheFICcondition,thelocalfeedbackinhibition(J

i)wasadjustedsuchthattheexcitatory

pool of each local brain area has a low firing rate 3 Hz.b, Adjacency matrix of the neuroanatomical connectivity.c, Attractorlandscapeasafunctionoftheglobalcouplingstrength G,forthethreelarge-scalemodels,(EE:long-rangeexcitatoryexcitatoryconnections;FIC: long-range excitatoryexcitatoryconnections and local feedback inhibition regulation; FFI long-range excitatory

excitatoryconnections and long-rangefeedforwardinhibition).Each pointrepresents themaximum firing rateactivityamong allexcitatory pools.In theEE model,for lowvalues ofG, thenetworkconverges toa singlestable state;forG 1.47(verticalline),a bifurcationappears whereby a newunstable statecoexiststogetherwiththespontaneousstate. Inthe FICmodel,for G 4.45,the optimization of feedback inhibition weights makes the network to converge to a single stable state of low firing activity; for

G 4.45,the low firingactivitysolutionbecomes unstable.In the FFI modelthe maximum firingrate monotonically increasesas

afunctionofG.d,Thestationary-stateofexcitatorypools(firingratevectorofdimensionN66)isshownforG2.0forthethreelarge-scaleDMFmodels.Blue,FICmodel(stablestate);theinsetshowsthestationaryfiringratesasafunctionofthelocalfeedbackinhibitionstrength;red, EE model(stable state); red,open bars,EE model(unstablestate);magenta,FFI model(stable-state).



8/13

model FC and SC, and the similarity between the model FC andthe empirical FC, for each model (Fig. 3a,b; see Materials and

Methods). Importantly, note that, for a given G, the large-scaleunderlying connectivity (i.e., G SC) is the same for the threemodels, while the local connectivity is different for the FIC

model. We found that, in the EE, the underlying structural con-nectivity is maximally expressed in the simulated FC at the edgeof the critical value ofG(Fig. 3a, red trace). Similarly; the empir-ical FC is optimally fittedby themodelnear criticality(Fig.3b,redtrace). For the FFI model and for the network with FIC, theregion where the SC is maximally expressed by the simulated FCand where theempirical data are optimallyfitted is much broader

(Figs. 3a,b, blue and magenta traces). Furthermore, the level ofagreement between the model and the data reached at the maxi-mum is improved in the FIC case.

We further compared the FC of the two models for the corre-sponding optimal value ofG, equal to 1.3,4.7, and 3.3 for the EEmodel, the FFI model, and the FIC model, respectively (Fig. 3ce). The scatter plot between the model and the empirical correla-tion coefficients is closer to the identity line for the FIC modelthan for the two other models, as can be appreciated by linearregression of the data. The agreement between the model FC andthe empirical FC is significantly higher for the FIC model thanboth for the EE model (p 107 Mengsztest for dependentcorrelations (Mz-test) and for the FFI model (p 107, Mz-

test). We also tested the ability of each model to predict the FC ofindividual fMRI scanning sessions. For this we used the followingjackknife procedure: for each of then 48 scanning sessions wecalculated the FC and we computed the agreement between thesingle-session FC and the FC of each model for which G wasoptimized using the averaged FC over the remaining n 1 ses-sions. The procedure was repeated such that each scanning ses-sion was held out once. The resulting distributions of similarityvalues for each model are shown in Figure 3f. The FIC modelgives significantly better predictions of the single-session FC ma-trices than both the EE model and the FFI model (ANOVA, p107).

Moreover, we further quantified the agreement between thesimulated FC matrices and the empirical FC by comparing their

first principalcomponent (PC), or dominant spatial mode.Fora given covariance matrix, the dominant spatial mode is given bythe first eigenvector of the matrix. We calculated the vector pro-jection between the first PC of the empirical data and the first PCof the three models, calculated for the corresponding optimalvalues ofG, as previously (Fig. 4). We found that, under FIC, thenetwork approximates better the first PC of the empirical datathan do the EE model and the FFI model.

Altogether, the above results show that the quality of the op-timal fitting is better under the FIC condition compared with theunconstrained case. One could argue that the increase in the FCprediction for the FIC model is merely due to the optimization ofthe connection weights, which makes the model more complex

than the other two models. However, note that the parameters ofthe FIC model where optimized to bound the firing rate of eachnetwork node only and not in the optimization of the predictionof the empirical FC which uses only one free parameter ( G)asforthe other two models.

Correlation of linear noise fluctuations, ananalytical approximationThe reduction of the spiking network through dynamic meanfield approximation allowed investigating the large-scale modelunder the FIC condition. However, the nonlinear and stochasticnature of the DMF equations hinders analytical insights and ex-amination of the dynamics needs to be treated numerically. In

particular, estimation of second-order statistic of large networksrequires long and multiple time-consuming numerical simula-tions. In the following, we further reduce the dynamical system

Figure3. Model predictionof theempiricalfunctional connectivity.a, The similarity(corre-lationcoefficient)betweenthe empiricalanatomicalconnectivity(SC)matrix andthe modelFCwascalculated,asafunctionoftheglobalcouplingparameter G,forthethreedifferentmodels.In the E-E model, the highest correlation is achieved at the edge of the bifurcation (dashedverticalredline).Shadedareasrepresentthe95%confidenceintervalofthesimilaritymeasure.

b, Similarity (correlation coefficient) between the empirical fMRI FC and the model FC as afunction of the global coupling parameterG,for the three models. Shaded areas represent the95% confidence interval of the similarity measure. ce, Comparison between the empirical FCmatrix and the FC generated by each of the three models, EE (c), FIC (d), and FFI (e), for thecorresponding optimal valuesofG,equaltoG 1.3, G 3.3,and G 4.7,respectively. Solidlines indicate linear regressions. Ellipses are 95% confidence ellipses. r

cindicates the level of

similarity reach for each model.f, For each individual fMRI scanning session the FC was pre-dicted after optimization of the parameter Gusing the FC matrix averaged over the remaining47 scanning sessions. The distribution of similarity measures is presented for each of the threemodels. The mean similarity is significantly higher for the FIC model compared with the meansimilarity of models EE and FFI (ANOVA, *p 107).



9/13

by expressing it in terms of the first and second-order statistics,means and covariances, of thedistribution of gatingvariables andby deriving deterministic differential equations for thesestatistics(see Materials and Methods). Briefly, the moments equations forthe reduced nonlinear DMF are derived by Taylor expanding the

dynamical equations around the mean values of gating variablesand expressing motion equations for the covariances of the fluc-tuations around the means. This analytical simplification is es-

sential, because it provides an explicit link between structure,dynamics, and FC. Indeed, within this linear approximation, thecovariance matrix of spontaneous fluctuations is determined bythe eigenvalues of the Jacobian matrix (A) of the large-scale net-work, which in turn is related to the local and large-scale connec-tivity matrix and the dynamics (see Materials and Methods).Hence, because manipulating the feedback inhibition strength

within local networks changes the eigenvalues ofA, the correla-tion structure is modified, even though the firing rates of allmodel cortical areas remain constant. Using this linear approxi-mation, we calculated the similarity between the correlation ma-trix of excitatory gating variables, notedQ, and the empirical FCmatrix. Note that, in this case, the model correlations matrix isnot based on BOLD signals, but on the excitatory gating variableof all cortical areas. We found that the agreement betweenQandthe empirical FC is higher for the FIC model than for the othertwo models (Fig. 5a,b). Moreover, the empirical distribution ofcorrelation coefficients is better approximated by the FIC modelthan for the other two models(Fig. 5c,d).

Note that the decrease of the fitting of the empirical FC for

small values ofGobserved in simulations of BOLD signals (Fig.3b) is more pronounced that the one obtained using the linearprediction of Q (Fig. 5a). This discrepancy arises from the distri-bution of functional correlation coefficients rij. Indeed, if thevalues are narrowly distributed, as forGapproaching zero for allmodels(Fig. 5c), the precise estimation of the correlation struc-ture through stochastic simulations would require a large num-ber of simulation steps, so that the estimation error ofrijbecomesvery small compared with the variance of the distribution ofrij.Opposite to this, the analytic solution does not suffer from thesampling error and, thus, it correctly estimates the fine structureofQwith infinite resolution.

Furthermore, the linear approximation allows for an analyti-cal estimation of the time-scale of the gating variables fluctua-

tions. Since the hemodynamic model used to simulate the BOLDfMRI signal can be seen as a low-pass filterthat passes frequencies1 Hz(Robinson et al., 2006), only gating variables correlationsat slow time scales are transmitted through the hemodynamicmodel. We thus calculated the power spectrum of fluctuationsaround the spontaneous state, by taking the Fourier transform ofthe equation governing the time evolution of fluctuations (seeMaterials and Methods; Fig. 5e). Wefound that inthe FIC modelthe power of low-frequency (1 Hz) fluctuations is maintainedhigh for all values of G, whereas for the other two models slowfluctuations are expected for small values ofGonly.

Altogether, the linear approximation shows that the FICmodelbetter approximates the functional correlations and main-

tains the dynamics in a slow time-scale, so that the correlationstructure of gating variables is seen through the hemodynami-cally filtered response.

Feedback inhibition control increases the dynamicalrepertoire of the network evoked activityTo examine the functional implications of FIC, we analyzed theresponse of the model network to exogenous stimuli, which areassumed to represent ideal task-related signals. We simulated1000 different hypothetical task conditions by stimulating exog-enously 10% of the brain areas, randomly selected. Stimulationwas modeled by imposing an external input to the excitatorypools, i.e., for the set of stimulated excitatory pools we imposed

Iexternal 0.02. The increased excitatory activity induces anevoked pattern of activity at the stationary state. We first calcu-lated, for each model, the activity of cortical excitatory pool av-

Figure4. Prediction ofthe principalmode.The firstPC ofthe empiricalcovariancematrix ofBOLD signals (turquoise) and the first PC of the model covariance matrix generated by each ofthe three models, for the corresponding optimal values ofG. The projection (scalar product)between the first PC of the empirical data and the first PC of model data are equal to 0.57 0.05, 0.87 0.02, and 0.71 0.03 for the EE, FIC, and FFI models, respectively.



10/13

eraged over all stimuli, for the corresponding optimal values ofG(Fig. 6a). Interesting, in both the EE model and the FFI model,the activity is systematically much higher for some nodes,whether they are directly stimulated or not. These nodes are cen-tral nodes of the network, as revealed by their correspondingbetweenness centrality (Fig. 6b), a network measure that quanti-fies the number of shortest paths that pass through a given node.Note that, as previously shown (Hagmann et al., 2008), centralcortical areas are members of the default mode network(Fig. 6c).

We next characterized the information capacity of the large-scale model by quantifying the size of the repertoire of differentevoked patterns of both models. Indeed, a network that has few

degrees of freedom, i.e., few different evoked patterns, has a lowcapability to transmit information. We thus hypothesized thatthe networks without FIC, due to their tendency to elevated thefiring rate of central nodes in response to distinct stimuli, haveless information capacity. We quantify this by calculating theentropy Hevoked of binary evoked patterns (see Materials andMethods) to measure the extent of the repertoire of evoked ac-tivity. Binary patterns were constructed by imposing a thresholdand setting the steady-state evoked activity of a given area to 0 or1 whether it is below or above the threshold, respectively. Thethresholdwas defined as.SD, where SD is thestandarddeviationacross all possible evoked responses of each model. Several valuesof the multiplierwere tested. For each of the three large-scale

models, we compared the entropy of evoked patterns to the max-imum entropy by computingthe reductionof entropy, defined asH (Hmax Hevoked)/Hmax, where the maximum entropy

Hmaxis equal to log2(n) for a set ofnpos-sible binary patterns. Values ofHcloseto 0 indicate that the network has a largerepertoire size, close to themaximum rep-ertoire size, while values near 1 indicate alimited repertoire size. We found that, un-der FIC, the model has more entropy than

the two other models (Fig. 6d), and,hence,it hasa largerinformationcapacity.The same result is obtained when stimuliare imposed to both theexcitatory and theinhibitory population of the cortical areas(Fig. 6e).

Feedback inhibition control increasesthe accuracy of the externalstimulus encodingAt last, we further asses the sensibility to ex-ternal stimuli of thelarge-scalenetwork.Forthis, wecalculatedthe FI,which gives an up-

per bound to the accuracy that any popula-tion code can achieve (Abbott and Dayan,1999). The FI takes into account the changeof both themeanactivityandthe covariancewith respect to a smallvariation of thestim-ulus strengthto quantify theabilityforstim-ulus discrimination (see Materials andMethods). Here, a visual stimulus wasmodeled by imposing an equal external in-put to both the right and the leftLOCC.Weused the moments equations to preciselyestimate the evoked stationary mean andcovariance for varying stimulus intensity.The FI was calculated for each of the large-

scale models (Fig. 6f), where G wassettothecorresponding optimal value for each model. We found that theregulation of feedback inhibition increases the FI, thus in-creasing the accuracy of the stimulus encoding. Relaxing theFIC condition leads to a decrease of the FI because the centralnodes are systematically activated in response to the stimulus,thus saturating the network response, although the FIC pro-vides a graded response of the stimulated nodes with practi-cally no activation of the other nodes (Fig. 6g).

DiscussionIn this study, we investigated the impact of the local FIC on alarge-scale model of the brain. We found several important and

functionally relevant effects of the local FIC on both the sponta-neous andthe evokedpatternsof activity of thelarge-scalemodel.First, we showed that the FIC significantly enhances the modelsprediction of the fMRI human resting functional connectivity,even for single fMRI scanning sessions. Furthermore, we foundthat the optimal parameter space where the model best approxi-mates the empirical FC is enlarged in the FIC condition. This isimportant since a common result of all previous resting-statemodelsis that theoptimal parameter space is confined at theedgeof criticality(Honey et al., 2007, 2009; Ghosh et al., 2008; Deco etal., 2009, 2013a,b; Deco andHughes, 2012) posingthe problem offine tuning for which self-organization rules remain unknown.Opposite to this, it has been shown that inhibitory synapses can

rapidly adapt to changes in the local network activity to scale theactivity in cortical circuits (Hartmann et al., 2008), thus provid-inga natural implementation of theFIC by biological synapses.In

Figure5. Linearfluctuations.a,Similarity(correlationcoefficient)betweentheempiricalBOLDFCandthecorrelationstructureofgatingvariablesasobtainedbythemomentsmethod,forthethreemodels.Shadedareasrepresentthe95%confidenceintervalof the similarity measure. In the FIC case, the same local feedback inhibition weights (J

i) used inFigure 2a,bwere used here.b,

Comparison of the maximum similarity between the empirical BOLD FC and the correlation structure of gating variables for thethreemodels. c, Correlationcoefficients of all pairwise correlationsbetweenexcitatorygating variables of the 66 cortical areasasafunctionoftheglobalcouplingG,forthethreemodels.Top,TheredlineindicatesthebifurcationoftheEEmodel.d,Inverseofthe KullbackLeiblerdivergence(D

KL) between the empirical distributionof correlation coefficients and the distributionof corre-

lation coefficients between gating variables for each model. e, Mean power spectrum of the excitatory gating variables as afunction of the global couplingG, for the three different models. Top, The white line indicates the bifurcation of the EE model.



11/13

this view the local FIC may provide a homeostatic mechanismthat generates the observed resting-state FC. Nevertheless, in thepresent studywe have regulatedthe inhibitory-to-excitatorycou-pling, but manipulating other local weights to adjust the ratiobetween excitation and inhibition in the large-scale model maylead to similar results and would provide a local decorrelationmechanism, providing that excitation and inhibition balanceeach other(Renart et al., 2010).

Nevertheless, note that the agreementbetween themodels FCand the empirical FC is not perfect. This imperfect fitting is ex-pected principally due to the missed of connections of the diffu-sion tensor/spectrum imaging (DTI/DSI) tractography, usedhere to estimate the anatomical connectivity that constrains the

large-scale connectivity of the model. Indeed, precise predictionof the FC strongly depends on the quality of the estimated struc-tural connectivity. However, interhemispherical connections arenot well captured by the DTI/DSI tractography (Hagmann et al.,2008) and the anatomical matrix used here did not include sub-cortical routes that are known to play an important role in shap-ing the spontaneous activity of the brain(Robinson et al., 2001;Freyer et al., 2011). Estimation of subcortical connections is achallenging issue because DTI systematically leads to more con-nections for proximal regions than distal ones, and thus, subcor-tical structures are particularly subject to this bias (Jones, 2008).Moreover, neural structure is different in the cortex and subcor-tical nuclei, for example, the thalamus is composed of GABAergic

interneurons in the reticular nucleus of the thalamus andthalamocortical relay neurons in relay nuclei, for which relativenumber of neurons is unknown (Izhikevich and Edelman, 2008),

and thus, how both the cortex and the subcortical nuclei can bedescribed in a parsimonious model is an open question.

In addition, we have made several simplifying assumptions thatmay impose an upper bound to the agreement between the modelpredictionsandtheempirical observations. Specifically, in thisstudywe consider that all connections between brain areas are instanta-neous, thus neglecting the effects of conduction delays which arelikely to shape thebrain dynamics, giving riseto complexspatiotem-poral patterns, oscillations, multistability, and chaos(Roxin et al.,2005;Ghosh et al., 2008;Deco et al., 2009). Indeed, a recent MEGstudy found robust frequency-specific laggedcoherence betweenin-terhemispheric functional connections in the dorsal attention net-work, or between the dorsal attention and other networks (e.g.,

visual and somatomotor; Marzetti et al., 2013). Considering the de-lays wouldmakemore complex themodel andadd a newparameterto explore: the propagation velocity.

In this work, we assumed that functional connectivity is astationary process that arises from the interplay between the un-derlying anatomical connectivity structure and the neural dy-namics on the stationary regime. This assumption is commonlymade by the current resting-state models that seek to link thestructural and the functional connectivity (Honey et al., 2007,2009;Ghosh et al., 2008;Deco et al., 2009,2013a,b;Deco andHughes, 2012). However, recent studies have demonstrated thatthe correlations among brain regions evolve over time (Changand Glover, 2010;Kiviniemi et al., 2011;de Pasquale et al., 2012;

Hutchison et al., 2013;Allen et al., 2014). Because nonstationari-ties are likely to substantially contribute to the resting-state activ-ity (Messe et al., 2014), it is thus crucial to analyze and model the

Figure6. Theeffectof FICon theevokedactivityof thelarge-scale brainmodel.a, Mean activityin each localbrainarea(withrespectto theactivity averagedoverall brainareas) foreachmodelobtained in response to 1000 different hypothetical task conditions. Tasks were simulated by imposing an external inputIexternal 0.02 to the excitatory population of 10% of the brain areas,randomlyselected.Darkcolorsindicatetheareascomposingthedefaultmodenetwork.b,Betweennesscentrality(BC)ofeachbrainarea.BCwascalculatedfromtheanatomicalconnectivitymatrix.Itrepresentsthenumberofshortestpathspassingthroughagivennode. c,Thedefaultmodenetworkiscomposedofmidlinefrontalandparietalareas,posteriorinferiorparietallobule,andmedialand lateral temporal lobe regions.d, The entropyHevokedof evoked binary patterns was calculated for different activity thresholds, defined as .SD, were SD is the standard deviation across allpossible evoked responses.Bars indicate thereductionof entropyH, forthe threedifferentmodels,for differentvaluesof( 2.5,3,or4).HwasdefinedasH (Hmax Hevoked)/Hmax,where Hmax isthe maximum entropyfor thesetofn patterns,i.e., Hmax log2(n). Error barsindicate estimationerrors (50%)given by the quadratic extrapolation procedure, usedfor theentropy

sampling bias correction.e, Entropyreductionwhenexternalstimuli areimposedto both theexcitatory andtheinhibitory populations.The valuesofarelowerthanin(d) to avoid patternswithnullentries. f, Theencoding accuracyof themodels wascalculatedusingtheFI. TheFI wascalculatedfor various stimulusintensities(I).The stimulus wasapplied tothe excitatory population ofbothrightandleftLOCC;i.e.,IexternalIforrLOCCandlLOCC, and Iexternal 0 forall othercorticalareas.g, Evokedresponseof thenetworkfor theEE model(top), theFFImodel(middle), andfor the FIC model (bottom). The colors indicate the intensity (I) of the applied stimulus. The arrows indicate the stimulated nodes.



12/13

time-varying behavior of the functional connectivity. How non-stationary functional connectivity emerges in the brain networkremains an open question that needs further investigation.

In thepresent study,we assumed that thespontaneousactivitythroughout the cortex is low. This is supported by early record-ings of cortical activityin vivo (Burns andWebb,1976; Softky andKoch, 1993;Wilson et al., 1994), as well as recent experiments in

mammalian neocortex using diverse recording techniques, suchas whole-cell patch-clamp, sharp-electrode recordings andCa2-imaging, in different brain states (awake or under anesthe-sia), indicating that the spontaneous activity of pyramidal neu-rons in sensory cortices ranges between 15 Hz, with furtherlaminar differences (Sakata and Harris, 2012; for review, seeBarth and Poulet, 2012). Nevertheless, more investigation com-paring the spontaneous activity of different sensory and associa-tion cortices is needed.

By studying the large-scale patterns evokedby external inputs,we showed that, if the FIC constraint is relaxed, external stimu-lation of the brain model leads to a systematic large activation ofcortical areas that are components of the default mode network.

This is unlikely to occur in the real brain, because only few exper-imental conditions leading to activation of the default mode net-work have been reported. Indeed, a myriad of reports shows thatthe default network is deactivated during attentionally demand-ing and goal-directed tasks (Shulman et al., 1997;Raichle et al.,2001;Fox and Raichle, 2007;Thomason et al., 2008;Christoff etal., 2009). Nevertheless, the default mode network is activated bycognitive processes that are internally driven, such as, memory re-trieval (Sestieri et al., 2011), internal mentation (Mason et al., 2007;Bar, 2009), and self-reference (Gusnard and Raichle, 2001;DArgembeau et al., 2005). However, these internal processes aremore likely to be initiated spontaneously, possibly due to spontane-ousfluctuations in thecortex, as recently proposed in thecontext of

self-initiated movements (Schurger et al., 2012), and thus, they maynot be well modeled by imposing external inputs to some corticalareas. Altogether, we believethatthe systematic activation of corticalareas belonging to thedefaultmode network,observed in theevokedresponses of the brain models without FIC, is not consistent eitherwith current experimental data or with current assumptions aboutthe generation of internal mental states. Here we showed that regu-lating the local level of feedback inhibition in the brain has an im-portant role at the global level, because it attenuates the response ofcortical areas in the default mode network.

A further effect of local FIC on large-scale brain patterns is toincrease the entropy of the evoked activity patterns, thus increasingthe dynamic repertoire of the network. Hence, the local FIC en-

hances the information capacity of the global network, i.e., it in-creases the ability of the network to map different inputs intodistinguishable network outputs. This result complements previ-ously reported evidence showing that neural systems tend to maxi-mize the entropy at the level of single neurons (Tsubo et al., 2012)and neural populations (Shew et al., 2011). It has been shown thatwhen excitation is sufficiently restrained by inhibition in local corti-calnetworks, theinformationcapacityof cortical circuits is increased(Shew et al., 2011; Deco and Hughes, 2012). Furthermore, weshowedthatregulation of thefeedbackinhibition enhancesthe stim-ulus discriminability, i.e., it increases thesensitivity of thenetworktoa smallvariation of thestimulus.Hence, our results indicatethat thecontrol of theexcitationinhibition ratio at thelocal level hasimpor-

tant implications for information transmission at the large-scalebrain level. Moreover, because the feedback inhibition acts as anactive mechanism for reducing pairwise correlations in local net-

works(Tetzlaff et al., 2012;Fig. 1), it improves the encoding andreadout within local circuits.

In summary, we had identified several effects of local regula-tion of feedback inhibition on brain dynamics at the large scale: itchanges the characteristics of the emergent resting and evokedactivity in a crucial way. Regulating the local excitationinhibi-tion ratio provides a better and more robust prediction of human

empirical resting state connectivity, together with more realisticresponses to external inputs and higher information capacity andencoding accuracy.

ReferencesAbbott LF, Dayan P (1999) The effect of correlated variability on the accu-

racy of a population code. Neural Comput 11:91101.CrossRefMedlineAchard S, Salvador R, Whitcher B, Suckling J, Bullmore E (2006) A resilient,

low-frequency, small-world human brain functional network with highlyconnected association cortical hubs. J Neurosci 26:6372. CrossRefMedline

Allen EA, Damaraju E, Plis SM, Erhardt EB, Eichele T, Calhoun VD (2014)Tracking whole-brain connectivity dynamics in the resting state. CerebCortex 24:663676.CrossRefMedline

Bar M (2009) The proactive brain: memory for predictions. Philos Trans RSoc Lond B Biol Sci 364:12351243.CrossRefMedline

Barth AL, Poulet JF (2012) Experimental evidence for sparse firing in theneocortex. Trends Neurosci 35:345355.CrossRefMedline

Bassett DS, Meyer-Lindenberg A, Achard S, Duke T, Bullmore E (2006)Adaptive reconfiguration of fractal small-world human brain functionalnetworks. Proc Natl Acad Sci U S A 103:1951819523.CrossRefMedline

Biswal B, Yetkin FZ, Haughton VM, Hyde JS (1995) Functional connectiv-ity in the motor cortex of resting human brain using echo-planar MRI.Magn Reson Med 34:537541.CrossRefMedline

Brookes MJ, Woolrich M, Luckhoo H, Price D, Hale JR, Stephenson MC,Barnes GR, Smith SM, Morris PG (2011) Investigating the electrophys-iological basis of resting state networks using magnetoencephalography.Proc Natl Acad Sci U S A 108:1678316788.CrossRefMedline

Burns BD, Webb AC (1976) Thespontaneous activity of neurons inthe catscerebral cortex. Proc R Soc Lond Biol 194:211223.CrossRefMedline

Chang C, Glover GH (2010) Time-frequency dynamics of resting-state

brain connectivity measured with fMRI. Neuroimage 50:8198. CrossRefMedline

Christoff K, Gordon AM, Smallwood J, Smith R, Schooler JW (2009) Expe-rience sampling during fMRI reveals default network and executive sys-tem contributions to mind wandering. Proc Natl Acad Sci U S A 106:87198724.CrossRefMedline

DArgembeau A, Collette F, Van der Linden M, Laureys S, Del Fiore G, Deg-ueldre C, Luxen A, Salmon E (2005) Self-referential reflective activityand its relationship with rest: a PET study. Neuroimage 25:616624.CrossRefMedline

Deco G, Hugues E (2012) Balanced input allows optimal encoding in a sto-chastic binary neural network model: an analytical study. PLoS ONE7:e30723.CrossRefMedline

DecoG, Jirsa VK (2012) Ongoingcorticalactivity at rest: criticality,multistabil-ity, and ghost attractors. J Neurosci 32:33663375. CrossRefMedline

Deco G, Jirsa V, McIntosh AR, Sporns O, Kotter R (2009) Key role of cou-pling, delay, and noise in resting brain fluctuations. Proc Natl Acad SciU S A 106:1030210307.CrossRefMedline

Deco G, Ponce-Alvarez A, Mantini D, Romani GL, Hagmann P, Corbetta M(2013a) Resting-state functional connectivity emerges from structurallyand dynamically shaped slow linear fluctuations. J Neurosci 33:1123911252.CrossRefMedline

Deco G, Jirsa VK, McIntosh AR (2013b) Resting brains never rest: compu-tational insights into potential cognitive architectures. Trends Neurosci36:268274.CrossRefMedline

de Pasquale F, Della Penna S, Snyder AZ, Marzetti L, Pizzella V, Romani GL,Corbetta M (2012) A cortical core fordynamic integration of functionalnetworks in the resting human brain. Neuron 74:753764. CrossRefMedline

Doucet G, Naveau M, Petit L, Delcroix N, Zago L, Crivello F, Jobard G,Tzourio-Mazoyer N, Mazoyer B, Mellet E, Joliot M (2011) Brain activity

at rest: a multiscale hierarchical functional organization. J Neurophysiol105:27532763.CrossRefMedline

Ecker AS, Berens P, Keliris GA, Bethge M, Logothetis NK, Tolias AS (2010)

http://dx.doi.org/10.1162/089976699300016827http://www.ncbi.nlm.nih.gov/pubmed/9950724http://dx.doi.org/10.1523/JNEUROSCI.3874-05.2006http://www.ncbi.nlm.nih.gov/pubmed/16399673http://dx.doi.org/10.1093/cercor/bhs352http://www.ncbi.nlm.nih.gov/pubmed/23146964http://dx.doi.org/10.1098/rstb.2008.0310http://www.ncbi.nlm.nih.gov/pubmed/19528004http://dx.doi.org/10.1016/j.tins.2012.03.008http://www.ncbi.nlm.nih.gov/pubmed/22579264http://dx.doi.org/10.1073/pnas.0606005103http://www.ncbi.nlm.nih.gov/pubmed/17159150http://dx.doi.org/10.1002/mrm.1910340409http://www.ncbi.nlm.nih.gov/pubmed/8524021http://dx.doi.org/10.1073/pnas.1112685108http://www.ncbi.nlm.nih.gov/pubmed/21930901http://dx.doi.org/10.1098/rspb.1976.0074http://www.ncbi.nlm.nih.gov/pubmed/11486http://dx.doi.org/10.1016/j.neuroimage.2009.12.011http://www.ncbi.nlm.nih.gov/pubmed/20006716http://dx.doi.org/10.1073/pnas.0900234106http://www.ncbi.nlm.nih.gov/pubmed/19433790http://dx.doi.org/10.1016/j.neuroimage.2004.11.048http://www.ncbi.nlm.nih.gov/pubmed/15784441http://dx.doi.org/10.1371/journal.pone.0030723http://www.ncbi.nlm.nih.gov/pubmed/22359550http://dx.doi.org/10.1523/JNEUROSCI.2523-11.2012http://www.ncbi.nlm.nih.gov/pubmed/22399758http://dx.doi.org/10.1073/pnas.0901831106http://www.ncbi.nlm.nih.gov/pubmed/19497858http://dx.doi.org/10.1523/JNEUROSCI.1091-13.2013http://www.ncbi.nlm.nih.gov/pubmed/23825427http://dx.doi.org/10.1016/j.tins.2013.03.001http://www.ncbi.nlm.nih.gov/pubmed/23561718http://dx.doi.org/10.1016/j.neuron.2012.03.031http://www.ncbi.nlm.nih.gov/pubmed/22632732http://dx.doi.org/10.1152/jn.00895.2010http://www.ncbi.nlm.nih.gov/pubmed/21430278http://www.ncbi.nlm.nih.gov/pubmed/21430278http://dx.doi.org/10.1152/jn.00895.2010http://www.ncbi.nlm.nih.gov/pubmed/22632732http://dx.doi.org/10.1016/j.neuron.2012.03.031http://www.ncbi.nlm.nih.gov/pubmed/23561718http://dx.doi.org/10.1016/j.tins.2013.03.001http://www.ncbi.nlm.nih.gov/pubmed/23825427http://dx.doi.org/10.1523/JNEUROSCI.1091-13.2013http://www.ncbi.nlm.nih.gov/pubmed/19497858http://dx.doi.org/10.1073/pnas.0901831106http://www.ncbi.nlm.nih.gov/pubmed/22399758http://dx.doi.org/10.1523/JNEUROSCI.2523-11.2012http://www.ncbi.nlm.nih.gov/pubmed/22359550http://dx.doi.org/10.1371/journal.pone.0030723http://www.ncbi.nlm.nih.gov/pubmed/15784441http://dx.doi.org/10.1016/j.neuroimage.2004.11.048http://www.ncbi.nlm.nih.gov/pubmed/19433790http://dx.doi.org/10.1073/pnas.0900234106http://www.ncbi.nlm.nih.gov/pubmed/20006716http://dx.doi.org/10.1016/j.neuroimage.2009.12.011http://www.ncbi.nlm.nih.gov/pubmed/11486http://dx.doi.org/10.1098/rspb.1976.0074http://www.ncbi.nlm.nih.gov/pubmed/21930901http://dx.doi.org/10.1073/pnas.1112685108http://www.ncbi.nlm.nih.gov/pubmed/8524021http://dx.doi.org/10.1002/mrm.1910340409http://www.ncbi.nlm.nih.gov/pubmed/17159150http://dx.doi.org/10.1073/pnas.0606005103http://www.ncbi.nlm.nih.gov/pubmed/22579264http://dx.doi.org/10.1016/j.tins.2012.03.008http://www.ncbi.nlm.nih.gov/pubmed/19528004http://dx.doi.org/10.1098/rstb.2008.0310http://www.ncbi.nlm.nih.gov/pubmed/23146964http://dx.doi.org/10.1093/cercor/bhs352http://www.ncbi.nlm.nih.gov/pubmed/16399673http://dx.doi.org/10.1523/JNEUROSCI.3874-05.2006http://www.ncbi.nlm.nih.gov/pubmed/9950724http://dx.doi.org/10.1162/089976699300016827


13/13

Decorrelated neuronal firing in cortical microcircuits. Science 327:584587.CrossRefMedline

Fox MD, Raichle ME (2007) Spontaneous fluctuations in brain activity ob-served with functional magnetic resonance imaging. Nat Rev Neurosci8:700711.CrossRefMedline

Fransson P (2005) Spontaneous low-frequency BOLD signal fluctuations:an fMRI investigation of the resting-state default mode of brain functionhypothesis. Hum Brain Mapp 26:1529.CrossRefMedline

Freyer F, Roberts JA, Becker R, Robinson PA, Ritter P, Breakspear M (2011)Biophysical mechanisms of multistability in resting-state corticalrhythms. J Neurosci 31:63536361.CrossRefMedline

Friston KJ, Harrison L, Penny W (2003) Dynamic causal modelling. Neuro-image 19:12731302.CrossRefMedline

Ghosh A, Rho Y, McIntosh AR, Kotter R, Jirsa VK (2008) Noise during restenables the exploration of the brains dynamic repertoire. PLoS ComputBiol 4:e1000196.CrossRefMedline

Greicius MD, Krasnow B, Reiss AL,MenonV (2003) Functional connectiv-ityin the resting brain:a network analysis of thedefault mode hypothesis.Proc Natl Acad Sci U S A 100:253258. CrossRefMedline

Gusnard DA, Raichle ME (2001) Searching for a baseline: functional imag-ing and the resting human brain. Nat Rev Neurosci 2:685694. CrossRefMedline

Hacker CD, Laumann TO, Szrama NP, Baldassarre A, Snyder AZ, LeuthardtEC, Corbetta M (2013) Resting state network estimation in individual

subjects. Neuroimage 82:616633.CrossRefMedlineHagmann P, Cammoun L, Gigandet X, Meuli R, Honey CJ, Wedeen VJ,

Sporns O (2008) Mapping the structural core of human cerebral cortex.PLoS Biol 6:e159.CrossRefMedline

Hartmann K, Bruehl C, Golovko T, Draguhn A (2008) Fast homeostaticplasticity of inhibition via activity-dependent vesicular filling. PLoS ONE3:e2979.CrossRefMedline

Honey CJ, Kotter R, Breakspear M, Sporns O (2007) Network structure ofcerebral cortex shapes functional connectivity on multiple time scales.Proc Natl Acad Sci U S A 104:1024010245.CrossRefMedline

HoneyCJ, SpornsO, Cammoun L,GigandetX, ThiranJP,MeuliR, HagmannP (2009) Predicting human resting-state functional connectivity fromstructural connectivity. Proc Natl Acad Sci U S A 106:20352040.CrossRefMedline

Hutchison RM, Womelsdorf T, Gati JS, Everling S, Menon RS (2013)

Resting-state networks show dynamic functional connectivity in awakehumans and anesthetized macaques. Hum Brain Mapp 34:21542177.CrossRefMedline

Izhikevich EM, Edelman GM (2008) Large-scale model of mammalianthalamocortical systems. Proc Natl Acad Sci U S A 105:35933598.CrossRefMedline

Jones DK (2008) Studying connections in the living human brain with dif-fusion MRI. Cortex 44:936952.CrossRefMedline

Kiviniemi V, Vire T, Remes J, Elseoud AA, Starck T, Tervonen O, Nikkinen J(2011) A sliding time-window ICA reveals spatial variability of the de-fault mode network in time. Brain Connectivity 1:339347. CrossRefMedline

Liu Z, Fukunaga M, de Zwart JA, Duyn JH (2010) Large-scale spontaneousfluctuations and correlations in brain electrical activity observed withmagnetoencephalography. Neuroimage 51:102111.CrossRefMedline

Luckhoo H, Hale JR, Stokes MG, Nobre AC, Morris PG, Brookes MJ, Wool-rich MW (2012) Inferring task-related networks using independentcomponent analysis in magnetoencephalography. Neuroimage 62:530541.CrossRefMedline

Mantini D, Perrucci MG, Del Gratta C, Romani GL, Corbetta M (2007)Electrophysiological signatures of resting state networks in the humanbrain. Proc Natl Acad Sci U S A 104:1317013175.CrossRefMedline

Mantini D, Corbetta M, Romani GL, Orban GA, Vanduffel W (2013) Evo-lutionarily novel functional networks in the human brain? J Neurosci33:32593275.CrossRefMedline

MarzettiL, DellaPenna S, Snyder AZ,Pizzella V,NolteG, dePasqualeF, RomaniGL,Corbetta M (2013) Frequency specificinteractions ofMEGresting stateactivity within and across brain networks as revealed by the multivariateinteraction measure. Neuroimage 79:172183. CrossRefMedline

Mason MF, Norton MI, Van Horn JD, Wegner DM, Grafton ST, Macrae CN(2007) Wandering minds: the default network and stimulus-

independent thought. Science 315:393395.CrossRefMedlineMesse A, Rudrauf D, Benali H, Marrelec G (2014) Relating structure and

function in the human brain: relative contributions of anatomy, station-

ary dynamics, and non-stationarities. PLoS Comput Biol 10:e1003530.CrossRefMedline

Power JD, Cohen AL, Nelson SM, Wig GS, Barnes KA, Church JA, Vogel AC,

Laumann TO, Miezin FM, Schlaggar BL, Petersen SE (2011) Functionalnetwork organization of the human brain. Neuron 72:665678. CrossRefMedline

Raichle ME, MacLeod AM, Snyder AZ, Powers WJ, Gusnard DA, Shulman

GL (2001) A default mode of brain function. Proc Natl Acad Sci U S A98:676682.CrossRefMedlineRenart A, de la Rocha J, Bartho P, Hollender L, Parga N, Reyes A, Harris KD

(2010) The asynchronous state in cortical circuits. Science 327:587590.CrossRefMedline

Robinson PA, Rennie CJ, Wright JJ, Bahramali H, Gordon E, Rowe DL(2001) Prediction of electroencephalographic spectra from neurophysi-

ology. Phys Rev E Stat Nonlin Soft Matter Phys 63:021903. CrossRefMedline

Robinson PA, Drysdale PM, Van der Merwe H, Kyriakou E, Rigozzi MK,

Germanoska B, Rennie CJ (2006) BOLD responses to stimuli: depen-dence on frequency, stimulus form, amplitude, and repetition rate. Neu-roimage 31:585599.CrossRefMedline

Roxin A, BrunelN, HanselD (2005) Role of delaysin shaping spatiotempo-

ral dynamics of neuronal activity in large networks. Phys Rev Lett 94:238103.CrossRefMedline

Sakata S, Harris KD (2012) Laminar-dependent effects of cortical state on

auditory cortical spontaneous activity. Front Neural Circuits 6:109.CrossRefMedline

Schurger A, Sitt JD, Dehaene S (2012) An accumulatormodelfor spontane-

ous neural activity pr

Deco, G., Et. Al. (2014) How Local Excitation–Inhibition Ratio Impacts the Whole Brain Dynamics

Documents

Transcript of Deco, G., Et. Al. (2014) How Local Excitation–Inhibition Ratio Impacts the Whole Brain Dynamics