Using the Virtual Brain to Reveal the Role of Oscillations ... · PDF fileDipanjan Roy,1,2...

ORIGINAL ARTICLE

Using the Virtual Brain to Reveal the Role of Oscillationsand Plasticity in Shaping Brain’s Dynamical Landscape

Dipanjan Roy,1,2 Rodrigo Sigala,1,2 Michael Breakspear,3–5 Anthony Randal McIntosh,6

Viktor K. Jirsa,7 Gustavo Deco,8 and Petra Ritter1,2,9,10

Abstract

Spontaneous brain activity, that is, activity in the absence of controlled stimulus input or an explicit active task, istopologically organized in multiple functional networks (FNs) maintaining a high degree of coherence. These ‘‘rest-ing state networks’’ are constrained by the underlying anatomical connectivity between brain areas. They are alsoinfluenced by the history of task-related activation. The precise rules that link plastic changes and ongoing dynamicsof resting-state functional connectivity (rs-FC) remain unclear. Using the framework of the open source neuroinfor-matics platform ‘‘The Virtual Brain,’’ we identify potential computational mechanisms that alter the dynamical land-scape, leading to reconfigurations of FNs. Using a spiking neuron model, we first demonstrate that network activityin the absence of plasticity is characterized by irregular oscillations between low-amplitude asynchronous states andhigh-amplitude synchronous states. We then demonstrate the capability of spike-timing-dependent plasticity (STDP)combined with intrinsic alpha (8–12 Hz) oscillations to efficiently influence learning. Further, we show how alpha-state-dependent STDP alters the local area dynamics from an irregular to a highly periodic alpha-like state. This isan important finding, as the cortical input from the thalamus is at the rate of alpha. We demonstrate how resultingrhythmic cortical output in this frequency range acts as a neuronal tuner and, hence, leads to synchronization or de-synchronization between brain areas. Finally, we demonstrate that locally restricted structural connectivity changesinfluence local as well as global dynamics and lead to altered rs-FC.

Key words: STDP; plasticity; resting state; alpha rhythm; network dynamics; The Virtual Brain; whole brainsimulations

Introduction

Structure and function

One of the major open questions in neuroscience isthe relationship between structure and function. Several

spatiotemporal features of resting-state functional connectiv-ity (rs-FC) have been captured by existing modeling ap-proaches (Deco et al., 2011, 2013b). A systematic frameworkfor relating structural connectivity (SC) and functional con-nectivity (FC) has been recently provided by The VirtualBrain (TVB), a simulation platform of large-scale brain ac-tivity (Ritter et al., 2013; Sanz et al., 2013). There is a lack

of mechanistic understanding of changes of network statesdue to learning/plasticity (Sigala et al., 2014). This article ex-plores how to describe learning and plasticity-relatedchanges of FC with biophysically plausible brain models.With learning and plasticity, we refer to training/exposure-related changes of SC at all spatial brain scales and the result-ing functional consequences. Computational insights gaineddue to structural modifications will add to our understandingof the structure-function relationship provided by previouscomputational studies (Alstott et al., 2009; Cabral et al.,2012a, 2012b). A key ingredient of our model is the structuralbrain network defined by empirically derived long-range

1Department of Neurology, Charite—University Medicine, Berlin, Germany.2Bernstein Focus State Dependencies of Learning & Bernstein Center for Computational Neuroscience, Berlin, Germany.3Division of Mental Health Research, Queensland Institute of Medical Research, Brisbane, QLD, Australia.4School of Psychiatry, University of New South Wales and The Black Dog Institute, Sydney, NSW, Australia.5The Royal Brisbane and Woman’s Hospital, Brisbane, QLD, Australia.6Rotman Research Institute of Baycrest Centre, University of Toronto, Toronto, Canada.7Institut de Neurosciences des Systemes UMR INSERM 1106, Aix-Marseille Universite Faculte de Medecine, Marseille, France.8Center for Brain and Cognition, Universitat Pompeu Fabra, ICREA (Institut Catala Recerca i Estudis Avancats), Barcelona, Spain.9Minerva Research Group BrainModes, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany.

10Berlin School of Mind and Brain & Mind and Brain Institute, Humboldt University, Berlin, Germany.

BRAIN CONNECTIVITYVolume XX, Number XX, 2014ª Mary Ann Liebert, Inc.DOI: 10.1089/brain.2014.0252

1

brain connectivity between regions, resulting in biologicallyplausible conduction delays. We use a subset of cortical re-gions represented as nodes in the large-scale brain network.The nodes are dynamical units built of highly interconnectedexcitatory and inhibitory neurons. The interaction betweenthose regions in the network needs to be uncovered to under-stand the origin of correlated activity fluctuations in the brainduring resting-state and task conditions. Here, we evaluateexisting modeling approaches and advance them by incorpo-rating state-dependent local plasticity mechanisms. Specifi-cally, we explore how subcortical input to a cortical regionshapes the local SC at a microscopic scale. Subsequently,we investigate the interaction with other cortical regionsconnected via the realistic anatomical connectivity matrix.Using computational and analytical methods, we show howinput oscillations in the alpha (8–12 Hz) frequency rangealong with plasticity parameters (plasticity time constant,input oscillation frequency) critically influence transitionfrom asynchronous to synchronous state in a local neuronalpopulation. Local oscillations, in turn, reshape evolution of co-variance on a longer time scale across a subset of anatomicallyconnected cortical regions. We evaluate theoretical scenarios,how brain states in terms of slow power fluctuation of the localfield potential’s (LFP) alpha frequency band influence localplasticity. Restructuring of cortical node level synapticweights due to spike-timing-dependent plasticity (STDP) re-sults in learning phases of firing. In other words, the neuronslearn to elicit output population spikes at specific phases ofinput background oscillations. We find that spatiotemporallow frequency fluctuations ( < 0.1 Hz) of the simulated sig-nal—similar to those observed in blood oxygenation level-de-pendent (BOLD) functional magnetic resonance imaging(fMRI) signals during rest—are significantly shaped not onlyby given anatomical connectivity but also by ongoing synapticplasticity within cortical regions. Combining brain states andplasticity provides a general theoretical framework for alter-ations of rs-FC, which reflects ongoing network dynamicsand, hence, predicts the outcome of behavioral performance.

Plasticity shapes rs-FC

Typical large-scale interactions between brain areas areconcerned with neural assemblies that are farther apart inthe brain ( > 1 cm) with transmission delays in the order of8–10 msec spanning poly-synapses (Varela et al., 2001).Resting-state networks (RSN) arise from coordinated distrib-uted functional clusters. They give rise to coherent neural ac-tivity as a signature of large-scale brain operations in theabsence of an explicit task or stimuli (Fox and Raichle,2007; Smith et al., 2009). RSNs resemble both task-relatedfunctional networks (FNs) (Biswal et al., 1995; Fox andRaichle, 2007; Vincent et al., 2007) and anatomical networks,that is, regions directly connected via anatomical pathways(Honey et al., 2009). Recent studies have shown that corticalactivation can restructure resting-state activity after task per-formance (Lewis et al., 2009; Riedl et al., 2011; Tambiniet al., 2010; Urner et al., 2013; Zhang et al., 2012). Finally,evidence suggests that perceptual learning modifies thelarge-scale functional covariance between networks engagedin a task (Cole et al., 2012; Lewis et al., 2009). In line withthis, only 30 min of repetitive sensory stimulation (RSS)(Freyer et al., 2012a)—a paradigm known to induce neural

plasticity and counteracting sensory decline due to neurolog-ical trauma or aging (Kalisch et al., 2008, 2010)—leads tosignificant changes of the time-lagged coherence in resting-state alpha rhythm within sensorimotor cortical areas (Freyeret al., 2012a). While learning alters resting-state activity, thisactivity also influences the ability to learn. A recent electro-encephalography (EEG) study on perceptual learning showedthat high resting-state alpha power contralateral to the stimu-lated finger is predictive for a greater behavioral improve-ment after RSS at an inter-subject level (Freyer et al.,2013). These findings provide evidence that the restingbrain is not a passive sensory-motor analyzer driven by sen-sory inputs. Rather, it actively generates predictions aboutforthcoming sensory stimuli by maintaining a structuredmemory of past activations that finds expression in the ongo-ing brain states. Here, we explore the effects of the interplayof RSS-induced plasticity and ongoing brain states in thealpha frequency range as a mechanism that could provide ex-planation for the corresponding change in FC between so-matosensory and motor cortex connected via realistic SC.

Computational modeling

To understand the mechanisms underlying the complex in-teraction at the neuronal population level during rest andunder task-based conditions, brain imaging as well as compu-tational models play complementary roles. Brain imagingmonitors cognitive states in the whole brain network at a mac-roscopic scale. For example, in fMRI, a cortical voxel de-scribes the population activity of a few million neurons.Computational models provide potential underlying mecha-nisms of interaction between neuronal populations that giverise to the observed spatiotemporal dynamics of BOLD orEEG activity. This is realized by representing functional clus-ters of neurons by mean field or neural mass models. Meanfield or neural mass models attempt to model the dynamicsof large (theoretically infinite) populations of neurons.Numerous recent resting-state modeling studies (Cabralet al., 2011; Deco et al., 2013a, 2013c) successfully recon-structed empirically observed RSNs between clusters, patternsof positive and negative correlations as described in many ex-perimental studies by looking at the interplay between localnetwork dynamics and large-scale structure of the brain. Inprinciple, global FC can be altered within milliseconds by per-turbation, while the large-scale SC matrix remains fixed orunder natural conditions changes only over longer time periodsthrough plasticity processes. However, on a microscopic scale,synaptic dynamics and connectivity are altered within milli-seconds (Caporale and Dan, 2008). Emergent FC dependson the dynamics of individual nodes, which are shaped bythe local and global neuronal context. In the framework ofTVB, this is accounted for by allowing for inputs from mul-tiple connected regions to individual sub-cortical or corticalregions. Key signatures of emergent network dynamics areneuronal oscillations that can be detected by non-invasivebrain imaging methods such as EEG.

Overview of the study

In the first section, we discuss ongoing activity at rest andunderlying dynamics using two types of models: a spikingmodel (Deco and Jirsa, 2012), a mean field firing ratemodel derived from the spiking model (Deco and Jirsa,

2 ROY ET AL.

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2012; Deco et al., 2014). All are capable of generating a sim-ilar bifurcation structure. The dynamic mean field (DMF)model and the spiking model are capable of generating a sim-ilar bifurcation structure as shown qualitatively in Figure 2D.This is relevant, as empirical work shows multistable behav-ior in resting-state brain dynamics (Freyer et al. 2009).

In the second section, we introduce time-dependent inputfrom the thalamus to the cortical neuron model equippedwith STDP. In the local brain area—that is somatosensory cor-tex in our model—synaptic plasticity results in learning tospike at input phases of oscillations in the feed-forward net-work between the thalamus and somatosensory cortex. More-over, when STDP is combined with an oscillation in theexternal input current, STDP acts robustly to detect andlearn repeating patterns. It has been previously demonstratedin single neurons that theoretically ongoing oscillations mayfacilitate information decoding using a principle known asphase-of-firing coding (PoFC) (Masquelier et al., 2009). Here,we extend this finding by implementing STDP and PoFCin a neuronal population model with anatomically derivedcortical connectivity between brain regions. There, STDPcombined with rhythmic input synchronizes the spike outputof the local spiking network model. The local node activityon a longer time scale yields periodic firing patterns in thealpha band range that exhibit local (within node) synchrony.

Finally, we carry out simulations by connecting a subset ofdistributed cortical areas in both right and left hemisphereswith synaptic plasticity implemented in the somatosensorycortical area. We use a small realistic SC matrix customizedfor our simulations comprising the thalamus, somatosensoryS1, and motor M1 areas of both hemispheres. We investigatethe organization of FC on a time scale of 60 sec. These sim-ulations provide a candidate framework to explore global co-herence between areas under structural modifications.

Ongoing Oscillatory Activity and DynamicalLandscape at Rest

RSNs have been interpreted as the ‘‘ground state’’ of cogni-tive architecture (Deco et al., 2013c). In Table 1, we summarizenetwork models that address the underlying neurodynamicalmechanisms of RSN features as observed in fMRI, EEG, andmagnetencephalography (MEG) (Cabral et al., 2011; Deco andJirsa, 2012; Deco et al., 2013c; Freyer et al., 2011, 2012b;Ghosh et al., 2008a,b; Honey et al., 2007, 2009; Ritter et al.,2013). We list those mean field models that exhibit eitherfixed-point attractor or oscillatory or chaotic dynamics. Figure1 summarizes the basic ingredients required to build up a re-alistic large-scale model of the cortex as done in TVB [for de-tails, see Ritter and coworkers (2013)]. The main ingredientsare a large-scale SC matrix determining connections betweenbrain areas in terms of their distance and strength and a choiceof cortical node models; for example, oscillatory (Cabral et al.,2011; Ghosh et al., 2008a), chaotic (Honey et al., 2009), andnon-oscillatory (Deco and Jirsa et al., 2012). Ghosh et al.(2008a) proposed a stochastic mechanism to underlie the rest-ing-state fluctuations via a careful optimization of the operat-ing point close to criticality, that is, at the edge of dynamicinstability. This mechanism has been adopted in many ofthe network models (Deco and Jirsa, 2012; Deco et al., 2013c).

Single brain area spiking model

We introduce a network of integrate-and-fire (IF) spikingneurons with excitatory (a-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid [AMPA] receptors, N-methyl-D-aspartate[NMDA] receptors) and inhibitory populations with gamma-aminobutyric acid (GABA) receptor types. This spiking neu-ron model is similar to the one used in Brunel and Wang(2001) and Deco and Jirsa (2012). Each cortical region is

FIG. 1. External input as well aslocal and global context shape on-going brain dynamics. In the VirtualBrain (TVB) framework, we useinformed structural connectivity(SC) (orange box) combined withlocal models described as nodes A,B, C, and D, respectively. TVBprovides the choice of definingspecific node dynamics using spik-ing attractor dynamics, firing ratedynamics, or oscillator models. Thelocal models receive external time-varying input reflecting externalstimuli, e.g. noisy input, externalconstant current input, local inputfrom adjacent neural populations,and a global contextual input fromdistant populations. There are vari-ous ways to parametrically modu-late the input received by anindividual node; for example, bymodifying SC, the local networkconnectivity (local scaling factor),long distance connectivity (globalcoupling scaling factor), and exter-nal input. Color images availableonline at www.liebertpub.com/brain

4 ROY ET AL.

modeled as a fully recurrently connected network comprisingNE excitatory neurons and NI inhibitory neurons (Table 2). Wedescribe the dynamical evolution of a single neuron’s mem-brane potential V(t) that is driven by incoming total excitatoryand inhibitory inputs of the same cortical area and the long-range excitatory input from directly connected brain areas.Hence, the time evolution of the membrane potential for an ar-bitrary neuron i obeys the following differential equation:

Cm

dVi(t)

dt= IL� Iext

AMPA� Ii, syn

IL = � gm(V(t)�VL) (1)

where gm is the membrane leak conductance, Cm is the mem-brane capacitance, and VL is the resting potential; membranetime constant is defined as sm = Cm

gm.

Isyn is the synaptic current and comprises AMPA currents,NMDA currents, and GABA-A currents as defined next. Thespike is transmitted to other neurons, and the membrane po-tential is instantaneously reset to Vreset and further main-tained there until a refractory period is reached sref duringwhich neurons are unable to produce further spikes.

FIG. 2. Resting-state dynamical landscape. Figure adapted and modified from Freyer and coworkers (2012b). (A) Dynam-ical instability in the form of a subcritical Hopf bifurcation and the emergence of steady states. The system exhibits bistabilityas a function of the control parameter driven by nonlinearities present in the state variables. (B) First derivatives or slopes ofthe state variables showing the corresponding inflection points on the displayed curve, that is, maxima and minima of steadystate solutions. In the bistable scenario depicted with a green solid line, the system exhibits double well potential form withtwo prominent bumps. (C) Noise-driven exploration of possible solutions. Three different ongoing dynamics are observed:subthreshold fluctuations around low firing steady state followed by a multistable attractor landscape (coexistence of low andhigh firing rate fluctuations) and subsequently transitions to high amplitude firing rate dynamics via change of the stateparameter global coupling strength. (D) The state variable ‘‘population-firing rate’’ is a function of the state parameter globalcoupling strength. Two stable solutions on either side of the bifurcation points are visible. One is the low amplitude asyn-chronous stable spontaneous solution, and the other is the high amplitude unstable spontaneous dynamics. In between, theresting-state spontaneous activity reflects a multi-stable attractor landscape and exhibits structure fluctuations as shown(C, middle). Color images available online at www.liebertpub.com/brain

Table 2. Neurons, Connections, and Synaptic

Parameters in Each Local Brain Area

Excitatoryneurons

Inhibitoryneurons Synapses

NE 400 NI 100 VE 0 mVCm 0.5 nF Cm 0.2 nF VI �70 mVVthershold �50 mV Vthershold �50 mV sAMPA,e. 5 msec

Vreset �55 mV Vreset �55 mV sAMPA,r. 5 msecgm 25 nS gm 20 nS sNMDA,r 2 msecVL �70 mV VL �70 mV sNMDA,g 100 msecgAMPA,ext 3.18 nS gAMPA,ext 2.08 nS sGABA 10 msecgAMPA,rec 0.104 nS gAMPA,rec 0.081 nS k 0.062gAMPA,rec 0.327 nS gAMPA,rec 0.307 nS b 0.5 kHzgGABA 4.575 nS gGABA 3.514 nS kNMDA 0.28

Plasticity parameters rhythmic input frequencyA + 0.019 f = 10 HzA� 0.010s + 20 msecs- 20 msec

PLASTICITY SHAPES FUNCTIONAL CONNECTIVITY AND DYNAMICS 5

Postsynaptic excitatory potentials are generated on the targetneuron mediated via the conductance-based model specified bysynaptic receptors, namely: glutamatergic AMPA external ex-citatory currents, AMPA, NMDA recurrent excitatory currents,and GABAergic recurrent inhibitory currents. The respectivesynaptic conduct gAMPA,ext, gAMPA,rec, gNMDA,rec and gGABA,rec,VE, V1 are excitatory and inhibitory reversal potentials, respec-tively. Each one of the current excitatory feed-forward inputcurrents, recurrent excitatory as well as inhibitory synaptic cur-rents are described next:

IextAMPA(t) = gAMPA, ext(Vi(t)�VE) +

Next

j = 1

s AMPA, extj (t)

Iisyn(t) = gAMPA, rec(Vi(t)�VE) +

NE

j = 1

wijsAMPA, recj (t)

þ gNMDA(Vi(t)�VE)

(1þ kNMDAe� kVi(t))+NE

j = 1

wijsNMDA, recj (t)

þ gGABA(Vi(t)�VI) +NI

j = 1

wijsGABA, recj (t) ð2Þ

Dimensionless parameters wij are the synaptic weights of re-current all-to-all connectivity between excitatory and inhibitoryneurons in each local brain area. By modifying these weights,one can either up- or down regulate the four local connectivitystrength parameters (wEE, wEI, wIE, wII). Unless otherwise spec-ified, synaptic weights of the local recurrent connectivity areheld at fixed values throughout our simulation of models. Therecurrent self-excitation wEE = W+ = 1.4 and the remainingthree synaptic weights are wEI = wIE = wII = 1, respectively.

The fraction of open channels of neurons are given by thekinetics of the gating variables sI

j modeled as

dsIj (t)

dt= �

sIj

sI

þ +p

d(t� tpj ), for I = AMPA or GABA (3)

NMDA channels are represented by a separate decay andrise-time kinetics. The sums over index p represent all the spikesemitted by presynaptic neuron j at times t

pj �sAMPA and sGABA

represent the decay times for AMPA and GABA synapses.sNMDA,rise and sNMDA,decay are the rise and decay time constantsfor the NMDA synapses in the model. The NMDA currents arevoltage dependent, and they are modulated via intracellularmagnesium concentrations that are defined as x NMDA

j (t)

ds NMDAj

dt= �

s NMDAj (t)

sNMDA, decay

þ bx NMDAj (t)(1� s NMDA

j (t))

dx NMDAj (t)

dt= �

x NMDAj (t)

sNMDA, rise

þ +p

d(t� tpj ): (4)

In addition, all neurons in the network receive an AMPA-mediated external background current derived from a Pois-son process of uncorrelated spikes with time-varying firingrate f k

ext(t) governed by a simple Brownian process given by

df kext

dt=

( f kext(t)� f0)

sn

þ rf

ffiffiffiffiffi2

sn

rdW(t) (5)

where sn = 30 msec, baseline firing rate = 2.18 kHz (back-ground). Local and global connectivity parameters are givenin Table 2. Parameter values in Table 2 are modified from Bru-nel and Wang (2001)—where the network balance is shifted

more toward an inhibitory regime—to incorporate local balanceof excitatory and inhibitory synaptic currents as shown in Decoand Jirsa (2012), Albantakis and Deco (2011), and Deco and co-workers (2013c, 2014). Parameters for the single cortical areaneuronal synapse model are summarized in Table 2. One ofthe key motivations for the choice of single area parametersas shown in Table 2 was to keep the uncoupled local area net-work to fire asynchronously at around 3–4 Hz, which closely re-sembles the biological range of spontaneous firing activity givenin any isolated cortical region (Haider et al., 2006). Hence, thisasynchronous spontaneous firing rate is maintained at about 3–4 Hz when isolated from the global network and in the absenceof plasticity and brain state-dependent feed-forward drive. Thistype of local balance of excitation and inhibition in local corticalnetworks is sufficient to achieve oscillations in the desired fre-quency range, maximal synchrony and criticality in the rest-ing-state dynamics (Poil et al., 2012). The balance (localexcitation-inhibition ratio) impacts the spontaneous and evokedlarge-scale brain dynamics (Deco et al., 2014).

Single brain area represented by a DMF model

To model the RSN dynamics and prediction of empirical func-tional connectivity at the macroscopic level, Deco and coworkers(2013b, 2014) proposed a large-scale DMF model derived fromthe spiking model described earlier. As shown in Deco and as-sociates (2014), the reduced DMF model consistently expressesthe time evolution of the ensemble activity of the different ex-citatory and inhibitory neural populations building up the spik-ing network. In the DMF approach, each population’s firing ratedepends on the input currents into that population. The inputcurrents, in turn, depend on the cortical pool population firingrates. The populations firing rate can be determined by a re-duced system of coupled nonlinear differential equations thatare driven by the respective input currents. The large-scalemodel connects these local sub-networks according to the SCmatrix defined by the anatomical connections between thosebrain areas in the human, as obtained by diffusion spectrumimaging (DSI) and described earlier. The inter-area connectionsare established as long-range excitatory synaptic connections ei-ther exclusively between excitatory pools of different areas orboth between excitatory pools as well as excitatory pools and in-hibitory pools of different areas. Inter-areal connections areweighted by the strength specified in the SC matrix, denotingthe density of fibers between those regions and by the state pa-rameter global coupling strength G. When each cortical area isembedded in a large-scale network, their global brain dynamicsare governed by the following sets of coupled stochastic nonlin-ear differential equations for the excitatory pool and the inhibi-tory pool, respectively:

dEexcn

dt= � Eexc

n

sexc

þ (1�Eexcn )crexc

n þ rvn(t),

dEinhn

dt= � Einh

n

sinh

þ rinhn þrvn(t),

rTn = HT (IT

n ) =aT (IT

n )� bT

1� exp (� dT (aT ITn � bT ))

T = exc, inh

Iexcn = Iext þW þ JNMDAEexc

n þGJNMDA +j

CnjEexcj � JnEinh

n

Iinhn = JNMDAEexc

n �Einhn (6)

6 ROY ET AL.

In Eq. (6), rTn describes the excitatory and inhibitory pop-

ulation firing rate in each cortical region. Eexcn , Einh

n describethe average excitatory and inhibitory synaptic strength ineach local area n. Iexc

n , Iinhn represent the input currents to

the excitatory and inhibitory population, respectively. Iext

is the external drive to the cortical neurons. W + = 1.4 repre-sents the self-excitatory recurrent synaptic strength as in thespiking model. Cnj is the SC matrix that connects individualbrain areas, where n and j are two arbitrary brain areas. Inthis model, only excitatory-excitatory long-range connec-tions are taken into account; hence, global coupling strengthappears only in the first equation of (7) for the description ofthe excitatory population firing rates. Neuronal input-outputrelationship is expressed as sigmoidal and denoted as H(T)

n ,

where T = exc,inh pools, respectively, in each cortical regionn. This function converts incoming inputs to firing rates. Addi-tional paramters are the excitatory recurrent coupling strengthJNMDA = 0.15(nA), the kinetic parameters c = 0.0641/1000,sexc = 100ms, sinh = 10ms, and the local feedback inhibitorycoupling Jn = 1. Other parameters that are specific to calcula-tion of input currents are as follows:

aexc = 310(nC� 1), bexc = 125(Hz), dexc = 0:16(s)

ainh = 615(nC� 1), binh = 177(Hz), dinh = 0:087(s)

In order to obtain maximum excitatory firing rate, theglobal coupling strength is varied as a free parameter. The re-sult is displayed in Figure 2D. Simulation of the global modelwith a range of low global coupling strength G = [0.0 – 0.5]shows spontaneous population activity with an excitatorymean firing rate of 3–4 Hz, which is what we have obtainedfor the global spiking model by varying the global couplingstrength parameter. At even higher values of G = [1.5 – 4.0]both low and high population firing rates co-exist as steady-state solutions. For coupling above G > 4.0, fixed point attrac-tors destabilize and the system enters into a regime coincidingwith a high mean excitatory population firing rate. This isshown for both the spiking model and the DMF model sepa-rately to visualize their dynamical transition properties with arange of control parameters. The critical values for phase tran-sition are shown in Figure 2C and D as well as in Figure 8.

Numerical procedure

The local pool represented by a cortical spiking IF modelwhen uncoupled from the global network is simulated usingPython 2.7, scipy, and numpy. Resting-state spontaneous ac-tivity and the mean firing rate of each cortical module areobtained using a numerical integration procedure in the Ccode environment. STDP in local cortical areas is imple-mented using an exponential STDP class as implementedin Brian, a spiking network simulator, version 1.4. Time-frequency domain analysis is carried out on the LFP-like ac-tivity from cortical pools using the custom-made MATLABcode. BOLD signals are simulated using hemodynamic re-sponse function, and covariance between relevant brainareas is estimated using custom-made MATLAB scripts.DMF model with fully connected brain areas is simulatedusing custom-made MATLAB scripts that are availablefrom the open source computational models database http://senselab.med.yale.edu/ModelDB. In the near future, we willincorporate relevant parts of our script in TVB as well.

Alteration of Dynamic Landscape Due to LocallyRestricted Plasticity

In principle, it is possible to implement plasticity in bothspiking and DMF models while taking advantage of a mech-anism such as the balance of excitatory and inhibitory cur-rents as recently proposed by Deco and coworkers (2014).This mechanism can be introduced in the DMF to clip thelocal area asynchronous firing rate to 3–4 Hz. Plasticity cru-cially depends on neurons with a similarly timed activity.Hence, in this study, we are more focused on the presynap-tic-postsynaptic spike timing difference and the role offeed-forward input oscillations for the spiking of the outputneurons at the precise phases of the input oscillations.Hence, amplification of network firing rates can be realizedvia appropriate modifications of spike timing in a meanfield rate model setting. For the investigation of various ef-fects of plasticity, we chose a spiking neuron model with abiophysically realistic attractor network. This attractor net-work as shown in Eqs. (1–5) is a dynamical system withan intrinsic tendency to settle in stationary states—alsocalled ‘‘attractors.’’ Attractors are typically characterizedby stable patterns of firing (Fig. 2). Individual neurons aremodeled as IF spiking neurons with biologically realistic ex-citatory (AMPA and NMDA) and inhibitory (GABA-A) syn-aptic receptor types. Realistic description of the synapses andnonlinear dependency of the synaptic current on the excit-atory currents received from other neurons allow for includ-ing STDP. However, integrating the full spiking model iscomputationally expensive. This makes the exploration ofthe parameter space to find the parametric conditions match-ing the experimental findings a challenge. We know fromempirical data that learning alters the rs-FC by restructuringconnections employing Hebbian-like rules (Freyer et al.,2012a; Harmelech et al., 2013). We aim here to reproducesimilar effects with a large-scale model implementing localSTDP. The implementation of local plasticity at the nodelevel is motivated from several relevant studies of microcir-cuit modeling (Morrison et al., 2007; Vogels et al., 2011).The implication for decoding of afferents in readout neuronalassemblies has been recently demonstrated, in studies thatcombine the PoFC and STDP mechanisms (Deco et al.,2011; Masquelier et al., 2009). It still remains an open ques-tion how these mechanisms may influence learning-relatedchanges in distant brain areas. Recently, STDP was intro-duced in hierarchically modular realistic brain networkscomprising leaky IF neurons (Rubinov et al., 2011) to inves-tigate emergent criticality in spontaneous network dynamics.In this study, authors have found that STDP enabled a phasetransition from random subcritical dynamics to ordered su-percritical dynamics, hence broadening the parameter regimein which balanced criticality reigns. We here go beyond thiswork by (1) exploring the role of ongoing states for STDP-related local reorganization and (2) illuminating the spatial(global) effects that evolve from local plastic changes andresulting altered dynamic repertoire at the node level.

Implementing STDP and PoFC in a spike model

In this section, we test the hypothesis that background os-cillations alter capability for plasticity in a connected net-work of cortical neurons. We build a spike model withSTDP, where the cortical layer receives about 1000 thalamic


afferent external inputs mediated via conductance-based ex-citatory AMPA synapses (Fig. 3). In the present spike model,node level dynamics is asynchronous with a firing rate of3–4 Hz in the absence of an oscillatory input—as shown inFigure 4. In addition, cortical populations receive a periodicmodulation of feed-forward thalamic input spikes generatedat a rate of the alpha frequency (8–12 Hz). Put differently, af-ferent spike output from thalamus to cortex is modulated viaa sinusoid as shown in Figure 3D. As a consequence, firingrates of the inputs change on a timescale highly relevant toSTDP. Thalamic input spike trains are approximated as acontinuous sinusoid. Randomness in the thalamic spikephases is introduced via a Poisson process. About 1000 tha-lamic spike trains drive a cortical node represented by IFneurons. Plasticity introduced between thalamic input layerand cortex induces a systematic change in the local microcir-cuit on a short time scale of milliseconds. This is carried outby systematic potentiation and depression of local cortico-thalamic excitatory synaptic weights wtc and altering recur-rent connectivity between excitatory neurons (Figs. 4 and5). In the spiking model, the recurrent self-excitation withineach excitatory population is given by the weight wEE = W +

and recurrent all-to-all connectivity between excitatory-inhibitory population is given by the weights wEI = wIE =wII = 1 and further described in detail in the spiking modelsection. We include plasticity in the local AMPA receptor-

mediated excitatory-excitatory synapses between thalamusand cortical area S1 neurons with synaptic weight wtc be-tween thalamus and cortex. Recurrent self-excitation isused as a fixed parameter in the node model with and withoutplasticity (Deco and Jirsa, 2012). In this model, thalamocort-ical feed-forward synaptic weight changes in the excitatorysynapses due to plasticity serve as a critical control parame-ter. We assume that local excitatory synapses between pyra-midal cells have at least two distinct conductance states dueto plasticity: a high conductance state resulting from longterm potentiation (LTP) of AMPA receptors at the postsyn-aptic site as described by Eq. (4), and conversely a low con-ductance state due to long term depression (LTD) of AMPAreceptors (Brunel, 2003). Transitions from a low conductanceto a high conductance state can be mediated by Hebbian plas-ticity, that is, selective potentiation and depression of synapses(Brunel, 2003; Mikkelsen et al., 2013). In our work, LTP/LTDwindowing functions are based on those proposed by Songet al. (2000). LTP/LTD can be elicited by activatingNMDA-type glutamate receptors, typically by the coincidentactivity of pre- and postsynaptic neurons. The windowingfunctions describe the time window when consequences ofthe near-coincidence of pre- and postsynaptic neuronal activitytake place. Figure 3 illustrates a model combining oscillatoryinput patterns with cortical spiking IF neurons equipped withlocal STDP. The local neural population comprising excitatory

FIG. 3. Interplay between rhythmic input and spike-timing dependent plasticity (STDP) modulates learning at the node level.(A) One thousand periodically modulated Poisson-process spike inputs to a neural population model. (B) Population modelcomprising excitatory neurons (red) and inhibitory neurons (green). For simplicity, a few neurons are shown. Recurrent weightsare indicated by blue arrows, and self-connections are indicated by yellow arrows. (C) The STDP kernel proposed for our workis a piecewise exponential function of pre- and postsynaptic spike times (tpost� tpre) based on (Song et al., 2000); s+ and s� arethe STDP time constants for long term potentiation (LTP) and long term depression (LTD) (LTP/LTD). A + and A� are themaximal changes for synaptic weights as a function of maximum weight updates denoted as wmax. (D) Weight change as a func-tion of output spike phase. A late phase spike receives a net potentiation, and conversely an early phase spike receives net de-pression. The fixed point of this system is shown with a red dot. If the spike phase is at the fixed point of this system, no netupdate in weights occurs. Color images available online at www.liebertpub.com/brain

8 ROY ET AL.

FIG. 4. Learning with STDP in a local population S1 cortical integrate-and-fire (IF) neuron model with feed-forward os-cillatory thalamic drive at alpha frequency around 10 Hz. A primary somatosensory cortical network neuron group is simu-lated for a total duration of 12 sec. STDP is turned on after about 2000 msec of simulation time (shown with a red marker). Forclarity, 1800–2400 msec of cortical output activity are shown. Intrinsic network parameters are the same as shown in Table 2.(A) Raster plot of population spikes from 100 cortical neurons. Before 2000 msec, when STDP is off, cortical output exhibitsasynchronous spiking activity independent of the phase of oscillations of thalamic input drive. When STDP is turned on after2000 msec, cortical neurons start exhibiting a precise phase of firing (1:1 phase locking—a criterion that is used in this studyfor learning in local population spikes) with silence corresponding to phasic inhibition. (B) Simulated thalamic oscillatorydrive (green) approximated as a sinusoid is plotted for the entire duration. Here, those spike times are shaded with a graybox, where 1:1 phase locking (learning in output populations) for all neuron IDs in S1 population is observed. (C) Simulatedpostsynaptic membrane potential is shown before and after STDP (18–2400 msec), which is in concordance with the popu-lation response, that is, before STDP membrane potential oscillates due to oscillatory feed-forward thalamic input; however,membrane potential reaches a threshold of �20 mV once in every cycle (no phase preference at all). After STDP (after2000 msec), postsynaptic membrane response is strongly modulated via the input phase. Membrane potential reaches athreshold only when there is potentiation due to phase matching of spikes at the peak of the input oscillation cycle. (C) Exci-tatory synaptic conductance (in blue), inhibitory synaptic conductance (green) are shown. Effect of phasic inhibition isstrongly present in the temporal response of conductance. Before STDP, excitatory conductance is typically higher thanthe inhibitory conductance due to the feed-forward excitatory drive, resulting in a number of spikes at arbitrary spiketimes as displayed in the spike raster plot (A). After STDP, excitatory and inhibitory conductance shows strong phase mod-ulation. Potentiation leads to a homeostatic balance between excitatory-inhibitory conductance, leading to phase locking ofspikes as shown in the raster plot. However, depotentiation of thalamocortical weight leads to lowering of the excitatory drivereceived by the cortical neurons and resulting in strong lateral inhibition as shown in green (between 2000–2400 msec) andsilencing of cortical output as shown in the raster plot (A). Color images available online at www.liebertpub.com/brain


and inhibitory spiking neuron populations receives rhythmicspike inputs from multiple neurons—1000 input neurons areshown in Figure 3A. Figure 3C illustrates how Hebbian plastic-ity is realized through STDP and depends on the relative timingof pre-and postsynaptic spikes. In addition, here we employ aprecise relationship between phase of the background oscilla-tions and the spike phase of output neurons. This is schemati-cally illustrated in Figure 3D. If the phase of the backgroundoscillations, that is, phase of oscillatory LFP activity, and thespike phase, that is, phase of oscillatory postsynaptic spikes(phase delay A� or advance A+ ) matches, then the synaptic re-current excitatory weights are updated via a linear additive ruleas proposed by Song et al. (2000) shown in Figure 3D. STDPexploits this precise relationship between LFP to spike phaseand has previously been successfully employed as a parsimoni-ous learning mechanism to demonstrate stable phase locking ina feed-forward network model (Muller et al., 2011). The synap-tic AMPA kinetics is governed by the following equations:

ds AMPA, extj

dt= �

s AMPA, extj

sexc

þ +p

d(t� tpj )

IextAMPA(t) = gAMPA, ext(Vi(t)�VE) +

Next

j = 1

wtc, ijsAMPA, extj (t) (7)

Input connections to the IF neuron are mediated by expo-nential synapses with excitatory-excitatory corticothalamicsynaptic weights wtc without delays. When a presynapticspike occurs, the excitatory synaptic weight is incrementedby an amount w. The STDP rule is implemented with all-to-all spike pairings (Song et al., 2000). The synaptic weightsare restricted to a range between 0 and wmax. For a given spike

pairing with temporal difference x (spike time window), thesynapse between the pre- and postsynaptic neurons is modi-fied according to wtc = w + f(x)wmax. Thus, the value of theSTDP window is given by a piecewise exponential functionf(x) for a given temporal difference x between pre- and post-synaptic spike times. Further, relative spike times determinethe percentage of wmax added to the feed-forward corticotha-lamic synaptic weights wtc. In our simulation, when a presyn-aptic spike occurs in the input, the fraction of open AMPA

receptor channels is updated as s AMPA, extj /s AMPA, ext

j þwtc.

Since we study a plastic system with intrinsic stability inthe coupling between STDP and oscillations, it is not neces-sary to include a stabilizing mechanism in the STDP rule, pro-vided that the learning rate A + is a reasonable value. We firstassume an STDP rule with linear, all-to-all spike pairings.After previous theoretical work on STDP (Carroll et al.,2014; Kilpatrick and Bressloff, 2010; Song et al., 2000), weformulate the STDP rule as a piecewise exponential function:

f (x) = Aþ e� x

sþ , x > 0

A� e�x

s� , x < 0

�(8)

where x is defined as the difference in pre- and postsynapticspike times (tpost � tpre), s + and s� are the STDP time con-stants for potentiation and de-potentiation, A + is the amountof potentiation for an optimally potentiating pre-post pairing,and A� is the same for a de-potentiating post-pre pairing. Theratio of de-potentiation to potentiation (A�s�/A +s + ) will betermed the STDP ratio. For the case of identical time con-stants considered here, we write (A�/A + ). The value of thefunction f(x) determines the percent change for a synapticweight on a given pairing, relative to wmax. Each of the

FIG. 5. Alteration of thalamus-S1 synaptic weights (coupling strength) due to STDP, with and without brain state depend-ent input. Here, for clarity, only 100 excitatory presynaptic thalamic inputs are shown. (A) Connectivity changes betweenexcitatory pre- and postsynaptic neuron pairs for the case of STDP applied for 10 seconds in the absence of rhythmicinput. Synaptic weights are normalized between 0 and 1. Depressed synapses are color coded in blue (weight = 0) and con-versely potentiated synapses are color-coded in red (weight = 1). (B) Connectivity changes between neuron pairs are shownfor the combination of rhythmic input and STDP. Without rhythmic input, effectively, there are no input patterns to learn,hence, almost all excitatory synaptic weights are close to 1. With rhythmic modulation of the rate of thalamic presynapticinput afferent spikes, structural connectivity gets modified between thalamus and primary somatosensory cortex S1 as dis-played in the layout of connectivity between pre- and postsynaptic neurons. Local clustering shapes the output dynamics ofthe postsynaptic population, i.e. here of S1. Color images available online at www.liebertpub.com/brain

10 ROY ET AL.

input neurons in Figure 3 is modeled as an oscillating inho-mogeneous Poisson process. In Figure 3A, we show 1000 pe-riodically modulated Poisson process spike inputs. Thenumber of inputs is chosen as a compromise between biolog-ical realism and computational feasibility. Inputs are fed tothe IF neuron by exponential, current-based synapses witha 5-ms decay time constant. As shown in the scheme in Fig-ure 3D, recurrent weights are potentiated and depresseddepending on the phase of the background oscillation. By de-fault, the local node model is in a balanced Ex/Inh regime forintrinsic network parameter combinations characterized bylow-amplitude asynchronous firing activity. When input os-cillations are in the alpha frequency range yielding themost prominent spontaneous oscillations of the humanbrain, the presynaptic firing rate changes on a time scale rel-evant for the STDP time window Dt = 0 to 5 msec (Babadiand Abbott, 2013; Caporale and Dan, 2008). A defining fea-ture of STDP is very high temporal asymmetry (Guetig et al.,2003). When a presynaptic spike precedes the postsynapticspike in time, then the synapse between the two is potentiated(pre-post pairing); while in the converse scenario, the syn-apse between the two is depressed (post-pre pairing). The in-terplay between thalamic input in the presence of oscillationsand STDP is illustrated with a simulation of a node modelrepresenting primary somatosensory cortical area S1 com-posed of 100 excitatory neurons and 25 inhibitory IF spikingneurons. The node model is simulated for a total duration of12 sec. STDP is turned on after 2000 msec of simulationtime. The network runs for another 10 sec. In Figure 4, forclarity, the simulation results for cortical output neuronsare shown for the time period 1800 to 2400 msec. Intrinsicnetwork parameters are the same as displayed in Table 2.In Figure 4A, a raster plot of population spikes from 100 cor-tical excitatory neurons is shown. Before 2000 msec, corticaloutput exhibits asynchronous spiking activity even in thepresence of oscillations in the thalamic input. When STDPis turned on after 2000 msec, cortical neurons start exhibitinga precise phase of firing, that is, phase locking, followed bytransient events of silence that corresponds to phasic inhibi-tion. If the output spike occurs at the trough of the input os-cillation cycle, that is, ‘‘early,’’ it leads to de-potentiation inthe cortico-thalamic synaptic weights wtc in accordancewith phase-dependent STDP. In contrast, when the spike oc-curs at the peak of input oscillation cycle, that is, ‘‘late,’’ thisleads to net potentiation in the cortico-thalamic synapticweights (Fig. 3). In Figure 4B, the simulated postsynapticmembrane potential is shown both before and after STDP.Before STDP, the membrane potential oscillates due to oscil-latory feed-forward thalamic input. The membrane potentialreaches the threshold of �20 mV once in every cycle.There is no phase preference. After STDP, that is, after2000 msec, the postsynaptic membrane potential is modu-lated by the input phase. The membrane potential reachesthe threshold only when there is potentiation due to phasematching of spikes at the peak of the input oscillationcycle. In Figure 4C, excitatory synaptic conductance (blue)and inhibitory synaptic conductance (green) are shown. Theeffect of phasic inhibition is strongly present in the temporaldynamics of both conductance types. Before STDP, excit-atory conductance is typically higher than the inhibitory con-ductance due to the feed-forward excitatory drive, resulting ina number of spikes at arbitrary times as shown in the popula-

tion raster plot between 1800 and 2000 msec. After STDP, ex-citatory conductance as well as inhibitory conductanceexhibits strong phase modulation. Potentiation in this sce-nario leads to a homeostatic balance between excitatory-in-hibitory conductance, leading to phase locking of spikes asshown in the raster plot. However, depression in corticothala-mic synaptic weights leads to lowering of the excitatory drivereceived by the cortical neurons and thus resulting in a strongcortical, that is, recurrent or lateral inhibition dominating theexcitatory conductance as shown in green (between 2000 and2400 msec). As a consequence, silencing takes place in corti-cal output neurons at those time points as shown in the rasterplot in Figure 4A. An increase in phase locking of spikes tothe background input oscillatory phase (LFP-spike precisephase coupling) after STDP paves way for learning in thelocal node model that, in turn, plays a crucial role in influenc-ing network dynamics in the globally connected nodes.

Next, we investigate how systematic potentiation and de-pression of local excitatory synaptic weights wtc may modifylocal connectivity between pre- and postsynaptic neuronpairs in a node model in the presence and absence ofbrain-state dependent input. To address this, we accesslocal cortical SC by calculating synaptic weights in the pres-ence and absence of rhythmic input and STDP (Fig. 5). Ini-tially, presynaptic and postsynaptic neurons are connected inan all-to-all fashion. Hence, all synaptic weights are 1. With-out rhythmicity in the input, that is, if STDP is random,weight changes between pre-post are also random andshow up in the result (Fig. 5A). This is intuitively correct,as plasticity in this scenario is less prevalent and any changein weights between pairs, that is, potentiation or depression,due to the realization of STDP is rather random. In contrast,with a rhythmic background input, structure emerges in thelayout of connectivity between pre- and postsynaptic neu-rons and local clustering is observed (Fig. 5B). The cluster-ing of weights plays an important role in constraining localarea node dynamics as shown in computational (Voges andPerrinet, 2012) and experimental work using two-photon cal-cium imaging in vivo and multiple whole-cell recordingsin vitro in rodents’ primary visual cortex (Ko et al., 2013).To obtain a systematic insight about local node model behav-ior under various conditions on a longer time scale, activityof the node network is simulated for 60 sec. Resultingsummed membrane potential activity, that is, LFP and corre-sponding time frequency plots are displayed in Figure 6.The rhythmic input leads to an oscillation in the popula-tion-firing rate, as otherwise is not possible when relyingonly on the intrinsic network parameters used for the spikingnode model. Integrated spontaneous activity shows intermit-tent low-frequency (3–8 Hz) locking (Fig. 6B). With a rhyth-mic input, LFP network activity exhibits network oscillationsin the alpha frequency range (Fig. 6C). For a rhythmic inputwith STDP network, activity is shown in a time frequencyplot in Figure 6D demonstrating continuous periodic oscilla-tions and phase locking to the alpha frequency band.

Analytical approximation of synaptic weight changein time due to STDP in the cortical model

Rates of the presynaptic spike trains are approximated by acontinuous sinusoid. Hence, feed-forward input to a corticalregion is described as an inhomogeneous Poisson process:


I(t) = r(1� cos ( ft)) (9)

where f is the angular frequency, and r is the peak firing rate.The spikes in the output are delivered as series of delta pulsesof the following form:

J(t) = +k

d(t� 2kpþwf

) (10)

where w is the phase offset of the output spikes. The phasedistribution of the delta function reflects the assumption ofphase locking in population spikes. We have verified numer-ically the behavior that is similar for any moderately peakedunimodal distributions.

In order to compute a correlation between input oscilla-tions and output pulses, we perform the following integration:

D(J) =fr

2p

Z1�1

[1� cos ( ft)]d t� wf�Dt

� �dt (11)

where Dt is the difference in the spike times betweentpre �tpost. In other words, this reflects the STDP time win-dow. The correlation integral is further simplified:

D(J) =fr

2p[1� cos (w� fJ)] (12)

To obtain the change of weight w(t) over time, we makeuse of D(J) in Eq. (12) to write it as a function of inputphase of oscillations:

dw

dt= wmax

Z1�1

F(J)D(J)dJ (13)

Now, we can carry out an explicit integration in the subse-quent steps,

dw

dt=

frwmax

2p

Z10

Aþ e� J

sþ [1� cos (w� fJ)]dJ

264

�Z0

�1A� e

Js� [1� cos (w� fJ)]dJ

35

dw

dt=

frwmax

2p

Z10

Aþ e� J

sþ dJ�Z0

1Aþ e

� Jsþ cos (w� fJ)dJ

264

�Z0

�1A� e

Js� dJþ

Z0

�1A� e

Js� s� cos (w� fJ)dJ

35

ð14Þ

We can further simplify Eq. (14) as follows:

dw

dt=

frwmax

2pA�

1s2�þ f 2

cos ws�

� f sin w

� �264

� Aþ1

s2þþ f 2

cos wsþ

þ f sin w

� ��A� s� þAþ sþ

375ð15Þ

FIG. 6. Spiking IF neuronmodel network activity is sim-ulated for 60 sec. It exhibitsband-restricted oscillations inthe alpha frequency range. (A)Simulated spontaneous localfield potential (LFP) activity(10 ms sliding window) in theabsence of rhythmic input andSTDP (3 sec) exhibits oscilla-tions in the 8–12 Hz frequencyrange. (B) Time-frequency plotfor integrated network activityis shown for the entire durationof spontaneous activity withintermittent locking to alphaand also low-frequency scale.(C) Time-frequency plot forintegrated network activitywith rhythmic input displaysperiodic 10 Hz oscillations withan intermittent decrease inpower. (D) After enablingSTDP band-specific power inlocal node increases and fre-quency locks to the rhythmicmodulation of phase of thefeed-forward drive (intrinsicnetwork parameters are held atthe same values as displayed inTable 2). Color images avail-able online at www.liebertpub.com/brain

12 ROY ET AL.

Eq. (15) describes how—in the presence of plasticity—thesynaptic weights w(t) evolve in time as a function of fre-quency of input oscillation f, input modulatory phase w, syn-aptic plasticity time constants s + , s�, or the ratio ofdepotentiation-potentiation Aþ

A�. We simulate a spiking net-

work of neurons numerically with the oscillation frequencyf being 10 Hz, the STDP time constants being equal and setto 20 ms, A + being 0.01, and the STDP ratio being held inthe range of [1.4–1.9].

Alteration of FC and Dynamic LandscapeDue to Locally Restricted Plasticity

In this section, we test the hypothesis that a change in localnode spiking dynamics due to altered SC between thalamusand a single cortical node has an impact on adjacent as wellas on distant node correlations. Here, we systematically ex-plore how the local plasticity alters the global repertoire.How the local plastic change translates into global functionaland structural restructuring is illustrated schematically inFigure 7. In a previous work, we have reported learning-re-lated changes in empirical rs-FC as reflected by the differ-ence in the imaginary component of coherence before andafter learning (Freyer et al., 2012a). Imaginary coherence re-flects the functional correlation between the areas fromwhich EEG waveforms are recorded on the scalp, avoidingeffects of volume conduction. To access the FC before andafter plasticity, we simulate a global brain model consistingof six brain areas connected via long-range SC. Therefore, itwill have an impact on global functional correlations acrossbrain areas. As a first step, in the absence of plastic changes,we obtain a bifurcation diagram by varying the global scaling

input parameter G to six brain regions using both spiking andthe DMF model. A comparison of global dynamics betweenthe spiking and mean field description is plotted in Figure8A. Qualitatively, both models exhibit multistability in arange of global coupling parameter values. As shown in Fig-ure 8B using the DMF model, a value of global scaling pa-rameter G > 4.0 network destabilizes and the selected sixcortical regions exhibit high firing rates. For the color-coded representative points, we obtain population firingrates from the six selected brain regions. They display lowasynchronous population firing rates around 3–4 Hz andhigh firing rates around 50–60 Hz for stronger scaling param-eter values. In between, we obtain multi stability in theglobal model (Fig. 8C). Next, we introduced brain state-driven feed-forward thalamic input to a cortical node andmodified the synaptic weights within that node in accordancewith our synaptic plasticity rule. Using plasticity in the nodemodel, first we estimate local coherence from resultingspike times and subsequently using local coherence toestimate a free energy function. The degree of synchroniza-tion of the spiking neurons in the local cortical area ismeasured by order parameter R(t) =

�� 1N

+keihk

��, wherehk(t) = 2p(t� tm

k )=(tkmþ 1� tk

m) is the phase of the kth neuronat time t between mth and (m + 1)th spike times. For asynchro-nous systems, R = 0 and R = 1 for a perfectly synchronoussystem; while for intermediate values, groups of neuronsare partially synchronized. The probability distribution func-tion (PDF) of the order parameter R(t) is estimated by ob-serving its long time averaged trajectory, and theassociated energy profile is given by F(R) =�log P(R),

where P is the probability density of R. Local landscapemodifications due to synaptic plasticity as well as globalchange in dynamics as a function of global input scaling pa-rameter G are plotted in Figure 9A and B. We find that in ad-dition to noise, synaptic plasticity also systematically drivesthe mean firing activity between various cortical states (a lowas well as high firing activity as a function of global scalingparameter). In the absence of plasticity, thalamic noise inputdrives the local cortical brain area from low firing asynchro-nous activity to high synchronous firing activity (Fig. 9B). Inthe presence of STDP in the local cortical pool, the jumps be-tween minima are driven by the macroscopic evolution oflocal synaptic plasticity via synaptic weight updates w(t).This constrains the mean firing rate of populations whenthey are linked via global coupling as shown in Figure 9A.Now, globally they achieve a partially synchronous oscilla-tory state, thereby elevating firing rates of a substantial num-ber of connected cortical regions for low coupling G values.For the high global input scaling values of G, they exhibitvery high synchronous firing activity. Figure 10 shows theSC distance and capacity matrices reflecting the connectionlengths and strengths of fiber tracts connecting these brain re-gions. As a toy data set, we chose the bilateral areas primarysomatosensory area S1 (where plasticity is implemented),primary motor area M1, and thalamus. Realistic SC wastaken from TVB database. Next, we look at global FC beforeand after plasticity-related change in the mean firing activityof relevant cortical pools. We compute FC between the sixareas before and after plastic change as shown in Figure10C–E. FC between distantly connected areas are ratherweak as shown in the correlation map, while the FC betweenadjacent areas are relatively stronger. FC is determined by

FIG. 7. SC between six simulated cortical nodes andchanges in global SC due to local plastic effects. Upperpanel: A functional network is represented by six intercon-nected neural populations or regions represented by sixlarge circles. Each node comprises the same number of excit-atory and inhibitory neurons connected via recurrent connec-tions within regions, represented by three small white pelletsconnected by white lines in the central-upper large pellet. SCis illustrated by black lines connecting the regions. Resting-state functional connectivity (rs-FC), that is, degree of corre-lation, is represented by the gray scales in the six regions,with similar scales indicating a high degree of coherence.After learning, as the dashed arrow indicates, local plasticitywithin a region changes. This is exemplified by the change ofwhite local connections. Postlearning local changes are par-alleled by global changes in FC, illustrated here by the recon-figuration of the connecting lines and the gray colors amongthe six regions.


the connection strengths between regions displayed in Figure10B. After local plastic alterations in right S1, FC show en-hancement between adjacent as well as between distantlyconnected areas in the thalamus, S1, and M1, respectively(Fig. 10C, D). This demonstrates an important link betweenlocal structure and global FC. After plastic alterations inlocal SC, there is also a high number of de-correlated brainareas as can be seen in Figure 10D. The change in rs-FCmay indicate specific switches in brain states. This can be un-derstood by studying slow ( < 0.1 Hz) oscillations (Biswalet al., 1995) commonly thought to signal general changesin network excitability (Honey et al., 2007), whereas oscilla-tions on a faster timescale (8–12 Hz) may be more wellsuited to more specific information flow between areas(Honey et al., 2012). Interactions between relevant networkareas on a faster time scale can be examined by looking atthe pair-wise LFP network activity. If two areas were highly

synchronized, the coherence measure would yield valuesclose to 1, while in the opposite scenario values would stayclose to zero. One could also look at the spectrogram by fil-tering the LFP network activity and obtain a measure of thedominant band specific activity as displayed in Figure 6.Next, we look at the spontaneous activity recorded from asingle human subject EEG from somato-sensory cortical re-gions versus simulated neuronal signals filtered at the rateof EEG. For cortical area S1, we can obtain qualitativelysimilar spontaneous activity in the range of (8–10 Hz fre-quency band) in our network model (with local parametersfixed wEI = wIE = wII = 1) by adjusting feed-forward tha-lamic weights (an important control parameter in the plasti-city model) using updates according to the synaptic plasticityrule or in the absence of plasticity purely driven by thalamicnoisy input. In Figure 11A and B, we plotted spontaneousalpha-like activity and the corresponding spectrogram in

FIG. 8. Bifurcation diagrams of the full spiking model and the reduced dynamic mean field (DMF) model. (A) Mean-fieldanalyses of the attractor landscape of the spiking network (black) and the reduced DMF model (blue) yields maximum firingrate activity among all nodes as a function of a single free parameter global coupling strength G. The models incorporate arealistic SC matrix composed of 74 regions obtained from a TVB database. Solid lines (black, blue) indicate the stablebranches in the bifurcation diagram. In both cases, depending on the coupling strength G and the initial conditions, the networkconverges to one of three possible dynamical regimens. (B) Firing rate (red) for a representative point as shown in red in (A)using the DMF model and a value of G > 4.0. For this value, the network destabilizes and relevant cortical regions exhibit highfiring rates. (C) Firing rates generated by the spiking neuron model for three representative points as shown in gray, blue, andgreen in (A). A selection of six cortical and subcortical regions of interest is depicted. For low values of G, the network con-verges to a single stable state of low firing activity, that is, the spontaneous state. For increasing values of G, new stable statesof high activity along with the spontaneous state coexist. For even larger values of G, the spontaneous state becomes unstable.Color images available online at www.liebertpub.com/brain

14 ROY ET AL.

terms of signal amplitude and frequency power. In Figure11C and D, amplitude waveform from simulated signal inthe bandwidth of (8–15 Hz) shows remarkable concordancewith empirical EEG signals. Finally, we look at the powerin the signal bandwidth of 10 Hz (Fig. 11E) which showsthat fluctuations are organized into two specific modes(low and high power fluctuations in the both model and em-pirical signal) as previously reported in Freyer and col-leagues (2011). As hypothesized by Freyer and associates(2011), we have just verified that the transition from corticallow to high power resting-state activity is influenced by tha-lamic noisy input.

Analytical approximation of activity covariancein the global cortical model

In order to estimate the network activity and statistics, weuse statistical first- and second-order moments equations toapproximate the deterministic gating equations in the DMFmodel as displayed in Eq. (6). We first express stochastic dif-ferential equations in terms of their first and second momentsof the distribution of the gating variable: km

a mean gating var-

iable of local neural population (m = E or 1) of the corticalarea a. We also define a covariance matrix between two dis-tinct neural populations {a, b} and {m, n} reflecting arbitrarycortical areas as pmn

ab . Now, we can write the statistical mo-ments as follows:

kmi = ÆEm

i æ (16)

pmnab (t) = Æ[Em

a � kma ][En

b � knb]æ (17)

where < . > expectation values over many realizations. In thevector field form, synaptic gating variable equations areexpressed as

d

dt(~Eexc) = (Fexc(~Eexc,~Einh))

d

dt(~Einh) = (Finh(~Eexc,~Einh)) (18)

where for excitatory and inhibitory populations Eq. (18) canbe expressed as (simply following as defined in Eq. (6) deter-ministic dynamics of SDE) follows:

FIG. 9. Bifurcation in the global cortical model and relationship with local area dynamics unfolded on a free energy land-scape with STDP. (A) Mean-field analyses of the attractor landscape of the global cortical spiking network as a function of asingle free parameter global coupling strength (G) that regulates the amount of the global input current. Black: without STDP.Red: with STDP in locally restricted (thalamus-S1). Each point residing on the solid lines (black, red, indicating the stablebranches in the bifurcation diagram) represents the maximum firing rate activity among all relevant cortical nodes (here 6nodes). In both cases, depending on the coupling strength (G) and the initial conditions, the network converges to one ofthree possible dynamical regimens: 1) a single fixed point regime - the region is indicated by a red point - with asynchronouslow firing (without STDP) or medium firing activity (with STDP); 2) a regime of low as well as high firing activity withpartial synchrony (multistability) indicated by a representative point in green and; 3) a regime with high firing synchronousactivity indicated by a representative point in blue. (B) STDP alters correlations between left thalamus and S1. Inter-nodecorrelations are assessed by a free energy diagram. The free energy function is plotted in black solid line (without STDP)and in red solid line (with STDP). A change was found in local fixed-point dynamics as a function of synchrony, i.e.order parameter R, in left S1. The energy landscape indicates modified output dynamics of local brain area S1 mediatedby feed-forward input oscillation and synaptic plasticity. Subsequently this change modifies the resulting global activityof connected brain areas as indicated by altered maximum firing rates of the cortical pools. Without STDP, the energy func-tion f(R) exhibits two minima at phases R=0 (asynchronous fixed point dynamics) and R=0.85 (synchronous dynamics). Thelocal minima are separated by a saddle located at R=0.3. Jumps between minima are mainly carried out by noise driven tran-sitions (when isolated from global input). With STDP, f(R) has two minima. In this case the asynchronous fixed point is sub-stituted by a partially low synchronous fixed-point dynamics at phase R=0.35 and the high synchronous fixed point at phaseR=0.82. They are also separated by a saddle at R=0.56, however there is noticeable difference in the depth of the energylandscape compared to the case without STDP. Color images available online at www.liebertpub.com/brain


~E = f~Eexc,~Einhg= fEexc1 , . . . . . . : , Eexc

N , Einh1 , . . . . . . : , Einh

N g

Fexcn = � Eexc

n

sexc

þ (1�Eexcn )crexc(Iexc

n )

Finhn = � Einh

n

sinh

þ rinh(Iexcn ) for 8n = 1, . . . . . . , N (19)

Sincewearedealingwithadeterministicsystem,aTaylorexpan-sion of the vector field of gating variable~E about moments~k = Æ~Eæup to only the first-order terms, this allows us to write:

Fmn (~E) = Fm

n (~k)þ +a

qFmn

qEexcn

(~k) � dEexcn þ +

a

qFmn

qEinhn

(~k) � dEinhn

(20)

With many such realizations, one can average out

ÆdEmn (t)æ = Æv(t)æ = 0 (21)

Using the equation cited earlier, we can rewrite the equa-tions for the mean of the gating variables as

dkexca

dt=

d

dtÆ~Eexcæ = � kexc

a

sexc

þ (1� kexca )crexc(sexc

a )

dkinha

dt=

d

dtÆ~Einhæ = � kinh

a

sinh

þ rinh(sinha ) (22)

where in Eq. (22), mean input current to cortical region a isthus given by sexc, inh

a .These mean input currents for cortical area a are given as

follows:

sexca = Iext þW þ JNMDAkexc

a þGJNMDA +b

Cabkexcb � JaEinh

a

Iext = wtcJNMDAkexca , wtc = w(t)þ f (x)wmax

sinha = JNMDAkexc

a � kinha (23)

In Eq. (23), wtc, w(t) are the corticothlamic synapticweights and weight update due to synaptic plasticity.

In the equation cited earlier, widely used Bienstock-Cooper-Munro (BCM) rate-based plasticity rule replacesSTDP rule. We compute a change of corticothalamic synap-tic weight wtc(t) directly as

dwtc(t)

dt=

rIij

sþ(r� h� )

dh� (t)

dt=

1

s�(r2� h� ) (24)

In Eq. (24) h� is a sliding threshold that approximates piece-wise the exponential function f(x). Ii = (Ii

1, . . . . . . . . . , Iin) is

an input stimuli pattern, which in this case approximates asinusoid with specific phase preference. r = wtc � Ii is the

FIG. 10. Realistic SC and simulated FC between salient brain regions. (A) SC capacity matrix indicating connection strengthsand (B) SC distance matrix indicating fiber tract lengths between six cortical regions comprising bilateral primary somatosensoryareas (right, left S1), primary motor areas (right, left M1), and thalamus (left, right Th). The color bar indicates the weights and theedge lengths between corresponding cortical areas. Simulated brain nodes (IF neurons) and FC accessed computing pair-wisecorrelations before and after structural connectivity change between left S1-left Th. The FC matrices represent six brain areascorresponding to regions in the SC matrices above. (C) Functional correlation map shows weak or zero correlations betweenstructurally not connected areas. (D) Correlation map shows changed FC; for example, enhanced correlations between someareas that were weakly correlated before local plasticity, for example, right S1-M1. Self-correlation between same areas thatis always 1 is represented by the diagonal in the correlation map and is set to zero. (E) In the top (red) and bottom panel(gray), FC (before and after plasticity) are shown with a bar diagram (corresponding region pairs are labeled). Increases, de-creases, and no alterations in positive as well as negative correlations between cortical regions before (red) and after (gray) plas-ticity can be seen. Color images available online at www.liebertpub.com/brain

16 ROY ET AL.

FIG. 11. Time series analysis of experimental electroencephalography (EEG) data and the output of a mean field model.(A) Spectrogram of the EEG of a single subject. The signal comes from channel CP3 in the EEG field map, which is locatedover the somatosensory cortex. EEG data from Freyer and coworkers (2012a, 2013). (B) Spectrogram of the signal outputof the mean field model at cortical area S1. The model is driven by thalamic noise in the absence of state-dependent inputand synaptic plasticity with intrinsic recurrent network parameters as described in single brain area spiking model. For (A)and (B), the colorbar indicates the amplitude of the signal. (C, D) Time series signal power of the experimental and sim-ulated data. High power is found in the alpha range. (E, F) Amplitude waveform for EEG data as well for the model outputin the alpha frequency band. Waxing and waning of alpha power corresponding to low and high amplitude bursts can beobserved. (G) Signal power at 10 Hz is plotted over time for experimental and simulated data. Switching of power fromlow to high values can be seen—indicating multistability that in the model is driven by thalamic noise coming from feed-forward glutamatergic synapses. Color images available online at www.liebertpub.com/brain


postsynaptic firing rate, and wtc = (w1, . . . . . . ::, wn) representsthe synaptic weights.

Moreover, one can write the following for fluctuationsabout the mean gating variables:

d

dtÆdEm

a dEnbæ = +

p = exc, inh

+n

qFma (~k)

qEpn

ÆdEpndEn

bæ

þ +p = exc, inh

+n

qFma (~k)

qEpn

ÆdEpndEn

aæþ r2Ævavbæ

(25)

If p is the covariance matrix between gating variables, it iswritten as a block diagonal matrix as given next:

P = Æ~E~ET æ = pEE pEI

pIE pII

� �(26)

where in Eq. (27) ~ET is the matrix transposition of the vec-tor field ~E. Using Eq. (25), we can write the equation forcovariance as

dP

dt= MPþ PMT þ gb (27)

The equation cited earlier expresses a continuity equation forthe covariance matrix, which can be solved finally to obtainthe Jacobian M of the deterministic system and the noise fac-tor gb coming from other cortical areas. The derivatives arewritten out explicitly using Eq. (27):

qFma (~k)

qEnb

= � 1

sm

� crexc(sexca )dEmdEn

� �dab

þ 1þ (1� kexca )cdEmdEn

qrm(sna)

qs� Kmn

ab

K =KEE KEI

KIE KII

" #, KEI

ab = � Jadab, KIE = JNMDAI

þ kGJNMDAC, KII = � I,

KEE = wtcJNMDAIþW þ JNMDAIþGJNMDAC (28)

In Eq. (27), I is an identity matrix of the dimension of theSC matrix. C is the SC between connected brain regions.Taken together, Eqs. (27) and (28) indicate the evolution ofthe covariance matrix and are clearly dependent on bothglobal anatomical structure and local underlying dynamicalinputs between cortical regions a, b. Since we have noother assumptions here, the result is very general. The station-ary solution corresponds to a spontaneous asynchronous stateas shown in Figure 11 for a specific regime of cortical stabil-ity as a function of global coupling parameter G. Moreover,these solutions of the vector field can be constructed analyti-cally using Eigenvalue decompositions of the correspondingmatrix equation of covariance as displayed in Eq. (27).

Discussion

In this work, we used a modeling approach to investigatethe role of locally restricted plasticity in shaping the dynamicrepertoire of the brain. A modification of synaptic weightsbetween subcortical and cortical structure while the brain islearning or in a consolidation stage can have a dramatic im-

pact on the resulting FNs organization. We demonstratedthat incorporating plasticity in between thalamus (driver)and a local brain area of a full brain computational model en-ables the theoretical exploration of these mechanisms. We in-duced changes in the local microcircuit on a short millisecondtime scale via synaptic scaling of excitatory and inhibitoryconductance. This results from systematic potentiation anddepression of feed-forward cortico thalamic excitatory synap-tic weights wtc, which serve as a control parameter in ourSTDP model. The STDP description in the local cortical re-gion is based on all-to-all spike pairing. When looking atlocal network activity, there are several possible sources ofscaling synaptic conductance (excitatory as well as inhibito-ry). Hence, one should be careful with the potentiation of syn-aptic weights. We have applied a hard bound [0, wmax] to clipthe synaptic weights. Specifically, due to the phase lockedstability as shown semi-analytically in the analytical approx-imation of synaptic weight change, overall stability of synap-tic plasticity in this model is ensured. However, one should becareful of getting close to a parameter regime where the net-work firing rate increases monotonically without any bound,leading to an unstable spontaneous high firing rate (runawayexcitation). The other important point is the spike rate adap-tation in the recurrent spiking network. We have not testedthis exhaustively in the local area spiking model.

One more critical assumption in this study is the low asyn-chronous firing activity in the local brain areas. This is in-deed well supported by recent in vivo studies in the neocortex (Haider et al., 2006; Sakata and Harris, 2009) aswell applying diverse recording techniques (whole-cellpatch clamp, sharp electrode recording, and two photon cal-cium imaging) probing laminar differences of cortical activ-ity in a variety of sensory cortex, leading to the observationthat spontaneous activity ranges between 1 and 5 Hz [for areview see Barth and Poulet (2012)]. While these observa-tions are certainly valid, more careful comparisons are nec-essary to monitor the range of large-scale cortical activitiesfrom various sensory and other association cortices to furthersee concordance between different brain scales.

The other simplifying assumption that allows for analyti-cal approximations is the stationary behavior of functionalconnectivity at rest throughout the cortex. Numerous rest-ing-state modeling studies describe emergence of stationaryresting FC as an interplay between anatomical SC and under-lying cortical dynamics (Deco et al., 2011; Ghosh et al.,2008b). However, many recent studies have shown that thetime-varying aspect of functional correlations plays a substan-tial role in the formation and dissolution of spatiotemporal pat-terns over the entire cortex (Allen et al., 2014; de Pasqualeet al., 2012). In the context of synaptic plasticity/homeostasis,the time-varying nature of FC is even more crucial.

Nevertheless, in this study, we have exploited oscillatoryfeatures of neuronal population via STDP to explain modi-fied FC under repetitive time-dependent stimulation. More-over, with an analytical estimation of covariance matrix,we have made an attempt to demonstrate that among otherimportant factors, local oscillations (local dynamics) alsoplays a crucial role in determining FC on slower time scalesby modifying the underlying dynamical landscape.

More specifically, we have demonstrated that rhythmicinput provides an oscillatory context and it is essential forneurons equipped with STDP in the output layer to detect

18 ROY ET AL.

and learn input spikes extending the concept of Masquelierand colleagues (2009), where a similar idea was imple-mented for a single downstream neuron equipped withSTDP to facilitate learning (Masquelier et al., 2009). Sec-ond, as a result of brain-state dependent learning, local con-nectivity between excitatory neurons changes and clusteringof local recurrent connectivity emerges. This finding is par-ticularly interesting in the light of a recent study where Rubi-nov and coworkers (2011) have shown that spiking leaky IFneurons equipped with STDP with a hierarchically modularnetwork exhibit self-organized critical dynamics (Rubinovet al., 2011). Moreover, a transition to supercritical dynam-ics, that is, random-order spike timing, is more evident ina regime where between-module connectivity follows apower law density distribution. Sparser local connectivitydue to plastic influences and hierarchically modular SCmay provide an ideal neurobiological determinant of con-strained local as well as global dynamics.

Finally, we verify our hypothesis about how state-depen-dent input oscillations in the alpha frequency band combinedwith STDP facilitate learning phases of population spikes inthe readout neuronal populations at a faster time scale. Basedon local neuronal spike times, we analytically estimate thephases at which the system makes a transition from partiallysynchronous to highly synchronous fixed points (Fig. 9).Local and global population mean that firing rate is system-atically modulated depending on whether the local input isreceived at the asynchronous or synchronous phase of firing.When the cortical region where synaptic plasticity is imple-mented is embedded in a larger network using realistic SCand conduction delays, the FC on a slower time scale inthe order of multiple seconds is altered. Finally, we analyti-cally approximate the prediction of FC and its dependence onlocal dynamics as well as given anatomical connectivity. Asa possible extension of this work, it would interesting to lookat a global model where plasticity/homeostatics is imple-mented in multiple cortical areas.

In summary, large-scale neural models of brain dynamicsare promising tools to explore the non-trivial relationship be-tween anatomical and functional brain connectivity. In par-ticular, these models enable an investigation of the role ofdifferent factors in the network dynamics and their topolog-ical properties. Furthermore, investigating the impact of suchfactors in the SC-FC relationship helps understanding themechanisms underlying healthy resting-state activity andits breakdown in disease or aging. We expect that similar re-sults could be reproduced with virtually any model of mac-roscopic brain dynamics with brain-inspired SC. The DMFmodel discussed in our work in Eq. (6) simplifies a descrip-tion of neural population at the node level and allows for an-alytic descriptions. One could, in principle, also exploreplasticity-driven stochastic Wilson–Cowan units as shownin a recent study (Benayoun et al., 2010). It would be inter-esting to see how the correlated input shapes the dynamicallandscape locally and globally in such models or any system-atic difference than the one found in this study.

Positive and negative correlations often exhibit band lim-ited power fluctuations (Deco and Corbetta, 2011; Fox andRaichle, 2007). The underlying mechanism of this observa-tion may be rhythm-specific neural synchronizations. Recentcomputational studies further suggest that selective commu-nication is achieved by coherence mechanisms between gain

(signal to noise ratio, amplitude scaling) and firing rate mod-ulations (Akam and Kullmann, 2012). For example, rhyth-mic synchrony decreases reaction time in attention andenhances speed of information transfer between differentneuronal assemblies as reviewed in few recent studies (Bat-taglia et al., 2012; Deco et al., 2011). Hence, knowing themechanisms in the brain that lead to altered FC is crucialto understand basic principles of brain function. A tool fortheir systematic exploration in a standardized and well-docu-mented fashion is offered by TVB. In line with the synaptichomeostasis hypothesis (Tononi and Cirelli, 2014), the pres-ent simulation results suggest that an energetically, costlycontinuous change of synaptic weights yields the brain’sfull dynamic repertoire.

Acknowledgments

The authors acknowledge the support of the German Min-istry of Education and Research (Bernstein Focus StateDependencies of Learning 01GQ0971) to P.R., the JamesS. McDonnell Foundation (Brain Network Recovery GroupJSMF22002082) to M.B., A.R.M., V.J., G.D., and P.R.,and the Max-Planck Society (Minerva Program) to P.R. G.D.was supported by ERC Advanced grant DYSTRUCTURE

Author Disclosure Statement

No competing financial interests exist.

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Address correspondence to:Dipanjan Roy

Department of NeurologyCharite Universitaetsmedizin

Chariteplatz 1Berlin 10117

Germany

E-mail: [email protected]

Petra RitterDepartment of Neurology

Charite UniversitaetsmedizinChariteplatz 1

Berlin 10117Germany

E-mail: [email protected]


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