Functional strengthening through synaptic scaling upon connectivity disruption in neuronal cultures

RESEARCH Functional strengthening through synaptic scaling upon connectivity disruption in neuronal cultures Estefanía Estévez-Priego1,2, Sara Teller1,2, Clara Granell3,4, Alex Arenas5, and Jordi Soriano 1,2 1Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona, Spain 2Universitat de Barcelona Institute of Complex Systems (UBICS), Barcelona, Spain 3GOTHAM Lab – Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza, Spain 4Department of Condensed Matter Physics, University of Zaragoza, Zaragoza, Spain 5Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain Keywords: Neuronal cultures, Calcium imaging, CNQX, Effective connectivity, Global efficiency, Functional organization, Synaptic scaling ABSTRACT An elusive phenomenon in network neuroscience is the extent of neuronal activity remodeling upon damage. Here, we investigate the action of gradual synaptic blockade on the effective connectivity in cortical networks in vitro. We use two neuronal cultures configurations—one formed by about 130 neuronal aggregates and another one formed by about 600 individual neurons—and monitor their spontaneous activity upon progressive weakening of excitatory connectivity. We report that the effective connectivity in all cultures exhibits a first phase of transient strengthening followed by a second phase of steady deterioration. We quantify these phases by measuring GEFF, the global efficiency in processing network information. We term hyperefficiency the sudden strengthening of GEFF upon network deterioration, which increases by 20–50% depending on culture type. Relying on numerical simulations we reveal the role of synaptic scaling, an activity–dependent mechanism for synaptic plasticity, in counteracting the perturbative action, neatly reproducing the observed hyperefficiency. Our results demonstrate the importance of synaptic scaling as resilience mechanism. AUTHOR SUMMARY Neuronal circuits exhibit homeostatic plasticity mechanisms to cope with perturbations or damage. A central mechanism is ‘synaptic scaling,’ a self-organized response in which the strength of neurons’ excitatory synapses is adjusted to compensate for activity variations. Here we present experiments in which the excitatory connectivity of in vitro cortical networks is progressively weakened through chemical action. The spontaneous activity and effective connectivity of the whole network is monitored as degradation progresses, and the capacity of the network for broad information communication is quantified through the global efficiency. We observed that the network responded to the perturbation by strengthening the effective connectivity, reaching a hyperefficient state for moderate perturbations. The study proves the importance of ‘synaptic scaling’ as a driver for functional reorganization and network-wide resilience. a n o p e n a c c e s s j o u r n a l Citation: Estévez-Priego, E., Teller, S., Granell, C., Arenas, A., & Soriano, J. (2020). Functional strengthening through synaptic scaling upon connectivity disruption in neuronal cultures. Network Neuroscience, 4(4), 1160–1180. https://doi.org/10.1162 /netn_a_00156 DOI: https://doi.org/10.1162/netn_a_00156 Received: 16 January 2020 Accepted: 15 July 2020 Competing Interests: The authors have declared that no competing interests exist. Corresponding Author: Jordi Soriano [email protected] Handling Editor: Olaf Sporns Copyright: ©2020 Massachusetts Institute of Technology Published under a Creative Commons Attribution 4.0 International (CC BY 4.0) license The MIT Press Functional strengthening through synaptic scaling INTRODUCTION Response to perturbations or damage in living neuronal circuits is a central yet unresolved problem in neuroscience. A simple network description of damage intuitively suggests that the failure of connectivity pathways precipitates a progressive deterioration of network activity that ultimately compromises the functionality of the system. Realistic descriptions of living neuronal circuits, however, expose the complex interplay between the physical architecture of the network, neuronal dynamics, and plasticity mechanisms in governing circuit behavior, framing scenarios in which response to damage is not only possible, but fast and networkwide. This is particularly important in the context of brain and neurological disorders, since adequate prognosis of functional alterations may help to elucidate actions to stop or revert damage. Studies in stroke, for instance, have pointed out the important role of plasticity in preventing a cascade of degradation and fostering recovery (Calabresi, Centonze, Pisani, Cupini, & Bernardi, 2003;Murphy & Corbett,2009). Current multidisciplinary approaches for prognosis are making an effort to integrate acquired experimental data with numerical models to characterize neuronal damage and subsequent network responses (Bassett & Sporns,2017;Fornito, Zalesky, & Breakspear, 2015). Thus, understanding the different actors at play—connectivity, dynamics, and plasticity—and their interrelation has become a central goal in medical network neuroscience. In the last few years, substantial efforts have been invested in linking structural characteristics of neuronal networks with their capacity to cope with perturbations and damage (Aerts, Fias, Caeyenberghs, & Marinazzo, 2016;Farooq, Chen, Georgiou, Tannenbaum, & Lenglet, 2019;Majdandzic et al.,2013). Specifically for brain functional networks, studies unveiled the importance of modular and hierarchical organizations (Meunier, Lambiotte, Fornito, Ersche, & Bullmore, 2009), hubs (van den Heuvel & Sporns,2013), and other node structural aspects (Bassett & Sporns,2017;Bassett, Zurn, & Gold,2018;Sporns,2014;Stam,2014). Despite the progress and enlightenment in this direction, the incorporation of plasticity and self-regulatory mechanisms as additional actors is opening new avenues for understanding resilience to inResilience: The capacity of a neuronal circuit to maintain activity and functional characteristics upon loss or weakening of neurons or connections. sult. Indeed, the brain and other living neuronal circuits are reliant on diverse adaptive mechanisms for proper performance and stability that include synaptic plasticity and structural Synaptic plasticity: The strengthening or weakening of synapses according to neuronal activity, for instance, to potentiate specific connectivity pathways. plasticity (Butz, Steenbuck, & van Ooyen,2014;Fauth & Tetzlaff,2016;Fauth, Wörgötter, & Tetzlaff, 2015). These mechanisms are central to regain circuits’ operability upon severe perturbations or injury (Barral & Reyes,2016;Costa, Mizusaki, Sjöström, & van Rossum,2017; Marder,2011;Murphy & Corbett,2009;Teller et al.,2019). One of the most important synaptic plasticity mechanisms is synaptic scaling, in which the strength of excitatory synapses is adSynaptic scaling: A regulatory mechanism of neuronal circuits by which synaptic strength is adjusted to compensate for chronic changes in activity. justed to compensate for variations in activity (Desai, Rutherford, & Turrigiano,1999;Fong, Newman, Potter, & Wenner, 2015;G. G. Turrigiano, Leslie, Desai, Rutherford, & Nelson, 1998). The capacity of synaptic scaling to regulate neuronal activity was demonstrated both in vivo (Echegoyen, Neu, Graber, & Soltesz,2007;G. Turrigiano,2012;G. G. Turrigiano,2008) and in vitro (Barral & Reyes,2016;Hanes et al.,2020) at a synapse level. Although different investigations pointed out the role of synaptic scaling in correcting neuronal activity after damage, for instance in relation to Alzheimer’s patients cognitive deficits (Borge-Holthoefer, Moreno, & Arenas, 2011) and retinal lesions (Keck et al.,2013), there are no studies demonstrating its impact in the functional organization of a neuronal circuit. Functional organization: A set of global network traits, such as modularity or global efficiency, that imprint distinct organizational characteristics to a network. The aim of this study is to analyze the action of synaptic scaling from a network neuroscience perspective and expose its potential as a resilience mechanism. To this end, we designed an experimental pipeline in which small cortical circuits in vitro were exposed to a malfunctionlike event that graduallyweakened the connectivity among interconnected neuronal assemblies Network Neuroscience 1 161 Functional strengthening through synaptic scaling (clusters), and analyzed simultaneously the activity of the entire network. The perturbative action was delivered through increasing doses of CNQX, an AMPA-glutamate receptor antagonist CNQX (6-cyano-7-nitroquinoxaline2,3-dione): Antagonist of AMPA-glutamate receptors in excitatory neurons, frequently used to either weaken excitatory synaptic communication or block it entirely. in excitatory synapses (Soriano, Martínez, Tlusty, and Moses,2008;Tibau, Valencia, & Soriano, 2013a). Although CNQX targeted synaptic connectivity, we measured solely its impact on the spontaneous activity, that is, the spontaneous dynamic interactions among clusters. Functional characteristics of the cultured networks were therefore quantified by measuring the alterations in activity as the blockade progressed and by computing the global efficiency (Latora & Global efficiency: A measure of network capacity for information exchange. The higher the overall connectivity among nodes, the higher the global efficiency. Marchiori, 2001;Rubinov & Sporns,2010), a measure of the integration of the flow of information in a networked system. Our experiments showed that, as CNQX was applied, there was an initial phase in which the global efficiency raised, revealing an increased information flow capacity in the network. This hyperefficiency was reproducible among network realizations, Hyperefficiency: In the context of our work, an abrupt increase of global efficiency resulting from a strengthening of effective connections. although the level of impact depended on culture details. Beyond this phase, global efficiency progressively decayed until activity ceased. By using numerical simulations we showed that synaptic scaling, simulated as a local strengthening of remaining effective connections upon damage, was sufficient to explain the experimental behavior. Simple models based on bond percolation (Kirkpatrick,1973), that is, the degradation or deletion of connections without any Percolation: Behavior of information or other measure as nodes or connections are removed, typically separating a ‘connected’ and a ‘disconnected’ phase. scaling, failed at capturing this hyperefficiency phenomenon. To our knowledge, the experiments and modeling presented here is the first strong evidence of the impact of synaptic scaling in preserving network efficiency and whole-system performance, thus exposing synaptic scaling as an intrinsic mechanism for resilience in living neuronal networks. Our study strengthens the vision of synaptic scaling as an emergent and general property of living neuronal circuits, and paves the way toward a better prediction of the action of perturbations and damage in such circuits. RESULTS Weakening of Synaptic Communication Alters Functional Organization We investigated spontaneous activity in clustered neuronal cultures prepared in 6-mm-diameter PDMS wells on glass, as illustrated in Figure 1A. These cultures emerged as a self-organized process in which the absence of adhesive proteins in the glass substrate favored neuronal mobility and aggregation (Segev, Benveniste, Shapira, & Ben-Jacob,2003;Teller et al.,2014; Teller, Tahirbegi, Mir, Samitier, & Soriano,2015). By day in vitro (DIV) 7 upon preparation, aggregation shaped highly compact neuronal islands termed clusters that remained stable in position and size. In our experiments, about 130 neuronal clusters typically formed in the 6-mm-diameter wells (Figure 1B). Table 1 summarizes the set of networks investigated and their characteristics. The spontaneous activity in the clustered networks was monitored at DIV 8–12 through calcium fluorescence imaging (Figure 1B), which allowed us to follow the evolution of all clusters in the culture with high spatial and temporal resolution. Active clusters appeared as bright objects whose fluorescence intensity ramped up upon activation. The advantage of clustered neuronal cultures is that they exhibit spontaneous activity with a rich spatiotemporal structure (Teller et al.,2014,2015), in which clusters coactivate in groups of varying size and timing (Figure 1B–C). Since the structure of coactivation patterns, and in turn network functional characteristics, is grounded on the coupling among clusters, these cultures stand out as a particularly suited experimental preparation to investigate the impact of chemical perturbations or damage (Teller et al.,2014 ,2015,2019). The richly structured dynamics of clustered networks—and sister designs in the form of engineered circuits (Kanner et al.,2015; Yamamoto et al.,2018)—is enlightening since dynamics shape networks with a functional organization qualitatively similar to that of the brain, with modular traits and hubs (Teller et al., 2015;Yamamoto et al.,2018). Thus, our clustered cultures combine the controllability and Network Neuroscience 1162 Functional strengthening through synaptic scaling Figure 1. Clustered neuronal cultures and experimental procedure. (A) Schematic preparation of clustered neuronal networks. Dissociated rat cortical neurons were plated on a 6-mm-diameter PDMS wells. The absence of adhesive proteins facilitated neuronal aggregation, giving rise to an assembly of neuronal islands (clusters) by day in vitro (DIV7). (B) Fluorescence image of a typical neuronal culture. Circular objects are neuronal clusters. Labels highlight four the location of four clusters whose fluorescence traces are shown in panel C. (C) Representative fluorescence traces of four clusters for gradually higher levels of the AMPA glutamate receptor antagonist CNQX. Sharp increases of the signal correspond to activity events. Yellow boxes illustrate episodes of coordinated activity. The overall activity of the clusters decreases with CNQX as a result of the reduced excitatory drive. DFF indicates normalized fluorescence signal, given by DFF(%) = 100.(F−F0)/F−0, with F0the fluorescence signal at rest. accessibility of an in vitro system with some of the dynamical richness and functional complexity of naturally formed neuronal circuits. In our experiments we were interested in analyzing the dynamics of a clustered network as the connectivity strength among clusters, and in turn their dynamic coupling, was reduced. The ability of our experimental system to simultaneously monitor the entire network made it unique to investigate the action of perturbations and their impact on network functional organization. Since spontaneous coordinated activity is mostly mediated by the excitatory drive of AMPA-glutamate receptors, both the capacity of the network to fire and cluster-to-cluster synaptic coupling could be altered in a controlled manner through the blockade of AMPA receptors. Thus, following Soriano, Rodríguez Martínez, Tlusty, and Moses (2008), we targeted the excitatory AMPA-glutamate receptors with gradually higher doses of the antagonist CNQX, causing a progressive reduction of spontaneous activity until it ceased. For clarity in the analysis of the data and its interpretation, NMDA excitatory receptors (which account for about 20% of Network Neuroscience 1 163 Functional strengthening through synaptic scaling Table 1. Summary of the structural and dynamical characteristics of the eight clustered networks investigated. Experiment DIV Nφ(µm)d(µm)a(bursts/min) hki hwi 1 8 157 156 ±56 406 ±16 7.10 6.0 ±3.1 2.8 ±0.5 2 8 125 170 ±55 437 ±15 2.52 5.9 ±2.8 3.2 ±0.6 3 8 116 177 ±60 455 ±14 1.47 6.3 ±2.7 2.9 ±0.5 4 9 152 137 ±34 282 ±8 5.51 5.3 ±2.1 3.0 ±0.4 5 9 144 177 ±53 411 ±15 1.71 4.4 ±1.9 3.3 ±0.7 6 9 124 160 ±52 452 ±15 7.14 5.0 ±1.7 2.9 ±0.6 7 9 118 215 ±68 469 ±18 3.85 4.9 ±1.9 3.1 ±1.1 8 12 128 193 ±70 462 ±15 2.91 5.7 ±2.2 2.9 ±0.5 Note. DIV is the day in vitro of the culture, Nthe number of clusters, φtheir average diameter, dthe typical clusters’ interdistance, athe average collective activity, hkithe average effective connectivity per cluster, and hwithe average weight of effective connections. φ,d,hki, and hwi are reported as the means ±standard deviations. the total excitatory drive in cortical neurons) and GABA inhibitory receptors were fully blocked with the corresponding antagonists. An example of the impact of CNQX on network spontaneous activity is shown in Figure 1C. Here, the fluorescence traces of four representative clusters are depicted for gradually higher CNQX levels. Without blockade, all four clusters exhibited a rich activity with strong coordination. As CNQX was applied, the level of activity and coordination swiftly decreased, and for full synaptic blockade the clusters either fired weakly and independently or became silent. The fall of spontaneous activity and the breakdown of clusters’ coactivation patterns for the entire network are shown as raster plots in Figure 2A. In the plots, the dots mark the timing of clusters’ activation, data that are directly obtained from the analysis of the fluorescence signal. In the sequence of raster plots, [CNQX] =0(unperturbed network) shapes a strongly coherent dynamics in which most of the clusters coactivate at unison, a feature that reflects the strong coupling among clusters. The strength of spontaneous activity was quantified through the collective activity a, defined as the frequency of activity episodes (bursts) in which at least five clusters participated (about 5% of the network). Activity awas high for [CNQX] =0, with clusters exhibiting about 7 bursts/min. Activity severely dropped to about 4.4 bursts/min for the small perturbation with [CNQX] =60 nM, which was accompanied by a strong disruption of the unison behavior, rendering an overall dynamic in which clusters activated in groups of varying size. The decay in activity accentuated as CNQX grew, although some groups of clusters still maintained strong coordinated activity even for relatively large doses of [CNQX] =600 nM. Spontaneous activity finally stopped by [CNQX] &1, 000 nM. In our study we investigated a total of eight clustered networks. All of them exhibited a similar qualitative trend, although the structure of coordinated activity and its changes on degradation depended on the cluster-tocluster wiring details in the culture (Table 1). Activity data was next analyzed in detail to compute the effective connectivity of the netEffective connectivity: Causal statistical relationship among the activity patterns of neurons in a network, leading to directed and weighted adjacency connectivity matrices. works, allowing us to quantify whole-network alterations on CNQX action. The effective networks (weighted and directed) were extracted using transfer entropy, an approach that we showed appropriate for neuronal cultures in previous studies (Stetter, Battaglia, Soriano, & Geisel, 2012;Teller et al.,2014;Tibau, Ludl, Rüdiger, Orlandi, & Soriano,2020). From the inferred effective networks we extracted the global efficiency GEFF, which informs about the capability of the network to operate as a whole. For clarity, the global efficiency was always Network Neuroscience 1164 Functional strengthening through synaptic scaling Figure 2. Network activity and functional organization upon degradation. (A) Representative raster plots of spontaneous activity for gradually higher excitatory blockade. Blue dots mark the clusters’ activations. The concentration of CNQX and the average collective spontaneous activity aare indicated above each panel. Rasters are limited to 10 min for clarity. (B) Corresponding effective connectivity matrices. The brighter the color, the higher the connectivity weight among two clusters. Matrices are ordered according to the functional communities at [CNQX] = 60 nM. The scaled global efficiency GEFF increases at [CNQX] = 60 nM to steadily decrease afterwards. (C) Effective connectivity maps of perturbed and control experiments. Clusters’ and links’ colors identify different functional communities. Control experiments experienced the same experimental pipeline as perturbed ones, but only GABAAand NMDA receptors were blocked. No significant alterations in the effective connectivity were observed. The perturbed experiment corresponds to the data shown in (A). scaled relative to its value in the unperturbed condition. We note that the global efficiency is based on the calculation of the shortest topological paths among connected nodes in a network, and that for weighted networks the shorter paths are those with stronger weight. Thus, an increase in GEFF can arise from either a higher number of links, stronger weights, or both. Figure 2B provides an example of the inferred effective connectivity matrices. A summary of the average connectivity hkiand average weight hwifor the eight studied cultures is provided Network Neuroscience 1 165 Functional strengthening through synaptic scaling in Table 1. Functional communities were already present for [CNQX] =0, a feature that indicates that the observed coordinated activity was shaped by strongly interacting groups of clusters. This is clear in the corresponding connectivity map of Figure 2C, in which the majority of the clusters belonged to the same community, as calculated by modularity optimization Modularity: Tendency of the nodes in a network to connect within a group more strongly than with nodes in another group. using the Louvain algorithm (Blondel, Guillaume, Lambiotte, & Lefebvre,2008). Well-defined communities emerged for [CNQX] =60 nM and higher concentrations, as indicated by the richer structure of the connectivity maps, which show gradually smaller and more isolated communities. For [CNQX] &600 nM activity practically ceased and no functional characteristics could be rendered. The connectivity maps of Figure 2C also helped to picture the CNQX degradation process in terms of the spatial arrangement of the clusters. The maps showed that the functional communities were physically compact, that is, they were constituted by groups of adjacent clusters. This indicates that the clusters typically connected to their immediate neighbors upon network formation, and suggests that the overall dynamics of the network are mediated by local interactions. In this direction, the maps also show that the physical location of the functional communities was preserved, but that they reduced in size as CNQX grew. Emergence of Hyperefficiency in CNQX-Perturbed Networks The above gradual fragmentation of the network with CNQX was not accompanied by a steady loss of clusters’ intercommunication. Surprisingly, for the moderate CNQX concentration of 60 nM, the global efficiency GEFF increased by 8%—for the particular experiment of Figure 2— with respect to the initial condition, to later fall as expected. We note that the increase in GEFF strongly contrasts with the fall of spontaneous activity, which is reduced by 60%. We term hyperefficiency this abrupt increase in GEFF and, as we elaborate later, its presence indicates the nonlinear relationship between the structural alterations caused by CNQX and the effective connectivity ones that emerge from dynamical interactions among the clusters. In other words, while CNQX action on excitatory synapses is steady and follows a percolation-like silencing process (Soriano, Rodríguez Martínez, et al., 2008), the effective connectivity obeys more complex mechanisms in which switching dynamic interactions and plasticity-driven adaptation play a central role. Before investigating the possible hyperefficiency mechanisms, we verified that this phenomenon was not an experimental artifact by comparing the evolution of CNQX-dosed networks with control ones that were prepared and manipulated identically. Figure 2C compares the connectivity maps of the representative perturbed network with a control one. Along the experiment, which lasted 75 min, the control culture retained the same functional traits across the network with small variations, while the degraded one significantly changed. The data of the representative experiment of Figure 2 was a general trend that consistently repeated across eight different cultures, despite their variability in number of clusters, spontaneous activity, and effective connectivity traits. In all cases, CNQX caused a fragmentation of the network into communities together with a sudden increase of GEFF for moderate CNQX levels. To average over culture realizations, however, we observed that each culture responded slightly differently upon perturbation. This resulted in specific CNQX concentrations for the beginning of functional alterations and the end of activity. Thus, for each culture, we considered a reference value [CNQX]ref above which dynamic alterations were detectable, and a maximum [CNQX]max at which activity fully ceased (Figure 3A). Data was then rescaled according to these points to obtain the global efficiency as a function of an adequate control Network Neuroscience 1 166 Functional strengthening through synaptic scaling Figure 3. Treatment of experimental curves and relationship between spontaneous activity and global efficiency. (A) Definition of [CNQX]ref (concentration before any network alteration occurred) and [CNQX]max (no network activity). (B) Alignment of the eight experiments (gray curves), their average (blue), and comparison with four averaged controls (orange). (C) Evolution of GEFF as a function of the average global activity afor every CNQX concentration. Data is scaled relative to [CNQX]ref to pool all experiments together and highlight deviations from the unperturbed condition (dotted lines). The plot shows that hyperefficiency states (GEFF >1) are compatible with low spontaneous activity rates (gray box). The thick blue line is a nonlinear scatter plot smoothing to indicate the general trend of the data. Its shading is the confidence interval set as 80%. parameter that we term degradation level d. The degradation level d=0means that no CNQX is applied and therefore the culture exhibits its natural dynamics, while d=1corresponds to the CNQX dose that is able to fully silence the culture’s activity. The resulting GEFF(d)curves for the eight experiments and their average are shown Figure 3B. All analyzed cultures exhibited hyperefficiency, which ranged from a minimum of 3% to a maximum of 50%, and that on average procured about 20% GEFF increase. This clear peak in global efficiency was inexistent in controls. An aspect that is important to point out is the complex relationship between clusters’ collective activity aand global efficiency GEFF. The data of Figure 2A and B shows that the hyperefficiency observed at [CNQX] =60 nM coincides with a prominent decay in network’s collective activity. The reason for this apparent contradiction is that the global activity just informs about the frequency of collective behavior, but does not capture the local dynamic interaction among clusters. This information is provided by the effective connectivity, from which the global efficiency is computed. Thus, we hypothesize that the clusters strengthen their coupling despite coactivating together less often. The complex relationship between aand GEFF is illustrated in Figure 3C, in which we plotted one against the other for each CNQX concentration, but scaled the values relative to [CNQX]ref to pool all eight experiments in a single plot. Interestingly, several of the points corresponding to a drop in activity, for example, in the range 0.5–1, are associated to GEFF values above 1 (shaded area). These points are precisely the ones that are behind the observed hyperefficiency, and that we associate to a strengthening of the effective coupling among clusters. This analysis thus suggests that a drop in global activity caused by CNQX is responded to by an increase in clusters’ effective coupling. A Degradation Model with Synaptic Scaling Reproduces the Hyperefficiency Phenomenon We carried out numerical simulations to understand the origin of hyperefficiency in the CNQX perturbed experiments. In the simulations we considered the same effective networks as in the experiments for [CNQX]ref and applied two connectivity degradation schemes, namely percolative degradation (PD) and synaptic scaling degradation (SSD). As sketched in Figure 4A, on the one hand, PD corresponds to a standard bond percolation in which links are gradually Network Neuroscience 1 167 Functional strengthening through synaptic scaling Figure 4. Numerical models and hyperefficiency. (A) Sketch of the models used to simulate the impact of a gradual loss of effective connections. In this example, the two models target an effective connection with weight tH=2. For percolative degradation (PD, left) the bottom connection is simply removed upon attack. For synaptic scaling degradation (SSD, right) the same connection is removed, but the surviving outgoing connections are upscaled to distribute the lost weight proportionally among theirs. All curves are averages over eight realizations, and shadings indicate standard deviation. (B) Comparison of the degradation action between experiments (blue) and numerical models (PD, pink; SSD, green). PD portrays a fast-decaying behavior and the network becomes disconnected by d≃0.4. SSD reproduces the hyperefficiency (HE) peak and the gentle decay of GEFF with dup to the end of the disintegration process. The inset shows the distribution of maximum hyperefficiency values for experiments and model. Despite the dispersion in the data, SSD procured overall similar values. removed from weaker to stronger according to a threshold tH. This model reflects the situation in which clusters’ dynamic interaction progressively vanish as degradation grows. On the other hand, SSD consists in the same link removal but with the crucial inclusion of synaptic scaling, which is simulated as the strengthening of the surviving links’ weights proportionally to the lost link’s weight. This model captures a compensatory response mechanism for the loss in activity. In both models, the thresholds are recalculated after the removal process to target the next weakest link, yielding a naturally increasing sequence of thresholds. To compare the models with the experiments, the thresholds tHwere rescaled in the range [0, 1]to concord with the degradation level d. Network Neuroscience 1 168 Functional strengthening through synaptic scaling rate of 50 frames per second (fps), a size of 1,024 ×1,024 pixels, and a spatial resolution of 5.76 µm/pixel. Spontaneous Activity and Network Bursts Clustered cultures were measured at DIV 8–12, a developmental stage in which the clusters exhibited spontaneous activity with at least 1 collective activation (burst) per minute (Table 1). Since, as observed previously by Teller et al. (2014,2015), spontaneous activity in clustered cultures is often of a modular nature, in which the size of collective activations encompasses from few clusters to the entire network, we considered as burst those activity events in which at least five clusters coactivated in a window of 200 ms (Teller et al.,2014). Homgeneous cultures were measured at DIV 12 and exhibited strongly coherent dynamics, in which the whole network activated together during a bursting episode, remaining practically silent in between bursts. Average bursting frequency in the four studied cultures was 9.6 ±4.9 bursts/min. Experimental Procedure and Pharmacology Both excitatory and inhibitory connections were present in the clustered cultures. To investigate the changes in activity induced solely by progressively weaker AMPA glutamate excitation in neurons, NMDA excitatory receptors, which account for 20% of excitatory drive in cortical neurons, were blocked with 20 µM of the receptor antagonist APV (Sigma A5282), and GABAA inhibitory receptors were blocked with 40 µM of the antagonist bicuculline (Sigma B7561). Both antagonists were applied simultaneously and the culture was left 5 min in darkness for biochemical stabilization. A 15-min recording was then conducted and swiftly analyzed to evaluate the initial state of the network. Cultures exhibiting poor or fragmented activity were discarded. For the highly active cultures, AMPA glutamate excitatory connectivity was then gradually weakened by application of the receptor antagonist CNQX, with preset concentrations of [CNQX] (nM) =30, 60, 120, 300, 600, 1,000. For each CNQX concentration, spontaneous activity was recorded for 15 min. Cultures were kept in darkness for 5 min in between recordings for the next drug application to take effect. To investigate whether the neuronal cultures were able to recover the activity patterns prior to CNQX action, the studied clustered cultures were washed off with fresh RS at the end of the recording session, APV and bicuculine applied again, and activity monitored for additional 20 min. Control experiments were carried out to verify that the entire procedure and duration of the recordings did not affect the health of the neurons. Control recordings consisted identical manipulations as standard experiments but without addition of CNQX. A practically identical procedure was followed with homogeneous cultures, with the only difference that the CNQX concentrations were adjusted following Tibau et al. (2020) and Tibau et al. (2013b), and used [CNQX] (nM) =100, 200, 400, 800, 1,000, 2,000. Data Analysis Fluorescence traces. For each experiment, neuronal clusters or individual neurons were manually identified on a highly contrasted fluorescence image and ascribed as regions of interest (ROIs). The average fluorescence (gray scale level) within each ROI was then computed, and the raw fluorescence traces Fi(t)for each cluster iextracted. Each trace was then corrected Network Neuroscience 1 175 Functional strengthening through synaptic scaling from global drifts and artifacts and normalized as DFFi(%)≡100 ·(Fi(t)−Fi,0)/Fi,0, where Fi,0 if the basal fluorescence of each cluster. The onset times of activation of clusters or individual neurons were determined as those events in which the fluorescence trace crossed a preset threshold, set as the mean + 2 times the standard deviation of the entire fluorescence trace (Teller et al.,2014,2015). Trains of activity were then built by ascribing as ‘1’ the existence of an activation at a given time point, and ‘0’ otherwise. Network Analysis Effective connectivity. It was inferred using a modified version of transfer entropy (TE) (Schreiber, 2000). TE was computed for each pair of nodes Xand Y(either clusters or neurons) with signals xmand ymindexed by 0≤m≤mmax, where mmax is the total number of time steps in the data, as TEY→X=−∑ 0≤n≤nmax 0≤i≤iM pxm+1,x(i) m,y(i) m×log2 pxm+1  x(i) m,y(i) m pxm+1  x(i) m,(1) where iis the index of the past time step considered, that is, the length of the vectors {x(i) m}, and iM=2is the Markov order of the model. Here, instantaneous feedback was assumed, meaning that Xand Ycould interact within a time bin, as in generalized transfer entropy (Orlandi, Stetter, Soriano, Geisel, & Battaglia,2014;Stetter et al.,2012). Effective connectivity was inferred for the 15-min-long raster plots (mmax =45, 000 points with an acquisition rate of 50 fps). TE =0for an identical or random pair of signals. Since experimental recordings are short, it may occur that random activations in nearby time bins are taken as causal interactions. Thus, to reject spurious connections, significance zwas established for any connection Xto Yby comparing the TEY→Xestimate with the joint distribution of TE for all input scores X′ to Yand output scores Xto Y′(for any X′and Y′), as z=TEY→X− hTEjointi σjoint ,(2) where hTEjointiis the average value of the joint distribution and σjoint is its standard deviation. Significant connections were then set as those with z≥2. This threshold was considered optimal since it captured the flow of neuronal communication during activity at both local and global scales. A lower threshold of z=1yielded networks that excessively emphasized whole-network coordinated activity, effectively shaping random graphs in all studied cases. Thresholds z&3emphasized the strongest neuron-to-neuron interactions only and often yielded empty matrices. All results presented here were consistent with thresholds in the range 1.5 ≤z≤2.5. By construction, the adjacency matrix A={aij}of significant connections was directed and weighted, conceptually capturing the strength of dynamic interactions between clusters or neurons, and with the weight of the connection given in standard deviation units of the joint distribution. Density of links D. For a network with Nnodes, it was defined as the fraction of total existing effective links (regardless their weight) to all possible links, that is, D=∑ij bij/(N(N−1)), where B={bij}is the binarized adjacency matrix of A. Single realization global efficiency G. The analysis of the data for each investigated culture provided a set effective adjacency matrices {aij}k, where kis the step of CNQX application. Network Neuroscience 1 176 Functional strengthening through synaptic scaling For each of these matrices, the global efficiency Gof a network with Nnodes was determined following the standard definition (Latora & Marchiori,2001;Rubinov & Sporns,2010) G=1 N(N−1)∑ i6=j 1 d(i,j),(3) where d(i,j)is the shortest weighted path calculated on the matrix {aij}, that is, the smallest sum of weights throughout all possible paths between iand j. In this construction, higher connection weights correspond to shorter lengths, and therefore the global efficiency increases with the weight of the connections. If no path exists between nodes iand jthen d(i,j) = ∞, so that there is no contribution to the summation in Equation 3. The term N(N−1)in this equation is a normalization factor that accounts for all possible directed links that can be formed by the Nnodes. Global efficiency was calculated using the Brain Connectivity Toolbox in Matlab. Degradation Level dand Alignment of Experimental Curves The CNQX concentrations were converted into a well-defined parameter that captured in a range [0, 1]the progressive damage of a neuronal network. Thus, for each experiment n, the CNQX concentrations were transformed into steps of a degradation level dby defining d(n) k=[CNQX](n) k−[CNQX](n) ref [CNQX](n) max ,(4) where kis the step of CNQX application along the experiment, [CNQX]kthe corresponding concentration value, [CNQX]ref the reference concentration above which the dynamic alterations in the network are measurable, and [CNQX]max the concentration that fully silenced the network. With this construction, the degradation level dvaried between 0 (no alteration to the network) to 1 (full silencing of activity and complete effective network breakdown). Data outside these bounds was disregarded. Since [CNQX]ref and [CNQX]max varied across cultures, the use of dprovided a robust manner to average among cultures. Scaled Global Efficiency GEFF and Averaged GEFF(d)Curves The set of global efficiency values for each experiment, G(n)(d), was scaled with respect to its reference value prior damage, as G(n) EFF(d) = G(n)(d)/G(n) ref , where G(n) ref is the global efficiency measured at d=0. The G(n) EFF(d)curves were then interpolated as 100 equidistant points by using a cubic interpolation that preserved the shape of the curves, and averaged over n=8 experimental realizations (clustered cultures) or n=4(homogeneous cultures). Numerical Models for Network Degradation Two numerical models were proposed to elucidate the impact of gradual degradation on network global efficiency. Both models considered the same initial effective networks as in the experiments for d=0, denoted as {a(0) ij }, and applied a series of rules for the deletion of links. Since the effective connectivity matrices were obtained from transfer entropy with a significance threshold z=2, the values {a(0) ij }were bounded between amin =2and a given amax that depended on each network. Percolative degradation (PD). This model progressively deleted the effective output links whose weights were equal or lower than a threshold tH, starting at tH=amin and progressively Network Neuroscience 1 177 Functional strengthening through synaptic scaling targeting stronger links (Figure 4A, left). Thus, at a given simulation step, the deleted links were those that fulfilled tH=aij, increasing tHafterward to target the next weak link in the network, until all links of the network were deleted. The global efficiency Gwas computed at each threshold, and the final GPD(tH)values stored for further analysis. Synaptic scaling degradation (SSD). This model also progressively deleted the weakest output links, but with the crucial additional rule that, upon link removal (with weight tH), all surviving output links shared the weight of the removed one, increasing theirs proportionally (Figure 4A, right). Thus, if there were at least two links and the total output strength before deletion was sbef i=∑jabef ij , the new weights were given by aij =abef ij ·sbef i/(sbef i−tH). If only one output link was present, it was deleted as in PD. The new global efficiency of the network GSSD(tH)was then computed, the threshold updated to seek for the new weakest links, and the process started again. Simulation ended when all links in the network were removed, and the final GSSD(tH)values stored. The GPD(tH)and GSSD(tH)data obtained from the models was finally treated as in the experiments. First, for each simulated network, the tHvalues (which ranged from amin to amax in the PD model, and from amin to a certain a∗ max ≥amax for SSD) were scaled as d∈[0, 1]. The new GPD(d)and GSSD(d)curves were then scaled relative to their values at d=0and averaged among realizations to obtain the scaled global efficiencies GEFF(d), which could be directly compared with the experiments. Ethics Statement All procedures were approved by the Ethical Committee for Animal Experimentation of the University of Barcelona, under order DMAH-5461, and in accordance to the regulations of the Generalitat de Catalunya (Spain). AUTHOR CONTRIBUTIONS Estefanía Estévez-Priego: Data curation; Formal analysis; Investigation; Methodology; Software; Visualization; Writing - Original Draft. Sara Teller: Data curation; Methodology; Resources; Software; Supervision; Validation. Clara Granell: Data curation; Formal analysis; Methodology; Validation; Visualization; Writing - Review & Editing. Alex Arenas: Conceptualization; Formal analysis; Funding acquisition; Investigation; Project administration; Resources; Supervision; Writing - Review & Editing. Jordi Soriano: Conceptualization; Funding acquisition; Investigation; Methodology; Resources; Software; Supervision; Validation; Writing - Original Draft; Writing - Review & Editing. FUNDING INFORMATION Jordi Soriano, Fundació Bancària “La Caixa” (http://dx.doi.org/10.13039/100000778), Award ID: LCF/PR/HR19/52160007. Jordi Soriano, H2020 Future and Emerging Technologies (http://dx.doi.org/10.13039/100010664), Award ID: 713140 MESOBRAIN. Estefanía EstévezPriego, H2020 Future and Emerging Technologies (http://dx.doi.org/10.13039/100010664), Award ID: 713140 MESOBRAIN. Jordi Soriano, Secretaría de Estado de Investigación, Desarrollo e Innovación (http://dx.doi.org/10.13039/501100007136), Award ID: FIS201341144-P, FIS201678507-C2-2-P, FIS2017-90782-REDT. Sara Teller, Secretaría de Estado de Investigacíón, Desarrollo e Innovación (http://dx.doi.org/10.13039/501100007136),Award ID: FIS2013-41144-P, FIS201678507-C2-2-P, FIS2017-90782-REDT. Jordi Soriano, Departament Network Neuroscience 1 178 Functional strengthening through synaptic scaling d’Innovació, Universitats i Empresa, Generalitat de Catalunya (http://dx.doi.org/10.13039 /501100002943), Award ID: 2017-SGR-1061. Alex Arenas, Departament d’Innovació, Universitats i Empresa, Generalitat de Catalunya (http://dx.doi.org/10.13039/501100002943), Award ID: 2017-SGR-896. Alex Arenas, Secretaría de Estado de Investigación, Desarrollo e Innovación (http://dx.doi.org/10.13039/501100007136),Award ID: PGC2018-094754-B-C21. Alex Arenas, Universitat Rovira i Virgili (http://dx.doi.org/10.13039/501100007512), Award ID: 2017PFRURV-B2-41. Alex Arenas, ICREA Academia . Alex Arenas, James S. McDonnell Foundation (http://dx.doi.org/10.13039/100000913), Award ID: 220020325. Clara Granell, James S. 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