Structural Modularity Tunes Mesoscale Criticality in Biological Neuronal Networks.

Numerous studies suggest that biological neuronal networks self-organize toward a critical state with stable recruitment dynamics. Individual neurons would then statistically activate exactly one further neuron during activity cascades termed neuronal avalanches. Yet, it is unclear if and how this can be reconciled with the explosive recruitment dynamics within neocortical minicolumns in vivo and within neuronal clusters in vitro, which indicates that neurons form supercritical local circuits. Theoretical studies propose that modular networks with a mix of regionally subcritical and supercritical dynamics would create apparently critical dynamics, resolving this inconsistency. Here, we provide experimental support by manipulating the structural self-organization process of networks of cultured rat cortical neurons (either sex). Consistent with the prediction, we show that increasing clustering in neuronal networks developing in vitro strongly correlates with avalanche size distributions transitioning from supercritical to subcritical activity dynamics. Avalanche size distributions approximated a power law in moderately clustered networks, indicating overall critical recruitment. We propose that activity-dependent self-organization can tune inherently supercritical networks toward mesoscale criticality by creating a modular structure in neuronal networks.SIGNIFICANCE STATEMENT Critical recruitment dynamics in neuronal networks are considered optimal for information processing in the brain. However, it remains heavily debated how neuronal networks would self-organize criticality by detailed fine-tuning of connectivity, inhibition, and excitability. We provide experimental support for theoretical considerations that modularity tunes critical recruitment dynamics at the mesoscale level of interacting neuron clusters. This reconciles reports of supercritical recruitment dynamics in local neuron clusters with findings on criticality sampled at mesoscopic network scales. Intriguingly, altered mesoscale organization is a prominent aspect of various neuropathological diseases currently investigated in the framework of criticality. We therefore believe that our findings would also be of interest for clinical scientists searching to link the functional and anatomic signatures of such brain disorders.

Mesoscale Architecture Shapes Initiation and Richness of Spontaneous Network Activity.

Spontaneous activity in the absence of external input, including propagating waves of activity, is a robust feature of neuronal networks in vivo and in vitro The neurophysiological and anatomical requirements for initiation and persistence of such activity, however, are poorly understood, as is their role in the function of neuronal networks. Computational network studies indicate that clustered connectivity may foster the generation, maintenance, and richness of spontaneous activity. Since this mesoscale architecture cannot be systematically modified in intact tissue, testing these predictions is impracticable in vivo Here, we investigate how the mesoscale structure shapes spontaneous activity in generic networks of rat cortical neurons in vitro In these networks, neurons spontaneously arrange into local clusters with high neurite density and form fasciculating long-range axons. We modified this structure by modulation of protein kinase C, an enzyme regulating neurite growth and cell migration. Inhibition of protein kinase C reduced neuronal aggregation and fasciculation of axons, i.e., promoted uniform architecture. Conversely, activation of protein kinase C promoted aggregation of neurons into clusters, local connectivity, and bundling of long-range axons. Supporting predictions from theory, clustered networks were more spontaneously active and generated diverse activity patterns. Neurons within clusters received stronger synaptic inputs and displayed increased membrane potential fluctuations. Intensified clustering promoted the initiation of synchronous bursting events but entailed incomplete network recruitment. Moderately clustered networks appear optimal for initiation and propagation of diverse patterns of activity. Our findings support a crucial role of the mesoscale architectures in the regulation of spontaneous activity dynamics.SIGNIFICANCE STATEMENT Computational studies predict richer and persisting spatiotemporal patterns of spontaneous activity in neuronal networks with neuron clustering. To test this, we created networks of varying architecture in vitro Supporting these predictions, the generation and spatiotemporal patterns of propagation were most variable in networks with intermediate clustering and lowest in uniform networks. Grid-like clustering, on the other hand, facilitated spontaneous activity but led to degenerating patterns of propagation. Neurons outside clusters had weaker synaptic input than neurons within clusters, in which increased membrane potential fluctuations facilitated the initiation of synchronized spike activity. Our results thus show that the intermediate level organization of neuronal networks strongly influences the dynamics of their activity.

Autonomous Optimization of Targeted Stimulation of Neuronal Networks.

Driven by clinical needs and progress in neurotechnology, targeted interaction with neuronal networks is of increasing importance. Yet, the dynamics of interaction between intrinsic ongoing activity in neuronal networks and their response to stimulation is unknown. Nonetheless, electrical stimulation of the brain is increasingly explored as a therapeutic strategy and as a means to artificially inject information into neural circuits. Strategies using regular or event-triggered fixed stimuli discount the influence of ongoing neuronal activity on the stimulation outcome and are therefore not optimal to induce specific responses reliably. Yet, without suitable mechanistic models, it is hardly possible to optimize such interactions, in particular when desired response features are network-dependent and are initially unknown. In this proof-of-principle study, we present an experimental paradigm using reinforcement-learning (RL) to optimize stimulus settings autonomously and evaluate the learned control strategy using phenomenological models. We asked how to (1) capture the interaction of ongoing network activity, electrical stimulation and evoked responses in a quantifiable 'state' to formulate a well-posed control problem, (2) find the optimal state for stimulation, and (3) evaluate the quality of the solution found. Electrical stimulation of generic neuronal networks grown from rat cortical tissue in vitro evoked bursts of action potentials (responses). We show that the dynamic interplay of their magnitudes and the probability to be intercepted by spontaneous events defines a trade-off scenario with a network-specific unique optimal latency maximizing stimulus efficacy. An RL controller was set to find this optimum autonomously. Across networks, stimulation efficacy increased in 90% of the sessions after learning and learned latencies strongly agreed with those predicted from open-loop experiments. Our results show that autonomous techniques can exploit quantitative relationships underlying activity-response interaction in biological neuronal networks to choose optimal actions. Simple phenomenological models can be useful to validate the quality of the resulting controllers.

Quantitative examination of stimulus-response relations in cortical networks in vitro.

Variable responses of neuronal networks to repeated sensory or electrical stimuli reflect the interaction of the stimulus' response with ongoing activity in the brain and its modulation by adaptive mechanisms, such as cognitive context, network state, or cellular excitability and synaptic transmission capability. Here, we focus on reliability, length, delays, and variability of evoked responses with respect to their spatial distribution, interaction with spontaneous activity in the networks, and the contribution of GABAergic inhibition. We identified network-intrinsic principles that underlie the formation and modulation of spontaneous activity and stimulus-response relations with the use of state-dependent stimulation in generic neuronal networks in vitro. The duration of spontaneously recurring network-wide bursts of spikes was best predicted by the length of the preceding interval. Length, delay, and structure of responses to identical stimuli systematically depended on stimulus timing and distance to the stimulation site, which were described by a set of simple functions of spontaneous activity. Response length at proximal recording sites increased with the duration of prestimulus inactivity and was best described by a saturation function y(t) = A(1 - e(-αt)). Concomitantly, the delays of polysynaptic late responses at distant sites followed an exponential decay y(t) = Be(-ßt) + C. In addition, the speed of propagation was determined by the overall state of the network at the moment of stimulation. Disinhibition increased the number of spikes/network burst and interburst interval length at unchanged gross firing rate, whereas the response modulation by the duration of prestimulus inactivity was preserved. Our data suggest a process of network depression during bursts and subsequent recovery that limit evoked responses following distinct rules. We discuss short-term synaptic depression due to depletion of neurotransmitter vesicles as an underlying mechanism. The seemingly unreliable patterns of spontaneous activity and stimulus-response relations thus follow a predictable structure determined by the interdependencies of network structures and activity states.

Self-organized criticality in developing neuronal networks.

Recently evidence has accumulated that many neural networks exhibit self-organized criticality. In this state, activity is similar across temporal scales and this is beneficial with respect to information flow. If subcritical, activity can die out, if supercritical epileptiform patterns may occur. Little is known about how developing networks will reach and stabilize criticality. Here we monitor the development between 13 and 95 days in vitro (DIV) of cortical cell cultures (n = 20) and find four different phases, related to their morphological maturation: An initial low-activity state (≈19 DIV) is followed by a supercritical (≈20 DIV) and then a subcritical one (≈36 DIV) until the network finally reaches stable criticality (≈58 DIV). Using network modeling and mathematical analysis we describe the dynamics of the emergent connectivity in such developing systems. Based on physiological observations, the synaptic development in the model is determined by the drive of the neurons to adjust their connectivity for reaching on average firing rate homeostasis. We predict a specific time course for the maturation of inhibition, with strong onset and delayed pruning, and that total synaptic connectivity should be strongly linked to the relative levels of excitation and inhibition. These results demonstrate that the interplay between activity and connectivity guides developing networks into criticality suggesting that this may be a generic and stable state of many networks in vivo and in vitro.

Layers II/III of Prefrontal Cortex in Df(h22q11)/+ Mouse Model of the 22q11.2 Deletion Display Loss of Parvalbumin Interneurons and Modulation of Neuronal Morphology and Excitability.

The 22q11.2 deletion has been identified as a risk factor for multiple neurodevelopmental disorders. Behavioral and cognitive impairments are common among carriers of the 22q11.2 deletion. Parvalbumin expressing (PV+) interneurons provide perisomatic inhibition of excitatory neuronal circuits through GABAA receptors, and a deficit of PV+ inhibitory circuits may underlie a multitude of the behavioral and functional deficits in the 22q11.2 deletion syndrome. We investigated putative deficits of PV+ inhibitory circuits and the associated molecular, morphological, and functional alterations in the prefrontal cortex (PFC) of the Df(h22q11)/+ mouse model of the 22q11.2 hemizygous deletion. We detected a significant decrease in the number of PV+ interneurons in layers II/III of PFC in Df(h22q11)/+ mice together with a reduction in the mRNA and protein levels of GABAA (α3), a PV+ putative postsynaptic receptor subunit. Pyramidal neurons from the same layers further experienced morphological reorganizations of spines and dendrites. Accordingly, a decrease in the levels of the postsynaptic density protein 95 (PSD95) and a higher neuronal activity in response to the GABAA antagonist bicuculline were measured in these layers in PFC of Df(h22q11)/+ mice compared with their wild-type littermates. Our study shows that a hemizygotic deletion of the 22q11.2 locus leads to deficit in the GABAergic control of network activity and involves molecular and morphological changes in both the inhibitory and excitatory synapses of parvalbumin interneurons and pyramidal neurons specifically in layers II/III PFC.

Inhomogeneities in Network Structure and Excitability Govern Initiation and Propagation of Spontaneous Burst Activity.

The mesoscale architecture of neuronal networks strongly influences the initiation of spontaneous activity and its pathways of propagation. Spontaneous activity has been studied extensively in networks of cultured cortical neurons that generate complex yet reproducible patterns of synchronous bursting events that resemble the activity dynamics in developing neuronal networks in vivo. Synchronous bursts are mostly thought to be triggered at burst initiation sites due to build-up of noise or by highly active neurons, or to reflect reverberating activity that circulates within larger networks, although neither of these has been observed directly. Inferring such collective dynamics in neuronal populations from electrophysiological recordings crucially depends on the spatial resolution and sampling ratio relative to the size of the networks assessed. Using large-scale microelectrode arrays with 1024 electrodes at 0.3 mm pitch that covered the full extent of in vitro networks on about 1 cm2, we investigated where bursts of spontaneous activity arise and how their propagation patterns relate to the regions of origin, the network's structure, and to the overall distribution of activity. A set of alternating burst initiation zones (BIZ) dominated the initiation of distinct bursting events and triggered specific propagation patterns. Moreover, BIZs were typically located in areas with moderate activity levels, i.e., at transitions between hot and cold spots. The activity-dependent alternation between these zones suggests that the local networks forming the dominating BIZ enter a transient depressed state after several cycles (similar to Eytan et al., 2003), allowing other BIZs to take over temporarily. We propose that inhomogeneities in the network structure define such BIZs and that the depletion of local synaptic resources limit repetitive burst initiation.

Self-organization of modular network architecture by activity-dependent neuronal migration and outgrowth.

The spatial distribution of neurons and activity-dependent neurite outgrowth shape long-range interaction, recurrent local connectivity and the modularity in neuronal networks. We investigated how this mesoscale architecture develops by interaction of neurite outgrowth, cell migration and activity in cultured networks of rat cortical neurons and show that simple rules can explain variations of network modularity. In contrast to theoretical studies on activity-dependent outgrowth but consistent with predictions for modular networks, spontaneous activity and the rate of synchronized bursts increased with clustering, whereas peak firing rates in bursts increased in highly interconnected homogeneous networks. As Ca2+ influx increased exponentially with increasing network recruitment during bursts, its modulation was highly correlated to peak firing rates. During network maturation, long-term estimates of Ca2+ influx showed convergence, even for highly different mesoscale architectures, neurite extent, connectivity, modularity and average activity levels, indicating homeostatic regulation towards a common set-point of Ca2+ influx.