Homeostatic scaling of excitability in recurrent neural networks

Anxious individuals shift emotion control from lateral frontal pole to dorsolateral prefrontal cortex

Anxious individuals consistently fail in controlling emotional behavior, leading to excessive avoidance, a trait that prevents learning through exposure. Although the origin of this failure is unclear, one candidate system involves control of emotional actions, coordinated through lateral frontopolar cortex (FPl) via amygdala and sensorimotor connections. Using structural, functional, and neurochemical evidence, we show how FPl-based emotional action control fails in highly-anxious individuals. Their FPl is overexcitable, as indexed by GABA/glutamate ratio at rest, and receives stronger amygdalofugal projections than non-anxious male participants. Yet, high-anxious individuals fail to recruit FPl during emotional action control, relying instead on dorsolateral and medial prefrontal areas. This functional anatomical shift is proportional to FPl excitability and amygdalofugal projections strength. The findings characterize circuit-level vulnerabilities in anxious individuals, showing that even mild emotional challenges can saturate FPl neural range, leading to a neural bottleneck in the control of emotional action tendencies.

Noise-modulated multistable synapses in a Wilson-Cowan-based model of plasticity

Frequency-dependent plasticity refers to changes in synaptic strength in response to different stimulation frequencies. Resonance is a factor known to be of importance in such frequency dependence, however, the role of neural noise in the process remains elusive. Considering the brain is an inherently noisy system, understanding its effects may prove beneficial in shaping therapeutic interventions based on non-invasive brain stimulation protocols. The Wilson-Cowan (WC) model is a well-established model to describe the average dynamics of neural populations and has been shown to exhibit bistability in the presence of noise. However, the important question of how the different stable regimes in the WC model can affect synaptic plasticity when cortical populations interact has not yet been addressed. Therefore, we investigated plasticity dynamics in a WC-based model of interacting neural populations coupled with activity-dependent synapses in which a periodic stimulation was applied in the presence of noise of controlled intensity. The results indicate that for a narrow range of the noise variance, synaptic strength can be optimized. In particular, there is a regime of noise intensity for which synaptic strength presents a triple-stable state. Regulating noise intensity affects the probability that the system chooses one of the stable states, thereby controlling plasticity. These results suggest that noise is a highly influential factor in determining the outcome of plasticity induced by stimulation.

Local Homeostatic Regulation of the Spectral Radius of Echo-State Networks

Recurrent cortical networks provide reservoirs of states that are thought to play a crucial role for sequential information processing in the brain. However, classical reservoir computing requires manual adjustments of global network parameters, particularly of the spectral radius of the recurrent synaptic weight matrix. It is hence not clear if the spectral radius is accessible to biological neural networks. Using random matrix theory, we show that the spectral radius is related to local properties of the neuronal dynamics whenever the overall dynamical state is only weakly correlated. This result allows us to introduce two local homeostatic synaptic scaling mechanisms, termed flow control and variance control, that implicitly drive the spectral radius toward the desired value. For both mechanisms the spectral radius is autonomously adapted while the network receives and processes inputs under working conditions. We demonstrate the effectiveness of the two adaptation mechanisms under different external input protocols. Moreover, we evaluated the network performance after adaptation by training the network to perform a time-delayed XOR operation on binary sequences. As our main result, we found that flow control reliably regulates the spectral radius for different types of input statistics. Precise tuning is however negatively affected when interneural correlations are substantial. Furthermore, we found a consistent task performance over a wide range of input strengths/variances. Variance control did however not yield the desired spectral radii with the same precision, being less consistent across different input strengths. Given the effectiveness and remarkably simple mathematical form of flow control, we conclude that self-consistent local control of the spectral radius via an implicit adaptation scheme is an interesting and biological plausible alternative to conventional methods using set point homeostatic feedback controls of neural firing.

Consequences of Dale's law on the stability-complexity relationship of random neural networks

In the study of randomly connected neural network dynamics there is a phase transition from a simple state with few equilibria to a complex state characterized by the number of equilibria growing exponentially with the neuron population. Such phase transitions are often used to describe pathological brain state transitions observed in neurological diseases such as epilepsy. In this paper we investigate how more realistic heterogeneous network structures affect these phase transitions using techniques from random matrix theory. Specifically, we parametrize the network structure according to Dale's law and use the Kac-Rice formalism to compute the change in the number of equilibria when a phase transition occurs. We also examine the condition where the network is not balanced between excitation and inhibition causing outliers to appear in the eigenspectrum. This enables us to compute the effects of different heterogeneous network connectivities on brain state transitions, which can provide insights into pathological brain dynamics.

Green model to adapt classical conditioning learning in the hippocampus

Compared with the biological paradigms of classical conditioning, non-adaptive computational models are not capable of realistically simulating the biological behavioural functions of the hippocampal regions, because of their implausible requirement for a large number of learning trials, which can be on the order of hundreds. Additionally, these models did not attain a unified, final stable state even after hundreds of learning trials. Conversely, the output response has a different threshold for similar tasks in various models with prolonged transient response of unspecified status via the training or even testing phases. Accordingly, a green model is a combination of adaptive neuro-computational hippocampal and cortical models that is proposed by adaptively updating the whole weights in all layers for both intact networks and lesion networks using instar and outstar learning rules with adaptive resonance theory (ART). The green model sustains and expands the classical conditioning biological paradigms of the non-adaptive models. The model also overcomes the irregular output response behaviour by using the proposed feature of adaptivity. Further, the model successfully simulates the hippocampal regions without passing the final output response back to the whole network, which is considered to be biologically implausible. The results of the Green model showed a significant improvement confirmed by empirical studies of different tasks. In addition, the results indicated that the model outperforms the previously published models. All the obtained results successfully and quickly attained a stable, desired final state (with a unified concluding state of either "1" or "0") with a significantly shorter transient duration.

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < 4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law–tailed synchronization durations, with τ_t ≃ 1.2(1), away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: τ_t ≃ 1.6(1). However, below the transition of the connectome we found global coupling control-parameter dependent exponents 1 < τ_t ≤ 2, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.

A Dynamic Connectome Supports the Emergence of Stable Computational Function of Neural Circuits through Reward-Based Learning

Synaptic connections between neurons in the brain are dynamic because of continuously ongoing spine dynamics, axonal sprouting, and other processes. In fact, it was recently shown that the spontaneous synapse-autonomous component of spine dynamics is at least as large as the component that depends on the history of pre- and postsynaptic neural activity. These data are inconsistent with common models for network plasticity and raise the following questions: how can neural circuits maintain a stable computational function in spite of these continuously ongoing processes, and what could be functional uses of these ongoing processes? Here, we present a rigorous theoretical framework for these seemingly stochastic spine dynamics and rewiring processes in the context of reward-based learning tasks. We show that spontaneous synapse-autonomous processes, in combination with reward signals such as dopamine, can explain the capability of networks of neurons in the brain to configure themselves for specific computational tasks, and to compensate automatically for later changes in the network or task. Furthermore, we show theoretically and through computer simulations that stable computational performance is compatible with continuously ongoing synapse-autonomous changes. After reaching good computational performance it causes primarily a slow drift of network architecture and dynamics in task-irrelevant dimensions, as observed for neural activity in motor cortex and other areas. On the more abstract level of reinforcement learning the resulting model gives rise to an understanding of reward-driven network plasticity as continuous sampling of network configurations.

Evidence for frequency-dependent cortical plasticity in the human brain

Frequency-dependent plasticity (FDP) describes adaptation at the synapse in response to stimulation at different frequencies. Its consequence on the structure and function of cortical networks is unknown. We tested whether cortical "resonance," favorable stimulation frequencies at which the sensory cortices respond maximally, influenced the impact of FDP on perception, functional topography, and connectivity of the primary somatosensory cortex using psychophysics and functional imaging (fMRI). We costimulated two digits on the hand synchronously at, above, or below the resonance frequency of the somatosensory cortex, and tested subjects' accuracy and speed on tactile localization before and after costimulation. More errors and slower response times followed costimulation at above- or below-resonance, respectively. Response times were faster after at-resonance costimulation. In the fMRI, the cortical representations of the two digits costimulated above-resonance shifted closer, potentially accounting for the poorer performance. Costimulation at-resonance did not shift the digit regions, but increased the functional coupling between them, potentially accounting for the improved response time. To relate these results to synaptic plasticity, we simulated a network of oscillators incorporating Hebbian learning. Two neighboring patches embedded in a cortical sheet, mimicking the two digit regions, were costimulated at different frequencies. Network activation outside the stimulated patches was greatest at above-resonance frequencies, reproducing the spread of digit representations seen with fMRI. Connection strengths within the patches increased following at-resonance costimulation, reproducing the increased fMRI connectivity. We show that FDP extends to the cortical level and is influenced by cortical resonance.

A Model of Fast Hebbian Spike Latency Normalization

Hebbian changes of excitatory synapses are driven by and enhance correlations between pre- and postsynaptic neuronal activations, forming a positive feedback loop that can lead to instability in simulated neural networks. Because Hebbian learning may occur on time scales of seconds to minutes, it is conjectured that some form of fast stabilization of neural firing is necessary to avoid runaway of excitation, but both the theoretical underpinning and the biological implementation for such homeostatic mechanism are to be fully investigated. Supported by analytical and computational arguments, we show that a Hebbian spike-timing-dependent metaplasticity rule, accounts for inherently-stable, quick tuning of the total input weight of a single neuron in the general scenario of asynchronous neural firing characterized by UP and DOWN states of activity.

Modeling of Age-Dependent Epileptogenesis by Differential Homeostatic Synaptic Scaling

Homeostatic synaptic plasticity (HSP) has been implicated in the development of hyperexcitability and epileptic seizures following traumatic brain injury (TBI). Our in vivo experimental studies in cats revealed that the severity of TBI-mediated epileptogenesis depends on the age of the animal. To characterize mechanisms of these differences, we studied the properties of the TBI-induced epileptogenesis in a biophysically realistic cortical network model with dynamic ion concentrations. After deafferentation, which was induced by dissection of the afferent inputs, there was a reduction of the network activity and upregulation of excitatory connections leading to spontaneous spike-and-wave type seizures. When axonal sprouting was implemented, the seizure threshold increased in the model of young but not the older animals, which had slower or unidirectional homeostatic processes. Our study suggests that age-related changes in the HSP mechanisms are sufficient to explain the difference in the likelihood of seizure onset in young versus older animals. Significance statement: Traumatic brain injury (TBI) is one of the leading causes of intractable epilepsy. Likelihood of developing epilepsy and seizures following severe brain trauma has been shown to increase with age. Specific mechanisms of TBI-related epileptogenesis and how these mechanisms are affected by age remain to be understood. We test a hypothesis that the failure of homeostatic synaptic regulation, a slow negative feedback mechanism that maintains neural activity within a physiological range through activity-dependent modulation of synaptic strength, in older animals may augment TBI-induced epileptogenesis. Our results provide new insight into understanding this debilitating disorder and may lead to novel avenues for the development of effective treatments of TBI-induced epilepsy.

Stability of Neuronal Networks with Homeostatic Regulation

Neurons are equipped with homeostatic mechanisms that counteract long-term perturbations of their average activity and thereby keep neurons in a healthy and information-rich operating regime. While homeostasis is believed to be crucial for neural function, a systematic analysis of homeostatic control has largely been lacking. The analysis presented here analyses the necessary conditions for stable homeostatic control. We consider networks of neurons with homeostasis and show that homeostatic control that is stable for single neurons, can destabilize activity in otherwise stable recurrent networks leading to strong non-abating oscillations in the activity. This instability can be prevented by slowing down the homeostatic control. The stronger the network recurrence, the slower the homeostasis has to be. Next, we consider how non-linearities in the neural activation function affect these constraints. Finally, we consider the case that homeostatic feedback is mediated via a cascade of multiple intermediate stages. Counter-intuitively, the addition of extra stages in the homeostatic control loop further destabilizes activity in single neurons and networks. Our theoretical framework for homeostasis thus reveals previously unconsidered constraints on homeostasis in biological networks, and identifies conditions that require the slow time-constants of homeostatic regulation observed experimentally.

Despite their apparent robustness many biological system work best in controlled environments, the tightly regulated mammalian body temperature being a good example. Biological homeostatic control systems, not unlike those used in engineering, ensure that the right operating conditions are met. Similarly, neurons appear to adjust the amount of activity they produce to be neither too high nor too low by, among other ways, regulating their excitability. However, for no apparent reason the neural homeostatic processes are very slow, taking hours or even days to regulate the neuron. Here we use results from mathematical control theory to examine under which conditions such slow control is necessary to prevent instabilities that lead to strong, sustained oscillations in the activity. Our results lead to a deeper understanding of neural homeostasis and can help the design of artificial neural systems.

Homeostatic plasticity for single node delay-coupled reservoir computing

Supplementing a differential equation with delays results in an infinite-dimensional dynamical system. This property provides the basis for a reservoir computing architecture, where the recurrent neural network is replaced by a single nonlinear node, delay-coupled to itself. Instead of the spatial topology of a network, subunits in the delay-coupled reservoir are multiplexed in time along one delay span of the system. The computational power of the reservoir is contingent on this temporal multiplexing. Here, we learn optimal temporal multiplexing by means of a biologically inspired homeostatic plasticity mechanism. Plasticity acts locally and changes the distances between the subunits along the delay, depending on how responsive these subunits are to the input. After analytically deriving the learning mechanism, we illustrate its role in improving the reservoir's computational power. To this end, we investigate, first, the increase of the reservoir's memory capacity. Second, we predict a NARMA-10 time series, showing that plasticity reduces the normalized root-mean-square error by more than 20%. Third, we discuss plasticity's influence on the reservoir's input-information capacity, the coupling strength between subunits, and the distribution of the readout coefficients.

Expression of specific ionotropic glutamate and GABA-A receptor subunits is decreased in central amygdala of alcoholics

The central amygdala (CeA) has a role for mediating fear and anxiety responses. It is also involved in emotional imbalance caused by alcohol abuse and dependence and in regulating relapse to alcohol abuse. Growing evidences suggest that excitatory glutamatergic and inhibitory γ-aminobutyric acid-ergic (GABAergic) transmissions in the CeA are affected by chronic alcohol exposure. Human post-mortem CeA samples from male alcoholics (n = 9) and matched controls (n = 9) were assayed for the expression level of ionotropic glutamate and GABA-A receptors subunit mRNAs using quantitative real-time reverse transcription-PCR (RT-qPCR). Our data revealed that out of the 16 ionotropic glutamate receptor subunits, mRNAs encoding two AMPA [2-amino-3-(3-hydroxy-5-methyl-isoxazol-4-yl)propanoic acid] receptor subunits GluA1 and GluA4; one kainate receptor subunit GluK2; one NMDA (N-methyl-D-aspartate) receptor subunit GluN2D and one delta receptor subunit GluD2 were significantly decreased in the CeA of alcoholics. In contrast, of the 19 GABA-A receptor subunits, only the mRNA encoding the α2 subunit was significantly down-regulated in the CeA of the alcoholics as compared with control subjects. Our findings imply that the down-regulation of specific ionotropic glutamate and GABA-A receptor subunits in the CeA of alcoholics may represent one of the molecular substrates underlying the new balance between excitatory and inhibitory neurotransmission in alcohol dependence.

Neuronal networks and energy bursts in epilepsy

Epilepsy can be defined as the abnormal activities of neurons. The occurrence, propagation and termination of epileptic seizures rely on the networks of neuronal cells that are connected through both synaptic- and non-synaptic interactions. These complicated interactions contain the modified functions of normal neurons and glias as well as the mediation of excitatory and inhibitory mechanisms with feedback homeostasis. Numerous spread patterns are detected in disparate networks of ictal activities. The cortical-thalamic-cortical loop is present during a general spike wave seizure. The thalamic reticular nucleus (nRT) is the major inhibitory input traversing the region, and the dentate gyrus (DG) controls CA3 excitability. The imbalance between γ-aminobutyric acid (GABA)-ergic inhibition and glutamatergic excitation is the main disorder in epilepsy. Adjustable negative feedback that mediates both inhibitory and excitatory components affects neuronal networks through neurotransmission fluctuation, receptor and transmitter signaling, and through concomitant influences on ion concentrations and field effects. Within a limited dynamic range, neurons slowly adapt to input levels and have a high sensitivity to synaptic changes. The stability of the adapting network depends on the ratio of the adaptation rates of both the excitatory and inhibitory populations. Thus, therapeutic strategies with multiple effects on seizures are required for the treatment of epilepsy, and the therapeutic functions on networks are reviewed here. Based on the high-energy burst theory of epileptic activity, we propose a potential antiepileptic therapeutic strategy to transfer the high energy and extra electricity out of the foci.

Behavior control in the sensorimotor loop with short-term synaptic dynamics induced by self-regulating neurons

The behavior and skills of living systems depend on the distributed control provided by specialized and highly recurrent neural networks. Learning and memory in these systems is mediated by a set of adaptation mechanisms, known collectively as neuronal plasticity. Translating principles of recurrent neural control and plasticity to artificial agents has seen major strides, but is usually hampered by the complex interactions between the agent's body and its environment. One of the important standing issues is for the agent to support multiple stable states of behavior, so that its behavioral repertoire matches the requirements imposed by these interactions. The agent also must have the capacity to switch between these states in time scales that are comparable to those by which sensory stimulation varies. Achieving this requires a mechanism of short-term memory that allows the neurocontroller to keep track of the recent history of its input, which finds its biological counterpart in short-term synaptic plasticity. This issue is approached here by deriving synaptic dynamics in recurrent neural networks. Neurons are introduced as self-regulating units with a rich repertoire of dynamics. They exhibit homeostatic properties for certain parameter domains, which result in a set of stable states and the required short-term memory. They can also operate as oscillators, which allow them to surpass the level of activity imposed by their homeostatic operation conditions. Neural systems endowed with the derived synaptic dynamics can be utilized for the neural behavior control of autonomous mobile agents. The resulting behavior depends also on the underlying network structure, which is either engineered or developed by evolutionary techniques. The effectiveness of these self-regulating units is demonstrated by controlling locomotion of a hexapod with 18 degrees of freedom, and obstacle-avoidance of a wheel-driven robot.

Selective increases of AMPA, NMDA, and kainate receptor subunit mRNAs in the hippocampus and orbitofrontal cortex but not in prefrontal cortex of human alcoholics

Glutamate is the main excitatory transmitter in the human brain. Drugs that affect the glutamatergic signaling will alter neuronal excitability. Ethanol inhibits glutamate receptors. We examined the expression level of glutamate receptor subunit mRNAs in human post-mortem samples from alcoholics and compared the results to brain samples from control subjects. RNA from hippocampal dentate gyrus (HP-DG), orbitofrontal cortex (OFC), and dorso-lateral prefrontal cortex (DL-PFC) samples from 21 controls and 19 individuals with chronic alcohol dependence were included in the study. Total RNA was assayed using quantitative RT-PCR. Out of the 16 glutamate receptor subunits, mRNAs encoding two AMPA [2-amino-3-(3-hydroxy-5-methyl-isoxazol-4-yl)propanoic acid] receptor subunits GluA2 and GluA3; three kainate receptor subunits GluK2, GluK3 and GluK5 and five NMDA (N-methyl-D-aspartate) receptor subunits GluN1, GluN2A, GluN2C, GluN2D, and GluN3A were significantly increased in the HP-DG region in alcoholics. In the OFC, mRNA encoding the NMDA receptor subunit GluN3A was increased, whereas in the DL-PFC, no differences in mRNA levels were observed. Our laboratory has previously shown that the expression of genes encoding inhibitory GABA-A receptors is altered in the HP-DG and OFC of alcoholics (Jin et al., 2011). Whether the changes in one neurotransmitter system drives changes in the other or if they change independently is currently not known. The results demonstrate that excessive long-term alcohol consumption is associated with altered expression of genes encoding glutamate receptors in a brain region-specific manner. It is an intriguing possibility that genetic predisposition to alcoholism may contribute to these gene expression changes.

Transcriptional and epigenetic regulation of Hebbian and non-Hebbian plasticity

The epigenome is uniquely positioned as a point of convergence, integrating multiple intracellular signaling cascades into a cohesive gene expression profile necessary for long-term behavioral change. The last decade of neuroepigenetic research has primarily focused on learning-induced changes in DNA methylation and chromatin modifications. Numerous studies have independently demonstrated the importance of epigenetic modifications in memory formation and retention as well as Hebbian plasticity. However, how these mechanisms operate in the context of other forms of plasticity is largely unknown. In this review, we examine evidence for epigenetic regulation of Hebbian plasticity. We then discuss how non-Hebbian forms of plasticity, such as intrinsic plasticity and synaptic scaling, may also be involved in producing the cellular adaptations necessary for learning-related behavioral change. Furthermore, we consider the likely roles for transcriptional and epigenetic mechanisms in the regulation of these plasticities. In doing so, we aim to expand upon the idea that epigenetic mechanisms are critical regulators of both Hebbian and non-Hebbian forms of plasticity that ultimately drive learning and memory.

Effects of cellular homeostatic intrinsic plasticity on dynamical and computational properties of biological recurrent neural networks

Homeostatic intrinsic plasticity (HIP) is a ubiquitous cellular mechanism regulating neuronal activity, cardinal for the proper functioning of nervous systems. In invertebrates, HIP is critical for orchestrating stereotyped activity patterns. The functional impact of HIP remains more obscure in vertebrate networks, where higher order cognitive processes rely on complex neural dynamics. The hypothesis has emerged that HIP might control the complexity of activity dynamics in recurrent networks, with important computational consequences. However, conflicting results about the causal relationships between cellular HIP, network dynamics, and computational performance have arisen from machine-learning studies. Here, we assess how cellular HIP effects translate into collective dynamics and computational properties in biological recurrent networks. We develop a realistic multiscale model including a generic HIP rule regulating the neuronal threshold with actual molecular signaling pathways kinetics, Dale's principle, sparse connectivity, synaptic balance, and Hebbian synaptic plasticity (SP). Dynamic mean-field analysis and simulations unravel that HIP sets a working point at which inputs are transduced by large derivative ranges of the transfer function. This cellular mechanism ensures increased network dynamics complexity, robust balance with SP at the edge of chaos, and improved input separability. Although critically dependent upon balanced excitatory and inhibitory drives, these effects display striking robustness to changes in network architecture, learning rates, and input features. Thus, the mechanism we unveil might represent a ubiquitous cellular basis for complex dynamics in neural networks. Understanding this robustness is an important challenge to unraveling principles underlying self-organization around criticality in biological recurrent neural networks.

Long-term optical stimulation of channelrhodopsin-expressing neurons to study network plasticity

Neuronal plasticity produces changes in excitability, synaptic transmission, and network architecture in response to external stimuli. Network adaptation to environmental conditions takes place in time scales ranging from few seconds to days, and modulates the entire network dynamics. To study the network response to defined long-term experimental protocols, we setup a system that combines optical and electrophysiological tools embedded in a cell incubator. Primary hippocampal neurons transduced with lentiviruses expressing channelrhodopsin-2/H134R were subjected to various photostimulation protocols in a time window in the order of days. To monitor the effects of light-induced gating of network activity, stimulated transduced neurons were simultaneously recorded using multi-electrode arrays (MEAs). The developed experimental model allows discerning short-term, long-lasting, and adaptive plasticity responses of the same neuronal network to distinct stimulation frequencies applied over different temporal windows.