A homeostatic model of neuronal firing governed by feedback signals from the extracellular matrix

Molecules of the extracellular matrix (ECM) can modulate the efficacy of synaptic transmission and neuronal excitability. These mechanisms are crucial for the homeostatic regulation of neuronal firing over extended timescales. In this study, we introduce a simple mathematical model of neuronal spiking balanced by the influence of the ECM. We consider a neuron receiving random synaptic input in the form of Poisson spike trains and the ECM, which is modeled by a phenomenological variable involved in two feedback mechanisms. One feedback mechanism scales the values of the input synaptic conductance to compensate for changes in firing rate. The second feedback accounts for slow fluctuations of the excitation threshold and depends on the ECM concentration. We show that the ECM-mediated feedback acts as a robust mechanism to provide a homeostatic adjustment of the average firing rate. Interestingly, the activation of feedback mechanisms may lead to a bistability in which two different stable levels of average firing rates can coexist in a spiking network. We discuss the mechanisms of the bistability and how they may be related to memory function.     

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.     

Nitric oxide is an activity-dependent regulator of target neuron intrinsic excitability

Activity-dependent changes in synaptic strength are well established as mediating long-term plasticity underlying learning and memory, but modulation of?target neuron excitability could complement changes in synaptic strength and regulate network activity. It is thought that homeostatic mechanisms match intrinsic excitability to the incoming synaptic drive, but evidence for involvement of voltage-gated conductances is sparse. Here, we show that glutamatergic synaptic activity modulates target neuron excitability and switches the basis of action potential repolarization from Kv3 to Kv2 potassium channel dominance, thereby adjusting neuronal signaling between low and high activity states, respectively. This nitric oxide-mediated signaling dramatically increases Kv2 currents in both the auditory brain stem and hippocampus (>3-fold) transforming synaptic integration and information transmission but with only modest changes in action potential waveform. We conclude that nitric oxide is a homeostatic regulator, tuning neuronal excitability to the recent history of excitatory synaptic inputs over intervals of minutes to hours.     

Hebb and homeostasis in neuronal plasticity

The positive-feedback nature of Hebbian plasticity can destabilize the properties of neuronal networks. Recent work has demonstrated that this destabilizing influence is counteracted by a number of homeostatic plasticity mechanisms that stabilize neuronal activity. Such mechanisms include global changes in synaptic strengths, changes in neuronal excitability, and the regulation of synapse number. These recent studies suggest that Hebbian and homeostatic plasticity often target the same molecular substrates, and have opposing effects on synaptic or neuronal properties. These advances significantly broaden our framework for understanding the effects of activity on synaptic function and neuronal excitability.     

Homeostatic synaptic plasticity: local and global mechanisms for stabilizing neuronal function

Neural circuits must maintain stable function in the face of many plastic challenges, including changes in synapse number and strength, during learning and development. Recent work has shown that these destabilizing influences are counterbalanced by homeostatic plasticity mechanisms that act to stabilize neuronal and circuit activity. One such mechanism is synaptic scaling, which allows neurons to detect changes in their own firing rates through a set of calcium-dependent sensors that then regulate receptor trafficking to increase or decrease the accumulation of glutamate receptors at synaptic sites. Additional homeostatic mechanisms may allow local changes in synaptic activation to generate local synaptic adaptations, and network-wide changes in activity to generate network-wide adjustments in the balance between excitation and inhibition. The signaling pathways underlying these various forms of homeostatic plasticity are currently under intense scrutiny, and although dozens of molecular pathways have now been implicated in homeostatic plasticity, a clear picture of how homeostatic feedback is structured at the molecular level has not yet emerged. On a functional level, neuronal networks likely use this complex set of regulatory mechanisms to achieve homeostasis over a wide range of temporal and spatial scales.     

Network reconfiguration and neuronal plasticity in rhythm-generating networks

Neuronal networks are highly plastic and reconfigure in a state-dependent manner. The plasticity at the network level emerges through multiple intrinsic and synaptic membrane properties that imbue neurons and their interactions with numerous nonlinear properties. These properties are continuously regulated by neuromodulators and homeostatic mechanisms that are critical to maintain not only network stability and also adapt networks in a short- and long-term manner to changes in behavioral, developmental, metabolic, and environmental conditions. This review provides concrete examples from neuronal networks in invertebrates and vertebrates, and illustrates that the concepts and rules that govern neuronal networks and behaviors are universal.     

Homeostatic plasticity in the CNS: synaptic and intrinsic forms

The study of experience-dependent plasticity has been dominated by questions of how Hebbian plasticity mechanisms act during learning and development. This is unsurprising as Hebbian plasticity constitutes the most fully developed and influential model of how information is stored in neural circuits and how neural circuitry can develop without extensive genetic instructions. Yet Hebbian plasticity may not be sufficient for understanding either learning or development: the dramatic changes in synapse number and strength that can be produced by this kind of plasticity tend to threaten the stability of neural circuits. Recent work has suggested that, in addition to Hebbian plasticity, homeostatic regulatory mechanisms are active in a variety of preparations. These mechanisms alter both the synaptic connections between neurons and the intrinsic electrical properties of individual neurons, in such a way as to maintain some constancy in neuronal properties despite the changes wrought by Hebbian mechanisms. Here we review the evidence for homeostatic plasticity in the central nervous system, with special emphasis on results from cortical preparations.     

Endosomal phosphatidylinositol 3‐phosphate controls synaptic vesicle cycling and neurotransmission

Neural circuit function requires mechanisms for controlling neurotransmitter release and the activity of neuronal networks, including modulation by synaptic contacts, synaptic plasticity, and homeostatic scaling. However, how neurons intrinsically monitor and feedback control presynaptic neurotransmitter release and synaptic vesicle (SV) recycling to restrict neuronal network activity remains poorly understood at the molecular level. Here, we investigated the reciprocal interplay between neuronal endosomes, organelles of central importance for the function of synapses, and synaptic activity. We show that elevated neuronal activity represses the synthesis of endosomal lipid phosphatidylinositol 3‐phosphate [PI(3)P] by the lipid kinase VPS34. Neuronal activity in turn is regulated by endosomal PI(3)P, the depletion of which reduces neurotransmission as a consequence of perturbed SV endocytosis. We find that this mechanism involves Calpain 2‐mediated hyperactivation of Cdk5 downstream of receptor‐ and activity‐dependent calcium influx. Our results unravel an unexpected function for PI(3)P‐containing neuronal endosomes in the control of presynaptic vesicle cycling and neurotransmission, which may explain the involvement of the PI(3)P‐producing VPS34 kinase in neurological disease and neurodegeneration.     

Homeostatic plasticity and excitation-inhibition balance: The good,the bad,and the ugly

In this review, we discuss the significance of the synaptic excitation/inhibition (E/I) balance in the context of homeostatic plasticity, whose primary goal is thought to maintain neuronal firing rates at a set point. We first provide an overview of the processes through which patterned input activity drives synaptic E/I tuning and maturation of circuits during development. Next, we emphasize the importance of the E/I balance at the synaptic level (homeostatic control of message reception) as a means to achieve the goal (homeostatic control of information transmission) at the network level and consider how compromised homeostatic plasticity associated with neurological diseases leads to hyperactivity, network instability, and ultimately improper information processing. Lastly, we highlight several pathological conditions related to sensory deafferentation and describe how, in some cases, homeostatic compensation without appropriate sensory inputs can result in phantom perceptions.     

MiR‐134‐dependent regulation of Pumilio‐2 is necessary for homeostatic synaptic depression

Neurons employ a set of homeostatic plasticity mechanisms to counterbalance altered levels of network activity. The molecular mechanisms underlying homeostatic plasticity in response to increased network excitability are still poorly understood. Here, we describe a sequential homeostatic synaptic depression mechanism in primary hippocampal neurons involving miRNA‐dependent translational regulation. This mechanism consists of an initial phase of synapse elimination followed by a reinforcing phase of synaptic downscaling. The activity‐regulated microRNA miR‐134 is necessary for both synapse elimination and the structural rearrangements leading to synaptic downscaling. Results from miR‐134 inhibition further uncover a differential requirement for GluA1/2 subunits for the functional expression of homeostatic synaptic depression. Downregulation of the miR‐134 target Pumilio‐2 in response to chronic activity, which selectively occurs in the synapto‐dendritic compartment, is required for miR‐134‐mediated homeostatic synaptic depression. We further identified polo‐like kinase 2 (Plk2) as a novel target of Pumilio‐2 involved in the control of GluA2 surface expression. In summary, we have described a novel pathway of homeostatic plasticity that stabilizes neuronal circuits in response to increased network activity.     

Network Self-Organization Explains the Statistics and Dynamics of Synaptic Connection Strengths in Cortex

The information processing abilities of neural circuits arise from their synaptic connection patterns. Understanding the laws governing these connectivity patterns is essential for understanding brain function. The overall distribution of synaptic strengths of local excitatory connections in cortex and hippocampus is long-tailed, exhibiting a small number of synaptic connections of very large efficacy. At the same time, new synaptic connections are constantly being created and individual synaptic connection strengths show substantial fluctuations across time. It remains unclear through what mechanisms these properties of neural circuits arise and how they contribute to learning and memory. In this study we show that fundamental characteristics of excitatory synaptic connections in cortex and hippocampus can be explained as a consequence of self-organization in a recurrent network combining spike-timing-dependent plasticity (STDP), structural plasticity and different forms of homeostatic plasticity. In the network, associative synaptic plasticity in the form of STDP induces a rich-get-richer dynamics among synapses, while homeostatic mechanisms induce competition. Under distinctly different initial conditions, the ensuing self-organization produces long-tailed synaptic strength distributions matching experimental findings. We show that this self-organization can take place with a purely additive STDP mechanism and that multiplicative weight dynamics emerge as a consequence of network interactions. The observed patterns of fluctuation of synaptic strengths, including elimination and generation of synaptic connections and long-term persistence of strong connections, are consistent with the dynamics of dendritic spines found in rat hippocampus. Beyond this, the model predicts an approximately power-law scaling of the lifetimes of newly established synaptic connection strengths during development. Our results suggest that the combined action of multiple forms of neuronal plasticity plays an essential role in the formation and maintenance of cortical circuits.     

Molecular signals of plasticity at the tetrapartite synapse

The emergence of astroglia as an important participant of the synaptic machinery has led to the 'tripartite synapse' hypothesis. Recent findings suggest that synaptic signaling also involves the surrounding extracellular matrix (ECM). The ECM can incorporate and store molecular traces of both neuronal and glial activities. It can also modulate function of local receptors or ion channels and send diffuse molecular signals using products of its use-dependent proteolytic cleavage. Recent experimental findings implicate the ECM in mechanisms of synaptic plasticity and glial remodeling, thus lending support to the 'tetrapartite synapse' concept. This inclusive view might help to understand better the mechanisms underlying signal integration and novel forms of long-term homeostatic regulation in the brain.     

Molecular mechanisms of homeostatic plasticity in central pattern generator networks

Central pattern generator (CPG) networks rely on a balance of intrinsic and network properties to produce reliable, repeatable activity patterns. This balance is maintained by homeostatic plasticity where alterations in neuronal properties dynamically maintain appropriate neural output in the face of changing environmental conditions and perturbations. However, it remains unclear just how these neurons and networks can both monitor their ongoing activity and use this information to elicit homeostatic physiological responses to ensure robustness of output over time. Evidence exists that CPG networks use a mixed strategy of activity‐dependent, activity‐independent, modulator‐dependent, and synaptically regulated homeostatic plasticity to achieve this critical stability. In this review, we focus on some of the current understanding of the molecular pathways and mechanisms responsible for this homeostatic plasticity in the context of central pattern generator function, with a special emphasis on some of the smaller invertebrate networks that have allowed for extensive cellular‐level analyses that have brought recent insights to these questions.     

Surprising Effects of Synaptic Excitation

Typically, excitatory synaptic coupling is thought of as an influence that accelerates and propagates firing in neuronal networks. This paper reviews recent results explaining how, contrary to these expectations, the presence of excitatory synaptic coupling can drastically slow oscillations in a network and how localized, sustained activity can arise in a network with purely excitatory coupling, without sustained inputs. These two effects stem from interactions of excitatory coupling with two different forms of intrinsic neuronal dynamics, and both serve to highlight the fact that the influence of synaptic coupling in a network depends strongly on the intrinsic properties of cells in the network.This work was partially supported by the National Science Foundation, under award DMS-0414023     

Transitions between irregular and rhythmic firing patterns in excitatory-inhibitory neuronal networks

Changes in firing patterns are an important hallmark of the functional status of neuronal networks. We apply dynamical systems methods to understand transitions between irregular and rhythmic firing in an excitatory-inhibitory neuronal network model. Using the geometric theory of singular perturbations, we systematically reduce the full model to a simpler set of equations, one that can be studied analytically. The analytic tools are used to understand how an excitatory-inhibitory network with a fixed architecture can generate both activity patterns for possibly different values of the intrinsic and synaptic parameters. These results are applied to a recently developed model for the subthalamopallidal network of the basal ganglia. The results suggest that an increase in correlated activity, corresponding to a pathological state, may be due to an increased level of inhibition from the striatum to the inhibitory GPe cells along with an increased ability of the excitatory STN neurons to generate rebound bursts. Action Editor: Carson Chow     

A Model of Visuospatial Working Memory in Prefrontal Cortex: Recurrent Network and Cellular Bistability

We report a computer simulation of the visuospatial delayed-response experiments of Funahashi et al. (1989), using a firing-rate model that combines intrinsic cellular bistability with the recurrent local network architecture of the neocortex. In our model, the visuospatial working memory is stored in the form of a continuum of network activity profiles that coexist with a spontaneous activity state. These neuronal firing patterns provide a population code for the cue position in a graded manner. We show that neuronal persistent activity and tuning curves of delay-period activity (memory fields) can be generated by an excitatory feedback circuit and recurrent synaptic inhibition. However, if the memory fields are constructed solely by network mechanisms, noise may induce a random drift over time in the encoded cue position, so that the working memory storage becomes unreliable. Furthermore, a distraction stimulus presented during the delay period produces a systematic shift in the encoded cue position. We found that the working memory performance can be rendered robust against noise and distraction stimuli if single neurons are endowed with cellular bistability (presumably due to intrinsic ion channel mechanisms) that is conditional and realized only with sustained synaptic inputs from the recurrent network. We discuss how cellular bistability at the single cell level may be detected by analysis of spike trains recorded during delay-period activity and how local modulation of intrinsic cell properties and/or synaptic transmission can alter the memory fields of individual neurons in the prefrontal cortex.     

Communication between neurons and astrocytes: relevance to the modulation of synaptic and network activity

Neuromodulation is a fundamental process in the brain that regulates synaptic transmission, neuronal network activity and behavior. Emerging evidence demonstrates that astrocytes, a major population of glial cells in the brain, play previously unrecognized functions in neuronal modulation. Astrocytes can detect the level of neuronal activity and release chemical transmitters to influence neuronal function. For example, recent findings show that astrocytes play crucial roles in the control of Hebbian plasticity, the regulation of neuronal excitability and the induction of homeostatic plasticity. This review discusses the importance of astrocyte-to-neuron signaling in different aspects of neuronal function from the activity of single synapses to that of neuronal networks.     

Exciting Times: New Advances Towards Understanding the Regulation and Roles of Kainate Receptors

Kainate receptors (KARs) are glutamate-gated ion channels that play fundamental roles in regulating neuronal excitability and network function in the brain. After being cloned in the 1990s, important progress has been made in understanding the mechanisms controlling the molecular and cellular properties of KARs, and the nature and extent of their regulation of wider neuronal activity. However, there have been significant recent advances towards understanding KAR trafficking through the secretory pathway, their precise synaptic positioning, and their roles in synaptic plasticity and disease. Here we provide an overview highlighting these new findings about the mechanisms controlling KARs and how KARs, in turn, regulate other proteins and pathways to influence synaptic function.