Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity.     

Synaptic mechanisms underlying auditory processing

In vivo voltage clamp recordings have provided new insights into the synaptic mechanisms that underlie processing in the primary auditory cortex. Of particular importance are the discoveries that excitatory and inhibitory inputs have similar frequency and intensity tuning, that excitation is followed by inhibition with a short delay, and that the duration of inhibition is briefer than expected. These findings challenge existing models of auditory processing in which broadly tuned lateral inhibition is used to limit excitatory receptive fields and suggest new mechanisms by which inhibition and short term plasticity shape neural responses.     

The Effect of STDP Temporal Kernel Structure on the Learning Dynamics of Single Excitatory and Inhibitory Synapses

Spike-Timing Dependent Plasticity (STDP) is characterized by a wide range of temporal kernels. However, much of the theoretical work has focused on a specific kernel – the “temporally asymmetric Hebbian” learning rules. Previous studies linked excitatory STDP to positive feedback that can account for the emergence of response selectivity. Inhibitory plasticity was associated with negative feedback that can balance the excitatory and inhibitory inputs. Here we study the possible computational role of the temporal structure of the STDP. We represent the STDP as a superposition of two processes: potentiation and depression. This allows us to model a wide range of experimentally observed STDP kernels, from Hebbian to anti-Hebbian, by varying a single parameter. We investigate STDP dynamics of a single excitatory or inhibitory synapse in purely feed-forward architecture. We derive a mean-field-Fokker-Planck dynamics for the synaptic weight and analyze the effect of STDP structure on the fixed points of the mean field dynamics. We find a phase transition along the Hebbian to anti-Hebbian parameter from a phase that is characterized by a unimodal distribution of the synaptic weight, in which the STDP dynamics is governed by negative feedback, to a phase with positive feedback characterized by a bimodal distribution. The critical point of this transition depends on general properties of the STDP dynamics and not on the fine details. Namely, the dynamics is affected by the pre-post correlations only via a single number that quantifies its overlap with the STDP kernel. We find that by manipulating the STDP temporal kernel, negative feedback can be induced in excitatory synapses and positive feedback in inhibitory. Moreover, there is an exact symmetry between inhibitory and excitatory plasticity, i.e., for every STDP rule of inhibitory synapse there exists an STDP rule for excitatory synapse, such that their dynamics is identical.     

Nonmonotonic synaptic excitation and imbalanced inhibition underlying cortical intensity tuning

Intensity-tuned neurons, characterized by their nonmonotonic response-level function, may play important roles in the encoding of sound intensity-related information. The synaptic mechanisms underlying intensity tuning remain unclear. Here, in vivo whole-cell recordings in rat auditory cortex revealed that intensity-tuned neurons, mostly clustered in a posterior zone, receive imbalanced tone-evoked excitatory and inhibitory synaptic inputs. Excitatory inputs exhibit nonmonotonic intensity tuning, whereas with tone intensity increments, the temporally delayed inhibitory inputs increase monotonically in strength. In addition, this delay reduces with the increase of intensity, resulting in an enhanced suppression of excitation at high intensities and a significant sharpening of intensity tuning. In contrast, non-intensity-tuned neurons exhibit covaried excitatory and inhibitory inputs, and the relative time interval between them is stable with intensity increments, resulting in monotonic response-level function. Thus, cortical intensity tuning is primarily determined by excitatory inputs and shaped by cortical inhibition through a dynamic control of excitatory and inhibitory timing.     

Building excitatory and inhibitory synapses: balancing neuroligin partnerships

Processing of neural information is thought to occur by integration of excitatory and inhibitory synaptic inputs. As such, precise control mechanisms must exist to maintain an appropriate balance between each synapse type. Recent findings indicate that neuroligins and their synaptic binding partners modulate the development of both excitatory and inhibitory synapses. Here we highlight these findings and discuss a mechanism potentially involved in controlling the balance between excitation and inhibition.     

Robustness of neuronal tuning to binaural sound localization cues against age-related loss of inhibitory synaptic inputs

Sound localization relies on minute differences in the timing and intensity of sound arriving at both ears. Neurons of the lateral superior olive (LSO) in the brainstem process these interaural disparities by precisely detecting excitatory and inhibitory synaptic inputs. Aging generally induces selective loss of inhibitory synaptic transmission along the entire auditory pathways, including the reduction of inhibitory afferents to LSO. Electrophysiological recordings in animals, however, reported only minor functional changes in aged LSO. The perplexing discrepancy between anatomical and physiological observations suggests a role for activity-dependent plasticity that would help neurons retain their binaural tuning function despite loss of inhibitory inputs. To explore this hypothesis, we use a computational model of LSO to investigate mechanisms underlying the observed functional robustness against age-related loss of inhibitory inputs. The LSO model is an integrate-and-fire type enhanced with a small amount of low-voltage activated potassium conductance and driven with (in)homogeneous Poissonian inputs. Without synaptic input loss, model spike rates varied smoothly with interaural time and level differences, replicating empirical tuning properties of LSO. By reducing the number of inhibitory afferents to mimic age-related loss of inhibition, overall spike rates increased, which negatively impacted binaural tuning performance, measured as modulation depth and neuronal discriminability. To simulate a recovery process compensating for the loss of inhibitory fibers, the strength of remaining inhibitory inputs was increased. By this modification, effects of inhibition loss on binaural tuning were considerably weakened, leading to an improvement of functional performance. These neuron-level observations were further confirmed by population modeling, in which binaural tuning properties of multiple LSO neurons were varied according to empirical measurements. These results demonstrate the plausibility that homeostatic plasticity could effectively counteract known age-dependent loss of inhibitory fibers in LSO and suggest that behavioral degradation of sound localization might originate from changes occurring more centrally.     

Top-Down Modulation on Perceptual Decision with Balanced Inhibition through Feedforward and Feedback Inhibitory Neurons

Recent physiological studies have shown that neurons in various regions of the central nervous systems continuously receive noisy excitatory and inhibitory synaptic inputs in a balanced and covaried fashion. While this balanced synaptic input (BSI) is typically described in terms of maintaining the stability of neural circuits, a number of experimental and theoretical studies have suggested that BSI plays a proactive role in brain functions such as top-down modulation for executive control. Two issues have remained unclear in this picture. First, given the noisy nature of neuronal activities in neural circuits, how do the modulatory effects change if the top-down control implements BSI with different ratios between inhibition and excitation? Second, how is a top-down BSI realized via only excitatory long-range projections in the neocortex? To address the first issue, we systematically tested how the inhibition/excitation ratio affects the accuracy and reaction times of a spiking neural circuit model of perceptual decision. We defined an energy function to characterize the network dynamics, and found that different ratios modulate the energy function of the circuit differently and form two distinct functional modes. To address the second issue, we tested BSI with long-distance projection to inhibitory neurons that are either feedforward or feedback, depending on whether these inhibitory neurons do or do not receive inputs from local excitatory cells, respectively. We found that BSI occurs in both cases. Furthermore, when relying on feedback inhibitory neurons, through the recurrent interactions inside the circuit, BSI dynamically and automatically speeds up the decision by gradually reducing its inhibitory component in the course of a trial when a decision process takes too long.     

Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.     

Modulation of the dynamics of cerebellar Purkinje cells through the interaction of excitatory and inhibitory feedforward pathways

The dynamics of cerebellar neuronal networks is controlled by the underlying building blocks of neurons and synapses between them. For which, the computation of Purkinje cells (PCs), the only output cells of the cerebellar cortex, is implemented through various types of neural pathways interactively routing excitation and inhibition converged to PCs. Such tuning of excitation and inhibition, coming from the gating of specific pathways as well as short-term plasticity (STP) of the synapses, plays a dominant role in controlling the PC dynamics in terms of firing rate and spike timing. PCs receive cascade feedforward inputs from two major neural pathways: the first one is the feedforward excitatory pathway from granule cells (GCs) to PCs; the second one is the feedforward inhibition pathway from GCs, via molecular layer interneurons (MLIs), to PCs. The GC-PC pathway, together with short-term dynamics of excitatory synapses, has been a focus over past decades, whereas recent experimental evidence shows that MLIs also greatly contribute to controlling PC activity. Therefore, it is expected that the diversity of excitation gated by STP of GC-PC synapses, modulated by strong inhibition from MLI-PC synapses, can promote the computation performed by PCs. However, it remains unclear how these two neural pathways are interacted to modulate PC dynamics. Here using a computational model of PC network installed with these two neural pathways, we addressed this question to investigate the change of PC firing dynamics at the level of single cell and network. We show that the nonlinear characteristics of excitatory STP dynamics can significantly modulate PC spiking dynamics mediated by inhibition. The changes in PC firing rate, firing phase, and temporal spike pattern, are strongly modulated by these two factors in different ways. MLIs mainly contribute to variable delays in the postsynaptic action potentials of PCs while modulated by excitation STP. Notably, the diversity of synchronization and pause response in the PC network is governed not only by the balance of excitation and inhibition, but also by the synaptic STP, depending on input burst patterns. Especially, the pause response shown in the PC network can only emerge with the interaction of both pathways. Together with other recent findings, our results show that the interaction of feedforward pathways of excitation and inhibition, incorporated with synaptic short-term dynamics, can dramatically regulate the PC activities that consequently change the network dynamics of the cerebellar circuit.     

Lateral sharpening of cortical frequency tuning by approximately balanced inhibition

Cortical inhibition plays an important role in shaping neuronal processing. The underlying synaptic mechanisms remain controversial. Here, in vivo whole-cell recordings from neurons in the rat primary auditory cortex revealed that the frequency tuning curve of inhibitory input was broader than that of excitatory input. This results in relatively stronger inhibition in frequency domains flanking the preferred frequencies of the cell and a significant sharpening of the frequency tuning of membrane responses. The less selective inhibition can be attributed to a broader bandwidth and lower threshold of spike tonal receptive field of fast-spike inhibitory neurons than nearby excitatory neurons, although both types of neurons receive similar ranges of excitatory input and are organized into the same tonotopic map. Thus, the balance between excitation and inhibition is only approximate, and intracortical inhibition with high sensitivity and low selectivity can laterally sharpen the frequency tuning of neurons, ensuring their highly selective representation.     

Gephyrin-independent GABA(A)R mobility and clustering during plasticity

The activity-dependent modulation of GABA-A receptor (GABA(A)R) clustering at synapses controls inhibitory synaptic transmission. Several lines of evidence suggest that gephyrin, an inhibitory synaptic scaffold protein, is a critical factor in the regulation of GABA(A)R clustering during inhibitory synaptic plasticity induced by neuronal excitation. In this study, we tested this hypothesis by studying relative gephyrin dynamics and GABA(A)R declustering during excitatory activity. Surprisingly, we found that gephyrin dispersal is not essential for GABA(A)R declustering during excitatory activity. In cultured hippocampal neurons, quantitative immunocytochemistry showed that the dispersal of synaptic GABA(A)Rs accompanied with neuronal excitation evoked by 4-aminopyridine (4AP) or N-methyl-D-aspartic acid (NMDA) precedes that of gephyrin. Single-particle tracking of quantum dot labeled-GABA(A)Rs revealed that excitation-induced enhancement of GABA(A)R lateral mobility also occurred before the shrinkage of gephyrin clusters. Physical inhibition of GABA(A)R lateral diffusion on the cell surface and inhibition of a Ca(2+) dependent phosphatase, calcineurin, completely eliminated the 4AP-induced decrease in gephyrin cluster size, but not the NMDA-induced decrease in cluster size, suggesting the existence of two different mechanisms of gephyrin declustering during activity-dependent plasticity, a GABA(A)R-dependent regulatory mechanism and a GABA(A)R-independent one. Our results also indicate that GABA(A)R mobility and clustering after sustained excitatory activity is independent of gephyrin.     

Activity-dependent matching of excitatory and inhibitory inputs during refinement of visual receptive fields

The receptive field (RF) of single visual neurons undergoes progressive refinement during development. It remains largely unknown how the excitatory and inhibitory inputs on single developing neurons are refined in a coordinated manner to allow the formation of functionally correct circuits. Using whole-cell voltage-clamp recording from Xenopus tectal neurons, we found that RFs determined by excitatory and inhibitory inputs in more mature tectal neurons are spatially matched, with each spot stimulus evoking balanced synaptic excitation and inhibition. This emerges during development through a gradual reduction in the RF size and a transition from disparate to matched topography of excitatory and inhibitory inputs to the tectal neurons. Altering normal spiking activity of tectal neurons by either blocking or elevating GABA(A) receptor activity significantly impeded the developmental reduction and topographic matching of RFs. Thus, appropriate inhibitory activity is essential for the coordinated refinement of excitatory and inhibitory connections.     

Retrograde GABA signaling adjusts sound localization by balancing excitation and inhibition in the brainstem

Central processing of acoustic cues is critically dependent on the balance between excitation and inhibition. This balance is particularly important for auditory neurons in the lateral superior olive, because these compare excitatory inputs from one ear and inhibitory inputs from the other ear to compute sound source location. By applying GABA(B) receptor antagonists during sound stimulation in vivo, it was revealed that these neurons adjust their binaural sensitivity through GABA(B) receptors. Using an in vitro approach, we then demonstrate that these neurons release GABA during spiking activity. Consequently, GABA differentially regulates transmitter release from the excitatory and inhibitory terminals via feedback to presynaptic GABA(B) receptors. Modulation of the synaptic input strength, by putative retrograde release of neurotransmitter, may enable these auditory neurons to rapidly adjust the balance between excitation and inhibition, and thus their binaural sensitivity, which could play an important role as an adaptation to various listening situations.     

Maturation of GABAergic Inhibition Promotes Strengthening of Temporally Coherent Inputs among Convergent Pathways

Spike-timing-dependent plasticity (STDP), a form of Hebbian plasticity, is inherently stabilizing. Whether and how GABAergic inhibition influences STDP is not well understood. Using a model neuron driven by converging inputs modifiable by STDP, we determined that a sufficient level of inhibition was critical to ensure that temporal coherence (correlation among presynaptic spike times) of synaptic inputs, rather than initial strength or number of inputs within a pathway, controlled postsynaptic spike timing. Inhibition exerted this effect by preferentially reducing synaptic efficacy, the ability of inputs to evoke postsynaptic action potentials, of the less coherent inputs. In visual cortical slices, inhibition potently reduced synaptic efficacy at ages during but not before the critical period of ocular dominance (OD) plasticity. Whole-cell recordings revealed that the amplitude of unitary IPSCs from parvalbumin positive (Pv+) interneurons to pyramidal neurons increased during the critical period, while the synaptic decay time-constant decreased. In addition, intrinsic properties of Pv+ interneurons matured, resulting in an increase in instantaneous firing rate. Our results suggest that maturation of inhibition in visual cortex ensures that the temporally coherent inputs (e.g. those from the open eye during monocular deprivation) control postsynaptic spike times of binocular neurons, a prerequisite for Hebbian mechanisms to induce OD plasticity.     

Shunting inhibition controls the gain modulation mediated by asynchronous neurotransmitter release in early development

The sensitivity of a neuron to its input can be modulated in several ways. Changes in the slope of the neuronal input-output curve depend on factors such as shunting inhibition, background noise, frequency-dependent synaptic excitation, and balanced excitation and inhibition. However, in early development GABAergic interneurons are excitatory and other mechanisms such as asynchronous transmitter release might contribute to regulating neuronal sensitivity. We modeled both phasic and asynchronous synaptic transmission in early development to study the impact of activity-dependent noise and short-term plasticity on the synaptic gain. Asynchronous release decreased or increased the gain depending on the membrane conductance. In the high shunt regime, excitatory input due to asynchronous release was divisive, whereas in the low shunt regime it had a nearly multiplicative effect on the firing rate. In addition, sensitivity to correlated inputs was influenced by shunting and asynchronous release in opposite ways. Thus, asynchronous release can regulate the information flow at synapses and its impact can be flexibly modulated by the membrane conductance.     

Inferring synaptic inputs given a noisy voltage trace via sequential Monte Carlo methods

We discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques ("particle filtering"). We demonstrate, on model data, that these methods can recover the time course of excitatory and inhibitory synaptic inputs accurately on a single trial. Depending on the observation noise level, no averaging over multiple trials may be required. However, excitatory inputs are consistently inferred more accurately than inhibitory inputs at physiological resting potentials, due to the stronger driving force associated with excitatory conductances. Once these synaptic input time courses are recovered, it becomes possible to fit (via tractable convex optimization techniques) models describing the relationship between the sensory stimulus and the observed synaptic input. We develop both parametric and nonparametric expectation-maximization (EM) algorithms that consist of alternating iterations between these synaptic recovery and model estimation steps. We employ a fast, robust convex optimization-based method to effectively initialize the filter; these fast methods may be of independent interest. The proposed methods could be applied to better understand the balance between excitation and inhibition in sensory processing in vivo.     

Repeated neonatal separation stress alters the composition of neurochemically characterized interneuron subpopulations in the rodent dentate gyrus and basolateral amygdala

Emotional experience during early life has been shown to interfere with the development of excitatory synaptic networks in the prefrontal cortex, hippocampus, and the amygdala of rodents and primates. The aim of the present study was to investigate a developmental "homoeostatic synaptic plasticity" hypothesis and to test whether stress-induced changes of excitatory synaptic composition are counterbalanced by parallel changes of inhibitory synaptic networks. The impact of repeated early separation stress on the development of two GABAergic neuronal subpopulations was quantitatively analyzed in the brain of the semiprecocial rodent Octodon degus. Assuming that PARV- and CaBP-D28k-expression are negatively correlated to the level of inhibitory activity, the previously described reduced density of excitatory spine synapses in the dentate gyrus of stressed animals appears to be "amplified" by elevated GABAergic inhibition, reflected by reduced PARV- (down to 85%) and CaBP-D28k-immunoreactivity (down to 74%). In opposite direction, the previously observed elevated excitatory spine density in the CA1 region of stressed animals appears to be amplified by reduced inhibition, reflected by elevated CaPB-D28k-immunoreactivity (up to 149%). In the (baso)lateral amygdala, the previously described reduction of excitatory spine synapses appears to be "compensated" by reduced inhibitory activity, reflected by dramatically elevated PARV- (up to 395%) and CaPB-D28k-immunoreactivity (up to 327%). No significant differences were found in the central nucleus of the amygdala, the piriform, and somatosensory cortices and in the hypothalamic paraventricular nucleus. Thus during stress-evoked neuronal and synaptic reorganization, a homeostatic balance between excitation and inhibition is not maintained in all regions of the juvenile brain.     

Dual synaptic plasticity in the hippocampus: Hebbian and spatiotemporal learning dynamics

We assume that Hebbian learning dynamics (HLD) and spatiotemporal learning dynamics (SLD) are involved in the mechanism of synaptic plasticity in the hippocampal neurons. While HLD is driven by pre- and postsynaptic spike timings through the backpropagating action potential, SLD is evoked by presynaptic spike timings alone. Since the backpropagation attenuates as it nears the distal dendrites, we assume an extreme case as a neuron model where HLD exists only at proximal dendrites and SLD exists only at the distal dendrites. We examined how the synaptic weights change in response to three types of synaptic inputs in computer simulations. First, in response to a Poisson train having a constant mean frequency, the synaptic weights in HLD and SLD are qualitatively similar. Second, SLD responds more rapidly than HLD to synchronous input patterns, while each responds to them. Third, HLD responds more rapidly to more frequent inputs, while SLD shows fluctuating synaptic weights. These results suggest an encoding hypothesis in that a transient synchronous structure in spatiotemporal input patterns will be encoded into distal dendrites through SLD and that persistent synchrony or firing rate information will be encoded into proximal dendrites through HLD.     

Preserved Excitatory-Inhibitory Balance of Cortical Synaptic Inputs following Deprived Eye Stimulation after a Saturating Period of Monocular Deprivation in Rats

Monocular deprivation (MD) during development leads to a dramatic loss of responsiveness through the deprived eye in primary visual cortical neurons, and to degraded spatial vision (amblyopia) in all species tested so far, including rodents. Such loss of responsiveness is accompanied since the beginning by a decreased excitatory drive from the thalamo-cortical inputs. However, in the thalamorecipient layer 4, inhibitory interneurons are initially unaffected by MD and their synapses onto pyramidal cells potentiate. It remains controversial whether ocular dominance plasticity similarly or differentially affects the excitatory and inhibitory synaptic conductances driven by visual stimulation of the deprived eye and impinging onto visual cortical pyramids, after a saturating period of MD. To address this issue, we isolated visually-driven excitatory and inhibitory conductances by in vivo whole-cell recordings from layer 4 regular-spiking neurons in the primary visual cortex (V1) of juvenile rats. We found that a saturating period of MD comparably reduced visually–driven excitatory and inhibitory conductances driven by visual stimulation of the deprived eye. Also, the excitatory and inhibitory conductances underlying the synaptic responses driven by the ipsilateral, left open eye were similarly potentiated compared to controls. Multiunit recordings in layer 4 followed by spike sorting indicated that the suprathreshold loss of responsiveness and the MD-driven ocular preference shifts were similar for narrow spiking, putative inhibitory neurons and broad spiking, putative excitatory neurons. Thus, by the time the plastic response has reached a plateau, inhibitory circuits adjust to preserve the normal balance between excitation and inhibition in the cortical network of the main thalamorecipient layer.