Inhibitory Synaptic Conductances Research Articles

On the physiological and structural contributors to the overall balance of excitation and inhibition in local cortical networks

Overall balance of excitation and inhibition in cortical networks is central to their functionality and normal operation. Such orchestrated co-evolution of excitation and inhibition is established through convoluted local interactions between neurons, which are organized by specific network connectivity structures and are dynamically controlled by modulating synaptic activities. Therefore, identifying how such structural and physiological factors contribute to establishment of overall balance of excitation and inhibition is crucial in understanding the homeostatic plasticity mechanisms that regulate the balance. We use biologically plausible mathematical models to extensively study the effects of multiple key factors on overall balance of a network. We characterize a network’s baseline balanced state by certain functional properties, and demonstrate how variations in physiological and structural parameters of the network deviate this balance and, in particular, result in transitions in spontaneous activity of the network to high-amplitude slow oscillatory regimes. We show that deviations from the reference balanced state can be continuously quantified by measuring the ratio of mean excitatory to mean inhibitory synaptic conductances in the network. Our results suggest that the commonly observed ratio of the number of inhibitory to the number of excitatory neurons in local cortical networks is almost optimal for their stability and excitability. Moreover, the values of inhibitory synaptic decay time constants and density of inhibitory-to-inhibitory network connectivity are critical to overall balance and stability of cortical networks. However, network stability in our results is sufficiently robust against modulations of synaptic quantal conductances, as required by their role in learning and memory. Our study based on extensive bifurcation analyses thus reveal the functional optimality and criticality of structural and physiological parameters in establishing the baseline operating state of local cortical networks.

A numerical population density technique for N-dimensional neuron models

Population density techniques can be used to simulate the behavior of a population of neurons which adhere to a common underlying neuron model. They have previously been used for analyzing models of orientation tuning and decision making tasks. They produce a fully deterministic solution to neural simulations which often involve a non-deterministic or noise component. Until now, numerical population density techniques have been limited to only one- and two-dimensional models. For the first time, we demonstrate a method to take an N-dimensional underlying neuron model and simulate the behavior of a population. The technique enables so-called graceful degradation of the dynamics allowing a balance between accuracy and simulation speed while maintaining important behavioral features such as rate curves and bifurcations. It is an extension of the numerical population density technique implemented in the MIIND software framework that simulates networks of populations of neurons. Here, we describe the extension to N dimensions and simulate populations of leaky integrate-and-fire neurons with excitatory and inhibitory synaptic conductances then demonstrate the effect of degrading the accuracy on the solution. We also simulate two separate populations in an E-I configuration to demonstrate the technique's ability to capture complex behaviors of interacting populations. Finally, we simulate a population of four-dimensional Hodgkin-Huxley neurons under the influence of noise. Though the MIIND software has been used only for neural modeling up to this point, the technique can be used to simulate the behavior of a population of agents adhering to any system of ordinary differential equations under the influence of shot noise. MIIND has been modified to render a visualization of any three of an N-dimensional state space of a population which encourages fast model prototyping and debugging and could prove a useful educational tool for understanding dynamical systems.

Voltage Clamp Errors During Estimation of Concurrent Excitatory and Inhibitory Synaptic Input to Neurons with Dendrites

The whole-cell voltage clamp technique is commonly used to estimate synaptic conductances. While previous work has shown how these estimates are affected by series resistance and space clamp errors during isolated synaptic events, how voltage clamp errors impact on synaptic conductance estimates during concurrent excitation and inhibition is less clear. This issue is particularly relevant given that many studies now use the whole-cell voltage clamp technique to estimate synaptic conductances in vivo, where both excitation and inhibition are intact. Using both simplistic and morphologically realistic models, we investigate how imperfect voltage clamp conditions distort estimates of excitatory and inhibitory synaptic conductance estimated using the Borg-Graham method during concurrent synaptic input onto dendrites. These simulations demonstrate that dendritically located conductances are underestimated even when dynamic clamp reinjection faithfully reproduces the voltage response at the soma to the actual conductances. Inhibitory conductances are underestimated more than excitatory conductances, leading to errors in the excitatory to inhibitory conductance ratio and negative inhibitory conductance estimates during distal inhibition. Interactions between unclamped dendritic excitatory and inhibitory conductances also introduce correlations when the actual conductances are uncorrelated, as well as distortions in the time course of estimated excitatory and inhibitory conductances. Finally, we show that space clamp errors are exacerbated by the inclusion of dendritic voltage-activated conductances. In summary, we highlight issues with the interpretation of synaptic conductance estimates obtained using somatic whole-cell voltage clamp during concurrent excitatory and inhibitory input to neurons with dendrites.

Phase bistability between anticipated and delayed synchronization in neuronal populations.

Two dynamical systems unidirectionally coupled in a sender-receiver configuration can synchronize with a nonzero phase lag. In particular, the system can exhibit anticipated synchronization (AS), which is characterized by a negative phase lag, if the receiver also receives a delayed negative self-feedback. Recently, AS was shown to occur between cortical-like neuronal populations in which the self-feedback is mediated by inhibitory synapses. In this biologically plausible scenario, a transition from the usual delayed synchronization (with positive phase lag) to AS can be mediated by the inhibitory conductances in the receiver population. Here we show that depending on the relation between excitatory and inhibitory synaptic conductances the system can also exhibit phase bistability between anticipated and delayed synchronization. Furthermore, we show that the amount of noise at the receiver and the synaptic conductances can mediate the transition from stable phase locking to a bistable regime and eventually to a phase drift. We suggest that our spiking neuronal populations model could be potentially useful to study phase bistability in cortical regions related to bistable perception.

Inferring synaptic inputs from spikes with a conductance-based neural encoding model.

Descriptive statistical models of neural responses generally aim to characterize the mapping from stimuli to spike responses while ignoring biophysical details of the encoding process. Here, we introduce an alternative approach, the conductance-based encoding model (CBEM), which describes a mapping from stimuli to excitatory and inhibitory synaptic conductances governing the dynamics of sub-threshold membrane potential. Remarkably, we show that the CBEM can be fit to extracellular spike train data and then used to predict excitatory and inhibitory synaptic currents. We validate these predictions with intracellular recordings from macaque retinal ganglion cells. Moreover, we offer a novel quasi-biophysical interpretation of the Poisson generalized linear model (GLM) as a special case of the CBEM in which excitation and inhibition are perfectly balanced. This work forges a new link between statistical and biophysical models of neural encoding and sheds new light on the biophysical variables that underlie spiking in the early visual pathway.

Balanced synaptic currents underlie low-frequency oscillations in the subiculum.

Numerous synaptic and intrinsic membrane mechanisms have been proposed for generating oscillatory activity in the hippocampus. Few studies, however, have directly measured synaptic conductances and membrane properties during oscillations. The time course and relative contribution of excitatory and inhibitory synaptic conductances, as well as the role of intrinsic membrane properties in amplifying synaptic inputs, remains unclear. To address this issue, we used an isolated whole hippocampal preparation that generates autonomous low-frequency oscillations near the theta range. Using 2-photon microscopy and expression of genetically encoded fluorophores, we obtained on-cell and whole-cell patch recordings of pyramidal cells and fast-firing interneurons in the distal subiculum. Pyramidal cell and interneuron spiking shared similar phase-locking to local field potential oscillations. In pyramidal cells, spiking resulted from a concomitant and balanced increase in excitatory and inhibitory synaptic currents. In contrast, interneuron spiking was driven almost exclusively by excitatory synaptic current. Thus, similar to tightly balanced networks underlying hippocampal gamma oscillations and ripples, balanced synaptic inputs in the whole hippocampal preparation drive highly phase-locked spiking at the peak of slower network oscillations.

Information Processing in GLIF Neuron Model with Noisy Conductance

In this article, we investigate the generalized leaky integrate-and-fire (GLIF) neuron model with stochastic synaptic conductance. A neuron remains connected with other neuron via dendrites and axons at synapse, which can be treated as an electrical capacitor. Dendrites carry electro-chemical signals from input neuron to synapse whereas axons are responsible for their transmission form synapse to other neurons. Concentration of these electro-chemicals in synapse varies during entire time period. We investigate the effect of varying concentration of electro-chemicals at synapse in a single neuron model. Concentration variation of electro-chemicals at synapse is incorporated as noise in GLIF model. Excitatory and inhibitory synaptic conductance of neuron in GLIF is assumed as stochastic entities driven by Gaussian White noise. Stationary state membrane potential distribution for the proposed model is computed with reflecting boundary conditions, which is noticed as geometrically distributed. In order to investigate spiking activity and information encoding mechanism, an extensive simulation based study has been carried out. Temporal encoding technique is used to analyze the encoding mechanism. It is noticed that ISI distribution has higher variance with respect to excitatory input than inhibitory input.

Controlling Complexity of Cerebral Cortex Simulations-II: Streamlined Microcircuits.

Recently, Markram et al. (2015) presented a model of the rat somatosensory microcircuit (Markram model). Their model is high in anatomical and physiological detail, and its simulation requires supercomputers. The lack of neuroinformatics and computing power is an obstacle for using a similar approach to build models of other cortical areas or larger cortical systems. Simplified neuron models offer an attractive alternative to high-fidelity Hodgkin-Huxley-type neuron models, but their validity in modeling cortical circuits is unclear. We simplified the Markram model to a network of exponential integrate-and-fire (EIF) neurons that runs on a single CPU core in reasonable time. We analyzed the electrophysiology and the morphology of the Markram model neurons with eFel and NeuroM tools, provided by the Blue Brain Project. We then constructed neurons with few compartments and averaged parameters from the reference model. We used the CxSystem simulation framework to explore the role of short-term plasticity and GABA and NMDA synaptic conductances in replicating oscillatory phenomena in the Markram model. We show that having a slow inhibitory synaptic conductance (GABA allows replication of oscillatory behavior in the high-calcium state. Furthermore, we show that qualitatively similar dynamics are seen even with a reduced number of cell types (from 55 to 17 types). This reduction halved the computation time. Our results suggest that qualitative dynamics of cortical microcircuits can be studied using limited neuroinformatics and computing resources supporting parameter exploration and simulation of cortical systems. The simplification procedure can easily be adapted to studying other microcircuits for which sparse electrophysiological and morphological data are available.

Using computational models to predict in vivo synaptic inputs to interneuron specific 3 (IS3) cells of CA1 hippocampus that also allow their recruitment during rhythmic states.

Brain coding strategies are enabled by the balance of synaptic inputs that individual neurons receive as determined by the networks in which they reside. Inhibitory cell types contribute to brain function in distinct ways but recording from specific, inhibitory cell types during behaviour to determine their contributions is highly challenging. In particular, the in vivo activities of vasoactive intestinal peptide-expressing interneuron specific 3 (IS3) cells in the hippocampus that only target other inhibitory cells are unknown at present. We perform a massive, computational exploration of possible synaptic inputs to IS3 cells using multi-compartment models and optimized synaptic parameters. We find that asynchronous, in vivo-like states that are sensitive to additional theta-timed inputs (8 Hz) exist when excitatory and inhibitory synaptic conductances are approximately equally balanced and with low numbers of activated synapses receiving correlated inputs. Specifically, under these balanced conditions, the input resistance is larger with higher mean spike firing rates relative to other activated synaptic conditions investigated. Incoming theta-timed inputs result in strongly increased spectral power relative to baseline. Thus, using a generally applicable computational approach we predict the existence and features of background, balanced states in hippocampal circuits.

Method of experimental synaptic conductance estimation: Limitations of the basic approach and extension to voltage-dependent conductances

Abstract Estimating the synaptic conductances impinging on a single neuron is one of the open problems that need to be solved in order to understand the flow of information in the brain. Conventional method of evaluating excitatory and inhibitory synaptic conductances has some limitations due to incorrect assumptions about the voltage independence of the conductances. The limitations of the basic method and its generalization to NMDA receptors are the focus of this study. Using numerical simulations with a passive neuron, the effects of different aspects on the residual error—voltage-clamp versus current-clamp modes, linearity of the current–voltage relationship, NMDA receptor contribution, and noise contamination—are investigated. In addition, the effectiveness of experimental tests using the voltage reconstruction method is challenged. In the range of physiologically plausible parameters, the basic method reveals qualitatively wrong modulation of the excitatory and inhibitory conductances. A modified method of estimating voltage-independent AMPA- and GABA-receptor-mediated conductances and voltage-dependent NMDA-receptor-mediated conductances is proposed. This method requires voltage-clamp recordings at three voltage levels, and its estimations of oscillating conductances are accurate. Therefore, the modified method can be recommended for experiments, particularly those involving evaluation of excitatory and inhibitory synaptic conductance modulation in the visual cortex. The basic method, however, compromises the results of excitation and inhibition counterphase modulation during grating visual stimulation of a cat’s striate cortex because it does not account for the NMDA component.

Functional Organization of Flash-Induced V1 Offline Reactivation.

The long-delayed responses of neocortical neurons are thought to arise from cortical feedback activity that is related to sensory perception and cognition. The mechanism of neocortical late responses was investigated using multiple electrophysiological techniques and the findings indicate that it actually arises from the thalamus. In addition, during the late response, excitation and inhibition are balanced, but inhibition is dominant in patterning action potentials.

Simultaneous Bayesian Estimation of Excitatory and Inhibitory Synaptic Conductances by Exploiting Multiple Recorded Trials.

Advanced statistical methods have enabled trial-by-trial inference of the underlying excitatory and inhibitory synaptic conductances (SCs) of membrane-potential recordings. Simultaneous inference of both excitatory and inhibitory SCs sheds light on the neural circuits underlying the neural activity and advances our understanding of neural information processing. Conventional Bayesian methods can infer excitatory and inhibitory SCs based on a single trial of observed membrane potential. However, if multiple recorded trials are available, this typically leads to suboptimal estimation because they neglect common statistics (of synaptic inputs (SIs)) across trials. Here, we establish a new expectation maximization (EM) algorithm that improves such single-trial Bayesian methods by exploiting multiple recorded trials to extract common SI statistics across the trials. In this paper, the proposed EM algorithm is embedded in parallel Kalman filters or particle filters for multiple recorded trials to integrate their outputs to iteratively update the common SI statistics. These statistics are then used to infer the excitatory and inhibitory SCs of individual trials. We demonstrate the superior performance of multiple-trial Kalman filtering (MtKF) and particle filtering (MtPF) relative to that of the corresponding single-trial methods. While relative estimation error of excitatory and inhibitory SCs is known to depend on the level of current injection into a cell, our numerical simulations using MtKF show that both excitatory and inhibitory SCs are reliably inferred using an optimal level of current injection. Finally, we validate the robustness and applicability of our technique through simulation studies, and we apply MtKF to in vivo data recorded from the rat barrel cortex.

Synaptic Conductances during Interictal Discharges in Pyramidal Neurons of Rat Entorhinal Cortex.

In epilepsy, the balance of excitation and inhibition underlying the basis of neural network activity shifts, resulting in neuronal network hyperexcitability and recurrent seizure-associated discharges. Mechanisms involved in ictal and interictal events are not fully understood, in particular, because of controversial data regarding the dynamics of excitatory and inhibitory synaptic conductances. In the present study, we estimated AMPAR-, NMDAR-, and GABAA R-mediated conductances during two distinct types of interictal discharge (IID) in pyramidal neurons of rat entorhinal cortex in cortico-hippocampal slices. Repetitively emerging seizure-like events and IIDs were recorded in high extracellular potassium, 4-aminopyridine, and reduced magnesium-containing solution. An original procedure for estimating synaptic conductance during IIDs was based on the differences among the current-voltage characteristics of the synaptic components. The synaptic conductance dynamics obtained revealed that the first type of IID is determined by activity of GABAA R channels with depolarized reversal potential. The second type of IID is determined by the interplay between excitation and inhibition, with early AMPAR and prolonged depolarized GABAA R and NMDAR-mediated components. The study then validated the contribution of these components to IIDs by intracellular pharmacological isolation. These data provide new insights into the mechanisms of seizures generation, development, and cessation.

Estimation of excitatory and inhibitory synaptic conductance variations in motoneurons during locomotor-like rhythmic activity

The rhythmic activity of motoneurons (MNs) that underlies locomotion in mammals is generated by synaptic inputs from the locomotor network in the spinal cord. Thus, the quantitative estimation of excitatory and inhibitory synaptic conductances is essential to understand the mechanism by which the network generates the functional motor output. Conductance estimation is obtained from the voltage–current relationship measured by voltage-clamp- or current-clamp-recording with knowledge of the leak parameters of the recorded neuron. However, it is often difficult to obtain sufficient data to estimate synaptic conductances due to technical difficulties in electrophysiological experiments using in vivo or in vitro preparations. To address this problem, we estimated the average variations in excitatory and inhibitory synaptic conductance during a locomotion cycle from a single voltage trace without measuring the leak parameters. We found that the conductance variations can be accurately reconstructed from a voltage trace of 10 cycles by analyzing synthetic data generated from a computational model. Next, the conductance variations were estimated from mouse spinal MNs in vitro during drug-induced-locomotor-like activity. We found that the peak of excitatory conductance occurred during the depolarizing phase of the locomotor cycle, whereas the peak of inhibitory conductance occurred during the hyperpolarizing phase. These results suggest that the locomotor-like activity is generated by push–pull modulation via excitatory and inhibitory synaptic inputs.

Inferring presynaptic population spiking from single-trial membrane potential recordings

BackgroundThe time-varying membrane potential of a cortical neuron contains important information about the network activity. Extracting this information requires separating excitatory and inhibitory synaptic inputs from single-trial membrane potential recordings without averaging across trials. New methodWe propose a method to extract the time course of excitatory and inhibitory synaptic inputs to a neuron from a single-trial membrane potential recording. The method takes advantage of the differences in the time constants and the reversal potentials of the excitatory and inhibitory synaptic currents, which allows the untangling of the two conductance types. ResultsWe evaluate the applicability of the method on a leaky integrate-and-fire model neuron and find high quality of estimation of excitatory synaptic conductance changes and presynaptic population spikes. Application of the method to a real cortical neuron with known synaptic inputs in a brain slice returns high-quality estimation of the time course of the excitatory synaptic conductance. Application of the method to membrane potential recordings from a cortical pyramidal neuron of an intact brain reveals complex network activity. Comparison with existing methodsExisting methods are based on repeated trials and thus are limited to estimating the statistical features of synaptic conductance changes, or, when based on single trials, are limited to special cases, have low temporal resolution, or are impractically complicated. ConclusionsWe propose and test an efficient method for estimating the full time course of excitatory and inhibitory synaptic conductances from single-trial membrane potential recordings. The method is sufficiently simple to ensure widespread use in neuroscience.

Hidden synaptic differences in a neural circuit underlie differential behavioral susceptibility to a neural injury.

Individuals vary in their responses to stroke and trauma, hampering predictions of outcomes. One reason might be that neural circuits contain hidden variability that becomes relevant only when those individuals are challenged by injury. We found that in the mollusc, Tritonia diomedea, subtle differences between animals within the neural circuit underlying swimming behavior had no behavioral relevance under normal conditions but caused differential vulnerability of the behavior to a particular brain lesion. The extent of motor impairment correlated with the site of spike initiation in a specific neuron in the neural circuit, which was determined by the strength of an inhibitory synapse onto this neuron. Artificially increasing or decreasing this inhibitory synaptic conductance with dynamic clamp correspondingly altered the extent of motor impairment by the lesion without affecting normal operation. The results suggest that neural circuit differences could serve as hidden phenotypes for predicting the behavioral outcome of neural damage.

Corrigendum: Firing clamp: a novel method for single-trial estimation of excitatory and inhibitory synaptic neuronal conductances

Corrigendum: Firing clamp: a novel method for single-trial estimation of excitatory and inhibitory synaptic neuronal conductances

Glutamate-bound NMDARs arising from in vivo-like network activity extend spatio-temporal integration in a L5 cortical pyramidal cell model.

In vivo, cortical pyramidal cells are bombarded by asynchronous synaptic input arising from ongoing network activity. However, little is known about how such ‘background’ synaptic input interacts with nonlinear dendritic mechanisms. We have modified an existing model of a layer 5 (L5) pyramidal cell to explore how dendritic integration in the apical dendritic tuft could be altered by the levels of network activity observed in vivo. Here we show that asynchronous background excitatory input increases neuronal gain and extends both temporal and spatial integration of stimulus-evoked synaptic input onto the dendritic tuft. Addition of fast and slow inhibitory synaptic conductances, with properties similar to those from dendritic targeting interneurons, that provided a ‘balanced’ background configuration, partially counteracted these effects, suggesting that inhibition can tune spatio-temporal integration in the tuft. Excitatory background input lowered the threshold for NMDA receptor-mediated dendritic spikes, extended their duration and increased the probability of additional regenerative events occurring in neighbouring branches. These effects were also observed in a passive model where all the non-synaptic voltage-gated conductances were removed. Our results show that glutamate-bound NMDA receptors arising from ongoing network activity can provide a powerful spatially distributed nonlinear dendritic conductance. This may enable L5 pyramidal cells to change their integrative properties as a function of local network activity, potentially allowing both clustered and spatially distributed synaptic inputs to be integrated over extended timescales.

Firing clamp: a novel method for single-trial estimation of excitatory and inhibitory synaptic neuronal conductances.

Understanding non-stationary neuronal activity as seen in vivo requires estimation of both excitatory and inhibitory synaptic conductances from a single trial of recording. For this purpose, we propose a new intracellular recording method, called “firing clamp.” Synaptic conductances are estimated from the characteristics of artificially evoked probe spikes, namely the spike amplitude and the mean subthreshold potential, which are sensitive to both excitatory and inhibitory synaptic input signals. The probe spikes, timed at a fixed rate, are evoked in the dynamic-clamp mode by injected meander-like current steps, with the step duration depending on neuronal membrane voltage. We test the method with perforated-patch recordings from isolated cells stimulated by external application or synaptic release of transmitter, and validate the method with simulations of a biophysically-detailed neuron model. The results are compared with the conductance estimates based on conventional current-clamp recordings.

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.