Excitatory Synaptic Conductances Research Articles

A Mathematical Model of Spontaneous Action Potential Based on Stochastics Synaptic Noise Dynamics in Non-Neural Cells

We developed a mathematical model to simulate the dynamics of background synaptic noise in non-neuronal cells. By employing the stochastic Ornstein–Uhlenbeck process, we represented excitatory synaptic conductance and integrated it into a whole-cell model to generate spontaneous and evoke cellular electrical activities. This single-cell model encompasses numerous biophysically detailed ion channels, depicted by a set of ordinary differential equations in Hodgkin–Huxley and Markov formalisms. Consequently, this approach effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potentials (sAPs), resembling electrical activity observed in vitro. The input resistance decreased significantly, while the firing rate of spontaneous action potentials increased. Moreover, alterations in the ability to reach the action potential threshold were observed. Background synaptic activity can modify the input/output characteristics of non-neuronal excitatory cells. Hence, suppressing these baseline activities could aid in identifying new pharmaceutical targets for various clinical diseases.

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.

Spiral wave chimera states in regular and fractal neuronal networks

Chimera states are spatial patterns in which coherent and incoherent patterns coexist. It was reported that small populations of coupled oscillators can exhibit chimera with transient nature. This spatial coexistence has been observed in various network topologies of coupled systems, such as coupled pendula, coupled chemical oscillators, and neuronal networks. In this work, we build two-dimensional neuronal networks with regular and fractal topologies to study chimera states. In the regular network, we consider a coupling between the nearest neighbours neurons, while the fractal network is constructed according to the square Cantor set. Our networks are composed of coupled adaptive exponential integrate-and-fire neurons, that can exhibit spike or burst activities. Depending on the parameters, we find spiral wave chimeras in both regular and fractal networks. The spiral wave chimeras arise for different values of the intensity of the excitatory synaptic conductance. In our simulations, we verify the existence of multicore chimera states. The cores are made up of neurons with desynchronous behaviour and the spiral waves rotates around them. The cores can be related to bumps or spatially localised pulses of neuronal activities. We also show that the initial value of the adaptation current plays an important role in the existence of spiral wave chimera states.

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.

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.

Respiratory Rhythm in a Simplified Respiratory Network Model

The regulatory mechanism of the respiratory system is always a hot topic in the neurobiology field. Many researchers proposed multitudinous respiratory network models and explored their internal connections. For further understanding the effect of the respiratory system in breathing, we have built a simplified respiratory network model and studied the relations between each neuron in this network. We, firstly, removed the pre-I neuron from the network and found that there are abundant bifurcation phenomena with respect for the interspike intervals (ISIs). In addition, a large number of unusual firing patterns were observed in the network under conditions of AC stimulation. After adjusting the potassium conductance in the pre-I neuron by a different tonic drive from the d1 input, we show the transition from bursting patterns to analogous single spiking and, subsequently, convert-bursting patterns. Moreover, when sodium ion channels were removed or synaptic connections and tonic drives in the network were excluded, the network activity showed relevant variations. This may help to explain some functions of ion channels or certain neurons of the network. Finally, the biparametric screening plane with the excitatory synaptic conductance and persistent sodium conductance has been drawn. Graduations in this plane reflected different firing patterns, such as tonic spiking, bursting, and aperiodic bursting. Our results provide important insights for understanding the regulatory mechanisms of the respiratory network and the surrounding structures.

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.

Coupling of synaptic inputs to local cortical activity differs among neurons and adapts after stimulus onset.

Cortical activity contributes significantly to the high variability of sensory responses of interconnected pyramidal neurons, which has crucial implications for sensory coding. Yet, largely because of technical limitations of in vivo intracellular recordings, the coupling of a pyramidal neuron's synaptic inputs to the local cortical activity has evaded full understanding. Here we obtained excitatory synaptic conductance ( g) measurements from putative pyramidal neurons and local field potential (LFP) recordings from adjacent cortical circuits during visual processing in the turtle whole brain ex vivo preparation. We found a range of g-LFP coupling across neurons. Importantly, for a given neuron, g-LFP coupling increased at stimulus onset and then relaxed toward intermediate values during continued visual stimulation. A model network with clustered connectivity and synaptic depression reproduced both the diversity and the dynamics of g-LFP coupling. In conclusion, these results establish a rich dependence of single-neuron responses on anatomical, synaptic, and emergent network properties. NEW & NOTEWORTHY Cortical neurons are strongly influenced by the networks in which they are embedded. To understand sensory processing, we must identify the nature of this influence and its underlying mechanisms. Here we investigate synaptic inputs to cortical neurons, and the nearby local field potential, during visual processing. We find a range of neuron-to-network coupling across cortical neurons. This coupling is dynamically modulated during visual processing via biophysical and emergent network properties.

Phasic Firing and Coincidence Detection by Subthreshold Negative Feedback: Divisive or Subtractive or, Better, Both.

Phasic neurons typically fire only for a fast-rising input, say at the onset of a step current, but not for steady or slow inputs, a property associated with type III excitability. Phasic neurons can show extraordinary temporal precision for phase locking and coincidence detection. Exemplars are found in the auditory brain stem where precise timing is used in sound localization. Phasicness at the cellular level arises from a dynamic, voltage-gated, negative feedback that can be recruited subthreshold, preventing the neuron from reaching spike threshold if the voltage does not rise fast enough. We consider two mechanisms for phasicness: a low threshold potassium current (subtractive mechanism) and a sodium current with subthreshold inactivation (divisive mechanism). We develop and analyze three reduced models with either divisive or subtractive mechanisms or both to gain insight into the dynamical mechanisms for the potentially high temporal precision of type III-excitable neurons. We compare their firing properties and performance for a range of stimuli. The models have characteristic non-monotonic input-output relations, firing rate vs. input intensity, for either stochastic current injection or Poisson-timed excitatory synaptic conductance trains. We assess performance according to precision of phase-locking and coincidence detection by the models' responses to repetitive packets of unitary excitatory synaptic inputs with more or less temporal coherence. We find that each mechanism contributes features but best performance is attained if both are present. The subtractive mechanism confers extraordinary precision for phase locking and coincidence detection but only within a restricted parameter range when the divisive mechanism of sodium inactivation is inoperative. The divisive mechanism guarantees robustness of phasic properties, without compromising excitability, although with somewhat less precision. Finally, we demonstrate that brief transient inhibition if properly timed can enhance the reliability of firing.

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.

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

Cellular mechanisms for response heterogeneity among L2/3 pyramidal cells in whisker somatosensory cortex.

Whisker deflection evokes sparse, low-probability spiking among L2/3 pyramidal cells in rodent somatosensory cortex (S1), with spiking distributed nonuniformly between more and less responsive cells. The cellular and local circuit factors that determine whisker responsiveness across neurons are unclear. To identify these factors, we used two-photon calcium imaging and loose-seal recording to identify more and less responsive L2/3 neurons in S1 slices in vitro, during feedforward recruitment of the L2/3 network by L4 stimulation. We observed a broad gradient of spike recruitment thresholds within local L2/3 populations, with low- and high-threshold cells intermixed. This recruitment gradient was significantly correlated across different L4 stimulation sites, and between L4-evoked and whisker-evoked responses in vivo, indicating that a substantial component of responsiveness is independent of tuning to specific feedforward inputs. Low- and high-threshold L2/3 pyramidal cells differed in L4-evoked excitatory synaptic conductance and intrinsic excitability, including spike threshold and the likelihood of doublet spike bursts. A gradient of intrinsic excitability was observed across neurons. Cells that spiked most readily to L4 stimulation received the most synaptic excitation but had the lowest intrinsic excitability. Low- and high-threshold cells did not differ in dendritic morphology, passive membrane properties, or L4-evoked inhibitory conductance. Thus multiple gradients of physiological properties exist across L2/3 pyramidal cells, with excitatory synaptic input strength best predicting overall spiking responsiveness during network recruitment.