A spontaneous state of weakly correlated synaptic excitation and inhibition in visual cortex

Subthreshold moment analysis of neuronal populations driven by synchronous synaptic inputs

Even when driven by the same stimulus, neuronal responses are well-known to exhibit a striking level of spiking variability. In-vivo electrophysiological recordings also reveal a surprisingly large degree of variability at the subthreshold level. In prior work, we considered biophysically relevant neuronal models to account for the observed magnitude of membrane voltage fluctuations. We found that accounting for these fluctuations requires weak but nonzero synchrony in the spiking activity, in amount that are consistent with experimentally measured spiking correlations. Here we investigate whether such synchrony can explain additional statistical features of the measured neural activity, including neuronal voltage covariability and voltage skewness. Addressing this question involves conducting a generalized moment analysis of conductance-based neurons in response to input drives modeled as correlated jump processes. Technically, we perform such an analysis using fixed-point techniques from queuing theory that are applicable in the stationary regime of activity. We found that weak but nonzero synchrony can consistently explain the experimentally reported voltage covariance and skewness. This confirms the role of synchrony as a primary driver of cortical variability and supports that physiological neural activity emerges as a population-level phenomenon, especially in the spontaneous regime.

Subthreshold variability of neuronal populations driven by synchronous synaptic inputs

Even when driven by the same stimulus, neuronal responses are well-known to exhibit a striking level of spiking variability. In-vivo electrophysiological recordings also reveal a surprisingly large degree of variability at the subthreshold level. In prior work, we considered biophysically relevant neuronal models to account for the observed magnitude of membrane voltage fluctuations. We found that accounting for these fluctuations requires weak but nonzero synchrony in the spiking activity, in amount that are consistent with experimentally measured spiking correlations. Here we investigate whether such synchrony can explain additional statistical features of the measured neural activity, including neuronal voltage covariability and voltage skewness. Addressing this question involves conducting a generalized moment analysis of conductance-based neurons in response to input drives modeled as correlated jump processes. Technically, we perform such an analysis using fixed-point techniques from queuing theory that are applicable in the stationary regime of activity. We found that weak but nonzero synchrony can consistently explain the experimentally reported voltage covariance and skewness. This confirms the role of synchrony as a primary driver of cortical variability and supports that physiological neural activity emerges as a population-level phenomenon, especially in the spontaneous regime.

Efficient coding in biophysically realistic excitatory-inhibitory spiking networks

The principle of efficient coding posits that sensory cortical networks are designed to encode maximal sensory information with minimal metabolic cost. Despite the major influence of efficient coding in neuroscience, it has remained unclear whether fundamental empirical properties of neural network activity can be explained solely based on this normative principle. Here, we derive the structural, coding, and biophysical properties of excitatory-inhibitory recurrent networks of spiking neurons that emerge directly from imposing that the network minimizes an instantaneous loss function and a time-averaged performance measure enacting efficient coding. We assumed that the network encodes a number of independent stimulus features varying with a time scale equal to the membrane time constant of excitatory and inhibitory neurons. The optimal network has biologically plausible biophysical features, including realistic integrate-and-fire spiking dynamics, spike-triggered adaptation, and a non-specific excitatory external input. The excitatory-inhibitory recurrent connectivity between neurons with similar stimulus tuning implements feature-specific competition, similar to that recently found in visual cortex. Networks with unstructured connectivity cannot reach comparable levels of coding efficiency. The optimal ratio of excitatory vs inhibitory neurons and the ratio of mean inhibitory-to-inhibitory vs excitatory-to-inhibitory connectivity are comparable to those of cortical sensory networks. The efficient network solution exhibits an instantaneous balance between excitation and inhibition. The network can perform efficient coding even when external stimuli vary over multiple time scales. Together, these results suggest that key properties of biological neural networks may be accounted for by efficient coding.

Primate neocortex performs balanced sensory amplification

The sensory cortex amplifies relevant features of external stimuli. This sensitivity and selectivity arise through the transformation of inputs by cortical circuitry. We characterize the circuit mechanisms and dynamics of cortical amplification by making large-scale simultaneous measurements of single cells in awake primates and testing computational models. By comparing network activity in both driven and spontaneous states with models, we identify the circuit as operating in a regime of non-normal balanced amplification. Incoming inputs are strongly but transiently amplified by strong recurrent feedback from the disruption of excitatory-inhibitory balance in the network. Strong inhibition rapidly quenches responses, thereby permitting the tracking of time-varying stimuli.

Exact Analysis of the Subthreshold Variability for Conductance-Based Neuronal Models with Synchronous Synaptic Inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state, neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically, we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects postspiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime yields realistic subthreshold variability (voltage variance ≃4-9 mV2) only when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that, without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≃ 4 - 9 m V 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects post-spiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime only yields realistic subthreshold variability (voltage variance ≅ 4-9mV 2 ) when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Heterogeneous mechanisms for synchronization of networks of resonant neurons under different E/I balance regimes

Rhythmic synchronization of neuronal firing patterns is a widely present phenomenon in the brain-one that seems to be essential for many cognitive processes. A variety of mechanisms contribute to generation and synchronization of network oscillations, ranging from intrinsic cellular excitability to network mediated effects. However, it is unclear how these mechanisms interact together. Here, using computational modeling of excitatory-inhibitory neural networks, we show that different synchronization mechanisms dominate network dynamics at different levels of excitation and inhibition (i.e. E/I levels) as synaptic strength is systematically varied. Our results show that with low synaptic strength networks are sensitive to external oscillatory drive as a synchronizing mechanism-a hallmark of resonance. In contrast, in a strongly-connected regime, synchronization is driven by network effects via the direct interaction between excitation and inhibition, and spontaneous oscillations and cross-frequency coupling emerge. Unexpectedly, we find that while excitation dominates network synchrony at low excitatory coupling strengths, inhibition dominates at high excitatory coupling strengths. Together, our results provide novel insights into the oscillatory modulation of firing patterns in different excitation/inhibition regimes.

Different Excitation-Inhibition Correlations Between Spontaneous and Tone-evoked Activity in Primary Auditory Cortex Neurons

Tone-evoked synaptic excitation and inhibition are highly correlated in many neurons with V-shaped tuning curves in the primary auditory cortex of pentobarbital-anesthetized rats. In contrast, there is less correlation between spontaneous excitation and inhibition in visual cortex neurons under the same anesthetic conditions. However, it was not known whether the primary auditory cortex resembles visual cortex in having spontaneous excitation and inhibition that is less correlated than tone-evoked excitation and inhibition. Here we report whole-cell voltage-clamp measurements of spontaneous excitation and inhibition in primary auditory cortex neurons of pentobarbital-anesthetized rats. Spontaneous excitatory and inhibitory currents appeared to mainly consist of distinct events, with the inhibitory event rate typically lower than the excitatory event rate. We use the ratio of the excitatory event rate to the inhibitory event rate, and the assumption that the excitatory and inhibitory synaptic currents can each be reasonably described as a filtered Poisson process, to estimate the maximum spontaneous excitatory-inhibitory correlation for each neuron. In a subset of neurons, we also measured tone-evoked excitation and inhibition. In neurons with V-shaped tuning curves, although tone-evoked excitation and inhibition were highly correlated, the spontaneous inhibitory event rate was typically sufficiently lower than the spontaneous excitatory event rate to indicate a lower excitatory-inhibitory correlation for spontaneous activity than for tone-evoked responses.

Network and cellular mechanisms underlying heterogeneous excitatory/inhibitory balanced states

Recent work has explored spatiotemporal relationships between excitatory (E) and inhibitory (I) signaling within neural networks, and the effect of these relationships on network activity patterns. Data from these studies have indicated that excitation and inhibition are maintained at a similar level across long time periods and that excitatory and inhibitory currents may be tightly synchronized. Disruption of this balance-leading to an aberrant E/I ratio-is implicated in various brain pathologies. However, a thorough characterization of the relationship between E and I currents in experimental settings is largely impossible, due to their tight regulation at multiple cellular and network levels. Here, we use biophysical neural network models to investigate the emergence and properties of balanced states by heterogeneous mechanisms. Our results show that a network can homeostatically regulate the E/I ratio through interactions among multiple cellular and network factors, including average firing rates, synaptic weights and average neural depolarization levels in excitatory/inhibitory populations. Complex and competing interactions between firing rates and depolarization levels allow these factors to alternately dominate network dynamics in different synaptic weight regimes. This leads to the emergence of distinct mechanisms responsible for determining a balanced state and its dynamical correlate. Our analysis provides a comprehensive picture of how E/I ratio changes when manipulating specific network properties, and identifies the mechanisms regulating E/I balance. These results provide a framework to explain the diverse, and in some cases, contradictory experimental observations on the E/I state in different brain states and conditions.

Information transmission of mean and variance coding in integrate-and-fire neurons

Neurons process information by translating continuous signals into patterns of discrete spike times. An open question is how much information these spike times contain about signals which modulate either the mean or the variance of the somatic currents in neurons, as is observed experimentally. Here we calculate the exact information contained in discrete spike times about a continuous signal in both encoding strategies. We show that the information content about mean modulating signals is generally substantially larger than about variance modulating signals for biological parameters. Our analysis further reveals that higher information transmission is associated with a larger proportion of nonlinear signal encoding. Our study measures the complete information content of mean and variance coding and provides a method to determine what fraction of the total information is linearly decodable.

UP-DOWN cortical dynamics reflect state transitions in a bistable network

In the idling brain, neuronal circuits transition between periods of sustained firing (UP state) and quiescence (DOWN state), a pattern the mechanisms of which remain unclear. Here we analyzed spontaneous cortical population activity from anesthetized rats and found that UP and DOWN durations were highly variable and that population rates showed no significant decay during UP periods. We built a network rate model with excitatory (E) and inhibitory (I) populations exhibiting a novel bistable regime between a quiescent and an inhibition-stabilized state of arbitrarily low rate. Fluctuations triggered state transitions, while adaptation in E cells paradoxically caused a marginal decay of E-rate but a marked decay of I-rate in UP periods, a prediction that we validated experimentally. A spiking network implementation further predicted that DOWN-to-UP transitions must be caused by synchronous high-amplitude events. Our findings provide evidence of bistable cortical networks that exhibit non-rhythmic state transitions when the brain rests.

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.

Efficient codes and balanced networks

Recent years have seen a growing interest in inhibitory interneurons and their circuits. A striking property of cortical inhibition is how tightly it balances excitation. Inhibitory currents not only match excitatory currents on average, but track them on a millisecond time scale, whether they are caused by external stimuli or spontaneous fluctuations. We review, together with experimental evidence, recent theoretical approaches that investigate the advantages of such tight balance for coding and computation. These studies suggest a possible revision of the dominant view that neurons represent information with firing rates corrupted by Poisson noise. Instead, tight excitatory/inhibitory balance may be a signature of a highly cooperative code, orders of magnitude more precise than a Poisson rate code. Moreover, tight balance may provide a template that allows cortical neurons to construct high-dimensional population codes and learn complex functions of their inputs.

Bringing the dynamics of movement under control

The mechanisms underlying the dynamics of movement-related neural activity are not known. In this issue of Neuron, Hennequin et al. (2014) show that a recurrent network whose spontaneous activity is stabilized by learning reproduces many aspects of preparatory and movement-related activity.