Origin of information-limiting noise correlations

The ability to discriminate between similar sensory stimuli relies on the amount of information encoded in sensory neuronal populations. Such information can be substantially reduced by correlated trial-to-trial variability. Noise correlations have been measured across a wide range of areas in the brain, but their origin is still far from clear. Here we show analytically and with simulations that optimal computation on inputs with limited information creates patterns of noise correlations that account for a broad range of experimental observations while at same time causing information to saturate in large neural populations. With the example of a network of V1 neurons extracting orientation from a noisy image, we illustrate to our knowledge the first generative model of noise correlations that is consistent both with neurophysiology and with behavioral thresholds, without invoking suboptimal encoding or decoding or internal sources of variability such as stochastic network dynamics or cortical state fluctuations. We further show that when information is limited at the input, both suboptimal connectivity and internal fluctuations could similarly reduce the asymptotic information, but they have qualitatively different effects on correlations leading to specific experimental predictions. Our study indicates that noise at the sensory periphery could have a major effect on cortical representations in widely studied discrimination tasks. It also provides an analytical framework to understand the functional relevance of different sources of experimentally measured correlations.The response of cortical neurons to an identical stimulus varies from trial to trial. Moreover, this variability tends to be correlated among pairs of nearby neurons. These correlations, known as noise correlations, have been the subject of numerous experimental as well as theoretical studies because they can have a profound impact on behavioral performance (1–7). Indeed, behavioral performance in discrimination tasks is inversely proportional to the Fisher information available in the neural responses, which itself is strongly dependent on the pattern of correlations. In particular, correlations can strongly limit information in the sense that some patterns of correlations can lead information to saturate to a finite value in large populations, in sharp contrast to the case of independent neurons for which information grows proportionally to the number of neurons. However, the saturation is observed for only one type of correlations known as differential correlations. If the correlation pattern slightly deviates from differential correlations, information typically scales with the number of neurons, just like it does for independent neurons (7). These previous results clarify how correlations impact information and consequently behavioral performance but fail to address another fundamental question, namely, Where do noise correlations, and in particular information-limiting differential correlation, come from? Understanding the origin of information-limiting correlation is a key step toward understanding how neural circuits can increase information transfer, thereby improving behavioral performance, via either perceptual learning or attentional selection.Several groups have started to investigate sources of noise correlations such as shared connectivity (2), feedback signals (8), internal dynamics (9–11), or global fluctuations in the excitability of cortical circuits (12–16). Global fluctuations have received a lot of attention recently as they appear to account for a large fraction of the measured correlations in the primary visual cortex. Correlations induced by global fluctuations, however, do not limit information in most discrimination tasks (with the possible exception of contrast discrimination for visual stimuli). Therefore, if cortex indeed operates at information saturation, the source of information-limiting correlations is still very much unclear.In this paper, we focus on correlations induced by feedforward processing of stimuli whose information content is small compared with the information capacity of neural circuits. Using orientation selectivity as a case study, we find that feedforward processing induces correlations that share many properties of the correlations observed in vivo. Moreover, we also show feedforward processing leads to information-limiting correlations as a direct consequence of the data processing inequality. Interestingly, these information-limiting correlations represent only a small fraction of the overall correlations induced by feedforward processing, making them difficult to detect through direct measurements of correlations. Finally, we demonstrate that correlations induced by global fluctuations cannot limit information on their own, but can reduce the level at which information saturates in the presence of information-limiting correlations. Despite our focus on orientation selectivity, our results can be generalized to other modalities, stimuli, and brain areas.In summary, this work identifies a major source of noise correlations and, importantly, a source of information-limiting noise correlations, while clarifying the interactions between information-limiting correlations and correlations induced by global fluctuations.     

Brain state limits propagation of neural signals in laminar cortical circuits

Our perception of the environment relies on the efficient propagation of neural signals across cortical networks. During the time course of a day, neural responses fluctuate dramatically as the state of the brain changes to possibly influence how electrical signals propagate across neural circuits. Despite the importance of this issue, how patterns of spiking activity propagate within neuronal circuits in different brain states remains unknown. Here, we used multielectrode laminar arrays to reveal that brain state strongly modulates the propagation of neural activity across the layers of early visual cortex (V1). We optogenetically induced synchronized state transitions within a group of neurons and examined how far electrical signals travel during wakefulness and rest. Although optogenetic stimulation elicits stronger neural responses during wakefulness relative to rest, signals propagate only weakly across the cortical column during wakefulness, and the extent of spread is inversely related to arousal level. In contrast, the light-induced population activity vigorously propagates throughout the entire cortical column during rest, even when neurons are in a desynchronized wake-like state prior to light stimulation. Mechanistically, the influence of global brain state on the propagation of spiking activity across laminar circuits can be explained by state-dependent changes in the coupling between neurons. Our results impose constraints on the conclusions of causal manipulation studies attempting to influence neural function and behavior, as well as on previous computational models of perception assuming robust signal propagation across cortical layers and areas.

The extent and accuracy with which neural signals propagate within and across neural circuits play a critical role in shaping behavior and cognition. One key variable that could potentially influence signal propagation across neural networks is global brain state (1–4). Indeed, during the time course of a day, the state of the brain undergoes dramatic changes from wakefulness to drowsiness and sleep (3, 5–7). Multiple lines of evidence in rodents and monkeys have shown that distinct brain states are associated with specific changes in neural responses (2–4, 8). Neurons strongly respond during wakefulness when animals are in an aroused state, and responses diminish during drowsiness and sleep (6, 9–11). However, despite significant progress in our understanding of state-dependent sensory coding across neural circuits (2–5, 8, 12, 13), the influence of brain state on the propagation of electrical signals remains unknown.The cortical column constitutes an ideal locus to examine the propagation of neural signals. For over a century, neuroscientists have observed remarkable regularity in the cortical microarchitecture: Clusters of cells are synaptically connected to form small columns orthogonal to the cortical surface (14, 15). These microcolumns constitute the elementary functional units of cortical circuitry (16) and consist of distinct layers that each contain a characteristic distribution of cell types and connections with other layers (15, 17–19). Understanding how neural signals propagate across laminar circuits would greatly contribute to deciphering the functional principles of cortical column operation.In principle, the strong intracortical connections within and between cortical layers (17–20) imply that signals emitted by individual neurons would vigorously propagate across the entire microcolumn. Indeed, during wakefulness, the input granular (G) cortical layers relay stimulus information to the output supragranular (SG) layers, which send feedforward projections to downstream areas (18, 20). Furthermore, neurons in SG layers project back to infragranular (IG) layers, which in turn project to granular layers; hence, signals are circulated across the entire microcolumn (17, 18). Thus, from a theoretical standpoint, it can be argued that electrical signals are robustly transmitted during wakefulness across cortical layers to contribute to perception and cognition. In reality, how robustly signals travel across layers in different states of wakefulness, and especially when the state of the brain undergoes dramatic changes, such as during drowsiness and sleep, remains unknown.Previous studies were unable to address these issues due to inherent restrictions of techniques such as in vitro slice recordings [e.g., (21)] and in vivo recordings during anesthesia (6, 10, 22) that severely limit the behavioral repertoire and hence the interpretation of cortical dynamics across laminar circuits. Even studies focused on in vivo laminar recordings failed to investigate state-dependent signal propagation across cortical layers (23–25). Here, we examined the propagation of neural signals across the cortical column in different brain states using multielectrode laminar arrays. We discovered that the global brain state strongly modulates the propagation of neural activity across the layers of the early visual cortex (area V1). We optogenetically activated specific cell populations during wakefulness to find that even though the elicited neural signals were stronger than those during rest, they propagated to other layers only weakly. Further, arousal was inversely related to the extent of signal spread. In contrast, the light-induced activity of the same neural population robustly propagated throughout the entire cortical column during rest, even when neurons were in a desynchronized wake-like state prior to light stimulation. The differential propagation of electrical signals in different brain states can be explained by state-dependent changes in the degree of coupling between individual neurons and their local population. Our results impose constraints on the conclusions of causal manipulation studies attempting to influence neural function and behavior, as well as on previous computational models of perception assuming robust signal propagation across cortical layers and areas.     

Neuronal circuits overcome imbalance in excitation and inhibition by adjusting connection numbers

The interplay between excitation and inhibition is crucial for neuronal circuitry in the brain. Inhibitory cell fractions in the neocortex and hippocampus are typically maintained at 15 to 30%, which is assumed to be important for stable dynamics. We have studied systematically the role of precisely controlled excitatory/inhibitory (E/I) cellular ratios on network activity using mice hippocampal cultures. Surprisingly, networks with varying E/I ratios maintain stable bursting dynamics. Interburst intervals remain constant for most ratios, except in the extremes of 0 to 10% and 90 to 100% inhibitory cells. Single-cell recordings and modeling suggest that networks adapt to chronic alterations of E/I compositions by balancing E/I connectivity. Gradual blockade of inhibition substantiates the agreement between the model and experiment and defines its limits. Combining measurements of population and single-cell activity with theoretical modeling, we provide a clearer picture of how E/I balance is preserved and where it fails in living neuronal networks.

Neuronal circuits in the brain are composed of a combination of excitatory and inhibitory neurons. While the role of excitatory cells is directly related to the spreading of network activity in and outside of these networks, the inhibitory neurons provide recurrent feedback regulation of the activity. Clearly, a circuit will need the negative feedback realized by the inhibitory population to function in a complementary and coordinated relation with the excitatory cells. The balance of these two opposing forces is the focus of most network models comprised of both neuron types. However, a definite quantitative resolution of how the excitation/inhibition (E/I) balance is maintained has not yet been formulated.The E/I ratio has been shown to control many aspects of the activity of large-scale neural networks. For instance, experimental studies show that precise coordination of excitatory and inhibitory inputs shape the activity of populations of neurons in sensory cortices (1, 2). At the same time, the interplay of excitation and inhibition is often proposed as a fundamental mechanism for generating oscillations in the brain (1). Theoretical work has shown that changing the overall E/I ratio plays a major role in controlling dynamic states, stability, and coding capabilities of neuronal networks, with the resulting network activity ranging from asynchronous, irregular firing to synchronized network bursting (3, 4).Inhibition in the cortical areas is implemented by GABAergic neurons, which comprise about 20 to 30% of all cortical neurons. This proportion is conserved across mammalian species and during the lifespan of an animal (5). The importance of keeping a specific fixed inhibitory percentage has been postulated to be linked to efficient storage capacity (6) and to multitask learning (7), among many other functions related to the hippocampus. However, the importance of having this particular fraction of inhibitory neurons for the general control of network dynamics remains unclear.Another well-studied aspect of cortical organization is that excitation and inhibition are balanced both structurally and dynamically. Dynamically, excitatory, and inhibitory inputs strongly correlate and synchronize in both spontaneous and evoked activity (2, 8, 9). Structurally, the ratio of excitatory and inhibitory synapses converging onto one cell is approximately constant (8), but the location of the synapses determines the efficacy of network firing. Inhibitory synapses can be located on remote or proximal dendrites, as well as on the axon initial segment, where they block the ability of the neuron to discharge action potentials. The role of inhibition is further complicated by the fact that there are several types of inhibitory neurons that can be clustered by their locus of action on the excitatory neurons as well as the formation of inhibitory synapses on interneurons (10). For the sake of simplicity, we will not discuss in the present study the role of different types of interneurons on network activity.Perturbations of the E/I ratio that move the network away from its balance have been reported recently and can be applied both acutely and chronically. Acute blockade of inhibitory synapses in vitro by application of pharmacological agents causes the dynamics to be excitatory dominated, more uniform, and synchronized (11, 12). Blocking inhibition acutely in vivo has been found to create epileptic seizures (13). In contrast, chronic blockade (about 48 h) or overactivation of inhibition causes neuronal networks to adjust their activity (8). Changes in the E/I balance have been linked to different brain states like deep anesthesia (14). Furthermore, shifts in E/I balance were found to have far-reaching behavioral effects in freely moving mice (15).Given that the conservation of E/I balance is a basic property of large-scale neuronal networks, it is pertinent to ask what mechanisms contribute to the creation of this balance and where their limitations become apparent. E/I balance was extensively studied in brain areas with 20 to 40% inhibitory cells (2, 16); however, there is no systematic view of how the inhibitory cell fraction and balance are related. To address this, we have engineered cultures of hippocampal neurons with precisely controlled numbers of excitatory and inhibitory cells over a wide range of E/I ratios from 0% inhibitory neurons to 100%. Our design imposes a global and chronic change to which the network must respond. We have asked whether, given enough time to adapt and rewire, a neuronal network can compensate for the perturbation and reach balanced and stable dynamics.In the present study, we focus on the ability of neuronal networks with artificially obtained E/I ratios to adapt during their development in vitro by monitoring both the whole network dynamics and the single cell behavior. In parallel, we employ finite network models to directly relate the network properties with the collective dynamics. This enables the emergence of a unified picture of the accommodation to changing E/I ratios in the ensemble of active neurons.     

Altered temporal correlations in parietal alpha and prefrontal theta oscillations in early-stage Alzheimer disease

Encoding and retention of information in memory are associated with a sustained increase in the amplitude of neuronal oscillations for up to several seconds. We reasoned that coordination of oscillatory activity over time might be important for memory and, therefore, that the amplitude modulation of oscillations may be abnormal in Alzheimer disease (AD). To test this hypothesis, we measured magnetoencephalography (MEG) during eyes-closed rest in 19 patients diagnosed with early-stage AD and 16 age-matched control subjects and characterized the autocorrelation structure of ongoing oscillations using detrended fluctuation analysis and an analysis of the life- and waiting-time statistics of oscillation bursts. We found that Alzheimer's patients had a strongly reduced incidence of alpha-band oscillation bursts with long life- or waiting-times (< 1 s) over temporo-parietal regions and markedly weaker autocorrelations on long time scales (1–25 seconds). Interestingly, the life- and waiting-times of theta oscillations over medial prefrontal regions were greatly increased. Whereas both temporo-parietal alpha and medial prefrontal theta oscillations are associated with retrieval and retention of information, metabolic and structural deficits in early-stage AD are observed primarily in temporo-parietal areas, suggesting that the enhanced oscillations in medial prefrontal cortex reflect a compensatory mechanism. Together, our results suggest that amplitude modulation of neuronal oscillations is important for cognition and that indices of amplitude dynamics of oscillations may prove useful as neuroimaging biomarkers of early-stage AD.     

Non-Linear Response of Cable-Mass-Spring System in High-Rise Buildings under Stochastic Seismic Excitation

In high-rise buildings earthquake ground motions induce bending deformation of the host structure. Large dynamic displacements at the top of the building can be observed which in turn lead to the excitation of the cables/ropes within lift installations. In this paper, the stochastic dynamics of a cable with a spring-damper and a mass system deployed in a tall cantilever structure under earthquake excitation is considered. The non-linear system is developed to describe lateral displacements of a vertical cable with a concentrated mass attached at its lower end. The system is moving slowly in the vertical direction. The horizontal displacements of the main mass are constrained by a spring-viscous damping element. The earthquake ground motions are modelled as a filtered Gaussian white noise stochastic process. The equivalent linearization technique is then used to replace the original non-linear system with a linear one with the coefficients determined by utilising the minimization of the mean-square error between both systems. Mean values, variances and covariances of particular random state variables have been obtained by using the numerical calculation. The received results were compared with the deterministic response of the system to the harmonic process and were verified against results obtained by Monte Carlo simulation.     

Special Feature: Complex Systems: From Chemistry to Systems Biology Special Feature: Exploring the roles of noise in the eukaryotic cell cycle

The DNA replication–division cycle of eukaryotic cells is controlled by a complex network of regulatory proteins, called cyclin-dependent kinases, and their activators and inhibitors. Although comprehensive and accurate deterministic models of the control system are available for yeast cells, reliable stochastic simulations have not been carried out because the full reaction network has yet to be expressed in terms of elementary reaction steps. As a first step in this direction, we present a simplified version of the control system that is suitable for exact stochastic simulation of intrinsic noise caused by molecular fluctuations and extrinsic noise because of unequal division. The model is consistent with many characteristic features of noisy cell cycle progression in yeast populations, including the observation that mRNAs are present in very low abundance (≈1 mRNA molecule per cell for each expressed gene). For the control system to operate reliably at such low mRNA levels, some specific mRNAs in our model must have very short half-lives (<1 min). If these mRNA molecules are longer-lived (perhaps 2 min), then the intrinsic noise in our simulations is too large, and there must be some additional noise suppression mechanisms at work in cells.