Population spikes in cortical networks during different functional states

Mathematical models of learning and what can be learned from them

Learning is a multi-faceted phenomenon of critical importance and hence attracted a great deal of research, both experimental and theoretical. In this review, we will consider some of the paradigmatic examples of learning and discuss the common themes in theoretical learning research, such as levels of modeling and their corresponding relation to experimental observations and mathematical ideas common to different types of learning.

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity patterns are propagating bursts of place-cell activities called hippocampal replay, which is critical for memory consolidation. The sudden and repeated occurrences of these burst states during ongoing neural activity suggest metastable neural circuit dynamics. As metastability has been attributed to noise and/or slow fatigue mechanisms, we propose a concise mesoscopic model which accounts for both. Crucially, our model is bottom-up: it is analytically derived from the dynamics of finite-size networks of Linear-Nonlinear Poisson neurons with short-term synaptic depression. As such, noise is explicitly linked to stochastic spiking and network size, and fatigue is explicitly linked to synaptic dynamics. To derive the mesoscopic model, we first consider a homogeneous spiking neural network and follow the temporal coarse-graining approach of Gillespie to obtain a "chemical Langevin equation", which can be naturally interpreted as a stochastic neural mass model. The Langevin equation is computationally inexpensive to simulate and enables a thorough study of metastable dynamics in classical setups (population spikes and Up-Down-states dynamics) by means of phase-plane analysis. An extension of the Langevin equation for small network sizes is also presented. The stochastic neural mass model constitutes the basic component of our mesoscopic model for replay. We show that the mesoscopic model faithfully captures the statistical structure of individual replayed trajectories in microscopic simulations and in previously reported experimental data. Moreover, compared to the deterministic Romani-Tsodyks model of place-cell dynamics, it exhibits a higher level of variability regarding order, direction and timing of replayed trajectories, which seems biologically more plausible and could be functionally desirable. This variability is the product of a new dynamical regime where metastability emerges from a complex interplay between finite-size fluctuations and local fatigue.

Shared increased entropy of brain signals across patients with different mental illnesses: A coordinate-based activation likelihood estimation meta-analysis

Entropy is a measurement of brain signal complexity. Studies have found increased/decreased entropy of brain signals in psychiatric patients. There is no consistent conclusion regarding the relationship between the entropy of brain signals and mental illness. Therefore, this meta-analysis aimed to identify consistent abnormalities in the brain signal entropy in patients with different mental illnesses. We conducted a systematic search to collect resting-state functional magnetic resonance imaging (rs-fMRI) studies in patients with psychiatric disorders. This work identified 9 eligible rs-fMRI studies, which included a total of 14 experiments, 67 activation foci, and 1383 subjects. We tested the convergence across their findings by using the activation likelihood estimation method. P-value maps were corrected by using cluster-level family-wise error p < 0.05 and permuting 2000 times. Results showed that patients with different psychiatric disorders shared commonly increased entropy of brain signals in the left inferior and middle frontal gyri, and the right fusiform gyrus, cuneus, precuneus. No shared alterations were found in the subcortical regions and cerebellum in the patient group. Our findings suggested that the increased entropy of brain signals in the cortex, not subcortical regions and cerebellum, might have associations with the pathophysiology across mental illnesses. This meta-analysis study provided the first comprehensive understanding of the abnormality in brain signal complexity across patients with different psychiatric disorders.

Feature Detection in Visual Cortex during Different Functional States

Cortical activity exhibits distinct characteristics in different functional states. In awake behaving animals it shows less synchrony, while in rest or sleeping state cortical activity is most synchronous. Previous studies showed that switching between functional states can change the efficiency of flowing sensory information. Switching between functional states can be triggered by releasing neuromodulators which affect neurotransmitter release probability and depolarization of cortical neurons. In this work we focus on studying primary visual area V1, by using firing rate ring model with short-term synaptic depression (STD). We show that reconstruction of visual features from V1 activity depends on the functional state, with best precision achieved at the state with intermediate release probability. We suggest that this regime corresponds to the state of maximal visual attention.

Network Anisotropy Trumps Noise for Efficient Object Coding in Macaque Inferior Temporal Cortex

How neuronal ensembles compute information is actively studied in early visual cortex. Much less is known about how local ensembles function in inferior temporal (IT) cortex, the last stage of the ventral visual pathway that supports visual recognition. Previous reports suggested that nearby neurons carry information mostly independently, supporting efficient processing (Barlow, 1961). However, others postulate that noise covariation effects may depend on network anisotropy/homogeneity and on how the covariation relates to representation. Do slow trial-by-trial noise covariations increase or decrease IT's object coding capability, how does encoding capability relate to correlational structure (i.e., the spatial pattern of signal and noise redundancy/homogeneity across neurons), and does knowledge of correlational structure matter for decoding? We recorded simultaneously from ∼80 spiking neurons in ∼1 mm(3) of macaque IT under light neurolept anesthesia. Noise correlations were stronger for neurons with correlated tuning, and noise covariations reduced object encoding capability, including generalization across object pose and illumination. Knowledge of noise covariations did not lead to better decoding performance. However, knowledge of anisotropy/homogeneity improved encoding and decoding efficiency by reducing the number of neurons needed to reach a given performance level. Such correlated neurons were found mostly in supragranular and infragranular layers, supporting theories that link recurrent circuitry to manifold representation. These results suggest that redundancy benefits manifold learning of complex high-dimensional information and that subsets of neurons may be more immune to noise covariation than others.

SIGNIFICANCE STATEMENT

How noise affects neuronal population coding is poorly understood. By sampling densely from local populations supporting visual object recognition, we show that recurrent circuitry supports useful representations and that subsets of neurons may be more immune to noise covariation than others.

Rich spectrum of neural field dynamics in the presence of short-term synaptic depression

In continuous attractor neural networks (CANNs), spatially continuous information such as orientation, head direction, and spatial location is represented by Gaussian-like tuning curves that can be displaced continuously in the space of the preferred stimuli of the neurons. We investigate how short-term synaptic depression (STD) can reshape the intrinsic dynamics of the CANN model and its responses to a single static input. In particular, CANNs with STD can support various complex firing patterns and chaotic behaviors. These chaotic behaviors have the potential to encode various stimuli in the neuronal system.

A reduction for spiking integrate-and-fire network dynamics ranging from homogeneity to synchrony

In this paper we provide a general methodology for systematically reducing the dynamics of a class of integrate-and-fire networks down to an augmented 4-dimensional system of ordinary-differential-equations. The class of integrate-and-fire networks we focus on are homogeneously-structured, strongly coupled, and fluctuation-driven. Our reduction succeeds where most current firing-rate and population-dynamics models fail because we account for the emergence of 'multiple-firing-events' involving the semi-synchronous firing of many neurons. These multiple-firing-events are largely responsible for the fluctuations generated by the network and, as a result, our reduction faithfully describes many dynamic regimes ranging from homogeneous to synchronous. Our reduction is based on first principles, and provides an analyzable link between the integrate-and-fire network parameters and the relatively low-dimensional dynamics underlying the 4-dimensional augmented ODE.

Adaptation to prolonged neuromodulation in cortical cultures: an invariable return to network synchrony

Background

Prolonged neuromodulatory regimes, such as those critically involved in promoting arousal and suppressing sleep-associated synchronous activity patterns, might be expected to trigger adaptation processes and, consequently, a decline in neuromodulator-driven effects. This possibility, however, has rarely been addressed.

Results

Using networks of cultured cortical neurons, acetylcholine microinjections and a novel closed-loop ‘synchrony-clamp’ system, we found that acetylcholine pulses strongly suppressed network synchrony. Over the course of many hours, however, synchrony invariably reemerged, even when feedback was used to compensate for declining cholinergic efficacy. Network synchrony also reemerged following its initial suppression by noradrenaline, but this did not occlude the suppression of synchrony or its gradual reemergence following subsequent cholinergic input. Importantly, cholinergic efficacy could be restored and preserved over extended time scales by periodically withdrawing cholinergic input.

Conclusions

These findings indicate that the capacity of neuromodulators to suppress network synchrony is constrained by slow-acting, reactive processes. A multiplicity of neuromodulators and ultimately neuromodulator withdrawal periods might thus be necessary to cope with an inevitable reemergence of network synchrony.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-014-0083-3) contains supplementary material, which is available to authorized users.

Emergent spike patterns in neuronal populations

This numerical study documents and analyzes emergent spiking behavior in local neuronal populations. Emphasis is given to a phenomenon we call clustering, by which we refer to a tendency of random groups of neurons large and small to spontaneously coordinate their spiking activity in some fashion. Using a sparsely connected network of integrate-and-fire neurons, we demonstrate that spike clustering occurs ubiquitously in both high firing and low firing regimes. As a practical tool for quantifying such spike patterns, we propose a simple scheme with two parameters, one setting the temporal scale and the other the amount of deviation from the mean to be regarded as significant. Viewing population activity as a sequence of events, meaning relatively brief durations of elevated spiking, separated by inter-event times, we observe that background activity tends to give rise to extremely broad distributions of event sizes and inter-event times, while driving a system imposes a certain regularity on its inter-event times, producing a rhythm consistent with broad-band gamma oscillations. We note also that event sizes and inter-event times decorrelate very quickly. Dynamical analyses supported by numerical evidence are offered.

A network model of the periodic synchronization process in the dynamics of calcium concentration in GnRH neurons

Mathematical neuroendocrinology is a branch of mathematical neurosciences that is specifically interested in endocrine neurons, which have the uncommon ability of secreting neurohormones into the blood. One of the most striking features of neuroendocrine networks is their ability to exhibit very slow rhythms of neurosecretion, on the order of one or several hours. A prototypical instance is that of the pulsatile secretion pattern of GnRH (gonadotropin releasing hormone), the master hormone controlling the reproductive function, whose origin remains a puzzle issue since its discovery in the seventies. In this paper, we investigate the question of GnRH neuron synchronization on a mesoscopic scale, and study how synchronized events in calcium dynamics can arise from the average electric activity of individual neurons. We use as reference seminal experiments performed on embryonic GnRH neurons from rhesus monkeys, where calcium imaging series were recorded simultaneously in tens of neurons, and which have clearly shown the occurrence of synchronized calcium peaks associated with GnRH pulses, superposed on asynchronous, yet oscillatory individual background dynamics. We design a network model by coupling 3D individual dynamics of FitzHugh-Nagumo type. Using phase-plane analysis, we constrain the model behavior so that it meets qualitative and quantitative specifications derived from the experiments, including the precise control of the frequency of the synchronization episodes. In particular, we show how the time scales of the model can be tuned to fit the individual and synchronized time scales of the experiments. Finally, we illustrate the ability of the model to reproduce additional experimental observations, such as partial recruitment of cells within the synchronization process or the occurrence of doublets of synchronization.

Neuronal avalanches differ from wakefulness to deep sleep--evidence from intracranial depth recordings in humans

Neuronal activity differs between wakefulness and sleep states. In contrast, an attractor state, called self-organized critical (SOC), was proposed to govern brain dynamics because it allows for optimal information coding. But is the human brain SOC for each vigilance state despite the variations in neuronal dynamics? We characterized neuronal avalanches--spatiotemporal waves of enhanced activity--from dense intracranial depth recordings in humans. We showed that avalanche distributions closely follow a power law--the hallmark feature of SOC--for each vigilance state. However, avalanches clearly differ with vigilance states: slow wave sleep (SWS) shows large avalanches, wakefulness intermediate, and rapid eye movement (REM) sleep small ones. Our SOC model, together with the data, suggested first that the differences are mediated by global but tiny changes in synaptic strength, and second, that the changes with vigilance states reflect small deviations from criticality to the subcritical regime, implying that the human brain does not operate at criticality proper but close to SOC. Independent of criticality, the analysis confirms that SWS shows increased correlations between cortical areas, and reveals that REM sleep shows more fragmented cortical dynamics.

Stable learning of functional maps in self-organizing spiking neural networks with continuous synaptic plasticity

This study describes a spiking model that self-organizes for stable formation and maintenance of orientation and ocular dominance maps in the visual cortex (V1). This self-organization process simulates three development phases: an early experience-independent phase, a late experience-independent phase and a subsequent refinement phase during which experience acts to shape the map properties. The ocular dominance maps that emerge accommodate the two sets of monocular inputs that arise from the lateral geniculate nucleus (LGN) to layer 4 of V1. The orientation selectivity maps that emerge feature well-developed iso-orientation domains and fractures. During the last two phases of development the orientation preferences at some locations appear to rotate continuously through ±180° along circular paths and referred to as pinwheel-like patterns but without any corresponding point discontinuities in the orientation gradient maps. The formation of these functional maps is driven by balanced excitatory and inhibitory currents that are established via synaptic plasticity based on spike timing for both excitatory and inhibitory synapses. The stability and maintenance of the formed maps with continuous synaptic plasticity is enabled by homeostasis caused by inhibitory plasticity. However, a prolonged exposure to repeated stimuli does alter the formed maps over time due to plasticity. The results from this study suggest that continuous synaptic plasticity in both excitatory neurons and interneurons could play a critical role in the formation, stability, and maintenance of functional maps in the cortex.