How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains

Dependence of Contextual Modulation in Macaque V1 on Interlaminar Signal Flow

In visual cortex, neural correlates of subjective perception can be generated by modulation of activity from beyond the classical receptive field (CRF). In macaque V1, activity generated by nonclassical receptive field (nCRF) stimulation involves different intracortical circuitry than activity generated by CRF stimulation, suggesting that interactions between neurons across V1 layers differ under CRF and nCRF stimulus conditions. Using Neuropixels probes, we measured border ownership modulation within large, local populations of V1 neurons. We found that neurons in single columns preferred the same side of objects located outside of the CRF. In addition, we found that cross-correlations between pairs of neurons situated across feedback/horizontal and input layers differed between CRF and nCRF stimulation. Furthermore, independent of the comparison with CRF stimulation, we observed that the magnitude of border ownership modulation increased with the proportion of information flow from feedback/horizontal layers to input layers. These results demonstrate that the flow of signals between layers covaries with the degree to which neurons integrate information from beyond the CRF.

Anesthetic Effect on the Subthalamic Nucleus in Microelectrode Recording and Local Field Potential of Parkinson's Disease

OBJECTIVES

Anesthetic agents used during deep brain stimulation (DBS) surgery might interfere with microelectrode recording (MER) and local field potential (LFP) and thus affect the accuracy of surgical target localization. This review aimed to identify the effects of different anesthetic agents on neuronal activity of the subthalamic nucleus (STN) during the MER procedure.

MATERIALS AND METHODS

We used Medical Subject Heading terms to search the PubMed, EMBASE, EBSCO, and ScienceDirect data bases. MER characteristics were sorted into quantitative and qualitative data types. Quantitative data included the burst index, pause index, firing rate (FR), and interspike interval. Qualitative data included background activity, burst discharge (BD), and anesthetic agent effect. We also categorized the reviewed manuscripts into those describing local anesthesia with sedation (LAWS) and those describing general anesthesia (GA) and compiled the effects of anesthetic agents on MER and LFP characteristics.

RESULTS

In total, 26 studies on MER were identified, of which 12 used LAWS and 14 used GA. Three studies on LFP also were identified. We found that the FR was preserved under LAWS but tended to be lower under GA, and BD was reduced in both groups. Individually, propofol enhanced BD but was better used for sedation, or the dosage should be minimized in GA. Similarly, low-dose dexmedetomidine sedation did not disturb MER. Opioids could be used as adjunctive anesthetic agents. Volatile anesthesia had the least adverse effect on MER under GA, with minimal alveolar concentration at 0.5. Dexmedetomidine anesthesia did not affect LFP, whereas propofol interfered with the power of LFP.

CONCLUSIONS

The effects of the tested anesthetics on the STN in MER and LFP of Parkinson's disease varied; however, identifying the STN and achieving a good clinical outcome are possible under controlled anesthetic conditions. For patient comfort, anesthesia should be considered in STN-DBS.

Ensemble learning and ground-truth validation of synaptic connectivity inferred from spike trains

Probing the architecture of neuronal circuits and the principles that underlie their functional organization remains an important challenge of modern neurosciences. This holds true, in particular, for the inference of neuronal connectivity from large-scale extracellular recordings. Despite the popularity of this approach and a number of elaborate methods to reconstruct networks, the degree to which synaptic connections can be reconstructed from spike-train recordings alone remains controversial. Here, we provide a framework to probe and compare connectivity inference algorithms, using a combination of synthetic ground-truth and in vitro data sets, where the connectivity labels were obtained from simultaneous high-density microelectrode array (HD-MEA) and patch-clamp recordings. We find that reconstruction performance critically depends on the regularity of the recorded spontaneous activity, i.e., their dynamical regime, the type of connectivity, and the amount of available spike-train data. We therefore introduce an ensemble artificial neural network (eANN) to improve connectivity inference. We train the eANN on the validated outputs of six established inference algorithms and show how it improves network reconstruction accuracy and robustness. Overall, the eANN demonstrated strong performance across different dynamical regimes, worked well on smaller datasets, and improved the detection of synaptic connectivity, especially inhibitory connections. Results indicated that the eANN also improved the topological characterization of neuronal networks. The presented methodology contributes to advancing the performance of inference algorithms and facilitates our understanding of how neuronal activity relates to synaptic connectivity.

Classification of Hippocampal Ripples: Convolutional Neural Network Learns Episode-Specific Changes

The hippocampus is known to play an important role in memory by processing spatiotemporal information of episodic experiences. By recording synchronized multiple-unit firing events (ripple firings with 300 Hz-10 kHz) of hippocampal CA1 neurons in freely moving rats, we previously found an episode-dependent diversity in the waveform of ripple firings. In the present study, we hypothesized that changes in the diversity would depend on the type of episode experienced. If this hypothesis holds, we can identify the ripple waveforms associated with each episode. Thus, we first attempted to classify the ripple firings measured from rats into five categories: those experiencing any of the four episodes and those before experiencing any of the four episodes. In this paper, we construct a convolutional neural network (CNN) to classify the current stocks of ripple firings into these five categories and demonstrate that the CNN can successfully classify the ripple firings. We subsequently indicate partial ripple waveforms that the CNN focuses on for classification by applying gradient-weighted class activation mapping (Grad-CAM) to the CNN. The method of t-distributed stochastic neighbor embedding (t-SNE) maps ripple waveforms into a two-dimensional feature space. Analyzing the distribution of partial waveforms extracted by Grad-CAM in a t-SNE feature space suggests that the partial waveforms may be representative of each category.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons allow signals from the cerebellar cortex to influence the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many PC inputs are thought to converge onto each CbN neuron to suppress its firing. It has been proposed that PCs convey information using a rate code, a synchrony and timing code, or both. The influence of PCs on CbN neuron firing was primarily examined for the combined effects of many PC inputs with comparable strengths, and the influence of individual PC inputs has not been extensively studied. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modeling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, individual PC-CbN synapses are suited to concurrently convey rate codes and generate precisely timed responses in CbN neurons. Either synchronous firing or synchronous pauses of PCs promote CbN neuron firing on rapid time scales for nonuniform inputs, but less effectively than for uniform inputs. This is a secondary consequence of variable input sizes elevating the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. These findings may generalize to other brain regions with highly variable inhibitory synapse sizes.

Laminar compartmentalization of attention modulation in area V4 aligns with the demands of visual processing hierarchy in the cortex

Attention selectively enhances neural responses to low contrast stimuli in visual area V4, a critical hub that sends projections both up and down the visual hierarchy. Veridical encoding of contrast information is a key computation in early visual areas, while later stages encoding higher level features benefit from improved sensitivity to low contrast. How area V4 meets these distinct information processing demands in the attentive state is unknown. We found that attentional modulation in V4 is cortical layer and cell-class specific. Putative excitatory neurons in the superficial layers show enhanced boosting of low contrast information, while those of deep layers exhibit contrast-independent scaling. Computational modeling suggested the extent of spatial integration of inhibitory neurons as the mechanism behind such laminar differences. Considering that superficial neurons are known to project to higher areas and deep layers to early visual areas, our findings suggest that the interactions between attention and contrast in V4 are compartmentalized, in alignment with the demands of the visual processing hierarchy.

How network structure affects the dynamics of a network of stochastic spiking neurons

Up to now, it still remains an open question about the relation between the structure of brain networks and their functions. The effects of structure on the dynamics of neural networks are usually investigated via extensive numerical simulations, while analytical analysis is always very difficult and thus rare. In this work, we explored the effects of a random regular graph on the dynamics of a neural network of stochastic spiking neurons, which has a bistable region when fully connected. We showed by numerical simulations that as the number of each neuron's neighbors decreases, the bistable region shrinks and eventually seems to disappear, and a critical-like transition appears. In the meantime, we made analytical analysis that explains numerical results. We hope this would give some insights into how structure affects the dynamics of neural networks from a theoretical perspective, rather than merely by numerical simulations.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons convey signals from the cerebellar cortex to the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many uniform sized PC inputs are thought to converge onto each CbN neuron to suppress or eliminate firing. Leading theories maintain that PCs encode information using either a rate code, or by synchrony and precise timing. Individual PCs are thought to have limited influence on CbN neuron firing. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modelling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, PC-CbN synapses are suited to concurrently convey rate codes, and generate precisely-timed responses in CbN neurons. Variable input sizes also elevate the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. Although this reduces the relative influence of PC synchrony on the firing rate of CbN neurons, synchrony can still have important consequences, because synchronizing even two large inputs can significantly increase CbN neuron firing. These findings may be generalized to other brain regions with highly variable sized synapses.

Uncovering hidden network architecture from spiking activities using an exact statistical input-output relation of neurons

Identifying network architecture from observed neural activities is crucial in neuroscience studies. A key requirement is knowledge of the statistical input-output relation of single neurons in vivo. By utilizing an exact analytical solution of the spike-timing for leaky integrate-and-fire neurons under noisy inputs balanced near the threshold, we construct a framework that links synaptic type, strength, and spiking nonlinearity with the statistics of neuronal population activity. The framework explains structured pairwise and higher-order interactions of neurons receiving common inputs under different architectures. We compared the theoretical predictions with the activity of monkey and mouse V1 neurons and found that excitatory inputs given to pairs explained the observed sparse activity characterized by strong negative triple-wise interactions, thereby ruling out the alternative explanation by shared inhibition. Moreover, we showed that the strong interactions are a signature of excitatory rather than inhibitory inputs whenever the spontaneous rate is low. We present a guide map of neural interactions that help researchers to specify the hidden neuronal motifs underlying observed interactions found in empirical data.

Reconstruction of sparse recurrent connectivity and inputs from the nonlinear dynamics of neuronal networks

Reconstructing the recurrent structural connectivity of neuronal networks is a challenge crucial to address in characterizing neuronal computations. While directly measuring the detailed connectivity structure is generally prohibitive for large networks, we develop a novel framework for reverse-engineering large-scale recurrent network connectivity matrices from neuronal dynamics by utilizing the widespread sparsity of neuronal connections. We derive a linear input-output mapping that underlies the irregular dynamics of a model network composed of both excitatory and inhibitory integrate-and-fire neurons with pulse coupling, thereby relating network inputs to evoked neuronal activity. Using this embedded mapping and experimentally feasible measurements of the firing rate as well as voltage dynamics in response to a relatively small ensemble of random input stimuli, we efficiently reconstruct the recurrent network connectivity via compressive sensing techniques. Through analogous analysis, we then recover high dimensional natural stimuli from evoked neuronal network dynamics over a short time horizon. This work provides a generalizable methodology for rapidly recovering sparse neuronal network data and underlines the natural role of sparsity in facilitating the efficient encoding of network data in neuronal dynamics.

Dynamical response of Autaptic Izhikevich Neuron disturbed by Gaussian white noise

Using the improved memristive Izhikevich neuron model, the effects of autaptic connection as well as electromagnetic induction are studied on the dynamical behavior of neuronal spiking. Using bifurcation analysis for membrane potentials, the effects of autaptic and electromagnetic parameters on the mode transition in electrical activities of the neuron model are investigated. Furthermore, white Gaussian noise is considered in the neuron model, to evaluate the effect of electromagnetic disturbance on the firing pattern of the neuron using the coefficient of variation. The bifurcation diagram versus autaptic conductance and time delay has been extensively studied. The results show that the effects of autaptic connection as well as electromagnetic induction on the spiking behavior of neurons can be well demonstrated by using the Izhikevich model. The electrical activities of the Izhikevich neuron model become more complex when the effects of autaptic connection and electromagnetic induction are considered in the neuron model. Using the Izhikevich neuron model, the high variety of spiking/bursting patterns is represented in the bifurcation diagram of inter-spike interval versus autaptic or electromagnetic parameters. Noise can have distinct effects on the spiking activity of the neuron, for the subthreshold input current, increasing the intensity of the electromagnetic noise increases the regularity of the neuron spiking, but for the suprathreshold input current, the regularity of spiking decreases with noise.

Inferring the temporal evolution of synaptic weights from dynamic functional connectivity

How to capture the temporal evolution of synaptic weights from measures of dynamic functional connectivity between the activity of different simultaneously recorded neurons is an important and open problem in systems neuroscience. Here, we report methodological progress to address this issue. We first simulated recurrent neural network models of spiking neurons with spike timing-dependent plasticity mechanisms that generate time-varying synaptic and functional coupling. We then used these simulations to test analytical approaches that infer fixed and time-varying properties of synaptic connectivity from directed functional connectivity measures, such as cross-covariance and transfer entropy. We found that, while both cross-covariance and transfer entropy provide robust estimates of which synapses are present in the network and their communication delays, dynamic functional connectivity measured via cross-covariance better captures the evolution of synaptic weights over time. We also established how measures of information transmission delays from static functional connectivity computed over long recording periods (i.e., several hours) can improve shorter time-scale estimates of the temporal evolution of synaptic weights from dynamic functional connectivity. These results provide useful information about how to accurately estimate the temporal variation of synaptic strength from spiking activity measures.

Functional interactions among neurons within single columns of macaque V1

Recent developments in high-density neurophysiological tools now make it possible to record from hundreds of single neurons within local, highly interconnected neural networks. Among the many advantages of such recordings is that they dramatically increase the quantity of identifiable, functional interactions between neurons thereby providing an unprecedented view of local circuits. Using high-density, Neuropixels recordings from single neocortical columns of primary visual cortex in nonhuman primates, we identified 1000s of functionally interacting neuronal pairs using established crosscorrelation approaches. Our results reveal clear and systematic variations in the synchrony and strength of functional interactions within single cortical columns. Despite neurons residing within the same column, both measures of interactions depended heavily on the vertical distance separating neuronal pairs, as well as on the similarity of stimulus tuning. In addition, we leveraged the statistical power afforded by the large numbers of functionally interacting pairs to categorize interactions between neurons based on their crosscorrelation functions. These analyses identified distinct, putative classes of functional interactions within the full population. These classes of functional interactions were corroborated by their unique distributions across defined laminar compartments and were consistent with known properties of V1 cortical circuitry, such as the lead-lag relationship between simple and complex cells. Our results provide a clear proof-of-principle for the use of high-density neurophysiological recordings to assess circuit-level interactions within local neuronal networks.

Classification of Contrasting Discrete Emotional States Indicated by EEG Based Graph Theoretical Network Measures

The present study shows new findings that reveal the high association between emotional arousal and neuro-functional brain connectivity measures. For this purpose, contrasting discrete emotional states (happiness vs sadness, amusement vs disgust, calmness vs excitement, calmness vs anger, fear vs anger) are classified by using Support Vector Machines (SVMs) driven by Graph Theoretical segregation (clustering coefficients, transitivity, modularity) and integration (global efficiency, local efficiency) measures of the brain network. Emotional EEG data mediated by short duration video film clips is downloaded from publicly available database called DREAMER. Pearson Correlation (PC) and Spearman Correlation have been examined to estimate statistical dependencies between relatively shorter (6 sec) and longer (12 sec) non-overlapped EEG segments across the cortex. Then the corresponding brain connectivity encoded as a graph is transformed into binary numbers with respect to two different thresholds (60%max and mean). Statistical differences between contrasting emotions are obtained by using both one-way Anova tests and step-wise logistic regression modelling in accordance with variables (dependency estimation, segment length, threshold, network measure). Combined integration measures provided the highest classification accuracies (CAs) (75.00% 80.65%) when PC is applied to longer segments in accordance with particular threshold as the mean. The segregation measures also provided useful CAs (74.13% 80.00%), while the combination of both measures did not. The results reveal that discrete emotional states are characterized by balanced network measures even if both segregation and integration measures vary depending on arousal scores of audio-visual stimuli due to neurotransmitter release during video watching.

The structures and functions of correlations in neural population codes

The collective activity of a population of neurons, beyond the properties of individual cells, is crucial for many brain functions. A fundamental question is how activity correlations between neurons affect how neural populations process information. Over the past 30 years, major progress has been made on how the levels and structures of correlations shape the encoding of information in population codes. Correlations influence population coding through the organization of pairwise-activity correlations with respect to the similarity of tuning of individual neurons, by their stimulus modulation and by the presence of higher-order correlations. Recent work has shown that correlations also profoundly shape other important functions performed by neural populations, including generating codes across multiple timescales and facilitating information transmission to, and readout by, downstream brain areas to guide behaviour. Here, we review this recent work and discuss how the structures of correlations can have opposite effects on the different functions of neural populations, thus creating trade-offs and constraints for the structure-function relationships of population codes. Further, we present ideas on how to combine large-scale simultaneous recordings of neural populations, computational models, analyses of behaviour, optogenetics and anatomy to unravel how the structures of correlations might be optimized to serve multiple functions.

Deconvolution improves the detection and quantification of spike transmission gain from spike trains

Accurate detection and quantification of spike transmission between neurons is essential for determining neural network mechanisms that govern cognitive functions. Using point process and conductance-based simulations, we found that existing methods for determining neuronal connectivity from spike times are highly affected by burst spiking activity, resulting in over- or underestimation of spike transmission. To improve performance, we developed a mathematical framework for decomposing the cross-correlation between two spike trains. We then devised a deconvolution-based algorithm for removing effects of second-order spike train statistics. Deconvolution removed the effect of burst spiking, improving the estimation of neuronal connectivity yielded by state-of-the-art methods. Application of deconvolution to neuronal data recorded from hippocampal region CA1 of freely-moving mice produced higher estimates of spike transmission, in particular when spike trains exhibited bursts. Deconvolution facilitates the precise construction of complex connectivity maps, opening the door to enhanced understanding of the neural mechanisms underlying brain function.

Information transmission in recurrent networks: Consequences of network noise for synchronous and asynchronous signal encoding

Information about natural time-dependent stimuli encoded by the sensory periphery or communication between cortical networks may span a large frequency range or be localized to a smaller frequency band. Biological systems have been shown to multiplex such disparate broadband and narrow-band signals and then discriminate them in later populations by employing either an integration (low-pass) or coincidence detection (bandpass) encoding strategy. Analytical expressions have been developed for both encoding methods in feedforward populations of uncoupled neurons and confirm that the integration of a population's output low-pass filters the information, whereas synchronous output encodes less information overall and retains signal information in a selected frequency band. The present study extends the theory to recurrent networks and shows that recurrence may sharpen the synchronous bandpass filter. The frequency of the pass band is significantly influenced by the synaptic strengths, especially for inhibition-dominated networks. Synchronous information transfer is also increased when network models take into account heterogeneity that arises from the stochastic distribution of the synaptic weights.

Astrocytic Gap Junctions Contribute to Aberrant Neuronal Synchronization in a Mouse Model of MeCP2 Duplication Syndrome

Abnormal synchronous neuronal activity has been widely detected by brain imaging of autistic patients, but its underlying neural mechanism remains unclear. Compared with wild-type mice, our in vivo two-photon imaging showed that transgenic (Tg1) mice over-expressing human autism risk gene MeCP2 exhibited higher neuronal synchrony in the young but lower synchrony in the adult stage. Whole-cell recording of neuronal pairs in brain slices revealed that higher neuronal synchrony in young postnatal Tg1 mice was attributed mainly to more prevalent giant slow inward currents (SICs). Both in vivo and slice imaging further demonstrated more dynamic activity and higher synchrony in astrocytes from young Tg1 mice. Blocking astrocytic gap junctions markedly decreased the generation of SICs and overall cell synchrony in the Tg1 brain. Furthermore, the expression level of Cx43 protein and the coupling efficiency of astrocyte gap junctions remained unchanged in Tg1 mice. Thus, astrocytic gap junctions facilitate but do not act as a direct trigger for the abnormal neuronal synchrony in young Tg1 mice, revealing the potential role of the astrocyte network in the pathogenesis of MeCP2 duplication syndrome.

Critical current for giant Fano factor in neural models with bistable firing dynamics and implications for signal transmission

Bistability in the firing rate is a prominent feature in different types of neurons as well as in neural networks. We show that for a constant input below a critical value, such bistability can lead to a giant spike-count diffusion. We study the transmission of a periodic signal and demonstrate that close to the critical bias current, the signal-to-noise ratio suffers a sharp increase, an effect that can be traced back to the giant diffusion and large Fano factor.

The Mean Field Approach for Populations of Spiking Neurons

Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural circuits, these parameters are typically the firing rates of distinct, homogeneous subgroups of neurons. Knowledge of the firing rates under conditions of interest can reveal essential information on both the dynamics of neural circuits and the way they can subserve brain function. The goal of this chapter is to provide an elementary introduction to the mean field approach for populations of spiking neurons. We introduce the general idea in networks of binary neurons, starting from the most basic results and then generalizing to more relevant situations. This allows to derive the mean field equations in a simplified setting. We then derive the mean field equations for populations of integrate-and-fire neurons. An effort is made to derive the main equations of the theory using only elementary methods from calculus and probability theory. The chapter ends with a discussion of the assumptions of the theory and some of the consequences of violating those assumptions. This discussion includes an introduction to balanced and metastable networks and a brief catalogue of successful applications of the mean field approach to the study of neural circuits.

Differences in olfactory bulb mitral cell spiking with ortho- and retronasal stimulation revealed by data-driven models

The majority of olfaction studies focus on orthonasal stimulation where odors enter via the front nasal cavity, while retronasal olfaction, where odors enter the rear of the nasal cavity during feeding, is understudied. The coding of retronasal odors via coordinated spiking of neurons in the olfactory bulb (OB) is largely unknown despite evidence that higher level processing is different than orthonasal. To this end, we use multi-electrode array in vivo recordings of rat OB mitral cells (MC) in response to a food odor with both modes of stimulation, and find significant differences in evoked firing rates and spike count covariances (i.e., noise correlations). Differences in spiking activity often have implications for sensory coding, thus we develop a single-compartment biophysical OB model that is able to reproduce key properties of important OB cell types. Prior experiments in olfactory receptor neurons (ORN) showed retro stimulation yields slower and spatially smaller ORN inputs than with ortho, yet whether this is consequential for OB activity remains unknown. Indeed with these specifications for ORN inputs, our OB model captures the salient trends in our OB data. We also analyze how first and second order ORN input statistics dynamically transfer to MC spiking statistics with a phenomenological linear-nonlinear filter model, and find that retro inputs result in larger linear filters than ortho inputs. Finally, our models show that the temporal profile of ORN is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the OB. Using data-driven modeling, we detail how ORN inputs result in differences in OB dynamics and MC spiking statistics. These differences may ultimately shape how ortho and retro odors are coded.

Olfaction is a key sense for many cognitive and behavioral tasks, and is particularly unique because odors can naturally enter the nasal cavity from the front or rear, i.e., ortho- and retro-nasal, respectively. Yet little is known about the differences in coordinated spiking in the olfactory bulb with ortho versus retro stimulation, let alone how these different modes of olfaction may alter coding of odors. We simultaneously record many cells in rat olfactory bulb to assess the differences in spiking statistics, and develop a biophysical olfactory bulb network model to study the reasons for these differences. Using theoretical and computational methods, we find that the olfactory bulb transfers input statistics differently for retro stimulation relative to ortho stimulation. Furthermore, our models show that the temporal profile of inputs is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the olfactory bulb. Understanding the spiking dynamics of the olfactory bulb with both ortho and retro stimulation is a key step for ultimately understanding how the brain codes odors with different modes of olfaction.

Improved Method for Efficient Generation of Functional Neurons from Murine Neural Progenitor Cells

Neuronal culture was used to investigate neuronal function in physiological and pathological conditions. Despite its inevitability, primary neuronal culture remained a gold standard method that requires laborious preparation, intensive training, and animal resources. To circumvent the shortfalls of primary neuronal preparations and efficiently give rise to functional neurons, we combine a neural stem cell culture method with a direct cell type-conversion approach. The lucidity of this method enables the efficient preparation of functional neurons from mouse neural progenitor cells on demand. We demonstrate that induced neurons (NPC-iNs) by this method make synaptic connections, elicit neuronal activity-dependent cellular responses, and develop functional neuronal networks. This method will provide a concise platform for functional neuronal assessments. This indeed offers a perspective for using these characterized neuronal networks for investigating plasticity mechanisms, drug screening assays, and probing the molecular and biophysical basis of neurodevelopmental and neurodegenerative diseases.

Chaos in memory function of sleep: A nonlinear dynamical analysis in thalamocortical study

Studying the dynamical behaviors of neuronal models may help in better understanding of real nervous system. In addition, it can help researchers to understand some specific phenomena in neuronal system. The thalamocortical network is made of neurons in the thalamus and cortex. In it, the memory function is consolidated in sleep by creating up and down state oscillations (1 Hz) and fast (13-17 Hz) - slow (8-12 Hz) spindles. Recently, a nonlinear biological model for up-down oscillations and fast-slow spindles of the thalamocortical network has been proposed. In this research, the power spectral for the fast-slow spindle of the model is extracted. Dynamical properties of the model, such as the bifurcation diagrams, and attractors are investigated. The results show that the variation of the synaptic power between the excitatory neurons of the cortex and the reticular neurons in the thalamus changes the spindles' activity. According to previous experimental findings, it is an essential rule for consolidating the memory function during sleep. It is also pointed out that when the fast-slow spindles of the brain increase, the dynamics of the thalamocortical system tend to chaos.

Correlations enhance the behavioral readout of neural population activity in association cortex

Noise correlations (that is, trial-to-trial covariations in neural activity for a given stimulus) limit the stimulus information encoded by neural populations, leading to the widely held prediction that they impair perceptual discrimination behaviors. However, this prediction neglects the effects of correlations on information readout. We studied how correlations affect both encoding and readout of sensory information. We analyzed calcium imaging data from mouse posterior parietal cortex during two perceptual discrimination tasks. Correlations reduced the encoded stimulus information, but, seemingly paradoxically, were higher when mice made correct rather than incorrect choices. Single-trial behavioral choices depended not only on the stimulus information encoded by the whole population, but unexpectedly also on the consistency of information across neurons and time. Because correlations increased information consistency, they enhanced the conversion of sensory information into behavioral choices, overcoming their detrimental information-limiting effects. Thus, correlations in association cortex can benefit task performance even if they decrease sensory information.

Duplicate Detection of Spike Events: A Relevant Problem in Human Single-Unit Recordings

Single-unit recordings in the brain of behaving human subjects provide a unique opportunity to advance our understanding of neural mechanisms of cognition. These recordings are exclusively performed in medical centers during diagnostic or therapeutic procedures. The presence of medical instruments along with other aspects of the hospital environment limit the control of electrical noise compared to animal laboratory environments. Here, we highlight the problem of an increased occurrence of simultaneous spike events on different recording channels in human single-unit recordings. Most of these simultaneous events were detected in clusters previously labeled as artifacts and showed similar waveforms. These events may result from common external noise sources or from different micro-electrodes recording activity from the same neuron. To address the problem of duplicate recorded events, we introduce an open-source algorithm to identify these artificial spike events based on their synchronicity and waveform similarity. Applying our method to a comprehensive dataset of human single-unit recordings, we demonstrate that our algorithm can substantially increase the data quality of these recordings. Given our findings, we argue that future studies of single-unit activity recorded under noisy conditions should employ algorithms of this kind to improve data quality.

Inferring thalamocortical monosynaptic connectivity in vivo

As the tools to simultaneously record electrophysiological signals from large numbers of neurons within and across brain regions become increasingly available, this opens up for the first time the possibility of establishing the details of causal relationships between monosynaptically connected neurons and the patterns of neural activation that underlie perception and behavior. Although recorded activity across synaptically connected neurons has served as the cornerstone for much of what we know about synaptic transmission and plasticity, this has largely been relegated to ex vivo preparations that enable precise targeting under relatively well-controlled conditions. Analogous studies in vivo, where image-guided targeting is often not yet possible, rely on indirect, data-driven measures, and as a result such studies have been sparse and the dependence upon important experimental parameters has not been well studied. Here, using in vivo extracellular single-unit recordings in the topographically aligned rodent thalamocortical pathway, we sought to establish a general experimental and computational framework for inferring synaptic connectivity. Specifically, attacking this problem within a statistical signal detection framework utilizing experimentally recorded data in the ventral-posterior medial (VPm) region of the thalamus and the homologous region in layer 4 of primary somatosensory cortex (S1) revealed a trade-off between network activity levels needed for the data-driven inference and synchronization of nearby neurons within the population that results in masking of synaptic relationships. Here, we provide a framework for establishing connectivity in multisite, multielectrode recordings based on statistical inference, setting the stage for large-scale assessment of synaptic connectivity within and across brain structures.NEW & NOTEWORTHY Despite the fact that all brain function relies on the long-range transfer of information across different regions, the tools enabling us to measure connectivity across brain structures are lacking. Here, we provide a statistical framework for identifying and assessing potential monosynaptic connectivity across neuronal circuits from population spiking activity that generalizes to large-scale recording technologies that will help us to better understand the signaling within networks that underlies perception and behavior.

The Geometry of Information Coding in Correlated Neural Populations

Neurons in the brain represent information in their collective activity. The fidelity of this neural population code depends on whether and how variability in the response of one neuron is shared with other neurons. Two decades of studies have investigated the influence of these noise correlations on the properties of neural coding. We provide an overview of the theoretical developments on the topic. Using simple, qualitative, and general arguments, we discuss, categorize, and relate the various published results. We emphasize the relevance of the fine structure of noise correlation, and we present a new approach to the issue. Throughout this review, we emphasize a geometrical picture of how noise correlations impact the neural code.

Malleability of gamma rhythms enhances population-level correlations

An important problem in systems neuroscience is to understand how information is communicated among brain regions, and it has been proposed that communication is mediated by neuronal oscillations, such as rhythms in the gamma band. We sought to investigate this idea by using a network model with two components, a source (sending) and a target (receiving) component, both built to resemble local populations in the cerebral cortex. To measure the effectiveness of communication, we used population-level correlations in spike times between the source and target. We found that after correcting for a response time that is independent of initial conditions, spike-time correlations between the source and target are significant, due in large measure to the alignment of firing events in their gamma rhythms. But, we also found that regular oscillations cannot produce the results observed in our model simulations of cortical neurons. Surprisingly, it is the irregularity of gamma rhythms, the absence of internal clocks, together with the malleability of these rhythms and their tendency to align with external pulses - features that are known to be present in gamma rhythms in the real cortex - that produced the results observed. These findings and the mechanistic explanations we offered are our primary results. Our secondary result is a mathematical relationship between correlations and the sizes of the samples used for their calculation. As improving technology enables recording simultaneously from increasing numbers of neurons, this relationship could be useful for interpreting results from experimental recordings.

Microcircuit Rules Governing Impact of Single Interneurons on Purkinje Cell Output In Vivo

The functional impact of single interneurons on neuronal output in vivo and how interneurons are recruited by physiological activity patterns remain poorly understood. In the cerebellar cortex, molecular layer interneurons and their targets, Purkinje cells, receive excitatory inputs from granule cells and climbing fibers. Using dual patch-clamp recordings from interneurons and Purkinje cells in vivo, we probe the spatiotemporal interactions between these circuit elements. We show that single interneuron spikes can potently inhibit Purkinje cell output, depending on interneuron location. Climbing fiber input activates many interneurons via glutamate spillover but results in inhibition of those interneurons that inhibit the same Purkinje cell receiving the climbing fiber input, forming a disinhibitory motif. These interneuron circuits are engaged during sensory processing, creating diverse pathway-specific response functions. These findings demonstrate how the powerful effect of single interneurons on Purkinje cell output can be sculpted by various interneuron circuit motifs to diversify cerebellar computations.

Detecting interactions in discrete-time dynamics by random variable resetting

Detecting the interactions in networks helps us to understand the collective behaviors of complex systems. However, doing so is challenging due to systemic noise, nonlinearity, and a lack of information. Very few researchers have attempted to reconstruct discrete-time dynamic networks. Recently, Shi et al. proposed resetting a random state variable to infer the interactions in a continuous-time dynamic network. In this paper, we introduce a random resetting method for discrete-time dynamic networks. The statistical characteristics of the method are investigated and verified with numerical simulations. In addition, this reconstruction method was evaluated for limited data and weak coupling and within multiple-attractor systems.

A three-compartment non-linear model of myocardial cell conduction block during photosensitization

This study constructed a new non-linear model of myocardial electrical conduction block during photosensitization reaction to identify the vulnerable cell population and generate an index for recurrent risk following catheter ablation for tachyarrhythmia. A three-compartment model of conductive, vulnerable, and blocked cells was proposed. To determine the non-linearity of the rate parameter for the change from vulnerable cells to conductive cells, we compared a previously reported non-linear model and our newly proposed model with non-linear rate parameters in the modeling of myocardial cell electrical conduction block during photosensitization reaction. The rate parameters were optimized via a bi-nested structure using measured synchronicity data during the photosensitization reaction of myocardial cell wires. The newly proposed model had a better fit to the measured data than the conventional model. The sum of the error until the time where the measured value was higher than 0.6, was 0.22 in the conventional model and 0.07 in our new model. The non-linear rate parameter from the vulnerable cell to the conductive cell compartment may be the preferred structure of the electrical conduction block model induced by photosensitization reaction. This simulation model provides an index to evaluate recurrent risk after tachyarrhythmia catheter ablation by photosensitization reaction. A three-compartment non-linear model of myocardial cell conduction block during photosensitization.

Monosynaptic inference via finely-timed spikes

Observations of finely-timed spike relationships in population recordings have been used to support partial reconstruction of neural microcircuit diagrams. In this approach, fine-timescale components of paired spike train interactions are isolated and subsequently attributed to synaptic parameters. Recent perturbation studies strengthen the case for such an inference, yet the complete set of measurements needed to calibrate statistical models is unavailable. To address this gap, we study features of pairwise spiking in a large-scale in vivo dataset where presynaptic neurons were explicitly decoupled from network activity by juxtacellular stimulation. We then construct biophysical models of paired spike trains to reproduce the observed phenomenology of in vivo monosynaptic interactions, including both fine-timescale spike-spike correlations and firing irregularity. A key characteristic of these models is that the paired neurons are coupled by rapidly-fluctuating background inputs. We quantify a monosynapse's causal effect by comparing the postsynaptic train with its counterfactual, when the monosynapse is removed. Subsequently, we develop statistical techniques for estimating this causal effect from the pre- and post-synaptic spike trains. A particular focus is the justification and application of a nonparametric separation of timescale principle to implement synaptic inference. Using simulated data generated from the biophysical models, we characterize the regimes in which the estimators accurately identify the monosynaptic effect. A secondary goal is to initiate a critical exploration of neurostatistical assumptions in terms of biophysical mechanisms, particularly with regards to the challenging but arguably fundamental issue of fast, unobservable nonstationarities in background dynamics.

Linear Response of General Observables in Spiking Neuronal Network Models

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow us to predict the influence of a weak amplitude time dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics. We illustrate our results with numerical simulations performed over a discrete time integrate and fire model.

Inferring Neuronal Couplings From Spiking Data Using a Systematic Procedure With a Statistical Criterion

Recent remarkable advances in experimental techniques have provided a background for inferring neuronal couplings from point process data that include a great number of neurons. Here, we propose a systematic procedure for pre- and postprocessing generic point process data in an objective manner to handle data in the framework of a binary simple statistical model, the Ising or generalized McCulloch-Pitts model. The procedure has two steps: (1) determining time bin size for transforming the point process data into discrete-time binary data and (2) screening relevant couplings from the estimated couplings. For the first step, we decide the optimal time bin size by introducing the null hypothesis that all neurons would fire independently, then choosing a time bin size so that the null hypothesis is rejected with the strict criteria. The likelihood associated with the null hypothesis is analytically evaluated and used for the rejection process. For the second postprocessing step, after a certain estimator of coupling is obtained based on the preprocessed data set (any estimator can be used with the proposed procedure), the estimate is compared with many other estimates derived from data sets obtained by randomizing the original data set in the time direction. We accept the original estimate as relevant only if its absolute value is sufficiently larger than those of randomized data sets. These manipulations suppress false positive couplings induced by statistical noise. We apply this inference procedure to spiking data from synthetic and in vitro neuronal networks. The results show that the proposed procedure identifies the presence or absence of synaptic couplings fairly well, including their signs, for the synthetic and experimental data. In particular, the results support that we can infer the physical connections of underlying systems in favorable situations, even when using a simple statistical model.

Extracellular recording of direct synaptic signals with a CMOS-nanoelectrode array

The synaptic connections between neurons are traditionally determined by correlating the action potentials (APs) of a pre-synaptic neuron and small-amplitude subthreshold potentials of a post-synaptic neuron using invasive intracellular techniques, such as patch clamping. Extracellular recording by a microelectrode array can non-invasively monitor network activities of a large number of neurons, but its reduced sensitivity usually prevents direct measurements of synaptic signals. Here, we demonstrate that a newly developed complementary metal-oxide-semiconductor (CMOS) nanoelectrode array (CNEA) is capable of extracellularly determining direct synaptic connections in dense, multi-layer cultures of dissociated rat neurons. We spatiotemporally correlate action potential signals of hundreds of active neurons, detect small (∼1 pA after averaging) extracellular synaptic signals at the region where pre-synaptic axons and post-synaptic dendrites/somas overlap, and use those signals to map synaptic connections. We use controlled stimulation to assess stimulation-dependent synaptic strengths and to titrate a synaptic blocker (CNQX: IC50 ∼ 1 μM). The new capabilities demonstrated here significantly enhance the utilities of CNEAs in connectome mapping and drug screening applications.

Two-Photon Voltage Imaging of Spontaneous Activity from Multiple Neurons Reveals Network Activity in Brain Tissue

Recording the electrical activity of multiple neurons simultaneously would greatly facilitate studies on the function of neuronal circuits. The combination of the fast scanning by random-access multiphoton microscopy (RAMP) and the latest two-photon-compatible high-performance fluorescent genetically encoded voltage indicators (GEVIs) has enabled action potential detection in deep layers in in vivo brain. However, neuron connectivity analysis on optically recorded action potentials from multiple neurons in brain tissue has yet to be achieved. With high expression of a two-photon-compatible GEVI, ASAP3, via in utero electroporation and RAMP, we achieved voltage recording of spontaneous activities from multiple neurons in brain slice. We provide evidence for the developmental changes in intralaminar horizontal connections in somatosensory cortex layer 2/3 with a greater sensitivity than calcium imaging. This method thus enables investigation of neuronal network connectivity at the cellular resolution in brain tissue.

Self-consistent formulations for stochastic nonlinear neuronal dynamics

Neural dynamics is often investigated with tools from bifurcation theory. However, many neuron models are stochastic, mimicking fluctuations in the input from unknown parts of the brain or the spiking nature of signals. Noise changes the dynamics with respect to the deterministic model; in particular classical bifurcation theory cannot be applied. We formulate the stochastic neuron dynamics in the Martin-Siggia-Rose de Dominicis-Janssen (MSRDJ) formalism and present the fluctuation expansion of the effective action and the functional renormalization group (fRG) as two systematic ways to incorporate corrections to the mean dynamics and time-dependent statistics due to fluctuations in the presence of nonlinear neuronal gain. To formulate self-consistency equations, we derive a fundamental link between the effective action in the Onsager-Machlup (OM) formalism, which allows the study of phase transitions, and the MSRDJ effective action, which is computationally advantageous. These results in particular allow the derivation of an OM effective action for systems with non-Gaussian noise. This approach naturally leads to effective deterministic equations for the first moment of the stochastic system; they explain how nonlinearities and noise cooperate to produce memory effects. Moreover, the MSRDJ formulation yields an effective linear system that has identical power spectra and linear response. Starting from the better known loopwise approximation, we then discuss the use of the fRG as a method to obtain self-consistency beyond the mean. We present a new efficient truncation scheme for the hierarchy of flow equations for the vertex functions by adapting the Blaizot, Méndez, and Wschebor approximation from the derivative expansion to the vertex expansion. The methods are presented by means of the simplest possible example of a stochastic differential equation that has generic features of neuronal dynamics.

Inferring and validating mechanistic models of neural microcircuits based on spike-train data

The interpretation of neuronal spike train recordings often relies on abstract statistical models that allow for principled parameter estimation and model selection but provide only limited insights into underlying microcircuits. In contrast, mechanistic models are useful to interpret microcircuit dynamics, but are rarely quantitatively matched to experimental data due to methodological challenges. Here we present analytical methods to efficiently fit spiking circuit models to single-trial spike trains. Using derived likelihood functions, we statistically infer the mean and variance of hidden inputs, neuronal adaptation properties and connectivity for coupled integrate-and-fire neurons. Comprehensive evaluations on synthetic data, validations using ground truth in-vitro and in-vivo recordings, and comparisons with existing techniques demonstrate that parameter estimation is very accurate and efficient, even for highly subsampled networks. Our methods bridge statistical, data-driven and theoretical, model-based neurosciences at the level of spiking circuits, for the purpose of a quantitative, mechanistic interpretation of recorded neuronal population activity.

It is difficult to fit mechanistic, biophysically constrained circuit models to spike train data from in vivo extracellular recordings. Here the authors present analytical methods that enable efficient parameter estimation for integrate-and-fire circuit models and inference of the underlying connectivity structure in subsampled networks.

Simultaneous electrophysiological and morphological assessment of functional damage to neural networks in vitro after 30-300 g impacts

An enigma of mild traumatic brain injury are observations of substantial behavior and performance deficits in the absence of bleeding or other observable structural damage. Altered behavior and performance reflect changes in action potential (AP) patterns within neuronal networks, which could result from subtle subcellular responses that affect synaptic efficacy and AP production. The aim of this study was to investigate and quantify network activity changes after simulated concussions in vitro and therewith develop a platform for simultaneous and direct observations of morphological and electrophysiological changes in neural networks. We used spontaneously active networks grown on microelectrode arrays (MEAs) to allow long-term multisite monitoring with simultaneous optical observations before and after impacts delivered by a ballistic pendulum (30 to 300 g accelerations). The monitoring of AP waveshape templates for long periods before and after impact provided an internal control for cell death or loss of cell-electrode coupling in the observed set of neurons. Network activity patterns were linked in real-time to high power phase contrast microscopy. There was no overt loss of glial or neuronal adhesion, even at high-g impacts. All recording experiments showed repeatable spike production responses: a loss of activity with recovery to near reference in 1 hr, followed by a slow activity decay to a stable, level plateau approximately 30–40% below reference. The initial recovery occurred in two steps: a rapid return of activity to an average 24% below reference, forming a level plateau lasting from 5 to 20 min, followed by a climb to within 10% of reference where a second plateau was established for 1 to 2 hrs. Cross correlation profiles revealed changes in firing hierarchy as well as in Phase 1 in spontaneous network oscillations that were reduced by as much as 20% 6–8 min post impact with only a partial recovery at 30 min. We also observed that normally stable nuclei developed irregular rotational motion after impact in 27 out of 30 networks. The evolution of network activity deficits and recovery can be linked with microscopically observable changes in the very cells that are generating the activity. The repeatable electrophysiological impact response profiles and oscillation changes can provide a quantitative basis for systematic evaluations of pharmacological intervention strategies. Future expansion to include fluorescent microscopy should allow detailed investigations of damage mechanisms on the subcellular level.

Cortical computations via metastable activity

Metastable brain dynamics are characterized by abrupt, jump-like modulations so that the neural activity in single trials appears to unfold as a sequence of discrete, quasi-stationary 'states'. Evidence that cortical neural activity unfolds as a sequence of metastable states is accumulating at fast pace. Metastable activity occurs both in response to an external stimulus and during ongoing, self-generated activity. These spontaneous metastable states are increasingly found to subserve internal representations that are not locked to external triggers, including states of deliberations, attention and expectation. Moreover, decoding stimuli or decisions via metastable states can be carried out trial-by-trial. Focusing on metastability will allow us to shift our perspective on neural coding from traditional concepts based on trial-averaging to models based on dynamic ensemble representations. Recent theoretical work has started to characterize the mechanistic origin and potential roles of metastable representations. In this article we review recent findings on metastable activity, how it may arise in biologically realistic models, and its potential role for representing internal states as well as relevant task variables.

Dimensionality in recurrent spiking networks: Global trends in activity and local origins in connectivity

The dimensionality of a network's collective activity is of increasing interest in neuroscience. This is because dimensionality provides a compact measure of how coordinated network-wide activity is, in terms of the number of modes (or degrees of freedom) that it can independently explore. A low number of modes suggests a compressed low dimensional neural code and reveals interpretable dynamics [1], while findings of high dimension may suggest flexible computations [2, 3]. Here, we address the fundamental question of how dimensionality is related to connectivity, in both autonomous and stimulus-driven networks. Working with a simple spiking network model, we derive three main findings. First, the dimensionality of global activity patterns can be strongly, and systematically, regulated by local connectivity structures. Second, the dimensionality is a better indicator than average correlations in determining how constrained neural activity is. Third, stimulus evoked neural activity interacts systematically with neural connectivity patterns, leading to network responses of either greater or lesser dimensionality than the stimulus.

Electrophysiological monitoring of inhibition in mammalian species, from rodents to humans

GABAergic interneurons constitute a highly diverse family of neurons that play a critical role in cortical functions. Due to their prominent role in cortical network dynamics, genetic, developmental, or other dysfunctions in GABAergic neurons have been linked to neurological disorders such as epilepsy. Thus, it is crucial to investigate the interaction of these various neurons and to develop methods to specifically and directly monitor inhibitory activity in vivo. While research in small mammals has benefited from a wealth of recent technological development, bridging the gap to large mammals and humans remains a challenge. This is of particular interest since single neuron monitoring with intracranial electrodes in epileptic patients is developing quickly, opening new avenues for understanding the role of different cell types in epilepsy. Here, we review currently available techniques that monitor inhibitory activity in the brain and the respective validations in rodents. Finally, we discuss the future developments of these techniques and how knowledge from animal research can be translated to the study of neuronal circuit dynamics in the human brain.

In vitro validation of in silico identified inhibitory interactions

BACKGROUND

Understanding how neuronal signals propagate in local network is an important step in understanding information processing. As a result, spike trains recorded with multi-electrode arrays (MEAs) have been widely used to study the function of neural networks. Studying the dynamics of neuronal networks requires the identification of both excitatory and inhibitory connections. The detection of excitatory relationships can robustly be inferred by characterizing the statistical relationships of neural spike trains. However, the identification of inhibitory relationships is more difficult: distinguishing endogenous low firing rates from active inhibition is not obvious.

NEW METHOD

In this paper, we propose an in silico interventional procedure that makes predictions about the effect of stimulating or inhibiting single neurons on other neurons, and thereby gives the ability to accurately identify inhibitory effects.

COMPARISON

To experimentally test these predictions, we have developed a Neural Circuit Probe (NCP) that delivers drugs transiently and reversibly on individually identified neurons to assess their contributions to the neural circuit behavior.

RESULTS

Using the NCP, putative inhibitory connections identified by the in silico procedure were validated through in vitro interventional experiments.

CONCLUSIONS

Together, these results demonstrate how detailed microcircuitry can be inferred from statistical models derived from neurophysiology data.

A Theoretical Framework to Derive Simple, Firing-Rate-Dependent Mathematical Models of Synaptic Plasticity

Synaptic plasticity serves as an essential mechanism underlying cognitive processes as learning and memory. For a better understanding detailed theoretical models combine experimental underpinnings of synaptic plasticity and match experimental results. However, these models are mathematically complex impeding the comprehensive investigation of their link to cognitive processes generally executed on the neuronal network level. Here, we derive a mathematical framework enabling the simplification of such detailed models of synaptic plasticity facilitating further mathematical analyses. By this framework we obtain a compact, firing-rate-dependent mathematical formulation, which includes the essential dynamics of the detailed model and, thus, of experimentally verified properties of synaptic plasticity. Amongst others, by testing our framework by abstracting the dynamics of two well-established calcium-dependent synaptic plasticity models, we derived that the synaptic changes depend on the square of the presynaptic firing rate, which is in contrast to previous assumptions. Thus, the here-presented framework enables the derivation of biologically plausible but simple mathematical models of synaptic plasticity allowing to analyze the underlying dependencies of synaptic dynamics from neuronal properties such as the firing rate and to investigate their implications in complex neuronal networks.

Correlated states in balanced neuronal networks

Understanding the magnitude and structure of interneuronal correlations and their relationship to synaptic connectivity structure is an important and difficult problem in computational neuroscience. Early studies show that neuronal network models with excitatory-inhibitory balance naturally create very weak spike train correlations, defining the "asynchronous state." Later work showed that, under some connectivity structures, balanced networks can produce larger correlations between some neuron pairs, even when the average correlation is very small. All of these previous studies assume that the local network receives feedforward synaptic input from a population of uncorrelated spike trains. We show that when spike trains providing feedforward input are correlated, the downstream recurrent network produces much larger correlations. We provide an in-depth analysis of the resulting "correlated state" in balanced networks and show that, unlike the asynchronous state, it produces a tight excitatory-inhibitory balance consistent with in vivo cortical recordings.

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.

Stochastic bursting in unidirectionally delay-coupled noisy excitable systems

We show that "stochastic bursting" is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation, i.e., when the time delays in each connection are much larger than the characteristic duration of the spikes, the observed rather coherent spike pattern can be described by an idealized coupled point process with a leader-follower relationship. We derive analytically the statistics of the spikes in each unit, the pairwise correlations between any two units, and the spectrum of the total output from the network. Theory is in good agreement with the simulations with a network of theta-neurons.