State-space analysis of time-varying higher-order spike correlation for multiple neural spike train data

Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.     

Correlations and Functional Connections in a Population of Grid Cells

We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a maximum entropy kinetic pairwise model (kinetic Ising model), study their functional connectivity. Even when we account for the covariations in firing rates due to overlapping fields, both the pairwise correlations and functional connections decay as a function of the shortest distance between the vertices of the spatial firing pattern of pairs of grid cells, i.e. their phase difference. They take positive values between cells with nearby phases and approach zero or negative values for larger phase differences. We find similar results also when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs. The inferred connections between neurons in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections found between cells of the same module. Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of grid pattern.     

Dynamical features of higher-order correlation events: impact on cortical cells

Cortical neurons receive signals from thousands of other neurons. The statistical properties of the input spike trains substantially shape the output response properties of each neuron. Experimental and theoretical investigations have mostly focused on the second order statistical features of the input spike trains (mean firing rates and pairwise correlations). Little is known of how higher order correlations affect the integration and firing behavior of a cell independently of the second order statistics. To address this issue, we simulated the dynamics of a population of 5000 neurons, controlling both their second order and higher-order correlation properties to reflect physiological data. We then used these ensemble dynamics as the input stage to morphologically reconstructed cortical cells (layer 5 pyramidal, layer 4 spiny stellate cell), and to an integrate and fire neuron. Our results show that changes done solely to the higher-order correlation properties of the network’s dynamics significantly affect the response properties of a target neuron, both in terms of output rate and spike timing. Moreover, the neuronal morphology and voltage dependent mechanisms of the target neuron considerably modulate the quantitative aspects of these effects. Finally, we show how these results affect sparseness of neuronal representations, tuning properties, and feature selectivity of cortical cells. An erratum to this article can be found at     

Searching for Collective Behavior in a Large Network of Sensory Neurons

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such “K-pairwise” models—being systematic extensions of the previously used pairwise Ising models—provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population''s capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.     

高阶Boltzmann机的平均场理论学习算法

用统计力学中的平均场理论及模拟退火技术,将一般高阶神经网络及玻尔兹曼机的优点结合在一起,以不同于文献［２］的方法,推导出高阶玻尔兹曼机的驰豫动力学的确定性方程和平均场理论学习算法。二者皆便于ＶＬＳＩ实现,且学习算法省去很多ＣＰＵ时间,对二维镜像对称问题及Ｔ－问题的计算机仿真结果表明三阶玻尔兹曼机的平均场理论学习算法是正确的,且性能较二阶玻尔兹曼机好。     

Innate visual learning through spontaneous activity patterns

Patterns of spontaneous activity in the developing retina, LGN, and cortex are necessary for the proper development of visual cortex. With these patterns intact, the primary visual cortices of many newborn animals develop properties similar to those of the adult cortex but without the training benefit of visual experience. Previous models have demonstrated how V1 responses can be initialized through mechanisms specific to development and prior to visual experience, such as using axonal guidance cues or relying on simple, pairwise correlations on spontaneous activity with additional developmental constraints. We argue that these spontaneous patterns may be better understood as part of an "innate learning" strategy, which learns similarly on activity both before and during visual experience. With an abstraction of spontaneous activity models, we show how the visual system may be able to bootstrap an efficient code for its natural environment prior to external visual experience, and we continue the same refinement strategy upon natural experience. The patterns are generated through simple, local interactions and contain the same relevant statistical properties of retinal waves and hypothesized waves in the LGN and V1. An efficient encoding of these patterns resembles a sparse coding of natural images by producing neurons with localized, oriented, bandpass structure-the same code found in early visual cortical cells. We address the relevance of higher-order statistical properties of spontaneous activity, how this relates to a system that may adapt similarly on activity prior to and during natural experience, and how these concepts ultimately relate to an efficient coding of our natural world.     

Mixtures of conditional gaussian scale mixtures applied to multiscale image representations

We present a probabilistic model for natural images that is based on mixtures of Gaussian scale mixtures and a simple multiscale representation. We show that it is able to generate images with interesting higher-order correlations when trained on natural images or samples from an occlusion-based model. More importantly, our multiscale model allows for a principled evaluation. While it is easy to generate visually appealing images, we demonstrate that our model also yields the best performance reported to date when evaluated with respect to the cross-entropy rate, a measure tightly linked to the average log-likelihood. The ability to quantitatively evaluate our model differentiates it from other multiscale models, for which evaluation of these kinds of measures is usually intractable.     

Scalability of Asynchronous Networks Is Limited by One-to-One Mapping between Effective Connectivity and Correlations

Network models are routinely downscaled compared to nature in terms of numbers of nodes or edges because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics are conserved, here we show that limitations already arise if also second-order statistics are to be maintained. The temporal structure of pairwise averaged correlations in the activity of recurrent networks is determined by the effective population-level connectivity. We first show that in general the converse is also true and explicitly mention degenerate cases when this one-to-one relationship does not hold. The one-to-one correspondence between effective connectivity and the temporal structure of pairwise averaged correlations implies that network scalings should preserve the effective connectivity if pairwise averaged correlations are to be held constant. Changes in effective connectivity can even push a network from a linearly stable to an unstable, oscillatory regime and vice versa. On this basis, we derive conditions for the preservation of both mean population-averaged activities and pairwise averaged correlations under a change in numbers of neurons or synapses in the asynchronous regime typical of cortical networks. We find that mean activities and correlation structure can be maintained by an appropriate scaling of the synaptic weights, but only over a range of numbers of synapses that is limited by the variance of external inputs to the network. Our results therefore show that the reducibility of asynchronous networks is fundamentally limited.     

Learning to represent visual input

One of the central problems in computational neuroscience is to understand how the object-recognition pathway of the cortex learns a deep hierarchy of nonlinear feature detectors. Recent progress in machine learning shows that it is possible to learn deep hierarchies without requiring any labelled data. The feature detectors are learned one layer at a time and the goal of the learning procedure is to form a good generative model of images, not to predict the class of each image. The learning procedure only requires the pairwise correlations between the activations of neuron-like processing units in adjacent layers. The original version of the learning procedure is derived from a quadratic ‘energy’ function but it can be extended to allow third-order, multiplicative interactions in which neurons gate the pairwise interactions between other neurons. A technique for factoring the third-order interactions leads to a learning module that again has a simple learning rule based on pairwise correlations. This module looks remarkably like modules that have been proposed by both biologists trying to explain the responses of neurons and engineers trying to create systems that can recognize objects.     

CuBIC: cumulant based inference of higher-order correlations in massively parallel spike trains

Recent developments in electrophysiological and optical recording techniques enable the simultaneous observation of large numbers of neurons. A meaningful interpretation of the resulting multivariate data, however, presents a serious challenge. In particular, the estimation of higher-order correlations that characterize the cooperative dynamics of groups of neurons is impeded by the combinatorial explosion of the parameter space. The resulting requirements with respect to sample size and recording time has rendered the detection of coordinated neuronal groups exceedingly difficult. Here we describe a novel approach to infer higher-order correlations in massively parallel spike trains that is less susceptible to these problems. Based on the superimposed activity of all recorded neurons, the cumulant-based inference of higher-order correlations (CuBIC) presented here exploits the fact that the absence of higher-order correlations imposes also strong constraints on correlations of lower order. Thus, estimates of only few lower-order cumulants suffice to infer higher-order correlations in the population. As a consequence, CuBIC is much better compatible with the constraints of in vivo recordings than previous approaches, which is shown by a systematic analysis of its parameter dependence.     

A new method to infer higher-order spike correlations from membrane potentials

What is the role of higher-order spike correlations for neuronal information processing? Common data analysis methods to address this question are devised for the application to spike recordings from multiple single neurons. Here, we present a new method which evaluates the subthreshold membrane potential fluctuations of one neuron, and infers higher-order correlations among the neurons that constitute its presynaptic population. This has two important advantages: Very large populations of up to several thousands of neurons can be studied, and the spike sorting is obsolete. Moreover, this new approach truly emphasizes the functional aspects of higher-order statistics, since we infer exactly those correlations which are seen by a neuron. Our approach is to represent the subthreshold membrane potential fluctuations as presynaptic activity filtered with a fixed kernel, as it would be the case for a leaky integrator neuron model. This allows us to adapt the recently proposed method CuBIC (cumulant based inference of higher-order correlations from the population spike count; Staude et al., J Comput Neurosci 29(1–2):327–350, 2010c) with which the maximal order of correlation can be inferred. By numerical simulation we show that our new method is reasonably sensitive to weak higher-order correlations, and that only short stretches of membrane potential are required for their reliable inference. Finally, we demonstrate its remarkable robustness against violations of the simplifying assumptions made for its construction, and discuss how it can be employed to analyze in vivo intracellular recordings of membrane potentials.     

Coordinated activity of ventral tegmental neurons adapts to appetitive and aversive learning

Our understanding of how value-related information is encoded in the ventral tegmental area (VTA) is based mainly on the responses of individual putative dopamine neurons. In contrast to cortical areas, the nature of coordinated interactions between groups of VTA neurons during motivated behavior is largely unknown. These interactions can strongly affect information processing, highlighting the importance of investigating network level activity. We recorded the activity of multiple single units and local field potentials (LFP) in the VTA during a task in which rats learned to associate novel stimuli with different outcomes. We found that coordinated activity of VTA units with either putative dopamine or GABA waveforms was influenced differently by rewarding versus aversive outcomes. Specifically, after learning, stimuli paired with a rewarding outcome increased the correlation in activity levels between unit pairs whereas stimuli paired with an aversive outcome decreased the correlation. Paired single unit responses also became more redundant after learning. These response patterns flexibly tracked the reversal of contingencies, suggesting that learning is associated with changing correlations and enhanced functional connectivity between VTA neurons. Analysis of LFP recorded simultaneously with unit activity showed an increase in the power of theta oscillations when stimuli predicted reward but not an aversive outcome. With learning, a higher proportion of putative GABA units were phase locked to the theta oscillations than putative dopamine units. These patterns also adapted when task contingencies were changed. Taken together, these data demonstrate that VTA neurons organize flexibly as functional networks to support appetitive and aversive learning.     

Random Wiring,Ganglion Cell Mosaics,and the Functional Architecture of the Visual Cortex

The architecture of iso-orientation domains in the primary visual cortex (V1) of placental carnivores and primates apparently follows species invariant quantitative laws. Dynamical optimization models assuming that neurons coordinate their stimulus preferences throughout cortical circuits linking millions of cells specifically predict these invariants. This might indicate that V1’s intrinsic connectome and its functional architecture adhere to a single optimization principle with high precision and robustness. To validate this hypothesis, it is critical to closely examine the quantitative predictions of alternative candidate theories. Random feedforward wiring within the retino-cortical pathway represents a conceptually appealing alternative to dynamical circuit optimization because random dimension-expanding projections are believed to generically exhibit computationally favorable properties for stimulus representations. Here, we ask whether the quantitative invariants of V1 architecture can be explained as a generic emergent property of random wiring. We generalize and examine the stochastic wiring model proposed by Ringach and coworkers, in which iso-orientation domains in the visual cortex arise through random feedforward connections between semi-regular mosaics of retinal ganglion cells (RGCs) and visual cortical neurons. We derive closed-form expressions for cortical receptive fields and domain layouts predicted by the model for perfectly hexagonal RGC mosaics. Including spatial disorder in the RGC positions considerably changes the domain layout properties as a function of disorder parameters such as position scatter and its correlations across the retina. However, independent of parameter choice, we find that the model predictions substantially deviate from the layout laws of iso-orientation domains observed experimentally. Considering random wiring with the currently most realistic model of RGC mosaic layouts, a pairwise interacting point process, the predicted layouts remain distinct from experimental observations and resemble Gaussian random fields. We conclude that V1 layout invariants are specific quantitative signatures of visual cortical optimization, which cannot be explained by generic random feedforward-wiring models.     

A new method for detecting human recombination hotspots and its applications to the HapMap ENCODE data

Computational detection of recombination hotspots from population polymorphism data is important both for understanding the nature of recombination and for applications such as association studies. We propose a new method for this task based on a multiple-hotspot model and an (approximate) log-likelihood ratio test. A truncated, weighted pairwise log-likelihood is introduced and applied to the calculation of the log-likelihood ratio, and a forward-selection procedure is adopted to search for the optimal hotspot predictions. The method shows a relatively high power with a low false-positive rate in detecting multiple hotspots in simulation data and has a performance comparable to the best results of leading computational methods in experimental data for which recombination hotspots have been characterized by sperm-typing experiments. The method can be applied to both phased and unphased data directly, with a very fast computational speed. We applied the method to the 10 500-kb regions of the HapMap ENCODE data and found 172 hotspots among the three populations, with average hotspot width of 2.4 kb. By comparisons with the simulation data, we found some evidence that hotspots are not all identical across populations. The correlations between detected hotspots and several genomic characteristics were examined. In particular, we observed that DNaseI-hypersensitive sites are enriched in hotspots, suggesting the existence of human beta hotspots similar to those found in yeast.     

RBM4 promotes neuronal differentiation and neurite outgrowth by modulating Numb isoform expression

RBM4 participates in cell differentiation by regulating tissue-specific alternative pre-mRNA splicing. RBM4 also has been implicated in neurogenesis in the mouse embryonic brain. Using mouse embryonal carcinoma P19 cells as a neural differentiation model, we observed a temporal correlation between RBM4 expression and a change in splicing isoforms of Numb, a cell-fate determination gene. Knockdown of RBM4 affected the inclusion/exclusion of exons 3 and 9 of Numb in P19 cells. RBM4-deficient embryonic mouse brain also exhibited aberrant splicing of Numb pre-mRNA. Using a splicing reporter minigene assay, we demonstrated that RBM4 promoted exon 3 inclusion and exon 9 exclusion. Moreover, we found that RBM4 depletion reduced the expression of the proneural gene Mash1, and such reduction was reversed by an RBM4-induced Numb isoform containing exon 3 but lacking exon 9. Accordingly, induction of ectopic RBM4 expression in neuronal progenitor cells increased Mash1 expression and promoted cell differentiation. Finally, we found that RBM4 was also essential for neurite outgrowth from cortical neurons in vitro. Neurite outgrowth defects of RBM4-depleted neurons were rescued by RBM4-induced exon 9–lacking Numb isoforms. Therefore our findings indicate that RBM4 modulates exon selection of Numb to generate isoforms that promote neuronal cell differentiation and neurite outgrowth.     

RBM5 and p53 expression after rat spinal cord injury: Implications for neuronal apoptosis

RBM5 (RNA-binding motif protein 5), a nuclear RNA binding protein, is known to trigger apoptosis and induce cell cycle arrest by regulating the activity of the tumor suppressor protein p53. However, its expression and function in spinal cord injury (SCI) are still unknown. To investigate whether RBM5 is involved in central nervous system injury and repair, we performed an acute SCI model in adult rats in this study. Our results showed RBM5 was unregulated significantly after SCI, which was accompanied with an increase in the levels of apoptotic proteins such as p53, Bax, and active caspase-3. Immunofluorescent labeling also showed that traumatic SCI induced RBM5 location changes and co-localization with active caspase-3 in neurons. To further probe the role of RBM5, a neuronal cell line PC12 was employed to establish an apoptotic model. Knockdown of RBM5 apparently decreased the level of p53 as well as active caspase-3, demonstrating its pro-apoptotic role in neurons by regulating expressions of p53 and caspase-3. Taken together, our findings indicate that RBM5 promotes neuronal apoptosis through modulating p53 signaling pathway following SCI.     

The information theory of developmental pruning: Optimizing global network architectures using local synaptic rules

During development, biological neural networks produce more synapses and neurons than needed. Many of these synapses and neurons are later removed in a process known as neural pruning. Why networks should initially be over-populated, and the processes that determine which synapses and neurons are ultimately pruned, remains unclear. We study the mechanisms and significance of neural pruning in model neural networks. In a deep Boltzmann machine model of sensory encoding, we find that (1) synaptic pruning is necessary to learn efficient network architectures that retain computationally-relevant connections, (2) pruning by synaptic weight alone does not optimize network size and (3) pruning based on a locally-available measure of importance based on Fisher information allows the network to identify structurally important vs. unimportant connections and neurons. This locally-available measure of importance has a biological interpretation in terms of the correlations between presynaptic and postsynaptic neurons, and implies an efficient activity-driven pruning rule. Overall, we show how local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. We relate these findings to biology as follows: (I) Synaptic over-production is necessary for activity-dependent connectivity optimization. (II) In networks that have more neurons than needed, cells compete for activity, and only the most important and selective neurons are retained. (III) Cells may also be pruned due to a loss of synapses on their axons. This occurs when the information they convey is not relevant to the target population.     

RBM10: Harmful or helpful‐many factors to consider

RBM10 is an RNA binding motif (RBM) protein expressed in most, if not all, human and animal cells. Interest in RBM10 is rapidly increasing and its clinical importance is highlighted by its identification as the causative agent of TARP syndrome, a developmental condition that significantly impacts affected children. RBM10's cellular functions are beginning to be explored, with initial studies demonstrating a tumor suppressor role. Very recently, however, contradictory results have emerged, suggesting a tumor promoter role for RBM10. In this review, we describe the current state of knowledge on RBM10, and address this dichotomy in RBM10 function. Furthermore, we discuss what may be regulating RBM10 function, particularly the importance of RBM10 alternative splicing, and the relationship between RBM10 and its paralogue, RBM5. As RBM10‐related work is gaining momentum, it is critical that the various aspects of RBM10 molecular biology revealed by recent studies be considered moving forward. It is only if these recent advances in RBM10 structure and function are considered that a clearer insight into RBM10 function, and the disease states with which RBM10 mutation is associated, will be gained.