Temporal population code of concurrent vocal signals in the auditory midbrain

Unique patterns of spike activity across neuron populations have been implicated in the coding of complex sensory stimuli. Delineating the patterns of neural activity in response to varying stimulus parameters and their relationships to the tuning characteristics of individual neurons is essential to ascertaining the nature of population coding within the brain. Here, we address these points in the midbrain coding of concurrent vocal signals of a sound-producing fish, the plainfin midshipman. Midshipman produce multiharmonic vocalizations which frequently overlap to produce beats. We used multivariate statistical analysis from single-unit recordings across multiple animals to assess the presence of a temporal population code. Our results show that distinct patterns of temporal activity emerge among midbrain neurons in response to concurrent signals that vary in their difference frequency. These patterns can serve to code beat difference frequencies. The patterns directly result from the differential temporal coding of difference frequency by individual neurons. Difference frequency encoding, based on temporal patterns of activity, could permit the segregation of concurrent vocal signals on time scales shorter than codes requiring averaging. Given the ubiquity across vertebrates of auditory midbrain tuning to the temporal structure of acoustic signals, a similar temporal population code is likely present in other species.     

Maximum decoding abilities of temporal patterns and synchronized firings: application to auditory neurons responding to click trains and amplitude modulated white noise

Simultaneous recordings of an increasing number of neurons have recently become available, but few methods have been proposed to handle this activity. Here, we extract and investigate all the possible temporal neural activity patterns based on synchronized firings of neurons recorded on multiple electrodes, or based on bursts of single-electrode activity in cat primary auditory cortex. We apply this to responses to periodic click trains or sinusoïdal amplitude modulated noise by obtaining for each pattern its temporal modulation transfer function. An algorithm that maximizes the mutual information between all patterns and stimuli subsequently leads to the identification of patterns that optimally decode modulation frequency (MF). We show that stimulus information contained in multi-electrode synchronized firing is not redundant with single-electrode firings and leads to improved efficiency of MF decoding. We also show that the combined use of firing rate and temporal codes leads to a better discrimination of the MF.     

Extracting temporal relationships between weakly coupled peptidergic and motoneuronal signaling: Application to Drosophila ecdysis behavior

Neuromodulators, such as neuropeptides, can regulate and reconfigure neural circuits to alter their output, affecting in this way animal physiology and behavior. The interplay between the activity of neuronal circuits, their modulation by neuropeptides, and the resulting behavior, is still poorly understood. Here, we present a quantitative framework to study the relationships between the temporal pattern of activity of peptidergic neurons and of motoneurons during Drosophila ecdysis behavior, a highly stereotyped motor sequence that is critical for insect growth. We analyzed, in the time and frequency domains, simultaneous intracellular calcium recordings of peptidergic CCAP (crustacean cardioactive peptide) neurons and motoneurons obtained from isolated central nervous systems throughout fictive ecdysis behavior induced ex vivo by Ecdysis triggering hormone. We found that the activity of both neuronal populations is tightly coupled in a cross-frequency manner, suggesting that CCAP neurons modulate the frequency of motoneuron firing. To explore this idea further, we used a probabilistic logistic model to show that calcium dynamics in CCAP neurons can predict the oscillation of motoneurons, both in a simple model and in a conductance-based model capable of simulating many features of the observed neural dynamics. Finally, we developed an algorithm to quantify the motor behavior observed in videos of pupal ecdysis, and compared their features to the patterns of neuronal calcium activity recorded ex vivo. We found that the motor activity of the intact animal is more regular than the motoneuronal activity recorded from ex vivo preparations during fictive ecdysis behavior; the analysis of the patterns of movement also allowed us to identify a new post-ecdysis phase.     

Timing as an intrinsic property of neural networks: evidence from in vivo and in vitro experiments

The discrimination and production of temporal patterns on the scale of hundreds of milliseconds are critical to sensory and motor processing. Indeed, most complex behaviours, such as speech comprehension and production, would be impossible in the absence of sophisticated timing mechanisms. Despite the importance of timing to human learning and cognition, little is known about the underlying mechanisms, in particular whether timing relies on specialized dedicated circuits and mechanisms or on general and intrinsic properties of neurons and neural circuits. Here, we review experimental data describing timing and interval-selective neurons in vivo and in vitro. We also review theoretical models of timing, focusing primarily on the state-dependent network model, which proposes that timing in the subsecond range relies on the inherent time-dependent properties of neurons and the active neural dynamics within recurrent circuits. Within this framework, time is naturally encoded in populations of neurons whose pattern of activity is dynamically changing in time. Together, we argue that current experimental and theoretical studies provide sufficient evidence to conclude that at least some forms of temporal processing reflect intrinsic computations based on local neural network dynamics.     

Partial correlation analysis for the identification of synaptic connections

In this paper, we investigate the use of partial correlation analysis for the identification of functional neural connectivity from simultaneously recorded neural spike trains. Partial correlation analysis allows one to distinguish between direct and indirect connectivities by removing the portion of the relationship between two neural spike trains that can be attributed to linear relationships with recorded spike trains from other neurons. As an alternative to the common frequency domain approach based on the partial spectral coherence we propose a new statistic in the time domain. The new scaled partial covariance density provides additional information on the direction and the type, excitatory or inhibitory, of the connectivities. In simulation studies, we investigated the power and limitations of the new statistic. The simulations show that the detectability of various connectivity patterns depends on various parameters such as connectivity strength and background activity. In particular, the detectability decreases with the number of neurons included in the analysis and increases with the recording time. Further, we show that the method can also be used to detect multiple direct connectivities between two neurons. Finally, the methods of this paper are illustrated by an application to neurophysiological data from spinal dorsal horn neurons.     

On the Number of Neurons and Time Scale of Integration Underlying the Formation of Percepts in the Brain

All of our perceptual experiences arise from the activity of neural populations. Here we study the formation of such percepts under the assumption that they emerge from a linear readout, i.e., a weighted sum of the neurons’ firing rates. We show that this assumption constrains the trial-to-trial covariance structure of neural activities and animal behavior. The predicted covariance structure depends on the readout parameters, and in particular on the temporal integration window w and typical number of neurons K used in the formation of the percept. Using these predictions, we show how to infer the readout parameters from joint measurements of a subject’s behavior and neural activities. We consider three such scenarios: (1) recordings from the complete neural population, (2) recordings of neuronal sub-ensembles whose size exceeds K, and (3) recordings of neuronal sub-ensembles that are smaller than K. Using theoretical arguments and artificially generated data, we show that the first two scenarios allow us to recover the typical spatial and temporal scales of the readout. In the third scenario, we show that the readout parameters can only be recovered by making additional assumptions about the structure of the full population activity. Our work provides the first thorough interpretation of (feed-forward) percept formation from a population of sensory neurons. We discuss applications to experimental recordings in classic sensory decision-making tasks, which will hopefully provide new insights into the nature of perceptual integration.     

Visual pattern discrimination by population retinal ganglion cells’ activities during natural movie stimulation

In the visual system, neurons often fire in synchrony, and it is believed that synchronous activities of group neurons are more efficient than single cell response in transmitting neural signals to down-stream neurons. However, whether dynamic natural stimuli are encoded by dynamic spatiotemporal firing patterns of synchronous group neurons still needs to be investigated. In this paper we recorded the activities of population ganglion cells in bullfrog retina in response to time-varying natural images (natural scene movie) using multi-electrode arrays. In response to some different brief section pairs of the movie, synchronous groups of retinal ganglion cells (RGCs) fired with similar but different spike events. We attempted to discriminate the movie sections based on temporal firing patterns of single cells and spatiotemporal firing patterns of the synchronous groups of RGCs characterized by a measurement of subsequence distribution discrepancy. The discrimination performance was assessed by a classification method based on Support Vector Machines. Our results show that different movie sections of the natural movie elicited reliable dynamic spatiotemporal activity patterns of the synchronous RGCs, which are more efficient in discriminating different movie sections than the temporal patterns of the single cells’ spike events. These results suggest that, during natural vision, the down-stream neurons may decode the visual information from the dynamic spatiotemporal patterns of the synchronous group of RGCs’ activities.     

A Neural Population Model Incorporating Dopaminergic Neurotransmission during Complex Voluntary Behaviors

Assessing brain activity during complex voluntary motor behaviors that require the recruitment of multiple neural sites is a field of active research. Our current knowledge is primarily based on human brain imaging studies that have clear limitations in terms of temporal and spatial resolution. We developed a physiologically informed non-linear multi-compartment stochastic neural model to simulate functional brain activity coupled with neurotransmitter release during complex voluntary behavior, such as speech production. Due to its state-dependent modulation of neural firing, dopaminergic neurotransmission plays a key role in the organization of functional brain circuits controlling speech and language and thus has been incorporated in our neural population model. A rigorous mathematical proof establishing existence and uniqueness of solutions to the proposed model as well as a computationally efficient strategy to numerically approximate these solutions are presented. Simulated brain activity during the resting state and sentence production was analyzed using functional network connectivity, and graph theoretical techniques were employed to highlight differences between the two conditions. We demonstrate that our model successfully reproduces characteristic changes seen in empirical data between the resting state and speech production, and dopaminergic neurotransmission evokes pronounced changes in modeled functional connectivity by acting on the underlying biological stochastic neural model. Specifically, model and data networks in both speech and rest conditions share task-specific network features: both the simulated and empirical functional connectivity networks show an increase in nodal influence and segregation in speech over the resting state. These commonalities confirm that dopamine is a key neuromodulator of the functional connectome of speech control. Based on reproducible characteristic aspects of empirical data, we suggest a number of extensions of the proposed methodology building upon the current model.     

Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.     

用电压敏感染料光学记录膜电位

应用传统电生理方法如微电极和膜片钳技术,在记录较小的神经细胞和纤细的神经突起膜电位及同步记录神经细胞群的电活动等方面目前仍是一大难题。随着生理科学和神经生物学的发展,利用电压敏感染料光学记录膜电位技术已成为一种较为理想的新手段。本文对光学记录膜电位技术的发展史、染料特性和作用机制、光学成像及膜电位记录原理、目前的光学方法中某些不足及未来前景等做了较系统的介绍,并且简述了光学记录膜电位在电生理和神经生物学中的应用。     

Encoding time in neural dynamic regimes with distinct computational tradeoffs

Converging evidence suggests the brain encodes time in dynamic patterns of neural activity, including neural sequences, ramping activity, and complex dynamics. Most temporal tasks, however, require more than just encoding time, and can have distinct computational requirements including the need to exhibit temporal scaling, generalize to novel contexts, or robustness to noise. It is not known how neural circuits can encode time and satisfy distinct computational requirements, nor is it known whether similar patterns of neural activity at the population level can exhibit dramatically different computational or generalization properties. To begin to answer these questions, we trained RNNs on two timing tasks based on behavioral studies. The tasks had different input structures but required producing identically timed output patterns. Using a novel framework we quantified whether RNNs encoded two intervals using either of three different timing strategies: scaling, absolute, or stimulus-specific dynamics. We found that similar neural dynamic patterns at the level of single intervals, could exhibit fundamentally different properties, including, generalization, the connectivity structure of the trained networks, and the contribution of excitatory and inhibitory neurons. Critically, depending on the task structure RNNs were better suited for generalization or robustness to noise. Further analysis revealed different connection patterns underlying the different regimes. Our results predict that apparently similar neural dynamic patterns at the population level (e.g., neural sequences) can exhibit fundamentally different computational properties in regards to their ability to generalize to novel stimuli and their robustness to noise—and that these differences are associated with differences in network connectivity and distinct contributions of excitatory and inhibitory neurons. We also predict that the task structure used in different experimental studies accounts for some of the experimentally observed variability in how networks encode time.     

Connectivity and dynamics in the olfactory bulb

Dendrodendritic interactions between excitatory mitral cells and inhibitory granule cells in the olfactory bulb create a dense interaction network, reorganizing sensory representations of odors and, consequently, perception. Large-scale computational models are needed for revealing how the collective behavior of this network emerges from its global architecture. We propose an approach where we summarize anatomical information through dendritic geometry and density distributions which we use to calculate the connection probability between mitral and granule cells, while capturing activity patterns of each cell type in the neural dynamical systems theory of Izhikevich. In this way, we generate an efficient, anatomically and physiologically realistic large-scale model of the olfactory bulb network. Our model reproduces known connectivity between sister vs. non-sister mitral cells; measured patterns of lateral inhibition; and theta, beta, and gamma oscillations. The model in turn predicts testable relationships between network structure and several functional properties, including lateral inhibition, odor pattern decorrelation, and LFP oscillation frequency. We use the model to explore the influence of cortex on the olfactory bulb, demonstrating possible mechanisms by which cortical feedback to mitral cells or granule cells can influence bulbar activity, as well as how neurogenesis can improve bulbar decorrelation without requiring cell death. Our methodology provides a tractable tool for other researchers.     

Temporal encoding in a nervous system

We examined the extent to which temporal encoding may be implemented by single neurons in the cercal sensory system of the house cricket Acheta domesticus. We found that these neurons exhibit a greater-than-expected coding capacity, due in part to an increased precision in brief patterns of action potentials. We developed linear and non-linear models for decoding the activity of these neurons. We found that the stimuli associated with short-interval patterns of spikes (ISIs of 8 ms or less) could be predicted better by second-order models as compared to linear models. Finally, we characterized the difference between these linear and second-order models in a low-dimensional subspace, and showed that modification of the linear models along only a few dimensions improved their predictive power to parity with the second order models. Together these results show that single neurons are capable of using temporal patterns of spikes as fundamental symbols in their neural code, and that they communicate specific stimulus distributions to subsequent neural structures.     

The locust olfactory system as a case study for modeling dynamics of neurobiological networks: from discrete time neurons to continuous time neurons

Both chaotic and periodic activities are observed in networks of the central nervous systems. We choose the locust olfactory system as a good case study to analyze the relationships between networks' structure and the types of dynamics involved in coding mechanisms. In our modeling approach, we first build a fully connected recurrent network of synchronously updated McCulloch and Pitts neurons (MC-P type). In order to measure the use of the temporal dimension in the complex spatio-temporal patterns produced by the networks, we have defined an index the Normalized Euclidian Distance NED. We find that for appropriate parameters of input and connectivity, when adding some strong connections to the initial random synaptic matrices, it was easy to get the emergence of both robust oscillations and distributed synchrony in the spatiotemporal patterns. Then, in order to validate the MC-P model as a tool for analysis for network properties, we examine the dynamic behavior of networks of continuous time model neuron (Izhikevitch Integrate and Fire model -IFI-), implementing the same network characteristics. In both models, similarly to biological PN, the activity of excitatory neurons are phase-locked to different cycles of oscillations which remind the ones of the local field potential (LFP), and nevertheless exhibit dynamic behavior complex enough to be the basis of spatio-temporal codes.     

Synchronization without oscillatory neurons

Experimental results suggest that neurons in the cortex synchronize their action potentials on the millisecond time scale. More importantly this binding expresses functional relationships between the neurons. A model of neuronal interactions is proposed in which simultaneous discharges of neurons develop through specialized synaptic circuits. As an important prerequisite for this synchronization it is demonstrated that SynFire chains, generating different levels of excitation, propagate their activity waves at distinct velocities. Two chains were coupled by excitatory synapses and their activity was initiated at different times. Due to synaptic interactions, activity in the earlier-initiated chain accelerates propagation in the other chain until the two activity waves are synchronized. Compared with several neural network models with oscillatory units, physiologically more plausible neurons are simulated. It is still under debate whether neurons in the cortex show oscillatory dischargesper se. In particular, a high rate of noise relative to very weak synaptic gains cannot impair our results in the neural network simulations.     

Classification using functional data analysis for temporal gene expression data

MOTIVATION: Temporal gene expression profiles provide an important characterization of gene function, as biological systems are predominantly developmental and dynamic. We propose a method of classifying collections of temporal gene expression curves in which individual expression profiles are modeled as independent realizations of a stochastic process. The method uses a recently developed functional logistic regression tool based on functional principal components, aimed at classifying gene expression curves into known gene groups. The number of eigenfunctions in the classifier can be chosen by leave-one-out cross-validation with the aim of minimizing the classification error. RESULTS: We demonstrate that this methodology provides low-error-rate classification for both yeast cell-cycle gene expression profiles and Dictyostelium cell-type specific gene expression patterns. It also works well in simulations. We compare our functional principal components approach with a B-spline implementation of functional discriminant analysis for the yeast cell-cycle data and simulations. This indicates comparative advantages of our approach which uses fewer eigenfunctions/base functions. The proposed methodology is promising for the analysis of temporal gene expression data and beyond. AVAILABILITY: MATLAB programs are available upon request.     

Activity-dependent enhancement in the reliability of correlated spike timings in cultured cortical neurons

To study the use-dependent modification of activity in neural networks, we investigated the spike timing by simultaneously recording activity at multiple sites in a network of cultured cortical neurons. We used dynamical analysis to study the temporal structure of spike trains and the activity-dependent changes in the reliability and reproducibility of spike patterns evoked by a stimulus. We also used cross-correlation analysis to evaluate the interactions of neuron pairs. Our main conclusions are that even when no obvious change in spike numbers can be seen, use-dependent modification occurs, either enhancing or reducing in the reliability and reproducibility of spike trains evoked by a stimulus, and the fine temporal structure of stimulus-evoked spike trains and interactions between neurons are also modified by tetanic stimulation. Received: 25 February 1998 / Accepted in revised form: 24 August 1998     

Oscillation and coding in a formal neural network considered as a guide for plausible simulations of the insect olfactory system

For the analysis of coding mechanisms in the insect olfactory system, a fully connected network of synchronously updated McCulloch and Pitts neurons (MC-P type) was developed [Quenet, B., Horn, D., 2003. The dynamic neural filter: a binary model of spatio-temporal coding. Neural Comput. 15 (2), 309-329]. Considering the update time as an intrinsic clock, this "Dynamic Neural Filter" (DNF), which maps regions of input space into spatio-temporal sequences of neuronal activity, is able to produce exact binary codes extracted from the synchronized activities recorded at the level of projection neurons (PN) in the locust antennal lobe (AL) in response to different odors [Wehr, M., Laurent, G., 1996. Odor encoding by temporal sequences of firing in oscillating neural assemblies. Nature 384, 162-166]. Here, in a first step, we separate the populations of PN and local inhibitory neurons (LN) and use the DNF as a guide for simulations based on biological plausible neurons (Hodgkin-Huxley: H-H type). We show that a parsimonious network of 10 H-H neurons generates action potentials whose timing represents the required codes. In a second step, we construct a new type of DNF in order to study the population dynamics when different delays are taken into account. We find synaptic matrices which lead to both the emergence of robust oscillations and spatio-temporal patterns, using a formal criterion, based on a Normalized Euclidian Distance (NED), in order to measure the use of the temporal dimension as a coding dimension by the DNF. Similarly to biological PN, the activity of excitatory neurons in the model can be both phase-locked to different cycles of oscillations which remind local field potential (LFP), and nevertheless exhibit dynamic behavior complex enough to be the basis of spatio-temporal codes.     

Biodiversity and ecosystem functioning in aquatic microbial systems: a new analysis of temporal variation and species richness-predictability relations

Studies of microbial communities from aquatic ecosystems provide important insights into relations between various aspects of ecosystem functioning and changes in biodiversity. Aquatic microbial systems provide a valuable counterpoint to studies of terrestrial systems, because patterns reflect consequences of interactions occurring over many generations of community development, and are unlikely to represent artifacts of the initial conditions established in experimental communities. In this paper we re-analyse our previously published data to separate the contributions of temporal and spatial variation to overall variation in ecosystem functioning. A new analysis based on re-sampling confirms a negative relationship between richness and the variability of one ecosystem process, carbon dioxide flux. The negative relationship reflects high variation among communities of low species richness, rather than high temporal variation within communities of low richness. We also review the various transformations and summary statistics proposed as alternate measures of variability in ecosystem functioning, to point out that different measures are often appropriate for different kinds of data. Finally, we conclude that arguments about the cosmopolitan distribution of microbes do not preclude the existence of important relations between microbial species richness and ecosystem functioning.     

Model-checking ecological state-transition graphs

Model-checking is a methodology developed in computer science to automatically assess the dynamics of discrete systems, by checking if a system modelled as a state-transition graph satisfies a dynamical property written as a temporal logic formula. The dynamics of ecosystems have been drawn as state-transition graphs for more than a century, ranging from state-and-transition models to assembly graphs. Model-checking can provide insights into both empirical data and theoretical models, as long as they sum up into state-transition graphs. While model-checking proved to be a valuable tool in systems biology, it remains largely underused in ecology apart from precursory applications.This article proposes to address this situation, through an inventory of existing ecological STGs and an accessible presentation of the model-checking methodology. This overview is illustrated by the application of model-checking to assess the dynamics of a vegetation pathways model. We select management scenarios by model-checking Computation Tree Logic formulas representing management goals and built from a proposed catalogue of patterns. In discussion, we sketch bridges between existing studies in ecology and available model-checking frameworks. In addition to the automated analysis of ecological state-transition graphs, we believe that defining ecological concepts with temporal logics could help clarify and compare them.