Simple codes versus efficient codes

Decoding neurobiological spike trains using recurrent neural networks: a case study with electrophysiological auditory cortex recordings

Recent advancements in multielectrode methods and spike-sorting algorithms enable the in vivo recording of the activities of many neurons at a high temporal resolution. These datasets offer new opportunities in the investigation of the biological neural code, including the direct testing of specific coding hypotheses, but they also reveal the limitations of present decoder algorithms. Classical methods rely on a manual feature extraction step, resulting in a feature vector, like the firing rates of an ensemble of neurons. In this paper, we present a recurrent neural-network-based decoder and evaluate its performance on experimental and artificial datasets. The experimental datasets were obtained by recording the auditory cortical responses of rats exposed to sound stimuli, while the artificial datasets represent preset encoding schemes. The task of the decoder was to classify the action potential timeseries according to the corresponding sound stimuli. It is illustrated that, depending on the coding scheme, the performance of the recurrent-network-based decoder can exceed the performance of the classical methods. We also show how randomized copies of the training datasets can be used to reveal the role of candidate spike-train features. We conclude that artificial neural network decoders can be a useful alternative to classical population vector-based techniques in studies of the biological neural code.

Active dendrites enable strong but sparse inputs to determine orientation selectivity

The dendrites of neocortical pyramidal neurons are excitable. However, it is unknown how synaptic inputs engage nonlinear dendritic mechanisms during sensory processing in vivo, and how they in turn influence action potential output. Here, we provide a quantitative account of the relationship between synaptic inputs, nonlinear dendritic events, and action potential output. We developed a detailed pyramidal neuron model constrained by in vivo dendritic recordings. We drive this model with realistic input patterns constrained by sensory responses measured in vivo and connectivity measured in vitro. We show mechanistically that under realistic conditions, dendritic Na+ and NMDA spikes are the major determinants of neuronal output in vivo. We demonstrate that these dendritic spikes can be triggered by a surprisingly small number of strong synaptic inputs, in some cases even by single synapses. We predict that dendritic excitability allows the 1% strongest synaptic inputs of a neuron to control the tuning of its output. Active dendrites therefore allow smaller subcircuits consisting of only a few strongly connected neurons to achieve selectivity for specific sensory features.

Degeneracy in hippocampal physiology and plasticity

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis that point to the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve the conjoint goals of encoding and homeostasis without cross-interferences. We postulate that biological complexity, involving interactions among the numerous parameters spanning different scales of analysis, could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encoding-homeostasis system in accomplishing its tasks in an input- and state-dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals.

Temporal coding and rate remapping: Representation of nonspatial information in the hippocampus

Hippocampal place cells represent nonspatial information through a process called rate remapping, which involves a change in the firing rate of a place cell without changes in its spatial specificity. However, many hippocampal phenomena occur on very short time scales over which long-term average firing rates are not an appropriate description of activity. To understand how rate remapping relates to fine-scale temporal firing phenomena, we asked how rate remapping affected burst firing and trial-to-trial spike count variability. In addition, we looked at how rate remapping relates to the theta-frequency oscillations of the hippocampus, which are thought to temporally organize firing on time scales faster than 100 ms. We found that theta phase coding was preserved through changes in firing rate due to rate remapping. Interestingly, rate remapping in CA1 in response to task demands preferentially occurred during the first half of the theta cycle. The other half of the theta cycle contained preferential expression of phase precession, a phenomenon associated with place cell sequences, in agreement with previous results. This difference of place cell coding during different halves of the theta cycle supports recent theoretical suggestions that different processes occur during the two halves of the theta cycle. The differentiation between the halves of the theta cycle was not clear in recordings from CA3 during rate remapping induced by task-irrelevant sensory changes. These findings provide new insight into the way that temporal coding is utilized in the hippocampus and how rate remapping is expressed through that temporal code.

Sensory Metrics of Neuromechanical Trust

Today digital sources supply a historically unprecedented component of human sensorimotor data, the consumption of which is correlated with poorly understood maladies such as Internet addiction disorder and Internet gaming disorder. Because both natural and digital sensorimotor data share common mathematical descriptions, one can quantify our informational sensorimotor needs using the signal processing metrics of entropy, noise, dimensionality, continuity, latency, and bandwidth. Such metrics describe in neutral terms the informational diet human brains require to self-calibrate, allowing individuals to maintain trusting relationships. With these metrics, we define the trust humans experience using the mathematical language of computational models, that is, as a primitive statistical algorithm processing finely grained sensorimotor data from neuromechanical interaction. This definition of neuromechanical trust implies that artificial sensorimotor inputs and interactions that attract low-level attention through frequent discontinuities and enhanced coherence will decalibrate a brain's representation of its world over the long term by violating the implicit statistical contract for which self-calibration evolved. Our hypersimplified mathematical understanding of human sensorimotor processing as multiscale, continuous-time vibratory interaction allows equally broad-brush descriptions of failure modes and solutions. For example, we model addiction in general as the result of homeostatic regulation gone awry in novel environments (sign reversal) and digital dependency as a sub-case in which the decalibration caused by digital sensorimotor data spurs yet more consumption of them. We predict that institutions can use these sensorimotor metrics to quantify media richness to improve employee well-being; that dyads and family-size groups will bond and heal best through low-latency, high-resolution multisensory interaction such as shared meals and reciprocated touch; and that individuals can improve sensory and sociosensory resolution through deliberate sensory reintegration practices. We conclude that we humans are the victims of our own success, our hands so skilled they fill the world with captivating things, our eyes so innocent they follow eagerly.

Temporal pairwise spike correlations fully capture single-neuron information

To crack the neural code and read out the information neural spikes convey, it is essential to understand how the information is coded and how much of it is available for decoding. To this end, it is indispensable to derive from first principles a minimal set of spike features containing the complete information content of a neuron. Here we present such a complete set of coding features. We show that temporal pairwise spike correlations fully determine the information conveyed by a single spiking neuron with finite temporal memory and stationary spike statistics. We reveal that interspike interval temporal correlations, which are often neglected, can significantly change the total information. Our findings provide a conceptual link between numerous disparate observations and recommend shifting the focus of future studies from addressing firing rates to addressing pairwise spike correlation functions as the primary determinants of neural information.

ASSET: Analysis of Sequences of Synchronous Events in Massively Parallel Spike Trains

With the ability to observe the activity from large numbers of neurons simultaneously using modern recording technologies, the chance to identify sub-networks involved in coordinated processing increases. Sequences of synchronous spike events (SSEs) constitute one type of such coordinated spiking that propagates activity in a temporally precise manner. The synfire chain was proposed as one potential model for such network processing. Previous work introduced a method for visualization of SSEs in massively parallel spike trains, based on an intersection matrix that contains in each entry the degree of overlap of active neurons in two corresponding time bins. Repeated SSEs are reflected in the matrix as diagonal structures of high overlap values. The method as such, however, leaves the task of identifying these diagonal structures to visual inspection rather than to a quantitative analysis. Here we present ASSET (Analysis of Sequences of Synchronous EvenTs), an improved, fully automated method which determines diagonal structures in the intersection matrix by a robust mathematical procedure. The method consists of a sequence of steps that i) assess which entries in the matrix potentially belong to a diagonal structure, ii) cluster these entries into individual diagonal structures and iii) determine the neurons composing the associated SSEs. We employ parallel point processes generated by stochastic simulations as test data to demonstrate the performance of the method under a wide range of realistic scenarios, including different types of non-stationarity of the spiking activity and different correlation structures. Finally, the ability of the method to discover SSEs is demonstrated on complex data from large network simulations with embedded synfire chains. Thus, ASSET represents an effective and efficient tool to analyze massively parallel spike data for temporal sequences of synchronous activity.

Neural Synchrony, Axonal Path Lengths, and General Anesthesia: A Hypothesis

Despite decades of research, the mechanism by which general anesthetics produce loss of consciousness remains mysterious. A clue may be provided by the evidence that synchronous firing of cortical neurons underlies higher forms of neural processing. In order for these synchrony codes to be precise, transmission time must be independent of path length over all the connected sites between any two cortical areas. Because path lengths vary, developmental mechanisms must compensate for the resulting delay variations. Delay variations could be detected by spike-timing-dependent cues and compensation implemented by systematic changes in axon diameter, myelin thickness, or internodal distance. Anesthetics have been shown to increase conduction velocity in myelinated fibers and may therefore disrupt path-length compensation by changing velocities by different amounts in different types of axon. This simple and testable theory explains why anesthetics interfere selectively with higher cognitive functions but leave those dominated by rate-based firing relatively intact.

Nociceptor Sensitization Depends on Age and Pain Chronicity(1,2,3)

Peripheral inflammation causes mechanical pain behavior and increased action potential firing. However, most studies examine inflammatory pain at acute, rather than chronic time points, despite the greater burden of chronic pain on patient populations, especially aged individuals. Furthermore, there is disagreement in the field about whether primary afferents contribute to chronic pain. Therefore, we sought to evaluate the contribution of nociceptor activity to the generation of pain behaviors during the acute and chronic phases of inflammation in both young and aged mice. We found that both young (2 months old) and aged (>18 months old) mice exhibited prominent pain behaviors during both acute (2 day) and chronic (8 week) inflammation. However, young mice exhibited greater behavioral sensitization to mechanical stimuli than their aged counterparts. Teased fiber recordings in young animals revealed a twofold mechanical sensitization in C fibers during acute inflammation, but an unexpected twofold reduction in firing during chronic inflammation. Responsiveness to capsaicin and mechanical responsiveness of A-mechanonociceptor (AM) fibers were also reduced chronically. Importantly, this lack of sensitization in afferent firing during chronic inflammation occurred even as these inflamed mice exhibited continued behavioral sensitization. Interestingly, C fibers from inflamed aged animals showed no change in mechanical firing compared with controls during either the acute or chronic inflammatory phases, despite strong behavioral sensitization to mechanical stimuli at these time points. These results reveal the following two important findings: (1) nociceptor sensitization to mechanical stimulation depends on age and the chronicity of injury; and (2) maintenance of chronic inflammatory pain does not rely on enhanced peripheral drive.

Philosophy of the Spike: Rate-Based vs. Spike-Based Theories of the Brain

Does the brain use a firing rate code or a spike timing code? Considering this controversial question from an epistemological perspective, I argue that progress has been hampered by its problematic phrasing. It takes the perspective of an external observer looking at whether those two observables vary with stimuli, and thereby misses the relevant question: which one has a causal role in neural activity? When rephrased in a more meaningful way, the rate-based view appears as an ad hoc methodological postulate, one that is practical but with virtually no empirical or theoretical support.

Dynamic synchronization of ongoing neuronal activity across spinal segments regulates sensory information flow

Previous studies on the correlation between spontaneous cord dorsum potentials recorded in the lumbar spinal segments of anaesthetized cats suggested the operation of a population of dorsal horn neurones that modulates, in a differential manner, transmission along pathways mediating Ib non-reciprocal postsynaptic inhibition and pathways mediating primary afferent depolarization and presynaptic inhibition. In order to gain further insight into the possible neuronal mechanisms that underlie this process, we have measured changes in the correlation between the spontaneous activity of individual dorsal horn neurones and the cord dorsum potentials associated with intermittent activation of these inhibitory pathways. We found that high levels of neuronal synchronization within the dorsal horn are associated with states of incremented activity along the pathways mediating presynaptic inhibition relative to pathways mediating Ib postsynaptic inhibition. It is suggested that ongoing changes in the patterns of functional connectivity within a distributed ensemble of dorsal horn neurones play a relevant role in the state-dependent modulation of impulse transmission along inhibitory pathways, among them those involved in the central control of sensory information. This feature would allow the same neuronal network to be involved in different functional tasks.

When less is more: non-monotonic spike sequence processing in neurons

Fundamental response properties of neurons centrally underly the computational capabilities of both individual nerve cells and neural networks. Most studies on neuronal input-output relations have focused on continuous-time inputs such as constant or noisy sinusoidal currents. Yet, most neurons communicate via exchanging action potentials (spikes) at discrete times. Here, we systematically analyze the stationary spiking response to regular spiking inputs and reveal that it is generically non-monotonic. Our theoretical analysis shows that the underlying mechanism relies solely on a combination of the discrete nature of the communication by spikes, the capability of locking output to input spikes and limited resources required for spike processing. Numerical simulations of mathematically idealized and biophysically detailed models, as well as neurophysiological experiments confirm and illustrate our theoretical predictions.

Ex vivo cultured neuronal networks emit in vivo-like spontaneous activity

Spontaneous neuronal activity is present in virtually all brain regions, but neither its function nor spatiotemporal patterns are fully understood. Ex vivo organotypic slice cultures may offer an opportunity to investigate some aspects of spontaneous activity, because they self-restore their networks that collapsed during slicing procedures. In hippocampal networks, we compared the levels and patterns of in vivo spontaneous activity to those in acute and cultured slices. We found that the firing rates and excitatory synaptic activity in the in vivo hippocampus are more similar to those in slice cultures compared to acute slices. The soft confidence-weighted algorithm, a machine learning technique without human bias, also revealed that hippocampal slice cultures resemble the in vivo hippocampus in terms of the overall tendency of the parameters of spontaneous activity.

Cell assemblies in the cerebral cortex

Donald Hebb's concept of cell assemblies is a physiology-based idea for a distributed neural representation of behaviorally relevant objects, concepts, or constellations. In the late 70s Valentino Braitenberg started the endeavor to spell out the hypothesis that the cerebral cortex is the structure where cell assemblies are formed, maintained and used, in terms of neuroanatomy (which was his main concern) and also neurophysiology. This endeavor has been carried on over the last 30 years corroborating most of his findings and interpretations. This paper summarizes the present state of cell assembly theory, realized in a network of associative memories, and of the anatomical evidence for its location in the cerebral cortex.

The meaning of spikes from the neuron's point of view: predictive homeostasis generates the appearance of randomness

The conventional interpretation of spikes is from the perspective of an external observer with knowledge of a neuron's inputs and outputs who is ignorant of the contents of the "black box" that is the neuron. Here we consider a neuron to be an observer and we interpret spikes from the neuron's perspective. We propose both a descriptive hypothesis based on physics and logic, and a prescriptive hypothesis based on biological optimality. Our descriptive hypothesis is that a neuron's membrane excitability is "known" and the amplitude of a future excitatory postsynaptic conductance (EPSG) is "unknown". Therefore excitability is an expectation of EPSG amplitude and a spike is generated only when EPSG amplitude exceeds its expectation ("prediction error"). Our prescriptive hypothesis is that a diversity of synaptic inputs and voltage-regulated ion channels implement "predictive homeostasis", working to insure that the expectation is accurate. The homeostatic ideal and optimal expectation would be achieved when an EPSP reaches precisely to spike threshold, so that spike output is exquisitely sensitive to small variations in EPSG input. To an external observer who knows neither EPSG amplitude nor membrane excitability, spikes would appear random if the neuron is making accurate predictions. We review experimental evidence that spike probabilities are indeed maintained near an average of 0.5 under natural conditions, and we suggest that the same principles may also explain why synaptic vesicle release appears to be "stochastic". Whereas the present hypothesis accords with principles of efficient coding dating back to Barlow (1961), it contradicts decades of assertions that neural activity is substantially "random" or "noisy". The apparent randomness is by design, and like many other examples of apparent randomness, it corresponds to the ignorance of external macroscopic observers about the detailed inner workings of a microscopic system.

Toward unified hybrid simulation techniques for spiking neural networks

In the field of neural network simulation techniques, the common conception is that spiking neural network simulators can be divided in two categories: time-step-based and event-driven methods. In this letter, we look at state-of-the art simulation techniques in both categories and show that a clear distinction between both methods is increasingly difficult to define. In an attempt to improve the weak points of each simulation method, ideas of the alternative method are, sometimes unknowingly, incorporated in the simulation engine. Clearly the ideal simulation method is a mix of both methods. We formulate the key properties of such an efficient and generally applicable hybrid approach.

The influence of synaptic weight distribution on neuronal population dynamics

The manner in which different distributions of synaptic weights onto cortical neurons shape their spiking activity remains open. To characterize a homogeneous neuronal population, we use the master equation for generalized leaky integrate-and-fire neurons with shot-noise synapses. We develop fast semi-analytic numerical methods to solve this equation for either current or conductance synapses, with and without synaptic depression. We show that its solutions match simulations of equivalent neuronal networks better than those of the Fokker-Planck equation and we compute bounds on the network response to non-instantaneous synapses. We apply these methods to study different synaptic weight distributions in feed-forward networks. We characterize the synaptic amplitude distributions using a set of measures, called tail weight numbers, designed to quantify the preponderance of very strong synapses. Even if synaptic amplitude distributions are equated for both the total current and average synaptic weight, distributions with sparse but strong synapses produce higher responses for small inputs, leading to a larger operating range. Furthermore, despite their small number, such synapses enable the network to respond faster and with more stability in the face of external fluctuations.

A spike-timing-based integrated model for pattern recognition

During the past few decades, remarkable progress has been made in solving pattern recognition problems using networks of spiking neurons. However, the issue of pattern recognition involving computational process from sensory encoding to synaptic learning remains underexplored, as most existing models or algorithms target only part of the computational process. Furthermore, many learning algorithms proposed in the literature neglect or pay little attention to sensory information encoding, which makes them incompatible with neural-realistic sensory signals encoded from real-world stimuli. By treating sensory coding and learning as a systematic process, we attempt to build an integrated model based on spiking neural networks (SNNs), which performs sensory neural encoding and supervised learning with precisely timed sequences of spikes. With emerging evidence of precise spike-timing neural activities, the view that information is represented by explicit firing times of action potentials rather than mean firing rates has been receiving increasing attention. The external sensory stimulation is first converted into spatiotemporal patterns using a latency-phase encoding method and subsequently transmitted to the consecutive network for learning. Spiking neurons are trained to reproduce target signals encoded with precisely timed spikes. We show that when a supervised spike-timing-based learning is used, different spatiotemporal patterns are recognized by different spike patterns with a high time precision in milliseconds.

Rates and rhythms: a synergistic view of frequency and temporal coding in neuronal networks

In the CNS, activity of individual neurons has a small but quantifiable relationship to sensory representations and motor outputs. Coactivation of a few 10s to 100s of neurons can code sensory inputs and behavioral task performance within psychophysical limits. However, in a sea of sensory inputs and demand for complex motor outputs how is the activity of such small subpopulations of neurons organized? Two theories dominate in this respect: increases in spike rate (rate coding) and sharpening of the coincidence of spiking in active neurons (temporal coding). Both have computational advantages and are far from mutually exclusive. Here, we review evidence for a bias in neuronal circuits toward temporal coding and the coexistence of rate and temporal coding during population rhythm generation. The coincident expression of multiple types of gamma rhythm in sensory cortex suggests a mechanistic substrate for combining rate and temporal codes on the basis of stimulus strength.

Functional maps within a single neuron

The presence and plasticity of dendritic ion channels are well established. However, the literature is divided on what specific roles these dendritic ion channels play in neuronal information processing, and there is no consensus on why neuronal dendrites should express diverse ion channels with different expression profiles. In this review, we present a case for viewing dendritic information processing through the lens of the sensory map literature, where functional gradients within neurons are considered as maps on the neuronal topograph. Under such a framework, drawing analogies from the sensory map literature, we postulate that the formation of intraneuronal functional maps is driven by the twin objectives of efficiently encoding inputs that impinge along different dendritic locations and of retaining homeostasis in the face of changes that are required in the coding process. In arriving at this postulate, we relate intraneuronal map physiology to the vast literature on sensory maps and argue that such a metaphorical association provides a fresh conceptual framework for analyzing and understanding single-neuron information encoding. We also describe instances where the metaphor presents specific directions for research on intraneuronal maps, derived from analogous pursuits in the sensory map literature. We suggest that this perspective offers a thesis for why neurons should express and alter ion channels in their dendrites and provides a framework under which active dendrites could be related to neural coding, learning theory, and homeostasis.

Neuronal variability of MSTd neurons changes differentially with eye movement and visually related variables

Neurons in macaque cortical area MSTd are driven by visual motion and eye movement related signals. This multimodal characteristic makes MSTd an ideal system for studying the dependence of neuronal activity on different variables. Here, we analyzed the temporal structure of spiking patterns during visual motion stimulation using 2 distinct behavioral paradigms: fixation (FIX) and optokinetic response. For the FIX condition, inter- and intra-trial variability of spiking activity decreased with increasing stimulus strength, complying with a recent neurophysiological study reporting stimulus-related decline of neuronal variability. In contrast, for the optokinetic condition variability increased together with increasing eye velocity while retinal image velocity remained low. Analysis of stimulus signal variability revealed a correlation between the normalized variance of image velocity and neuronal variability, but no correlation with normalized eye velocity variance. We further show that the observed difference in neuronal variability allows classifying spike trains according to the paradigm used, even when mean firing rates (FRs) were similar. The stimulus-dependence of neuronal variability may result from the local network structure and/or the variability characteristics of the input signals, but may also reflect additional timing-based mechanisms independent of the neuron's mean FR and related to the modality driving the neuron.

Digital kinases: A cell model for sensing, integrating and making choices

Protein kinases mediate most of the signal transduction in eukaryotic cells, controlling important cellular processes. Functioning as sensors and switches, kinases play a critical role in the regulation of cell fate decisions: proliferation, differentiation or death. Cellular sensors must have signaling properties well suited for the processing and propagation of external or internal stimuli that promote irreversible processes. These properties include ultrasensitivity, hysteresis and digital responses. Ultrasensitivity means to produce a very large response to a small increase in stimulus after a threshold is crossed, hysteresis (a form of biochemical memory) means sustained activation when the stimulus has disappeared, and digital is an all-ornone response at a single cell level. These properties are present in JNK, a stress protein kinase that regulates cell death. In a recent article, we have characterized Xenopus AMPK, a stress protein kinase that controls energy levels in the cell, showing that is regulated similar to the mammalian ortholog. By using Xenopus oocytes we studied the AMPK signaling system and compared to JNK. Our work showed that AMPK is ultrasensitive to an apoptotic stimulus (hyperosmolar sorbitol) but, in contrast to JNK, does not show hysteresis. By single cell analysis we found that the response of AMPK and JNK to hyperosmolar sorbitol is all-or-none (digital) in character, and that initial graded responses of both protein kinases are converted into digital during the critical period of cytochrome c release. We proposed a model to explain the cell death program as integration of multiple digital signals from stress sensors, that now I extend to a more general model for sensing, integrating and making choices in the cell and the organism.

Suprathreshold stochastic resonance in neural processing tuned by correlation

Suprathreshold stochastic resonance (SSR) is examined in the context of integrate-and-fire neurons, with an emphasis on the role of correlation in the neuronal firing. We employed a model based on a network of spiking neurons which received synaptic inputs modeled by Poisson processes stimulated by a stepped input signal. The smoothed ensemble firing rate provided an output signal, and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons. It was found that an SSR effect was present in this context. We then examined a more biophysically plausible scenario where the noise was not controlled directly, but instead was tuned by the correlation between the inputs. The SSR effect remained present in this scenario with nonzero noise providing improved information transmission, and it was found that negative correlation between the inputs was optimal. Finally, an examination of SSR in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade-off between supratheshold and subthreshold components. We discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing.

Dual roles for spike signaling in cortical neural populations

A prominent feature of signaling in cortical neurons is that of randomness in the action potential. The output of a typical pyramidal cell can be well fit with a Poisson model, and variations in the Poisson rate repeatedly have been shown to be correlated with stimuli. However while the rate provides a very useful characterization of neural spike data, it may not be the most fundamental description of the signaling code. Recent data showing γ frequency range multi-cell action potential correlations, together with spike timing dependent plasticity, are spurring a re-examination of the classical model, since precise timing codes imply that the generation of spikes is essentially deterministic. Could the observed Poisson randomness and timing determinism reflect two separate modes of communication, or do they somehow derive from a single process? We investigate in a timing-based model whether the apparent incompatibility between these probabilistic and deterministic observations may be resolved by examining how spikes could be used in the underlying neural circuits. The crucial component of this model draws on dual roles for spike signaling. In learning receptive fields from ensembles of inputs, spikes need to behave probabilistically, whereas for fast signaling of individual stimuli, the spikes need to behave deterministically. Our simulations show that this combination is possible if deterministic signals using γ latency coding are probabilistically routed through different members of a cortical cell population at different times. This model exhibits standard features characteristic of Poisson models such as orientation tuning and exponential interval histograms. In addition, it makes testable predictions that follow from the γ latency coding.

Dynamical entropy production in spiking neuron networks in the balanced state

We demonstrate deterministic extensive chaos in the dynamics of large sparse networks of theta neurons in the balanced state. The analysis is based on numerically exact calculations of the full spectrum of Lyapunov exponents, the entropy production rate, and the attractor dimension. Extensive chaos is found in inhibitory networks and becomes more intense when an excitatory population is included. We find a strikingly high rate of entropy production that would limit information representation in cortical spike patterns to the immediate stimulus response.

Effects of correlated Gaussian noise on the mean firing rate and correlations of an electrically coupled neuronal network

In this paper, we examine the effects of correlated Gaussian noise on a two-dimensional neuronal network that is locally modeled by the Rulkov map. More precisely, we study the effects of the noise correlation on the variations of the mean firing rate and the correlations among neurons versus the noise intensity. Via numerical simulations, we show that the mean firing rate can always be optimized at an intermediate noise intensity, irrespective of the noise correlation. On the other hand, variations of the population coherence with respect to the noise intensity are strongly influenced by the ratio between local and global Gaussian noisy inputs. Biological implications of our findings are also discussed.

Higher-order correlations in non-stationary parallel spike trains: statistical modeling and inference

The extent to which groups of neurons exhibit higher-order correlations in their spiking activity is a controversial issue in current brain research. A major difficulty is that currently available tools for the analysis of massively parallel spike trains (N >10) for higher-order correlations typically require vast sample sizes. While multiple single-cell recordings become increasingly available, experimental approaches to investigate the role of higher-order correlations suffer from the limitations of available analysis techniques. We have recently presented a novel method for cumulant-based inference of higher-order correlations (CuBIC) that detects correlations of higher order even from relatively short data stretches of length T = 10-100 s. CuBIC employs the compound Poisson process (CPP) as a statistical model for the population spike counts, and assumes spike trains to be stationary in the analyzed data stretch. In the present study, we describe a non-stationary version of the CPP by decoupling the correlation structure from the spiking intensity of the population. This allows us to adapt CuBIC to time-varying firing rates. Numerical simulations reveal that the adaptation corrects for false positive inference of correlations in data with pure rate co-variation, while allowing for temporal variations of the firing rates has a surprisingly small effect on CuBICs sensitivity for correlations.

Long-term modifications in motor cortical dynamics induced by intensive practice

The planning of goal-directed movements requires sensory, temporal, and contextual information to be combined. Sensorimotor functions are embedded in large neuronal networks, but it is unclear how networks organize their activity in space and time to optimize behavior. Temporal coordination of activity in many neurons within a network, e.g., spike synchrony, might be complementary to a firing rate code, allowing efficient computation with overall less population activity. Here we asked the question whether intensive practice induces long-term modifications in the temporal structure of synchrony and firing rate at the population level. Three monkeys were trained in a delayed pointing task in which the selection of movement direction depended on correct time estimation. The synchronous firing among pairs of simultaneously recorded neurons in motor cortex was analyzed using the "unitary event" technique. The evolution of synchrony in both time, within the trial, and temporal precision was then quantified at the level of an entire population of neurons by using two different quantification techniques and compared with the population firing rate. We find that the task timing was represented in the temporal structure of significant spike synchronization at the population level. During practice, the temporal structure of synchrony was shaped, with synchrony becoming stronger and more localized in time during late experimental sessions, in parallel with an improvement in behavioral performance. Concurrently, the average population firing rate mainly decreased. Performance optimization through practice might therefore be achieved by boosting the computational contribution of spike synchrony, allowing an overall reduction in population activity.

Locally balanced dendritic integration by short-term synaptic plasticity and active dendritic conductances

The high degree of variability observed in spike trains and membrane potentials of pyramidal neurons in vivo is thought to be a consequence of a balance between excitatory and inhibitory inputs, which depends on the dynamics of the network. We simulated synaptic currents and ion channels in a reconstructed hippocampal CA1 pyramidal cell and show here that a local balance can be achieved on a dendritic branch with a different mechanism, based on presynaptic depression of quantal release interacting with active dendritic conductances. This mechanism, which does not require synaptic inhibition, allows each dendritic branch to remain sensitive to correlated synaptic inputs, induces a high degree of variability in the output spike train, and can be combined with other balance mechanisms based on network dynamics. This hypothesis makes a testable prediction for the cause of the observed variability in the firing of hippocampal place cells.

Accelerating event-driven simulation of spiking neurons with multiple synaptic time constants

The simulation of spiking neural networks (SNNs) is known to be a very time-consuming task. This limits the size of SNN that can be simulated in reasonable time or forces users to overly limit the complexity of the neuron models. This is one of the driving forces behind much of the recent research on event-driven simulation strategies. Although event-driven simulation allows precise and efficient simulation of certain spiking neuron models, it is not straightforward to generalize the technique to more complex neuron models, mostly because the firing time of these neuron models is computationally expensive to evaluate. Most solutions proposed in literature concentrate on algorithms that can solve this problem efficiently. However, these solutions do not scale well when more state variables are involved in the neuron model, which is, for example, the case when multiple synaptic time constants for each neuron are used. In this letter, we show that an exact prediction of the firing time is not required in order to guarantee exact simulation results. Several techniques are presented that try to do the least possible amount of work to predict the firing times. We propose an elegant algorithm for the simulation of leaky integrate-and-fire (LIF) neurons with an arbitrary number of (unconstrained) synaptic time constants, which is able to combine these algorithmic techniques efficiently, resulting in very high simulation speed. Moreover, our algorithm is highly independent of the complexity (i.e., number of synaptic time constants) of the underlying neuron model.

Dendritic excitability and synaptic plasticity

Most synaptic inputs are made onto the dendritic tree. Recent work has shown that dendrites play an active role in transforming synaptic input into neuronal output and in defining the relationships between active synapses. In this review, we discuss how these dendritic properties influence the rules governing the induction of synaptic plasticity. We argue that the location of synapses in the dendritic tree, and the type of dendritic excitability associated with each synapse, play decisive roles in determining the plastic properties of that synapse. Furthermore, since the electrical properties of the dendritic tree are not static, but can be altered by neuromodulators and by synaptic activity itself, we discuss how learning rules may be dynamically shaped by tuning dendritic function. We conclude by describing how this reciprocal relationship between plasticity of dendritic excitability and synaptic plasticity has changed our view of information processing and memory storage in neuronal networks.

Discharge synchrony during the transition of behavioral goal representations encoded by discharge rates of prefrontal neurons

To investigate the temporal relationship between synchrony in the discharge of neuron pairs and modulation of the discharge rate, we recorded the neuronal activity of the lateral prefrontal cortex of monkeys performing a behavioral task that required them to plan an immediate goal of action to attain a final goal. Information about the final goal was retrieved via visual instruction signals, whereas information about the immediate goal was generated internally. The synchrony of neuron pair discharges was analyzed separately from changes in the firing rate of individual neurons during a preparatory period. We focused on neuron pairs that exhibited a representation of the final goal followed by a representation of the immediate goal at a later stage. We found that changes in synchrony and discharge rates appeared to be complementary at different phases of the behavioral task. Synchrony was maximized during a specific phase in the preparatory period corresponding to a transitional stage when the neuronal activity representing the final goal was replaced with that representing the immediate goal. We hypothesize that the transient increase in discharge synchrony is an indication of a process that facilitates dynamic changes in the prefrontal neural circuits in order to undergo profound state changes.

Balanced excitatory and inhibitory inputs to cortical neurons decouple firing irregularity from rate modulations

In vivo cortical neurons are known to exhibit highly irregular spike patterns. Because the intervals between successive spikes fluctuate greatly, irregular neuronal firing makes it difficult to estimate instantaneous firing rates accurately. If, however, the irregularity of spike timing is decoupled from rate modulations, the estimate of firing rate can be improved. Here, we introduce a novel coding scheme to make the firing irregularity orthogonal to the firing rate in information representation. The scheme is valid if an interspike interval distribution can be well fitted by the gamma distribution and the firing irregularity is constant over time. We investigated in a computational model whether fluctuating external inputs may generate gamma process-like spike outputs, and whether the two quantities are actually decoupled. Whole-cell patch-clamp recordings of cortical neurons were performed to confirm the predictions of the model. The output spikes were well fitted by the gamma distribution. The firing irregularity remained approximately constant regardless of the firing rate when we injected a balanced input, in which excitatory and inhibitory synapses are activated concurrently while keeping their conductance ratio fixed. The degree of irregular firing depended on the effective reversal potential set by the balance between excitation and inhibition. In contrast, when we modulated conductances out of balance, the irregularity varied with the firing rate. These results indicate that the balanced input may improve the efficiency of neural coding by clamping the firing irregularity of cortical neurons. We demonstrate how this novel coding scheme facilitates stimulus decoding.

Temporal patterning of saccadic eye movement signals

Electrical microstimulation is used widely in experimental neurophysiology to examine causal links between specific brain areas and their behavioral functions and is used clinically to treat neurological and psychiatric disorders in patients. Typically, microstimulation is applied to local brain regions as a train of equally spaced current pulses. We were interested in the sensitivity of a neural circuit to a train of variably spaced pulses, as is observed in physiological spike trains. We compared the effect of fixed, decelerating, accelerating, and randomly varying microstimulation patterns on the likelihood and metrics of eye movements evoked from the frontal eye field of monkeys, while holding the mean interpulse interval constant. Our results demonstrate that the pattern of microstimulation pulses strongly influences the probability of evoking a saccade, as well as the metrics of the saccades themselves. Specifically, the pattern most closely resembling physiological spike trains (accelerating pattern) was most effective at evoking a saccade, three times more so than the least effective decelerating pattern. A saccade-triggered average of effective random trains confirmed the positive relationship between accelerating rate and efficacy. These results have important implications for the use of electrical microstimulation in both experimental and clinical settings and suggest a means to study the role of temporal pattern in the encoding of behavioral and cognitive functions.

Generalized rate-code model for neuron ensembles with finite populations

We have proposed a generalized Langevin-type rate-code model subjected to multiplicative noise, in order to study stationary and dynamical properties of an ensemble containing a finite number N of neurons. Calculations using the Fokker-Planck equation have shown that, owing to the multiplicative noise, our rate model yields various kinds of stationary non-Gaussian distributions such as Gamma , inverse-Gaussian-like, and log-normal-like distributions, which have been experimentally observed. The dynamical properties of the rate model have been studied with the use of the augmented moment method (AMM), which was previously proposed by the author from a macroscopic point of view for finite-unit stochastic systems. In the AMM, the original N -dimensional stochastic differential equations (DEs) are transformed into three-dimensional deterministic DEs for the means and fluctuations of local and global variables. The dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the AMM are in good agreement with those obtained by direct simulation. The synchronization in the neuronal ensemble is discussed. The variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise, which may be a conceivable origin of the observed large variability in cortical neurons.

Spike timing and reliability in cortical pyramidal neurons: effects of EPSC kinetics, input synchronization and background noise on spike timing

In vivo studies have shown that neurons in the neocortex can generate action potentials at high temporal precision. The mechanisms controlling timing and reliability of action potential generation in neocortical neurons, however, are still poorly understood. Here we investigated the temporal precision and reliability of spike firing in cortical layer V pyramidal cells at near-threshold membrane potentials. Timing and reliability of spike responses were a function of EPSC kinetics, temporal jitter of population excitatory inputs, and of background synaptic noise. We used somatic current injection to mimic population synaptic input events and measured spike probability and spike time precision (STP), the latter defined as the time window (Δt) holding 80% of response spikes. EPSC rise and decay times were varied over the known physiological spectrum. At spike threshold level, EPSC decay time had a stronger influence on STP than rise time. Generally, STP was highest (≤2.45 ms) in response to synchronous compounds of EPSCs with fast rise and decay kinetics. Compounds with slow EPSC kinetics (decay time constants>6 ms) triggered spikes at lower temporal precision (≥6.58 ms). We found an overall linear relationship between STP and spike delay. The difference in STP between fast and slow compound EPSCs could be reduced by incrementing the amplitude of slow compound EPSCs. The introduction of a temporal jitter to compound EPSCs had a comparatively small effect on STP, with a tenfold increase in jitter resulting in only a five fold decrease in STP. In the presence of simulated synaptic background activity, precisely timed spikes could still be induced by fast EPSCs, but not by slow EPSCs.

Fast oscillations trigger bursts of action potentials in neocortical neurons in vitro: A quasi-white-noise analysis study

PURPOSE

Recent evidence supports the importance of action potential bursts in physiological neural coding, as well as in pathological epileptogenesis. To better understand the temporal dynamics of neuronal input currents that trigger burst firing, we characterized spectral patterns of stimulation current that generate bursts of action potentials from regularly spiking neocortical neurons in vitro.

METHODS

Sharp microelectrodes were used for intracellular recording and stimulation of cortical neurons in rat brain slices. Quasi-white-noise (0-2 kHz) and "chirp" sine wave currents of decreasing wavelength were applied to represent a broad spectrum of stimulation frequencies. Action potential-related averaging of the stimulation current variations preceding bursting was used to characterize stimulation current patterns more likely to result in a burst rather than a single-spike response.

RESULTS

Bursts of action potentials were most reliably generated by a preceding series of > or = 2 positive current transients at 164+/-37 Hz of the quasi-white-noise, and to sine wave currents with frequencies greater than 90 Hz. The intraburst action potential rate was linearly related to the frequency of the input sine wave current.

CONCLUSIONS

This study demonstrates that regularly spiking cortical neurons in vitro burst in response to fast oscillations of input currents. In the presence of positive cortical feedback loops, encoding input frequency in the intraburst action potential rate may be safer than producing a high-frequency regular output spike train. This leads to the experimentally testable and therapeutically important hypothesis that burst firing could be an antiepileptogenic and/or anti-ictogenic mechanism.

Discrete stimulus estimation from neural responses in the turtle retina

In this paper, we investigate the decoding of flashed, full-field visual stimuli while recording from a population of retinal ganglion cells. We present a direct statistical method for determining the likelihood that a response was evoked by a particular stimulus, and use this method to estimate stimuli based on microelectrode array recordings in the turtle retina. This method uses the well-known time-varying Poisson model of neural firing, along with extensions to accommodate neural refractory periods. Unlike other approaches commonly used for Poisson processes, the specific formulation presented here is bin free and requires few user-specified parameters. Statistical dependency issues and the effects of stationarity on the estimation method are also discussed.

Global rhythmic activities in hippocampal neural fields and neural coding

Global oscillations of the neural field represent some of the most interesting expressions of the hippocampal activity, being related also to learning and memory. To study oscillatory activities of the CA3 field in theta range, a model of this sub-field of Hippocampus has been formulated. The model describes the firing activity of CA3 neuronal populations within the frame of a kinetic theory of neural systems and it has been used for computer simulations. The results show that the propagation of activities induced in the neural field by hippocampal afferents occurs only in narrow time windows confined by inhibitory barrages, whose time-course follows the theta rhythm. Moreover, during each period of a theta wave, the entire CA3 field bears a firing activity with peculiar space-time patterns, a sort of specific imprint, which can induce effects with similar patterns on brain regions driven by the hippocampal formation. The simulation has also demonstrated the ability of medial septum to influence the global activity of the CA3 pyramidal population through the control of the population of inhibitory interneurons. At last, the possible involvement of global population oscillations in neural coding has been discussed.

Multisynaptic activity in a pyramidal neuron model and neural code

The highly irregular firing of mammalian cortical pyramidal neurons is one of the most striking observation of the brain activity. This result affects greatly the discussion on the neural code, i.e. how the brain codes information transmitted along the different cortical stages. In fact it seems to be in favor of one of the two main hypotheses about this issue, named the rate code. But the supporters of the contrasting hypothesis, the temporal code, consider this evidence inconclusive. We discuss here a leaky integrate-and-fire model of a hippocampal pyramidal neuron intended to be biologically sound to investigate the genesis of the irregular pyramidal firing and to give useful information about the coding problem. To this aim, the complete set of excitatory and inhibitory synapses impinging on such a neuron has been taken into account. The firing activity of the neuron model has been studied by computer simulation both in basic conditions and allowing brief periods of over-stimulation in specific regions of its synaptic constellation. Our results show neuronal firing conditions similar to those observed in experimental investigations on pyramidal cortical neurons. In particular, the variation coefficient (CV) computed from the inter-spike intervals (ISIs) in our simulations for basic conditions is close to the unity as that computed from experimental data. Our simulation shows also different behaviors in firing sequences for different frequencies of stimulation.