Related Articles

Summary

Background

The conversion of an analog stimulus into the digital form of spikes is a fundamental step in encoding sensory information. Here, we investigate this transformation in the visual system of fish by in vivo calcium imaging and electrophysiology of retinal bipolar cells, which have been assumed to be purely graded neurons.

Results

Synapses of all major classes of retinal bipolar cell encode visual information by using a combination of spikes and graded signals. Spikes are triggered within the synaptic terminal and, although sparse, phase-lock to a stimulus with a jitter as low as 2–3 ms. Spikes in bipolar cells encode a visual stimulus less reliably than spikes in ganglion cells but with similar temporal precision. The spike-generating mechanism does not alter the temporal filtering of a stimulus compared with the generator potential. The amplitude of the graded component of the presynaptic calcium signal can vary in time, and small fluctuations in resting membrane potential alter spike frequency and even switch spiking on and off.

Conclusions

In the retina of fish, the millisecond precision of spike coding begins in the synaptic terminal of bipolar cells. This neural compartment regulates the frequency of digital signals transmitted to the inner retina as well as the strength of graded signals.

Graphical Abstract

Highlights

► The spike code of vision begins in retinal bipolar cells ► Spikes in bipolar cells phase-lock to visual stimuli with millisecond precision ► Spiking and graded calcium signals can switch on and off at individual synapses ► Spikes in bipolar cells encode a stimulus less reliably than spikes in ganglion cells

While oscillations of the local field potential (LFP) are commonly attributed to the synchronization of neuronal firing rate on the same time scale, their relationship to coincident spiking in the millisecond range is unknown. Here, we present experimental evidence to reconcile the notions of synchrony at the level of spiking and at the mesoscopic scale. We demonstrate that only in time intervals of significant spike synchrony that cannot be explained on the basis of firing rates, coincident spikes are better phase locked to the LFP than predicted by the locking of the individual spikes. This effect is enhanced in periods of large LFP amplitudes. A quantitative model explains the LFP dynamics by the orchestrated spiking activity in neuronal groups that contribute the observed surplus synchrony. From the correlation analysis, we infer that neurons participate in different constellations but contribute only a fraction of their spikes to temporally precise spike configurations. This finding provides direct evidence for the hypothesized relation that precise spike synchrony constitutes a major temporally and spatially organized component of the LFP.

During natural vision, primates perform frequent saccadic eye movements, allowing only a narrow time window for processing the visual information at each location. Individual neurons may contribute only with a few spikes to the visual processing during each fixation, suggesting precise spike timing as a relevant mechanism for information processing. We recently found in V1 of monkeys freely viewing natural images, that fixation-related spike synchronization occurs at the early phase of the rate response after fixation-onset, suggesting a specific role of the first response spikes in V1. Here, we show that there are strong local field potential (LFP) modulations locked to the onset of saccades, which continue into the successive fixation periods. Visually induced spikes, in particular the first spikes after the onset of a fixation, are locked to a specific epoch of the LFP modulation. We suggest that the modulation of neural excitability, which is reflected by the saccade-related LFP changes, serves as a corollary signal enabling precise timing of spikes in V1 and thereby providing a mechanism for spike synchronization.

Neuronal oscillations in the gamma frequency range have been reported in many cortical areas, but the role they play in cortical processing remains unclear. We tested a recently proposed hypothesis that the intensity of sensory input is coded in the timing of action potentials relative to the phase of gamma oscillations, thus converting amplitude information to a temporal code. We recorded spikes and local field potential (LFP) from secondary somatosensory (SII) cortex in awake monkeys while presenting a vibratory stimulus at different amplitudes. We developed a novel technique based on matching pursuit to study the interaction between the highly transient gamma oscillations and spikes with high time-frequency resolution. We found that spikes were weakly coupled to LFP oscillations in the gamma frequency range (40−80 Hz), and strongly coupled to oscillations in higher gamma frequencies. However, the phase relationship of neither low-gamma nor high-gamma oscillations changed with stimulus intensity, even with a ten-fold increase. We conclude that, in SII, gamma oscillations are synchronized with spikes, but their phase does not vary with stimulus intensity. Furthermore, high-gamma oscillations (>60 Hz) appear to be closely linked to the occurrence of action potentials, suggesting that LFP high-gamma power could be a sensitive index of the population firing rate near the microelectrode.

Summary

We measured the time course of sodium entry during action potentials of mouse central neurons at 37 °C to examine how efficiently sodium entry is coupled to depolarization. In cortical pyramidal neurons, sodium entry was nearly completely confined to the rising phase of the spike: only ~25% more sodium enters than the theoretical minimum necessary for spike depolarization. However, in fast-spiking GABAergic neurons (cerebellar Purkinje cells and cortical interneurons), twice as much sodium enters as the theoretical minimum. The extra entry occurs because sodium channel inactivation is incomplete during the falling phase of the spike. The efficiency of sodium entry in different cell types is primarily a function of action potential shape and not cell type-specific differences in sodium channel kinetics. The narrow spikes of fast-spiking GABAergic neurons result in incomplete inactivation of sodium channels; this reduces metabolic efficiency but likely enhances the ability to fire spikes at high frequency.

We describe a novel mechanism that mediates the rapid and selective pattern formation of neuronal network activity in response to changing correlations of sub-threshold level input. The mechanism is based on the classical resonance and experimentally observed phenomena that the resonance frequency of a neuron shifts as a function of membrane depolarization. As the neurons receive varying sub-threshold input, their natural frequency is shifted in and out of its resonance range. In response, the neuron fires a sequence of action potentials, corresponding to the specific values of signal currents, in a highly organized manner. We show that this mechanism provides for the selective activation and phase locking of the cells in the network, underlying input-correlated spatio-temporal pattern formation, and could be the basis for reliable spike-timing dependent plasticity. We compare the selectivity and efficiency of this pattern formation to a supra-threshold network activation and a non-resonating network/neuron model to demonstrate that the resonance mechanism is the most effective. Finally we show that this process might be the basis of the phase precession phenomenon observed during firing of hippocampal place cells, and that it may underlie the active switching of neuronal networks to locking at various frequencies.

Background

In nonlinear dynamic systems, synchrony through oscillation and frequency modulation is a general control strategy to coordinate multiple modules in response to external signals. Conversely, the synchrony information can be utilized to infer interaction. Increasing evidence suggests that frequency modulation is also common in transcription regulation.

Results

In this study, we investigate the potential of phase locking analysis, a technique to study the synchrony patterns, in the transcription network modeling of time course gene expression data. Using the yeast cell cycle data, we show that significant phase locking exists between transcription factors and their targets, between gene pairs with prior evidence of physical or genetic interactions, and among cell cycle genes. When compared with simple correlation we found that the phase locking metric can identify gene pairs that interact with each other more efficiently. In addition, it can automatically address issues of arbitrary time lags or different dynamic time scales in different genes, without the need for alignment. Interestingly, many of the phase locked gene pairs exhibit higher order than 1:1 locking, and significant phase lags with respect to each other. Based on these findings we propose a new phase locking metric for network reconstruction using time course gene expression data. We show that it is efficient at identifying network modules of focused biological themes that are important to cell cycle regulation.

Conclusions

Our result demonstrates the potential of phase locking analysis in transcription network modeling. It also suggests the importance of understanding the dynamics underlying the gene expression patterns.

A phase resetting curve (PRC) keeps track of the extent to which a perturbation at a given phase advances or delays the next spike, and can be used to predict phase locking in networks of oscillators. The PRC can be estimated by convolving the waveform of the perturbation with the infinitesimal PRC (iPRC) under the assumption of weak coupling. The iPRC is often defined with respect to an infinitesimal current as zi(ϕ), where ϕ is phase, but can also be defined with respect to an infinitesimal conductance change as zg(ϕ). In this paper, we first show that the two approaches are equivalent. Coupling waveforms corresponding to synapses with different time courses sample zg(ϕ) in predictably different ways. We show that for oscillators with Type I excitability, an anomalous region in zg(ϕ) with opposite sign to that seen otherwise is often observed during an action potential. If the duration of the synaptic perturbation is such that it effectively samples this region, PRCs with both advances and delays can be observed despite Type I excitability. We also show that changing the duration of a perturbation so that it preferentially samples regions of stable or unstable slopes in zg(ϕ) can stabilize or destabilize synchrony in a network with the corresponding dynamics.

The timing of action potentials in spiking neurons depends on the temporal dynamics of their inputs and contains information about temporal fluctuations in the stimulus. Leaky integrate-and-fire neurons constitute a popular class of encoding models, in which spike times depend directly on the temporal structure of the inputs. However, optimal decoding rules for these models have only been studied explicitly in the noiseless case. Here, we study decoding rules for probabilistic inference of a continuous stimulus from the spike times of a population of leaky integrate-and-fire neurons with threshold noise. We derive three algorithms for approximating the posterior distribution over stimuli as a function of the observed spike trains. In addition to a reconstruction of the stimulus we thus obtain an estimate of the uncertainty as well. Furthermore, we derive a ‘spike-by-spike’ online decoding scheme that recursively updates the posterior with the arrival of each new spike. We use these decoding rules to reconstruct time-varying stimuli represented by a Gaussian process from spike trains of single neurons as well as neural populations.

The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a ‘quasi-renewal equation’ which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.

Author Summary

How can information be encoded and decoded in populations of adapting neurons? A quantitative answer to this question requires a mathematical expression relating neuronal activity to the external stimulus, and, conversely, stimulus to neuronal activity. Although widely used equations and models exist for the special problem of relating external stimulus to the action potentials of a single neuron, the analogous problem of relating the external stimulus to the activity of a population has proven more difficult. There is a bothersome gap between the dynamics of single adapting neurons and the dynamics of populations. Moreover, if we ignore the single neurons and describe directly the population dynamics, we are faced with the ambiguity of the adapting neural code. The neural code of adapting populations is ambiguous because it is possible to observe a range of population activities in response to a given instantaneous input. Somehow the ambiguity is resolved by the knowledge of the population history, but how precisely? In this article we use approximation methods to provide mathematical expressions that describe the encoding and decoding of external stimuli in adapting populations. The theory presented here helps to bridge the gap between the dynamics of single neurons and that of populations.

In the hippocampus and the neocortex, the coupling between local field potential (LFP) oscillations and the spiking of single neurons can be highly precise, across neuronal populations and cell types. Spike phase (i.e., the spike time with respect to a reference oscillation) is known to carry reliable information, both with phase-locking behavior and with more complex phase relationships, such as phase precession. How this precision is achieved by neuronal populations, whose membrane properties and total input may be quite heterogeneous, is nevertheless unknown. In this note, we investigate a simple mechanism for learning precise LFP-to-spike coupling in feed-forward networks – the reliable, periodic modulation of presynaptic firing rates during oscillations, coupled with spike-timing dependent plasticity. When oscillations are within the biological range (2–150 Hz), firing rates of the inputs change on a timescale highly relevant to spike-timing dependent plasticity (STDP). Through analytic and computational methods, we find points of stable phase-locking for a neuron with plastic input synapses. These points correspond to precise phase-locking behavior in the feed-forward network. The location of these points depends on the oscillation frequency of the inputs, the STDP time constants, and the balance of potentiation and de-potentiation in the STDP rule. For a given input oscillation, the balance of potentiation and de-potentiation in the STDP rule is the critical parameter that determines the phase at which an output neuron will learn to spike. These findings are robust to changes in intrinsic post-synaptic properties. Finally, we discuss implications of this mechanism for stable learning of spike-timing in the hippocampus.

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.

We report on an analysis of a well known three-pulse sequence for generating and detecting spin I=1 quadrupolar order when various pulse errors are taken into account. In the situation of a single quadrupolar frequency, such as the case found in a single crystal, we studied the potential leakage of single and/or double quantum coherence when a pulse flip error, finite pulse width effect, RF transient or a resonance offset is present. Our analysis demonstrates that the four-step phase cycling scheme studied is robust in suppressing unwanted double and single quantum coherence as well as Zeeman order that arise from the experimental artifacts, allowing for an unbiased measurement of the quadrupolar alignment relaxation time, T1Q. This work also reports on distortions in quadrupolar alignment echo spectra in the presence of experimental artifacts in the situation of a powdered sample, by simulation. Using our simulation tool, it is demonstrated that the spectral distortions associated with the pulse artifacts may be minimized, to some extent, by optimally choosing the time between the first two pulses. We highlight experimental results acquired on perdeuterated hexamethylbenzene and polyethelene that demonstrate the efficacy of the phase cycling scheme for suppressing unwanted quantum coherence when measuring T1Q. It is suggested that one employ two separate pulse sequences when measuring T1Q to properly analyze the short time behavior of quadrupolar alignment relaxation data.

Cortical responses can vary greatly between repeated presentations of an identical stimulus. Here we report that both trial-to-trial variability and faithfulness of auditory cortical stimulus representations depend critically on brain state. A frozen amplitude-modulated white noise stimulus was repeatedly presented while recording neuronal populations and local field potentials (LFPs) in auditory cortex of urethane-anesthetized rats. An information-theoretic measure was used to predict neuronal spiking activity from either the stimulus envelope or simultaneously recorded LFP. Evoked LFPs and spiking more faithfully followed high-frequency temporal modulations when the cortex was in a “desynchronized” state. In the “synchronized” state, neural activity was poorly predictable from the stimulus envelope, but the spiking of individual neurons could still be predicted from the ongoing LFP. Our results suggest that although auditory cortical activity remains coordinated as a population in the synchronized state, the ability of continuous auditory stimuli to control this activity is greatly diminished.

Spike timing precision is a fundamental aspect of neuronal information processing in the brain. Here we examined the temporal precision of input–output operation of dentate granule cells (DGCs) in an animal model of temporal lobe epilepsy (TLE). In TLE, mossy fibers sprout and establish recurrent synapses on DGCs that generate aberrant slow kainate receptor–mediated excitatory postsynaptic potentials (EPSPKA) not observed in controls. We report that, in contrast to time-locked spikes generated by EPSPAMPA in control DGCs, aberrant EPSPKA are associated with long-lasting plateaus and jittered spikes during single-spike mode firing. This is mediated by a selective voltage-dependent amplification of EPSPKA through persistent sodium current (INaP) activation. In control DGCs, a current injection of a waveform mimicking the slow shape of EPSPKA activates INaP and generates jittered spikes. Conversely in epileptic rats, blockade of EPSPKA or INaP restores the temporal precision of EPSP–spike coupling. Importantly, EPSPKA not only decrease spike timing precision at recurrent mossy fiber synapses but also at perforant path synapses during synaptic integration through INaP activation. We conclude that a selective interplay between aberrant EPSPKA and INaP severely alters the temporal precision of EPSP–spike coupling in DGCs of chronic epileptic rats.

Cerebellar Purkinje cells display complex intrinsic dynamics. They fire spontaneously, exhibit bistability, and via mutual network interactions are involved in the generation of high frequency oscillations and travelling waves of activity. To probe the dynamical properties of Purkinje cells we measured their phase response curves (PRCs). PRCs quantify the change in spike phase caused by a stimulus as a function of its temporal position within the interspike interval, and are widely used to predict neuronal responses to more complex stimulus patterns. Significant variability in the interspike interval during spontaneous firing can lead to PRCs with a low signal-to-noise ratio, requiring averaging over thousands of trials. We show using electrophysiological experiments and simulations that the PRC calculated in the traditional way by sampling the interspike interval with brief current pulses is biased. We introduce a corrected approach for calculating PRCs which eliminates this bias. Using our new approach, we show that Purkinje cell PRCs change qualitatively depending on the firing frequency of the cell. At high firing rates, Purkinje cells exhibit single-peaked, or monophasic PRCs. Surprisingly, at low firing rates, Purkinje cell PRCs are largely independent of phase, resembling PRCs of ideal non-leaky integrate-and-fire neurons. These results indicate that Purkinje cells can act as perfect integrators at low firing rates, and that the integration mode of Purkinje cells depends on their firing rate.

Author Summary

By observing how brief current pulses injected at different times between spikes change the phase of spiking of a neuron (and thus obtaining the so-called phase response curve), it should be possible to predict a full spike train in response to more complex stimulation patterns. When we applied this traditional protocol to obtain phase response curves in cerebellar Purkinje cells in the presence of noise, we observed a triangular region devoid of data points near the end of the spiking cycle. This “Bermuda Triangle” revealed a flaw in the classical method for constructing phase response curves. We developed a new approach to eliminate this flaw and used it to construct phase response curves of Purkinje cells over a range of spiking rates. Surprisingly, at low firing rates, phase changes were independent of the phase of the injected current pulses, implying that the Purkinje cell is a perfect integrator under these conditions. This mechanism has not yet been described in other cell types and may be crucial for the information processing capabilities of these neurons.

We consider and analyze the influence of spike-timing dependent plasticity (STDP) on homeostatic states in synaptically coupled neuronal oscillators. In contrast to conventional models of STDP in which spike-timing affects weights of synaptic connections, we consider a model of STDP in which the time lags between pre- and/or post-synaptic spikes change internal state of pre- and/or post-synaptic neurons respectively. The analysis reveals that STDP processes of this type, modeled by a single ordinary differential equation, may ensure efficient, yet coarse, phase-locking of spikes in the system to a given reference phase. Precision of the phase locking, i.e. the amplitude of relative phase deviations from the reference, depends on the values of natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanism. However, as we demonstrate, such deviations can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. Adaptation operating at a slow time scale may be associated with extracellular matter such as matrix and glia. Thus the findings may suggest a possible role of the latter in regulating synaptic transmission in neuronal circuits.

We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase-lock spike-to-spike for strong mutual coupling. But the shared input can desynchronize the locked spike-pairs by selectively eliminating the lagging spike or modulating its timing with respect to the leading spike depending on their separation time window. Such loss of synchrony is also found in a large network of sparsely coupled heterogeneous spiking neurons receiving shared input.

It is generally assumed that axons use action potentials (APs) to transmit information fast and reliably to synapses. Yet, the reliability of transmission along fibers below 0.5 μm diameter, such as cortical and cerebellar axons, is unknown. Using detailed models of rodent cortical and squid axons and stochastic simulations, we show how conduction along such thin axons is affected by the probabilistic nature of voltage-gated ion channels (channel noise). We identify four distinct effects that corrupt propagating spike trains in thin axons: spikes were added, deleted, jittered, or split into groups depending upon the temporal pattern of spikes. Additional APs may appear spontaneously; however, APs in general seldom fail (<1%). Spike timing is jittered on the order of milliseconds over distances of millimeters, as conduction velocity fluctuates in two ways. First, variability in the number of Na channels opening in the early rising phase of the AP cause propagation speed to fluctuate gradually. Second, a novel mode of AP propagation (stochastic microsaltatory conduction), where the AP leaps ahead toward spontaneously formed clusters of open Na channels, produces random discrete jumps in spike time reliability. The combined effect of these two mechanisms depends on the pattern of spikes. Our results show that axonal variability is a general problem and should be taken into account when considering both neural coding and the reliability of synaptic transmission in densely connected cortical networks, where small synapses are typically innervated by thin axons. In contrast we find that thicker axons above 0.5 μm diameter are reliable.

Author Summary

Neurons in cerebral cortex achieve wiring densities of 4 km per mm3 by using unmyelinated axons of 0.3 μm average diameter as wires. Many axons (e.g., pain fibers) are thinner. Although, as in computer chips, wire miniaturization economizes on space and energy, it increases the noise introduced by thermodynamic fluctuations in a neuron's “protein transistors,” voltage-gated ion channels. We investigated how well the relatively small number of ion channels found in the membranes of tiny axons propagate the brain's universal signal—the action potential. We built a stochastic model that incorporates the random behavior of individual ion channels and found noise effects much larger than previously assumed, because standard stochastic approximation techniques (Langevin) break down because single channels can produce whole-cell responses. Channel noise destroys information encoded in the timing of action potentials, by randomly varying the speed of conduction, and produces a novel mode of transmission, stochastic microsaltatory conduction. Ion channel populations retain memory of previous activity in the distribution of channel states, causing action potential reliability to vary with context. The effects and general relationships identified here will govern other cell-signaling systems that rely on inherently noisy protein switches to propagate signals, either for intracellular communication (Ca++/cAMP waves) or in nanotechnology.

The current study examined behavioral measures and response-locked event-related brain potentials (ERPs) derived from a Go/No-Go task in a large (N = 328) sample of 5- to 7-year-olds in order to better understand the early development of response monitoring and the impact of child age and sex. In particular, the error-related negativity (ERN, defined on both error trials alone and the difference between error and correct trials, or ΔERN), correct response negativity (CRN), and error positivity (Pe) were examined. Overall, the ERN, CRN, and the Pe were spatially and temporally similar to those measured in adults and older children. Even within our narrow age range, older children were faster and more accurate; a more negative ΔERN and a more positive Pe were associated with: increasing age, increased accuracy, and faster reaction times on errors, suggesting these enhanced components reflected more efficient response monitoring of errors over development. Girls were slower and more accurate than boys, although both genders exhibited comparable ERPs. Younger children and girls were characterized by increased posterror slowing, although they did not demonstrate improved posterror accuracy. Posterror slowing was also related to a larger Pe and reduced posterror accuracy. Collectively, these data suggest that posterror slowing may be unrelated to cognitive control and may, like the Pe, reflect an orienting response to errors.

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.

Author Summary

Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how. A prominent feature of many cortical neurons is spike frequency adaptation, which is caused by slow transmembrane currents. We investigated how these adaptation currents affect the synchronization tendency of coupled model neurons. Using the efficient adaptive exponential integrate-and-fire (aEIF) model and a biophysically detailed neuron model for validation, we found that increased adaptation currents promote synchronization of coupled excitatory neurons at lower spike frequencies, as long as the conduction delays between the neurons are negligible. Inhibitory neurons on the other hand synchronize in presence of conduction delays, with or without adaptation currents. Our results emphasize the utility of the aEIF model for computational studies of neuronal network dynamics. We conclude that adaptation currents provide a mechanism to generate low frequency oscillations in local populations of excitatory neurons, while faster rhythms seem to be caused by inhibition rather than excitation.

In this study, we analyze the processing of low-frequency sounds in the cochlear apex through responses of auditory nerve fibers (ANFs) that innervate the apex. Single tones and irregularly spaced tone complexes were used to evoke ANF responses in Mongolian gerbil. The spike arrival times were analyzed in terms of phase locking, peripheral frequency selectivity, group delays, and the nonlinear effects of sound pressure level (SPL). Phase locking to single tones was similar to that in cat. Vector strength was maximal for stimulus frequencies around 500 Hz, decreased above 1 kHz, and became insignificant above 4 to 5 kHz. We used the responses to tone complexes to determine amplitude and phase curves of ANFs having a characteristic frequency (CF) below 5 kHz. With increasing CF, amplitude curves gradually changed from broadly tuned and asymmetric with a steep low-frequency flank to more sharply tuned and asymmetric with a steep high-frequency flank. Over the same CF range, phase curves gradually changed from a concave-upward shape to a concave-downward shape. Phase curves consisted of two or three approximately straight segments. Group delay was analyzed separately for these segments. Generally, the largest group delay was observed near CF. With increasing SPL, most amplitude curves broadened, sometimes accompanied by a downward shift of best frequency, and group delay changed along the entire range of stimulus frequencies. We observed considerable across-ANF variation in the effects of SPL on both amplitude and phase. Overall, our data suggest that mechanical responses in the apex of the cochlea are considerably nonlinear and that these nonlinearities are of a different character than those known from the base of the cochlea.

In this study, we analyze the processing of low-frequency sounds in the cochlear apex through responses of auditory nerve fibers (ANFs) that innervate the apex. Single tones and irregularly spaced tone complexes were used to evoke ANF responses in Mongolian gerbil. The spike arrival times were analyzed in terms of phase locking, peripheral frequency selectivity, group delays, and the nonlinear effects of sound pressure level (SPL). Phase locking to single tones was similar to that in cat. Vector strength was maximal for stimulus frequencies around 500 Hz, decreased above 1 kHz, and became insignificant above 4 to 5 kHz. We used the responses to tone complexes to determine amplitude and phase curves of ANFs having a characteristic frequency (CF) below 5 kHz. With increasing CF, amplitude curves gradually changed from broadly tuned and asymmetric with a steep low-frequency flank to more sharply tuned and asymmetric with a steep high-frequency flank. Over the same CF range, phase curves gradually changed from a concave-upward shape to a concave-downward shape. Phase curves consisted of two or three approximately straight segments. Group delay was analyzed separately for these segments. Generally, the largest group delay was observed near CF. With increasing SPL, most amplitude curves broadened, sometimes accompanied by a downward shift of best frequency, and group delay changed along the entire range of stimulus frequencies. We observed considerable across-ANF variation in the effects of SPL on both amplitude and phase. Overall, our data suggest that mechanical responses in the apex of the cochlea are considerably nonlinear and that these nonlinearities are of a different character than those known from the base of the cochlea.

Transfer entropy (TE) is an information-theoretic measure which has received recent attention in neuroscience for its potential to identify effective connectivity between neurons. Calculating TE for large ensembles of spiking neurons is computationally intensive, and has caused most investigators to probe neural interactions at only a single time delay and at a message length of only a single time bin. This is problematic, as synaptic delays between cortical neurons, for example, range from one to tens of milliseconds. In addition, neurons produce bursts of spikes spanning multiple time bins. To address these issues, here we introduce a free software package that allows TE to be measured at multiple delays and message lengths. To assess performance, we applied these extensions of TE to a spiking cortical network model (Izhikevich, 2006) with known connectivity and a range of synaptic delays. For comparison, we also investigated single-delay TE, at a message length of one bin (D1TE), and cross-correlation (CC) methods. We found that D1TE could identify 36% of true connections when evaluated at a false positive rate of 1%. For extended versions of TE, this dramatically improved to 73% of true connections. In addition, the connections correctly identified by extended versions of TE accounted for 85% of the total synaptic weight in the network. Cross correlation methods generally performed more poorly than extended TE, but were useful when data length was short. A computational performance analysis demonstrated that the algorithm for extended TE, when used on currently available desktop computers, could extract effective connectivity from 1 hr recordings containing 200 neurons in ∼5 min. We conclude that extending TE to multiple delays and message lengths improves its ability to assess effective connectivity between spiking neurons. These extensions to TE soon could become practical tools for experimentalists who record hundreds of spiking neurons.

In the nucleus of the solitary tract (NTS), electrophysiological responses to taste stimuli representing four basic taste qualities (sweet, sour, salty, or bitter) can be often be discriminated by spike count, but, in units for which the number of spikes is variable across identical stimulus presentations, spike timing (i.e., temporal coding) can also support reliable discrimination. The present study examined the contribution of spike count and spike timing to the discrimination of stimuli that evoke the same taste quality but are of different chemical composition. Responses to between 3 and 21 repeated presentations of two pairs of quality-matched tastants were recorded from 38 single cells in the NTS of urethane-anesthetized rats. Temporal coding was assessed in 24 cells, most of which were tested with salty and sour tastants, using an information-theoretic approach (Victor & Purpura, 1996; 1997). Within a given cell, responses to tastants of similar quality were generally closer in magnitude than responses to dissimilar tastants; however, tastants of similar quality often reversed their order of effectiveness across replicate sets of trials. Typically, discrimination between tastants of dissimilar qualities could be made by spike count. Responses to tastants of similar quality typically evoked more similar response magnitudes but were more frequently, and to a proportionally greater degree, distinguishable based upon temporal information. Results showed that nearly every taste-responsive NTS cell has the capacity to generate temporal features in evoked spike trains that can be used to distinguish between stimuli of different qualities and chemical compositions.