Temporal encoding in a nervous system

Symmetry-Breaking Bifurcations of the Information Bottleneck and Related Problems

In this paper, we investigate the bifurcations of solutions to a class of degenerate constrained optimization problems. This study was motivated by the Information Bottleneck and Information Distortion problems, which have been used to successfully cluster data in many different applications. In the problems we discuss in this paper, the distortion function is not a linear function of the quantizer. This leads to a challenging annealing optimization problem, which we recast as a fixed-point dynamics problem of a gradient flow of a related dynamical system. The gradient system possesses an SN symmetry due to its invariance in relabeling representative classes. Its flow hence passes through a series of bifurcations with specific symmetry breaks. Here, we show that the dynamical system related to the Information Bottleneck problem has an additional spurious symmetry that requires more-challenging analysis of the symmetry-breaking bifurcation. For the Information Bottleneck, we determine that when bifurcations occur, they are only of pitchfork type, and we give conditions that determine the stability of the bifurcating branches. We relate the existence of subcritical bifurcations to the existence of first-order phase transitions in the corresponding distortion function as a function of the annealing parameter, and provide criteria with which to detect such transitions.

Roles of neural communication between the brain and thoracic ganglia in the selection and regulation of the cricket escape behavior

To survive a predator's attack, prey animals must exhibit escape responses that are appropriately regulated in terms of their moving speed, distance, and direction. Insect locomotion is considered to be controlled by an interaction between the brain, which is involved in behavioral decision-making, and the thoracic ganglia (TG), which are primary motor centers. However, it remains unknown which descending and ascending signals between these neural centers are involved in the regulation of the escape behavior. We addressed the distinct roles of the brain and TG in the wind-elicited escape behavior of crickets by assessing the effects of partial ablation of the intersegmental communications on escape responses. We unilaterally cut the ventral nerve cord (VNC) at different locations, between the brain and TG, or between the TG and terminal abdominal ganglion (TAG), a primary sensory center of the cercal system. The partial ablation of ascending signals to the brain greatly reduced the jumping response rather than running, indicating that sensory information processing in the brain is essential for the choice of escape responses. The ablation of descending signals from the brain to the TG impaired locomotor performance and directional control of the escape responses, suggesting that locomotion in the escape behavior largely depends on the descending signals from the brain. Finally, the extracellular recording from the cervical VNC indicated a difference in the descending activities preceding the escape responses between running and jumping. Our results demonstrated that the brain sends the descending signals encoding the behavioral choice and locomotor regulation to the TG, while the TG seem to have other specific roles, such as in the preparation of escape movement.

ENCODING OF SMALL-SCALE AIR MOTION DYNAMICS IN THE CRICKET ACHETA DOMESTICUS

The cercal sensory system of the cricket mediates the detection, localization and identification of air current signals generated by predators, mates and competitors. This mechanosensory system has been used extensively for experimental and theoretical studies of sensory coding at the cellular and system levels. It is currently thought that sensory interneurons in the terminal abdominal ganglion extract information about the direction, velocity, and acceleration of the air currents in the animal's immediate environment, and project a coarse-coded representation of those parameters to higher centers. All feature detection is thought to be carried out in higher ganglia by more complex, specialized circuits. We present results that force a substantial revision of current hypotheses. Using multiple extracellular recordings and a special sensory stimulation device, we demonstrate that four well-studied interneurons in this system respond with high sensitivity and selectivity to complex dynamic multi-directional features of air currents which have a spatial scale smaller than the physical dimensions of the cerci. The INs showed much greater sensitivity for these features than for unidirectional bulk-flow stimuli used in previous studies. Thus, in addition to participating in the ensemble encoding of bulk air flow stimulus characteristics, these interneurons are capable of operating as feature detectors for naturalistic stimuli. In this sense, these interneurons are encoding and transmitting information about different aspects of their stimulus environment: they are multiplexing information. Major aspects of the stimulus-response specificity of these interneurons can be understood from the dendritic anatomy and connectivity with the sensory afferent map.

Action selection based on multiple-stimulus aspects in wind-elicited escape behavior of crickets

Escape behavior is essential for animals to avoid attacks by predators. In some species, multiple escape responses could be employed. However, it remains unknown what aspects of threat stimuli affect the choice of an escape response. We focused on two distinct escape responses (running and jumping) to short airflow in crickets and examined the effects of multiple stimulus aspects including the angle, velocity, and duration on the choice between these responses. The faster and longer the airflow, the more frequently the crickets jumped. This meant that the choice of an escape response depends on both the velocity and duration of the stimulus and suggests that the neural basis for choosing an escape response includes the integration process of multiple stimulus parameters. In addition, the moving speed and distance changed depending on the stimulus velocity and duration for running but not for jumping. Running away would be more adaptive escape behavior.

Capturing spike train temporal pattern with wavelet average coefficient for brain machine interface

Motor brain machine interfaces (BMIs) directly link the brain to artificial actuators and have the potential to mitigate severe body paralysis caused by neurological injury or disease. Most BMI systems involve a decoder that analyzes neural spike counts to infer movement intent. However, many classical BMI decoders (1) fail to take advantage of temporal patterns of spike trains, possibly over long time horizons; (2) are insufficient to achieve good BMI performance at high temporal resolution, as the underlying Gaussian assumption of decoders based on spike counts is violated. Here, we propose a new statistical feature that represents temporal patterns or temporal codes of spike events with richer description-wavelet average coefficients (WAC)-to be used as decoder input instead of spike counts. We constructed a wavelet decoder framework by using WAC features with a sliding-window approach, and compared the resulting decoder against classical decoders (Wiener and Kalman family) and new deep learning based decoders ( Long Short-Term Memory) using spike count features. We found that the sliding-window approach boosts decoding temporal resolution, and using WAC features significantly improves decoding performance over using spike count features.

Circadian rhythms and the HPA axis: A systems view

The circadian timing system comprises a network of time-keeping clocks distributed across a living host whose responsibility is to allocate resources and distribute functions temporally to optimize fitness. The molecular structures generating these rhythms have evolved to accommodate the rotation of the earth in an attempt to primarily match the light/dark periods during the 24-hr day. To maintain synchrony of timing across and within tissues, information from the central clock, located in the suprachiasmatic nucleus, is conveyed using systemic signals. Leading among those signals are endocrine hormones, and while the hypothalamic-pituitary-adrenal axis through the release of glucocorticoids is a major pacesetter. Interestingly, the fundamental units at the molecular and physiological scales that generate local and systemic signals share critical structural properties. These properties enable time-keeping systems to generate rhythmic signals and allow them to adopt specific properties as they interact with each other and the external environment. The purpose of this review is to provide a broad overview of these structures, discuss their functional characteristics, and describe some of their fundamental properties as these related to health and disease. This article is categorized under: Immune System Diseases > Computational Models Immune System Diseases > Biomedical Engineering.

Invariant neural responses for sensory categories revealed by the time-varying information for communication calls

Although information theoretic approaches have been used extensively in the analysis of the neural code, they have yet to be used to describe how information is accumulated in time while sensory systems are categorizing dynamic sensory stimuli such as speech sounds or visual objects. Here, we present a novel method to estimate the cumulative information for stimuli or categories. We further define a time-varying categorical information index that, by comparing the information obtained for stimuli versus categories of these same stimuli, quantifies invariant neural representations. We use these methods to investigate the dynamic properties of avian cortical auditory neurons recorded in zebra finches that were listening to a large set of call stimuli sampled from the complete vocal repertoire of this species. We found that the time-varying rates carry 5 times more information than the mean firing rates even in the first 100 ms. We also found that cumulative information has slow time constants (100–600 ms) relative to the typical integration time of single neurons, reflecting the fact that the behaviorally informative features of auditory objects are time-varying sound patterns. When we correlated firing rates and information values, we found that average information correlates with average firing rate but that higher-rates found at the onset response yielded similar information values as the lower-rates found in the sustained response: the onset and sustained response of avian cortical auditory neurons provide similar levels of independent information about call identity and call-type. Finally, our information measures allowed us to rigorously define categorical neurons; these categorical neurons show a high degree of invariance for vocalizations within a call-type. Peak invariance is found around 150 ms after stimulus onset. Surprisingly, call-type invariant neurons were found in both primary and secondary avian auditory areas.

Just as the recognition of faces requires neural representations that are invariant to scale and rotation, the recognition of behaviorally relevant auditory objects, such as spoken words, requires neural representations that are invariant to the speaker uttering the word and to his or her location. Here, we used information theory to investigate the time course of the neural representation of bird communication calls and of behaviorally relevant categories of these same calls: the call-types of the bird’s repertoire. We found that neurons in both the primary and secondary avian auditory cortex exhibit invariant responses to call renditions within a call-type, suggestive of a potential role for extracting the meaning of these communication calls. We also found that time plays an important role: first, neural responses carry significantly more information when represented by temporal patterns calculated at the small time scale of 10 ms than when measured as average rates and, second, this information accumulates in a non-redundant fashion up to long integration times of 600 ms. This rich temporal neural representation is matched to the temporal richness found in the communication calls of this species.

Improved lower bound for the mutual information between signal and neural spike count

The mutual information between a stimulus signal and the spike count of a stochastic neuron is in many cases difficult to determine. Therefore, it is often approximated by a lower bound formula that involves linear correlations between input and output only. Here, we improve the linear lower bound for the mutual information by incorporating nonlinear correlations. For the special case of a Gaussian output variable with nonlinear signal dependencies of mean and variance we also derive an exact integral formula for the full mutual information. In our numerical analysis, we first compare the linear and nonlinear lower bounds and the exact integral formula for two different Gaussian models and show under which conditions the nonlinear lower bound provides a significant improvement to the linear approximation. We then inspect two neuron models, the leaky integrate-and-fire model with white Gaussian noise and the Na-K model with channel noise. We show that for certain firing regimes and for intermediate signal strengths the nonlinear lower bound can provide a substantial improvement compared to the linear lower bound. Our results demonstrate the importance of nonlinear input-output correlations for neural information transmission and provide a simple nonlinear approximation for the mutual information that can be applied to more complicated neuron models as well as to experimental data.

Linear-nonlinear-time-warp-poisson models of neural activity

Prominent models of spike trains assume only one source of variability - stochastic (Poisson) spiking - when stimuli and behavior are fixed. However, spike trains may also reflect variability due to internal processes such as planning. For example, we can plan a movement at one point in time and execute it at some arbitrary later time. Neurons involved in planning may thus share an underlying time course that is not precisely locked to the actual movement. Here we combine the standard Linear-Nonlinear-Poisson (LNP) model with Dynamic Time Warping (DTW) to account for shared temporal variability. When applied to recordings from macaque premotor cortex, we find that time warping considerably improves predictions of neural activity. We suggest that such temporal variability is a widespread phenomenon in the brain which should be modeled.

Noisy Juxtacellular Stimulation In Vivo Leads to Reliable Spiking and Reveals High-Frequency Coding in Single Neurons

Single cells in the motor and somatosensory cortex of rats were stimulated in vivo with broadband fluctuating currents applied juxtacellularly. Unlike the DC current steps used previously, fluctuating stimulation currents reliably evoked spike trains with precise timing of individual spikes. Fluctuating currents resulted in strong cellular responses at stimulation frequencies beyond the inverse membrane time constant and the mean firing rate of the neuron. Neuronal firing was associated with high rates of information transmission, even for the high-frequency components of the stimulus. Such response characteristics were also revealed in additional experiments with sinusoidal juxtacellular stimulation. For selected cells, we could reproduce these statistics with compartmental models of varying complexity. We also developed a method to generate Gaussian stimuli that evoke spike trains with prescribed spike times (under the constraint of a certain rate and coefficient of variation) and exemplify its ability to achieve precise and reliable spiking in cortical neurons in vivo Our results demonstrate a novel method for precise control of spike timing by juxtacellular stimulation, confirm and extend earlier conclusions from ex vivo work about the capacity of cortical neurons to generate precise discharges, and contribute to the understanding of the biophysics of information transfer of single neurons in vivo at high frequencies.

SIGNIFICANCE STATEMENT

Nanostimulation of single identified neurons in vivo can control spike frequency parametrically and, surprisingly, can even bias the animal's behavioral response. Here, we extend this stimulation protocol to time-dependent broadband noise stimulation in sensory and motor cortices of rat. In response to such stimuli, we found increased temporal spike-time reliability. The information transmission properties reveal, both experimentally and theoretically, that the neurons support high-frequency stimulation beyond the inverse membrane time. Generating a stimulus using the neuron's response properties, we could evoke prescribed spike times with high precision. Our work helps to establish a novel method for precise temporal control of single-cell spiking and provides a simplified biophysical description of single-neuron spiking under time-dependent in vivo-like stimulation.

Self-motion evokes precise spike timing in the primate vestibular system

The accurate representation of self-motion requires the efficient processing of sensory input by the vestibular system. Conventional wisdom is that vestibular information is exclusively transmitted through changes in firing rate, yet under this assumption vestibular neurons display relatively poor detection and information transmission. Here, we carry out an analysis of the system's coding capabilities by recording neuronal responses to repeated presentations of naturalistic stimuli. We find that afferents with greater intrinsic variability reliably discriminate between different stimulus waveforms through differential patterns of precise (∼6 ms) spike timing, while those with minimal intrinsic variability do not. A simple mathematical model provides an explanation for this result. Postsynaptic central neurons also demonstrate precise spike timing, suggesting that higher brain areas also represent self-motion using temporally precise firing. These findings demonstrate that two distinct sensory channels represent vestibular information: one using rate coding and the other that takes advantage of precise spike timing.

Early vestibular pathways are thought to code sensory inputs regarding self-motion via changes in firing rate. Here, the authors record from both regular and irregular afferents in macaques, and find both irregular afferents and central neurons also represent self-motion via temporally precise spike timing.

A minimum-error, energy-constrained neural code is an instantaneous-rate code

Sensory neurons code information about stimuli in their sequence of action potentials (spikes). Intuitively, the spikes should represent stimuli with high fidelity. However, generating and propagating spikes is a metabolically expensive process. It is therefore likely that neural codes have been selected to balance energy expenditure against encoding error. Our recently proposed optimal, energy-constrained neural coder (Jones et al. Frontiers in Computational Neuroscience, 9, 61 2015) postulates that neurons time spikes to minimize the trade-off between stimulus reconstruction error and expended energy by adjusting the spike threshold using a simple dynamic threshold. Here, we show that this proposed coding scheme is related to existing coding schemes, such as rate and temporal codes. We derive an instantaneous rate coder and show that the spike-rate depends on the signal and its derivative. In the limit of high spike rates the spike train maximizes fidelity given an energy constraint (average spike-rate), and the predicted interspike intervals are identical to those generated by our existing optimal coding neuron. The instantaneous rate coder is shown to closely match the spike-rates recorded from P-type primary afferents in weakly electric fish. In particular, the coder is a predictor of the peristimulus time histogram (PSTH). When tested against in vitro cortical pyramidal neuron recordings, the instantaneous spike-rate approximates DC step inputs, matching both the average spike-rate and the time-to-first-spike (a simple temporal code). Overall, the instantaneous rate coder relates optimal, energy-constrained encoding to the concepts of rate-coding and temporal-coding, suggesting a possible unifying principle of neural encoding of sensory signals.

Spatial dynamics of action potentials estimated by dendritic Ca(2+) signals in insect projection neurons

The spatial dynamics of action potentials, including their propagation and the location of spike initiation zone (SIZ), are crucial for the computation of a single neuron. Compared with mammalian central neurons, the spike dynamics of invertebrate neurons remain relatively unknown. Thus, we examined the spike dynamics based on single spike-induced Ca(2+) signals in the dendrites of cricket mechanosensory projection neurons, known as giant interneurons (GIs). The Ca(2+) transients induced by a synaptically evoked single spike were larger than those induced by an antidromic spike, whereas subthreshold synaptic potentials caused no elevation of Ca(2+). These results indicate that synaptic activity enhances the dendritic Ca(2+) influx through voltage-gated Ca(2+) channels. Stimulation of the presynaptic sensory afferents ipsilateral to the recording site evoked a dendritic spike with higher amplitude than contralateral stimulation, thereby suggesting that alteration of the spike waveform resulted in synaptic enhancement of the dendritic Ca(2+) transients. The SIZ estimated from the spatial distribution of the difference in the Ca(2+) amplitude was distributed throughout the right and left dendritic branches across the primary neurite connecting them in GIs.

A frequency-resolved mutual information rate and its application to neural systems

The encoding and processing of time-dependent signals into sequences of action potentials of sensory neurons is still a challenging theoretical problem. Although, with some effort, it is possible to quantify the flow of information in the model-free framework of Shannon's information theory, this yields just a single number, the mutual information rate. This rate does not indicate which aspects of the stimulus are encoded. Several studies have identified mechanisms at the cellular and network level leading to low- or high-pass filtering of information, i.e., the selective coding of slow or fast stimulus components. However, these findings rely on an approximation, specifically, on the qualitative behavior of the coherence function, an approximate frequency-resolved measure of information flow, whose quality is generally unknown. Here, we develop an assumption-free method to measure a frequency-resolved information rate about a time-dependent Gaussian stimulus. We demonstrate its application for three paradigmatic descriptions of neural firing: an inhomogeneous Poisson process that carries a signal in its instantaneous firing rate; an integrator neuron (stochastic integrate-and-fire model) driven by a time-dependent stimulus; and the synchronous spikes fired by two commonly driven integrator neurons. In agreement with previous coherence-based estimates, we find that Poisson and integrate-and-fire neurons are broadband and low-pass filters of information, respectively. The band-pass information filtering observed in the coherence of synchronous spikes is confirmed by our frequency-resolved information measure in some but not all parameter configurations. Our results also explicitly show how the response-response coherence can fail as an upper bound on the information rate.

Information transmission in cercal giant interneurons is unaffected by axonal conduction noise

What are the fundamental constraints on the precision and accuracy with which nervous systems can process information? One constraint must reflect the intrinsic “noisiness” of the mechanisms that transmit information between nerve cells. Most neurons transmit information through the probabilistic generation and propagation of spikes along axons, and recent modeling studies suggest that noise from spike propagation might pose a significant constraint on the rate at which information could be transmitted between neurons. However, the magnitude and functional significance of this noise source in actual cells remains poorly understood. We measured variability in conduction time along the axons of identified neurons in the cercal sensory system of the cricket Acheta domesticus, and used information theory to calculate the effects of this variability on sensory coding. We found that the variability in spike propagation speed is not large enough to constrain the accuracy of neural encoding in this system.

An ancestral axial twist explains the contralateral forebrain and the optic chiasm in vertebrates

Among the best-known facts of the brain are the contralateral visual, auditory, sensational, and motor mappings in the forebrain. How and why did these evolve? The few theories to this question provide functional answers, such as better networks for visuomotor control. However, these theories contradict the data, as discussed here. Instead we propose that a 90-deg turn on the left side evolved in a common ancestor of all vertebrates. Compensatory migrations of the tissues during development restore body symmetry. Eyes, nostrils and forebrain compensate in the direction of the turn, whereas more caudal structures migrate in the opposite direction. As a result of these opposite migrations the forebrain becomes crossed and inverted with respect to the rest of the nervous system. We show that such compensatory migratory movements can indeed be observed in the zebrafish (Danio rerio) and the chick (Gallus gallus). With a model we show how the axial twist hypothesis predicts that an optic chiasm should develop on the ventral side of the brain, whereas the olfactory tract should be uncrossed. In addition, the hypothesis explains the decussation of the trochlear nerve, why olfaction is non-crossed, why the cerebellar hemispheres represent the ipsilateral bodyside, why in sharks the forebrain halves each represent the ipsilateral eye, why the heart and other inner organs are asymmetric in the body. Due to the poor fossil record, the possible evolutionary scenarios remain speculative. Molecular evidence does support the hypothesis. The findings may shed new insight on the problematic structure of the forebrain.

Identifying temporal codes in spontaneously active sensory neurons

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.