Two-dimensional time coding in the auditory brainstem

The tuning of tuning: How adaptation influences single cell information transfer

Sensory neurons reconstruct the world from action potentials (spikes) impinging on them. To effectively transfer information about the stimulus to the next processing level, a neuron needs to be able to adapt its working range to the properties of the stimulus. Here, we focus on the intrinsic neural properties that influence information transfer in cortical neurons and how tightly their properties need to be tuned to the stimulus statistics for them to be effective. We start by measuring the intrinsic information encoding properties of putative excitatory and inhibitory neurons in L2/3 of the mouse barrel cortex. Excitatory neurons show high thresholds and strong adaptation, making them fire sparsely and resulting in a strong compression of information, whereas inhibitory neurons that favour fast spiking transfer more information. Next, we turn to computational modelling and ask how two properties influence information transfer: 1) spike-frequency adaptation and 2) the shape of the IV-curve. We find that a subthreshold (but not threshold) adaptation, the 'h-current', and a properly tuned leak conductance can increase the information transfer of a neuron, whereas threshold adaptation can increase its working range. Finally, we verify the effect of the IV-curve slope in our experimental recordings and show that excitatory neurons form a more heterogeneous population than inhibitory neurons. These relationships between intrinsic neural features and neural coding that had not been quantified before will aid computational, theoretical and systems neuroscientists in understanding how neuronal populations can alter their coding properties, such as through the impact of neuromodulators. Why the variability of intrinsic properties of excitatory neurons is larger than that of inhibitory ones is an exciting question, for which future research is needed.

Inferring neural dynamics of memory during naturalistic social communication

Memory processes in complex behaviors like social communication require forming representations of the past that grow with time. The neural mechanisms that support such continually growing memory remain unknown. We address this gap in the context of fly courtship, a natural social behavior involving the production and perception of long, complex song sequences. To study female memory for male song history in unrestrained courtship, we present 'Natural Continuation' (NC)-a general, simulation-based model comparison procedure to evaluate candidate neural codes for complex stimuli using naturalistic behavioral data. Applying NC to fly courtship revealed strong evidence for an adaptive population mechanism for how female auditory neural dynamics could convert long song histories into a rich mnemonic format. Song temporal patterning is continually transformed by heterogeneous nonlinear adaptation dynamics, then integrated into persistent activity, enabling common neural mechanisms to retain continuously unfolding information over long periods and yielding state-of-the-art predictions of female courtship behavior. At a population level this coding model produces multi-dimensional advection-diffusion-like responses that separate songs over a continuum of timescales and can be linearly transformed into flexible output signals, illustrating its potential to create a generic, scalable mnemonic format for extended input signals poised to drive complex behavioral responses. This work thus shows how naturalistic behavior can directly inform neural population coding models, revealing here a novel process for memory formation.

A small, computationally flexible network produces the phenotypic diversity of song recognition in crickets

How neural networks evolved to generate the diversity of species-specific communication signals is unknown. For receivers of the signals, one hypothesis is that novel recognition phenotypes arise from parameter variation in computationally flexible feature detection networks. We test this hypothesis in crickets, where males generate and females recognize the mating songs with a species-specific pulse pattern, by investigating whether the song recognition network in the cricket brain has the computational flexibility to recognize different temporal features. Using electrophysiological recordings from the network that recognizes crucial properties of the pulse pattern on the short timescale in the cricket Gryllus bimaculatus, we built a computational model that reproduces the neuronal and behavioral tuning of that species. An analysis of the model's parameter space reveals that the network can provide all recognition phenotypes for pulse duration and pause known in crickets and even other insects. Phenotypic diversity in the model is consistent with known preference types in crickets and other insects, and arises from computations that likely evolved to increase energy efficiency and robustness of pattern recognition. The model's parameter to phenotype mapping is degenerate - different network parameters can create similar changes in the phenotype - which likely supports evolutionary plasticity. Our study suggests that computationally flexible networks underlie the diverse pattern recognition phenotypes, and we reveal network properties that constrain and support behavioral diversity.

Wing structure and neural encoding jointly determine sensing strategies in insect flight

Animals rely on sensory feedback to generate accurate, reliable movements. In many flying insects, strain-sensitive neurons on the wings provide rapid feedback that is critical for stable flight control. While the impacts of wing structure on aerodynamic performance have been widely studied, the impacts of wing structure on sensing are largely unexplored. In this paper, we show how the structural properties of the wing and encoding by mechanosensory neurons interact to jointly determine optimal sensing strategies and performance. Specifically, we examine how neural sensors can be placed effectively on a flapping wing to detect body rotation about different axes, using a computational wing model with varying flexural stiffness. A small set of mechanosensors, conveying strain information at key locations with a single action potential per wingbeat, enable accurate detection of body rotation. Optimal sensor locations are concentrated at either the wing base or the wing tip, and they transition sharply as a function of both wing stiffness and neural threshold. Moreover, the sensing strategy and performance is robust to both external disturbances and sensor loss. Typically, only five sensors are needed to achieve near-peak accuracy, with a single sensor often providing accuracy well above chance. Our results show that small-amplitude, dynamic signals can be extracted efficiently with spatially and temporally sparse sensors in the context of flight. The demonstrated interaction of wing structure and neural encoding properties points to the importance of understanding each in the context of their joint evolution.

In addition to generating forces for flight, insect wings also serve an important role as sensory structures, providing rapid feedback about wing bending that is used to stabilize flight. While much is known about how wing structure affects aerodynamic performance, the effects of wing structure on sensing remain unexplored. Using a computational model of a flapping wing, we examine how sensing strategies depend on wing stiffness and sensor properties. We show that body rotations can be accurately detected with a small number of sensors on the wing across a wide range of conditions. Optimal sensor locations are clustered at either the wing base or wing tip, depending on a combination of wing stiffness and sensor properties. Moreover, sensing performance is robust to multiple kinds of perturbations. Our work provides a basis for understanding how wing structure impacts incoming sensory information during flight.

Identification of Multiple Noise Sources Improves Estimation of Neural Responses across Stimulus Conditions

Most models of neural responses are constructed to reproduce the average response to inputs but lack the flexibility to capture observed variability in responses. The origins and structure of this variability have significant implications for how information is encoded and processed in the nervous system, both by limiting information that can be conveyed and by determining processing strategies that are favorable for minimizing its negative effects. Here, we present a new modeling framework that incorporates multiple sources of noise to better capture observed features of neural response variability across stimulus conditions. We apply this model to retinal ganglion cells at two different ambient light levels and demonstrate that it captures the full distribution of responses. Further, the model reveals light level-dependent changes that could not be seen with previous models, showing both large changes in rectification of nonlinear circuit elements and systematic differences in the contributions of different noise sources under different conditions.

Interspike intervals within retinal spike bursts combinatorially encode multiple stimulus features

Neurons in various regions of the brain generate spike bursts. While the number of spikes within a burst has been shown to carry information, information coding by interspike intervals (ISIs) is less well understood. In particular, a burst with k spikes has k−1 intraburst ISIs, and these k−1 ISIs could theoretically encode k−1 independent values. In this study, we demonstrate that such combinatorial coding occurs for retinal bursts. By recording ganglion cell spikes from isolated salamander retinae, we found that intraburst ISIs encode oscillatory light sequences that are much faster than the light intensity modulation encoded by the number of spikes. When a burst has three spikes, the two intraburst ISIs combinatorially encode the amplitude and phase of the oscillatory sequence. Analysis of trial-to-trial variability suggested that intraburst ISIs are regulated by two independent mechanisms responding to orthogonal oscillatory components, one of which is common to bursts with a different number of spikes. Therefore, the retina encodes multiple stimulus features by exploiting all degrees of freedom of burst spike patterns, i.e., the spike number and multiple intraburst ISIs.

Neurons in various regions of the brain generate spike bursts. Bursts are typically composed of a few spikes generated within dozens of milliseconds, and individual bursts are separated by much longer periods of silence (~hundreds of milliseconds). Recent evidence indicates that the number of spikes in a burst, the interspike intervals (ISIs), and the overall duration of a burst, as well as the timing of burst onset, encode information. However, it remains unknown whether multiple ISIs within a single burst encode multiple input features. Here we demonstrate that such combinatorial ISI coding occurs for spike bursts in the retina. We recorded ganglion cell spikes from isolated salamander retinae stimulated with computer-generated movies. Visual response analyses indicated that multiple ISIs within a single burst combinatorially encode the phase and amplitude of oscillatory light sequences, which are different from the stimulus feature encoded by the spike number. The result demonstrates that the retina encodes multiple stimulus features by exploiting all degrees of freedom of burst spike patterns, i.e., the spike number and multiple intraburst ISIs. Because synaptic transmission in the visual system is highly sensitive to ISIs, the combinatorial ISI coding must have a major impact on visual information processing.

Distinct Manifestations of Cooperative, Multidimensional Stimulus Representations in Different Auditory Forebrain Stations

Classic spectrotemporal receptive fields (STRFs) for auditory neurons are usually expressed as a single linear filter representing a single encoded stimulus feature. Multifilter STRF models represent the stimulus-response relationship of primary auditory cortex (A1) neurons more accurately because they can capture multiple stimulus features. To determine whether multifilter processing is unique to A1, we compared the utility of single-filter versus multifilter STRF models in the medial geniculate body (MGB), anterior auditory field (AAF), and A1 of ketamine-anesthetized cats. We estimated STRFs using both spike-triggered average (STA) and maximally informative dimension (MID) methods. Comparison of basic filter properties of first maximally informative dimension (MID1) and second maximally informative dimension (MID2) in the 3 stations revealed broader spectral integration of MID2s in MGBv and A1 as opposed to AAF. MID2 peak latency was substantially longer than for STAs and MID1s in all 3 stations. The 2-filter MID model captured more information and yielded better predictions in many neurons from all 3 areas but disproportionately more so in AAF and A1 compared with MGBv. Significantly, information-enhancing cooperation between the 2 MIDs was largely restricted to A1 neurons. This demonstrates significant differences in how these 3 forebrain stations process auditory information, as expressed in effective and synergistic multifilter processing.

Intrinsic physiological properties underlie auditory response diversity in the avian cochlear nucleus

Sensory systems exploit parallel processing of stimulus features to enable rapid, simultaneous extraction of information. Mechanisms that facilitate this differential extraction of stimulus features can be intrinsic or synaptic in origin. A subdivision of the avian cochlear nucleus, nucleus angularis (NA), extracts sound intensity information from the auditory nerve and contains neurons that exhibit diverse responses to sound and current injection. NA neurons project to multiple regions ascending the auditory brain stem including the superior olivary nucleus, lateral lemniscus, and avian inferior colliculus, with functional implications for inhibitory gain control and sound localization. Here we investigated whether the diversity of auditory response patterns in NA can be accounted for by variation in intrinsic physiological features. Modeled sound-evoked auditory nerve input was applied to NA neurons with dynamic clamp during in vitro whole cell recording at room temperature. Temporal responses to auditory nerve input depended on variation in intrinsic properties, and the low-threshold K⁺ current was implicated as a major contributor to temporal response diversity and neuronal input-output functions. An auditory nerve model of acoustic amplitude modulation produced synchrony coding of modulation frequency that depended on the intrinsic physiology of the individual neuron. In Primary-Like neurons, varying low-threshold K⁺ conductance with dynamic clamp altered temporal modulation tuning bidirectionally. Taken together, these data suggest that intrinsic physiological properties play a key role in shaping auditory response diversity to both simple and more naturalistic auditory stimuli in the avian cochlear nucleus. NEW & NOTEWORTHY This article addresses the question of how the nervous system extracts different information in sounds. Neurons in the cochlear nucleus show diverse responses to acoustic stimuli that may allow for parallel processing of acoustic features. The present studies suggest that diversity in intrinsic physiological features of individual neurons, including levels of a low voltage-activated K⁺ current, play a major role in regulating the diversity of auditory responses.

Nonlinear Modeling of Neural Interaction for Spike Prediction Using the Staged Point-Process Model

Neurons communicate nonlinearly through spike activities. Generalized linear models (GLMs) describe spike activities with a cascade of a linear combination across inputs, a static nonlinear function, and an inhomogeneous Bernoulli or Poisson process, or Cox process if a self-history term is considered. This structure considers the output nonlinearity in spike generation but excludes the nonlinear interaction among input neurons. Recent studies extend GLMs by modeling the interaction among input neurons with a quadratic function, which considers the interaction between every pair of input spikes. However, quadratic effects may not fully capture the nonlinear nature of input interaction. We therefore propose a staged point-process model to describe the nonlinear interaction among inputs using a few hidden units, which follows the idea of artificial neural networks. The output firing probability conditioned on inputs is formed as a cascade of two linear-nonlinear (a linear combination plus a static nonlinear function) stages and an inhomogeneous Bernoulli process. Parameters of this model are estimated by maximizing the log likelihood on output spike trains. Unlike the iterative reweighted least squares algorithm used in GLMs, where the performance is guaranteed by the concave condition, we propose a modified Levenberg-Marquardt (L-M) algorithm, which directly calculates the Hessian matrix of the log likelihood, for the nonlinear optimization in our model. The proposed model is tested on both synthetic data and real spike train data recorded from the dorsal premotor cortex and primary motor cortex of a monkey performing a center-out task. Performances are evaluated by discrete-time rescaled Kolmogorov-Smirnov tests, where our model statistically outperforms a GLM and its quadratic extension, with a higher goodness-of-fit in the prediction results. In addition, the staged point-process model describes nonlinear interaction among input neurons with fewer parameters than quadratic models, and the modified L-M algorithm also demonstrates fast convergence.

Spike and burst coding in thalamocortical relay cells

Mammalian thalamocortical relay (TCR) neurons switch their firing activity between a tonic spiking and a bursting regime. In a combined experimental and computational study, we investigated the features in the input signal that single spikes and bursts in the output spike train represent and how this code is influenced by the membrane voltage state of the neuron. Identical frozen Gaussian noise current traces were injected into TCR neurons in rat brain slices as well as in a validated three-compartment TCR model cell. The resulting membrane voltage traces and spike trains were analyzed by calculating the coherence and impedance. Reverse correlation techniques gave the Event-Triggered Average (ETA) and the Event-Triggered Covariance (ETC). This demonstrated that the feature selectivity started relatively long before the events (up to 300 ms) and showed a clear distinction between spikes (selective for fluctuations) and bursts (selective for integration). The model cell was fine-tuned to mimic the frozen noise initiated spike and burst responses to within experimental accuracy, especially for the mixed mode regimes. The information content carried by the various types of events in the signal as well as by the whole signal was calculated. Bursts phase-lock to and transfer information at lower frequencies than single spikes. On depolarization the neuron transits smoothly from the predominantly bursting regime to a spiking regime, in which it is more sensitive to high-frequency fluctuations. The model was then used to elucidate properties that could not be assessed experimentally, in particular the role of two important subthreshold voltage-dependent currents: the low threshold activated calcium current (I_T) and the cyclic nucleotide modulated h current (I_h). The ETAs of those currents and their underlying activation/inactivation states not only explained the state dependence of the firing regime but also the long-lasting concerted dynamic action of the two currents. Finally, the model was used to investigate the more realistic “high-conductance state”, where fluctuations are caused by (synaptic) conductance changes instead of current injection. Under “standard” conditions bursts are difficult to initiate, given the high degree of inactivation of the T-type calcium current. Strong and/or precisely timed inhibitory currents were able to remove this inactivation.

Neurons in the brain respond to (sensory) stimuli by generating electrical pulses called ‘spikes’ or ‘action potentials’. Spikes are organized in different temporal patterns, such as ‘bursts’ in which they occur at a high frequency followed by a period of silence. Bursts are ubiquitous in the nervous system: they occur in different parts of the brain and in different species. Different mechanisms that generate them have been pointed out. Why the nervous system uses bursts in its communication, or what type of information is represented by bursts, remains largely unknown. Here, we looked at bursting in thalamocortical relay (TCR) cells, neurons that form a bridge between early sensory processing and higher-order structures (cortex). These cells fire bursts as a result of the activation of two distinct subthreshold ionic currents: the T-type calcium current and the h-type current. We investigated experimentally and computationally what features in the input makes TCR cells respond with bursts, and what features with single spikes. Bursts are a response to low-frequency slowly increasing input; single spikes are a response to faster fluctuations. Moreover, bursts are rare and highly informative, in line with an earlier hypothesis that bursts could play a ‘wake-up call’ role in the nervous system.

Tonotopic Optimization for Temporal Processing in the Cochlear Nucleus

In the auditory system, sounds are processed in parallel frequency-tuned circuits, beginning in the cochlea. Auditory nerve fibers reflect this tonotopy and encode temporal properties of acoustic stimuli by "locking" discharges to a particular stimulus phase. However, physiological constraints on phase-locking depend on stimulus frequency. Interestingly, low characteristic frequency (LCF) neurons in the cochlear nucleus improve phase-locking precision relative to their auditory nerve inputs. This is proposed to arise through synaptic integration, but the postsynaptic membrane's selectivity for varying levels of synaptic convergence is poorly understood. The chick cochlear nucleus, nucleus magnocellularis (NM), exhibits tonotopic distribution of both input and membrane properties. LCF neurons receive many small inputs and have low input thresholds, whereas high characteristic frequency (HCF) neurons receive few, large synapses and require larger currents to spike. NM therefore presents an opportunity to study how small membrane variations interact with a systematic topographic gradient of synaptic inputs. We investigated membrane input selectivity and observed that HCF neurons preferentially select faster input than their LCF counterparts, and that this preference is tolerant of changes to membrane voltage. We then used computational models to probe which properties are crucial to phase-locking. The model predicted that the optimal arrangement of synaptic and membrane properties for phase-locking is specific to stimulus frequency and that the tonotopic distribution of input number and membrane excitability in NM closely tracks a stimulus-defined optimum. These findings were then confirmed physiologically with dynamic-clamp simulations of inputs to NM neurons.

SIGNIFICANCE STATEMENT

One way that neurons represent temporal information is by phase-locking, which is discharging in response to a particular phase of the stimulus waveform. In the auditory system, central neurons are optimized to retain or improve phase-locking precision compared with input from the auditory nerve. However, the difficulty of this computation varies systematically with stimulus frequency. We examined properties that contribute to temporal processing both physiologically and in a computational model. Neurons processing low-frequency input benefit from integration of many weak inputs, whereas those processing higher frequencies progressively lose precision by integration of multiple inputs. Here, we reveal general features of input-output optimization that apply to all neurons that process time varying input.

Noise-enhanced coding in phasic neuron spike trains

The stochastic nature of neuronal response has lead to conjectures about the impact of input fluctuations on the neural coding. For the most part, low pass membrane integration and spike threshold dynamics have been the primary features assumed in the transfer from synaptic input to output spiking. Phasic neurons are a common, but understudied, neuron class that are characterized by a subthreshold negative feedback that suppresses spike train responses to low frequency signals. Past work has shown that when a low frequency signal is accompanied by moderate intensity broadband noise, phasic neurons spike trains are well locked to the signal. We extend these results with a simple, reduced model of phasic activity that demonstrates that a non-Markovian spike train structure caused by the negative feedback produces a noise-enhanced coding. Further, this enhancement is sensitive to the timescales, as opposed to the intensity, of a driving signal. Reduced hazard function models show that noise-enhanced phasic codes are both novel and separate from classical stochastic resonance reported in non-phasic neurons. The general features of our theory suggest that noise-enhanced codes in excitable systems with subthreshold negative feedback are a particularly rich framework to study.

Graphics Processing Unit-Accelerated Code for Computing Second-Order Wiener Kernels and Spike-Triggered Covariance

Sensory neuroscience seeks to understand and predict how sensory neurons respond to stimuli. Nonlinear components of neural responses are frequently characterized by the second-order Wiener kernel and the closely-related spike-triggered covariance (STC). Recent advances in data acquisition have made it increasingly common and computationally intensive to compute second-order Wiener kernels/STC matrices. In order to speed up this sort of analysis, we developed a graphics processing unit (GPU)-accelerated module that computes the second-order Wiener kernel of a system's response to a stimulus. The generated kernel can be easily transformed for use in standard STC analyses. Our code speeds up such analyses by factors of over 100 relative to current methods that utilize central processing units (CPUs). It works on any modern GPU and may be integrated into many data analysis workflows. This module accelerates data analysis so that more time can be spent exploring parameter space and interpreting data.

Perineuronal Nets Enhance the Excitability of Fast-Spiking Neurons

Perineuronal nets (PNNs) are specialized complexes of extracellular matrix molecules that surround the somata of fast-spiking neurons throughout the vertebrate brain. PNNs are particularly prevalent throughout the auditory brainstem, which transmits signals with high speed and precision. It is unknown whether PNNs contribute to the fast-spiking ability of the neurons they surround. Whole-cell recordings were made from medial nucleus of the trapezoid body (MNTB) principal neurons in acute brain slices from postnatal day 21 (P21) to P27 mice. PNNs were degraded by incubating slices in chondroitinase ABC (ChABC) and were compared to slices that were treated with a control enzyme (penicillinase). ChABC treatment did not affect the ability of MNTB neurons to fire at up to 1000 Hz when driven by current pulses. However, f–I (frequency–intensity) curves constructed by injecting Gaussian white noise currents superimposed on DC current steps showed that ChABC treatment reduced the gain of spike output. An increase in spike threshold may have contributed to this effect, which is consistent with the observation that spikes in ChABC-treated cells were delayed relative to control-treated cells. In addition, parvalbumin-expressing fast-spiking cortical neurons in >P70 slices that were treated with ChABC also had reduced excitability and gain. The development of PNNs around somata of fast-spiking neurons may be essential for fast and precise sensory transmission and synaptic inhibition in the brain.

Analysis of Neuronal Spike Trains, Deconstructed

As information flows through the brain, neuronal firing progresses from encoding the world as sensed by the animal to driving the motor output of subsequent behavior. One of the more tractable goals of quantitative neuroscience is to develop predictive models that relate the sensory or motor streams with neuronal firing. Here we review and contrast analytical tools used to accomplish this task. We focus on classes of models in which the external variable is compared with one or more feature vectors to extract a low-dimensional representation, the history of spiking and other variables are potentially incorporated, and these factors are nonlinearly transformed to predict the occurrences of spikes. We illustrate these techniques in application to datasets of different degrees of complexity. In particular, we address the fitting of models in the presence of strong correlations in the external variable, as occurs in natural sensory stimuli and in movement. Spectral correlation between predicted and measured spike trains is introduced to contrast the relative success of different methods.

Understanding spike-triggered covariance using Wiener theory for receptive field identification

Receptive field identification is a vital problem in sensory neurophysiology and vision. Much research has been done in identifying the receptive fields of nonlinear neurons whose firing rate is determined by the nonlinear interactions of a small number of linear filters. Despite more advanced methods that have been proposed, spike-triggered covariance (STC) continues to be the most widely used method in such situations due to its simplicity and intuitiveness. Although the connection between STC and Wiener/Volterra kernels has often been mentioned in the literature, this relationship has never been explicitly derived. Here we derive this relationship and show that the STC matrix is actually a modified version of the second-order Wiener kernel, which incorporates the input autocorrelation and mixes first- and second-order dynamics. It is then shown how, with little modification of the STC method, the Wiener kernels may be obtained and, from them, the principal dynamic modes, a set of compact and efficient linear filters that essentially combine the spike-triggered average and STC matrix and generalize to systems with both continuous and point-process outputs. Finally, using Wiener theory, we show how these obtained filters may be corrected when they were estimated using correlated inputs. Our correction technique is shown to be superior to those commonly used in the literature for both correlated Gaussian images and natural images.

Convergence, Divergence, and Reconvergence in a Feedforward Network Improves Neural Speed and Accuracy

One of the proposed canonical circuit motifs employed by the brain is a feedforward network where parallel signals converge, diverge, and reconverge. Here we investigate a network with this architecture in the Drosophila olfactory system. We focus on a glomerulus whose receptor neurons converge in an all-to-all manner onto six projection neurons that then reconverge onto higher-order neurons. We find that both convergence and reconvergence improve the ability of a decoder to detect a stimulus based on a single neuron's spike train. The first transformation implements averaging, and it improves peak detection accuracy but not speed; the second transformation implements coincidence detection, and it improves speed but not peak accuracy. In each case, the integration time and threshold of the postsynaptic cell are matched to the statistics of convergent spike trains.

Postnatal development attunes olfactory bulb mitral cells to high-frequency signaling

Mitral cells (MCs) are a major class of principal neurons in the vertebrate olfactory bulb, conveying odor-evoked activity from the peripheral sensory neurons to olfactory cortex. Previous work has described the development of MC morphology and connectivity during the first few weeks of postnatal development. However, little is known about the postnatal development of MC intrinsic biophysical properties. To understand stimulus encoding in the developing olfactory bulb, we have therefore examined the development of MC intrinsic biophysical properties in acute slices from postnatal day (P)7-P35 mice. Across development, we observed systematic changes in passive membrane properties and action potential waveforms consistent with a developmental increase in sodium and potassium conductances. We further observed developmental decreases in hyperpolarization-evoked membrane potential sag and firing regularity, extending recent links between MC sag heterogeneity and firing patterns. We then applied a novel combination of statistical analyses to examine how the evolution of these intrinsic biophysical properties specifically influenced the representation of fluctuating stimuli by MCs. We found that immature MCs responded to frozen fluctuating stimuli with lower firing rates, lower spike-time reliability, and lower between-cell spike-time correlations than more mature MCs. Analysis of spike-triggered averages revealed that these changes in spike timing were driven by a developmental shift from broad integration of inputs to more selective detection of coincident inputs. Consistent with this shift, generalized linear model fits to MC firing responses demonstrated an enhanced encoding of high-frequency stimulus features by mature MCs.

Subthreshold membrane currents confer distinct tuning properties that enable neurons to encode the integral or derivative of their input

Neurons rely on action potentials, or spikes, to encode information. But spikes can encode different stimulus features in different neurons. We show here through simulations and experiments how neurons encode the integral or derivative of their input based on the distinct tuning properties conferred upon them by subthreshold currents. Slow-activating subthreshold inward (depolarizing) current mediates positive feedback control of subthreshold voltage, sustaining depolarization and allowing the neuron to spike on the basis of its integrated stimulus waveform. Slow-activating subthreshold outward (hyperpolarizing) current mediates negative feedback control of subthreshold voltage, truncating depolarization and forcing the neuron to spike on the basis of its differentiated stimulus waveform. Depending on its direction, slow-activating subthreshold current cooperates or competes with fast-activating inward current during spike initiation. This explanation predicts that sensitivity to the rate of change of stimulus intensity differs qualitatively between integrators and differentiators. This was confirmed experimentally in spinal sensory neurons that naturally behave as specialized integrators or differentiators. Predicted sensitivity to different stimulus features was confirmed by covariance analysis. Integration and differentiation, which are themselves inverse operations, are thus shown to be implemented by the slow feedback mediated by oppositely directed subthreshold currents expressed in different neurons.

System identification of point-process neural systems using probability based Volterra kernels

BACKGROUND

Neural information processing involves a series of nonlinear dynamical input/output transformations between the spike trains of neurons/neuronal ensembles. Understanding and quantifying these transformations is critical both for understanding neural physiology such as short-term potentiation and for developing cognitive neural prosthetics.

NEW METHOD

A novel method for estimating Volterra kernels for systems with point-process inputs and outputs is developed based on elementary probability theory. These Probability Based Volterra (PBV) kernels essentially describe the probability of an output spike given q input spikes at various lags t1, t2, …, tq.

RESULTS

The PBV kernels are used to estimate both synthetic systems where ground truth is available and data from the CA3 and CA1 regions rodent hippocampus. The PBV kernels give excellent predictive results in both cases. Furthermore, they are shown to be quite robust to noise and to have good convergence and overfitting properties. Through a slight modification, the PBV kernels are shown to also deal well with correlated point-process inputs.

COMPARISON WITH EXISTING METHODS

The PBV kernels were compared with kernels estimated through least squares estimation (LSE) and through the Laguerre expansion technique (LET). The LSE kernels were shown to fair very poorly with real data due to the large amount of input noise. Although the LET kernels gave the best predictive results in all cases, they require prior parameter estimation. It was shown how the PBV and LET methods can be combined synergistically to maximize performance.

CONCLUSIONS

The PBV kernels provide a novel and intuitive method of characterizing point-process input-output nonlinear systems.

Context-dependent coding in single neurons

The linear-nonlinear cascade model (LN model) has proven very useful in representing a neural system's encoding properties, but has proven less successful in reproducing the firing patterns of individual neurons whose behavior is strongly dependent on prior firing history. While the cell's behavior can still usefully be considered as feature detection acting on a fluctuating input, some of the coding capacity of the cell is taken up by the increased firing rate due to a constant "driving" direct current (DC) stimulus. Furthermore, both the DC input and the post-spike refractory period generate regular firing, reducing the spike-timing entropy available for encoding time-varying fluctuations. In this paper, we address these issues, focusing on the example of motoneurons in which an afterhyperpolarization (AHP) current plays a dominant role regularizing firing behavior. We explore the accuracy and generalizability of several alternative models for single neurons under changes in DC and variance of the stimulus input. We use a motoneuron simulation to compare coding models in neurons with and without the AHP current. Finally, we quantify the tradeoff between instantaneously encoding information about fluctuations and about the DC.

Functional identification of spike-processing neural circuits

We introduce a novel approach for a complete functional identification of biophysical spike-processing neural circuits. The circuits considered accept multidimensional spike trains as their input and comprise a multitude of temporal receptive fields and conductance-based models of action potential generation. Each temporal receptive field describes the spatiotemporal contribution of all synapses between any two neurons and incorporates the (passive) processing carried out by the dendritic tree. The aggregate dendritic current produced by a multitude of temporal receptive fields is encoded into a sequence of action potentials by a spike generator modeled as a nonlinear dynamical system. Our approach builds on the observation that during any experiment, an entire neural circuit, including its receptive fields and biophysical spike generators, is projected onto the space of stimuli used to identify the circuit. Employing the reproducing kernel Hilbert space (RKHS) of trigonometric polynomials to describe input stimuli, we quantitatively describe the relationship between underlying circuit parameters and their projections. We also derive experimental conditions under which these projections converge to the true parameters. In doing so, we achieve the mathematical tractability needed to characterize the biophysical spike generator and identify the multitude of receptive fields. The algorithms obviate the need to repeat experiments in order to compute the neurons' rate of response, rendering our methodology of interest to both experimental and theoretical neuroscientists.

Emergence of adaptive computation by single neurons in the developing cortex

Adaptation is a fundamental computational motif in neural processing. To maintain stable perception in the face of rapidly shifting input, neural systems must extract relevant information from background fluctuations under many different contexts. Many neural systems are able to adjust their input-output properties such that an input's ability to trigger a response depends on the size of that input relative to its local statistical context. This "gain-scaling" strategy has been shown to be an efficient coding strategy. We report here that this property emerges during early development as an intrinsic property of single neurons in mouse sensorimotor cortex, coinciding with the disappearance of spontaneous waves of network activity, and can be modulated by changing the balance of spike-generating currents. Simultaneously, developing neurons move toward a common intrinsic operating point and a stable ratio of spike-generating currents. This developmental trajectory occurs in the absence of sensory input or spontaneous network activity. Through a combination of electrophysiology and modeling, we demonstrate that developing cortical neurons develop the ability to perform nearly perfect gain scaling by virtue of the maturing spike-generating currents alone. We use reduced single neuron models to identify the conditions for this property to hold.

Impact of neuronal properties on network coding: roles of spike initiation dynamics and robust synchrony transfer

Neural networks are more than the sum of their parts, but the properties of those parts are nonetheless important. For instance, neuronal properties affect the degree to which neurons receiving common input will spike synchronously, and whether that synchrony will propagate through the network. Stimulus-evoked synchrony can help or hinder network coding depending on the type of code. In this Perspective, we describe how spike initiation dynamics influence neuronal input-output properties, how those properties affect synchronization, and how synchronization affects network coding. We propose that synchronous and asynchronous spiking can be used to multiplex temporal (synchrony) and rate coding and discuss how pyramidal neurons would be well suited for that task.

Intermediate intrinsic diversity enhances neural population coding

Cell-to-cell variability in molecular, genetic, and physiological features is increasingly recognized as a critical feature of complex biological systems, including the brain. Although such variability has potential advantages in robustness and reliability, how and why biological circuits assemble heterogeneous cells into functional groups is poorly understood. Here, we develop analytic approaches toward answering how neuron-level variation in intrinsic biophysical properties of olfactory bulb mitral cells influences population coding of fluctuating stimuli. We capture the intrinsic diversity of recorded populations of neurons through a statistical approach based on generalized linear models. These models are flexible enough to predict the diverse responses of individual neurons yet provide a common reference frame for comparing one neuron to the next. We then use Bayesian stimulus decoding to ask how effectively different populations of mitral cells, varying in their diversity, encode a common stimulus. We show that a key advantage provided by physiological levels of intrinsic diversity is more efficient and more robust encoding of stimuli by the population as a whole. However, we find that the populations that best encode stimulus features are not simply the most heterogeneous, but those that balance diversity with the benefits of neural similarity.

Adaptation of spike timing precision controls the sensitivity to interaural time difference in the avian auditory brainstem

While adaptation is widely thought to facilitate neural coding, the form of adaptation should depend on how the signals are encoded. Monaural neurons early in the interaural time difference (ITD) pathway encode the phase of sound input using spike timing rather than firing rate. Such neurons in chicken nucleus magnocellularis (NM) adapt to ongoing stimuli by increasing firing rate and decreasing spike timing precision. We measured NM neuron responses while adapting them to simulated physiological input, and used these responses to construct inputs to binaural coincidence detector neurons in nucleus laminaris (NL). Adaptation of spike timing in NM reduced ITD sensitivity in NL, demonstrating the dominant role of timing in the short-term plasticity as well as the immediate response of this sound localization circuit.

Parallel coding of first- and second-order stimulus attributes by midbrain electrosensory neurons

Natural stimuli often have time-varying first-order (i.e., mean) and second-order (i.e., variance) attributes that each carry critical information for perception and can vary independently over orders of magnitude. Experiments have shown that sensory systems continuously adapt their responses based on changes in each of these attributes. This adaptation creates ambiguity in the neural code as multiple stimuli may elicit the same neural response. While parallel processing of first- and second-order attributes by separate neural pathways is sufficient to remove this ambiguity, the existence of such pathways and the neural circuits that mediate their emergence have not been uncovered to date. We recorded the responses of midbrain electrosensory neurons in the weakly electric fish Apteronotus leptorhynchus to stimuli with first- and second-order attributes that varied independently in time. We found three distinct groups of midbrain neurons: the first group responded to both first- and second-order attributes, the second group responded selectively to first-order attributes, and the last group responded selectively to second-order attributes. In contrast, all afferent hindbrain neurons responded to both first- and second-order attributes. Using computational analyses, we show how inputs from a heterogeneous population of ON- and OFF-type afferent neurons are combined to give rise to response selectivity to either first- or second-order stimulus attributes in midbrain neurons. Our study thus uncovers, for the first time, generic and widely applicable mechanisms by which parallel processing of first- and second-order stimulus attributes emerges in the brain.

Spike-interval triggered averaging reveals a quasi-periodic spiking alternative for stochastic resonance in catfish electroreceptors

Catfish detect and identify invisible prey by sensing their ultra-weak electric fields with electroreceptors. Any neuron that deals with small-amplitude input has to overcome sensitivity limitations arising from inherent threshold non-linearities in spike-generation mechanisms. Many sensory cells solve this issue with stochastic resonance, in which a moderate amount of intrinsic noise causes irregular spontaneous spiking activity with a probability that is modulated by the input signal. Here we show that catfish electroreceptors have adopted a fundamentally different strategy. Using a reverse correlation technique in which we take spike interval durations into account, we show that the electroreceptors generate a supra-threshold bias current that results in quasi-periodically produced spikes. In this regime stimuli modulate the interval between successive spikes rather than the instantaneous probability for a spike. This alternative for stochastic resonance combines threshold-free sensitivity for weak stimuli with similar sensitivity for excitations and inhibitions based on single interspike intervals.

Temporal precision and reliability in the velocity regime of a hair-cell sensory system: the mechanosensory lateral line of goldfish, Carassius auratus

Fish and aquatic frogs detect minute water motion by means of a specialized mechanosensory system, the lateral line. Ubiquitous in fish, the lateral-line system is characterized by hair-cell based sensory structures across the fish's surface called neuromasts. These neuromasts occur free-standing on the skin as superficial neuromasts (SN) or are recessed into canals as canal neuromasts. SNs respond to rapid changes of water velocity in a small layer of fluid around the fish, including the so-called boundary layer. Although omnipresent, the boundary layer's impact on the SN response is still a matter of debate. For the first time using an information-theoretic approach to this sensory system, we have investigated the SN afferents encoding capabilities. Combining covariance analysis, phase analysis, and modeling of recorded neuronal responses of primary lateral line afferents, we show that encoding by the SNs is adequately described as a linear, velocity-responsive mechanism. Afferent responses display a bimodal distribution of opposite Wiener kernels that likely reflected the two hair-cell populations within a given neuromast. Using frozen noise stimuli, we further demonstrate that SN afferents respond in an extremely precise manner and with high reproducibility across a broad frequency band (10-150 Hz), revealing that an optimal decoder would need to rely extensively on a temporal code. This was further substantiated by means of signal reconstruction of spike trains that were time shifted with respect to their original. On average, a time shift of 3.5 ms was enough to diminish the encoding capabilities of primary afferents by 70%. Our results further demonstrate that the SNs' encoding capability is linearly related to the stimulus outside the boundary layer, and that the boundary layer can, therefore, be neglected while interpreting lateral line response of SN afferents to hydrodynamic stimuli.

TYPE III EXCITABILITY, SLOPE SENSITIVITY AND COINCIDENCE DETECTION

Some neurons in the nervous system do not show repetitive firing for steady currents. For time-varying inputs, they fire once if the input rise is fast enough. This property of phasic firing is known as Type III excitability. Type III excitability has been observed in neurons in the auditory brainstem (MSO), which show strong phase-locking and accurate coincidence detection. In this paper, we consider a Hodgkin-Huxley type model (RM03) that is widely-used for phasic MSO neurons and we compare it with a modification of it, showing tonic behavior. We provide insight into the temporal processing of these neuron models by means of developing and analyzing two reduced models that reproduce qualitatively the properties of the exemplar ones. The geometric and mathematical analysis of the reduced models allows us to detect and quantify relevant features for the temporal computation such as nearness to threshold and a temporal integration window. Our results underscore the importance of Type III excitability for precise coincidence detection.

Balanced synaptic input shapes the correlation between neural spike trains

Stimulus properties, attention, and behavioral context influence correlations between the spike times produced by a pair of neurons. However, the biophysical mechanisms that modulate these correlations are poorly understood. With a combined theoretical and experimental approach, we show that the rate of balanced excitatory and inhibitory synaptic input modulates the magnitude and timescale of pairwise spike train correlation. High rate synaptic inputs promote spike time synchrony rather than long timescale spike rate correlations, while low rate synaptic inputs produce opposite results. This correlation shaping is due to a combination of enhanced high frequency input transfer and reduced firing rate gain in the high input rate state compared to the low state. Our study extends neural modulation from single neuron responses to population activity, a necessary step in understanding how the dynamics and processing of neural activity change across distinct brain states.

Two-dimensional adaptation in the auditory forebrain

Sensory neurons exhibit two universal properties: sensitivity to multiple stimulus dimensions, and adaptation to stimulus statistics. How adaptation affects encoding along primary dimensions is well characterized for most sensory pathways, but if and how it affects secondary dimensions is less clear. We studied these effects for neurons in the avian equivalent of primary auditory cortex, responding to temporally modulated sounds. We showed that the firing rate of single neurons in field L was affected by at least two components of the time-varying sound log-amplitude. When overall sound amplitude was low, neural responses were based on nonlinear combinations of the mean log-amplitude and its rate of change (first time differential). At high mean sound amplitude, the two relevant stimulus features became the first and second time derivatives of the sound log-amplitude. Thus a strikingly systematic relationship between dimensions was conserved across changes in stimulus intensity, whereby one of the relevant dimensions approximated the time differential of the other dimension. In contrast to stimulus mean, increases in stimulus variance did not change relevant dimensions, but selectively increased the contribution of the second dimension to neural firing, illustrating a new adaptive behavior enabled by multidimensional encoding. Finally, we demonstrated theoretically that inclusion of time differentials as additional stimulus features, as seen so prominently in the single-neuron responses studied here, is a useful strategy for encoding naturalistic stimuli, because it can lower the necessary sampling rate while maintaining the robustness of stimulus reconstruction to correlated noise.

Kv1 channels control spike threshold dynamics and spike timing in cortical pyramidal neurones

Previous studies showed that cortical pyramidal neurones (PNs) have a dynamic spike threshold that functions as a high-pass filter, enhancing spike timing in response to high-frequency input. While it is commonly assumed that Na(+) channel inactivation is the primary mechanism of threshold accommodation, the possible role of K(+) channel activation in fast threshold changes has not been well characterized. The present study tested the hypothesis that low-voltage activated Kv1 channels affect threshold dynamics in layer 2-3 PNs, using α-dendrotoxin (DTX) or 4-aminopyridine (4-AP) to block these conductances. We found that Kv1 blockade reduced the dynamic changes of spike threshold in response to a variety of stimuli, including stimulus-evoked synaptic input, current steps and ramps of varied duration, and noise. Analysis of the responses to noise showed that Kv1 channels increased the coherence of spike output with high-frequency components of the stimulus. A simple model demonstrates that a dynamic spike threshold can account for this effect. Our results show that the Kv1 conductance is a major mechanism that contributes to the dynamic spike threshold and precise spike timing of cortical PNs.

Analyzing multicomponent receptive fields from neural responses to natural stimuli

The challenge of building increasingly better models of neural responses to natural stimuli is to accurately estimate the multiple stimulus features that may jointly affect the neural spike probability. The selectivity for combinations of features is thought to be crucial for achieving classical properties of neural responses such as contrast invariance. The joint search for these multiple stimulus features is difficult because estimating spike probability as a multidimensional function of stimulus projections onto candidate relevant dimensions is subject to the curse of dimensionality. An attractive alternative is to search for relevant dimensions sequentially, as in projection pursuit regression. Here we demonstrate using analytic arguments and simulations of model cells that different types of sequential search strategies exhibit systematic biases when used with natural stimuli. Simulations show that joint optimization is feasible for up to three dimensions with current algorithms. When applied to the responses of V1 neurons to natural scenes, models based on three jointly optimized dimensions had better predictive power in a majority of cases compared to dimensions optimized sequentially, with different sequential methods yielding comparable results. Thus, although the curse of dimensionality remains, at least several relevant dimensions can be estimated by joint information maximization.

Difference in response reliability predicted by spectrotemporal tuning in the cochlear nuclei of barn owls

The brainstem auditory pathway is obligatory for all aural information. Brainstem auditory neurons must encode the level and timing of sounds, as well as their time-dependent spectral properties, the fine structure, and envelope, which are essential for sound discrimination. This study focused on envelope coding in the two cochlear nuclei of the barn owl, nucleus angularis (NA) and nucleus magnocellularis (NM). NA and NM receive input from bifurcating auditory nerve fibers and initiate processing pathways specialized in encoding interaural time (ITD) and level (ILD) differences, respectively. We found that NA neurons, although unable to accurately encode stimulus phase, lock more strongly to the stimulus envelope than NM units. The spectrotemporal receptive fields (STRFs) of NA neurons exhibit a pre-excitatory suppressive field. Using multilinear regression analysis and computational modeling, we show that this feature of STRFs can account for enhanced across-trial response reliability, by locking spikes to the stimulus envelope. Our findings indicate a dichotomy in envelope coding between the time and intensity processing pathways as early as at the level of the cochlear nuclei. This allows the ILD processing pathway to encode envelope information with greater fidelity than the ITD processing pathway. Furthermore, we demonstrate that the properties of the STRFs of the neurons can be quantitatively related to spike timing reliability.

Membrane voltage fluctuations reduce spike frequency adaptation and preserve output gain in CA1 pyramidal neurons in a high-conductance state

Modulating the gain of the input-output function of neurons is critical for processing of stimuli and network dynamics. Previous gain control mechanisms have suggested that voltage fluctuations play a key role in determining neuronal gain in vivo. Here we show that, under increased membrane conductance, voltage fluctuations restore Na(+) current and reduce spike frequency adaptation in rat hippocampal CA1 pyramidal neurons in vitro. As a consequence, membrane voltage fluctuations produce a leftward shift in the frequency-current relationship without a change in gain, relative to an increase in conductance alone. Furthermore, we show that these changes have important implications for the integration of inhibitory inputs. Due to the ability to restore Na(+) current, hyperpolarizing membrane voltage fluctuations mediated by GABA(A)-like inputs can increase firing rate in a high-conductance state. Finally, our data show that the effects on gain and synaptic integration are mediated by voltage fluctuations within a physiologically relevant range of frequencies (10-40 Hz).

System identification of Drosophila olfactory sensory neurons

The lack of a deeper understanding of how olfactory sensory neurons (OSNs) encode odors has hindered the progress in understanding the olfactory signal processing in higher brain centers. Here we employ methods of system identification to investigate the encoding of time-varying odor stimuli and their representation for further processing in the spike domain by Drosophila OSNs. In order to apply system identification techniques, we built a novel low-turbulence odor delivery system that allowed us to deliver airborne stimuli in a precise and reproducible fashion. The system provides a 1% tolerance in stimulus reproducibility and an exact control of odor concentration and concentration gradient on a millisecond time scale. Using this novel setup, we recorded and analyzed the in-vivo response of OSNs to a wide range of time-varying odor waveforms. We report for the first time that across trials the response of OR59b OSNs is very precise and reproducible. Further, we empirically show that the response of an OSN depends not only on the concentration, but also on the rate of change of the odor concentration. Moreover, we demonstrate that a two-dimensional (2D) Encoding Manifold in a concentration-concentration gradient space provides a quantitative description of the neuron's response. We then use the white noise system identification methodology to construct one-dimensional (1D) and two-dimensional (2D) Linear-Nonlinear-Poisson (LNP) cascade models of the sensory neuron for a fixed mean odor concentration and fixed contrast. We show that in terms of predicting the intensity rate of the spike train, the 2D LNP model performs on par with the 1D LNP model, with a root mean-square error (RMSE) increase of about 5 to 10%. Surprisingly, we find that for a fixed contrast of the white noise odor waveforms, the nonlinear block of each of the two models changes with the mean input concentration. The shape of the nonlinearities of both the 1D and the 2D LNP model appears to be, for a fixed mean of the odor waveform, independent of the stimulus contrast. This suggests that white noise system identification of Or59b OSNs only depends on the first moment of the odor concentration. Finally, by comparing the 2D Encoding Manifold and the 2D LNP model, we demonstrate that the OSN identification results depend on the particular type of the employed test odor waveforms. This suggests an adaptive neural encoding model for Or59b OSNs that changes its nonlinearity in response to the odor concentration waveforms.

From spiking neuron models to linear-nonlinear models

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.

Coding of Stimuli by Ampullary Afferents in Gnathonemus petersii

Weakly electric fish use electroreception for both active and passive electrolocation and for electrocommunication. While both active and passive electrolocation systems are prominent in weakly electric Mormyriform fishes, knowledge of their passive electrolocation ability is still scarce. To better estimate the contribution of passive electric sensing to the orientation toward electric stimuli in weakly electric fishes, we investigated frequency tuning applying classical input-output characterization and stimulus reconstruction methods to reveal the encoding capabilities of ampullary receptor afferents. Ampullary receptor afferents were most sensitive (threshold: 40 μV/cm) at low frequencies (<10 Hz) and appear to be tuned to a mix of amplitude and slope of the input signals. The low-frequency tuning was corroborated by behavioral experiments, but behavioral thresholds were one order of magnitude higher. The integration of simultaneously recorded afferents of similar frequency-tuning resulted in strongly enhanced signal-to-noise ratios and increased mutual information rates but did not increase the range of frequencies detectable by the system. Theoretically the neuronal integration of input from receptors experiencing opposite polarities of a stimulus (left and right side of the fish) was shown to enhance encoding of such stimuli, including an increase of bandwidth. Covariance and coherence analysis showed that spiking of ampullary afferents is sufficiently explained by the spike-triggered average, i.e., receptors respond to a single linear feature of the stimulus. Our data support the notion of a division of labor of the active and passive electrosensory systems in weakly electric fishes based on frequency tuning. Future experiments will address the role of central convergence of ampullary input that we expect to lead to higher sensitivity and encoding power of the system.

Feature selection in simple neurons: how coding depends on spiking dynamics

The relationship between a neuron's complex inputs and its spiking output defines the neuron's coding strategy. This is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the stimulus that are relevant for triggering spikes and a nonlinear function that relates stimulus to firing probability. In many sensory systems, these two components of the coding strategy are found to adapt to changes in the statistics of the inputs in such a way as to improve information transmission. Here, we show for two simple neuron models how feature selectivity as captured by the spike-triggered average depends on both the parameters of the model and the statistical characteristics of the input.

Tonotopic tuning in a sound localization circuit

Nucleus laminaris (NL) neurons encode interaural time difference (ITD), the cue used to localize low-frequency sounds. A physiologically based model of NL input suggests that ITD information is contained in narrow frequency bands around harmonics of the sound frequency. This suggested a theory, which predicts that, for each tone frequency, there is an optimal time course for synaptic inputs to NL that will elicit the largest modulation of NL firing rate as a function of ITD. The theory also suggested that neurons in different tonotopic regions of NL require specialized tuning to take advantage of the input gradient. Tonotopic tuning in NL was investigated in brain slices by separating the nucleus into three regions based on its anatomical tonotopic map. Patch-clamp recordings in each region were used to measure both the synaptic and the intrinsic electrical properties. The data revealed a tonotopic gradient of synaptic time course that closely matched the theoretical predictions. We also found postsynaptic band-pass filtering. Analysis of the combined synaptic and postsynaptic filters revealed a frequency-dependent gradient of gain for the transformation of tone amplitude to NL firing rate modulation. Models constructed from the experimental data for each tonotopic region demonstrate that the tonotopic tuning measured in NL can improve ITD encoding across sound frequencies.

Identifying Dendritic Processing

In system identification both the input and the output of a system are available to an observer and an algorithm is sought to identify parameters of a hypothesized model of that system. Here we present a novel formal methodology for identifying dendritic processing in a neural circuit consisting of a linear dendritic processing filter in cascade with a spiking neuron model. The input to the circuit is an analog signal that belongs to the space of bandlimited functions. The output is a time sequence associated with the spike train. We derive an algorithm for identification of the dendritic processing filter and reconstruct its kernel with arbitrary precision.

Two forms of feedback inhibition determine the dynamical state of a small hippocampal network

Pyramidal cells in the hippocampus are part of a small neuronal network that performs computations on external input. The network consists of principal cells and various forms of feedback inhibition. Experimental evidence indicates at least two functionally distinct inhibitory feedback loops in the CA3 area of the hippocampus: (1) a loop in which O-LM interneurons project to the distal dendrites of pyramidal cells with synapses that have slow kinetics, and (2) a loop in which basket interneurons project to the somata of pyramidal cells with synapses that have fast kinetics. There is an interconnection between the two loops in the form of O-LM to basket interneuron inhibition and the configuration is further complicated by the presence of distinct propagation delays and short-term facilitation and depression of certain synapses in the two basic loops. In this study we investigated the consequences of various configurations of the circuit and modulations of the components of inhibition for the computation that the network can perform on its input. Gaussian noise was used as the input to the dendrite of the pyramidal cell and evoked two types of events: spikes or bursts. The event-triggered average (ETA) and the event-triggered covariance (ETC) were determined and the inter-event-intervals between spikes and bursts were analyzed. The ETA and ETC on the pyramidal cell show that this model behaves in first approximation as an activity integrator: with sufficient positive input, bursts as well as spikes are evoked. Which of the two is determined by the input just after the (first) spike: positive input results in a burst; negative input results in a spike. Stronger feedback inhibition, in the slow as well as in the fast loop, increases the event rate of the pyramidal cell. For a single input and large propagation delays, the interaction between the two feedback loops is not of great importance. The consequences of the presence of the slow and/or fast feedback inhibitory loop, with or without facilitation and depression, were analyzed in relation to synapse strength. Facilitation and depression are most relevant when their recovery time constant is of the same order as the mean inter-event interval. Short-term depression can stop activity in the fast loop after several fast spikes and can switch the network to a different state, thus functioning as a kind of 'brake' on the fast inhibitory feedback loop. Thus inhibition and the details of the microcircuit organization play an important role in the information processing of the small neuronal circuit.

Sensitivity of firing rate to input fluctuations depends on time scale separation between fast and slow variables in single neurons

Neuronal responses are often characterized by the firing rate as a function of the stimulus mean, or the f-I curve. We introduce a novel classification of neurons into Types A, B-, and B+ according to how f-I curves are modulated by input fluctuations. In Type A neurons, the f-I curves display little sensitivity to input fluctuations when the mean current is large. In contrast, Type B neurons display sensitivity to fluctuations throughout the entire range of input means. Type B- neurons do not fire repetitively for any constant input, whereas Type B+ neurons do. We show that Type B+ behavior results from a separation of time scales between a slow and fast variable. A voltage-dependent time constant for the recovery variable can facilitate sensitivity to input fluctuations. Type B+ firing rates can be approximated using a simple "energy barrier" model.

Conditional bursting enhances resonant firing in neocortical layer 2-3 pyramidal neurons

The frequency response properties of neurons are critical for signal transmission and control of network oscillations. At subthreshold membrane potential, some neurons show resonance caused by voltage-gated channels. During action potential firing, resonance of the spike output may arise from subthreshold mechanisms and/or spike-dependent currents that cause afterhyperpolarizations (AHPs) and afterdepolarizations (ADPs). Layer 2-3 pyramidal neurons (L2-3 PNs) have a fast ADP that can trigger bursts. The present study investigated what stimuli elicit bursting in these cells and whether bursts transmit specific frequency components of the synaptic input, leading to resonance at particular frequencies. We found that two-spike bursts are triggered by step onsets, sine waves in two frequency bands, and noise. Using noise adjusted to elicit firing at approximately 10 Hz, we measured the gain for modulation of the time-varying firing rate as a function of stimulus frequency, finding a primary peak (7-16 Hz) and a high-frequency resonance (250-450 Hz). Gain was also measured separately for single and burst spikes. For a given spike rate, bursts provided higher gain at the primary peak and lower gain at intermediate frequencies, sharpening the high-frequency resonance. Suppression of bursting using automated current feedback weakened the primary and high-frequency resonances. The primary resonance was also influenced by the SK channel-mediated medium AHP (mAHP), because the SK blocker apamin reduced the sharpness of the primary peak. Our results suggest that resonance in L2-3 PNs depends on burst firing and the mAHP. Bursting enhances resonance in two distinct frequency bands.

Adaptation of firing rate and spike-timing precision in the avian cochlear nucleus

Adaptation is commonly defined as a decrease in response to a constant stimulus. In the auditory system such adaptation is seen at multiple levels. However, the first-order central neurons of the interaural time difference detection circuit encode information in the timing of spikes rather than the overall firing rate. We investigated adaptation during in vitro whole-cell recordings from chick nucleus magnocellularis neurons. Injection of noisy, depolarizing current caused an increase in firing rate and a decrease in spike time precision that developed over approximately 20 s. This adaptation depends on sustained depolarization, is independent of firing, and is eliminated by alpha-dendrotoxin (0.1 microM), implicating slow inactivation of low-threshold voltage-activated K+ channels as its mechanism. This process may alter both firing rate and spike-timing precision of phase-locked inputs to coincidence detector neurons in nucleus laminaris and thereby adjust the precision of sound localization.