Slope-based stochastic resonance: how noise enables phasic neurons to encode slow signals

Functional diversity along the anteroposterior axis of the ventromedial hypothalamus

Innate behaviors ensure animal survival and reproductive success. Defending their territory, escaping from predators or mating with a sexual partner, are fundamental behaviors determining the ecological fitness of individuals. Remarkably, all these behaviors share a common neural substrate, as they are under the control of the ventromedial hypothalamus (VMH). Decades of research have contributed to understanding the exquisite diversity of functional ensembles underlying the wide array of functions that the VMH carries out. These functional ensembles are usually distributed throughout the dorsoventral and mediolateral axes of this nucleus. However, increasing evidence is bringing to attention the functional diversity of the VMH across its anteroposterior axis. In this review, we will overview our current understanding of how different ensembles within the VMH control a wide array of animal behaviors, emphasizing the newly discovered roles for its anterior subdivision in the context of conspecific self-defense.

Detecting a periodic signal by a population of spiking neurons in the weakly nonlinear response regime

Motivated by experimental observations, we investigate a variant of the cocktail party problem: the detection of a weak periodic stimulus in the presence of fluctuations and another periodic stimulus which is stronger than the periodic signal to be detected. Specifically, we study the response of a population of stochastic leaky integrate-and-fire (LIF) neurons to two periodic signals and focus in particular on the question, whether the presence of one of the stimuli can be detected from the population activity. As a detection criterion, we use a simple threshold-crossing of the population activity over a certain time window. We show by means of the receiver operating characteristics (ROC) that the detectability depends only weakly on the time window of observation but rather strongly on the stimulus amplitude. Counterintuitively, the detection of the weak periodic signal can be facilitated by the presence of a strong periodic input current depending on the frequencies of the two signals and on the dynamical regime in which the neurons operate. Beside numerical simulations of the model, we present an analytical approximation for the ROC curve that is based on the weakly nonlinear response theory for a stochastic LIF neuron.

Structure and dynamics that specialize neurons for high-frequency coincidence detection in the barn owl nucleus laminaris

A principal cue for sound source localization is the difference in arrival times of sounds at an animal's two ears (interaural time difference, ITD). Neurons that process ITDs are specialized to compare the timing of inputs with submillisecond precision. In the barn owl, ITD processing begins in the nucleus laminaris (NL) region of the auditory brain stem. Remarkably, NL neurons are sensitive to ITDs in high-frequency sounds (kilohertz-range). This contrasts with ITD-based sound localization in analogous regions in mammals where ITD sensitivity is typically restricted to lower-frequency sounds. Guided by previous experiments and modeling studies of tone-evoked responses of NL neurons, we propose NL neurons achieve high-frequency ITD sensitivity if they respond selectively to the small-amplitude, high-frequency oscillations in their inputs, and remain relatively non-responsive to mean input level. We use a biophysically based model to study the effects of soma-axon coupling on dynamics and function in NL neurons. First, we show that electrical separation of the soma from the axon region in the neuron enhances high-frequency ITD sensitivity. This soma-axon coupling configuration promotes linear subthreshold dynamics and rapid spike initiation, making the model more responsive to input oscillations, rather than mean input level. Second, we provide new evidence for the essential role of phasic dynamics for high-frequency neural coincidence detection. Transforming our model to the phasic firing mode further tunes the model to respond selectively to the oscillating inputs that carry ITD information. Similar structural and dynamical mechanisms specialize mammalian auditory brain stem neurons for ITD sensitivity, and thus, our work identifies common principles of ITD processing and neural coincidence detection across species and for sounds at widely different frequencies.

Binaural Processing Deficits Due to Synaptopathy and Myelin Defects

Hidden hearing loss (HHL) is a deficit in auditory perception and speech intelligibility that occurs despite normal audiometric thresholds and results from noise exposure, aging, or myelin defects. While mechanisms causing perceptual deficits in HHL patients are still unknown, results from animal models indicate a role for peripheral auditory neuropathies in HHL. In humans, sound localization is particularly important for comprehending speech, especially in noisy environments, and its disruption may contribute to HHL. In this study, we hypothesized that neuropathies of cochlear spiral ganglion neurons (SGNs) that are observed in animal models of HHL disrupt the activity of neurons in the medial superior olive (MSO), a nucleus in the brainstem responsible for locating low-frequency sound in the horizontal plane using binaural temporal cues, leading to sound localization deficits. To test our hypothesis, we constructed a network model of the auditory processing system that simulates peripheral responses to sound stimuli and propagation of responses via SGNs to cochlear nuclei and MSO populations. To simulate peripheral auditory neuropathies, we used a previously developed biophysical SGN model with myelin defects at SGN heminodes (myelinopathy) and with loss of inner hair cell-SGN synapses (synaptopathy). Model results indicate that myelinopathy and synaptopathy in SGNs give rise to decreased interaural time difference (ITD) sensitivity of MSO cells, suggesting a possible mechanism for perceptual deficits in HHL patients. This model may be useful to understand downstream impacts of SGN-mediated disruptions on auditory processing and to eventually discover possible treatments for various mechanisms of HHL.

The Perception of Ramped Pulse Shapes in Cochlear Implant Users

The electric stimulation provided by current cochlear implants (CI) is not power efficient. One underlying problem is the poor efficiency by which information from electric pulses is transformed into auditory nerve responses. A novel stimulation paradigm using ramped pulse shapes has recently been proposed to remedy this inefficiency. The primary motivation is a better biophysical fit to spiral ganglion neurons with ramped pulses compared to the rectangular pulses used in most contemporary CIs. Here, we tested the hypotheses that ramped pulses provide more efficient stimulation compared to rectangular pulses and that a rising ramp is more efficient than a declining ramp. Rectangular, rising ramped and declining ramped pulse shapes were compared in terms of charge efficiency and discriminability, and threshold variability in seven CI listeners. The tasks included single-channel threshold detection, loudness-balancing, discrimination of pulse shapes, and threshold measurement across the electrode array. Results showed that reduced charge, but increased peak current amplitudes, was required at threshold and most comfortable levels with ramped pulses relative to rectangular pulses. Furthermore, only one subject could reliably discriminate between equally-loud ramped and rectangular pulses, suggesting variations in neural activation patterns between pulse shapes in that participant. No significant difference was found between rising and declining ramped pulses across all tests. In summary, the present findings show some benefits of charge efficiency with ramped pulses relative to rectangular pulses, that the direction of a ramped slope is of less importance, and that most participants could not perceive a difference between pulse shapes.

Physiological Diversity Influences Detection of Stimulus Envelope and Fine Structure in Neurons of the Medial Superior Olive

The neurons of the medial superior olive (MSO) of mammals extract azimuthal information from the delays between sounds reaching the two ears [interaural time differences (ITDs)]. Traditionally, all models of sound localization have assumed that MSO neurons represent a single population of cells with specialized and homogeneous intrinsic and synaptic properties that enable the detection of synaptic coincidence on a timescale of tens to hundreds of microseconds. Here, using patch-clamp recordings from large populations of anatomically labeled neurons in brainstem slices from male and female Mongolian gerbils (Meriones unguiculatus), we show that MSO neurons are far more physiologically diverse than previously appreciated, with properties that depend regionally on cell position along the topographic map of frequency. Despite exhibiting a similar morphology, neurons in the MSO exhibit subthreshold oscillations of differing magnitudes that drive action potentials at rates between 100 and 800 Hz. These oscillations are driven primarily by voltage-gated sodium channels and are distinct from resonant properties derived from other active membrane properties. We show that graded differences in these and other physiological properties across the MSO neuron population enable the MSO to duplex the encoding of ITD information in both fast, submillisecond time-varying signals as well as in slower envelopes.SIGNIFICANCE STATEMENT Neurons in the medial superior olive (MSO) encode sound localization cues by detecting microsecond differences in the arrival times of inputs from the left and right ears, and it has been assumed that this computation is made possible by highly stereotyped structural and physiological specializations. Here we report using a large (>400) sample size in which MSO neurons show a strikingly large continuum of functional properties despite exhibiting similar morphologies. We demonstrate that subthreshold oscillations mediated by voltage-gated Na+ channels play a key role in conferring graded differences in firing properties. This functional diversity likely confers capabilities of processing both fast, submillisecond-scale synaptic activity (acoustic "fine structure"), and slow-rising envelope information that is found in amplitude-modulated sounds and speech patterns.

Excitability and Threshold Mechanism for Enhanced Neuronal Response Induced by Inhibition Preceding Excitation

Postinhibitory facilitation (PIF) of neural firing presents a paradoxical phenomenon that the inhibitory effect induces enhancement instead of reduction of the firing activity, which plays important roles in sound location of the auditory nervous system, awaited theoretical explanations. In the present paper, excitability and threshold mechanism for the PIF phenomenon is presented in the Morris-Lecar model with type I, II, and III excitabilities. Firstly, compared with the purely excitatory stimulations applied to the steady state, the inhibitory preceding excitatory stimulation to form pairs induces the firing rate increased for type II and III excitabilities instead of type I excitability, when the interval between the inhibitory and excitatory stimulation within each pair is suitable. Secondly, the threshold mechanism for the PIF phenomenon is acquired. For type II and III excitabilities, the inhibitory stimulation induces subthreshold oscillations around the steady state. During the middle and ending phase of the ascending part and the beginning phase of the descending part within a period of the subthreshold oscillations, the threshold to evoke an action potential by an excitatory stimulation becomes weaker, which is the cause for the PIF phenomenon. Last, a theoretical estimation for the range of the interval between the inhibitory and excitatory stimulation for the PIF phenomenon is acquired, which approximates half of the intrinsic period of the subthreshold oscillations for the relatively strong stimulations and becomes narrower for the relatively weak stimulations. The interval for the PIF phenomenon is much shorter for type III excitability, which is closer to the experiment observation, due to the shorter period of the subthreshold oscillations. The results present the excitability and threshold mechanism for the PIF phenomenon, which provide comprehensive and deep explanations to the PIF phenomenon.

A practical guide to methodological considerations in the controllability of structural brain networks

OBJECTIVE

Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool from the physical and engineering sciences that can provide insights regarding that relationship; it formalizes the study of how the dynamics of a complex system can arise from its underlying structure of interconnected units.

APPROACH

Given the recent use of network control theory in neuroscience, it is now timely to offer a practical guide to methodological considerations in the controllability of structural brain networks. Here we provide a systematic overview of the framework, examine the impact of modeling choices on frequently studied control metrics, and suggest potentially useful theoretical extensions. We ground our discussions, numerical demonstrations, and theoretical advances in a dataset of high-resolution diffusion imaging with 730 diffusion directions acquired over approximately 1 h of scanning from ten healthy young adults.

MAIN RESULTS

Following a didactic introduction of the theory, we probe how a selection of modeling choices affects four common statistics: average controllability, modal controllability, minimum control energy, and optimal control energy. Next, we extend the current state-of-the-art in two ways: first, by developing an alternative measure of structural connectivity that accounts for radial propagation of activity through abutting tissue, and second, by defining a complementary metric quantifying the complexity of the energy landscape of a system. We close with specific modeling recommendations and a discussion of methodological constraints.

SIGNIFICANCE

Our hope is that this accessible account will inspire the neuroimaging community to more fully exploit the potential of network control theory in tackling pressing questions in cognitive, developmental, and clinical neuroscience.

Different dynamical behaviors induced by slow excitatory feedback for type II and III excitabilities

Neuronal excitability is classified as type I, II, or III, according to the responses of electronic activities, which play different roles. In the present paper, the effect of an excitatory autapse on type III excitability is investigated and compared to type II excitability in the Morris-Lecar model, based on Hopf bifurcation and characteristics of the nullcline. The autaptic current of a fast-decay autapse produces periodic stimulations, and that of a slow-decay autapse highly resembles sustained stimulations. Thus, both fast- and slow-decay autapses can induce a resting state for type II excitability that changes to repetitive firing. However, for type III excitability, a fast-decay autapse can induce a resting state to change to repetitive firing, while a slow-decay autapse can induce a resting state to change to a resting state following a transient spike instead of repetitive spiking, which shows the abnormal phenomenon that a stronger excitatory effect of a slow-decay autapse just induces weaker responses. Our results uncover a novel paradoxical phenomenon of the excitatory effect, and we present potential functions of fast- and slow-decay autapses that are helpful for the alteration and maintenance of type III excitability in the real nervous system related to neuropathic pain or sound localization.

Consequences of tuning network function by tonic and phasic locus coeruleus output and stress: Regulating detection and discrimination of peripheral stimuli

Flexible and adaptive behaviors have evolved with increasing complexity and numbers of neuromodulator systems. The neuromodulatory locus coeruleus-norepinephrine (LC-NE) system is central to regulating cognitive function in a behaviorally-relevant and arousal-dependent manner. Through its nearly ubiquitous efferent projections, the LC-NE system acts to modulate neuron function on a cell-by-cell basis and exert a spectrum of actions across different brain regions to optimize target circuit function. As LC neuron activity, NE signaling, and arousal level increases, cognitive performance improves over an inverted-U shaped curve. Additionally, LC neurons burst phasically in relation to novel or salient sensory stimuli and top-down decision- or response-related processes. Together, the variety of LC activity patterns and complex actions of the LC-NE system indicate that the LC-NE system may dynamically regulate the function of target neural circuits. The manner in which neural networks encode, represent, and perform neurocomputations continue to be revealed. This has improved our ability to understand the optimization of neural circuits by NE and generation of flexible and adaptive goal-directed behaviors. In this review, the rat vibrissa somatosensory system is explored as a model neural circuit to bridge known modulatory actions of NE and changes in cognitive function. It is argued that fluid transitions between neural computational states reflect the ability of this sensory system to shift between two principal functions: detection of novel or salient sensory information and detailed descriptions of sensory information. Such flexibility in circuit function is likely critical for producing context-appropriate sensory signal processing. Nonetheless, many challenges remain including providing a causal link between NE mediated changes in sensory neural coding and perceptual changes, as well as extending these principles to higher cognitive functions including behavioral flexibility and decision making.

Phasic and tonic cell types in the zebra finch auditory caudal mesopallium

The caudal mesopallium (CM) is a cortical-level area in the songbird auditory pathway where selective, invariant responses to familiar songs emerge. To characterize the cell types that perform this computation, we made whole cell recordings from brain slices in juvenile zebra finches ( Taeniopygia guttata) of both sexes. We found three groups of putatively excitatory neurons with distinct firing patterns. Tonic cells produced sustained responses to depolarizing step currents, phasic cells produced only a few spikes at the onset, and an intermediate group was also phasic but responded for up to a few hundred milliseconds. Phasic cells had smaller dendritic fields, higher resting potentials, and strong low-threshold outward rectification. Pharmacological treatment with voltage-gated potassium channel antagonists 4-aminopyridine and α-dendrotoxin converted phasic to tonic firing. When stimulated with broadband currents, phasic cells fired coherently with frequencies up to 20-30 Hz, whereas tonic neurons were more responsive to frequencies around 0-10 Hz. The distribution of peak coherence frequencies was similar to the distribution of temporal modulation rates in zebra finch song. We reproduced these observations in a single-compartment biophysical model by varying cell size and the magnitude of a slowly inactivating, low-threshold potassium current ( I_LT). These data suggest that intrinsic dynamics in CM are matched to the temporal statistics of conspecific song. NEW & NOTEWORTHY In songbirds, the caudal mesopallium is a key brain area involved in recognizing the songs of other individuals. This study identifies three cell types in this area with distinct firing patterns (tonic, phasic, and intermediate) that reflect differences in cell size and a low-threshold potassium current. The phasic-firing neurons, which do not have a counterpart in mammalian auditory cortex, are better able to follow rapid modulations at the frequencies found in song.

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.

Phasic Firing and Coincidence Detection by Subthreshold Negative Feedback: Divisive or Subtractive or, Better, Both

Phasic neurons typically fire only for a fast-rising input, say at the onset of a step current, but not for steady or slow inputs, a property associated with type III excitability. Phasic neurons can show extraordinary temporal precision for phase locking and coincidence detection. Exemplars are found in the auditory brain stem where precise timing is used in sound localization. Phasicness at the cellular level arises from a dynamic, voltage-gated, negative feedback that can be recruited subthreshold, preventing the neuron from reaching spike threshold if the voltage does not rise fast enough. We consider two mechanisms for phasicness: a low threshold potassium current (subtractive mechanism) and a sodium current with subthreshold inactivation (divisive mechanism). We develop and analyze three reduced models with either divisive or subtractive mechanisms or both to gain insight into the dynamical mechanisms for the potentially high temporal precision of type III-excitable neurons. We compare their firing properties and performance for a range of stimuli. The models have characteristic non-monotonic input-output relations, firing rate vs. input intensity, for either stochastic current injection or Poisson-timed excitatory synaptic conductance trains. We assess performance according to precision of phase-locking and coincidence detection by the models' responses to repetitive packets of unitary excitatory synaptic inputs with more or less temporal coherence. We find that each mechanism contributes features but best performance is attained if both are present. The subtractive mechanism confers extraordinary precision for phase locking and coincidence detection but only within a restricted parameter range when the divisive mechanism of sodium inactivation is inoperative. The divisive mechanism guarantees robustness of phasic properties, without compromising excitability, although with somewhat less precision. Finally, we demonstrate that brief transient inhibition if properly timed can enhance the reliability of firing.

Coding Properties of Three Intrinsically Distinct Retinal Ganglion Cells under Periodic Stimuli: A Computational Study

As the sole output neurons in the retina, ganglion cells play significant roles in transforming visual information into spike trains, and then transmitting them to the higher visual centers. However, coding strategies that retinal ganglion cells (RGCs) adopt to accomplish these processes are not completely clear yet. To clarify these issues, we investigate the coding properties of three types of RGCs (repetitive spiking, tonic firing, and phasic firing) by two different measures (spike-rate and spike-latency). Model results show that for periodic stimuli, repetitive spiking RGC and tonic RGC exhibit similar spike-rate patterns. Their spike- rates decrease gradually with increased stimulus frequency, moreover, variation of stimulus amplitude would change the two RGCs' spike-rate patterns. For phasic RGC, it activates strongly at medium levels of frequency when the stimulus amplitude is low. While if high stimulus amplitude is applied, phasic RGC switches to respond strongly at low frequencies. These results suggest that stimulus amplitude is a prominent factor in regulating RGCs in encoding periodic signals. Similar conclusions can be drawn when analyzes spike-latency patterns of the three RGCs. More importantly, the above phenomena can be accurately reproduced by Hodgkin's three classes of neurons, indicating that RGCs can perform the typical three classes of firing dynamics, depending on the distinctions of ion channel densities. Consequently, model results from the three RGCs may be not specific, but can also applicable to neurons in other brain regions which exhibit part(s) or all of the Hodgkin's three excitabilities.

Sensitivity to Interaural Time Differences Conveyed in the Stimulus Envelope: Estimating Inputs of Binaural Neurons Through the Temporal Analysis of Spike Trains

Sound-source localization in the horizontal plane relies on detecting small differences in the timing and level of the sound at the two ears, including differences in the timing of the modulated envelopes of high-frequency sounds (envelope interaural time differences (ITDs)). We investigated responses of single neurons in the inferior colliculus (IC) to a wide range of envelope ITDs and stimulus envelope shapes. By a novel means of visualizing neural activity relative to different portions of the periodic stimulus envelope at each ear, we demonstrate the role of neuron-specific excitatory and inhibitory inputs in creating ITD sensitivity (or the lack of it) depending on the specific shape of the stimulus envelope. The underlying binaural brain circuitry and synaptic parameters were modeled individually for each neuron to account for neuron-specific activity patterns. The model explains the effects of envelope shapes on sensitivity to envelope ITDs observed in both normal-hearing listeners and in neural data, and has consequences for understanding how ITD information in stimulus envelopes might be maximized in users of bilateral cochlear implants-for whom ITDs conveyed in the stimulus envelope are the only ITD cues available.

A review of methods for identifying stochastic resonance in simulations of single neuron models

Stochastic resonance (SR) is said to be observed when the presence of noise in a nonlinear system enables an output signal from the system to better represent some feature of an input signal than it does in the absence of noise. The effect has been observed in models of individual neurons, and in experiments performed on real neural systems. Despite the ubiquity of biophysical sources of stochastic noise in the nervous system, however, it has not yet been established whether neuronal computation mechanisms involved in performance of specific functions such as perception or learning might exploit such noise as an integral component, such that removal of the noise would diminish performance of these functions. In this paper we revisit the methods used to demonstrate stochastic resonance in models of single neurons. This includes a previously unreported observation in a multicompartmental model of a CA1-pyramidal cell. We also discuss, as a contrast to these classical studies, a form of 'stochastic facilitation', known as inverse stochastic resonance. We draw on the reviewed examples to argue why new approaches to studying 'stochastic facilitation' in neural systems need to be developed.

On the localization of complex sounds: temporal encoding based on input-slope coincidence detection of envelopes

Behavioral and neural findings demonstrate that animals can locate low-frequency sounds along the azimuth by detecting microsecond interaural time differences (ITDs). Information about ITDs is also available in the amplitude modulations (i.e., envelope) of high-frequency sounds. Since medial superior olivary (MSO) neurons encode low-frequency ITDs, we asked whether they employ a similar mechanism to process envelope ITDs with high-frequency carriers, and the effectiveness of this mechanism compared with the process of low-frequency sound. We developed a novel hybrid in vitro dynamic-clamp approach, which enabled us to mimic synaptic input to brain-slice neurons in response to virtual sound and to create conditions that cannot be achieved naturally but are useful for testing our hypotheses. For each simulated ear, a virtual sound, computer generated, was used as input to a computational auditory-nerve model. Model spike times were converted into synaptic input for MSO neurons, and ITD tuning curves were derived for several virtual-sound conditions: low-frequency pure tones, high-frequency tones modulated with two types of envelope, and speech sequences. Computational models were used to verify the physiological findings and explain the biophysical mechanism underlying the observed ITD coding. Both recordings and simulations indicate that MSO neurons are sensitive to ITDs carried by spectrotemporally complex virtual sounds, including speech tokens. Our findings strongly suggest that MSO neurons can encode ITDs across a broad-frequency spectrum using an input-slope-based coincidence-detection mechanism. Our data also provide an explanation at the cellular level for human localization performance involving high-frequency sound described by previous investigators.

Channel-noise-induced stochastic facilitation in an auditory brainstem neuron model

Neuronal membrane potentials fluctuate stochastically due to conductance changes caused by random transitions between the open and closed states of ion channels. Although it has previously been shown that channel noise can nontrivially affect neuronal dynamics, it is unknown whether ion-channel noise is strong enough to act as a noise source for hypothesized noise-enhanced information processing in real neuronal systems, i.e., "stochastic facilitation". Here we demonstrate that biophysical models of channel noise can give rise to two kinds of recently discovered stochastic facilitation effects in a Hodgkin-Huxley-like model of auditory brainstem neurons. The first, known as slope-based stochastic resonance (SBSR), enables phasic neurons to emit action potentials that can encode the slope of inputs that vary slowly relative to key time constants in the model. The second, known as inverse stochastic resonance (ISR), occurs in tonically firing neurons when small levels of noise inhibit tonic firing and replace it with burstlike dynamics. Consistent with previous work, we conclude that channel noise can provide significant variability in firing dynamics, even for large numbers of channels. Moreover, our results show that possible associated computational benefits may occur due to channel noise in neurons of the auditory brainstem. This holds whether the firing dynamics in the model are phasic (SBSR can occur due to channel noise) or tonic (ISR can occur due to channel noise).

Dual sensitivity of inferior colliculus neurons to ITD in the envelopes of high-frequency sounds: experimental and modeling study

Human listeners are sensitive to interaural time differences (ITDs) in the envelopes of sounds, which can serve as a cue for sound localization. Many high-frequency neurons in the mammalian inferior colliculus (IC) are sensitive to envelope-ITDs of sinusoidally amplitude-modulated (SAM) sounds. Typically, envelope-ITD-sensitive IC neurons exhibit either peak-type sensitivity, discharging maximally at the same delay across frequencies, or trough-type sensitivity, discharging minimally at the same delay across frequencies, consistent with responses observed at the primary site of binaural interaction in the medial and lateral superior olives (MSO and LSO), respectively. However, some high-frequency IC neurons exhibit dual types of envelope-ITD sensitivity in their responses to SAM tones, that is, they exhibit peak-type sensitivity at some modulation frequencies and trough-type sensitivity at other frequencies. Here we show that high-frequency IC neurons in the unanesthetized rabbit can also exhibit dual types of envelope-ITD sensitivity in their responses to SAM noise. Such complex responses to SAM stimuli could be achieved by convergent inputs from MSO and LSO onto single IC neurons. We test this hypothesis by implementing a physiologically explicit, computational model of the binaural pathway. Specifically, we examined envelope-ITD sensitivity of a simple model IC neuron that receives convergent inputs from MSO and LSO model neurons. We show that dual envelope-ITD sensitivity emerges in the IC when convergent MSO and LSO inputs are differentially tuned for modulation frequency.

Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection

We review some widely studied models and firing dynamics for neuronal systems, both at the single cell and network level, and dynamical systems techniques to study them. In particular, we focus on two topics in mathematical neuroscience that have attracted the attention of mathematicians for decades: single-cell excitability and bursting. We review the mathematical framework for three types of excitability and onset of repetitive firing behavior in single-neuron models and their relation with Hodgkin's classification in 1948 of repetitive firing properties. We discuss the mathematical dissection of bursting oscillations using fast/slow analysis and demonstrate the approach using single-cell and mean-field network models. Finally, we illustrate the properties of Type III excitability in which case repetitive firing for constant or slow inputs is absent. Rather, firing is in response only to rapid enough changes in the stimulus. Our case study involves neuronal computations for sound localization for which neurons in the auditory brain stem perform extraordinarily precise coincidence detection with submillisecond temporal resolution.

Adaptive coupling optimized spiking coherence and synchronization in Newman-Watts neuronal networks

In this paper, we have numerically studied the effect of adaptive coupling on the temporal coherence and synchronization of spiking activity in Newman-Watts Hodgkin-Huxley neuronal networks. It is found that random shortcuts can enhance the spiking synchronization more rapidly when the increment speed of adaptive coupling is increased and can optimize the temporal coherence of spikes only when the increment speed of adaptive coupling is appropriate. It is also found that adaptive coupling strength can enhance the synchronization of spikes and can optimize the temporal coherence of spikes when random shortcuts are appropriate. These results show that adaptive coupling has a big influence on random shortcuts related spiking activity and can enhance and optimize the temporal coherence and synchronization of spiking activity of the network. These findings can help better understand the roles of adaptive coupling for improving the information processing and transmission in neural systems.

Control strategies for underactuated neural ensembles driven by optogenetic stimulation

Motivated by experiments employing optogenetic stimulation of cortical regions, we consider spike control strategies for ensembles of uncoupled integrate and fire neurons with a common conductance input. We construct strategies for control of spike patterns, that is, multineuron trains of action potentials, up to some maximal spike rate determined by the neural biophysics. We emphasize a constructive role for parameter heterogeneity, and find a simple rule for controllability in pairs of neurons. In particular, we determine parameters for which common drive is not limited to inducing synchronous spiking. For large ensembles, we determine how the number of controllable neurons varies with the number of observed (recorded) neurons, and what collateral spiking occurs in the full ensemble during control of the subensemble. While complete control of spiking in every neuron is not possible with a single input, we find that a degree of subensemble control is made possible by exploiting dynamical heterogeneity. As most available technologies for neural stimulation are underactuated, in the sense that the number of target neurons far exceeds the number of independent channels of stimulation, these results suggest partial control strategies that may be important in the development of sensory neuroprosthetics and other neurocontrol applications.

Potassium conductance dynamics confer robust spike-time precision in a neuromorphic model of the auditory brain stem

A fundamental question in neuroscience is how neurons perform precise operations despite inherent variability. This question also applies to neuromorphic engineering, where low-power microchips emulate the brain using large populations of diverse silicon neurons. Biological neurons in the auditory pathway display precise spike timing, critical for sound localization and interpretation of complex waveforms such as speech, even though they are a heterogeneous population. Silicon neurons are also heterogeneous, due to a key design constraint in neuromorphic engineering: smaller transistors offer lower power consumption and more neurons per unit area of silicon, but also more variability between transistors and thus between silicon neurons. Utilizing this variability in a neuromorphic model of the auditory brain stem with 1,080 silicon neurons, we found that a low-voltage-activated potassium conductance (g(KL)) enables precise spike timing via two mechanisms: statically reducing the resting membrane time constant and dynamically suppressing late synaptic inputs. The relative contribution of these two mechanisms is unknown because blocking g(KL) in vitro eliminates dynamic adaptation but also lengthens the membrane time constant. We replaced g(KL) with a static leak in silico to recover the short membrane time constant and found that silicon neurons could mimic the spike-time precision of their biological counterparts, but only over a narrow range of stimulus intensities and biophysical parameters. The dynamics of g(KL) were required for precise spike timing robust to stimulus variation across a heterogeneous population of silicon neurons, thus explaining how neural and neuromorphic systems may perform precise operations despite inherent variability.

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.

A modeling study of the responses of the lateral superior olive to ipsilateral sinusoidally amplitude-modulated tones

The lateral superior olive (LSO) is a brainstem nucleus that is classically understood to encode binaural information in high-frequency sounds. Previous studies have shown that LSO cells are sensitive to envelope interaural time difference in sinusoidally amplitude-modulated (SAM) tones (Joris and Yin, J Neurophysiol 73:1043-1062, 1995; Joris, J Neurophysiol 76:2137-2156, 1996) and that a subpopulation of LSO neurons exhibit low-threshold potassium currents mediated by Kv1 channels (Barnes-Davies et al., Eur J Neurosci 19:325-333, 2004). It has also been shown that in many LSO cells the average response rate to ipsilateral SAM tones decreases with modulation frequency above a few hundred Hertz (Joris and Yin, J Neurophysiol 79:253-269, 1998). This low-pass feature is not directly inherited from the inputs to the LSO since the response rate of these input neurons changes little with increasing modulation frequency. In the current study, an LSO cell model is developed to investigate mechanisms consistent with the responses described above, notably the emergent rate decrease with increasing frequency. The mechanisms explored included the effects of after-hyperpolarization (AHP) channels, the dynamics of low-threshold potassium channels (KLT), and the effects of background inhibition. In the model, AHP channels alone were not sufficient to induce the observed rate decrease at high modulation frequencies. The model also suggests that the background inhibition alone, possibly from the medial nucleus of the trapezoid body, can account for the small rate decrease seen in some LSO neurons, but could not explain the large rate decrease seen in other LSO neurons at high modulation frequencies. In contrast, both the small and large rate decreases were replicated when KLT channels were included in the LSO neuron model. These results support the conclusion that KLT channels may play a major role in the large rate decreases seen in some units and that background inhibition may be a contributing factor, a factor that could be adequate for small decreases.