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.

Dynamics of the Auditory Continuity Illusion.

Illusions give intriguing insights into perceptual and neural dynamics. In the auditory continuity illusion, two brief tones separated by a silent gap may be heard as one continuous tone if a noise burst with appropriate characteristics fills the gap. This illusion probes the conditions under which listeners link related sounds across time and maintain perceptual continuity in the face of sudden changes in sound mixtures. Conceptual explanations of this illusion have been proposed, but its neural basis is still being investigated. In this work we provide a dynamical systems framework, grounded in principles of neural dynamics, to explain the continuity illusion. We construct an idealized firing rate model of a neural population and analyze the conditions under which firing rate responses persist during the interruption between the two tones. First, we show that sustained inputs and hysteresis dynamics (a mismatch between tone levels needed to activate and inactivate the population) can produce continuous responses. Second, we show that transient inputs and bistable dynamics (coexistence of two stable firing rate levels) can also produce continuous responses. Finally, we combine these input types together to obtain neural dynamics consistent with two requirements for the continuity illusion as articulated in a well-known theory of auditory scene analysis: responses persist through the noise-filled gap if noise provides sufficient evidence that the tone continues and if there is no evidence of discontinuities between the tones and noise. By grounding these notions in a quantitative model that incorporates elements of neural circuits (recurrent excitation, and mutual inhibition, specifically), we identify plausible mechanisms for the continuity illusion. Our findings can help guide future studies of neural correlates of this illusion and inform development of more biophysically-based models of the auditory continuity illusion.

Glycinergic axonal inhibition subserves acute spatial sensitivity to sudden increases in sound intensity.

Locomotion generates adventitious sounds which enable detection and localization of predators and prey. Such sounds contain brisk changes or transients in amplitude. We investigated the hypothesis that ill-understood temporal specializations in binaural circuits subserve lateralization of such sound transients, based on different time of arrival at the ears (interaural time differences, ITDs). We find that Lateral Superior Olive (LSO) neurons show exquisite ITD-sensitivity, reflecting extreme precision and reliability of excitatory and inhibitory postsynaptic potentials, in contrast to Medial Superior Olive neurons, traditionally viewed as the ultimate ITD-detectors. In vivo, inhibition blocks LSO excitation over an extremely short window, which, in vitro, required synaptically evoked inhibition. Light and electron microscopy revealed inhibitory synapses on the axon initial segment as the structural basis of this observation. These results reveal a neural vetoing mechanism with extreme temporal and spatial precision and establish the LSO as the primary nucleus for binaural processing of sound transients.

Soma-axon coupling configurations that enhance neuronal coincidence detection.

Coincidence detector neurons transmit timing information by responding preferentially to concurrent synaptic inputs. Principal cells of the medial superior olive (MSO) in the mammalian auditory brainstem are superb coincidence detectors. They encode sound source location with high temporal precision, distinguishing submillisecond timing differences among inputs. We investigate computationally how dynamic coupling between the input region (soma and dendrite) and the spike-generating output region (axon and axon initial segment) can enhance coincidence detection in MSO neurons. To do this, we formulate a two-compartment neuron model and characterize extensively coincidence detection sensitivity throughout a parameter space of coupling configurations. We focus on the interaction between coupling configuration and two currents that provide dynamic, voltage-gated, negative feedback in subthreshold voltage range: sodium current with rapid inactivation and low-threshold potassium current, IKLT. These currents reduce synaptic summation and can prevent spike generation unless inputs arrive with near simultaneity. We show that strong soma-to-axon coupling promotes the negative feedback effects of sodium inactivation and is, therefore, advantageous for coincidence detection. Furthermore, the feedforward combination of strong soma-to-axon coupling and weak axon-to-soma coupling enables spikes to be generated efficiently (few sodium channels needed) and with rapid recovery that enhances high-frequency coincidence detection. These observations detail the functional benefit of the strongly feedforward configuration that has been observed in physiological studies of MSO neurons. We find that IKLT further enhances coincidence detection sensitivity, but with effects that depend on coupling configuration. For instance, in models with weak soma-to-axon and weak axon-to-soma coupling, IKLT in the axon enhances coincidence detection more effectively than IKLT in the soma. By using a minimal model of soma-to-axon coupling, we connect structure, dynamics, and computation. Although we consider the particular case of MSO coincidence detectors, our method for creating and exploring a parameter space of two-compartment models can be applied to other neurons.

Gain control with A-type potassium current: IA as a switch between divisive and subtractive inhibition.

Neurons process and convey information by transforming barrages of synaptic inputs into spiking activity. Synaptic inhibition typically suppresses the output firing activity of a neuron, and is commonly classified as having a subtractive or divisive effect on a neuron's output firing activity. Subtractive inhibition can narrow the range of inputs that evoke spiking activity by eliminating responses to non-preferred inputs. Divisive inhibition is a form of gain control: it modifies firing rates while preserving the range of inputs that evoke firing activity. Since these two "modes" of inhibition have distinct impacts on neural coding, it is important to understand the biophysical mechanisms that distinguish these response profiles. In this study, we use simulations and mathematical analysis of a neuron model to find the specific conditions (parameter sets) for which inhibitory inputs have subtractive or divisive effects. Significantly, we identify a novel role for the A-type Potassium current (IA). In our model, this fast-activating, slowly-inactivating outward current acts as a switch between subtractive and divisive inhibition. In particular, if IA is strong (large maximal conductance) and fast (activates on a time-scale similar to spike initiation), then inhibition has a subtractive effect on neural firing. In contrast, if IA is weak or insufficiently fast-activating, then inhibition has a divisive effect on neural firing. We explain these findings using dynamical systems methods (plane analysis and fast-slow dissection) to define how a spike threshold condition depends on synaptic inputs and IA. Our findings suggest that neurons can "self-regulate" the gain control effects of inhibition via combinations of synaptic plasticity and/or modulation of the conductance and kinetics of A-type Potassium channels. This novel role for IA would add flexibility to neurons and networks, and may relate to recent observations of divisive inhibitory effects on neurons in the nucleus of the solitary tract.

Signatures of Somatic Inhibition and Dendritic Excitation in Auditory Brainstem Field Potentials.

Extracellular voltage recordings (Ve ; field potentials) provide an accessible view of in vivo neural activity, but proper interpretation of field potentials is a long-standing challenge. Computational modeling can aid in identifying neural generators of field potentials. In the auditory brainstem of cats, spatial patterns of sound-evoked Ve can resemble, strikingly, Ve generated by current dipoles. Previously, we developed a biophysically-based model of a binaural brainstem nucleus, the medial superior olive (MSO), that accounts qualitatively for observed dipole-like Ve patterns in sustained responses to monaural tones with frequencies >∼1000 Hz (Goldwyn et al., 2014). We have observed, however, that Ve patterns in cats of both sexes appear more monopole-like for lower-frequency tones. Here, we enhance our theory to accurately reproduce dipole and non-dipole features of Ve responses to monaural tones with frequencies ranging from 600 to 1800 Hz. By applying our model to data, we estimate time courses of paired input currents to MSO neurons. We interpret these inputs as dendrite-targeting excitation and soma-targeting inhibition (the latter contributes non-dipole-like features to Ve responses). Aspects of inferred inputs are consistent with synaptic inputs to MSO neurons including the tendencies of inhibitory inputs to attenuate in response to high-frequency tones and to precede excitatory inputs. Importantly, our updated theory can be tested experimentally by blocking synaptic inputs. MSO neurons perform a critical role in sound localization and binaural hearing. By solving an inverse problem to uncover synaptic inputs from Ve patterns we provide a new perspective on MSO physiology.SIGNIFICANCE STATEMENT Extracellular voltages (field potentials) are a common measure of brain activity. Ideally, one could infer from these data the activity of neurons and synapses that generate field potentials, but this "inverse problem" is not easily solved. We study brainstem field potentials in the region of the medial superior olive (MSO); a critical center in the auditory pathway. These field potentials exhibit distinctive spatial and temporal patterns in response to pure tone sounds. We use mathematical modeling in combination with physiological and anatomical knowledge of MSO neurons to plausibly explain how dendrite-targeting excitation and soma-targeting inhibition generate these field potentials. Inferring putative synaptic currents from field potentials advances our ability to study neural processing of sound in the MSO.

Neuronal coupling by endogenous electric fields: cable theory and applications to coincidence detector neurons in the auditory brain stem.

The ongoing activity of neurons generates a spatially and time-varying field of extracellular voltage (Ve). This Ve field reflects population-level neural activity, but does it modulate neural dynamics and the function of neural circuits? We provide a cable theory framework to study how a bundle of model neurons generates Ve and how this Ve feeds back and influences membrane potential (Vm). We find that these "ephaptic interactions" are small but not negligible. The model neural population can generate Ve with millivolt-scale amplitude, and this Ve perturbs the Vm of "nearby" cables and effectively increases their electrotonic length. After using passive cable theory to systematically study ephaptic coupling, we explore a test case: the medial superior olive (MSO) in the auditory brain stem. The MSO is a possible locus of ephaptic interactions: sounds evoke large (millivolt scale)Vein vivo in this nucleus. The Ve response is thought to be generated by MSO neurons that perform a known neuronal computation with submillisecond temporal precision (coincidence detection to encode sound source location). Using a biophysically based model of MSO neurons, we find millivolt-scale ephaptic interactions consistent with the passive cable theory results. These subtle membrane potential perturbations induce changes in spike initiation threshold, spike time synchrony, and time difference sensitivity. These results suggest that ephaptic coupling may influence MSO function.

A model of the medial superior olive explains spatiotemporal features of local field potentials.

Local field potentials are important indicators of in vivo neural activity. Sustained, phase-locked, sound-evoked extracellular fields in the mammalian auditory brainstem, known as the auditory neurophonic, reflect the activity of neurons in the medial superior olive (MSO). We develop a biophysically based model of the neurophonic that accounts for features of in vivo extracellular recordings in the cat auditory brainstem. By making plausible idealizations regarding the spatial symmetry of MSO neurons and the temporal synchrony of their afferent inputs, we reduce the challenging problem of computing extracellular potentials in a 3D volume conductor to a one-dimensional problem. We find that postsynaptic currents in bipolar MSO neuron models generate extracellular voltage responses that strikingly resemble in vivo recordings. Simulations reproduce distinctive spatiotemporal features of the in vivo neurophonic response to monaural pure tones: large oscillations (hundreds of microvolts to millivolts), broad spatial reach (millimeter scale), and a dipole-like spatial profile. We also explain how somatic inhibition and the relative timing of bilateral excitation may shape the spatial profile of the neurophonic. We observe in simulations, and find supporting evidence in in vivo data, that coincident excitatory inputs on both dendrites lead to a drastically reduced spatial reach of the neurophonic. This outcome surprises because coincident inputs are thought to evoke maximal firing rates in MSO neurons, and it reconciles previously puzzling evoked potential results in humans and animals. The success of our model, which has no axon or spike-generating sodium currents, suggests that MSO spikes do not contribute appreciably to the neurophonic.

A point process framework for modeling electrical stimulation of the auditory nerve.

Model-based studies of responses of auditory nerve fibers to electrical stimulation can provide insight into the functioning of cochlear implants. Ideally, these studies can identify limitations in sound processing strategies and lead to improved methods for providing sound information to cochlear implant users. To accomplish this, models must accurately describe spiking activity while avoiding excessive complexity that would preclude large-scale simulations of populations of auditory nerve fibers and obscure insight into the mechanisms that influence neural encoding of sound information. In this spirit, we develop a point process model of individual auditory nerve fibers that provides a compact and accurate description of neural responses to electric stimulation. Inspired by the framework of generalized linear models, the proposed model consists of a cascade of linear and nonlinear stages. We show how each of these stages can be associated with biophysical mechanisms and related to models of neuronal dynamics. Moreover, we derive a semianalytical procedure that uniquely determines each parameter in the model on the basis of fundamental statistics from recordings of single fiber responses to electric stimulation, including threshold, relative spread, jitter, and chronaxie. The model also accounts for refractory and summation effects that influence the responses of auditory nerve fibers to high pulse rate stimulation. Throughout, we compare model predictions to published physiological data of response to high and low pulse rate stimulation. We find that the model, although constructed to fit data from single and paired pulse experiments, can accurately predict responses to unmodulated and modulated pulse train stimuli. We close by performing an ideal observer analysis of simulated spike trains in response to sinusoidally amplitude modulated stimuli and find that carrier pulse rate does not affect modulation detection thresholds.

The what and where of adding channel noise to the Hodgkin-Huxley equations.

Conductance-based equations for electrically active cells form one of the most widely studied mathematical frameworks in computational biology. This framework, as expressed through a set of differential equations by Hodgkin and Huxley, synthesizes the impact of ionic currents on a cell's voltage--and the highly nonlinear impact of that voltage back on the currents themselves--into the rapid push and pull of the action potential. Later studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations or their counterparts. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the equations of Hodgkin-Huxley type. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic equations of Hodgkin-Huxley type as well as to more modern models of ion channel dynamics. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly MATLAB simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.

Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons.

The random transitions of ion channels between conducting and nonconducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling the states of ion channels nonlinearly couples continuous-time Markov chains to a differential equation for voltage. Beginning with the work of R. F. Fox and Y.-N. Lu [Phys. Rev. E 49, 3421 (1994)], there have been attempts to generate simpler models that use stochastic differential equation (SDEs) to approximate the stochastic spiking activity produced by Markov chain models. Recent numerical investigations, however, have raised doubts that SDE models can capture the stochastic dynamics of Markov chain models.We analyze three SDE models that have been proposed as approximations to the Markov chain model: one that describes the states of the ion channels and two that describe the states of the ion channel subunits. We show that the former channel-based approach can capture the distribution of channel noise and its effects on spiking in a Hodgkin-Huxley neuron model to a degree not previously demonstrated, but the latter two subunit-based approaches cannot. Our analysis provides intuitive and mathematical explanations for why this is the case. The temporal correlation in the channel noise is determined by the combinatorics of bundling subunits into channels, but the subunit-based approaches do not correctly account for this structure. Our study confirms and elucidates the findings of previous numerical investigations of subunit-based SDE models. Moreover, it presents evidence that Markov chain models of the nonlinear, stochastic dynamics of neural membranes can be accurately approximated by SDEs. This finding opens a door to future modeling work using SDE techniques to further illuminate the effects of ion channel fluctuations on electrically active cells.

Modeling the electrode-neuron interface of cochlear implants: effects of neural survival, electrode placement, and the partial tripolar configuration.

The partial tripolar electrode configuration is a relatively novel stimulation strategy that can generate more spatially focused electric fields than the commonly used monopolar configuration. Focused stimulation strategies should improve spectral resolution in cochlear implant users, but may also be more sensitive to local irregularities in the electrode-neuron interface. In this study, we develop a practical computer model of cochlear implant stimulation that can simulate neural activation in a simplified cochlear geometry and we relate the resulting patterns of neural activity to basic psychophysical measures. We examine how two types of local irregularities in the electrode-neuron interface, variations in spiral ganglion nerve density and electrode position within the scala tympani, affect the simulated neural activation patterns and how these patterns change with electrode configuration. The model shows that higher partial tripolar fractions activate more spatially restricted populations of neurons at all current levels and require higher current levels to excite a given number of neurons. We find that threshold levels are more sensitive at high partial tripolar fractions to both types of irregularities, but these effects are not independent. In particular, at close electrode-neuron distances, activation is typically more spatially localized which leads to a greater influence of neural dead regions.

Encoding and decoding amplitude-modulated cochlear implant stimuli--a point process analysis.

Cochlear implant speech processors stimulate the auditory nerve by delivering amplitude-modulated electrical pulse trains to intracochlear electrodes. Studying how auditory nerve cells encode modulation information is of fundamental importance, therefore, to understanding cochlear implant function and improving speech perception in cochlear implant users. In this paper, we analyze simulated responses of the auditory nerve to amplitude-modulated cochlear implant stimuli using a point process model. First, we quantify the information encoded in the spike trains by testing an ideal observer's ability to detect amplitude modulation in a two-alternative forced-choice task. We vary the amount of information available to the observer to probe how spike timing and averaged firing rate encode modulation. Second, we construct a neural decoding method that predicts several qualitative trends observed in psychophysical tests of amplitude modulation detection in cochlear implant listeners. We find that modulation information is primarily available in the sequence of spike times. The performance of an ideal observer, however, is inconsistent with observed trends in psychophysical data. Using a neural decoding method that jitters spike times to degrade its temporal resolution and then computes a common measure of phase locking from spike trains of a heterogeneous population of model nerve cells, we predict the correct qualitative dependence of modulation detection thresholds on modulation frequency and stimulus level. The decoder does not predict the observed loss of modulation sensitivity at high carrier pulse rates, but this framework can be applied to future models that better represent auditory nerve responses to high carrier pulse rate stimuli. The supplemental material of this article contains the article's data in an active, re-usable format.

Who foregoes survivor protection in employer-sponsored pension annuities?

PURPOSE: Retirees in traditional pension plans must generally choose between single life annuities, which provide regular payments until death, and joint and survivor annuities, which pay less each month but continue to make payments to the spouse after the death of the retired worker. This article examines the payout decision and measures the share of married retirees with pension annuities who forego survivor protection. DESIGN AND METHODS: The analysis consists of a probit model of the pension payout decision, based on data from the 1992-2000 waves of the Health and Retirement Study. RESULTS: More than one quarter (28%) of married men and two thirds of married women receiving employer-sponsored retirement annuities declined survivor protection. Men with small pensions and limited household wealth, men in better health than their spouses, and men whose spouses have pension coverage from their own employers are more likely than other men to reject survivor protection. IMPLICATIONS: Most workers appear to make payout decisions by rationally balancing the costs and benefits of each type of annuity, suggesting that existing measures to encourage joint and survivor annuities are adequate. However, the growth in 401(k) plans, which are generally not covered by existing laws protecting spousal pension rights, may leave widows vulnerable.