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Ashida G, Wang T, Kretzberg J. Integrate-and-fire-type models of the lateral superior olive. PLoS One 2024; 19:e0304832. [PMID: 38900820 PMCID: PMC11189240 DOI: 10.1371/journal.pone.0304832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2023] [Accepted: 05/20/2024] [Indexed: 06/22/2024] Open
Abstract
Neurons of the lateral superior olive (LSO) in the auditory brainstem play a fundamental role in binaural sound localization. Previous theoretical studies developed various types of neuronal models to study the physiological functions of the LSO. These models were usually tuned to a small set of physiological data with specific aims in mind. Therefore, it is unclear whether and how they can be related to each other, how widely applicable they are, and which model is suitable for what purposes. In this study, we address these questions for six different single-compartment integrate-and-fire (IF) type LSO models. The models are divided into two groups depending on their subthreshold responses: passive (linear) models with only the leak conductance and active (nonlinear) models with an additional low-voltage-activated potassium conductance that is prevalent among the auditory system. Each of these two groups is further subdivided into three subtypes according to the spike generation mechanism: one with simple threshold-crossing detection and voltage reset, one with threshold-crossing detection plus a current to mimic spike shapes, and one with a depolarizing exponential current for spiking. In our simulations, all six models were driven by identical synaptic inputs and calibrated with common criteria for binaural tuning. The resulting spike rates of the passive models were higher for intensive inputs and lower for temporally structured inputs than those of the active models, confirming the active function of the potassium current. Within each passive or active group, the simulated responses resembled each other, regardless of the spike generation types. These results, in combination with the analysis of computational costs, indicate that an active IF model is more suitable than a passive model for accurately reproducing temporal coding of LSO. The simulation of realistic spike shapes with an extended spiking mechanism added relatively small computational costs.
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Affiliation(s)
- Go Ashida
- Faculty 6, Department of Neuroscience, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
- Cluster of Excellence "Hearing4all", Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
| | - Tiezhi Wang
- Faculty 6, Department of Neuroscience, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
- Faculty 6, Department of Health Services Research, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
| | - Jutta Kretzberg
- Faculty 6, Department of Neuroscience, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
- Cluster of Excellence "Hearing4all", Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
- Research Center Neurosensory Science, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany
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2
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Kuenzel T. Modulatory influences on time-coding neurons in the ventral cochlear nucleus. Hear Res 2019; 384:107824. [DOI: 10.1016/j.heares.2019.107824] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Revised: 09/10/2019] [Accepted: 10/14/2019] [Indexed: 02/07/2023]
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Jamali M, Carriot J, Chacron MJ, Cullen KE. Coding strategies in the otolith system differ for translational head motion vs. static orientation relative to gravity. eLife 2019; 8:45573. [PMID: 31199243 PMCID: PMC6590985 DOI: 10.7554/elife.45573] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Accepted: 06/13/2019] [Indexed: 12/26/2022] Open
Abstract
The detection of gravito-inertial forces by the otolith system is essential for our sense of balance and accurate perception. To date, however, how this system encodes the self-motion stimuli that are experienced during everyday activities remains unknown. Here, we addressed this fundamental question directly by recording from single otolith afferents in monkeys during naturalistic translational self-motion and changes in static head orientation. Otolith afferents with higher intrinsic variability transmitted more information overall about translational self-motion than their regular counterparts, owing to stronger nonlinearities that enabled precise spike timing including phase locking. By contrast, more regular afferents better discriminated between different static head orientations relative to gravity. Using computational methods, we further demonstrated that coupled increases in intrinsic variability and sensitivity accounted for the observed functional differences between afferent classes. Together, our results indicate that irregular and regular otolith afferents use different strategies to encode naturalistic self-motion and static head orientation relative to gravity.
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Affiliation(s)
- Mohsen Jamali
- Department of Neurosurgery, Harvard Medical School, Massachusetts General Hospital, Boston, United States
| | - Jerome Carriot
- Department of Physiology, McGill University, Montreal, Canada
| | | | - Kathleen E Cullen
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, United States
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Huguet G, Meng X, Rinzel J. Phasic Firing and Coincidence Detection by Subthreshold Negative Feedback: Divisive or Subtractive or, Better, Both. Front Comput Neurosci 2017; 11:3. [PMID: 28210218 PMCID: PMC5288357 DOI: 10.3389/fncom.2017.00003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2016] [Accepted: 01/16/2017] [Indexed: 11/26/2022] Open
Abstract
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.
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Affiliation(s)
- Gemma Huguet
- Departament de Matemàtiques, Universitat Politècnica de Catalunya Barcelona, Spain
| | - Xiangying Meng
- Biology Department, University of Maryland College Park, MD, USA
| | - John Rinzel
- Center for Neural Science, New York UniversityNew York, NY, USA; Courant Institute of Mathematical Sciences, New York UniversityNew York, NY, USA
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Jamali M, Chacron MJ, Cullen KE. Self-motion evokes precise spike timing in the primate vestibular system. Nat Commun 2016; 7:13229. [PMID: 27786265 PMCID: PMC5095295 DOI: 10.1038/ncomms13229] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2016] [Accepted: 09/14/2016] [Indexed: 12/23/2022] Open
Abstract
The accurate representation of self-motion requires the efficient processing of sensory input by the vestibular system. Conventional wisdom is that vestibular information is exclusively transmitted through changes in firing rate, yet under this assumption vestibular neurons display relatively poor detection and information transmission. Here, we carry out an analysis of the system's coding capabilities by recording neuronal responses to repeated presentations of naturalistic stimuli. We find that afferents with greater intrinsic variability reliably discriminate between different stimulus waveforms through differential patterns of precise (∼6 ms) spike timing, while those with minimal intrinsic variability do not. A simple mathematical model provides an explanation for this result. Postsynaptic central neurons also demonstrate precise spike timing, suggesting that higher brain areas also represent self-motion using temporally precise firing. These findings demonstrate that two distinct sensory channels represent vestibular information: one using rate coding and the other that takes advantage of precise spike timing. Early vestibular pathways are thought to code sensory inputs regarding self-motion via changes in firing rate. Here, the authors record from both regular and irregular afferents in macaques, and find both irregular afferents and central neurons also represent self-motion via temporally precise spike timing.
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Affiliation(s)
- Mohsen Jamali
- Department of Physiology McGill University, Montreal, Quebec, Canada H3G1Y6
| | - Maurice J Chacron
- Department of Physiology McGill University, Montreal, Quebec, Canada H3G1Y6
| | - Kathleen E Cullen
- Department of Physiology McGill University, Montreal, Quebec, Canada H3G1Y6
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A model of the medial superior olive explains spatiotemporal features of local field potentials. J Neurosci 2014; 34:11705-22. [PMID: 25164666 DOI: 10.1523/jneurosci.0175-14.2014] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
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.
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Gai Y, Kotak VC, Sanes DH, Rinzel J. On the localization of complex sounds: temporal encoding based on input-slope coincidence detection of envelopes. J Neurophysiol 2014; 112:802-13. [PMID: 24848460 DOI: 10.1152/jn.00044.2013] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
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.
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Affiliation(s)
- Yan Gai
- Department of Neuroscience, University of Wisconsin Madison, Madison, Wisconsin; Center for Neural Science, New York University, New York, New York
| | - Vibhakar C Kotak
- Center for Neural Science, New York University, New York, New York
| | - Dan H Sanes
- Center for Neural Science, New York University, New York, New York; Department of Biology, New York University, New York, New York; and
| | - John Rinzel
- Department of Biology, New York University, New York, New York; and Courant Institute of Mathematical Science, New York University, New York, New York
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Ashida G, Funabiki K, Carr CE. Theoretical foundations of the sound analog membrane potential that underlies coincidence detection in the barn owl. Front Comput Neurosci 2013; 7:151. [PMID: 24265616 PMCID: PMC3821005 DOI: 10.3389/fncom.2013.00151] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2012] [Accepted: 10/11/2013] [Indexed: 11/15/2022] Open
Abstract
A wide variety of neurons encode temporal information via phase-locked spikes. In the avian auditory brainstem, neurons in the cochlear nucleus magnocellularis (NM) send phase-locked synaptic inputs to coincidence detector neurons in the nucleus laminaris (NL) that mediate sound localization. Previous modeling studies suggested that converging phase-locked synaptic inputs may give rise to a periodic oscillation in the membrane potential of their target neuron. Recent physiological recordings in vivo revealed that owl NL neurons changed their spike rates almost linearly with the amplitude of this oscillatory potential. The oscillatory potential was termed the sound analog potential, because of its resemblance to the waveform of the stimulus tone. The amplitude of the sound analog potential recorded in NL varied systematically with the interaural time difference (ITD), which is one of the most important cues for sound localization. In order to investigate the mechanisms underlying ITD computation in the NM-NL circuit, we provide detailed theoretical descriptions of how phase-locked inputs form oscillating membrane potentials. We derive analytical expressions that relate presynaptic, synaptic, and postsynaptic factors to the signal and noise components of the oscillation in both the synaptic conductance and the membrane potential. Numerical simulations demonstrate the validity of the theoretical formulations for the entire frequency ranges tested (1–8 kHz) and potential effects of higher harmonics on NL neurons with low best frequencies (<2 kHz).
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Affiliation(s)
- Go Ashida
- Department of Biology, University of Maryland College Park, MD, USA
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Ashida G, Funabiki K, Carr CE. Biophysical basis of the sound analog membrane potential that underlies coincidence detection in the barn owl. Front Comput Neurosci 2013; 7:102. [PMID: 24265615 PMCID: PMC3821004 DOI: 10.3389/fncom.2013.00102] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2012] [Accepted: 07/07/2013] [Indexed: 11/13/2022] Open
Abstract
Interaural time difference (ITD), or the difference in timing of a sound wave arriving at the two ears, is a fundamental cue for sound localization. A wide variety of animals have specialized neural circuits dedicated to the computation of ITDs. In the avian auditory brainstem, ITDs are encoded as the spike rates in the coincidence detector neurons of the nucleus laminaris (NL). NL neurons compare the binaural phase-locked inputs from the axons of ipsi- and contralateral nucleus magnocellularis (NM) neurons. Intracellular recordings from the barn owl's NL in vivo showed that tonal stimuli induce oscillations in the membrane potential. Since this oscillatory potential resembled the stimulus sound waveform, it was named the sound analog potential (Funabiki et al., 2011). Previous modeling studies suggested that a convergence of phase-locked spikes from NM leads to an oscillatory membrane potential in NL, but how presynaptic, synaptic, and postsynaptic factors affect the formation of the sound analog potential remains to be investigated. In the accompanying paper, we derive analytical relations between these parameters and the signal and noise components of the oscillation. In this paper, we focus on the effects of the number of presynaptic NM fibers, the mean firing rate of these fibers, their average degree of phase-locking, and the synaptic time scale. Theoretical analyses and numerical simulations show that, provided the total synaptic input is kept constant, changes in the number and spike rate of NM fibers alter the ITD-independent noise whereas the degree of phase-locking is linearly converted to the ITD-dependent signal component of the sound analog potential. The synaptic time constant affects the signal more prominently than the noise, making faster synaptic input more suitable for effective ITD computation.
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Affiliation(s)
- Go Ashida
- Department of Biology, University of Maryland, College Park MD, USA
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Wittig JH, Boahen K. Potassium conductance dynamics confer robust spike-time precision in a neuromorphic model of the auditory brain stem. J Neurophysiol 2013; 110:307-21. [PMID: 23554436 DOI: 10.1152/jn.00433.2012] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
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.
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Affiliation(s)
- John H Wittig
- Laboratory of Neuropsychology, National Institute of Mental Health, Bethesda, MD 20892, USA.
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Ashida G, Funabiki K, Kuokkanen PT, Kempter R, Carr CE. Signal-to-noise ratio in the membrane potential of the owl's auditory coincidence detectors. J Neurophysiol 2012; 108:2837-45. [PMID: 22933726 DOI: 10.1152/jn.00366.2012] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Owls use interaural time differences (ITDs) to locate a sound source. They compute ITD in a specialized neural circuit that consists of axonal delay lines from the cochlear nucleus magnocellularis (NM) and coincidence detectors in the nucleus laminaris (NL). Recent physiological recordings have shown that tonal stimuli induce oscillatory membrane potentials in NL neurons (Funabiki K, Ashida G, Konishi M. J Neurosci 31: 15245-15256, 2011). The amplitude of these oscillations varies with ITD and is strongly correlated to the firing rate. The oscillation, termed the sound analog potential, has the same frequency as the stimulus tone and is presumed to originate from phase-locked synaptic inputs from NM fibers. To investigate how these oscillatory membrane potentials are generated, we applied recently developed signal-to-noise ratio (SNR) analysis techniques (Kuokkanen PT, Wagner H, Ashida G, Carr CE, Kempter R. J Neurophysiol 104: 2274-2290, 2010) to the intracellular waveforms obtained in vivo. Our theoretical prediction of the band-limited SNRs agreed with experimental data for mid- to high-frequency (>2 kHz) NL neurons. For low-frequency (≤2 kHz) NL neurons, however, measured SNRs were lower than theoretical predictions. These results suggest that the number of independent NM fibers converging onto each NL neuron and/or the population-averaged degree of phase-locking of the NM fibers could be significantly smaller in the low-frequency NL region than estimated for higher best-frequency NL.
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Affiliation(s)
- Go Ashida
- Department of Biology, University of Maryland, College Park, Maryland 20742, USA.
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Kreeger LJ, Arshed A, MacLeod KM. Intrinsic firing properties in the avian auditory brain stem allow both integration and encoding of temporally modulated noisy inputs in vitro. J Neurophysiol 2012; 108:2794-809. [PMID: 22914650 DOI: 10.1152/jn.00092.2012] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
The intrinsic properties of tonically firing neurons in the cochlear nucleus contribute to representing average sound intensity by favoring synaptic integration across auditory nerve inputs, reducing phase locking to fine temporal acoustic structure and enhancing envelope locking. To determine whether tonically firing neurons of the avian cochlear nucleus angularis (NA) resemble ideal integrators, we investigated their firing responses to noisy current injections during whole cell patch-clamp recordings in brain slices. One subclass of neurons (36% of tonically firing neurons, mainly subtype tonic III) showed no significant changes in firing rate with noise fluctuations, acting like pure integrators. In contrast, many tonically firing neurons (>60%, mainly subtype tonic I or II) showed a robust sensitivity to noisy current fluctuations, increasing their firing rates with increased fluctuation amplitudes. For noise-sensitive tonic neurons, the firing rate vs. average current curves with noise had larger maximal firing rates, lower gains, and wider dynamic ranges compared with FI curves for current steps without noise. All NA neurons showed fluctuation-driven patterning of spikes with a high degree of temporal reliability and millisecond spike time precision. Single-spiking neurons in NA also responded to noisy currents with higher firing rates and reliable spike trains, although less precisely than nucleus magnocellularis neurons. Thus some NA neurons function as integrators by encoding average input levels over wide dynamic ranges regardless of current fluctuations, others detect the degree of coherence in the inputs, and most encode the temporal patterns contained in their inputs with a high degree of precision.
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Affiliation(s)
- Lauren J Kreeger
- Department of Biology, University of Maryland, College Park, Maryland 20742, USA
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Meng X, Huguet G, Rinzel J. TYPE III EXCITABILITY, SLOPE SENSITIVITY AND COINCIDENCE DETECTION. ACTA ACUST UNITED AC 2012; 32:2729-2757. [PMID: 23667306 DOI: 10.3934/dcds.2012.32.2729] [Citation(s) in RCA: 79] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
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.
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Affiliation(s)
- Xiangying Meng
- Dynamics and Control, Beihang University, Beijing, China, Center for Neural Science, New York University, USA
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Wang L, Colburn HS. A modeling study of the responses of the lateral superior olive to ipsilateral sinusoidally amplitude-modulated tones. J Assoc Res Otolaryngol 2011; 13:249-267. [PMID: 22160752 PMCID: PMC3298618 DOI: 10.1007/s10162-011-0300-5] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2011] [Accepted: 10/25/2011] [Indexed: 11/27/2022] Open
Abstract
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.
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Affiliation(s)
- Le Wang
- Department of Biomedical Engineering, Center for Hearing Research, Boston University, Boston, MA, 02215, USA
| | - H Steven Colburn
- Department of Biomedical Engineering, Center for Hearing Research, Boston University, Boston, MA, 02215, USA.
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15
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Day ML, Semple MN. Frequency-dependent interaural delays in the medial superior olive: implications for interaural cochlear delays. J Neurophysiol 2011; 106:1985-99. [DOI: 10.1152/jn.00131.2011] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Neurons in the medial superior olive (MSO) are tuned to the interaural time difference (ITD) of sound arriving at the two ears. MSO neurons evoke a strongest response at their best delay (BD), at which the internal delay between bilateral inputs to MSO matches the external ITD. We performed extracellular recordings in the superior olivary complex of the anesthetized gerbil and found a majority of single units localized to the MSO to exhibit BDs that shifted with tone frequency. The relation of best interaural phase difference to tone frequency revealed nonlinearities in some MSO units and others with linear relations with characteristic phase between 0.4 and 0.6 cycles. The latter is usually associated with the interaction of ipsilateral excitation and contralateral inhibition, as in the lateral superior olive, yet all MSO units exhibited evidence of bilateral excitation. Interaural cochlear delays and phase-locked contralateral inhibition are two mechanisms of internal delay that have been suggested to create frequency-dependent delays. Best interaural phase-frequency relations were compared with a cross-correlation model of MSO that incorporated interaural cochlear delays and an additional frequency-independent delay component. The model with interaural cochlear delay fit phase-frequency relations exhibiting frequency-dependent delays with precision. Another model of MSO incorporating inhibition based on realistic biophysical parameters could not reproduce observed frequency-dependent delays.
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Affiliation(s)
- Mitchell L. Day
- Center for Neural Science, New York University, New York, New York
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16
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Ashida G, Carr CE. Sound localization: Jeffress and beyond. Curr Opin Neurobiol 2011; 21:745-51. [PMID: 21646012 DOI: 10.1016/j.conb.2011.05.008] [Citation(s) in RCA: 88] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2011] [Revised: 05/05/2011] [Accepted: 05/11/2011] [Indexed: 12/01/2022]
Abstract
Many animals use the interaural time differences (ITDs) to locate the source of low frequency sounds. The place coding theory proposed by Jeffress has long been a dominant model to account for the neural mechanisms of ITD detection. Recent research, however, suggests a wider range of strategies for ITD coding in the binaural auditory brainstem. We discuss how ITD is coded in avian, mammalian, and reptilian nervous systems, and review underlying synaptic and cellular properties that enable precise temporal computation. The latest advances in recording and analysis techniques provide powerful tools for both overcoming and utilizing the large field potentials in these nuclei.
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Affiliation(s)
- Go Ashida
- Department of Biology, University of Maryland, College Park, MD 20742, USA
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17
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Gai Y, Doiron B, Rinzel J. Slope-based stochastic resonance: how noise enables phasic neurons to encode slow signals. PLoS Comput Biol 2010; 6:e1000825. [PMID: 20585612 PMCID: PMC2891698 DOI: 10.1371/journal.pcbi.1000825] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2010] [Accepted: 05/20/2010] [Indexed: 11/23/2022] Open
Abstract
Fundamental properties of phasic firing neurons are usually characterized in a noise-free condition. In the absence of noise, phasic neurons exhibit Class 3 excitability, which is a lack of repetitive firing to steady current injections. For time-varying inputs, phasic neurons are band-pass filters or slope detectors, because they do not respond to inputs containing exclusively low frequencies or shallow slopes. However, we show that in noisy conditions, response properties of phasic neuron models are distinctly altered. Noise enables a phasic model to encode low-frequency inputs that are outside of the response range of the associated deterministic model. Interestingly, this seemingly stochastic-resonance (SR) like effect differs significantly from the classical SR behavior of spiking systems in both the signal-to-noise ratio and the temporal response pattern. Instead of being most sensitive to the peak of a subthreshold signal, as is typical in a classical SR system, phasic models are most sensitive to the signal's rising and falling phases where the slopes are steep. This finding is consistent with the fact that there is not an absolute input threshold in terms of amplitude; rather, a response threshold is more properly defined as a stimulus slope/frequency. We call the encoding of low-frequency signals with noise by phasic models a slope-based SR, because noise can lower or diminish the slope threshold for ramp stimuli. We demonstrate here similar behaviors in three mechanistic models with Class 3 excitability in the presence of slow-varying noise and we suggest that the slope-based SR is a fundamental behavior associated with general phasic properties rather than with a particular biological mechanism. Principal brain cells, called neurons, show a tremendous amount of diversity in their responses to driving stimuli. A widely present but understudied class of neurons prefers to respond to high-frequency inputs and neglect slow variations; these cells are called phasic neurons. Although phasic neurons do not normally respond to slow signals, we show that noise, a ubiquitous neural input, can enable them to respond to distinct features of slow signals. We emphasize the fact that, in the presence of noise, they are still sensitive to the change in stimulus, rather than to the constant part of the slow inputs, just as they are for fast inputs without noise. This feature distinguishes the response of phasic neurons from those of other neurons, which show more sensitivity to the amplitude of their inputs. We believe that our study has significantly broadened the understanding about the information-processing ability and functional roles of phasic neurons.
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Affiliation(s)
- Yan Gai
- Center for Neural Science, New York University, New York, New York, United States of America.
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18
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Gai Y, Doiron B, Kotak V, Rinzel J. Noise-gated encoding of slow inputs by auditory brain stem neurons with a low-threshold K+ current. J Neurophysiol 2009; 102:3447-60. [PMID: 19812289 DOI: 10.1152/jn.00538.2009] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Phasic neurons, which do not fire repetitively to steady depolarization, are found at various stages of the auditory system. Phasic neurons are commonly described as band-pass filters because they do not respond to low-frequency inputs even when the amplitude is large. However, we show that phasic neurons can encode low-frequency inputs when noise is present. With a low-threshold potassium current (I(KLT)), a phasic neuron model responds to rising and falling phases of a subthreshold low-frequency signal with white noise. When the white noise was low-pass filtered, the phasic model also responded to the signal's trough but still not to the peak. In contrast, a tonic neuron model fired mostly to the signal's peak. To test the model predictions, whole cell slice recordings were obtained in the medial (MSO) and lateral (LSO) superior olivary neurons in gerbil from postnatal day 10 (P10) to 22. The phasic MSO neurons with strong I(KLT), mostly from gerbils aged P17 or older, showed firing patterns consistent with the preceding predictions. Moreover, injecting a virtual I(KLT) into weak-phasic MSO and tonic LSO neurons with putative weak or no I(KLT) (from gerbils younger than P17) shifted the neural response from the signal's peak to the rising phase. These findings advance our knowledge about how noise gates the signal pathway and how phasic neurons encode slow envelopes of sounds with high-frequency carriers.
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Affiliation(s)
- Yan Gai
- Center for Neural Science, New York University, New York, NY 10003, USA.
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19
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Increase of Kv3.1b expression in avian auditory brainstem neurons correlates with synaptogenesis in vivo and in vitro. Brain Res 2009; 1302:64-75. [PMID: 19766604 DOI: 10.1016/j.brainres.2009.09.046] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2009] [Revised: 06/22/2009] [Accepted: 09/14/2009] [Indexed: 10/20/2022]
Abstract
In the auditory system voltage-activated currents mediated by potassium channels Kv1.1 and Kv3.1b and their interaction with sodium inward currents play a crucial role for computational function. However, it is unresolved how these potassium channels are developmentally regulated. We have therefore combined a biochemical investigation of Kv1.1 and Kv3.1b protein expression with electrophysiological recordings of membrane currents to characterize neuronal differentiation in the auditory brain stem of the chick. Differentiation in vitro was compared with cells prepared from corresponding embryonic stages in vivo. Using a computer model based on the empirical data we were then able to predict physiological properties of developing auditory brain stem neurons. In vivo Kv3.1b expression increased strongly between E10 and E14, a time of functional synaptogenesis in the auditory brainstem. We also found this increase of expression in vitro, again coinciding with synaptogenesis in the cultures. Whole-cell patch recordings revealed a corresponding increase of the (Kv3.1-like) high threshold potassium current. In contrast, Kv1.1 protein expression failed to increase in vitro, and changes in (Kv1.1-like) low threshold potassium current with time in culture were not significant. Electrophysiological recordings revealed that sodium inward currents increased with cultivation time. Thus, our data suggest that Kv3.1b expression occurs with the onset of functional synaptogenesis, while a different signal, absent from cultures of dissociated auditory brain stem, is needed for Kv1.1 expression. A biophysical model constructed with parameters from our recordings was used to investigate the functional impact of the currents mediated by these channels. We found that during development both high and low threshold potassium currents need to be increased in a concerted manner with the sodium conductance for the neurons to exhibit fast and phasic action potential firing and a narrow time window of coincidence detection.
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Kuznetsova MS, Higgs MH, Spain WJ. Adaptation of firing rate and spike-timing precision in the avian cochlear nucleus. J Neurosci 2008; 28:11906-15. [PMID: 19005056 PMCID: PMC2693385 DOI: 10.1523/jneurosci.3827-08.2008] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2008] [Accepted: 10/01/2008] [Indexed: 11/21/2022] Open
Abstract
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.
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Affiliation(s)
- Marina S. Kuznetsova
- Department of Physiology and Biophysics
- Interdisciplinary Graduate Program in Neurobiology and Behavior, and
| | | | - William J. Spain
- Department of Physiology and Biophysics
- Department of Neurology, University of Washington, Seattle, Washington 98105, and
- Neurology Section, Veterans Affairs Puget Sound Health Care System, Seattle, Washington 98108
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