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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.

Sound localization relies on minute differences in the timing and intensity of sound arriving at both ears. Neurons of the lateral superior olive (LSO) in the brainstem process these interaural disparities by precisely detecting excitatory and inhibitory synaptic inputs. Aging generally induces selective loss of inhibitory synaptic transmission along the entire auditory pathways, including the reduction of inhibitory afferents to LSO. Electrophysiological recordings in animals, however, reported only minor functional changes in aged LSO. The perplexing discrepancy between anatomical and physiological observations suggests a role for activity-dependent plasticity that would help neurons retain their binaural tuning function despite loss of inhibitory inputs. To explore this hypothesis, we use a computational model of LSO to investigate mechanisms underlying the observed functional robustness against age-related loss of inhibitory inputs. The LSO model is an integrate-and-fire type enhanced with a small amount of low-voltage activated potassium conductance and driven with (in)homogeneous Poissonian inputs. Without synaptic input loss, model spike rates varied smoothly with interaural time and level differences, replicating empirical tuning properties of LSO. By reducing the number of inhibitory afferents to mimic age-related loss of inhibition, overall spike rates increased, which negatively impacted binaural tuning performance, measured as modulation depth and neuronal discriminability. To simulate a recovery process compensating for the loss of inhibitory fibers, the strength of remaining inhibitory inputs was increased. By this modification, effects of inhibition loss on binaural tuning were considerably weakened, leading to an improvement of functional performance. These neuron-level observations were further confirmed by population modeling, in which binaural tuning properties of multiple LSO neurons were varied according to empirical measurements. These results demonstrate the plausibility that homeostatic plasticity could effectively counteract known age-dependent loss of inhibitory fibers in LSO and suggest that behavioral degradation of sound localization might originate from changes occurring more centrally.

Many sensory neurons encode temporal information by detecting coincident arrivals of synaptic inputs. In the mammalian auditory brainstem, binaural neurons of the medial superior olive (MSO) are known to act as coincidence detectors, whereas in the lateral superior olive (LSO) roles of coincidence detection have remained unclear. LSO neurons receive excitatory and inhibitory inputs driven by ipsilateral and contralateral acoustic stimuli, respectively, and vary their output spike rates according to interaural level differences. In addition, LSO neurons are also sensitive to binaural phase differences of low-frequency tones and envelopes of amplitude-modulated (AM) sounds. Previous physiological recordings in vivo found considerable variations in monaural AM-tuning across neurons. To investigate the underlying mechanisms of the observed temporal tuning properties of LSO and their sources of variability, we used a simple coincidence counting model and examined how specific parameters of coincidence detection affect monaural and binaural AM coding. Spike rates and phase-locking of evoked excitatory and spontaneous inhibitory inputs had only minor effects on LSO output to monaural AM inputs. In contrast, the coincidence threshold of the model neuron affected both the overall spike rates and the half-peak positions of the AM-tuning curve, whereas the width of the coincidence window merely influenced the output spike rates. The duration of the refractory period affected only the low-frequency portion of the monaural AM-tuning curve. Unlike monaural AM coding, temporal factors, such as the coincidence window and the effective duration of inhibition, played a major role in determining the trough positions of simulated binaural phase-response curves. In addition, empirically-observed level-dependence of binaural phase-coding was reproduced in the framework of our minimalistic coincidence counting model. These modeling results suggest that coincidence detection of excitatory and inhibitory synaptic inputs is essential for LSO neurons to encode both monaural and binaural AM sounds.

Computations of acoustic information along the central auditory pathways start in the cochlear nucleus. Bushy cells in the anteroventral cochlear nucleus, which innervate monaural and binaural stations in the superior olivary complex, process and transfer temporal cues relevant for sound localization. These cells are categorized into two groups: spherical and globular bushy cells (SBCs/GBCs). Spontaneous rates of GBCs innervated by multiple auditory nerve (AN) fibers are generally lower than those of SBCs that receive a small number of large AN synapses. In response to low-frequency tonal stimulation, both types of bushy cells show improved phase-locking and entrainment compared to AN fibers. When driven by high-frequency tones, GBCs show primary-like-with-notch or onset-L peristimulus time histograms and relatively irregular spiking. However, previous in vivo physiological studies of bushy cells also found considerable unit-to-unit variability in these response patterns. Here we present a population of models that can simulate the observed variation in GBCs. We used a simple coincidence detection model with an adaptive threshold and systematically varied its six parameters. Out of 567000 parameter combinations tested, 7520 primary-like-with-notch models and 4094 onset-L models were selected that satisfied a set of physiological criteria for a GBC unit. Analyses of the model parameters and output measures revealed that the parameters of the accepted model population are weakly correlated with each other to retain major GBC properties, and that the output spiking patterns of the model are affected by a combination of multiple parameters. Simulations of frequency-dependent temporal properties of the model GBCs showed a reasonable fit to empirical data, supporting the validity of our population modeling. The computational simplicity and efficiency of the model structure makes our approach suitable for future large-scale simulations of binaural information processing that may involve thousands of GBC units.

In computational biology, modeling is a fundamental tool for formulating, analyzing and predicting complex phenomena. Most neuron models, however, are designed to reproduce certain small sets of empirical data. Hence their outcome is usually not compatible or comparable with other models or datasets, making it unclear how widely applicable such models are. In this study, we investigate these aspects of modeling, namely credibility and generalizability, with a specific focus on auditory neurons involved in the localization of sound sources. The primary cues for binaural sound localization are comprised of interaural time and level differences (ITD/ILD), which are the timing and intensity differences of the sound waves arriving at the two ears. The lateral superior olive (LSO) in the auditory brainstem is one of the locations where such acoustic information is first computed. An LSO neuron receives temporally structured excitatory and inhibitory synaptic inputs that are driven by ipsi- and contralateral sound stimuli, respectively, and changes its spike rate according to binaural acoustic differences. Here we examine seven contemporary models of LSO neurons with different levels of biophysical complexity, from predominantly functional ones ('shot-noise' models) to those with more detailed physiological components (variations of integrate-and-fire and Hodgkin-Huxley-type). These models, calibrated to reproduce known monaural and binaural characteristics of LSO, generate largely similar results to each other in simulating ITD and ILD coding. Our comparisons of physiological detail, computational efficiency, predictive performances, and further expandability of the models demonstrate (1) that the simplistic, functional LSO models are suitable for applications where low computational costs and mathematical transparency are needed, (2) that more complex models with detailed membrane potential dynamics are necessary for simulation studies where sub-neuronal nonlinear processes play important roles, and (3) that, for general purposes, intermediate models might be a reasonable compromise between simplicity and biological plausibility.

Information processing in the nervous system critically relies on temporally precise spiking activity. In the auditory system, various degrees of phase-locking can be observed from the auditory nerve to cortical neurons. The classical metric for quantifying phase-locking is the vector strength (VS), which captures the periodicity in neuronal spiking. More recently, another metric, called the correlation index (CI), was proposed to quantify the temporally reproducible response characteristics of a neuron. The CI is defined as the peak value of a normalized shuffled autocorrelogram (SAC). Both VS and CI have been used to investigate how temporal information is processed and propagated along the auditory pathways. While previous analyses of physiological data in cats suggested covariation of these two metrics, general characterization of their connection has never been performed. In the present study, we derive a rigorous relationship between VS and CI. To model phase-locking, we assume Poissonian spike trains with a temporally changing intensity function following a von Mises distribution. We demonstrate that VS and CI are mutually related via the so-called concentration parameter that determines the degree of phase-locking. We confirm that these theoretical results are largely consistent with physiological data recorded in the auditory brainstem of various animals. In addition, we generate artificial phase-locked spike sequences, for which recording and analysis parameters can be systematically manipulated. Our analysis results suggest that mismatches between empirical data and the theoretical prediction can often be explained with deviations from the von Mises distribution, including skewed or multimodal period histograms. Furthermore, temporal relations of spike trains across trials can contribute to higher CI values than predicted mathematically based on the VS. We find that, for most applications, a SAC bin width of 50 ms seems to be a favorable choice, leading to an estimated error below 2.5% for physiologically plausible conditions. Overall, our results provide general relations between the two measures of phase-locking and will aid future analyses of different physiological datasets that are characterized with these metrics.

Mechanosensory cells in the leech share several common features with mechanoreceptors in the human glabrous skin. Previous studies showed that the six T (touch) cells in each body segment of the leech are highly variable in their responses to somatic current injection and change their excitability over time. Here, we investigate three potential reasons for this variability in excitability by comparing the responses of T cells at two soma locations (T2 and T3): (1) Differential effects of time-dependent changes in excitability, (2) divergent synaptic input from the network, and (3) different anatomical structures. These hypotheses were explored with a combination of electrophysiological double recordings, 3D reconstruction of neurobiotin-filled cells, and compartmental model simulations. Current injection triggered significantly more spikes with shorter latency and larger amplitudes in cells at soma location T2 than at T3. During longer recordings, cells at both locations increased their excitability over time in the same way. T2 and T3 cells received the same amount of synaptic input from the unstimulated network, and the polysynaptic connections between both T cells were mutually symmetric. However, we found a striking anatomical difference: While in our data set all T2 cells innervated two roots connecting the ganglion with the skin, 50% of the T3 cells had only one root process. The sub-sample of T3 cells with one root process was significantly less excitable than the T3 cells with two root processes and the T2 cells. To test if the additional root process causes higher excitability, we simulated the responses of 3D reconstructed cells of both anatomies with detailed multi-compartment models. The anatomical subtypes do not differ in excitability when identical biophysical parameters and a homogeneous channel distribution are assumed. Hence, all three hypotheses may contribute to the highly variable T cell responses, but none of them is the only factor accounting for the observed systematic difference in excitability between cells at T2 vs. T3 soma location. Therefore, future patch clamp and modeling studies are needed to analyze how biophysical properties and spatial distribution of ion channels on the cell surface contribute to the variability and systematic differences of electrophysiological phenotypes.

Many neurons possess more than one spike initiation zone (SIZ), which adds to their computational power and functional flexibility. Integrating inputs from different origins is especially relevant for sensory neurons that rely on relative spike timing for encoding sensory information. Yet, it is poorly understood if and how the propagation of spikes generated at one SIZ in response to sensory stimulation is affected by synaptic inputs triggering activity of other SIZ, and by environmental factors like temperature. The mechanosensory Touch (T) cell in the medicinal leech is an ideal model system to study these potential interactions because it allows intracellular recording and stimulation of its soma while simultaneously touching the skin in a body-wall preparation. The T cell reliably elicits spikes in response to somatic depolarization, as well as to tactile skin stimulation. Latencies of spikes elicited in the skin vary across cells, depending on the touch location relative to the cell’s receptive field. However, repetitive stimulation reveals that tactilely elicited spikes are more precisely timed than spikes triggered by somatic current injection. When the soma is hyperpolarized to mimic inhibitory synaptic input, first spike latencies of tactilely induced spikes increase. If spikes from both SIZ follow shortly after each other, the arrival time of the second spike at the soma can be delayed. Although the latency of spikes increases by the same factor when the temperature decreases, the effect is considerably stronger for the longer absolute latencies of spikes propagating from the skin to the soma. We therefore conclude that the propagation time of spikes from the skin is modulated by internal factors like synaptic inputs, and by external factors like temperature. Moreover, fewer spikes are detected when spikes from both origins are expected to arrive at the soma in temporal proximity. Hence, the leech T cell might be a key for understanding how the interaction of multiple SIZ impacts temporal and rate coding of sensory information, and how cold-blooded animals can produce adequate behavioral responses to sensory stimuli based on temperature-dependent relative spike timing.

Measurement of the optomotor response is a common way to determine thresholds of the visual system in animals. Particularly in mice, it is frequently used to characterize the visual performance of different genetically modified strains or to test the effect of various drugs on visual performance. Several methods have been developed to facilitate the presentation of stimuli using computer screens or projectors. Common methods are either based on the measurement of eye movement during optokinetic reflex behavior or rely on the measurement of head and/or body-movements during optomotor responses. Eye-movements can easily and objectively be quantified, but their measurement requires invasive fixation of the animals. Head movements can be observed in freely moving animals, but until now depended on the judgment of a human observer who reported the counted tracking movements of the animal during an experiment. In this study we present a novel measurement and stimulation system based on open source building plans and software. This system presents appropriate 360° stimuli while simultaneously video-tracking the animal's head-movements without fixation. The on-line determined head gaze is used to adjust the stimulus to the head position, as well as to automatically calculate visual acuity. Exemplary, we show that automatically measured visual response curves of mice match the results obtained by a human observer very well. The spatial acuity thresholds yielded by the automatic analysis are also consistent with the human observer approach and with published results. Hence, OMR-arena provides an affordable, convenient and objective way to measure mouse visual performance.

Sound localization is a fundamental sensory function of a wide variety of animals. The interaural time difference (ITD), an important cue for sound localization, is computed in the auditory brainstem. In our previous modeling study, we introduced a two-compartment Hodgkin-Huxley type model to investigate how cellular and synaptic specializations may contribute to precise ITD computation of the barn owl's auditory coincidence detector neuron. Although our model successfully reproduced fundamental physiological properties observed in vivo, it was unsuitable for mathematical analyses and large scale simulations because of a number of nonlinear variables. In the present study, we reduce our former model into three types of conductance-based integrate-and-fire (IF) models. We test their electrophysiological properties using data from published in vivo and in vitro studies. Their robustness to parameter changes and computational efficiencies are also examined. Our numerical results suggest that the single-compartment active IF model is superior to other reduced models in terms of physiological reproducibility and computational performance. This model will allow future theoretical studies that use more rigorous mathematical analysis and network simulations.