Information analysis of posterior canal afferents in the turtle, Trachemys scripta elegans

Information transmission of mean and variance coding in integrate-and-fire neurons

Neurons process information by translating continuous signals into patterns of discrete spike times. An open question is how much information these spike times contain about signals which modulate either the mean or the variance of the somatic currents in neurons, as is observed experimentally. Here we calculate the exact information contained in discrete spike times about a continuous signal in both encoding strategies. We show that the information content about mean modulating signals is generally substantially larger than about variance modulating signals for biological parameters. Our analysis further reveals that higher information transmission is associated with a larger proportion of nonlinear signal encoding. Our study measures the complete information content of mean and variance coding and provides a method to determine what fraction of the total information is linearly decodable.

Multiscale modeling of mechanotransduction in the utricle

We review recent progress in using numerical models to relate utricular hair bundle and otoconial membrane (OM) structure to the functional requirements imposed by natural behavior in turtles. The head movements section reviews the evolution of experimental attempts to understand vestibular system function with emphasis on turtles, including data showing that accelerations occurring during natural head movements achieve higher magnitudes and frequencies than previously assumed. The structure section reviews quantitative anatomical data documenting topographical variation in the structures underlying macromechanical and micromechanical responses of the turtle utricle to head movement: hair bundles, OM, and bundle-OM coupling. The macromechanics section reviews macromechanical models that incorporate realistic anatomical and mechanical parameters and reveal that the system is significantly underdamped, contrary to previous assumptions. The micromechanics: hair bundle motion and met currents section reviews work based on micromechanical models, which demonstrates that topographical variation in the structure of hair bundles and OM, and their mode of coupling, result in regional specializations for signaling of low frequency (or static) head position and high frequency head accelerations. We conclude that computational models based on empirical data are especially promising for investigating mechanotransduction in this challenging sensorimotor system.

The quantal component of synaptic transmission from sensory hair cells to the vestibular calyx

Spontaneous and stimulus-evoked excitatory postsynaptic currents (EPSCs) were recorded in calyx nerve terminals from the turtle vestibular lagena to quantify key attributes of quantal transmission at this synapse. On average, EPSC events had a magnitude of ∼ 42 pA, a rise time constant of τ(0) ∼ 229 μs, decayed to baseline with a time constant of τ(R) ∼ 690 μs, and carried ∼ 46 fC of charge. Individual EPSCs varied in magnitude and decay time constant. Variability in the EPSC decay time constant was hair cell dependent and due in part to a slow protraction of the EPSC in some cases. Variability in EPSC size was well described by an integer summation of unitary quanta, with each quanta of glutamate gating a unitary postsynaptic current of ∼ 23 pA. The unitary charge was ∼ 26 fC for EPSCs with a simple exponential decay and increased to ∼ 48 fC for EPSCs exhibiting a slow protraction. The EPSC magnitude and the number of simultaneous unitary quanta within each event increased with presynaptic stimulus intensity. During tonic hair cell depolarization, both the EPSC magnitude and event rate exhibited adaptive run down over time. Present data from a reptilian calyx are remarkably similar to noncalyceal vestibular synaptic terminals in diverse species, indicating that the skewed EPSC size distribution and multiquantal release might be an ancestral property of inner ear ribbon synapses.

Task, muscle and frequency dependent vestibular control of posture

The vestibular system is crucial for postural control; however there are considerable differences in the task dependence and frequency response of vestibular reflexes in appendicular and axial muscles. For example, vestibular reflexes are only evoked in appendicular muscles when vestibular information is relevant to postural control, while in neck muscles they are maintained regardless of the requirement to maintain head on trunk balance. Recent investigations have also shown that the bandwidth of vestibular input on neck muscles is much broader than appendicular muscles (up to a factor of 3). This result challenges the notion that vestibular reflexes only contribute to postural control across the behavioral and physiological frequency range of the vestibular organ (i.e., 0-20 Hz). In this review, we explore and integrate these task-, muscle- and frequency-related differences in the vestibular system's contribution to posture, and propose that the human nervous system has adapted vestibular signals to match the mechanical properties of the system that each group of muscles controls.

Experimental measurement of utricle system dynamic response to inertial stimulus

The membranous utricle sac of the red-eared turtle was mounted in a piezoelectric actuated platform mounted on the stage of a light microscope. The piezoelectric actuator oscillated the base of the neuroepithelium along a linear axis. Displacements were in the plane of the utricle and consisted of a linear sinusoidal-sweep signal starting at 0 and increasing to 500 Hz over 5 s. This inertial stimulus caused measurable shear displacement of the otoconial layer's dorsal surface, resulting in shear deformation of the gelatinous and column filament layers. Displacements of the otoconial layer and a reference point on the neuroepithelium were filmed at 2,000 frames/s with a high-speed video camera during oscillations. Image registration was performed on the video to track displacements with a resolution better than 15 nm. The displacement waveforms were then matched to a linear second-order model of the dynamic system. The model match identified two system mechanical parameters-the natural circular frequency ω n and the damping ratio ζ-that characterized the utricle dynamic response. The median values found for the medial-lateral axis on 20 utricles with 95 % confidence intervals in parenthesis were as follows: ω n = 374 (353, 396) Hz and ζ = 0.50 (0.47, 0.53). The anterior-posterior axis values were not significantly different: ω n = 409 (390, 430) Hz and ζ = 0.53 (0.48, 0.57). The results have two relevant and significant dynamic system findings: (1) a higher than expected natural frequency and (2) significant under damping. Previous to this study, utricular systems were treated as overdamped and with natural frequencies much lower that measured here. Both of these system performance findings result in excellent utricle time response to acceleration stimuli and a broad frequency bandwidth up to 100 Hz. This study is the first to establish the upper end of this mechanical system frequency response of the utricle in any animal.

Functional analysis of ultra high information rates conveyed by rat vibrissal primary afferents

Sensory receptors determine the type and the quantity of information available for perception. Here, we quantified and characterized the information transferred by primary afferents in the rat whisker system using neural system identification. Quantification of "how much" information is conveyed by primary afferents, using the direct method (DM), a classical information theoretic tool, revealed that primary afferents transfer huge amounts of information (up to 529 bits/s). Information theoretic analysis of instantaneous spike-triggered kinematic stimulus features was used to gain functional insight on "what" is coded by primary afferents. Amongst the kinematic variables tested--position, velocity, and acceleration--primary afferent spikes encoded velocity best. The other two variables contributed to information transfer, but only if combined with velocity. We further revealed three additional characteristics that play a role in information transfer by primary afferents. Firstly, primary afferent spikes show preference for well separated multiple stimuli (i.e., well separated sets of combinations of the three instantaneous kinematic variables). Secondly, neurons are sensitive to short strips of the stimulus trajectory (up to 10 ms pre-spike time), and thirdly, they show spike patterns (precise doublet and triplet spiking). In order to deal with these complexities, we used a flexible probabilistic neuron model fitting mixtures of Gaussians to the spike triggered stimulus distributions, which quantitatively captured the contribution of the mentioned features and allowed us to achieve a full functional analysis of the total information rate indicated by the DM. We found that instantaneous position, velocity, and acceleration explained about 50% of the total information rate. Adding a 10 ms pre-spike interval of stimulus trajectory achieved 80-90%. The final 10-20% were found to be due to non-linear coding by spike bursts.

Discharge regularity in the turtle posterior crista: comparisons between experiment and theory

Intra-axonal recordings were made from bouton fibers near their termination in the turtle posterior crista. Spike discharge, miniature excitatory postsynaptic potentials (mEPSPs), and afterhyperpolarizations (AHPs) were monitored during resting activity in both regularly and irregularly discharging units. Quantal size (qsize) and quantal rate (qrate) were estimated by shot-noise theory. Theoretically, the ratio, σV/(dμV/dt), between synaptic noise (σV) and the slope of the mean voltage trajectory (dμV/dt) near threshold crossing should determine discharge regularity. AHPs are deeper and more prolonged in regular units; as a result, dμV/dt is larger, the more regular the discharge. The qsize is larger and qrate smaller in irregular units; these oppositely directed trends lead to little variation in σV with discharge regularity. Of the two variables, dμV/dt is much more influential than the nearly constant σV in determining regularity. Sinusoidal canal-duct indentations at 0.3 Hz led to modulations in spike discharge and synaptic voltage. Gain, the ratio between the amplitudes of the two modulations, and phase leads re indentation of both modulations are larger in irregular units. Gain variations parallel the sensitivity of the postsynaptic spike encoder, the set of conductances that converts synaptic input into spike discharge. Phase variations reflect both synaptic inputs to the encoder and postsynaptic processes. Experimental data were interpreted using a stochastic integrate-and-fire model. Advantages of an irregular discharge include an enhanced encoder gain and the prevention of nonlinear phase locking. Regular and irregular units are more efficient, respectively, in the encoding of low- and high-frequency head rotations, respectively.

Quantifying utricular stimulation during natural behavior

The use of natural stimuli in neurophysiological studies has led to significant insights into the encoding strategies used by sensory neurons. To investigate these encoding strategies in vestibular receptors and neurons, we have developed a method for calculating the stimuli delivered to a vestibular organ, the utricle, during natural (unrestrained) behaviors, using the turtle as our experimental preparation. High-speed digital video sequences are used to calculate the dynamic gravito-inertial (GI) vector acting on the head during behavior. X-ray computed tomography (CT) scans are used to determine the orientation of the otoconial layer (OL) of the utricle within the head, and the calculated GI vectors are then rotated into the plane of the OL. Thus, the method allows us to quantify the spatio-temporal structure of stimuli to the OL during natural behaviors. In the future, these waveforms can be used as stimuli in neurophysiological experiments to understand how natural signals are encoded by vestibular receptors and neurons. We provide one example of the method, which shows that turtle feeding behaviors can stimulate the utricle at frequencies higher than those typically used in vestibular studies. This method can be adapted to other species, to other vestibular end organs, and to other methods of quantifying head movements.

Identifying temporal codes in spontaneously active sensory neurons

The manner in which information is encoded in neural signals is a major issue in Neuroscience. A common distinction is between rate codes, where information in neural responses is encoded as the number of spikes within a specified time frame (encoding window), and temporal codes, where the position of spikes within the encoding window carries some or all of the information about the stimulus. One test for the existence of a temporal code in neural responses is to add artificial time jitter to each spike in the response, and then assess whether or not information in the response has been degraded. If so, temporal encoding might be inferred, on the assumption that the jitter is small enough to alter the position, but not the number, of spikes within the encoding window. Here, the effects of artificial jitter on various spike train and information metrics were derived analytically, and this theory was validated using data from afferent neurons of the turtle vestibular and paddlefish electrosensory systems, and from model neurons. We demonstrate that the jitter procedure will degrade information content even when coding is known to be entirely by rate. For this and additional reasons, we conclude that the jitter procedure by itself is not sufficient to establish the presence of a temporal code.