Information transmission by isolated frog muscle spindle

Transmission of sensory information was calculated for the isolated frog muscle spindle receptor, using Shannon's information measure. Sinusoidal movements, random noise stretches, and sinusoids with superimposed auxiliary noise were applied as stimuli. In addition, the static prestretch level of the intrafusal muscle bundle was adjusted between resting length (L0) and L0 + 600 micron, so that the analysis of the information transmission properties covered the entire dynamic range of the sensory receptor organ. Sinusoidal stretches below 2 Hz evoked smoothly modulated cycle histograms, which were approximately linearly related to the stimulating sinewave. The transinformation rates under these conditions were generally low (5-17 bit X s-1), regardless of the amplitude of the applied movement. Increasing prestretch enhanced the modulation depth of the cycle histograms considerably, but increased the transinformation rates by less than 10 bit X s-1. By contrast, sinusoids above 2 Hz evoked clearly nonlinear cycle histograms, because each action potential was firmly phase-locked to a small segment of the stretch cycle. Under these conditions the transinformation rates grew larger with increasing stimulus frequency and approached 130 bit X s-1 at 60 Hz. Small amplitude sinusoidal stretches, however, evoked considerable transinformation rates in the high frequency region only then, when the spindle receptor was extended to higher prestretch levels. Random stretches evoked transinformation rates between 5 and 30 bit X s-1 depending on both the prestretch level and the intensity of the noise stimulus. The linear response components carried only about 25% of the transinformation rates transmitted by both the linear and nonlinear response components. Auxiliary noise stimuli greatly improved the information transmission of sinusoidal stretches. For example, a pure sinusoid evoked 5 bit X s-1. Adding a noise signal with equal energy to the sinusoidal movement elicited 20 bit X s-1. This facilitation effect of auxiliary noise was restricted to low frequency sinusoidal stimuli. The present results are discussed with respect to the information transmission properties of various sensory systems evaluated by either the same or different information processing procedure as that used in the present study. The functional significance of high transinformation rates sent by the muscle spindle to the central nervous system is discussed with respect to motor control.     

Superimposing noise linearizes the responses of primary muscle spindle afferents to sinusoidal muscle stretch

Experiments were conducted in anaesthetized and spinalized cats to measure the extent to which the non-linear response of Ia afferent fibers to sinusoidal muscle stretch as expressed by the peristimulus-time-histograms, PSTHs, can be transformed into a linear one by means of the superposition of random stretch ("mechanical noise"). The gastrocnemius muscles of one hind leg were stretched and the response to sinewave muscle stretch (amplitudes between 0.01 and 4.0 mm, frequencies between 0.1 and 20 Hz) were investigated while band-limited mechanical noise was superimposed on the sinewave stretch. The random stretch upper cut-off frequency was varied between 60 and 300 Hz; the displacements were normally distributed. The noise amplitude sigma, i.e. the standard deviation of the displacement distributions, was varied systematically between 0.002 and 0.4 mm. Mechanical noise was very effective in raising the mean discharge rate. Added to the sinusoidal stretch it prevented the cessation of firing during the release phase of the stretch cycle, or at least reduced the duration of discharge pauses, i.e., a linearization occurred. In general, the larger the noise amplitude, the more the amplitude of the fundamental harmonic component was attenuated and the phase lead reduced. Apart from this rule the particular combination of superimposing small noise (sigma less than 0.02 mm) on small sinewave stretch (A less than 0.02 mm) could enhance the depth of sinusoidal modulation of cycle histograms (compared with responses to pure sinusoids). Linearizing the sinewave response by additional noise allowed the estimation of frequency response characteristics in the otherwise non-linear range of amplitudes (sinewave amplitude 0.5-1.0 mm).(ABSTRACT TRUNCATED AT 250 WORDS)     

Use of pseudorandom noise in studies of frequency selectivity: The periphery of the auditory system

Frequency selectivity of single auditory nerve fibers in the rat was studied using pseudorandom noise based on ternary m-sequences as the stimulus, and the results were compared to those of earlier studies in which noise based on binary m-sequences was used. Pseudorandom noise based on ternary m-sequences has fewer anomalies than noise based on binary m-sequences. Detailed tests using linear and nonlinear filters showed that the present method provides accurate measures of bandwidth and center frequency. Period histograms of the response, locked to the periodicity of the noise, were cross-correlated with one period of the noise to obtain estimates of the impulse response function of the peripheral auditory system. Fourier transforms of these cross-correlograms were used as estimates of the filter function of single auditory nerve fibers. The results obtained using ternary noise were not different from previous results showing a downward shift in center frequency and increase in bandwidth with increasing stimulus intensity for fibers with center frequencies between 1000 and 5000 Hz. The difference between spectral selectivity based on phase-locked responses and that based on discharge rate is discussed.     

The effects of synaptic noise on measurements of evoked excitatory postsynaptic response amplitudes.

Spontaneously occurring synaptic events (synaptic noise) recorded intracellularly are usually assumed to be independent of evoked postsynaptic responses and to contaminate measures of postsynaptic response amplitude in a roughly Gaussian manner. Here we derive analytically the expected noise distribution for excitatory synaptic noise and investigate its effects on amplitude histograms. We propose that some fraction of this excitatory noise is initiated at the same release sites that contribute to the evoked synaptic event and develop an analytical model of the interaction between this fraction of the noise and the evoked postsynaptic response amplitude. Recording intracellularly with sharp microelectrodes in the in vitro hippocampal slice preparation, we find that excitatory synaptic noise accounts for up to 70% of the intracellular recording noise, when inhibition is blocked pharmacologically. Up to 20% of this noise shows a significant correlation with the evoked event amplitude, and the behavior of this component of the noise is consistent with a model which assumes that each release site experiences a refractory period of approximately 60 ms after release. In contrast with classical models of quantal variance, our models predict that excitatory synaptic noise can cause the apparent variance of successive peaks in an excitatory synaptic amplitude histogram to decrease from left to right, and in some cases to be less than the variance of the measured noise.     

Are receptive fields of the visual cortex detectors or spatial frequency filters?

Besides its principal maximum, the spatial frequency characteristic curve of the complex visual cortical receptive field of curarized cats also has additional maxima and also negative regions, as predicted by the theory of piecewise Fourier analysis. Comparison of responses of the complex receptive field to sinusoidal gratings completely and incompletely contained in the field and comparison of responses to sinusoidal and square-wave gratings indicate that the receptive field, as a spatial frequency filter, has linear properties. The response of the complex receptive field rises with an increase in the number of periods of the sinusoidal grating. Several periods of optimal frequency match the complex field. Receptive fields tuned to a broad band of spatial frequencies were found in neuron columns. The results confirm the view that complex receptive fields are spatial frequency filters and not detectors.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 11, No. 5, pp. 403–411, September–October, 1979.     

Effects of linear acceleration on fish behavior and eye movements.

Behavioral responses and eye movements of fish during linear acceleration were reviewed. It is known that displacement of otoliths in the inner ear leads to body movements and/or eye movements. On the ground, the utriculus of the vestibular system is stimulated by otolith displacement caused by gravitational and inertial forces during horizontal acceleration of whole body. When the acceleration is imposed on the fish's longitudinal axis, the fish showed nose-down and nose-up posture for tailward and noseward displacement of otolith respectively. These responses were understood that the fish aligned his longitudinal body axis in a plane perpendicular to the direction of resultant force vector acting on the otoliths. When the acceleration was sideward, the fish rolled around his longitudinal body axis so that his back was tilted against the direction in which the inertial force acted on the otoliths. Linear acceleration applied to fish's longitudinal body axis evoked torsional eye movement. Direction of torsion coincided with the direction of acceleration, which compensate the change of resultant force vector produced by linear acceleration and gravity. Torsional movement of left and right eye coordinated with each other. In normal fish, both sinusoidal and rectangular acceleration of 0.1G could evoke clear eye torsion. Though the amplitude of response increased with increasing magnitude of acceleration up to 0.5 G, the torsion angle did not fully compensate the angle calculated from gravity and linear acceleration. Removal of the otolith on one side reduced the response amplitude of both eyes. The torsion angle evoked by rectangular acceleration was smaller than that evoked by sinusoidal acceleration in both normal and unilaterally labyrinthectomized fish. These results suggest that eye torsion of fish include both static and dynamic components.     

The estimation of the frequency response function of a mechanoreceptor

Widespread use has been made of linear systems theory to describe the input-output relations of receptors. The frequency response function of an insect mechanoreceptor, the tactile spine of the cockroach, has been estimated by using deterministic inputs (sines and step functions), deterministic inputs added to a stochastic, auxiliary signal (band-limited white noise), and a stochastic input alone. When a stochastic input is used, spectral analysis provides methods for estimating the coherence function as well as the frequency response function. The coherence function of the tactile spine is low, suggesting that the linear frequency response function is not a good characterization of the input-output relation of the receptor. Two non-linearities, rectification and phase-locking are described. Rectification can reduce the absolute value of the frequency response measured using sine waves of all frequencies without changing its form. Phase-locking changes the form of the frequency response function at high frequencies. Use of a stochastic auxiliary signal linearizes the input-output relations of the receptor in the sense that the cycle histograms obtained with sinusoidal inputs are more sinusoidal and the form of the frequency response function agrees with that predicted from the step response over a wider range of frequencies.     

White noise analysis of graded response in a wind-sensitive,nonspiking interneuron of the cockroach

1. A novel approach using a Gaussian white noise as stimulus is described which allowed quantitative analysis of neuronal responses in the cercal system of the cockroach, Periplaneta americana. Cerci were stimulated by air displacement which was modulated by a sinusoidal and a white noise signal. During the stimulation, intracellular recordings were made from a uniquely identifiable, nonspiking, local interneuron which locates within the terminal abdominal ganglion. The white noise stimulation was cross-correlated with the evoked response to compute first- and second-order kernels that could define the cell's response dynamics. 2. The interneuron, cell 101, has an exceptionally large transverse neurite that connects two asymmetrical dendritic arborizations located on both sides of the ganglion. 3. The first-order Wiener kernels in cell 101 were biphasic (differentiating). The waveforms of the kernels produced by the ipsilateral and contralateral stimulations were roughly mirror images of each other: the kernels produced by wind stimuli on the side ipsilateral to the cell body of the interneuron are initially depolarized and then hyperpolarized, whereas those on the other side are initially hyperpolarized. The polarity reversal occurred along the midline of the animal's body, and no well-defined kernel was produced by a stimulus directed head on or from the tail. 4. Mean square error (MSE) between the actual response and the model prediction suggests that the linear component in cell 101 comprises half of the cell's total response (MSEs for the linear models were about 50% at preferred directions), whereas the second-order, non-linear component is insignificant. The linear component of the wind-evoked response was bandpass with the preferred frequency of 70-90 Hz. 5. Accounting for a noise, we reasonably assumed that at high frequencies the graded response in cell 101 is linearly related to a modulation of the air displacement and sensitive to the rate of change of the signal (i.e., wind velocity) and the direction of its source. It is suggested that the dynamics of the first-order kernel simply reflect the dynamics of sensory receptors that respond linearly to wind stimulation.     

Adaptive processing techniques based on hidden Markov models for characterizing very small channel currents buried in noise and deterministic interferences.

Techniques for characterizing very small single-channel currents buried in background noise are described and tested on simulated data to give confidence when applied to real data. Single channel currents are represented as a discrete-time, finite-state, homogeneous, Markov process, and the noise that obscures the signal is assumed to be white and Gaussian. The various signal model parameters, such as the Markov state levels and transition probabilities, are unknown. In addition to white Gaussian noise, the signal can be corrupted by deterministic interferences of known form but unknown parameters, such as the sinusoidal disturbance stemming from AC interference and a drift of the base line owing to a slow development of liquid-junction potentials. To characterize the signal buried in such stochastic and deterministic interferences, the problem is first formulated in the framework of a Hidden Markov Model and then the Expectation Maximization algorithm is applied to obtain the maximum likelihood estimates of the model parameters (state levels, transition probabilities), signals, and the parameters of the deterministic disturbances. Using fictitious channel currents embedded in the idealized noise, we first show that the signal processing technique is capable of characterizing the signal characteristics quite accurately even when the amplitude of currents is as small as 5-10 fA. The statistics of the signal estimated from the processing technique include the amplitude, mean open and closed duration, open-time and closed-time histograms, probability of dwell-time and the transition probability matrix. With a periodic interference composed, for example, of 50 Hz and 100 Hz components, or a linear drift of the baseline added to the segment containing channel currents and white noise, the parameters of the deterministic interference, such as the amplitude and phase of the sinusoidal wave, or the rate of linear drift, as well as all the relevant statistics of the signal, are accurately estimated with the algorithm we propose. Also, if the frequencies of the periodic interference are unknown, they can be accurately estimated. Finally, we provide a technique by which channel currents originating from the sum of two or more independent single channels are decomposed so that each process can be separately characterized. This process is also formulated as a Hidden Markov Model problem and solved by applying the Expectation Maximization algorithm. The scheme relies on the fact that the transition matrix of the summed Markov process can be construed as a tensor product of the transition matrices of individual processes.     

Population Decoding in Rat Barrel Cortex: Optimizing the Linear Readout of Correlated Population Responses

Sensory information is encoded in the response of neuronal populations. How might this information be decoded by downstream neurons? Here we analyzed the responses of simultaneously recorded barrel cortex neurons to sinusoidal vibrations of varying amplitudes preceded by three adapting stimuli of 0, 6 and 12 µm in amplitude. Using the framework of signal detection theory, we quantified the performance of a linear decoder which sums the responses of neurons after applying an optimum set of weights. Optimum weights were found by the analytical solution that maximized the average signal-to-noise ratio based on Fisher linear discriminant analysis. This provided a biologically plausible decoder that took into account the neuronal variability, covariability, and signal correlations. The optimal decoder achieved consistent improvement in discrimination performance over simple pooling. Decorrelating neuronal responses by trial shuffling revealed that, unlike pooling, the performance of the optimal decoder was minimally affected by noise correlation. In the non-adapted state, noise correlation enhanced the performance of the optimal decoder for some populations. Under adaptation, however, noise correlation always degraded the performance of the optimal decoder. Nonetheless, sensory adaptation improved the performance of the optimal decoder mainly by increasing signal correlation more than noise correlation. Adaptation induced little systematic change in the relative direction of signal and noise. Thus, a decoder which was optimized under the non-adapted state generalized well across states of adaptation.     

Sensory transduction in an insect mechanoreceptor: Linear and nonlinear properties

Mechanotransduction in the femoral tactile spine of the cockroach, Periplaneta americana, was examined as a function of displacement of the spine axially in its socket. Linear behaviour was analyzed by measurement of the frequency response function between displacement and action potential output using sinusoidal stimulation and random noise stimulation. The measured frequency response functions can be well fitted by a relationship which is a fractional power of complex frequency. This power was close to 0.5 for all experiments. To distinguish between the effects of nonlinearity and of inherent variability, the averaged responses of the preparation to repeated sequences of pseudorandom noise were compared to those from experiments in which continuous pseudorandom noise were used. The lack of sensitivity of the coherence function to these two methods of measurement suggests that mechanical stimuli are encoded into action potentials with a large signal-to-noise ratio. The low value of the coherence function which is characteristics of insect mechanoreceptors is therefore due to the strong non-linearity of their responses. To investigate the nonlinear properties of transduction, the second-order frequency response function of the tactile spine was measured for random noise stimulation experiments. Two models of the transduction process were considered in which a linear element with memory was cascaded with a nonlinear element without memory in the two possible configurations. Comparison of the experimental second-order frequency response functions with predictions based upon these two models and the measured first-order frequency response suggests that the transduction mechanism can be modelled by a linear element, which may be associated with the viscoelastic properties of the dendritic tubular body, and a zeromemory nonlinearity, which is most likely to be rectification by the dendritic membrane.     

Harmonic analysis of two-tone discharge patterns in cochlear nerve fibers

Discharges in cochlear nerve fibers evoked by low frequency phase-locked sinusoidal acoustic stimuli are synchronized to the stimulus waveform. Excitation and suppression regions of single units were explored using a stimulus composed of either a fixed intensity test tone at the characteristic frequency, a variable intensity interfering tone with a simple integer frequency relation to the characteristic frequency, or both. Compound period histograms were constructed from period histograms in response to normal and reversed polarity stimuli. Discharge patterns were characterized by Fourier components of the histogram envelopes. The two stimulus frequencies constituted the principal harmonics in the histogram envelopes and their combination accounted for observed rate changes. Suppression of the test tone harmonic as a function of interfering tone intensity was always seen; rate suppression was not. The harmonic was typically suppressed by 20–30 dB compared to the value for the test tone alone and often reached the 40–60 dB resolution limit of the experiment. Suppression plots were nearly linear on a power scale with an average slope of-0.8. The onset of suppression occurred for an interfering tone 9 dB greater on average than the test tone intensity. Information transfer through the peripheral system was described by the ratio of the principal harmonic amplitudes versus the ratio of the intensities of the two stimulus tones. These plots were nearly linear on a power scale with an average slope of 0.9. Neither the onset of suppression nor the slopes of the harmonic plots displayed strong dependence on characteristic frequency or interfering tone frequency. These features of harmonic behavior, however, are closely related to system nonlinearity. Comparison of measured harmonics to the predictions of two phenomenological models suggest the presence of complex nonlinear transformations in the peripheral auditory system.     

Methods for the identification of evoked response components in the frequency and combined time/frequency domains

Two prominent frequency components designated f1 and f2 have been identified in the visual evoked response to the transient presentation of sinusoidal luminance gratings in the range of 0.5–8 c/deg. The components occur at temporal frequencies below the alpha band, with the f1 frequency roughly half that of the f2 frequency. The f1 component is largest at low spatial frequencies with f2 becoming progressively dominant as spatial frequency is increased.The frequency and amplitude of f1 and f2 change substantially over the time course of the response. This has been studied by calculating the temporal frequency spectrum of the transient evoked potential over successive short-time epochs running through the response. Using this technique, the response is shown to consist of narrow- and frequency peaks or ‘formants’ emerging at different times after stimulus onset. These formants occur at frequencies other than those of the spontaneous EEG and undergo changes in frequency and amplitude over the time course of the response.Two spectrum analysis techniques were employed: the Discrete Fourier Transform and Linear Predictive Coding. Frequency components were successfully identified in single-trial responses using the LPC technique.     

Response component analysis of simple and complex cells of area 18 during depression of area 17.

Simple and complex cells of visual areas of cats may be reliably classified according to the modulatory index (MI) of their responses. This investigation is aimed at analysing the MI in area 18 when a small region (about 200-400 microm in diameter) of area 17 was inactivated with a microinjection of GABA, in anesthetized cats. Cells were stimulated with sine-wave gratings whose orientation, spatial, and temporal frequencies were optimal for the studied unit. The AC and DC response components, and the MI were computed along with fast Fourier transforms of evoked discharges recorded as peristimulus time histograms. Results showed that these response components were relatively unaffected in simple cells, whereas complex cells exhibited large changes when area 17 was silenced. In particular, a large proportion of complex cells showed a MI greater than 1, thereby adopting a response pattern resembling simple cells. It is suggested that this subpopulation of complex cells receives a direct input from geniculate X cells.     

Improved processing of the steady-state evoked potential

Two related procedures for estimating the parameters of steady-state evoked potentials (SSEPs) are introduced. The first procedure involves an initial stage of digital bandpass filtering followed by a Discrete Fourier Transform analysis. In the second method, a high resolution method based on parametric modelling is applied to the filtered data. The digital pre-filter consists of a non-phase shifting Chebychev bandpass filter. The parametric modelling method considers the evoked-response-plus-noise distribution to consist of a set of exponentially damped sinusoids. The frequency, amplitude, phase and damping factors of these components are estimated by calculating the mean of the forward and backward prediction filters and linear regression.We compared the signal-to-noise ratio (SNR) of the new procedures to the conventional Discrete Fourier Transform method for Monte Carlo simulations utilizing known sinusoids buried in white noise, known sinusoids buried in human EEG noise and for a sample of visual evoked potential data. Both of the new methods produce substantially more accurate and less variable estimates of test sinusoid amplitude. For VEP recording, the EEG background noise level is reduced by 5–6 dB over that obtained with the DFT. The new methods also provide approximately 5 dB better SNR than the DFT for detection of sinusoids based on the Rayleigh statistic. The parametric modelling approach is particularly suited for the analysis of very short data records including cycle-by-cycle analysis of the SSEP.     

Abducens nerve responses of the frog during horizontal linear acceleration: data and model

Abducens nerve responses of frogs were evoked by sinusoidal oscillations on a horizontal linear sled. The depth of modulation of these responses and their phases depended on the orientation of the head with respect to the direction of linear acceleration. Longitudinal acceleration evoked abducens responses that consisted of two discharge maxima per stimulus cycle. At consecutively more oblique head orientations, one of these two discharge maxima increased and the other decreased. Transver se accelerations evoked abducens responses that consisted of only one discharge maximum per stimulus cycle. Removal of the labyrinthine organs on one side abolished these responses in the contralateral abducens nerve but did not affect the responses in the ipsilateral abducens nerve. The latter result indicates that the responses in each abducens nerve originate from hair cells on the contralateral utricle. The experimentally determined modulation and phase values and their dependence on the orientation ang le of the acceleration vector were used to characterize a functional cluster of hair cells located medially with respect to the striola in a fanlike sector on the utricle (‘lateral rectus fan’). Parameters of this fan were used to develop a model that satisfactorily simulates the recorded abducens responses. This model predicts a majority of afferents with excitatory and a few afferents with inhibitory contributions to the abducens nerve responses. The phasic response components of about 90% of these afferents are larger than their tonic response components. Received: 12 July 1993/Accepted in revised form: 11 October 1993     

Electrically-Evoked Frequency-Following Response (EFFR) in the Auditory Brainstem of Guinea Pigs

It is still a difficult clinical issue to decide whether a patient is a suitable candidate for a cochlear implant and to plan postoperative rehabilitation, especially for some special cases, such as auditory neuropathy. A partial solution to these problems is to preoperatively evaluate the functional integrity of the auditory neural pathways. For evaluating the strength of phase-locking of auditory neurons, which was not reflected in previous methods using electrically evoked auditory brainstem response (EABR), a new method for recording phase-locking related auditory responses to electrical stimulation, called the electrically evoked frequency-following response (EFFR), was developed and evaluated using guinea pigs. The main objective was to assess feasibility of the method by testing whether the recorded signals reflected auditory neural responses or artifacts. The results showed the following: 1) the recorded signals were evoked by neuron responses rather than by artifact; 2) responses evoked by periodic signals were significantly higher than those evoked by the white noise; 3) the latency of the responses fell in the expected range; 4) the responses decreased significantly after death of the guinea pigs; and 5) the responses decreased significantly when the animal was replaced by an electrical resistance. All of these results suggest the method was valid. Recording obtained using complex tones with a missing fundamental component and using pure tones with various frequencies were consistent with those obtained using acoustic stimulation in previous studies.     

Ladder network prediction of transients in linear spatially inhomogeneous cables

A numerical method is described for finding steady state and transient responses in electrically linear, spatially inhomogeneous cables. Spatial inhomogeneities are incorporated by representing the cable by a number of finite length uniform cylindrical segments, each having the radius and electrical characteristics of a small region along the cable. Input waveforms are approximated by truncated Fourier series of sinusoidal components. Output waveforms are produced by multiplying the input Fourier series sinusoids by their respective transfer functions between input and output points on the cable and summing the resultant output point sinusoids. The transfer functions, representing attenuation and phase shift for each input sinusoid, are obtained by numerical analysis of an electrical ladder network derived from the cylindrical segment model of the cable. Results are shown for application of this method to both cylindrical and expanding radius cable geometries.     

A robust orthogonal algorithm for system identification and time-series analysis

We describe and illustrate methods for obtaining a parsimonious sinusoidal series representation or model of biological time-series data. The methods are also used to identify nonlinear systems with unknown structure. A key aspect is a rapid search for significant terms to include in the model for the system or the time-series. For example, the methods use fast and robust orthogonal searches for significant frequencies in the time-series, and differ from conventional Fourier series analysis in several important respects. In particular, the frequencies in our resulting sinusoidal series need not be commensurate, nor integral multiples of the fundamental frequency corresponding to the record length. Freed of these restrictions, the methods produce a more economical sinusoidal series representation (than a Fourier series), finding the most significant frequencies first, and automatically determine model order. The methods are also capable of higher resolution than a conventional Fourier series analysis. In addition, the methods can cope with unequally-spaced or missing data, and are applicable to time-series corrupted by noise. Fially, we compare one of our methods with a wellknown technique for resolving sinusoidal signals in noise using published data for the test time-series.