The Effect of Correlated Neuronal Firing and Neuronal Heterogeneity on Population Coding Accuracy in Guinea Pig Inferior Colliculus

It has been suggested that the considerable noise in single-cell responses to a stimulus can be overcome by pooling information from a large population. Theoretical studies indicated that correlations in trial-to-trial fluctuations in the responses of different neurons may limit the improvement due to pooling. Subsequent theoretical studies have suggested that inherent neuronal diversity, i.e., the heterogeneity of tuning curves and other response properties of neurons preferentially tuned to the same stimulus, can provide a means to overcome this limit. Here we study the effect of spike-count correlations and the inherent neuronal heterogeneity on the ability to extract information from large neural populations. We use electrophysiological data from the guinea pig Inferior-Colliculus to capture inherent neuronal heterogeneity and single cell statistics, and introduce response correlations artificially. To this end, we generate pseudo-population responses, based on single-cell recording of neurons responding to auditory stimuli with varying binaural correlations. Typically, when pseudo-populations are generated from single cell data, the responses within the population are statistically independent. As a result, the information content of the population will increase indefinitely with its size. In contrast, here we apply a simple algorithm that enables us to generate pseudo-population responses with variable spike-count correlations. This enables us to study the effect of neuronal correlations on the accuracy of conventional rate codes. We show that in a homogenous population, in the presence of even low-level correlations, information content is bounded. In contrast, utilizing a simple linear readout, that takes into account the natural heterogeneity, even of neurons preferentially tuned to the same stimulus, within the neural population, one can overcome the correlated noise and obtain a readout whose accuracy grows linearly with the size of the population.     

Dynamics of turtle horizontal cell response

The small- and large-field (cone) horizontal cells produce similar dynamic responses to a stimulus whose mean luminance is modulated by a white-noise signal. Nonlinear components increase with an increase in the mean luminance and may produce a mean square error (MSE) of up to 15%. Increases in the mean luminance of the field stimulus bring about three major changes: the incremental sensitivity defined by the amplitude of the kernels decreases in a Weber-Fechner fashion; the waveforms of the kernels are transformed from monophasic (integrating) to biphasic (differentiating); the peak response time of the kernels becomes shorter and the cells respond to much higher-frequency inputs. The dynamics of the horizontal cell response also depend on the area of the retina stimulated. Smaller spots of light produce monophasic kernels of a longer peak response time. The presence of a steady background produces three major changes in the spot kernels: the kernel's amplitude becomes larger (incremental sensitivity increases); the peak response times become shorter; the waveform of the kernels changes in a fashion similar to that observed with an increase in the mean luminance of the field stimulus. A similar enhancement in the incremental sensitivity by a steady background has also been observed in catfish, which shows that this phenomenon is a common feature of the horizontal cells in the lower vertebrate retina.     

Frequency-invariant representation of interaural time differences in mammals

Interaural time differences (ITDs) are the major cue for localizing low-frequency sounds. The activity of neuronal populations in the brainstem encodes ITDs with an exquisite temporal acuity of about 10 μs. The response of single neurons, however, also changes with other stimulus properties like the spectral composition of sound. The influence of stimulus frequency is very different across neurons and thus it is unclear how ITDs are encoded independently of stimulus frequency by populations of neurons. Here we fitted a statistical model to single-cell rate responses of the dorsal nucleus of the lateral lemniscus. The model was used to evaluate the impact of single-cell response characteristics on the frequency-invariant mutual information between rate response and ITD. We found a rough correspondence between the measured cell characteristics and those predicted by computing mutual information. Furthermore, we studied two readout mechanisms, a linear classifier and a two-channel rate difference decoder. The latter turned out to be better suited to decode the population patterns obtained from the fitted model.     

Single-Cell Measurements of IgE-Mediated FcεRI Signaling Using an Integrated Microfluidic Platform

Heterogeneity in responses of cells to a stimulus, such as a pathogen or allergen, can potentially play an important role in deciding the fate of the responding cell population and the overall systemic response. Measuring heterogeneous responses requires tools capable of interrogating individual cells. Cell signaling studies commonly do not have single-cell resolution because of the limitations of techniques used such as Westerns, ELISAs, mass spectrometry, and DNA microarrays. Microfluidics devices are increasingly being used to overcome these limitations. Here, we report on a microfluidic platform for cell signaling analysis that combines two orthogonal single-cell measurement technologies: on-chip flow cytometry and optical imaging. The device seamlessly integrates cell culture, stimulation, and preparation with downstream measurements permitting hands-free, automated analysis to minimize experimental variability. The platform was used to interrogate IgE receptor (FcεRI) signaling, which is responsible for triggering allergic reactions, in RBL-2H3 cells. Following on-chip crosslinking of IgE-FcεRI complexes by multivalent antigen, we monitored signaling events including protein phosphorylation, calcium mobilization and the release of inflammatory mediators. The results demonstrate the ability of our platform to produce quantitative measurements on a cell-by-cell basis from just a few hundred cells. Model-based analysis of the Syk phosphorylation data suggests that heterogeneity in Syk phosphorylation can be attributed to protein copy number variations, with the level of Syk phosphorylation being particularly sensitive to the copy number of Lyn.     

Role of the response oscillator in inverse responses of Halobacterium halobium to weak light stimuli.

Under certain conditions Halobacterium halobium organisms respond to a weak attractant light stimulus with a repellent response and to a weak repellent stimulus with an attractant response. The appearance of inverse responses depends on the stimulus strength, on the interval length between spontaneous reversals, and on the moment of stimulation during the interval. Although the cells are absolutely refractory to repellent stimuli for 500 ms after a reversal, repellent responses can be evoked even during that period if they are inverse responses to weak attractant stimuli. Simultaneous attractant and repellent stimuli cancel each other even when one of them leads to an inverse response, indicating that normal cellular signals occur at the site of signal integration. We postulate that the inverse responses are caused by certain properties of a cellular oscillator for which we previously postulated a role in response regulation and sensory control in halobacteria (A. Schimz and E. Hildebrand, Nature [London] 317:641-643, 1985).     

Quantification and statistical verification of neuronal stimulus responses from noisy spike train data

Usually neuronal responses to short-lasting stimuli are displayed as peri-stimulus time histogram. The function estimated by such a histogram allows to obtain informations about stimulus-induced postsynaptic events as long as the interpretation is restricted to the first response component after the stimulus. The interpretation of secondary response components is much more difficult, as they may be either due to stimulus effects or represent an echo of the primary response. In the present paper two output functions are developed that do not show such an echoing of responses. The first one, the interspike interval change function, represents an ideal way to quantify a neuronal stimulus response as its amplitude was found to be almost independent of the stimulation strategy used during acquisition of the spike train data. The other function, the displaced impulses function, allows to verify the statistical significance of an observed response component. Both functions may be estimated from stimulus-correlated spike train data, even if the neuron under investigation shows considerable interspike-interval variability in the absence of stimulation. The concepts underlying these neuronal output functions are developed on simulated responses of a Hodgkin-Huxley-type model for a mammalian neuron at body temperature that is exposed to a transient excitatory conductance increase. Additionally, estimation of these output functions is also demonstrated on responses of human soleus motoneurons that were exposed to electrical stimuli of the tibial nerve in the popliteal fossa.     

Distinct responses of cones and melanopsin-expressing retinal ganglion cells in the human electroretinogram

ABSTRACT: BACKGROUND: The discovery of the novel photoreceptor, melanopsin-expressing retinal ganglion cells (mRGCs), has raised researchers' interest in photoreceptive tasks performed by the mRGC, especially in non-image-forming visual functions. In a prior study, we investigated the mRGC response to light stimuli independent of rods and cones with the four-primary illumination system, which modulates stimulus levels to the mRGC and cones independently, and mRGC baseline responses were recorded in the electroretinogram (ERG). METHODS: In the present study, we used the same illumination system to compare independent responses of the mRGC and cones in five subjects (mean +/- SD age, 23.0 +/- 1.7 years). The ERG waveforms were examined as direct measurements of responses of the mRGCs and cones to stimulation (250 msec). Implicit times (the time taken to peaks) and peak values from 30 stimuli given to each subject were analyzed. RESULTS: Two distinct positive peaks appeared in the mRGC response, approximately 80 msec after the onset of the stimuli and 30 msec after their offset, while no such peaks appeared in the cone response. The response to the mRGC stimulus was significantly higher than that to the cone stimulus at ~80 msec (p < 0.05) and tended to be higher than the cone stimulus at ~280 msec (p = 0.08). CONCLUSIONS: Implicit time of the first peak was much longer than that to the b-wave and this delay might reflect mRGC's sluggish responses. This is the first report of amplitudes and implicit time in the ERG from the response of the mRGC that is independent of rods and cones and obtained using the four-primary illumination system.     

Selectivity of neuronal adaptation does not match response selectivity: a single-cell study of the FMRI adaptation paradigm

fMRI-based adaptation paradigms (fMR-A) have been used to infer neuronal stimulus selectivities in humans. Inferring neuronal selectivities from fMR-A, however, requires an understanding of the relationship between the stimulus selectivity of neuronal adaptation and responses. We studied this relationship by recording single cells in macaque inferior temporal (IT) cortex, an area that shows fMRI adaptation. Repetition of identical object images reduced the responsiveness of single IT neurons. Presentation of an image to which the neuron was unresponsive did not alter the response to a subsequent image that activated the neuron. Successive presentation of two different images to which the neuron responded similarly produced adaptation, but less so than the repeated presentation of an image. The neuronal adaptation at the single-cell level showed a greater degree of stimulus selectivity than the responses. This complicates the interpretation of fMR-A paradigms when inferring neuronal selectivity.     

Cross-adaptation between olfactory responses induced by two subgroups of odorant molecules

It has long been believed that vertebrate olfactory signal transduction is mediated by independent multiple pathways (using cAMP and InsP3 as second messengers). However, the dual presence of parallel pathways in the olfactory receptor cell is still controversial, mainly because of the lack of information regarding the single-cell response induced by odorants that have been shown to produce InsP3 exclusively (but not cAMP) in the olfactory cilia. In this study, we recorded activities of transduction channels of single olfactory receptor cells to InsP3-producing odorants. When the membrane potential was held at -54 mV, application of InsP3-producing odorants to the ciliary region caused an inward current. The reversal potential was 0 +/- 7 mV (mean +/- SD, n = 10). Actually, InsP3-producing odorants generated responses in a smaller fraction of cells (lilial, 3.4%; lyral, 1.7%) than the cAMP-producing odorant (cineole, 26%). But, fundamental properties of responses were surprisingly homologous; namely, spatial distribution of the sensitivity, waveforms, I-V relation, and reversal potential, dose dependence, time integration of stimulus period, adaptation, and recovery. By applying both types of odorants alternatively to the same cell, furthermore, we observed cells to exhibit symmetrical cross-adaptation. It seems likely that even with odorants with different modalities adaptation occurs completely depending on the amount of current flow. The data will also provide evidence showing that olfactory response generation and adaptation are regulated by a uniform mechanism for a wide variety of odorants.     

Transformation of Stimulus Correlations by the Retina

Redundancies and correlations in the responses of sensory neurons may seem to waste neural resources, but they can also carry cues about structured stimuli and may help the brain to correct for response errors. To investigate the effect of stimulus structure on redundancy in retina, we measured simultaneous responses from populations of retinal ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure; these stimuli and recordings are publicly available online. Responding to spatio-temporally structured stimuli such as natural movies, pairs of ganglion cells were modestly more correlated than in response to white noise checkerboards, but they were much less correlated than predicted by a non-adapting functional model of retinal response. Meanwhile, responding to stimuli with purely spatial correlations, pairs of ganglion cells showed increased correlations consistent with a static, non-adapting receptive field and nonlinearity. We found that in response to spatio-temporally correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the pattern of pairwise correlations across stimuli where receptive field measurements were possible.     

Bias in the gradient-sensing response of chemotactic cells

We apply linear stability theory and perform perturbation studies to better characterize, and to generate new experimental predictions from, a model of chemotactic gradient sensing in eukaryotic cells. The model uses reaction-diffusion equations to describe 3(') phosphoinositide signaling and its regulation at the plasma membrane. It demonstrates a range of possible gradient-sensing mechanisms and captures such characteristic behaviors as strong polarization in response to static gradients, adaptation to differing mean levels of stimulus, and plasticity in response to changing gradients. An analysis of the stability of polarized steady-state solutions indicates that the model is most sensitive to off-axis perturbations. This biased sensitivity is also reflected in responses to localized external stimuli, and leads to a clear experimental prediction, namely, that a cell which is polarized in a background gradient will be most sensitive to transient point-source stimuli lying within a range of angles that are oblique with respect to the polarization axis. Stimuli at angles below this range will elicit responses whose directions overshoot the stimulus angle, while responses to stimuli applied at larger angles will undershoot the stimulus angle. We argue that such a bias is likely to be a general feature of gradient sensing in highly motile cells, particularly if they are optimized to respond to small gradients. Finally, an angular bias in gradient sensing might lead to preferred turn angles and zigzag movements of cells moving up chemotactic gradients, as has been noted under certain experimental conditions.     

Interweaving and overlapping of evoked potentials

The refractory effect of one stimulus upon the response to a closely following stimulus in a different modality is much less than upon the response to a stimulus in the same modality. It is therefore far more efficient to record responses to stimuli in different modalities concurrently than to record each one separately. We evaluated 2 techniques for concurrent recording. Interweaving involves recording the response to one stimulus in the intervals between recording responses to other stimuli. Overlapping occurs when two or more responses are at times being simulateneously recorded. Interweaving and overlapping reduced the time required to record auditory brain-stem responses, short-latency somatosensory evoked potentials and pattern-reversal visual evoked potentials by a factor of 3 over the time required to record each response separately. Overlapping caused no significant change in the evoked potentials. Depending upon the actual timing schedule, interweaving may distort the evoked potentials if later parts of the response to one stimulus override the evoked potential to a following stimulus. Filtering and randomization of stimulus timing may attenuate the effects of these overriding potentials.     

Assessing the Performance of Neural Encoding Models in the Presence of Noise

An analytical method is introduced for evaluating the performance of neural encoding models. The method addresses a critical question that arises during the course of the development and validation of encoding models: is a given model near optimal in terms of its accuracy in predicting the stimulus-elicited responses of a neural system, or can the predictive accuracy be improved significantly by further model development? The evaluation method is based on a derivation of the minimum mean-square error between actual responses and modeled responses. It is formulated as a comparison between the mean-square error of the candidate model and the theoretical minimum mean-square error attainable through an optimal model for the system. However, no a priori information about the nature of the optimal model is required. The theoretically minimum error is determined solely from the coherence function between pairs of system responses to repeated presentations of the same dynamic stimulus. Thus, the performance of the candidate model is judged against the performance of an optimal model rather than against that of an arbitrarily assumed model. Using this method, we evaluated a linear model for neural encoding by mechanosensory cells in the cricket cercal system. At low stimulus intensities, the best-fit linear model of encoding by single cells was found to be nearly optimal, even though the coherence between stimulus-response pairs (a commonly used measure of system linearity) was low. In this low-stimulus-intensity regime, the mean square error of the linear model was on the order of the power of the cell responses. In contrast, at higher stimulus intensities the linear model was not an accurate representation of neural encoding, even though the stimulus-response coherence was substantially higher than in the low-intensity regime.     

The response of the Limulus retina to moving stimuli: a prediction by Fourier synthesis

The Limulus retina responds as a linear system to light stimuli which vary moderately about a mean level. The dynamics of such a system may conveniently be summarized by means of a spatiotemporal transfer function, which describes the response of the system to moving sinusoidal gratings. The response of the system to an arbitrary stimulus may then be calculated by adding together the system's responses to suitably weighted sinusoidal stimuli. We have measured such a spatiotemporal transfer function for the Limulus eye. We have then accurately predicted, in a parameter-free calculation, the eye's response to various stimulus patterns which move across it at several different velocities.     

Characteristics of intracellular on - off responses of amacrine cells of the dark-adapted carp retina

The dependence of the amplitude and latent period of intracellular on and off responses of the amacrine cells of the isolated, dark-adapted carp retina on the intensity and diameter of the light spot was investigated. On and off responses of amacrine cells to light were shown to consist of fast depolarization responses with oscillations and spikes superposed upon them. With an increase in the intensity and area of the stimulus the latent period of the on response decreases but that of the off response increases. A near-linear relationship was found between the amplitude of the on response and the logarithm of the diameter of the spot up to 3 mm during changes in stimulus intensity of not more than 4 logarithmic units. With an increase in stimulus intensity the amplitude and zone of summation of the off response are reduced; it is suggested that under these circumstances this decrease may be connected with the different amplitude and temporal characteristics of off processes in the bipolar cells converging on the amacrine cells.     

Modeling immune responses with handling time

Simple predator-prey type models have brought much insight into the dynamics of both nonspecific and antigen-specific immune responses. However, until now most attention has been focused on examining how the dynamics of interactions between the parasite and the immune system depends on the nature of the function describing the rate of activation or proliferation of immune cells in response to the parasite. In this paper we focus on the term describing the killing of the parasite by cell-mediated immune responses. This term has previously been assumed to be a simple mass-action term dependent solely on the product of the densities of the parasite and the immune cells and does not take into account a handling time (which we define as the time of interaction between an immune cell and its target, during which the immune cell cannot interact with and/or destroy additional targets). We show how the handling time (i) can be incorporated into simple models of nonspecific and specific immunity and (ii) how it affects the dynamics of both nonspecific and antigen-specific immune responses, and in particular the ability of the immune response to control the infection.     

The pursuit response of the housefly and its interaction with the optomotor response

Summary Pursuit responses that are probably involved in chasing behavior can be evoked and quantitatively measured in male houseflies under conditions of tethered flight (Figs. 2, 3, 5). Pursuit responses of females are significantly different from those of males (Table 1).Characteristics of the pursuit response are compared with those of the optomotor response to show that they are mediated by different neural subsystems that are in parallel. A slow system mediates the optomotor response, while a much faster system mediates the pursuit response (Table 1).The interaction between the pursuit response and the optomotor response is one of switching. The optomotor stimulus, when presented alone, evokes the optomotor response. When the pursuit stimulus is superposed, the fly switches from the optomotor system to the pursuit system, and ignores the optomotor stimulus. When the pursuit stimulus is removed, the animal switches back to the optomotor system (Fig. 8).We wish to thank Dr. M.F. Land for his valuable suggestion for measuring the optomotor response. This work was supported by NEI grants EY 01140 and EY 00785.     

Estimating receptive fields from responses to natural stimuli with asymmetric intensity distributions

The reasons for using natural stimuli to study sensory function are quickly mounting, as recent studies have revealed important differences in neural responses to natural and artificial stimuli. However, natural stimuli typically contain strong correlations and are spherically asymmetric (i.e. stimulus intensities are not symmetrically distributed around the mean), and these statistical complexities can bias receptive field (RF) estimates when standard techniques such as spike-triggered averaging or reverse correlation are used. While a number of approaches have been developed to explicitly correct the bias due to stimulus correlations, there is no complementary technique to correct the bias due to stimulus asymmetries. Here, we develop a method for RF estimation that corrects reverse correlation RF estimates for the spherical asymmetries present in natural stimuli. Using simulated neural responses, we demonstrate how stimulus asymmetries can bias reverse-correlation RF estimates (even for uncorrelated stimuli) and illustrate how this bias can be removed by explicit correction. We demonstrate the utility of the asymmetry correction method under experimental conditions by estimating RFs from the responses of retinal ganglion cells to natural stimuli and using these RFs to predict responses to novel stimuli.