Neural Decision Boundaries for Maximal Information Transmission

We consider here how to separate multidimensional signals into two categories, such that the binary decision transmits the maximum possible information transmitted about those signals. Our motivation comes from the nervous system, where neurons process multidimensional signals into a binary sequence of responses (spikes). In a small noise limit, we derive a general equation for the decision boundary that locally relates its curvature to the probability distribution of inputs. We show that for Gaussian inputs the optimal boundaries are planar, but for non-Gaussian inputs the curvature is nonzero. As an example, we consider exponentially distributed inputs, which are known to approximate a variety of signals from natural environment.Comment: 5 pages, 3 figure

A Generalized Linear Model for Estimating Spectrotemporal Receptive Fields from Responses to Natural Sounds

In the auditory system, the stimulus-response properties of single neurons are often described in terms of the spectrotemporal receptive field (STRF), a linear kernel relating the spectrogram of the sound stimulus to the instantaneous firing rate of the neuron. Several algorithms have been used to estimate STRFs from responses to natural stimuli; these algorithms differ in their functional models, cost functions, and regularization methods. Here, we characterize the stimulus-response function of auditory neurons using a generalized linear model (GLM). In this model, each cell's input is described by: 1) a stimulus filter (STRF); and 2) a post-spike filter, which captures dependencies on the neuron's spiking history. The output of the model is given by a series of spike trains rather than instantaneous firing rate, allowing the prediction of spike train responses to novel stimuli. We fit the model by maximum penalized likelihood to the spiking activity of zebra finch auditory midbrain neurons in response to conspecific vocalizations (songs) and modulation limited (ml) noise. We compare this model to normalized reverse correlation (NRC), the traditional method for STRF estimation, in terms of predictive power and the basic tuning properties of the estimated STRFs. We find that a GLM with a sparse prior predicts novel responses to both stimulus classes significantly better than NRC. Importantly, we find that STRFs from the two models derived from the same responses can differ substantially and that GLM STRFs are more consistent between stimulus classes than NRC STRFs. These results suggest that a GLM with a sparse prior provides a more accurate characterization of spectrotemporal tuning than does the NRC method when responses to complex sounds are studied in these neurons

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

Network adaptation improves temporal representation of naturalistic stimuli in drosophila eye: II Mechanisms

Retinal networks must adapt constantly to best present the ever changing visual world to the brain. Here we test the hypothesis that adaptation is a result of different mechanisms at several synaptic connections within the network. In a companion paper (Part I), we showed that adaptation in the photoreceptors (R1-R6) and large monopolar cells (LMC) of the Drosophila eye improves sensitivity to under-represented signals in seconds by enhancing both the amplitude and frequency distribution of LMCs' voltage responses to repeated naturalistic contrast series. In this paper, we show that such adaptation needs both the light-mediated conductance and feedback-mediated synaptic conductance. A faulty feedforward pathway in histamine receptor mutant flies speeds up the LMC output, mimicking extreme light adaptation. A faulty feedback pathway from L2 LMCs to photoreceptors slows down the LMC output, mimicking dark adaptation. These results underline the importance of network adaptation for efficient coding, and as a mechanism for selectively regulating the size and speed of signals in neurons. We suggest that concert action of many different mechanisms and neural connections are responsible for adaptation to visual stimuli. Further, our results demonstrate the need for detailed circuit reconstructions like that of the Drosophila lamina, to understand how networks process information

Normalization of Voltage-Sensitive Dye Signal with Functional Activity Measures

In general, signal amplitude in optical imaging is normalized using the well-established ΔF/F method, where functional activity is divided by the total fluorescent light flux. This measure is used both directly, as a measure of population activity, and indirectly, to quantify spatial and spatiotemporal activity patterns. Despite its ubiquitous use, the stability and accuracy of this measure has not been validated for voltage-sensitive dye imaging of mammalian neocortex in vivo. In this report, we find that this normalization can introduce dynamic biases. In particular, the ΔF/F is influenced by dye staining quality, and the ratio is also unstable over the course of experiments. As methods to record and analyze optical imaging signals become more precise, such biases can have an increasingly pernicious impact on the accuracy of findings, especially in the comparison of cytoarchitechtonic areas, in area-of-activation measurements, and in plasticity or developmental experiments. These dynamic biases of the ΔF/F method may, to an extent, be mitigated by a novel method of normalization, ΔF/ΔFepileptiform. This normalization uses as a reference the measured activity of epileptiform spikes elicited by global disinhibition with bicuculline methiodide. Since this normalization is based on a functional measure, i.e. the signal amplitude of “hypersynchronized” bursts of activity in the cortical network, it is less influenced by staining of non-functional elements. We demonstrate that such a functional measure can better represent the amplitude of population mass action, and discuss alternative functional normalizations based on the amplitude of synchronized spontaneous sleep-like activity. These findings demonstrate that the traditional ΔF/F normalization of voltage-sensitive dye signals can introduce pernicious inaccuracies in the quantification of neural population activity. They further suggest that normalization-independent metrics such as waveform propagation patterns, oscillations in single detectors, and phase relationships between detector pairs may better capture the biological information which is obtained by high-sensitivity imaging

Genotype to phenotype mapping and the fitness landscape of the E. coli lac promoter

Genotype-to-phenotype maps and the related fitness landscapes that include epistatic interactions are difficult to measure because of their high dimensional structure. Here we construct such a map using the recently collected corpora of high-throughput sequence data from the 75 base pairs long mutagenized E. coli lac promoter region, where each sequence is associated with its phenotype, the induced transcriptional activity measured by a fluorescent reporter. We find that the additive (non-epistatic) contributions of individual mutations account for about two-thirds of the explainable phenotype variance, while pairwise epistasis explains about 7% of the variance for the full mutagenized sequence and about 15% for the subsequence associated with protein binding sites. Surprisingly, there is no evidence for third order epistatic contributions, and our inferred fitness landscape is essentially single peaked, with a small amount of antagonistic epistasis. There is a significant selective pressure on the wild type, which we deduce to be multi-objective optimal for gene expression in environments with different nutrient sources. We identify transcription factor (CRP) and RNA polymerase binding sites in the promotor region and their interactions without difficult optimization steps. In particular, we observe evidence for previously unexplored genetic regulatory mechanisms, possibly kinetic in nature. We conclude with a cautionary note that inferred properties of fitness landscapes may be severely influenced by biases in the sequence data

Adaptation and Selective Information Transmission in the Cricket Auditory Neuron AN2

Sensory systems adapt their neural code to changes in the sensory environment, often on multiple time scales. Here, we report a new form of adaptation in a first-order auditory interneuron (AN2) of crickets. We characterize the response of the AN2 neuron to amplitude-modulated sound stimuli and find that adaptation shifts the stimulus–response curves toward higher stimulus intensities, with a time constant of 1.5 s for adaptation and recovery. The spike responses were thus reduced for low-intensity sounds. We then address the question whether adaptation leads to an improvement of the signal's representation and compare the experimental results with the predictions of two competing hypotheses: infomax, which predicts that information conveyed about the entire signal range should be maximized, and selective coding, which predicts that “foreground” signals should be enhanced while “background” signals should be selectively suppressed. We test how adaptation changes the input–response curve when presenting signals with two or three peaks in their amplitude distributions, for which selective coding and infomax predict conflicting changes. By means of Bayesian data analysis, we quantify the shifts of the measured response curves and also find a slight reduction of their slopes. These decreases in slopes are smaller, and the absolute response thresholds are higher than those predicted by infomax. Most remarkably, and in contrast to the infomax principle, adaptation actually reduces the amount of encoded information when considering the whole range of input signals. The response curve changes are also not consistent with the selective coding hypothesis, because the amount of information conveyed about the loudest part of the signal does not increase as predicted but remains nearly constant. Less information is transmitted about signals with lower intensity

Fly Photoreceptors Encode Phase Congruency

More than five decades ago it was postulated that sensory neurons detect and selectively enhance behaviourally relevant features of natural signals. Although we now know that sensory neurons are tuned to efficiently encode natural stimuli, until now it was not clear what statistical features of the stimuli they encode and how. Here we reverse-engineer the neural code of Drosophila photoreceptors and show for the first time that photoreceptors exploit nonlinear dynamics to selectively enhance and encode phase-related features of temporal stimuli, such as local phase congruency, which are invariant to changes in illumination and contrast. We demonstrate that to mitigate for the inherent sensitivity to noise of the local phase congruency measure, the nonlinear coding mechanisms of the fly photoreceptors are tuned to suppress random phase signals, which explains why photoreceptor responses to naturalistic stimuli are significantly different from their responses to white noise stimuli

Contrast Adaptation Contributes to Contrast-Invariance of Orientation Tuning of Primate V1 Cells

BACKGROUND: Studies in rodents and carnivores have shown that orientation tuning width of single neurons does not change when stimulus contrast is modified. However, in these studies, stimuli were presented for a relatively long duration (e. g., 4 seconds), making it possible that contrast adaptation contributed to contrast-invariance of orientation tuning. Our first purpose was to determine, in marmoset area V1, whether orientation tuning is still contrast-invariant with the stimulation duration is comparable to that of a visual fixation. METHODOLOGY/PRINCIPAL FINDINGS: We performed extracellular recordings and examined orientation tuning of single-units using static sine-wave gratings that were flashed for 200 msec. Sixteen orientations and three contrast levels, representing low, medium and high values in the range of effective contrasts for each neuron, were randomly intermixed. Contrast adaptation being a slow phenomenon, cells did not have enough time to adapt to each contrast individually. With this stimulation protocol, we found that the tuning width obtained at intermediate contrast was reduced to 89% (median), and that at low contrast to 76%, of that obtained at high contrast. Therefore, when probed with briefly flashed stimuli, orientation tuning is not contrast-invariant in marmoset V1. Our second purpose was to determine whether contrast adaptation contributes to contrast-invariance of orientation tuning. Stationary gratings were presented, as previously, for 200 msec with randomly varying orientations, but the contrast was kept constant within stimulation blocks lasting >20 sec, allowing for adaptation to the single contrast in use. In these conditions, tuning widths obtained at low contrast were still significantly less than at high contrast (median 85%). However, tuning widths obtained with medium and high contrast stimuli no longer differed significantly. CONCLUSIONS/SIGNIFICANCE: Orientation tuning does not appear to be contrast-invariant when briefly flashed stimuli vary in both contrast and orientation, but contrast adaptation partially restores contrast-invariance of orientation tuning

Spike-Triggered Covariance Analysis Reveals Phenomenological Diversity of Contrast Adaptation in the Retina

When visual contrast changes, retinal ganglion cells adapt by adjusting their sensitivity as well as their temporal filtering characteristics. The latter has classically been described by contrast-induced gain changes that depend on temporal frequency. Here, we explored a new perspective on contrast-induced changes in temporal filtering by using spike-triggered covariance analysis to extract multiple parallel temporal filters for individual ganglion cells. Based on multielectrode-array recordings from ganglion cells in the isolated salamander retina, we found that contrast adaptation of temporal filtering can largely be captured by contrast-invariant sets of filters with contrast-dependent weights. Moreover, differences among the ganglion cells in the filter sets and their contrast-dependent contributions allowed us to phenomenologically distinguish three types of filter changes. The first type is characterized by newly emerging features at higher contrast, which can be reproduced by computational models that contain response-triggered gain-control mechanisms. The second type follows from stronger adaptation in the Off pathway as compared to the On pathway in On-Off-type ganglion cells. Finally, we found that, in a subset of neurons, contrast-induced filter changes are governed by particularly strong spike-timing dynamics, in particular by pronounced stimulus-dependent latency shifts that can be observed in these cells. Together, our results show that the contrast dependence of temporal filtering in retinal ganglion cells has a multifaceted phenomenology and that a multi-filter analysis can provide a useful basis for capturing the underlying signal-processing dynamics