Modeling the electric image produced by objects with complex impedance in weakly electric fish

Weakly electric fish generate an electric field around their body by electric organ discharge (EOD). By measuring the modulation of the electric field produced by an object in the field these fish are able to accurately locate an object. Theoretical and experimental studies have focused on the amplitude modulations of EODs produced by resistive objects. However, little is known about the phase modulations produced by objects with complex impedance. The fish must be able to detect changes in object impedance to discriminate between food and nonfood objects. To investigate the features of electric images produced by objects with complex impedance, we developed a model that can be used to map the electric field around the fish body. The present model allows us to calculate the spatial distribution of the amplitude and phase shift in an electric image. This is the first study to investigate the changes in amplitude and phase shift of electric images induced by objects with complex impedance in wave-type fish. Using the model, we show that the amplitude of the electric image exhibits a sigmoidal change as the capacitance and resistance of an object are increased. Similarly, the phase shift exhibits a significant change within the object capacitance range of 0.1–100 nF. We also show that the spatial distribution of the amplitude and phase shifts of the electric image resembles a “Mexican hat” in shape for varying object distances and sizes. The spatial distribution of the phase shift and the amplitude was dependent on the object distance and size. Changes in the skin capacitance were associated with a tradeoff relationship between the magnitude of the amplitude and phase shift of the electric image. The specific range of skin capacitance (1–100 nF) allows the receptor afferents to extract object features that are relevant to electrolocation. These results provide a useful basis for the study of the neural mechanisms by which weakly electric fish recognize object features such as distance, size, and impedance.     

Active electric imaging: body-object interplay and object's "electric texture"

This article deals with the role of fish's body and object's geometry on determining the image spatial shape in pulse Gymnotiforms. This problem was explored by measuring local electric fields along a line on the skin in the presence and absence of objects. We depicted object's electric images at different regions of the electrosensory mosaic, paying particular attention to the perioral region where a fovea has been described. When sensory surface curvature increases relative to the object's curvature, the image details depending on object's shape are blurred and finally disappear. The remaining effect of the object on the stimulus profile depends on the strength of its global polarization. This depends on the length of the object's axis aligned with the field, in turn depending on fish body geometry. Thus, fish's body and self-generated electric field geometries are embodied in this "global effect" of the object. The presence of edges or local changes in impedance at the nearest surface of closely located objects adds peaks to the image profiles ("local effect" or "object's electric texture"). It is concluded that two cues for object recognition may be used by active electroreceptive animals: global effects (informing on object's dimension along the field lines, conductance, and position) and local effects (informing on object's surface). Since the field has fish's centered coordinates, and electrosensory fovea is used for exploration of surfaces, fish fine movements are essential to perform electric perception. We conclude that fish may explore adjacent objects combining active movements and electrogenesis to represent them using electrosensory information.     

A computational theory of visual receptive fields

A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space–time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative agreement are obtained for (i) spatial on-center/off-surround and off-center/on-surround receptive fields in the fovea and the LGN, (ii) simple cells with spatial directional preference in V1, (iii) spatio-chromatic double-opponent neurons in V1, (iv) space–time separable spatio-temporal receptive fields in the LGN and V1, and (v) non-separable space–time tilted receptive fields in V1, all within the same unified theory. In addition, the paper presents a more general framework for relating and interpreting these receptive fields conceptually and possibly predicting new receptive field profiles as well as for pre-wiring covariance under scaling, affine, and Galilean transformations into the representations of visual stimuli. This paper describes the basic structure of the necessity results concerning receptive field profiles regarding the mathematical foundation of the theory and outlines how the proposed theory could be used in further studies and modelling of biological vision. It is also shown how receptive field responses can be interpreted physically, as the superposition of relative variations of surface structure and illumination variations, given a logarithmic brightness scale, and how receptive field measurements will be invariant under multiplicative illumination variations and exposure control mechanisms.     

"Clock-scan" protocol for image analysis

Comparative analysis of extra- and intracellular distributions of protein markers in immunohistochemical and immunofluorescent studies relies on techniques of image analysis. Line or region of interest pixel intensity scans are methods routinely used. However, although having good spatial resolution, linear pixel intensity scans fail to produce integral image of the cellular distribution of the label. On the other hand, the regions of interest scans have good integrative capacity but low spatial resolution. In this work, we describe a "clock-scan" protocol that, when applied to convex objects (such as neuronal cell bodies and the majority of cells in culture), combines advantages and circumnavigates limitations of the above-mentioned techniques. The protocol 1) collects multiple radial pixel intensity profiles scanned from the cell center to the periphery, 2) scales these profiles according to the cell radius measured in the direction of the scan, and finally, 3) averages these individual profiles into one integral radial pixel intensity profile. Because of scaling, the mean pixel intensity profiles produced by the clock-scan protocol depend on neither the cell size nor, within reasonable limits, the cell shape. This allows direct comparison or, if required, averaging or subtraction of profiles of different cells. We have successfully tested the clock-scan protocol in experiments with immunostained dorsal root ganglion neurons. In addition, the protocol seems to be equally applicable for studies in a variety of other preparations. techniques; methods; cell biology; histology; immunohistochemistry     

Peripheral electrosensory imaging by weakly electric fish

Different species have developed different solutions to the problem of constructing a representation of the environment from sensory images projected onto sensory surfaces. Comprehension of how these images are formed is an essential first step in understanding the representation of external reality by a given sensory system. Modeling of the electrical sensory images of objects began with the discovery of electroreception and continues to provide general insights into the mechanisms of imaging. Progress in electric image research has made it possible to establish the physical basis of electric imaging, as well as methods to accurately predict the electric images of objects alone and as a part of a natural electric scene. In this review, we show the following. (1) The internal low resistance of the fish’s body shapes the image in two different ways: by funneling the current generated by the electric organ to the sensory surface, it increases the fields rostrally, thus enhancing the perturbation produced by nearby objects; and by increasing the projected image. (2) The electric fish’s self-generated currents are modified by capacitive objects in a distinctive manner. These modulations can be detected by different receptor types, yielding the possibility of “electric color.” (3) The effects of different objects in a scene interact with each other, generating an image that is different from the simple addition of the images of individual objects, thus causing strong contextual effects.     

The electric image in weakly electric fish: I. A data-based model of waveform generation inGymnotus carapo

Understanding how electrosensory images are generated and perceived in actively electrolocating fish requires the study of the characteristics of fish bodies as electric sources. This paper presents a model ofGymnotus carapo based on measurements of the electromotive force generated by the electric organ and the impedance of the passive tissues. A good agreement between simulated and experimentally recorded transcutaneous currents was obtained. Passive structures participate in the transformation of the electromotive force pattern into transcutaneous current profiles. These spatial filtering properties of the fish's body were investigated using the model. The shape of the transcutaneous current profiles depends on tissue resistance and on the geometry and size of the fish. Skin impedance was mainly resistive. The effect of skin resistance on the spatial filtering properties of the fish's body was theoretically analyzed.The model results show that generators in the abdominal and central regions produce most of the currents through the head. This suggests that the electric organ discharge (EOD), generated in the abdominal and central regions is critical for active electrolocation. In addition, the well-synchronized EOD components generated all along the fish produce large potentials in the far field. These components are probably involved in long-distance electrocommunication.Preliminary results of this work were published as a symposium abstract.     

Phase and amplitude maps of the electric organ discharge of the weakly electric fish,Apteronotus leptorhynchus

Summary The electric organ discharge (EOD) potential was mapped on the skin and midplane of several Apteronotus leptorhynchus. The frequency components of the EOD on the surface of the fish have extremely stable amplitude and phase. However, the waveform varies considerably with different positions on the body surface. Peaks and zero crossings of the potential propagate along the fish's body, and there is no point where the potential is always zero. The EOD differs significantly from a sinusoid over at least one third of the body and tail. A qualitative comparison between fish showed that each individual had a unique spatiotemporal pattern of the EOD potential on its body.The potential waveforms have been assembled into high temporal and spatial resolution maps which show the dynamics of the EOD. Animation sequences and Macintosh software are available by anonymous ftp (mordor.cns.caltech.edu; cd/pub/ElectricFish).We interpret the EOD maps in terms of ramifications on electric organ control and electroreception. The electrocytes comprising the electric organ do not all fire in unison, indicating that the command pathway is not synchronized overall. The maps suggest that electroreceptors in different regions fulfill different computational roles in electroreception. Receptor mechanisms may exist to make use of the phase information or harmonic content of the EOD, so that both spatial and temporal patterns could contribute information useful for electrolocation and communication.Abbreviations EOD electric organ discharge - EO electric organ - CV coefficient of variance     

Spatial acuity and prey detection in weakly electric fish

It is well-known that weakly electric fish can exhibit extreme temporal acuity at the behavioral level, discriminating time intervals in the submicrosecond range. However, relatively little is known about the spatial acuity of the electrosense. Here we use a recently developed model of the electric field generated by Apteronotus leptorhynchus to study spatial acuity and small signal extraction. We show that the quality of sensory information available on the lateral body surface is highest for objects close to the fish's midbody, suggesting that spatial acuity should be highest at this location. Overall, however, this information is relatively blurry and the electrosense exhibits relatively poor acuity. Despite this apparent limitation, weakly electric fish are able to extract the minute signals generated by small prey, even in the presence of large background signals. In fact, we show that the fish's poor spatial acuity may actually enhance prey detection under some conditions. This occurs because the electric image produced by a spatially dense background is relatively “blurred” or spatially uniform. Hence, the small spatially localized prey signal “pops out” when fish motion is simulated. This shows explicitly how the back-and-forth swimming, characteristic of these fish, can be used to generate motion cues that, as in other animals, assist in the extraction of sensory information when signal-to-noise ratios are low. Our study also reveals the importance of the structure of complex electrosensory backgrounds. Whereas large-object spacing is favorable for discriminating the individual elements of a scene, small spacing can increase the fish's ability to resolve a single target object against this background.     

CentTracker: a trainable,machine-learning–based tool for large-scale analyses of Caenorhabditis elegans germline stem cell mitosis

Investigating the complex interactions between stem cells and their native environment requires an efficient means to image them in situ. Caenorhabditis elegans germline stem cells (GSCs) are distinctly accessible for intravital imaging; however, long-term image acquisition and analysis of dividing GSCs can be technically challenging. Here we present a systematic investigation into the technical factors impacting GSC physiology during live imaging and provide an optimized method for monitoring GSC mitosis under minimally disruptive conditions. We describe CentTracker, an automated and generalizable image analysis tool that uses machine learning to pair mitotic centrosomes and that can extract a variety of mitotic parameters rapidly from large-scale data sets. We employ CentTracker to assess a range of mitotic features in a large GSC data set. We observe spatial clustering of mitoses within the germline tissue but no evidence that subpopulations with distinct mitotic profiles exist within the stem cell pool. We further find biases in GSC spindle orientation relative to the germline’s distal–proximal axis and thus the niche. The technical and analytical tools provided herein pave the way for large-scale screening studies of multiple mitotic processes in GSCs dividing in situ, in an intact tissue, in a living animal, under seemingly physiological conditions.     

Analysis of confocal images using variable-width line profiles

A line profile of fluorescent intensities in confocal images is frequently examined. We have developed the computer software tool to analyse the profiles of intensities of fluorescent probes in confocal images. The software averages neighbouring pixels, adjacent to the central line, without reducing the spatial resolution of the image. As an experimental model, we have used the skeletal muscle fibre isolated from the rat skeletal muscle extensor digitorum brevis. As a marker of myofibrils' structure, we have used phalloidin–rhodamine staining and the anti-TIM antibody to label mitochondria. We also tested the distribution of the protein kinase B/Akt. Since signalling is ordered in modules and large protein complexes appear to direct signalling to organelles and regulate specific physiological functions, a software tool to analyse such complexes in fluorescent confocal images is required. The software displays the image, and the user defines the line for analysis. The image is rotated by the angle of the line. The line profile is calculated by averaging one dimension of the cropped rotated image matrix. The spatial resolution in averaged line profile is not decreased compared with single-pixel line profile, which was confirmed by the discrete Fourier transform computed with a fast Fourier transform algorithm. We conclude that the custom software tool presented here is a useful tool to analyse line profiles of fluorescence intensities in confocal images.     

The spatial region of integration for visual symmetry detection.

Symmetry is a complex image property that is exploited by a sufficiently wide range of species to indicate that it is detected using simple visual mechanisms. These mechanisms rely on measurements made close to the axis of symmetry. We investigated the size and shape of this integration region (IR) by measuring human detection of spatially band-pass symmetrical patches embedded in noise. Resistance to disruption of symmetry (in the form of random phase noise) improves with increasing patch size, and then asymptotes when the embedded region fills the IR. The size of the IR is shown to vary in inverse proportion to spatial frequency; i.e. symmetry detection exhibits scale invariance. The IR is shown to have rigid dimensions, elongated in the direction of the axis of symmetry, with an aspect ratio of ca. 2:1. These results are consistent with a central role for spatial filtering in symmetry detection.     

Dynamic Mechanisms of Neocortical Focal Seizure Onset

Recent experimental and clinical studies have provided diverse insight into the mechanisms of human focal seizure initiation and propagation. Often these findings exist at different scales of observation, and are not reconciled into a common understanding. Here we develop a new, multiscale mathematical model of cortical electric activity with realistic mesoscopic connectivity. Relating the model dynamics to experimental and clinical findings leads us to propose three classes of dynamical mechanisms for the onset of focal seizures in a unified framework. These three classes are: (i) globally induced focal seizures; (ii) globally supported focal seizures; (iii) locally induced focal seizures. Using model simulations we illustrate these onset mechanisms and show how the three classes can be distinguished. Specifically, we find that although all focal seizures typically appear to arise from localised tissue, the mechanisms of onset could be due to either localised processes or processes on a larger spatial scale. We conclude that although focal seizures might have different patient-specific aetiologies and electrographic signatures, our model suggests that dynamically they can still be classified in a clinically useful way. Additionally, this novel classification according to the dynamical mechanisms is able to resolve some of the previously conflicting experimental and clinical findings.     

Linking active sensing and spatial learning in weakly electric fish

Weakly electric fish can learn the spatial layout of their environment using only their short-range electric sense. During spatial learning, active sensing motions are used to memorize landmark locations so that they can serve as anchors for idiothetic-based navigation. A hindbrain feedback circuit selectively amplifies the electrosensory input arising from these motions. The ascending electrolocation pathway preferentially transmits this information to the pallial regions involved in spatial learning and navigation. Similarities in both behavioral patterns and hindbrain circuitry of gymnotiform and mormyrid fish, two families that independently evolved their electrosense, suggest that amplification and transmission of active sensing motion inputs are fundamental mechanisms for spatial memory acquisition.     

The electric organ discharges of the gymnotiform fishes: I. Apteronotus leptorhynchus

We present high temporal and spatial resolution maps in 3-dimensions of the electric field vector generated by the weakly electric fish, Apteronotus leptorhynchus. The waveforms and harmonic composition of the electric organ discharge (EOD) are variable around the fish but highly stable over long times at any position. We examine the role of harmonics on the temporal and spatial characteristics of the EOD, such as the slew rate and rostral-to-caudal propagation. We also explore the radial symmetry of the fish's field. There are major differences in the direction of the electric field vector at the head and caudal body. In the caudal part of the fish, the electric field vector rotates during the EOD cycle. However, rostral of the pectoral fin, the field magnitude and sign oscillate while maintaining relatively constant orientation. We discuss possible functional ramifications of these electric field patterns to electrolocation, communication, and electrogenesis.Abbreviations EOD electric organ discharge - EO electric organ - RMS root mean square - ADC analog-to-digital converter     

BMP signaling in wing development: A critical perspective on quantitative image analysis

Bone Morphogenetic Proteins (BMPs) are critical for pattern formation in many animals. In numerous tissues, BMPs become distributed in spatially non-uniform profiles. The gradients of signaling activity can be detected by a number of biological assays involving fluorescence microscopy. Quantitative analyses of BMP gradients are powerful tools to investigate the regulation of BMP signaling pathways during development. These approaches rely heavily on images as spatial representations of BMP activity levels, using them to infer signaling distributions that inform on regulatory mechanisms. In this perspective, we discuss current imaging assays and normalization methods used to quantify BMP activity profiles with a focus on the Drosophila wing primordium. We find that normalization tends to lower the number of samples required to establish statistical significance between profiles in controls and experiments, but the increased resolvability comes with a cost. Each normalization strategy makes implicit assumptions about the biology that impacts our interpretation of the data. We examine the tradeoffs for normalizing versus not normalizing, and discuss their impacts on experimental design and the interpretation of resultant data.     

Electric field interactions in pairs of electric fish: modeling and mimicking naturalistic inputs

Weakly electric fish acquire information about their surroundings by detecting and interpreting the spatial and temporal patterns of electric potential across their skin, caused by perturbations in a self-generated, oscillating electric field. Computational and experimental studies have focused on understanding the electric images due to simple, passive objects. The present study considers electric images of a conspecific fish. It is known that the electric fields of two fish interact to produce beats with spatially varying profiles of amplitude and phase. Such patterns have been shown to be critical for electrosensory-mediated behaviours, such as the jamming avoidance response, but they have yet to be well described. We have created a biophysically realistic model of a wave-type weakly electric fish by using a genetic algorithm to calibrate the parameters to the electric field of a real fish. We use the model to study a pair of fish and compute the electric images of one fish onto the other at three representative phases within a beat cycle. Analysis of the images reveals rostral/caudal and ipsilateral/contralateral patterns of amplitude and phase that have implications for localization of conspecifics (both position and orientation) and communication between conspecifics. We then show how the common stimulation paradigm used to mimic a conspecific during in vivo electrophysiological experiments, based on a transverse arrangement of two electrodes, can be improved in order to more accurately reflect the important qualitative features of naturalistic inputs, as revealed by our model.     

Mind the gap: the minimal detectable separation distance between two objects during active electrolocation

In a food‐rewarded two‐alternative forced‐choice procedure, it was determined how well the weakly electric elephantnose fish Gnathonemus petersii can sense gaps between two objects, some of which were placed in front of complex backgrounds. The results show that at close distances, G. petersii is able to detect gaps between two small metal cubes (2 cm × 2 cm × 2 cm) down to a width of c. 1·5 mm. When larger objects (3 cm × 3 cm × 3 cm) were used, gaps with a width of 2–3 mm could still be detected. Discrimination performance was better (c. 1 mm gap size) when the objects were placed in front of a moving background consisting of plastic stripes or plant leaves, indicating that movement in the environment plays an important role for object identification. In addition, the smallest gap size that could be detected at increasing distances was determined. A linear relationship between object distance and gap size existed. Minimal detectable gap sizes increased from c. 1·5 mm at a distance of 1 cm, to 20 mm at a distance of 7 cm. Measurements and simulations of the electric stimuli occurring during gap detection revealed that the electric images of two close objects influence each other and superimpose. A large gap of 20 mm between two objects induced two clearly separated peaks in the electric image, while a 2 mm gap caused just a slight indentation in the image. Therefore, the fusion of electric images limits spatial resolution during active electrolocation. Relative movements either between the fish and the objects or between object and background might improve spatial resolution by accentuating the fine details of the electric images.     

Three processing characteristics of visual texture segmentation

Three mechanisms are outlined which are sufficient to determine texture segmentation or discrimination. They are: (1) convolution of detector profiles with the input image; (2) impletion, where the perceptual 'filling in' of the input surface occurs via a nonlinear filtering operation on each detector's output (3) grouping, where areas are segregated according to their differences in detector responses after impletion occurs. These mechanisms are compared with those proposed to occur in human visual texture discrimination.     

Visual Features Underlying Perceived Brightness as Revealed by Classification Images

Along with physical luminance, the perceived brightness is known to depend on the spatial structure of the stimulus. Often it is assumed that neural computation of the brightness is based on the analysis of luminance borders of the stimulus. However, this has not been tested directly. We introduce a new variant of the psychophysical reverse-correlation or classification image method to estimate and localize the physical features of the stimuli which correlate with the perceived brightness, using a brightness-matching task. We derive classification images for the illusory Craik-O''Brien-Cornsweet stimulus and a “real” uniform step stimulus. For both stimuli, classification images reveal a positive peak at the stimulus border, along with a negative peak at the background, but are flat at the center of the stimulus, suggesting that brightness is determined solely by the border information. Features in the perceptually completed area in the Craik-O''Brien-Cornsweet do not contribute to its brightness, nor could we see low-frequency boosting, which has been offered as an explanation for the illusion. Tuning of the classification image profiles changes remarkably little with stimulus size. This supports the idea that only certain spatial scales are used for computing the brightness of a surface.