Luminance Steps Research Articles

Optimization and Validation of a Virtual Reality Orientation and Mobility Test for Inherited Retinal Degenerations.

To optimize a virtual reality (VR) orientation and mobility (O&M) test of functional vision in patients with inherited retinal degenerations (IRDs). We developed an O&M test using commercially available VR hardware and custom-generated software. Normally sighted subjects (n = 20, ages = 14-67 years) and patients with IRDs (n = 29, ages = 15-63 years) participated. Individuals followed a dim red arrow path to a "course exit," while trying to identify nine obstacles adjacent to, or directly in their path. Dark-adapted subjects completed 35 randomly selected VR courses at increasing luminances, twice per luminance step, binocularly, and uni-ocularly. Performance was graded automatically by the software. Patients with IRD completed a modified Visual Function Questionnaire (VFQ). Normally sighted subjects identified approximately 50% of the obstacles at the dimmest course luminance. Except for two patients with IRD with poor vision, all patients were able to complete the test, although they required brighter (by >2 log units) luminances to identify 50% of the obstacles. In a single-luminance screening test in which normal subjects detected at least eight of nine objects, most patients with IRD underperformed; their performance related to disease severity, as measured by visual acuity, kinetic visual field extent, and VFQ scores. Test-retest differences in object detection were similar to the differences between the two eyes (±2SD=±2 objects). This VR-O&M test was able to distinguish subjects with IRDs from normal subjects reliably and reproducibly. This easily implemented, flexible, and objectively scored VR-O&M test promises to become a useful tool to assess the impact that IRDs and their treatments have on functional vision.

Luminance texture boundaries and luminance step boundaries are segmented using different mechanisms

In natural scenes, two adjacent surfaces may differ in mean luminance without any sharp change in luminance at their boundary, but rather due to different relative proportions of light and dark regions within each surface. We refer to such boundaries as luminance texture boundaries (LTBs), and in this study we investigate whether LTBs are segmented using different mechanisms than luminance step boundaries (LSBs). We develop a novel method to generate luminance texture boundaries from natural uniform textures, and using these natural LTB stimuli in a boundary segmentation task, we find that observers are much more sensitive to identical luminance differences which are defined by textures (LTBs) than by uniform luminance steps (LSBs), consistent with the possibility of different mechanisms. In a second and third set of experiments, we characterize observer performance segmenting natural LTBs in the presence of masking LSBs which observers are instructed to ignore. We show that there is very little effect of masking LSBs on LTB segmentation performance. Furthermore, any masking effects we find are far less than those observed in a control experiment where both the masker and target are LSBs, and far less than those predicted by a model assuming identical mechanisms. Finally, we perform a fourth set of boundary segmentation experiments using artificial LTB stimuli comprised of differing proportions of white and black dots on opposite sides of the boundary. We find that these stimuli are also highly robust to masking by supra-threshold LSBs, consistent with our results using natural stimuli, and with our earlier studies using similar stimuli. Taken as a whole, these results suggest that the visual system contains mechanisms well suited to detecting surface boundaries that are robust to interference from luminance differences arising from luminance steps like those formed by cast shadows.

Neural edge integration model with different weights for positive and negative luminance steps explains lightness scaling in the Staircase Gelb effect

Neural edge integration model with different weights for positive and negative luminance steps explains lightness scaling in the Staircase Gelb effect

Segmenting surface boundaries using luminance cues

Segmenting scenes into distinct surfaces is a basic visual perception task, and luminance differences between adjacent surfaces often provide an important segmentation cue. However, mean luminance differences between two surfaces may exist without any sharp change in albedo at their boundary, but rather from differences in the proportion of small light and dark areas within each surface, e.g. texture elements, which we refer to as a luminance texture boundary. Here we investigate the performance of human observers segmenting luminance texture boundaries. We demonstrate that a simple model involving a single stage of filtering cannot explain observer performance, unless it incorporates contrast normalization. Performing additional experiments in which observers segment luminance texture boundaries while ignoring super-imposed luminance step boundaries, we demonstrate that the one-stage model, even with contrast normalization, cannot explain performance. We then present a Filter–Rectify–Filter model positing two cascaded stages of filtering, which fits our data well, and explains observers' ability to segment luminance texture boundary stimuli in the presence of interfering luminance step boundaries. We propose that such computations may be useful for boundary segmentation in natural scenes, where shadows often give rise to luminance step edges which do not correspond to surface boundaries.

Functional, molecular and morphological heterogeneity of superficial interneurons in the larval zebrafish tectum.

The superficial interneurons, SINs, of the zebrafish tectum, have been implicated in a range of visual functions, including size discrimination, directional selectivity, and looming-evoked escape. This raises the question if SIN subpopulations, despite their morphological similarities and shared anatomical position in the retinotectal processing stream, carry out diverse, task-specific functions in visual processing, or if they have simple tuning properties in common. Here we have further characterized the SINs through functional imaging, electrophysiological recordings, and neurotransmitter typing in two transgenic lines, the widely used Gal4s1156t and the recently reported LCRRH2-RH2-2:GFP. We found that about a third of the SINs strongly responded to changes in whole-field light levels, with a strong preference for OFF over ON stimuli. Interestingly, individual SINs were selectively tuned to a diverse range of narrow luminance decrements. Overall responses to whole-field luminance steps did not vary with the position of the SIN cell body along the depth of the tectal neuropil or with the orientation of its neurites. We ruled out the possibility that intrinsic photosensitivity of Gal4s1156t+ SINs contribute to the measured visual responses. We found that, while most SINs express GABAergic markers, a substantial minority express an excitatory neuronal marker, the vesicular glutamate transporter, expanding the possible roles of SIN function in the tectal circuitry. In conclusion, SINs represent a molecularly, morphologically, and functionally heterogeneous class of interneurons, with subpopulations that detect a range of specific visual features, to which we have now added narrow luminance decrements.

Inhibitory Interactions and Columnar Inputs to an Object Motion Detector in Drosophila

The direction-selective T4/T5 cells innervate optic-flow processing projection neurons in the lobula plate of the fly that mediate the visual control of locomotion. In the lobula, visual projection neurons coordinate complex behavioral responses to visual features, however, the input circuitry and computations that bestow their feature-detecting properties are less clear. Here, we study a highly specialized small object motion detector, LC11, and demonstrate that its responses are suppressed by local background motion. We show that LC11 expresses GABA-A receptors that serve to sculpt responses to small objects but are not responsible for the rejection of background motion. Instead, LC11 is innervated by columnar T2 and T3 neurons that are themselves highly sensitive to small static or moving objects, insensitive to wide-field motion and, unlike T4/T5, respond to both ON and OFF luminance steps.

Neurocomputational Lightness Model Explains the Appearance of Real Surfaces Viewed Under Gelb Illumination.

One of the primary functions of visual perception is to represent, estimate, and evaluate the properties of material surfaces in the visual environment. One such property is surface color, which can convey important information about ecologically relevant object characteristics such as the ripeness of fruit and the emotional reactions of humans in social interactions. This paper further develops and applies a neural model (Rudd, 2013, 2017) of how the human visual system represents the light/dark dimension of color-known as lightness-and computes the colors of achromatic material surfaces in real-world spatial contexts. Quantitative lightness judgments conducted with real surfaces viewed under Gelb (i.e., spotlight) illumination are analyzed and simulated using the model. According to the model, luminance ratios form the inputs to ON- and OFF-cells, which encode local luminance increments and decrements, respectively. The response properties of these cells are here characterized by physiologically motivated equations in which different parameters are assumed for the two cell types. Under non-saturating conditions, ON-cells respond in proportion to a compressive power law of the local incremental luminance in the image that causes them to respond, while OFF-cells respond linearly to local decremental luminance. ON- and OFF-cell responses to edges are log-transformed at a later stage of neural processing and then integrated across space to compute lightness via an edge integration process that can be viewed as a neurally elaborated version of Land's retinex model (Land & McCann, 1971). It follows from the model assumptions that the perceptual weights-interpreted as neural gain factors-that the model observer applies to steps in log luminance at edges in the edge integration process are determined by the product of a polarity-dependent factor 1-by which incremental steps in log luminance (i.e., edges) are weighted by the value <1.0 and decremental steps are weighted by 1.0-and a distance-dependent factor 2, whose edge weightings are estimated to fit perceptual data. The model accounts quantitatively (to within experimental error) for the following: lightness constancy failures observed when the illumination level on a simultaneous contrast display is changed (Zavagno, Daneyko, & Liu, 2018); the degree of dynamic range compression in the staircase-Gelb paradigm (Cataliotti & Gilchrist, 1995; Zavagno, Annan, & Caputo, 2004); partial releases from compression that occur when the staircase-Gelb papers are reordered (Zavagno, Annan, & Caputo, 2004); and the larger compression release that occurs when the display is surrounded by a white border (Gilchrist & Cataliotti, 1994).

Audio-Visual Integration in a Redundant Target Paradigm: A Comparison between Rhesus Macaque and Man.

The mechanisms underlying multi-sensory interactions are still poorly understood despite considerable progress made since the first neurophysiological recordings of multi-sensory neurons. While the majority of single-cell neurophysiology has been performed in anesthetized or passive-awake laboratory animals, the vast majority of behavioral data stems from studies with human subjects. Interpretation of neurophysiological data implicitly assumes that laboratory animals exhibit perceptual phenomena comparable or identical to those observed in human subjects. To explicitly test this underlying assumption, we here characterized how two rhesus macaques and four humans detect changes in intensity of auditory, visual, and audio-visual stimuli. These intensity changes consisted of a gradual envelope modulation for the sound, and a luminance step for the LED. Subjects had to detect any perceived intensity change as fast as possible. By comparing the monkeys' results with those obtained from the human subjects we found that (1) unimodal reaction times differed across modality, acoustic modulation frequency, and species, (2) the largest facilitation of reaction times with the audio-visual stimuli was observed when stimulus onset asynchronies were such that the unimodal reactions would occur at the same time (response, rather than physical synchrony), and (3) the largest audio-visual reaction-time facilitation was observed when unimodal auditory stimuli were difficult to detect, i.e., at slow unimodal reaction times. We conclude that despite marked unimodal heterogeneity, similar multisensory rules applied to both species. Single-cell neurophysiology in the rhesus macaque may therefore yield valuable insights into the mechanisms governing audio-visual integration that may be informative of the processes taking place in the human brain.

Pupillary light reflex, receptive field mechanism and correction for retinal position for the assessment of visual discomfort

Light sources causing annoyance or pain produce discomfort glare. Traditional glare metrics fail for non-uniform luminaires. As an alternative, visual discomfort is determined by a model incorporating the centre–surround receptive field mechanism, the pupillary light reflex and a correction for retinal position. The pupil area, controlled by the pupillary light reflex, regulates the retinal illuminance. A centre–surround receptive field, described by a difference of Gaussians, represents the visual signal. A correction according to the Guth position index accounts for the reduction in brightness perception when a light source is moved away from the line of sight. The model is analysed with a forced choice paired comparison experiment involving 17 non-uniform rear projected stimuli with different spatial frequencies and luminance steps. A coefficient of determination of 0.68 between the subjective assessment and the model is obtained. A paired comparison office luminaire experiment and a magnitude estimation experiment involving diffusor luminaires validate the model resulting in a coefficient of determination of 0.86 and 0.81, respectively. By including the pupillary light reflex, receptive field mechanism and a correction for retinal position, the more physiologically justified model is a promising alternative to current, often empirical, glare metrics, especially for non-uniform luminaires.

Lightness computation by the human visual system

A model of achromatic color computation by the human visual system is presented, which is shown to account in an exact quantitative way for a large body of appearance matching data collected with simple visual displays. The model equations are closely related to those of the original Retinex model of Land and McCann. However, the present model differs in important ways from Land and McCann’s theory in that it invokes additional biological and perceptual mechanisms, including contrast gain control, different inherent neural gains for incremental, and decremental luminance steps, and two types of top-down influence on the perceptual weights applied to local luminance steps in the display: edge classification and spatial integration attentional windowing. Arguments are presented to support the claim that these various visual processes must be instantiated by a particular underlying neural architecture. By pointing to correspondences between the architecture of the model and findings from visual neurophysiology, this paper suggests that edge classification involves a top-down gating of neural edge responses in early visual cortex (cortical areas V1 and/or V2) while spatial integration windowing occurs in cortical area V4 or beyond.

Rotating Snakes Illusion-Quantitative Analysis Reveals a Region in Luminance Space With Opposite Illusory Rotation.

The Rotating Snakes Illusion employs patterns with repetitive asymmetric luminance steps forming a “snake wheel.” In the underlying luminance sequence {black, dark grey, white, light grey}, coded as {0, g1, 100, g2}, we varied g1 and g2 and measured illusion strength via nulling: Saccades were performed next to a “snake wheel” that rotated physically; observers adjusted rotation until a stationary percept obtained. Observers performed the perceptual nulling of the seeming rotation reliably. Typical settings for (g1, g2), measured from images by Kitaoka, are around (20%, 60%). Indeed, we found a marked illusion in the region (g1≈{0%–25%}, g2≈{20%–75%}) with a rotation speed of ≈1°/s. Surprisingly, we detected a second “island” around (70%, 95%) with opposite direction of the illusory rotation and weaker illusion. Our quantitative measurements of illusion strength confirmed the optimal luminance choices of the standard snake wheel and, unexpectedly, revealed an opposite rotation illusion.

Editorial: Color Vision Sensation and Perception.

Color vision is one of the most intriguing phenomena of the visual experience and has been the object of study from vision scientists to philosophers of perception. The wavelengths, their intensity and purity are experienced as hue, brightness and saturation based on complex information processing of the light entering the eyes. This special research topic is devoted to covering from basic aspects based on light and retinal processes to perceptual and cognitive mechanisms and their respective applications in clinical settings. The reader will find a series of papers organized in two chapters, one devoted to the more basic phenomena and processing, the other focused on the more cognitive and cultural aspects. The integrative aspect of luminance in color vision starts our journey. Reduction in number of levels of luminance in pseudoisochromatic stimulations affects the chromaticity thresholds measured psychophysically, suggesting interactions between luminance and color in those stimuli with luminance steps lower than seven (Souza et al.). Color sensation was also investigated under low-light levels. Mesopic and scotopic conditions could be considered an interference zone for color vision since rods activities generate physiological interferences in cone-driven retinal chromatic pathways. This review paper keeps us up to date regarding the range and impact of rod–cone interactions on human visual function and performance (Zele and Cao). Clinical applications centered on congenital color blindness end the first chapter. Sensory psychophysical thresholds on the tritanopic color confusion axis were investigated in protanomalous and deuteranomalous subjects (Costa et al.). Reduction in discrimination was found for both types of congenital color blindness, protanomalous and deuteranomalous, but subjects in the latter group showed worse results. Electrophysiological assessments regarding luminance and compound stimuli (luminance plus red-green stimulus) were also evaluated in congenital color blindness subjects. Since compound stimuli elicited small or no response in red-green congenital color blinds, this finding could indicate that the cortical response for compound stimuli in the present experiment was dominated by chromatic contribution (Risuenho et al.). A search for discrimination thresholds addressed using the pseudoisochromatic plates configures a new psychophysical application for the traditional and widely used color test (Jurasevska et al.). Basic perceptual phenomena of Gestalt theories regarding color vision were addressed using figure-ground perception on saturation and contrast polarity modulations. The study conducted by Dresp-Langley and Reeves investigated the lightness dependency of the achromatic loci in color space. The results pointed toward a hitherto undocumented functional role of color saturation in the genesis of form, and in particular figure-ground percepts. Two experiments conducted by Kuriki showed that first, a color-appearance space normalized to daylight may be defined for the human visual system and second, that color space could reduce the discrepancy between the achromatic loci and the lightness axis of the color appearance models. The last study of the perceptual mechanism section relates retinal image quality for the display red and blue pixel radiation with the chromostereopsis retinal disparity achieved (zolinsh and Muizniece). Color is also important from an anthropological view in which a long debate regarding the existence of natural categories of hue and their universality has been addressed by ethological, electrophysiological, behavioral and psychophysical perspectives. The color naming and gender section presents contributions regarding the variations in color naming occurring in congenital color blindness subjects and the gender and cultural aspects related to color preferences. The study of Nagy et al. shows that dichromatic subjects involve the brightness properties of the different spectral stimuli when judging their chromatic content and that at the shorter wavelengths the signal of the intact tritos photoreceptor dominates the decision making in color naming tasks, even for the anopes. Al-Rasheed provides evidence that both sex differences and cultural differences are relevant in hue preference in terms of how stimulus-background cone-contrast was weighted summarizing color preference quantitatively rather than using subjective color names. The question of how we see colors and how we can discuss their impact in many dimensions of our life is an actual and multidiscipline inquiry to which we hope to contribute with this special research topic. Enjoy this special topic on color vision.

Retinex-like computations in human lightness perception and their possible realization in visual cortex

Land and McCann&#x2019;s original Retinex theory [1] described how the brain might achieve color constancy by spatially integrating the outputs of edge detector neurons in visual cortex (i.e., Hubel and Wiesel cells). Given a collection of reflective surfaces, separated by hard edges (a Mondrian stimulus) and viewed under uniform illumination, Retinex first computes luminance ratios at the borders between surfaces, then multiplies these ratios along image paths to compute the relative ratios of noncontiguous surfaces. This multiplication is equivalent to summing steps in log luminance. Here I review results from the human lightness literature supporting the key Retinex assumption that biological lightness computations involve a spatial integration of steps in log luminance. However, to explain perceptual data, the original Retinex algorithm must be supplemented with additional perceptual principles that together determine the weights given to particular image edges. These include: distance-dependent edge weighting, different weights for incremental and decremental luminance steps, contrast gain acting between edges, top-down control of edge weights, and computations in object-centered coordinates. I outline a theory, informed by recent findings from neurophysiology, of how these computations might be carried out by neural circuits in the ventral stream of visual cortex.

Transient twinkle perception is induced by sequential presentation of stimuli that flicker at frequencies above the critical fusion frequency.

The critical fusion frequency (CFF) is a threshold that represents the temporal limits of the human visual system. If two flickering stimuli with equal subjective luminances are presented simultaneously at different locations, the CFF is the temporal frequency above which they cannot be distinguished. However, when the stimuli are presented sequentially at the same position, a transient twinkle can be perceived around the moment of the changeover. To investigate the mechanism underlying this transient twinkle perception (TTP), we independently manipulated the luminance contrast and temporal frequency of the flicker, as well as the interstimulus interval (ISI). We found that TTP was greater as the luminance step was larger, was stably perceived for flicker frequencies up to 200Hz, and was robust for all ISIs if flicker frequencies were below 250Hz. For 250- and 300-Hz flickers, TTP was attenuated in conditions in which one-frame and two-frame ISIs were inserted. These results can be explained by a simple filtering model: TTP occurs if the temporal change in the weighted moving average of stimulus luminance exceeds a certain threshold. TTP gives additional evidence that the human visual system can detect the transient change of flicker stimuli at much higher temporal frequencies than the CFF, by an averaging mechanism of luminance.

Low number of luminance levels in the luminance noise increases color discrimination thresholds estimated with pseudoisochromatic stimuli.

In pseudoisochromatic stimuli the presence of spatial and luminance noise forces the subject to discriminate the target from the background solely on the basis of chromaticity difference. Color-blind subjects may show difficulty to identify the target due to the elimination of borders and brightness clues caused by the luminance and spatial noise. Few studies have fully described the features of pseudoisochromatic stimuli. Fewer investigators have focused their studies in the effects of specific pseudoisochromatic parameters on color discrimination. We used the Cambridge Color Test (CCT) to investigate the influence on color discrimination thresholds due to the number of luminance levels present in the luminance noise. The CCT default has six luminance steps; however, in our investigation a total of eight different conditions were tested from 2 to 16 luminance steps. It was found that the CCT provided very robust values for color discrimination thresholds, which were degraded only for very small number of luminance steps. When the number of steps was increased, the color discrimination thresholds improved from 2 to 6 luminance steps and gradually reached a plateau for 10 or more luminance steps. The area of color discrimination ellipses as a function of luminance steps matches the relative proportion of ineffective contrasts between mosaic patches as a function of luminance steps, assuming that contrast becomes ineffective for values 18.6% or less. The lower number of color and luminance interactions in these conditions could explain the measured increase of color discrimination thresholds. The primary conclusion from this investigation was that results from pseudoisochromatic tests should have their parameters described in more detail. This type of description would allow a better understanding of the results provided, interpretations, and therefore cross study comparison of results obtained from different laboratories.

A cortical edge-integration model of object-based lightness computation that explains effects of spatial context and individual differences.

Previous work has demonstrated that perceived surface reflectance (lightness) can be modeled in simple contexts in a quantitatively exact way by assuming that the visual system first extracts information about local, directed steps in log luminance, then spatially integrates these steps along paths through the image to compute lightness (Rudd and Zemach, 2004, 2005, 2007). This method of computing lightness is called edge integration. Recent evidence (Rudd, 2013) suggests that human vision employs a default strategy to integrate luminance steps only along paths from a common background region to the targets whose lightness is computed. This implies a role for gestalt grouping in edge-based lightness computation. Rudd (2010) further showed the perceptual weights applied to edges in lightness computation can be influenced by the observer's interpretation of luminance steps as resulting from either spatial variation in surface reflectance or illumination. This implies a role for top-down factors in any edge-based model of lightness (Rudd and Zemach, 2005). Here, I show how the separate influences of grouping and attention on lightness can be modeled in tandem by a cortical mechanism that first employs top-down signals to spatially select regions of interest for lightness computation. An object-based network computation, involving neurons that code for border-ownership, then automatically sets the neural gains applied to edge signals surviving the earlier spatial selection stage. Only the borders that survive both processing stages are spatially integrated to compute lightness. The model assumptions are consistent with those of the cortical lightness model presented earlier by Rudd (2010, 2013), and with neurophysiological data indicating extraction of local edge information in V1, network computations to establish figure-ground relations and border ownership in V2, and edge integration to encode lightness and darkness signals in V4.

Rotating Snakes Illusion - Quantitative analysis reveals islands in luminance space with opposite illusory rotation

The "Rotating Snakes" illusion is based on patterns with repeated asymmetric luminance steps, arranged in concentric bands forming a "snake wheel". In the underlying luminance sequence "black – darker grey (g1) – white – lighter grey (g2)" we varied the luminances of g1 and g2, and measured illusion strength via a nulling task: On a gamma-corrected VDU, repetitive saccades were performed passing a "snake wheel" that physically rotated, and the participants adjusted rotation direction and speed until a stationary percept obtained. We found that our participants performed perceptual nulling (in the range of ± 1°/s) of the seeming rotation quite reliably and convincingly; when the gaze was directed to the center of the wheel after null-adjustment, the actual rotation could be quite surprising (depending on the levels [g1, g2]). Typical settings for [g1, g2] as measured from images by A. Kitaoka, are around [20%, 60%]. Indeed, we found a marked illusion in an "island" region [g1≈{0–25%}, g2≈{20–75%}]. Unexpectedly, we detected a second island around [60%, 90%] with opposite rotation direction, although the relative order of g1 and g2 stayed the same. Furthermore, there was also some rotation illusion when altogether only 3 luminance levels were visible, e.g.: 0–0–50–100%. These quantitative measurements of illusion strength have revealed new phenomena in this illusion, which challenge the two explanatory models put forth so far. Meeting abstract presented at VSS 2014

Edge integration in achromatic color perception and the lightness-darkness asymmetry

To maintain color constancy, the human visual system must distinguish surface reflectance-based variations in wavelength and luminance from variations due to illumination. Edge integration theory proposes that this is accomplished by spatially integrating steps in luminance and color contrast that likely result from reflectance changes. Thus, a neural representation of relative reflectance within the visual scene is constructed. An anchoring rule-the largest reflectance in the neural representation appears white-is then applied to map relative lightness onto an absolute lightness scale. A large body of data on human lightness judgments is here shown to be consistent with an edge integration model in which the visual system performs a weighted sum of steps in log luminance across space. Three hypotheses are proposed regarding how weights are applied to edges. First, weights decline with distance from the target surface whose lightness is being computed. Second, larger weights are given to edges whose dark sides point towards the target. Third, edge integration is carried out along a path leading from a common background field, or surround, to the target location. The theory accounts for simultaneous contrast; quantitative lightness judgments made with classical disk-annulus, Gilchrist dome, and Gelb displays; and perceptual filling-in lightness. A cortical theory of lightness in the ventral stream of visual cortex (areas V1 → V4) is proposed to instantiate the edge integration algorithm. The neural model is shown to be capable of unifying the quantitative laws of edge integration in lightness perception with the laws governing brightness, including Stevens' power law brightness model, and makes novel predictions about the quantitative laws governing induced darkness.

Some Insights into Why the Perception of Mach Bands is Strong for Luminance Ramps and Weak or Vanishing for Luminance Steps

In this paper we present some demonstrations concerning the width of Mach bands and henceforth hypothesize certain relations. We show that it is the variation in width of Mach bands in relation to luminance gradients which is responsible for Mach bands being strong for luminance ramps and weak or vanishing for luminance steps. We present the results of the experiments carried out by us using some of these demonstrations to provide support for our claims.

MATE1 has an external COOH terminus, consistent with a 13-helix topology

The mammalian members of the Multidrug And Toxin Extruder family, i.e., MATE1 and MATE2-K, are suspected of mediating the luminal step in renal secretion of organic cations. The 1,000+ prokaryotic/fungal/plant MATE family members are predicted to have 12 transmembrane helices (TMHs), whereas MATE1/2-K appear to have an additional (13th) COOH-terminal helix. Here, we determined whether rabbit MATE1 has an external COOH terminus, consistent with the presence of 13 TMHs. A V5 epitope tag at the COOH terminus of MATE1 was freely accessible to external V5 antibody, whereas tags at the NH(2) terminus, or at sites of truncation within the long cytoplasmic loop between predicted TMHs 12 and 13, were only accessible to the V5 antibody following permeabilization of the membrane. The truncated mutants that lacked TMH13 still retained transport activity, indicating that the terminal helix was not necessary for transport function. Cells that expressed a mutant lacking only TMH13 displayed similar K(t) and J(max) values to those of the full-length protein, although when normalized to protein expressed at the plasma membrane, the transport rate of the mutant was <10% that of full-length MATE1. An effectively cysteine-less MATE1 mutant (Delta13Cys) was functional and refractory to reaction with the impermeant marker of accessible cysteine residues, maleimide-PEO(2)-biotin. Delta13Cys mutants with an added cysteine residue at the truncation sites within the terminal cytoplasmic loop reacted with maleimide biotin only after permeabilization of the membrane, whereas a mutant with a cysteine residue at the COOH terminus was freely accessible to maleimide biotin. These data are consistent with a mammalian MATE topology that includes 13 TMHs and indicate that the terminal TMH, although not necessary for transport function, may influence the turnover characteristics of the transporter.