The meaning of the Weber-Fechner law: IV. The psychometric curve and interhemispheric and intrahemispheric interactions

A subject was presented two horizontal lines. One of them was an objective reference line (Ro), whose length was unchanged. There were a total of five Ro lines. The other line was a test line (T), whose length varied. The subject had to say whether the longer line was above or below the shorter one. The results were treated using a model of neuronal constructions consisting of a number of similar constructions fulfilling different functions along the route from inputting information to obtaining Weber’s ΔL/L ratio. Psychometric curves and the reference stimulus (Rs) as their derivative were determined at the initial stage. In this case, Rs≠Ro. At the final stage of simulation, Rs = Ro. The Weber-Fechner fraction was calculated using the standard formula (T - Ro)/Ro. The same initial data introduced to the model yielded a curve entirely coinciding with the curve calculated experimentally. At the final stage of stimulation, Rs and Ro were equal to each other. Their inequality at the initial stages was necessary for calculating the mutual positions of the elements of a scene. It was concluded that the model constructions are similar to real neuronal constructions of the visual brain.     

The meaning of the Weber-Fechner law and description of scenes in terms of neural networks

An attempt was made to determine to which functions of the visual cortex the Weber-Fechner law pertains. Pairs of lines were presented in different halves of the visual field. One of them was a reference line with an unchanged length, and the other (the test line) was of variable length. Psychometric curves reflecting the probability of the answer that the test line was longer than the reference one were plotted. A neuronal scheme for calculating the subjective reference stimulus, which differed from the objective reference stimulus, was proposed. The central zone of the visual field was determined. Two psychometric curves were obtained in the zone of each hemisphere. One of them was based on the results of tests where the test stimulus was presented above the reference stimulus and the other, on those where the test stimulus was below the reference one. The mutual positions of the curves were asymmetric in the hemispheres. One psychometric curve was obtained outside the central zone in each hemisphere. There was no dependence on the positions of the test and reference stimuli. The obtained data, according to which ΔL = const in the central zone and ΔL/L = const outside it, served as the basis for postulating the existence of three neuronal mechanisms. One of them is responsible for the interaction of neural networks between the hemispheres and serves for describing the scene, estimating the perspective, and determining the relative distances between objects. The second and third mechanisms are responsible for the interactions within the left and right hemispheres and serve only for describing the scene. Only the mechanism of describing the scene operates outside the central zone. It is assumed that the three postulated mechanisms, together with the mechanism of image recognition, create the visual image of the world perceived by the brain.     

The meaning of the Weber-Fechner Law IV. The psychometric curve, the interaction between inter hemisphere and the interaction in intrahemisphere

The subject was presented with a pair of lines. One line was an objective referent line Ro and did not change its length. The other was a test line and changed the its length. The observer must report--where the longer line was--above or below in the pair. On the basis neurophysiological, psychophysical data and new type of the psychometrical curve a complex neuronal construction was built. The comparison of action of the neuronal construction with the psychophysical data on different stages of introduction the visual information showed that in both cases at first stages of introduction the information referent subjective stimulus Rs is not equal to Ro. But at the last stages, when Weber's fraction is obtained Rs = Ro. This result allows to suggest that the suggested neuronal contraction is near to the real constriction of the visual brain.     

Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex

Whether cognitive representations are better conceived as language-based, symbolic representations or perceptually related, analog representations is a subject of debate. If cognitive processes parallel perceptual processes, then fundamental psychophysical laws should hold for each. To test this, we analyzed both behavioral and neuronal representations of numerosity in the prefrontal cortex of rhesus monkeys. The data were best described by a nonlinearly compressed scaling of numerical information, as postulated by the Weber-Fechner law or Stevens' law for psychophysical/sensory magnitudes. This nonlinear compression was observed on the neural level during the acquisition phase of the task and maintained through the memory phase with no further compression. These results suggest that certain cognitive and perceptual/sensory representations share the same fundamental mechanisms and neural coding schemes.     

On the laws of psychophysics

Experiments by S. S. Stevens (Stevens, 1957, and Stevens and Galanter, 1957) and his collaborators indicate that the so-called logarithmic Weber-Fechner Law is not realized in most human perceptions. Instead, a power law seems to emerge over a large number of sensory continua. This is important because for a long time the logarithmic law was looked upon as almost the only possible psychophysical law. The logarithmic law appeared desirable intuitively because it made the sensation depend on the relative values of the stimuli and not on their absolute values. This is, of course, useful for evolutionary reasons. Some other reasons are also discussed by Stevens (1961).     

Genetic control of fruit shape acts prior to anthesis in melon (Cucumis melo L.)

Genetic control of fruit shape in Cucumis melo was studied using QTL analysis in two Recombinant Inbred (RI) populations consisting of 163 and 63 individuals, respectively, obtained by crossing the same round-fruited parent with two different elongated-fruit lines. Fruit shape is mainly explained by fruit length in these two populations. Most QTLs for fruit shape and ovary shape detected were found to co-segregate, thus demonstrating early control of fruit shape during ovary development. A high level of correlation between fruit shape and ovary shape was also found in 14 unrelated genetic lines, a finding which suggests that control of fruit shape by gene(s) active early in the ovary is a general feature in C. melo. Two major flower genes, a ( monoecious) and p ( pentamerous), were shown to have major effects on fruit shape. Major tightly linked QTLs for fruit and ovary shape were found close to the a and p genes, probably reflecting their pleiotropic effect on fruit shape. Moreover, one of the two QTLs detected in the Védrantais x PI 414723 population was also found in the Védrantais x PI 161375 population. Variation of fruit shape in melon could be due to variations having quantitative effects on a large set of genes that are probably involved in ovary development.     

Induction and rejoining of DNA double-strand breaks in human cervix carcinoma cell lines of differing radiosensitivity

Five recently established cell lines of human carcinoma of the cervix of varying radiosensitivity have been used to determine whether the induction or rejoining of DNA double-strand breaks (dsb) shows any correlation with radiosensitivity or radiation recovery capacity. Double-strand DNA breaks have been measured using neutral filter elution at pH 9.6. The number of breaks induced immediately after irradiation with doses of 10 to 40 Gy 60Co gamma rays appeared to show some correlation with radiosensitivity particularly after 10 Gy; the two more radiosensitive lines incurred more breaks than the more radioresistant lines. In addition, the shape of the induction curve with dose was linear for the two sensitive lines but curvilinear for the resistant lines. Despite the dose scales being different, this mirrored their respective cell survival curve shapes. After 30 or 50 Gy irradiation, rejoining of breaks appeared to be rapid and almost complete within 60 min at 37 degrees C for the three resistant lines. However, for the sensitive lines, one line (HX160c) in particular exhibited a reduced rate of dsb rejoining. In addition, a residual level of dsb was present in this line even after allowing rejoining for 3 h. While induction and rejoining of DNA dsb therefore appears to be a factor in determining radiosensitivity, at doses relevant to cellular survival (up to 10 Gy), the greater induction of DNA dsb in radiosensitive lines may play a significant role in determining the cellular response to ionizing radiation.     

A teleological explanation of Weber's law and the motor unit size law

It is shown that the Weber-Fechner law. which relates the response of a sensory biosystem to the intensity of the input stimulus, can be derived from a teleological principle of minimum transentropy (maximal noise reduction) provided the relative mean fluctuation (coefficient of variation) of the input intensity can be assumed to be (approximately) constant for all feasible mean input intensities. A law is then deduced from experimental results which quantifies the relationship existing between the relative amount of activated muscle mass and the “size” (which term is clearly defined) of a newly recruited motor unit. This law is found to be formally equivalent to the Weber-Fechner law when applied to motor unit recruitment. It is then shown that, in general, the ratio of the force increment upon recruitment, to the present force output does not obey Weber's law. Finally, it is proved that the “motor unit size law” as derived in this paper implies a fixed sequential order in the recruitment of motor units and that it may be viewed as the realization, by the mammalian neuromuscular system, of a general principle of maximum grading sensitivity.     

Shape and size of the human diaphragm in vivo

Serial computerized tomograph (CT) sections at 5-mm intervals of a human diaphragm in relaxed and contracted states were obtained in one subject while he held his breath and lay supine in a CT scanner. All sections for one state were scanned at the same chest wall configuration as monitored by rib cage and abdominal dimensions, using magnetometers. Sections were scanned at relaxed functional residual capacity and after inspiring approximately 1 liter in such a way that rib cage dimensions increased only slightly. Models of the diaphragm dome in the two states were constructed from the sets of serial sections. Diaphragm length and volume displaced were measured, the zone of apposition of diaphragm to rib cage was mapped, and the line of the diaphragm silhouette in anteroposterior and lateral X-rays identified. Coronal and sagittal sections were constructed. In the inspiration studied, the diaphragm movement displaced 680 ml. Meridian lines in sagittal, coronal, and transverse directions over the right hemidiaphragm dome shortened by 6.7-7.2 cm, but over the left dome by only 4.0-4.3 cm. Lines of X-ray silhouettes were close to meridian lines, and estimates of shortening were similar to those made previously from X-rays. The peculiar saddle shape of the muscle may help the hemidiaphragms to operate independently, the fibers of the saddle acting as an anchor for midline directed fibers of the hemidiaphragm domes. The shape of the diaphragm also has implications for the distribution of transdiaphragmatic pressure and for the kind of distortion of the lower rib cage margin that is seen during inspirations at high lung volume.     

Genetic Variation in the Shape of the Mouse Mandible and Its Relationship to Glucocorticoid-Induced Cleft Palate Analyzed by Using Recombinant Inbred Lines

Variation in mandible shape has been investigated in a set of recombinant inbred (RI) lines of mice, the C57BL/6J X A/J (BXA;AXB) RI lines. Considerable genetic variation was detected between the RI lines, but most lines were intermediate in shape when compared with the parent lines. Variation in mandible shape could not be explained by any single gene differences known between the parent lines including the H-2 locus. Some RI lines had mandible shapes unlike either parent, and one in particular, line BXA1, had an unusual shape with a pronounced condyloid process. It was concluded that mandible shape has a complex inheritance involving a number of genes, each with small effects. In some cases, recombination of the genes can produce bone shapes quite different from those of the original parent line.--There was no evidence that the variability in steroid-induced cleft palate incidence in the BXA;AXB RI lines is related to the variation in adult mandible shape as detected in this study.     

Do alignment thresholds define a critical boundary in long-range detection facilitation with co-linear lines?

Thresholds for line contrast detection (experiment 2) were measured with a two-alternative temporal forced-choice procedure as a function of the spatial position of a vertical target line with regard to two co-linear context lines. The different spatial positions of the target line corresponded to values near the position discrimination threshold (experiment 1) reflecting the just detectable lateral offset, or non-co-linearity, between the context lines which were vertically separated by about 100 minutes of visual arc. Target and context lines were vertically separated by about 30 minutes of arc, had equal contrast polarity in one case, and opposite contrast polarity in the other. Strong line contrast detection facilitation is found at perceptually co-linear target locations. This facilitation decreases noticeably at a horizontal target offset that corresponds to the alignment threshold measured with the context lines. The effects are independent of the relative contrast polarity of target and context and, as shown in a third experiment, also independent of both the relative length or number of lines, and the magnitude of their absolute co-axial separation. This independence seems to hold, provided individual line length and co-axial distance between lines are larger than what appears to be the lower limit of the long-range spatial domain for orientation or contour integration (i.e. 20 minutes of arc), as determined by previous studies. The findings reported here suggest that alignment thresholds are likely to define a critical lateral boundary in long-range detection facilitation with co-linear lines. They support models of contour integration based on interactions between neural mechanisms that integrate local signals of contrast, orientation, and relative position or end-to-end alignment. Such mechanisms may help to explain the formation of representations of virtual contours and object contours in human perception.     

Thermal phenotypic plasticity of body size in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis>: sexual dimorphism and genetic correlations

Thirty isofemale lines collected in three different years from the same wild French population were grown at seven different temperatures (12–31°C). Two linear measures, wing and thorax length, were taken on 10 females and 10 males of each line at each temperature, also enabling the calculation of the wing/thorax (W/T) ratio, a shape index related to wing loading. Genetic correlations were calculated using family means. The W–T correlation was independent of temperature and on average, 0.75. For each line, characteristic values of the temperature reaction norm were calculated, i.e. maximum value, temperature of maximum value and curvature. Significant negative correlations were found between curvature and maximum value or temperature of maximum value. Sexual dimorphism was analysed by considering either the correlation between sexes or the female/male ratio. Female–male correlation was on average 0.75 at the within line, within temperature level but increased up to 0.90 when all temperatures were averaged for each line. The female/male ratio was genetically variable among lines but without any temperature effect. For the female/male ratio, heritability (intraclass correlation) was about 0.20 and evolvability (genetic coefficient of variation) close to 1. Although significant, these values are much less than for the traits themselves. Phenotypic plasticity of sexual dimorphism revealed very similar reaction norms for wing and thorax length, i.e. a monotonically increasing sigmoid curve from about 1.11 up to 1.17. This shows that the males are more sensitive to a thermal increase than females. In contrast, the W/T ratio was almost identical in both sexes, with only a very slight temperature effect.     

Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.     

ARTIFICIAL SELECTION ON HORN LENGTH-BODY SIZE ALLOMETRY IN THE HORNED BEETLE ONTHOPHAGUS ACUMINATUS (COLEOPTERA: SCARABAEIDAE)

Males of the horned beetle Onthophagus acuminatus Har. (Coleoptera: Scarabaeidae) exhibit horn length dimorphism due to a sigmoidal allometric relationship between horn length and body size: the steep slope of the allometry around the inflection of the sigmoid curve separates males into two groups; those larger than this inflection possess long horns, and those smaller than this inflection have short horns or lack horns. I examined the genetic basis of the allometric relationship between horn length and body size by selecting males that produced unusually long horns, and males that produced unusually short horns, for their respective body sizes. After seven generations of selection, lines selected for relatively long horns had significantly longer horn lengths for a given body size than lines selected for relatively short horns, indicating a heritable component to variation in the allometry. The sigmoidal shape of the allometry was not affected by this selection regime. Rather, selected lines differed in the position of the allometry along the body size axis. One consequence of lateral shifts in this allometric relationship was that the body size separating horned from hornless males (the point of inflection of the sigmoid curve) differed between selection lines: lines in which males were selected for relatively long horns began horn production at smaller body sizes than lines selected for relatively short horns. These results suggest that populations can evolve in response to selection on male horn length through modification of the growth relationship between horn length and body size.     

DNA fingerprinting of human cell lines using PCR amplification of fragment length polymorphisms

Summary Methods for monitoring cell line identification and authentication include species-specific immunofluorescence, isoenzyme phenotyping, chromosome analysis, and DNA fingerprinting. Most previous studies of DNA fingerprinting of cell lines have used restriction fragment length polymorphism analysis. In this study, we examined the utility of an alternative and simpler method of cell line DNA fingerprinting—polymerase chain reaction (PCR) amplification of fragment length polymorphisms. Fourteen human cell lines previously found by other methods to be either related or disparate were subjected to DNA fingerprinting by PCR amplification of selected fragment length polymorphism loci. Cell identification patterns by this method were concordant with those obtained by isoenzyme phenotyping and restriction fragment length polymorphism-DNA fingerprinting, and were reproducible within and between assays on different DNA extracts of the same cell line. High precision was achieved with electrophoretic separation of amplified DNA products on high resolution agarose or polyacrylamide gels, and with fragment length polymorphism (FLP) loci-specific “allelic ladders” to identify individual FLP alleles. Determination of the composite fingerprint of a cell line at six appropriately chosen fragment length polymorphism loci should achieve a minimum discrimination power of 0.999. The ability of PCR-based fragment length polymorphism DNA fingerprinting to precisely and accurately identify the alleles of different human cell lines at multiple polymorphic fragment length polymorphism loci demonstrates the feasibility of developing a cell line DNA fingerprint reference database as a powerful additional tool for future cell line identification and authentication.     

Studies in the dynamics of disinfection: IV. The reaction between phenol and Bact. coli: the true shape of the probit-log survival-time curve

The results of numerous experiments on the disinfection of standard cultures of Bact. coli with phenol, under rigidly controlled conditions, have been combined and used to elucidate the true shape of the probit-log survival-time curve. It is concluded that the true shape is that of a very asymmetrical sigmoid curve. When the disinfection is slow, the curve approximates closely to a bilinear form with one line of small and one of large slope up to high probit values, but in faster disinfections the curvature of the steeper line is evident, especially above the probit value of 8.     

fs3.1: a major fruit shape QTL conserved in Capsicum.

fs3.1 is a major fruit shape (defined as the ratio of fruit length to fruit width) quantitative trait locus (QTL) originally detected in an intraspecific cross of Capsicum annuum between the blocky and elongated-fruited inbreds 'Maor' and 'Perennial', respectively. In addition to increasing fruit shape index, the 'Perennial' allele at fs3.1 increased fruit elongation and decreased fruit width and pericarp thickness. We verified the effect of fs3.1 in backcross inbred lines (BILs) derived from crossing 'Perennial' with 'Maor' and with a second blocky-type inbred line of C. annuum. To determine the effect of the fs3.1 region in additional Capsicum species, we constructed an advanced backcross population from the cross of 'Maor' and the oval-fruited Capsicum frutescens BG 2816 and an F2 of the introgression line IL 152 that contains an introgression of the fs3.1 region from Capsicum chinense PI 152225. QTLs for fruit shape, fruit width, and pericarp thickness, but not for fruit length, were detected in both crosses, indicating the conservation of the fs3.1 region as a QTL affecting fruit shape in pepper. We also tested tomato (Lycopersicon spp.) introgression lines containing the corresponding fs3.1 region from L. pennellii and L. hirsutum, but we did not detect a significant fruit shape QTL in these lines. The effect of fs3.1 on the growth of fruit dimensions varied with the genetic background. By measuring the length and width of ovaries and fruits of near-isogenic C. annuum lines that differ in fs3.1 during fruit development, we determined that fs3.1 controls shape predominantly by increasing the growth rate of the longitudinal axis in the first 2 weeks after pollination. However, in the crosses of C. annuum with C. frutescens and C. chinense, fs3.1 predominantly exerted its effect on the width dimension.     

An evaluation of some morphological traits in doubled haploid lines and their F1 hybrids of head cabbage Kamienna Głowa in the vegetative phase

The internal stump length, head mass and head shape of doubled haploid (DH) lines and their F1 hybrids of head cabbage Kamienna G?owa were compared. It was found that the range of variation in the investigated traits of DH lines was higher than that of their F1 hybrids. The head mass of the DH lines indicated some level of inbreeding depression, but their F1 hybrids showed a significant effect of heterosis. Genes responsible for flattened head shape were dominant over rounded shape genes. The longer internal stump trait was dominant over the shorter one.     

Patterns of variation in wing morphology in the cactophilic Drosophila buzzatii and its sibling D. koepferae

Drosophila buzzatii and D. koepferae are two sibling species that breed on the necrotic tissues of several cactus species and show a certain degree of niche overlap. Also, they show differences in several life history traits, such as body size and developmental time, which probably evolved as a consequence of adaptation to different host plants. In this work we investigate the ecological and genetic factors affecting wing morphology variation both within and between species. Three wing traits were scored, distal and proximal wing length and width in isofemale lines reared in two of the most important host cacti: Opuntia sulphurea and Trichocereus terschekii. Our results revealed that differences between species and sexes in wing size and shape were significant, whereas the cactus factor was only significant for wing size. Intraspecific analyses showed that differences among isofemale lines were highly significant for both size and shape in both species, suggesting that an important fraction of variation in wing morphology has a genetic basis. Moreover, the line by cactus interaction, which can be interpreted as a genotype by environment interaction, also accounted for a significant proportion of variation. In summary, our study shows that wing size is phenotypically plastic and that populations of D. buzzatii and D. koepferae harbour substantial amounts of genetic variation for wing size and shape. Interspecific differences in wing size and shape are interpreted in terms of spatial predictability of the different host plants in nature.