Visual perception and imagery: A new molecular hypothesis

Here, we put forward a redox molecular hypothesis about the natural biophysical substrate of visual perception and visual imagery. This hypothesis is based on the redox and bioluminescent processes of neuronal cells in retinotopically organized cytochrome oxidase-rich visual areas. Our hypothesis is in line with the functional roles of reactive oxygen and nitrogen species in living cells that are not part of haphazard process, but rather a very strict mechanism used in signaling pathways. We point out that there is a direct relationship between neuronal activity and the biophoton emission process in the brain. Electrical and biochemical processes in the brain represent sensory information from the external world. During encoding or retrieval of information, electrical signals of neurons can be converted into synchronized biophoton signals by bioluminescent radical and non-radical processes. Therefore, information in the brain appears not only as an electrical (chemical) signal but also as a regulated biophoton (weak optical) signal inside neurons.     

Emergence and transmission of visual awareness through optical coding in the brain: A redox molecular hypothesis on visual mental imagery

Does the primary visual cortex mediate consciousness for higher-level stages of information processing by providing an outlet for mental imagery? Evidence based on neural electrical activity is inconclusive as reflected in the “imagery debate” in cognitive science. Neural information and activity, however, also depend on regulated biophoton (optical) signaling. During encoding and retrieval of visual information, regulated electrical (redox) signals of neurons are converted into synchronized biophoton signals by bioluminescent radical processes. That is, visual information may be represented by regulated biophotons of mitochondrial networks in retinotopically organized cytochrome oxidase-rich neural networks within early visual areas. Therefore, we hypothesize that regulated biophotons can generate intrinsic optical representations in the primary visual cortex and then propagate variably degraded versions along cytochrome oxidase pathways during both perception and imagery. Testing this hypothesis requires to establish a methodology for measurement of in vivo and/or in vitro increases of biophoton emission in humans' brain during phosphene inductions by transcranial magnetic stimulation and to compare the decrease in phosphene thresholds during transcranial magnetic stimulation and imagery. Our hypothesis provides a molecular mechanism for the visual buffer and for imagery as the prevalent communication mode (through optical signaling) within the brain. If confirmed empirically, this hypothesis could resolve the imagery debate and the underlying issue of continuity between perception and abstract thought.     

Implications on visual apperception: Energy, duration, structure and synchronization

Although primary visual cortex (V1 or striate) activity per se is not sufficient for visual apperception (normal conscious visual experiences and conscious functions such as detection, discrimination, and recognition), the same is also true for extrastriate visual areas (such as V2, V3, V4/V8/VO, V5/M5/MST, IT, and GF). In the lack of V1 area, visual signals can still reach several extrastriate parts but appear incapable of generating normal conscious visual experiences. It is scarcely emphasized in the scientific literature that conscious perceptions and representations must have also essential energetic conditions. These energetic conditions are achieved by spatiotemporal networks of dynamic mitochondrial distributions inside neurons. However, the highest density of neurons in neocortex (number of neurons per degree of visual angle) devoted to representing the visual field is found in retinotopic V1. It means that the highest mitochondrial (energetic) activity can be achieved in mitochondrial cytochrome oxidase-rich V1 areas. Thus, V1 bear the highest energy allocation for visual representation.In addition, the conscious perceptions also demand structural conditions, presence of adequate duration of information representation, and synchronized neural processes and/or ‘interactive hierarchical structuralism.’ For visual apperception, various visual areas are involved depending on context such as stimulus characteristics such as color, form/shape, motion, and other features. Here, we focus primarily on V1 where specific mitochondrial-rich retinotopic structures are found; we will concisely discuss V2 where smaller riches of these structures are found. We also point out that residual brain states are not fully reflected in active neural patterns after visual perception. Namely, after visual perception, subliminal residual states are not being reflected in passive neural recording techniques, but require active stimulation to be revealed.     

Increase of Universality in Human Brain during Mental Imagery from Visual Perception

Background

Different complex systems behave in a similar way near their critical points of phase transitions which leads to an emergence of a universal scaling behaviour. Universality indirectly implies a long-range correlation between constituent subsystems. As the distributed correlated processing is a hallmark of higher complex cognition, I investigated a measure of universality in human brain during perception and mental imagery of complex real-life visual object like visual art.

Methodology/Principal Findings

A new method was presented to estimate the strength of hidden universal structure in a multivariate data set. In this study, I investigated this method in the electrical activities (electroencephalogram signals) of human brain during complex cognition. Two broad groups - artists and non-artists - were studied during the encoding (perception) and retrieval (mental imagery) phases of actual paintings. Universal structure was found to be stronger in visual imagery than in visual perception, and this difference was stronger in artists than in non-artists. Further, this effect was found to be largest in the theta band oscillations and over the prefrontal regions bilaterally.

Conclusions/Significance

Phase transition like dynamics was observed in the electrical activities of human brain during complex cognitive processing, and closeness to phase transition was higher in mental imagery than in real perception. Further, the effect of long-term training on the universal scaling was also demonstrated.     

Photon Hunting in the Twilight Zone: Visual Features of Mesopelagic Bioluminescent Sharks

The mesopelagic zone is a visual scene continuum in which organisms have developed various strategies to optimize photon capture. Here, we used light microscopy, stereology-assisted retinal topographic mapping, spectrophotometry and microspectrophotometry to investigate the visual ecology of deep-sea bioluminescent sharks [four etmopterid species (Etmopterus lucifer, E. splendidus, E. spinax and Trigonognathus kabeyai) and one dalatiid species (Squaliolus aliae)]. We highlighted a novel structure, a translucent area present in the upper eye orbit of Etmopteridae, which might be part of a reference system for counterillumination adjustment or acts as a spectral filter for camouflage breaking, as well as several ocular specialisations such as aphakic gaps and semicircular tapeta previously unknown in elasmobranchs. All species showed pure rod hexagonal mosaics with a high topographic diversity. Retinal specialisations, formed by shallow cell density gradients, may aid in prey detection and reflect lifestyle differences; pelagic species display areae centrales while benthopelagic and benthic species display wide and narrow horizontal streaks, respectively. One species (E. lucifer) displays two areae within its horizontal streak that likely allows detection of conspecifics'' elongated bioluminescent flank markings. Ganglion cell topography reveals less variation with all species showing a temporal area for acute frontal binocular vision. This area is dorsally extended in T. kabeyai, allowing this species to adjust the strike of its peculiar jaws in the ventro-frontal visual field. Etmopterus lucifer showed an additional nasal area matching a high rod density area. Peak spectral sensitivities of the rod visual pigments (λ_max) fall within the range 484–491 nm, allowing these sharks to detect a high proportion of photons present in their habitat. Comparisons with previously published data reveal ocular differences between bioluminescent and non-bioluminescent deep-sea sharks. In particular, bioluminescent sharks possess higher rod densities, which might provide them with improved temporal resolution particularly useful for bioluminescent communication during social interactions.     

The effects of reversible freezing inactivation and inhibitor binding on redox properties of l-amino-acid oxidase

We measured the redox potentials of frozen inactivated l-amino-acid oxidase (l-amino-acid:oxygen oxidoreductase (deaminating), EC 1.4.3.2) and inhibitor-bound (anthranilic acid) enzyme, and compared these redox properties to those of active l-amino-acid oxidase and benzoate-bound d-amino-acid oxidase (EC 1.4.3.3), respectively. The redox properties of the inactive enzyme are similar to the properties of free flavin; the potential is within 0.015 V of free flavin and no radical stabilization is seen. This corresponds to the loss of most interactions between apoprotein and flavin. In contrast, the anthranilic acid lowers the amount of radical stabilized from 85% to 35%. The potentials are still 0.150 V positive of free flavin, indicating that in the presence of inhibitor, many flavin-protein interactions remain intact. The difference between this behavior and that of d-amino-acid oxidase bound to benzoate, where the amount of radical declined from 95% to 5%, is explained on the basis of the relative tightness of binding of apoprotein to FAD. d-Amino-acid oxidase apoprotein has a relatively low K_a (10⁶) for FAD, and benzoate has a relatively high K_a (10⁵) for the enzyme. Therefore, the binding of benzoate increases the tightness of FAD binding to apo-d-amino-acid oxidase (10¹¹), indicating significant changes in flavin-protein interactions. In contrast, apo-l-amino-acid oxidase binds flavin tightly (the K_a is greater than 10⁷) and the enzyme binds to anthranilate much less tightly, with a K_a of 10³. The l-amino-acid oxidase apoprotein binding to FAD is tight initially, and the binding of anthranilate changes it only slightly. Therefore, redox studies indicate that the ability of a flavoprotein to be regulated may be influenced by the strength of the interaction of flavin with the apoprotein, as well as the strength of interaction of the substrate or activator.     

Occurrence and Expression of Luminescence in Vibrio cholerae

Several species of the genus Vibrio, including Vibrio cholerae, are bioluminescent or contain bioluminescent strains. Previous studies have reported that only 10% of V. cholerae strains are luminescent. Analysis of 224 isolates of non-O1/non-O139 V. cholerae collected from Chesapeake Bay, MD, revealed that 52% (116/224) were luminescent when an improved assay method was employed and 58% (130/224) of isolates harbored the luxA gene. In contrast, 334 non-O1/non-O139 V. cholerae strains isolated from two rural provinces in Bangladesh yielded only 21 (6.3%) luminescent and 35 (10.5%) luxA⁺ isolates. An additional 270 clinical and environmental isolates of V. cholerae serogroups O1 and O139 were tested, and none were luminescent or harbored luxA. These results indicate that bioluminescence may be a trait specific for non-O1/non-O139 V. cholerae strains that frequently occur in certain environments. Luminescence expression patterns of V. cholerae were also investigated, and isolates could be grouped based on expression level. Several strains with defective expression of the lux operon, including natural K variants, were identified.     

Online Classification of Multiple Motor Imagery Tasks Using Filter Bank Based Maximum-a-Posteriori Common Spatial Pattern Filters

ObjectiveThe main objective of this paper is to propose a novel technique, called filter bank maximum a-posteriori common spatial pattern (FB-MAP-CSP) algorithm, for online classification of multiple motor imagery activities using electroencephalography (EEG) signals. The proposed technique addresses the overfitting issue of CSP in addition to utilizing the spectral information of EEG signals inside the framework of filter banks while extending it to more than two conditions.Materials and methodsThe classification of motor imagery signals is based upon the detection of event-related de-synchronization (ERD) phenomena in the μ and β rhythms of EEG signals. Accordingly, two modifications in the existing MAP-CSP technique are presented: (i) The (pre-processed) EEG signals are spectrally filtered by a bank of filters lying in the μ and β brainwave frequency range, (ii) the framework of MAP-CSP is extended to deal with multiple (more than two) motor imagery tasks classification and the spatial filters thus obtained are calculated for each sub-band, separately. Subsequently, the most imperative features over all sub-bands are selected and un-regularized linear discriminant analysis is employed for classification of multiple motor imagery tasks.ResultsPublicly available dataset (BCI Competition IV Dataset I) is used to validate the proposed method i.e. FB-MAP-CSP. The results show that the proposed method yields superior classification results, in addition to be computationally more efficient in the case of online implementation, as compared to the conventional CSP based techniques and its variants for multiclass motor imagery classification.ConclusionThe proposed FB-MAP-CSP algorithm is found to be a potential / superior method for classifying multi-condition motor imagery EEG signals in comparison to FBCSP based techniques.     

Molecular electronics in pinnae of Mimosa pudica

Bioelectrochemical circuits operate in all plants including the sensitive plant Mimosa pudica Linn. The activation of biologically closed circuits with voltage gated ion channels can lead to various mechanical, hydrodynamical, physiological, biochemical and biophysical responses. Here the biologically closed electrochemical circuit in pinnae of Mimosa pudica is analyzed using the charged capacitor method for electrostimulation at different voltages. Also the equivalent electrical scheme of electrical signal transduction inside the plant''s pinna is evaluated. These circuits remain linear at small potentials not exceeding 0.5 V. At higher potentials the circuits become strongly non-linear pointing to the opening of ion channels in plant tissues. Changing the polarity of electrodes leads to a strong rectification effect and to different kinetics of a capacitor. These effects can be caused by a redistribution of K⁺, Cl⁻, Ca²⁺ and H⁺ ions through voltage gated ion channels. The electrical properties of Mimosa pudica were investigated and equivalent electrical circuits within the pinnae were proposed to explain the experimental data.Key words: electrophysiology, plant cell electrostimulation, charged capacitor method, electrical circuits, electrical signaling, Mimosa pudica     

Redox interconversion of geraniol and nerol in Rosa damascena

Use of ¹⁴C, ³H-labelled precursors revealed that flowerheads of Rosa damascena converted geraniol (3,7-dimethylocta-trans-2,6-dien-1-ol) into nerol (the corresponding cis-isomer) with loss of the pro-(1S) hydrogen, whereas the reverse isomerization involved loss of the pro-(1R) atom. The inference that the interconversion proceeded by redox reactions with the formation of the corresponding aldehydes was supported by the preparation of cell-free extracts from R. damascena and R. dilecta that sustained such processes. These reactions were NADP⁺-NADPH dependent and had pH optima at 7.0 and 9.0, respectively.     

Photolyase Confers Resistance to UV Light but Does Not Contribute to the Symbiotic Benefit of Bioluminescence in Vibrio fischeri ES114

Recent reports suggest that the selective advantage of bioluminescence for bacteria is mediated by light-dependent stimulation of photolyase to repair DNA lesions. Despite evidence for this model, photolyase mutants have not been characterized in a naturally bioluminescent bacterium, nor has this hypothesis been tested in bioluminescent bacteria under natural conditions. We have now characterized the photolyase encoded by phr in the bioluminescent bacterium Vibrio fischeri ES114. Consistent with Phr possessing photolyase activity, phr conferred light-dependent resistance to UV light. However, upon comparing ES114 to a phr mutant and a dark ΔluxCDABEG mutant, we found that bioluminescence did not detectably affect photolyase-mediated resistance to UV light. Addition of the light-stimulating autoinducer N-3-oxo-hexanoyl homoserine lactone appeared to increase UV resistance, but this was independent of photolyase or bioluminescence. Moreover, although bioluminescence confers an advantage for V. fischeri during colonization of its natural host, Euprymna scolopes, the phr mutant colonized this host to the same level as the wild type. Taken together, our results indicate that at least in V. fischeri strain ES114, the benefits of bioluminescence during symbiotic colonization are not mediated by photolyase, and although some UV resistance mechanism may be coregulated with bioluminescence, we found no evidence that light production benefits cells by stimulating photolyase in this strain.     

Control of the Ca2+-triggered bioluminescence of Veretillum cynomorium lumisomes

Calcium ions can trigger an emission of light from Veretillum cynomorium lumisomes (bioluminescent vesicles) under conditions where they are not lysed. This process does not require a metabolically-linked source of energy, but is dependent upon the nature of the ions present inside and outside the vesicles. The Ca²⁺-triggered bioluminescence is stimulated by an asymmetrical distribution of cations or anions. Either high internal sodium or high external chloride is required for the maximal effect. When sodium is present outside the structure and potassium inside, the slow inward diffusion of calcium is decreased. Unbalanced diffusion of internal cations also stimulates the bioluminescence, suggesting control of the calcium influx by an electrochemical gradient. It is assumed that rapid outward diffusion of sodium or inward diffusion of chloride generates an electrical potential difference (inside negative) which drives the Ca²⁺-influx. With purified lumisomes it has been shown that Ca²⁺-triggered bioluminescence and calcium uptake (presumably net uptake) were correlated. In two instances uptake of the lipophilic cation dibenzyldimethylammonium has given direct evidence for the existence of a potential difference. With NaCl-loaded vesicles, it has not been possible to demonstrate an uptake of lipophilic cations but experiments with ²²Na and ⁴²K indicated a higher rate of sodium efflux, in accord with the proposed hypothesis.     

Toxin–antitoxin-stabilized reporter plasmids for biophotonic imaging of Group A streptococcus

Bioluminescence is a rapid and cost-efficient optical imaging technology that allows the detection of bacteria in real-time during disease development. Here, we report a novel strategy to generate a wide range of bioluminescent group A streptococcus (GAS) strains by using a toxin–antitoxin-stabilized plasmid. The bacterial luciferin–luciferase operon (lux) or the firefly luciferase gene (ffluc) was introduced into GAS via a stabilized plasmid. The FFluc reporter gave significantly stronger bioluminescent signals than the Lux reporter, and was generally more stable. Plasmid-based luciferase reporters could easily be introduced into a variety of GAS strains and the signals correlated linearly with viable cell counts. Co-expression of the streptococcal ω–ε–ζ toxin–antitoxin operon provided segregational stability in the absence of antibiotics for at least 17 passages in vitro and up to 7 days in a mouse infection model. In addition, genome-integrated reporter constructs were also generated by site-specific recombination, but were found to be technically more challenging. The quick and efficient generation of various M-type GAS strains expressing plasmid-based luciferase reporters with comparable and quantifiable bioluminescence signals allows for comparative analysis of different GAS strains in vitro and in vivo.     

Autonomous Bioluminescent Expression of the Bacterial Luciferase Gene Cassette (lux) in a Mammalian Cell Line

Background

The bacterial luciferase (lux) gene cassette consists of five genes (luxCDABE) whose protein products synergistically generate bioluminescent light signals exclusive of supplementary substrate additions or exogenous manipulations. Historically expressible only in prokaryotes, the lux operon was re-synthesized through a process of multi-bicistronic, codon-optimization to demonstrate for the first time self-directed bioluminescence emission in a mammalian HEK293 cell line in vitro and in vivo.

Methodology/Principal Findings

Autonomous in vitro light production was shown to be 12-fold greater than the observable background associated with untransfected control cells. The availability of reduced riboflavin phosphate (FMNH₂) was identified as the limiting bioluminescence substrate in the mammalian cell environment even after the addition of a constitutively expressed flavin reductase gene (frp) from Vibrio harveyi. FMNH₂ supplementation led to a 151-fold increase in bioluminescence in cells expressing mammalian codon-optimized luxCDE and frp genes. When injected subcutaneously into nude mice, in vivo optical imaging permitted near instantaneous light detection that persisted independently for the 60 min length of the assay with negligible background.

Conclusions/Significance

The speed, longevity, and self-sufficiency of lux expression in the mammalian cellular environment provides a viable and powerful alternative for real-time target visualization not currently offered by existing bioluminescent and fluorescent imaging technologies.     

Studies on galactose oxidase active site model complexes: effects of ring substituents on Cu(II)-phenoxyl radical formation

Copper(II) complexes of new N₃O- and N₂O₂-donor tripodal ligands bearing one or two o-substituted phenol moieties have been synthesized as models for the galactose oxidase active site. The complexes of 2-[N-(1-methyl-2′-imidazolylmethyl)-N-(6″-methyl-2″-pyridylmethyl)-aminomethyl)]-4-methyl-6-methylthiophenol (MeSL), [Cu(MeSL)Cl], and N-(6-methyl-2-pyridylmethyl)-N,N-bis(2′-hydroxy-3′,5′-di-tert-butylbenzyl)amine (t-buL2mepy), [Cu(t-buL2mepy)(H₂O)], have been revealed by X-ray structural analysis to have a square-pyramidal structure with one and two phenolate oxygens in the basal plane, respectively. [Cu(MeSL)Cl] was converted into a Cu(II)-o-methylthiophenoxyl radical species by electrochemical or Ce(IV) oxidation. An o-methoxyphenoxyl radical in a similar complex was considerably more stable than the 2,4-di(tert-butyl)phenoxyl radical. While t-buL2mepy reacted with Cu(ClO₄)₂ to give [Cu(t-buL2mepy)(H₂O)] without disproportionation, an N2O2-donor ligand containing an o-methoxyphenol, a 2,4-di(tert-butyl)phenol, and an N-methylimidazole moiety gave a phenoxyl radical complex exhibiting the characteristic absorption peak at 478 nm as a reddish powder by the reaction with Cu(ClO₄)₂ as a result of spontaneous disproportionation. It exhibited a quasi-reversible redox wave at E_1/2=0.34 V (vs. Ag/AgCl) in CH₃CN, which is lower than the potentials of the copper complexes of various N₃O-donor ligands, and oxidized ethanol to acetaldehyde with a low turnover number.     

Spectral Sensitivities and Color Signals in a Polymorphic Damselfly

Animal communication relies on conspicuous signals and compatible signal perception abilities. Good signal perception abilities are particularly important for polymorphic animals where mate choice can be a challenge. Behavioral studies suggest that polymorphic damselflies use their varying body colorations and/or color patterns as communication signal for mate choice and to control mating frequencies. However, solid evidence for this hypothesis combining physiological with spectral and behavioral data is scarce. We investigated this question in the Australian common blue tail damselfly, Ischnura heterosticta, which has pronounced female-limited polymorphism: andromorphs have a male-like blue coloration and gynomorphs display green/grey colors. We measured body color reflectance and investigated the visual capacities of each morph, showing that I. heterosticta have at least three types of photoreceptors sensitive to UV, blue, and green wavelength, and that this visual perception ability enables them to detect the spectral properties of the color signals emitted from the various color morphs in both males and females. We further demonstrate that different color morphs can be discriminated against each other and the vegetation based on color contrast. Finally, these findings were supported by field observations of natural mating pairs showing that mating partners are indeed chosen based on their body coloration. Our study provides the first comprehensive evidence for the function of body coloration on mate choice in polymorphic damselflies.     

Gustatory imagery reveals functional connectivity from the prefrontal to insular cortices traced with magnetoencephalography

Our experience and prejudice concerning food play an important role in modulating gustatory information processing; gustatory memory stored in the central nervous system influences gustatory information arising from the peripheral nervous system. We have elucidated the mechanism of the “top-down” modulation of taste perception in humans using functional magnetic resonance imaging (fMRI) and demonstrated that gustatory imagery is mediated by the prefrontal (PFC) and insular cortices (IC). However, the temporal order of activation of these brain regions during gustatory imagery is still an open issue. To explore the source of “top-down” signals during gustatory imagery tasks, we analyzed the temporal activation patterns of activated regions in the cerebral cortex using another non-invasive brain imaging technique, magnetoencephalography (MEG). Gustatory imagery tasks were presented by words (Letter G-V) or pictures (Picture G-V) of foods/beverages, and participants were requested to recall their taste. In the Letter G-V session, 7/9 (77.8%) participants showed activation in the IC with a latency of 401.7±34.7 ms (n = 7) from the onset of word exhibition. In 5/7 (71.4%) participants who exhibited IC activation, the PFC was activated prior to the IC at a latency of 315.2±56.5 ms (n = 5), which was significantly shorter than the latency to the IC activation. In the Picture G-V session, the IC was activated in 6/9 (66.7%) participants, and only 1/9 (11.1%) participants showed activation in the PFC. There was no significant dominance between the right and left IC or PFC during gustatory imagery. These results support those from our previous fMRI study in that the Letter G-V session rather than the Picture G-V session effectively activates the PFC and IC and strengthen the hypothesis that the PFC mediates “top-down” control of retrieving gustatory information from the storage of long-term memories and in turn activates the IC.     

Signal transduction in Mimosa pudica: biologically closed electrical circuits

Biologically closed electrical circuits operate over large distances in biological tissues. The activation of such circuits can lead to various physiological and biophysical responses. Here, we analyse the biologically closed electrical circuits of the sensitive plant Mimosa pudica Linn. using electrostimulation of a petiole or pulvinus by the charged capacitor method, and evaluate the equivalent electrical scheme of electrical signal transduction inside the plant. The discharge of a 100 µF capacitor in the pulvinus resulted in the downward fall of the petiole in a few seconds, if the capacitor was charged beforehand by a 1.5 V power supply. Upon disconnection of the capacitor from Ag/AgCl electrodes, the petiole slowly relaxed to the initial position. The electrical properties of the M. pudica were investigated, and an equivalent electrical circuit was proposed that explains the experimental data.     

Behavioural responses of the yellow emitting annelid Tomopteris helgolandica to photic stimuli

In contrast to most mesopelagic bioluminescent organisms specialised in the emission and reception of blue light, the planktonic annelid Tomopteris helgolandica produces yellow light. This unusual feature has long been suggested to serve for intraspecific communication. Yet, this virtually admitted hypothesis has never been tested. In this behavioural study of spectral colour sensitivity, we first present an illustrated repertoire of the postures and action patterns described by captive specimens. Then video tracking and motion analysis are used to quantify the behavioural responses of singled out worms to photic stimuli imitating intraspecific (yellow) or interspecific (blue) bioluminescent signals. We show the ability of T. helgolandica to react and to contrast its responses to bioluminescent‐like blue and yellow light signals. In particular, the attractive effect of yellow light and the variation of angular velocity observed according to the pattern of yellow stimuli (flashes versus glows) support the intraspecific communication hypothesis. However, given the behavioural patterns of T. helgolandica, including mechanically induced light emission, the possibility that bioluminescence may be part of escape/defence responses to predation, should remain an open question.