Function follows form: ecological constraints on odor codes and olfactory percepts

Fast updating feedback from piriform cortex to the olfactory bulb relays multimodal identity and reward contingency signals during rule-reversal

While animals readily adjust their behavior to adapt to relevant changes in the environment, the neural pathways enabling these changes remain largely unknown. Here, using multiphoton imaging, we investigate whether feedback from the piriform cortex to the olfactory bulb supports such behavioral flexibility. To this end, we engage head-fixed male mice in a multimodal rule-reversal task guided by olfactory and auditory cues. Both odor and, surprisingly, the sound cues trigger responses in the cortical bulbar feedback axons which precede the behavioral report. Responses to the same sensory cue are strongly modulated upon changes in stimulus-reward contingency (rule-reversals). The re-shaping of individual bouton responses occurs within seconds of the rule-reversal events and is correlated with changes in behavior. Optogenetic perturbation of cortical feedback within the bulb disrupts the behavioral performance. Our results indicate that the piriform-to-olfactory bulb feedback axons carry stimulus identity and reward contingency signals which are rapidly re-formatted according to changes in the behavioral context.

Decomposition of an odorant in olfactory perception and neural representation

Molecules-the elementary units of substances-are commonly considered the units of processing in olfactory perception, giving rise to undifferentiated odour objects invariant to environmental variations. By selectively perturbing the processing of chemical substructures with adaptation ('the psychologist's microelectrode') in a series of psychophysical and neuroimaging experiments (458 participants), we show that two perceptually distinct odorants sharing part of their structural features become significantly less discernible following adaptation to a third odorant containing their non-shared structural features, in manners independent of olfactory intensity, valence, quality or general olfactory adaptation. The effect is accompanied by reorganizations of ensemble activity patterns in the posterior piriform cortex that parallel subjective odour quality changes, in addition to substructure-based neural adaptations in the anterior piriform cortex and amygdala. Central representations of odour quality and the perceptual outcome thus embed submolecular structural information and are malleable by recent olfactory encounters.

How does the "default mode" network contribute to semantic cognition?

This review examines whether and how the "default mode" network (DMN) contributes to semantic processing. We review evidence implicating the DMN in the processing of individual word meanings and in sentence- and discourse-level semantics. Next, we argue that the areas comprising the DMN contribute to semantic processing by coordinating and integrating the simultaneous activity of local neuronal ensembles across multiple unimodal and multimodal cortical regions, creating a transient, global neuronal ensemble. The resulting ensemble implements an integrated simulation of phenomenological experience - that is, an embodied situation model - constructed from various modalities of experiential memory traces. These situation models, we argue, are necessary not only for semantic processing but also for aspects of cognition that are not traditionally considered semantic. Although many aspects of this proposal remain provisional, we believe it provides new insights into the relationships between semantic and non-semantic cognition and into the functions of the DMN.

Fast updating feedback from piriform cortex to the olfactory bulb relays multimodal reward contingency signals during rule-reversal

While animals readily adjust their behavior to adapt to relevant changes in the environment, the neural pathways enabling these changes remain largely unknown. Here, using multiphoton imaging, we investigated whether feedback from the piriform cortex to the olfactory bulb supports such behavioral flexibility. To this end, we engaged head-fixed mice in a multimodal rule-reversal task guided by olfactory and auditory cues. Both odor and, surprisingly, the sound cues triggered cortical bulbar feedback responses which preceded the behavioral report. Responses to the same sensory cue were strongly modulated upon changes in stimulus-reward contingency (rule reversals). The re-shaping of individual bouton responses occurred within seconds of the rule-reversal events and was correlated with changes in the behavior. Optogenetic perturbation of cortical feedback within the bulb disrupted the behavioral performance. Our results indicate that the piriform-to-olfactory bulb feedback carries reward contingency signals and is rapidly re-formatted according to changes in the behavioral context.

Recent Advances in Nanomechanical Membrane-Type Surface Stress Sensors towards Artificial Olfaction

Nanomechanical sensors have gained significant attention as powerful tools for detecting, distinguishing, and identifying target analytes, especially odors that are composed of a complex mixture of gaseous molecules. Nanomechanical sensors and their arrays are a promising platform for artificial olfaction in combination with data processing technologies, including machine learning techniques. This paper reviews the background of nanomechanical sensors, especially conventional cantilever-type sensors. Then, we focus on one of the optimized structures for static mode operation, a nanomechanical Membrane-type Surface stress Sensor (MSS), and discuss recent advances in MSS and their applications towards artificial olfaction.

Biological constraints on configural odour mixture perception

Animals, including humans, detect odours and use this information to behave efficiently in the environment. Frequently, odours consist of complex mixtures of odorants rather than single odorants, and mixtures are often perceived as configural wholes, i.e. as odour objects (e.g. food, partners). The biological rules governing this 'configural perception' (as opposed to the elemental perception of mixtures through their components) remain weakly understood. Here, we first review examples of configural mixture processing in diverse species involving species-specific biological signals. Then, we present the original hypothesis that at least certain mixtures can be processed configurally across species. Indeed, experiments conducted in human adults, newborn rabbits and, more recently, in rodents and honeybees show that these species process some mixtures in a remarkably similar fashion. Strikingly, a mixture AB (A, ethyl isobutyrate; B, ethyl maltol) induces configural processing in humans, who perceive a mixture odour quality (pineapple) distinct from the component qualities (A, strawberry; B, caramel). The same mixture is weakly configurally processed in rabbit neonates, which perceive a particular odour for the mixture in addition to the component odours. Mice and honeybees also perceive the AB mixture configurally, as they respond differently to the mixture compared with its components. Based on these results and others, including neurophysiological approaches, we propose that certain mixtures are convergently perceived across various species of vertebrates/invertebrates, possibly as a result of a similar anatomical organization of their olfactory systems and the common necessity to simplify the environment's chemical complexity in order to display adaptive behaviours.

Molecular Strategies for Intensity-Dependent Olfactory Processing in Caenorhabditis elegans

Various odorants trigger complex animal behaviors across species in both quality- and quantity-dependent manners. However, how the intensity of olfactory input is encoded remains largely unknown. Here we report that isoamyl alcohol (IAA) induces bi-directional currents through a Gα- guanylate cyclase (GC)- cGMP signaling pathway in Caenorhabditis elegans olfactory neuron amphid wing “C” cell (AWC), while two opposite cGMP signaling pathways are responsible for odor-sensing in olfactory neuron amphid wing “B” cell (AWB): (1) a depolarizing Gα (GPA-3)- phosphodiesterase (PDE) – cGMP pathway which can be activated by low concentrations of isoamyl alcohol (IAA), and (2) a hyperpolarizing Gα (ODR-3)- GC- cGMP pathway sensing high concentrations of IAA. Besides, IAA induces Gα (ODR-3)-TRPV(OSM-9)-dependent currents in amphid wing “A” cell (AWA) and amphid neuron “H” cell with single ciliated sensory ending (ASH) neurons with different thresholds. Our results demonstrate that an elaborate combination of multiple signaling machineries encode the intensity of olfactory input, shedding light on understanding the molecular strategies on sensory transduction.

Octopaminergic neurons have multiple targets in Drosophila larval mushroom body calyx and can modulate behavioral odor discrimination

Discrimination of sensory signals is essential for an organism to form and retrieve memories of relevance in a given behavioral context. Sensory representations are modified dynamically by changes in behavioral state, facilitating context-dependent selection of behavior, through signals carried by noradrenergic input in mammals, or octopamine (OA) in insects. To understand the circuit mechanisms of this signaling, we characterized the function of two OA neurons, sVUM1 neurons, that originate in the subesophageal zone (SEZ) and target the input region of the memory center, the mushroom body (MB) calyx, in larval Drosophila. We found that sVUM1 neurons target multiple neurons, including olfactory projection neurons (PNs), the inhibitory neuron APL, and a pair of extrinsic output neurons, but relatively few mushroom body intrinsic neurons, Kenyon cells. PN terminals carried the OA receptor Oamb, a Drosophila α1-adrenergic receptor ortholog. Using an odor discrimination learning paradigm, we showed that optogenetic activation of OA neurons compromised discrimination of similar odors but not learning ability. Our results suggest that sVUM1 neurons modify odor representations via multiple extrinsic inputs at the sensory input area to the MB olfactory learning circuit.

Categorical face perception in fish: How a fish brain warps reality to dissociate "same" from "different"

Categorical perception (CP) is the phenomenon by which a smoothly varying stimulus property undergoes a nonlinear transformation during processing in the brain. Consequently, the stimuli are perceived as belonging to distinct categories separated by a sharp boundary. Originally thought to be largely innate, the discovery of CP in tasks such as novel image discrimination has piqued the interest of cognitive scientists because it provides compelling evidence that learning can shape a category's perceptual boundaries. CP has been particularly closely studied in human face perception. In nonprimates, there is evidence for CP for sound and color discrimination, but not for image or face discrimination. Here, we investigate the potential for learned CP in a lower vertebrate, the damselfish Pomacentrus amboinensis. Specifically, we tested whether the ability of these fish to discriminate complex facial patterns tracked categorical rather than metric differences in the stimuli. We first trained the fish to discriminate sets of two facial patterns. Next, we morphed between these patterns and determined the just noticeable difference (JND) between a morph and original image. Finally, we tested for CP by analyzing the discrimination ability of the fish for pairs of JND stimuli along the spectrum of morphs between two original images. Discrimination performance was significant for the image pair straddling the boundary between categories, and chance for equivalent stimulus pairs on either side, thus producing the classic "category boundary" effect. Our results reveal how perception can be influenced in a top-down manner even in the absence of a visual cortex.

Multiscale modeling of mechanotransduction in the utricle

We review recent progress in using numerical models to relate utricular hair bundle and otoconial membrane (OM) structure to the functional requirements imposed by natural behavior in turtles. The head movements section reviews the evolution of experimental attempts to understand vestibular system function with emphasis on turtles, including data showing that accelerations occurring during natural head movements achieve higher magnitudes and frequencies than previously assumed. The structure section reviews quantitative anatomical data documenting topographical variation in the structures underlying macromechanical and micromechanical responses of the turtle utricle to head movement: hair bundles, OM, and bundle-OM coupling. The macromechanics section reviews macromechanical models that incorporate realistic anatomical and mechanical parameters and reveal that the system is significantly underdamped, contrary to previous assumptions. The micromechanics: hair bundle motion and met currents section reviews work based on micromechanical models, which demonstrates that topographical variation in the structure of hair bundles and OM, and their mode of coupling, result in regional specializations for signaling of low frequency (or static) head position and high frequency head accelerations. We conclude that computational models based on empirical data are especially promising for investigating mechanotransduction in this challenging sensorimotor system.

Effect of early experience on neuronal and behavioral responses to con- and heterospecific odors in closely related Mus taxa: epigenetic contribution in formation of precopulatory isolation

BACKGROUND

The most effective learning occurs during sensitive periods. Olfactory plasticity to main social olfactory cues is limited to a critical period to a large degree. The objective was to evaluate the influence of early olfactory experience on the behavioral and neuronal responses of males to con- and heterospecific odors of receptive females in two species, M. musculus (subspecies musculus, wagneri) and M. spicilegus, and thus to determine the potential role of epigenetic contribution in the formation of precopulatory isolation.

RESULTS

Males were reciprocally cross-fostered shortly after the birth and were tested for response to con- and heterospecific urine odors of estrus females using two-choice tests at 70-85 days of age. Neuronal activity of non- and cross-fostered males was evaluated at 90-110 days of age in the MOB and AOB to con- and heterospecific female odor using fMRI (MEMRI). Non-cross-fostered males of three taxa demonstrated a strong preference for odor of conspecific females compared to odor of heterospecific ones. Spicilegus-nursed musculus preferred odor of heterospecific females. Wagneri-nursed spicilegus and spicilegus-nursed wagneri did not demonstrate significant choice of con - or heterospecific female odor. The level of MRI signal obtained from the evaluation of manganese accumulation in AOB neurons was significantly higher when the odor of conspecific estrus females was exposed, compared to urine exposure of heterospecific females. The response pattern changed to the opposite in males raised by heterospecific females. Response patterns of neuronal activity in the MOB to con- and heterospecific female odors were different in cross-fostered and control males.

CONCLUSION

The maternal environment, including odor, had a greater effect on the level of MRI signal in the AOB than the genetic relationships of the recipient and the donor of the odor stimulus. Behavioral and neuronal responses to con- and heterospecific odors changed in closely related Mus taxa as a result of early experience. We demonstrated the importance of early learning in mate choice in adulthood in mice and the possibility of epigenetic contribution in the formation of precopulatory reproductive isolation.

Food quality and conspicuousness shape improvements in olfactory discrimination by mice

How animals locate nutritious but camouflaged prey items with increasing accuracy is not well understood. Olfactory foraging is common in vertebrates and the nutritional desirability of food should influence the salience of odour cues. We used signal detection analysis to test the effect of nutritional value relative to the conspicuousness of food patches on rates of foraging improvement of wild house mice Mus musculus searching for buried food (preferred peanuts or non-preferred barley). Olfactory cues were arranged to make food patches conspicuous or difficult to distinguish using a novel form of olfactory camouflage. Regardless of food type or abundance, mice searching for conspicuous food patches performed significantly better than mice searching for camouflaged patches. However, food type influenced how mice responded to different levels of conspicuousness. Mice searching for peanuts improved by similar rates regardless of whether food was easy or hard to find, but mice searching for barley showed significant differences, improving rapidly when food was conspicuous but declining in accuracy when food was camouflaged. Our results demonstrate a fundamental tenet of olfactory foraging that nutritional desirability influences rates of improvement in odour discrimination, enabling nutritious but camouflaged prey to be located with increasing efficiency.

Molecularly Imprinted Filtering Adsorbents for Odor Sensing

Versatile odor sensors that can discriminate among huge numbers of environmental odorants are desired in many fields, including robotics, environmental monitoring, and food production. However, odor sensors comparable to an animal’s nose have not yet been developed. An animal’s olfactory system recognizes odor clusters with specific molecular properties and uses this combinatorial information in odor discrimination. This suggests that measurement and clustering of odor molecular properties (e.g., polarity, size) using an artificial sensor is a promising approach to odor sensing. Here, adsorbents composed of composite materials with molecular recognition properties were developed for odor sensing. The selectivity of the sensor depends on the adsorbent materials, so specific polymeric materials with particular solubility parameters were chosen to adsorb odorants with various properties. The adsorption properties of the adsorbents could be modified by mixing adsorbent materials. Moreover, a novel molecularly imprinted filtering adsorbent (MIFA), composed of an adsorbent substrate covered with a molecularly imprinted polymer (MIP) layer, was developed to improve the odor molecular recognition ability. The combination of the adsorbent and MIP layer provided a higher specificity toward target molecules. The MIFA thus provides a useful technique for the design and control of adsorbents with adsorption properties specific to particular odor molecules.

Neonatal representation of odour objects: distinct memories of the whole and its parts

Extraction of relevant information from highly complex environments is a prerequisite to survival. Within odour mixtures, such information is contained in the odours of specific elements or in the mixture configuration perceived as a whole unique odour. For instance, an AB mixture of the element A (ethyl isobutyrate) and the element B (ethyl maltol) generates a configural AB percept in humans and apparently in another species, the rabbit. Here, we examined whether the memory of such a configuration is distinct from the memory of the individual odorants. Taking advantage of the newborn rabbit's ability to learn odour mixtures, we combined behavioural and pharmacological tools to specifically eliminate elemental memory of A and B after conditioning to the AB mixture and evaluate consequences on configural memory of AB. The amnesic treatment suppressed responsiveness to A and B but not to AB. Two other experiments confirmed the specific perception and particular memory of the AB mixture. These data demonstrate the existence of configurations in certain odour mixtures and their representation as unique objects: after learning, animals form a configural memory of these mixtures, which coexists with, but is relatively dissociated from, memory of their elements. This capability emerges very early in life.

Chemical signals in terrestrial vertebrates: search for design features

We review current information on intraspecific chemical signals and search for patterns in signal chemistry among modern terrestrial vertebrates (Amniota), including tortoises, squamate reptiles (amphisbaenians, lizards, and snakes), birds, and mammals.

Newborn rabbit perception of 6-odorant mixtures depends on configural processing and number of familiar elements

Perception of odors, i.e. usually of mixtures of odorants, is elemental (the odorants' odor qualities are perceived in the mixture) or configural (the odor quality of the mixture differs from the one of each odorant). In human adults, the Red Cordial (RC) mixture is a configurally-processed, 6-odorant mixture. It evokes a red cordial odor quality while none of the elements carries that odor. Interestingly, in newborn rabbits, the same RC mixture is weak configurally perceived: the newborns behaviorally respond to all the elements after conditioning to the whole mixture, but not to the mixture after conditioning to a single element. Thus, they perceive in the RC mixture both the odor quality of the RC configuration and the quality of each element. Here, we aimed to determine whether this perception is modulated by quantitative (number of elements) and/or qualitative bits of information (nature of elements) previously learned by the animals. Newborns were conditioned to RC sub-mixtures of different complexity and composition before behavioral testing to RC. Pups generalized their sucking-related response to RC after learning at least 4 odorants. In contrast, after conditioning to sub-mixtures of another 6-odorant mixture, the elementally perceived M^V mixture, pups responded to M^V after learning one or two odorants. The different generalization to RC and M^V mixtures after learning some of their elements is discussed according to three hypotheses: i) the configural perception of RC sub-mixtures, ii) the ratio of familiar/unfamiliar individual information elementally and configurally perceived, iii) the perception of RC becoming purely elemental. The results allow the first hypothesis to be dismissed, while further experiments are required to distinguish between the remaining two.

Neuronal circuits and computations: pattern decorrelation in the olfactory bulb

Neuronal circuits in the olfactory bulb transform odor-evoked activity patterns across the input channels, the olfactory glomeruli, into distributed activity patterns across the output neurons, the mitral cells. One computation associated with this transformation is a decorrelation of activity patterns representing similar odors. Such a decorrelation has various benefits for the classification and storage of information by associative networks in higher brain areas. Experimental results from adult zebrafish show that pattern decorrelation involves a redistribution of activity across the population of mitral cells. These observations imply that pattern decorrelation cannot be explained by a global scaling mechanism but that it depends on interactions between distinct subsets of neurons in the network. This article reviews insights into the network mechanism underlying pattern decorrelation and discusses recent results that link pattern decorrelation in the olfactory bulb to odor discrimination behavior.

The perception of odor objects in everyday life: a review on the processing of odor mixtures

Smelling monomolecular odors hardly ever occurs in everyday life, and the daily functioning of the sense of smell relies primarily on the processing of complex mixtures of volatiles that are present in the environment (e.g., emanating from food or conspecifics). Such processing allows for the instantaneous recognition and categorization of smells and also for the discrimination of odors among others to extract relevant information and to adapt efficiently in different contexts. The neurophysiological mechanisms underpinning this highly efficient analysis of complex mixtures of odorants is beginning to be unraveled and support the idea that olfaction, as vision and audition, relies on odor-objects encoding. This configural processing of odor mixtures, which is empirically subject to important applications in our societies (e.g., the art of perfumers, flavorists, and wine makers), has been scientifically studied only during the last decades. This processing depends on many individual factors, among which are the developmental stage, lifestyle, physiological and mood state, and cognitive skills; this processing also presents striking similarities between species. The present review gathers the recent findings, as observed in animals, healthy subjects, and/or individuals with affective disorders, supporting the perception of complex odor stimuli as odor objects. It also discusses peripheral to central processing, and cognitive and behavioral significance. Finally, this review highlights that the study of odor mixtures is an original window allowing for the investigation of daily olfaction and emphasizes the need for knowledge about the underlying biological processes, which appear to be crucial for our representation and adaptation to the chemical environment.

The right dorsal habenula limits attraction to an odor in zebrafish

BACKGROUND

The habenula consists of an evolutionarily conserved set of nuclei that control neuromodulator release. In lower vertebrates, the dorsal habenula receives innervation from sensory regions, but the significance of this is unclear. Here, we address the role of the habenula in olfaction by imaging neural activity in larval zebrafish expressing GCaMP3 throughout the habenula and by carrying out behavioral assays.

RESULTS

Activity in several hundred neurons throughout the habenula was recorded using wide-field fluorescence microscopy, fast focusing, and deconvolution. This enabled the creation of 4D maps of odor-evoked activity. Odors activated the habenula in two broad spatiotemporal patterns. Increasing concentrations of a putative social cue (a bile salt) evoked a corresponding increase in neuronal activity in the right dorsal habenula. In behavioral assays, fish were attracted to intermediate concentration of this cue but avoided higher concentration. Increasing cholinergic activity through nicotine exposure rendered the intermediate concentration aversive in a habenula-dependent manner. Pharmacologically blocking nicotinic receptors or lesioning the right dorsal habenula attenuated avoidance.

CONCLUSIONS

These data provide physiological and functional evidence that the habenula functions as a higher center in zebrafish olfaction and suggest that activity in the right dorsal subdomain gates innate attraction to specific odors.

Categorical dimensions of human odor descriptor space revealed by non-negative matrix factorization

In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain unclear. Here, we use non-negative matrix factorization (NMF) – a dimensionality reduction technique – to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor dimensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.

Neuronal computations in the olfactory system of zebrafish

The main olfactory system encodes information about molecules in a combinatorial fashion by distributed spatiotemporal activity patterns. As activity propagates from sensory neurons to the olfactory bulb and to higher brain areas, odor information is processed by multiple transformations of these activity patterns. This review discusses neuronal computations associated with such transformations in the olfactory system of zebrafish, a small vertebrate that offers advantages for the quantitative analysis and manipulation of neuronal activity in the intact brain. The review focuses on pattern decorrelation in the olfactory bulb and on the readout of multiplexed sensory representations in the telencephalic area Dp, the homolog of the olfactory cortex. These computations are difficult to study in larger species and may provide insights into general information-processing strategies in the brain.

Exploiting olfactory learning in alien rats to protect birds' eggs

Predators must ignore unhelpful background "noise" within information-rich environments and focus on useful cues of prey activity to forage efficiently. Learning to disregard unrewarding cues should happen quickly, weakening future interest in the cue. Prey odor, which is rapidly investigated by predators, may be particularly appropriate for testing whether consistently unrewarded cues are ignored, and whether such behavior can be exploited to benefit prey. Using wild free-ranging populations of black rats, Rattus rattus, an alien predator of global concern, we tested whether the application of bird-nesting odors before the introduction of artificial nests (odor preexposure), enhanced the survival of birds eggs (prey) compared with areas where prey and nesting odors were introduced concurrently. In areas where predators had encountered prey odor before prey being available, the subsequently introduced eggs showed 62% greater survival than in areas where prey and odor were introduced together. We suggest that black rats preexposed to prey odor learned to ignore the unrewarding cue, leading to a significant improvement in prey survival that held for the 7-d monitoring period. Exploiting rapid learning that underpins foraging decisions by manipulating sensory contexts offers a nonlethal, but effective approach to reducing undesirable predatory impacts. Techniques based on olfactory preexposure may provide prey with protection during critical periods of vulnerability, such as immediately following a prey reintroduction. These results also highlight the potential benefits to species conservation to be gained from a greater understanding of the cognitive mechanisms driving alien predator behavior within ecological contexts.

Carbon chain length and the stimulus problem in olfaction

Understanding how odour quality perception is encoded in its molecular properties arguably poses one of the most significant problems in olfaction. Determining the odour structure-quality relationships of structurally similar odorants could provide a key tool to this problem. We tentatively explored whether a mixture of two molecules, differing only in carbon chain length (C), would yield the same percept as a single odorant with an intermediate carbon chain length, akin to colour vision, or be perceived as a different quality. Ability to discriminate between pairs of iso-intense solutions of n-butanol (4C), n-propanol (3C), n-pentanol (5C), and an intermediate 50/50 molecular weight mixture of n-propanol and n-pentanol (3C/5C) was assessed in 20 healthy young adults. We found that participants were able to discriminate 4C from the 50/50 molecular weight mixture of n-propanol and n-pentanol (3C/5C), and also from the other alcohols. In conclusion, we successfully replicated previous data demonstrating that participants are able to discriminate between structurally similar alcohols, and, more importantly, the present study shows that an odour mixture of two molecules differing only in carbon chain length is clearly distinguishable from a single odorant with an intermediate carbon chain length. These findings suggest that although carbon chain length matters to odour quality, carbon chain length is not a physical continuum within homologous series of substances that corresponds to a single qualitative dimension akin to the wavelength-hue relation for monochromatic light.