Olfactory receptor neurons use gain control and complementary kinetics to encode intermittent odorant stimuli

A molecular odorant transduction model and the complexity of spatio-temporal encoding in the Drosophila antenna

Over the past two decades, substantial amount of work has been conducted to characterize different odorant receptors, neuroanatomy and odorant response properties of the early olfactory system of Drosophila melanogaster. Yet many odorant receptors remain only partially characterized, and the odorant transduction process and the axon hillock spiking mechanism of the olfactory sensory neurons (OSNs) have yet to be fully determined. Identity and concentration, two key characteristics of the space of odorants, are encoded by the odorant transduction process. Detailed molecular models of the odorant transduction process are, however, scarce for fruit flies. To address these challenges we advance a comprehensive model of fruit fly OSNs as a cascade consisting of an odorant transduction process (OTP) and a biophysical spike generator (BSG). We model odorant identity and concentration using an odorant-receptor binding rate tensor, modulated by the odorant concentration profile, and an odorant-receptor dissociation rate tensor, and quantitatively describe the mechanics of the molecular ligand binding/dissociation of the OTP. We model the BSG as a Connor-Stevens point neuron. The resulting spatio-temporal encoding model of the Drosophila antenna provides a theoretical foundation for understanding the neural code of both odorant identity and odorant concentration and advances the state-of-the-art in a number of ways. First, it quantifies on the molecular level the spatio-temporal level of complexity of the transformation taking place in the antennae. The concentration-dependent spatio-temporal code at the output of the antenna circuits determines the level of complexity of olfactory processing in the downstream neuropils, such as odorant recognition and olfactory associative learning. Second, the model is biologically validated using multiple electrophysiological recordings. Third, the model demonstrates that the currently available data for odorant-receptor responses only enable the estimation of the affinity of the odorant-receptor pairs. The odorant-dissociation rate is only available for a few odorant-receptor pairs. Finally, our model calls for new experiments for massively identifying the odorant-receptor dissociation rates of relevance to flies.

Identity and concentration, intrinsically embedded in the odorant space, are two key characteristics of olfactory coding that define the level of complexity of neural processing throughout the olfactory system in the fruit fly. In this paper we advance a theoretical foundation for understanding these two characteristics by quantifying mathematically the odorant space and devising a biophysical model of the olfactory sensory neurons (OSNs). To validate our modeling approach, we propose and apply an algorithm to estimate the affinity value and the dissociation rate, the two characteristics that define odorant identity, of multiple odorant-receptor pairs. We then evaluate our model with a multitude of odorant waveforms and demonstrate that the model output reproduces the temporal responses of OSNs obtained from in vivo electrophysiology recordings. Furthermore, we evaluate the model at the OSN population level and quantify on the molecular level the spatio-temporal level of complexity of the transformation taking place between the odorant space and the OSNs. The resulting concentration-dependent spatio-temporal code determines the level of complexity of the input space driving olfactory processing in the downstream neuropils. Lastly, our model demonstrates that the currently available data for OSN responses only enables estimation of affinity value. This calls for new experiments for massively identifying the odorant-receptor dissociation rates of relevance to flies.

Odor Stimuli: Not Just Chemical Identity

In most sensory modalities the underlying physical phenomena are well understood, and stimulus properties can be precisely controlled. In olfaction, the situation is different. The presence of specific chemical compounds in the air (or water) is the root cause for perceived odors, but it remains unknown what organizing principles, equivalent to wavelength for light, determine the dimensions of odor space. Equally important, but less in the spotlight, odor stimuli are also complex with respect to their physical properties, including concentration and time-varying spatio-temporal distribution. We still lack a complete understanding or control over these properties, in either experiments or theory. In this review, we will concentrate on two important aspects of the physical properties of odor stimuli beyond the chemical identity of the odorants: (1) The amplitude of odor stimuli and their temporal dynamics. (2) The spatio-temporal structure of odor plumes in a natural environment. Concerning these issues, we ask the following questions: (1) Given any particular experimental protocol for odor stimulation, do we have a realistic estimate of the odorant concentration in the air, and at the olfactory receptor neurons? Can we control, or at least know, the dynamics of odorant concentration at olfactory receptor neurons? (2) What do we know of the spatio-temporal structure of odor stimuli in a natural environment both from a theoretical and experimental perspective? And how does this change if we consider mixtures of odorants? For both topics, we will briefly summarize the underlying principles of physics and review the experimental and theoretical Neuroscience literature, focusing on the aspects that are relevant to animals’ physiology and behavior. We hope that by bringing the physical principles behind odor plume landscapes to the fore we can contribute to promoting a new generation of experiments and models.

Adaptive integrate-and-fire model reproduces the dynamics of olfactory receptor neuron responses in a moth

In order to understand how olfactory stimuli are encoded and processed in the brain, it is important to build a computational model for olfactory receptor neurons (ORNs). Here, we present a simple and reliable mathematical model of a moth ORN generating spikes. The model incorporates a simplified description of the chemical kinetics leading to olfactory receptor activation and action potential generation. We show that an adaptive spike threshold regulated by prior spike history is an effective mechanism for reproducing the typical phasic-tonic time course of ORN responses. Our model reproduces the response dynamics of individual neurons to a fluctuating stimulus that approximates odorant fluctuations in nature. The parameters of the spike threshold are essential for reproducing the response heterogeneity in ORNs. The model provides a valuable tool for efficient simulations of olfactory circuits.

Front-end Weber-Fechner gain control enhances the fidelity of combinatorial odor coding

We showed previously (Gorur-Shandilya et al., 2017) that Drosophila olfactory receptor neurons (ORNs) expressing the co-receptor Orco scale their gain inversely with mean odor intensity according to Weber-Fechner's law. Here, we show that this front-end adaptation promotes the reconstruction of odor identity from dynamic odor signals, even in the presence of confounding background odors and rapid intensity fluctuations. These enhancements are further aided by known downstream transformations in the antennal lobe and mushroom body. Our results, which are applicable to various odor classification and reconstruction schemes, stem from the fact that this adaptation mechanism is not intrinsic to the identity of the receptor involved. Instead, a feedback mechanism adjusts receptor sensitivity based on the activity of the receptor-Orco complex, according to Weber-Fechner's law. Thus, a common scaling of the gain across Orco-expressing ORNs may be a key feature of ORN adaptation that helps preserve combinatorial odor codes in naturalistic landscapes.

Slow presynaptic mechanisms that mediate adaptation in the olfactory pathway of Drosophila

The olfactory system encodes odor stimuli as combinatorial activity of populations of neurons whose response depends on stimulus history. How and on which timescales previous stimuli affect these combinatorial representations remains unclear. We use in vivo optical imaging in Drosophila to analyze sensory adaptation at the first synaptic step along the olfactory pathway. We show that calcium signals in the axon terminals of olfactory receptor neurons (ORNs) do not follow the same adaptive properties as the firing activity measured at the antenna. While ORNs calcium responses are sustained on long timescales, calcium signals in the postsynaptic projection neurons (PNs) adapt within tens of seconds. We propose that this slow component of the postsynaptic response is mediated by a slow presynaptic depression of vesicle release and enables the combinatorial population activity of PNs to adjust to the mean and variance of fluctuating odor stimuli.

Olfactory Navigation and the Receptor Nonlinearity

The demands on a sensory system depend not only on the statistics of its inputs but also on the task. In olfactory navigation, for example, the task is to find the plume source; allocation of sensory resources may therefore be driven by aspects of the plume that are informative about source location, rather than concentration per se. Here we explore the implications of this idea for encoding odor concentration. To formalize the notion that sensory resources are limited, we considered coding strategies that partitioned the odor concentration range into a set of discriminable intervals. We developed a dynamic programming algorithm that, given the distribution of odor concentrations at several locations, determines the partitioning that conveys the most information about location. We applied this analysis to planar laser-induced fluorescence measurements of spatiotemporal odor fields with realistic advection speeds (5-20 cm/s), with or without a nearby boundary or obstacle. Across all environments, the optimal coding strategy allocated more resources (i.e., more and finer discriminable intervals) to the upper end of the concentration range than would be expected from histogram equalization, the optimal strategy if the goal were to reconstruct the plume, rather than to navigate. Finally, we show that ligand binding, as captured by the Hill equation, transforms odorant concentration into response levels in a way that approximates information maximization for navigation. This behavior occurs when the Hill dissociation constant is near the mean odor concentration, an adaptive set-point that has been observed in the olfactory system of flies.SIGNIFICANCE STATEMENT The first step of olfactory processing is receptor binding, and the resulting relationship between odorant concentration and the bound receptor fraction is a saturating one. While this Hill nonlinearity can be viewed as a distortion that is imposed by the biophysics of receptor binding, here we show that it also plays an important information-processing role in olfactory navigation. Specifically, by combining a novel dynamic-programming algorithm with physical measurements of turbulent plumes, we determine the optimal strategy for encoding odor concentration when the goal is to determine location. This strategy is distinct from histogram equalization, the strategy that maximizes information about plume concentration, and is closely approximated by the Hill nonlinearity when the binding constant is near the ambient mean.

Mechanisms of Sensory Discrimination: Insights from Drosophila Olfaction

All an animal can do to infer the state of its environment is to observe the sensory-evoked activity of its own neurons. These inferences about the presence, quality, or similarity of objects are probabilistic and inform behavioral decisions that are often made in close to real time. Neural systems employ several strategies to facilitate sensory discrimination: Biophysical mechanisms separate the neuronal response distributions in coding space, compress their variances, and combine information from sequential observations. We review how these strategies are implemented in the olfactory system of the fruit fly. The emerging principles of odor discrimination likely apply to other neural circuits of similar architecture.

Structured Odorant Response Patterns across a Complete Olfactory Receptor Neuron Population

Odor perception allows animals to distinguish odors, recognize the same odor across concentrations, and determine concentration changes. How the activity patterns of primary olfactory receptor neurons (ORNs), at the individual and population levels, facilitate distinguishing these functions remains poorly understood. Here, we interrogate the complete ORN population of the Drosophila larva across a broadly sampled panel of odorants at varying concentrations. We find that the activity of each ORN scales with the concentration of any odorant via a fixed dose-response function with a variable sensitivity. Sensitivities across odorants and ORNs follow a power-law distribution. Much of receptor sensitivity to odorants is accounted for by a single geometrical property of molecular structure. Similarity in the shape of temporal response filters across odorants and ORNs extend these relationships to fluctuating environments. These results uncover shared individual- and population-level patterns that together lend structure to support odor perceptions.

Stochastic thermodynamic limit on E. coli adaptation by information geometric approach

Biological systems process information under noisy environment. Sensory adaptation model of E. coli is suitable for investigation because of its simplicity. To understand the adaptation processing quantitatively, stochastic thermodynamic approach has been attempted. Information processing can be assumed as state transition of a system that consists of signal transduction molecules using thermodynamic approach, and efficiency can be measured as thermodynamic cost. Recently, using information geometry and stochastic thermodynamics, a relationship between speed of the transition and the thermodynamic cost has been investigated for a chemical reaction model. Here, we introduce this approach to sensory adaptation model of E. coli, and examined a relationship between adaptation speed and the thermodynamic cost, and efficiency of the adaptation speed. For increasing external noise level in stimulation, the efficiency decreased, but the efficiency was highly robust to external stimulation strength. Moreover, we demonstrated that there is the best noise to achieve the adaptation in the aspect of thermodynamic efficiency. Our quantification method provides a framework to understand the adaptation speed and the thermodynamic cost for various biological systems.

Odor Stimuli: Not Just Chemical Identity

In most sensory modalities the underlying physical phenomena are well understood, and stimulus properties can be precisely controlled. In olfaction, the situation is different. The presence of specific chemical compounds in the air (or water) is the root cause for perceived odors, but it remains unknown what organizing principles, equivalent to wavelength for light, determine the dimensions of odor space. Equally important, but less in the spotlight, odor stimuli are also complex with respect to their physical properties, including concentration and time-varying spatio-temporal distribution. We still lack a complete understanding or control over these properties, in either experiments or theory. In this review, we will concentrate on two important aspects of the physical properties of odor stimuli beyond the chemical identity of the odorants: (1) The amplitude of odor stimuli and their temporal dynamics. (2) The spatio-temporal structure of odor plumes in a natural environment. Concerning these issues, we ask the following questions: (1) Given any particular experimental protocol for odor stimulation, do we have a realistic estimate of the odorant concentration in the air, and at the olfactory receptor neurons? Can we control, or at least know, the dynamics of odorant concentration at olfactory receptor neurons? (2) What do we know of the spatio-temporal structure of odor stimuli in a natural environment both from a theoretical and experimental perspective? And how does this change if we consider mixtures of odorants? For both topics, we will briefly summarize the underlying principles of physics and review the experimental and theoretical Neuroscience literature, focusing on the aspects that are relevant to animals' physiology and behavior. We hope that by bringing the physical principles behind odor plume landscapes to the fore we can contribute to promoting a new generation of experiments and models.

Variance adaptation in navigational decision making

Sensory systems relay information about the world to the brain, which enacts behaviors through motor outputs. To maximize information transmission, sensory systems discard redundant information through adaptation to the mean and variance of the environment. The behavioral consequences of sensory adaptation to environmental variance have been largely unexplored. Here, we study how larval fruit flies adapt sensory-motor computations underlying navigation to changes in the variance of visual and olfactory inputs. We show that variance adaptation can be characterized by rescaling of the sensory input and that for both visual and olfactory inputs, the temporal dynamics of adaptation are consistent with optimal variance estimation. In multisensory contexts, larvae adapt independently to variance in each sense, and portions of the navigational pathway encoding mixed odor and light signals are also capable of variance adaptation. Our results suggest multiplication as a mechanism for odor-light integration.

Moth olfactory receptor neurons adjust their encoding efficiency to temporal statistics of pheromone fluctuations

The efficient coding hypothesis predicts that sensory neurons adjust their coding resources to optimally represent the stimulus statistics of their environment. To test this prediction in the moth olfactory system, we have developed a stimulation protocol that mimics the natural temporal structure within a turbulent pheromone plume. We report that responses of antennal olfactory receptor neurons to pheromone encounters follow the temporal fluctuations in such a way that the most frequent stimulus timescales are encoded with maximum accuracy. We also observe that the average coding precision of the neurons adjusted to the stimulus-timescale statistics at a given distance from the pheromone source is higher than if the same encoding model is applied at a shorter, non-matching, distance. Finally, the coding accuracy profile and the stimulus-timescale distribution are related in the manner predicted by the information theory for the many-to-one convergence scenario of the moth peripheral sensory system.

Algorithms for Olfactory Search across Species

Localizing the sources of stimuli is essential. Most organisms cannot eat, mate, or escape without knowing where the relevant stimuli originate. For many, if not most, animals, olfaction plays an essential role in search. While microorganismal chemotaxis is relatively well understood, in larger animals the algorithms and mechanisms of olfactory search remain mysterious. In this symposium, we will present recent advances in our understanding of olfactory search in flies and rodents. Despite their different sizes and behaviors, both species must solve similar problems, including meeting the challenges of turbulent airflow, sampling the environment to optimize olfactory information, and incorporating odor information into broader navigational systems.

Nonlinearization: naturalistic stimulation and nonlinear dynamic behavior in a spider mechanoreceptor

In a previous study, we used linear frequency response analysis to show that naturalistic stimulation of spider primary mechanosensory neurons produced different response dynamics than the commonly used Gaussian random noise. We isolated this difference to the production of action potentials from receptor potential and suggested that the different distribution of frequency components in the naturalistic signal increased the nonlinearity of action potential encoding. Here, we tested the relative contributions of first- and second-order processes to the action potential signal by measuring linear and quadratic coherence functions. Naturalistic stimulation shifted the linear coherence toward lower frequencies, while quadratic coherence was always higher than linear coherence and increased with naturalistic stimulation. In an initial attempt to separate the order of time-dependent and nonlinear processes, we fitted quadratic frequency response functions by two block-structured models consisting of a power-law filter and a static second-order nonlinearity in alternate cascade orders. The same cascade models were then fitted to the original time domain data by conventional numerical analysis algorithms, using a polynomial function as the static nonlinearity. Quadratic models with a linear filter followed by a static nonlinearity were favored over the reverse order, but with weak significance. Polynomial nonlinear functions indicated that rectification is a major nonlinearity. A complete quantitative description of sensory encoding in these primary mechanoreceptors remains elusive but clearly requires quadratic and higher nonlinear operations on the input signal to explain the sensitivity of dynamic behavior to different input signal patterns.

Elementary sensory-motor transformations underlying olfactory navigation in walking fruit-flies

Odor attraction in walking Drosophila melanogaster is commonly used to relate neural function to behavior, but the algorithms underlying attraction are unclear. Here, we develop a high-throughput assay to measure olfactory behavior in response to well-controlled sensory stimuli. We show that odor evokes two behaviors: an upwind run during odor (ON response), and a local search at odor offset (OFF response). Wind orientation requires antennal mechanoreceptors, but search is driven solely by odor. Using dynamic odor stimuli, we measure the dependence of these two behaviors on odor intensity and history. Based on these data, we develop a navigation model that recapitulates the behavior of flies in our apparatus, and generates realistic trajectories when run in a turbulent boundary layer plume. The ability to parse olfactory navigation into quantifiable elementary sensori-motor transformations provides a foundation for dissecting neural circuits that govern olfactory behavior.

Information-theoretic analysis of realistic odor plumes: What cues are useful for determining location?

Many species rely on olfaction to navigate towards food sources or mates. Olfactory navigation is a challenging task since odor environments are typically turbulent. While time-averaged odor concentration varies smoothly with the distance to the source, instaneous concentrations are intermittent and obtaining stable averages takes longer than the typical intervals between animals’ navigation decisions. How to effectively sample from the odor distribution to determine sampling location is the focus in this article. To investigate which sampling strategies are most informative about the location of an odor source, we recorded three naturalistic stimuli with planar lased-induced fluorescence and used an information-theoretic approach to quantify the information that different sampling strategies provide about sampling location. Specifically, we compared multiple sampling strategies based on a fixed number of coding bits for encoding the olfactory stimulus. When the coding bits were all allocated to representing odor concentration at a single sensor, information rapidly saturated. Using the same number of coding bits in two sensors provides more information, as does coding multiple samples at different times. When accumulating multiple samples at a fixed location, the temporal sequence does not yield a large amount of information and can be averaged with minimal loss. Furthermore, we show that histogram-equalization is not the most efficient way to use coding bits when using the olfactory sample to determine location.

Navigating towards a food source or mating partner based on an animals’ sense of smell is a difficult task due to the complex spatiotemporal distribution of odor molecules. The most basic aspect of this task is the acquisition of samples from the environment. It is clear that odor concentration does not vary smoothly across space in many natural foraging environments. Using data from three different naturalistic environments, we compare different sampling strategies and assess their efficacy in determining the sources’ location. Our findings show that coarsely encoding the concentration of samples at separate sensors and/or multiple times provides more information than encoding fewer samples with higher resolution. Furthermore, coding resources should be focused on discriminating rare high-concentration odor samples, which are very informative about the sampling location. Such a nonlinear transformation can be implemented biologically by the receptor binding kinetics that bind odorants as a first stage of the sampling process. A further implication is that animals as well as computational models of algorithms can operate efficiently with a coarse representation of the odor concentration.

Tuning Insect Odorant Receptors

Among the insect olfactory receptors the odorant receptors (ORs) evolved in parallel to the onset of insect flight. A special property of this receptor type is the capability to adjust sensitivity of odor detection according to previous odor contacts. This article presents a current view on regulatory processes affecting the performance of ORs and proposes a model of mechanisms contributing to OR sensitization.

Fast intensity adaptation enhances the encoding of sound in Drosophila

To faithfully encode complex stimuli, sensory neurons should correct, via adaptation, for stimulus properties that corrupt pattern recognition. Here we investigate sound intensity adaptation in the Drosophila auditory system, which is largely devoted to processing courtship song. Mechanosensory neurons (JONs) in the antenna are sensitive not only to sound-induced antennal vibrations, but also to wind or gravity, which affect the antenna's mean position. Song pattern recognition, therefore, requires adaptation to antennal position (stimulus mean) in addition to sound intensity (stimulus variance). We discover fast variance adaptation in Drosophila JONs, which corrects for background noise over the behaviorally relevant intensity range. We determine where mean and variance adaptation arises and how they interact. A computational model explains our results using a sequence of subtractive and divisive adaptation modules, interleaved by rectification. These results lay the foundation for identifying the molecular and biophysical implementation of adaptation to the statistics of natural sensory stimuli.

Odorant Receptor Desensitization in Insects

Insects and other arthropods transmit devastating human diseases, and these vectors use chemical senses to target humans. Understanding how these animals detect, respond, and adapt to volatile odorants may lead to novel ways to disrupt host localization or mate recognition in these pests. The past decade has led to remarkable progress in understanding odorant detection in arthropods. Insects use odorant-gated ion channels, first discovered in Drosophila melanogaster, to detect volatile chemicals. In flies, 60 "tuning" receptor subunits combine with a common subunit, Orco (odorant receptor coreceptor) to form ligand-gated ion channels. The mechanisms underlying odorant receptor desensitization in insects are largely unknown. Recent work reveals that dephosphorylation of serine 289 on the shared Orco subunit is responsible for slow, odor-induced receptor desensitization. Dephosphorylation has no effect on the localization of the receptor protein, and activation of the olfactory neurons in the absence of odor is sufficient to induce dephosphorylation and desensitization. These findings reveal a major component of receptor modulation in this important group of disease vectors, and implicate a second messenger feedback mechanism in this process.

Olfactory coding in the turbulent realm

Long-distance olfactory search behaviors depend on odor detection dynamics. Due to turbulence, olfactory signals travel as bursts of variable concentration and spacing and are characterized by long-tail distributions of odor/no-odor events, challenging the computing capacities of olfactory systems. How animals encode complex olfactory scenes to track the plume far from the source remains unclear. Here we focus on the coding of the plume temporal dynamics in moths. We compare responses of olfactory receptor neurons (ORNs) and antennal lobe projection neurons (PNs) to sequences of pheromone stimuli either with white-noise patterns or with realistic turbulent temporal structures simulating a large range of distances (8 to 64 m) from the odor source. For the first time, we analyze what information is extracted by the olfactory system at large distances from the source. Neuronal responses are analyzed using linear-nonlinear models fitted with white-noise stimuli and used for predicting responses to turbulent stimuli. We found that neuronal firing rate is less correlated with the dynamic odor time course when distance to the source increases because of improper coding during long odor and no-odor events that characterize large distances. Rapid adaptation during long puffs does not preclude however the detection of puff transitions in PNs. Individual PNs but not individual ORNs encode the onset and offset of odor puffs for any temporal structure of stimuli. A higher spontaneous firing rate coupled to an inhibition phase at the end of PN responses contributes to this coding property. This allows PNs to decode the temporal structure of the odor plume at any distance to the source, an essential piece of information moths can use in their tracking behavior.