Odour motion sensing enhances navigation of complex plumes.

Odour plumes in the wild are spatially complex and rapidly fluctuating structures carried by turbulent airflows1-4. To successfully navigate plumes in search of food and mates, insects must extract and integrate multiple features of the odour signal, including odour identity5, intensity6 and timing6-12. Effective navigation requires balancing these multiple streams of olfactory information and integrating them with other sensory inputs, including mechanosensory and visual cues9,12,13. Studies dating back a century have indicated that, of these many sensory inputs, the wind provides the main directional cue in turbulent plumes, leading to the longstanding model of insect odour navigation as odour-elicited upwind motion6,8-12,14,15. Here we show that Drosophila melanogaster shape their navigational decisions using an additional directional cue-the direction of motion of odours-which they detect using temporal correlations in the odour signal between their two antennae. Using a high-resolution virtual-reality paradigm to deliver spatiotemporally complex fictive odours to freely walking flies, we demonstrate that such odour-direction sensing involves algorithms analogous to those in visual-direction sensing16. Combining simulations, theory and experiments, we show that odour motion contains valuable directional information that is absent from the airflow alone, and that both Drosophila and virtual agents are aided by that information in navigating naturalistic plumes. The generality of our findings suggests that odour-direction sensing may exist throughout the animal kingdom and could improve olfactory robot navigation in uncertain environments.

Optimal inference of molecular interaction dynamics in FRET microscopy.

Intensity-based time-lapse fluorescence resonance energy transfer (FRET) microscopy has been a major tool for investigating cellular processes, converting otherwise unobservable molecular interactions into fluorescence time series. However, inferring the molecular interaction dynamics from the observables remains a challenging inverse problem, particularly when measurement noise and photobleaching are nonnegligible-a common situation in single-cell analysis. The conventional approach is to process the time-series data algebraically, but such methods inevitably accumulate the measurement noise and reduce the signal-to-noise ratio (SNR), limiting the scope of FRET microscopy. Here, we introduce an alternative probabilistic approach, B-FRET, generally applicable to standard 3-cube FRET-imaging data. Based on Bayesian filtering theory, B-FRET implements a statistically optimal way to infer molecular interactions and thus drastically improves the SNR. We validate B-FRET using simulated data and then apply it to real data, including the notoriously noisy in vivo FRET time series from individual bacterial cells to reveal signaling dynamics otherwise hidden in the noise.

Temporal novelty detection and multiple timescale integration drive Drosophila orientation dynamics in temporally diverse olfactory environments.

To survive, insects must effectively navigate odor plumes to their source. In natural plumes, turbulent winds break up smooth odor regions into disconnected patches, so navigators encounter brief bursts of odor interrupted by bouts of clean air. The timing of these encounters plays a critical role in navigation, determining the direction, rate, and magnitude of insects' orientation and speed dynamics. Disambiguating the specific role of odor timing from other cues, such as spatial structure, is challenging due to natural correlations between plumes' temporal and spatial features. Here, we use optogenetics to isolate temporal features of odor signals, examining how the frequency and duration of odor encounters shape the navigational decisions of freely-walking Drosophila. We find that fly angular velocity depends on signal frequency and intermittency-the fraction of time signal can be detected-but not directly on durations. Rather than switching strategies when signal statistics change, flies smoothly transition between signal regimes, by combining an odor offset response with a frequency-dependent novelty-like response. In the latter, flies are more likely to turn in response to each odor hit only when the hits are sparse. Finally, the upwind bias of individual turns relies on a filtering scheme with two distinct timescales, allowing rapid and sustained responses in a variety of signal statistics. A quantitative model incorporating these ingredients recapitulates fly orientation dynamics across a wide range of environments and shows that temporal novelty detection, when combined with odor motion detection, enhances odor plume navigation.

Optimal control methods for nonlinear parameter estimation in biophysical neuron models.

Functional forms of biophysically-realistic neuron models are constrained by neurobiological and anatomical considerations, such as cell morphologies and the presence of known ion channels. Despite these constraints, neuron models still contain unknown static parameters which must be inferred from experiment. This inference task is most readily cast into the framework of state-space models, which systematically takes into account partial observability and measurement noise. Inferring only dynamical state variables such as membrane voltages is a well-studied problem, and has been approached with a wide range of techniques beginning with the well-known Kalman filter. Inferring both states and fixed parameters, on the other hand, is less straightforward. Here, we develop a method for joint parameter and state inference that combines traditional state space modeling with chaotic synchronization and optimal control. Our methods are tailored particularly to situations with considerable measurement noise, sparse observability, very nonlinear or chaotic dynamics, and highly uninformed priors. We illustrate our approach both in a canonical chaotic model and in a phenomenological neuron model, showing that many unknown parameters can be uncovered reliably and accurately from short and noisy observed time traces. Our method holds promise for estimation in larger-scale systems, given ongoing improvements in calcium reporters and genetically-encoded voltage indicators.

A unifying view of synchronization for data assimilation in complex nonlinear networks.

Networks of nonlinear systems contain unknown parameters and dynamical degrees of freedom that may not be observable with existing instruments. From observable state variables, we want to estimate the connectivity of a model of such a network and determine the full state of the model at the termination of a temporal observation window during which measurements transfer information to a model of the network. The model state at the termination of a measurement window acts as an initial condition for predicting the future behavior of the network. This allows the validation (or invalidation) of the model as a representation of the dynamical processes producing the observations. Once the model has been tested against new data, it may be utilized as a predictor of responses to innovative stimuli or forcing. We describe a general framework for the tasks involved in the "inverse" problem of determining properties of a model built to represent measured output from physical, biological, or other processes when the measurements are noisy, the model has errors, and the state of the model is unknown when measurements begin. This framework is called statistical data assimilation and is the best one can do in estimating model properties through the use of the conditional probability distributions of the model state variables, conditioned on observations. There is a very broad arena of applications of the methods described. These include numerical weather prediction, properties of nonlinear electrical circuitry, and determining the biophysical properties of functional networks of neurons. Illustrative examples will be given of (1) estimating the connectivity among neurons with known dynamics in a network of unknown connectivity, and (2) estimating the biophysical properties of individual neurons in vitro taken from a functional network underlying vocalization in songbirds.

Nonlinear statistical data assimilation for HVC[Formula: see text] neurons in the avian song system.

With the goal of building a model of the HVC nucleus in the avian song system, we discuss in detail a model of HVC[Formula: see text] projection neurons comprised of a somatic compartment with fast Na[Formula: see text] and K[Formula: see text] currents and a dendritic compartment with slower Ca[Formula: see text] dynamics. We show this model qualitatively exhibits many observed electrophysiological behaviors. We then show in numerical procedures how one can design and analyze feasible laboratory experiments that allow the estimation of all of the many parameters and unmeasured dynamical variables, given observations of the somatic voltage [Formula: see text] alone. A key to this procedure is to initially estimate the slow dynamics associated with Ca, blocking the fast Na and K variations, and then with the Ca parameters fixed estimate the fast Na and K dynamics. This separation of time scales provides a numerically robust method for completing the full neuron model, and the efficacy of the method is tested by prediction when observations are complete. The simulation provides a framework for the slice preparation experiments and illustrates the use of data assimilation methods for the design of those experiments.

Bifurcation enhances temporal information encoding in the olfactory periphery.

Living systems continually respond to signals from the surrounding environment. Survival requires that their responses adapt quickly and robustly to the changes in the environment. One particularly challenging example is olfactory navigation in turbulent plumes, where animals experience highly intermittent odor signals while odor concentration varies over many length- and timescales. Here, we show theoretically that Drosophila olfactory receptor neurons (ORNs) can exploit proximity to a bifurcation point of their firing dynamics to reliably extract information about the timing and intensity of fluctuations in the odor signal, which have been shown to be critical for odor-guided navigation. Close to the bifurcation, the system is intrinsically invariant to signal variance, and information about the timing, duration, and intensity of odor fluctuations is transferred efficiently. Importantly, we find that proximity to the bifurcation is maintained by mean adaptation alone and therefore does not require any additional feedback mechanism or fine-tuning. Using a biophysical model with calcium-based feedback, we demonstrate that this mechanism can explain the measured adaptation characteristics of Drosophila ORNs.

Bifurcation enhances temporal information encoding in the olfactory periphery.

Living systems continually respond to signals from the surrounding environment. Survival requires that their responses adapt quickly and robustly to the changes in the environment. One particularly challenging example is olfactory navigation in turbulent plumes, where animals experience highly intermittent odor signals while odor concentration varies over many length- and timescales. Here, we show theoretically that Drosophila olfactory receptor neurons (ORNs) can exploit proximity to a bifurcation point of their firing dynamics to reliably extract information about the timing and intensity of fluctuations in the odor signal, which have been shown to be critical for odor-guided navigation. Close to the bifurcation, the system is intrinsically invariant to signal variance, and information about the timing, duration, and intensity of odor fluctuations is transferred efficiently. Importantly, we find that proximity to the bifurcation is maintained by mean adaptation alone and therefore does not require any additional feedback mechanism or fine-tuning. Using a biophysical model with calcium-based feedback, we demonstrate that this mechanism can explain the measured adaptation characteristics of Drosophila ORNs.

Sensing complementary temporal features of odor signals enhances navigation of diverse turbulent plumes.

We and others have shown that during odor plume navigation, walking Drosophila melanogaster bias their motion upwind in response to both the frequency of their encounters with the odor (Demir et al., 2020) and the intermittency of the odor signal, which we define to be the fraction of time the signal is above a detection threshold (Alvarez-Salvado et al., 2018). Here, we combine and simplify previous mathematical models that recapitulated these data to investigate the benefits of sensing both of these temporal features and how these benefits depend on the spatiotemporal statistics of the odor plume. Through agent-based simulations, we find that navigators that only use frequency or intermittency perform well in some environments - achieving maximal performance when gains are near those inferred from experiment - but fail in others. Robust performance across diverse environments requires both temporal modalities. However, we also find a steep trade-off when using both sensors simultaneously, suggesting a strong benefit to modulating how much each sensor is weighted, rather than using both in a fixed combination across plumes. Finally, we show that the circuitry of the Drosophila olfactory periphery naturally enables simultaneous intermittency and frequency sensing, enhancing robust navigation through a diversity of odor environments. Together, our results suggest that the first stage of olfactory processing selects and encodes temporal features of odor signals critical to real-world navigation tasks.

Walking Drosophila navigate complex plumes using stochastic decisions biased by the timing of odor encounters.

How insects navigate complex odor plumes, where the location and timing of odor packets are uncertain, remains unclear. Here we imaged complex odor plumes simultaneously with freely-walking flies, quantifying how behavior is shaped by encounters with individual odor packets. We found that navigation was stochastic and did not rely on the continuous modulation of speed or orientation. Instead, flies turned stochastically with stereotyped saccades, whose direction was biased upwind by the timing of prior odor encounters, while the magnitude and rate of saccades remained constant. Further, flies used the timing of odor encounters to modulate the transition rates between walks and stops. In more regular environments, flies continuously modulate speed and orientation, even though encounters can still occur randomly due to animal motion. We find that in less predictable environments, where encounters are random in both space and time, walking flies navigate with random walks biased by encounter timing.

When walking along a city street, you might encounter a range of scents and odors, from the smells of coffee and food to those of exhaust fumes and garbage. The odors are swept to your nose by air currents that move scents in two different ways. They carry them downwind in a process called advection, but they also mix them chaotically with clean air in a process called turbulence. What results is an odor plume: a complex ever-changing structure resembling the smoke rising from a chimney. Within a plume, areas of highly concentrated odor particles break up into smaller parcels as they travel further from the odor source. This means that the concentration of the odor does not vary along a smooth gradient. Instead, the odor arrives in brief and unpredictable bursts. Despite this complexity, insects are able to use odor plumes with remarkable ease to navigate towards food sources. But how do they do this? Answering this question has proved challenging because odor plumes are usually invisible. Over the years, scientists have come up with a number of creative solutions to this problem, including releasing soap bubbles together with odors, or using wind tunnels to generate simpler, straight plumes in known locations. These approaches have shown that when insects encounter an odor, they surge upwind towards its source. When they lose track of the odor, they cast themselves crosswind in an effort to regain contact. But this does not explain how insects are able to navigate irregular odor plumes, in which both the timing and location of the odor bursts are unpredictable. Demir, Kadakia et al. have now bridged this gap by showing how fruit flies are attracted to smoke, an odorant that is also visible. By injecting irregular smoke plumes into a custom-built wind tunnel, and then imaging flies as they walked through it, Demir, Kadakia et al. showed that flies make random halts when navigating the plume. Each time they stop, they use the timing of the odor bursts reaching them to decide when to start moving again. Rather than turning every time they detect an odor, flies initiate turns at random times. When several odor bursts arrive in a short time, the flies tend to orient these turns upwind rather than downwind. Flies therefore rely on a different strategy to navigate irregular odor plumes than the 'surge and cast' method they use for regular odor streams. Successful navigation through complex irregular plumes involves a degree of random behavior. This helps the flies gather information about an unpredictable environment as they search for the source of the odor. These findings may help to understand how other insects use odor to navigate in the real world, for example, how mosquitoes track down human hosts.

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.

Systematic variational method for statistical nonlinear state and parameter estimation.

In statistical data assimilation one evaluates the conditional expected values, conditioned on measurements, of interesting quantities on the path of a model through observation and prediction windows. This often requires working with very high dimensional integrals in the discrete time descriptions of the observations and model dynamics, which become functional integrals in the continuous-time limit. Two familiar methods for performing these integrals include (1) Monte Carlo calculations and (2) variational approximations using the method of Laplace plus perturbative corrections to the dominant contributions. We attend here to aspects of the Laplace approximation and develop an annealing method for locating the variational path satisfying the Euler-Lagrange equations that comprises the major contribution to the integrals. This begins with the identification of the minimum action path starting with a situation where the model dynamics is totally unresolved in state space, and the consistent minimum of the variational problem is known. We then proceed to slowly increase the model resolution, seeking to remain in the basin of the minimum action path, until a path that gives the dominant contribution to the integral is identified. After a discussion of some general issues, we give examples of the assimilation process for some simple, instructive models from the geophysical literature. Then we explore a slightly richer model of the same type with two distinct time scales. This is followed by a model characterizing the biophysics of individual neurons.