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Miniscope Recording Calcium Signals at Hippocampus of Mice Navigating an Odor Plume

Mice navigate an odor plume with a complex spatiotemporal structure in the dark to find the source of odorants. This article describes a protocol to ...

University of Colorado

We investigate a class of reactive advection-diffusion problems motivated by an ecological mixing process. We use analytical and numerical methods to determine reaction rates between two initially distinct scalar point masses that are separated from one another by a third (nonreactive) scalar. The scalars are stirred by a single two-dimensional vortex in a variety of geometrical configurations. We show that the aggregate second-order reaction rate in the low-concentration limit is enhanced by the instantaneous stirring processes, relative to the rate predicted by an equivalent eddy diffusivity. The peak reaction rate grows as P(1/3), and the time to reach the peak decreases as P(-2/3), where P is the Péclet number. The results of this study have important implications not only for ecological modeling, but for the general understanding of turbulent reactive flows.

Reaction enhancement of point sources due to vortex stirring.

Broadcast-spawning benthic invertebrates synchronously release sperm and eggs from separate locations into the surrounding flow, whereupon the process depends on structured stirring by the flow field (at large scales), and sperm motility and taxis (at small scales) to bring the gametes together. The details of the relevant physical and biological aspects of the problem that result in successful and efficient fertilization are not well understood. This review paper includes relevant work from both the physical and biological communities to synthesize a more complete understanding of the processes that govern fertilization success; the focus is on the role of structured stirring on the dispersal and aggregation of gametes. The review also includes a summary of current trends and approaches for numerical and experimental simulations of broadcast spawning.

The role of structured stirring and mixing on gamete dispersal and aggregation in broadcast spawning.

Most benthic invertebrates broadcast their gametes into the sea, whereupon successful fertilization relies on the complex interaction between the physics of the surrounding fluid flow and the biological properties and behavior of eggs and sperm. We present a holistic overview of the impact of instantaneous flow processes on fertilization across a range of scales. At large scales, transport and stirring by the flow control the distribution of gametes. Although mean dilution of gametes by turbulence is deleterious to fertilization, a variety of instantaneous flow phenomena can aggregate gametes before dilution occurs. We argue that these instantaneous flow processes are key to fertilization efficiency. At small scales, sperm motility and taxis enhance contact rates between sperm and chemoattractant-releasing eggs. We argue that sperm motility is a biological adaptation that replaces molecular diffusion in conventional mixing processes and enables gametes to bridge the gap that remains after aggregation by the flow.

The physics of broadcast spawning in benthic invertebrates.

Inhalant flows draw fluid into an orifice from a reservoir and are ubiquitous in engineering and biology. Surprisingly, there is a lack of quantitative information on viscous inhalant flows. We consider here laminar flows (Reynolds number Re≤100) developing after impulsive inhalation begins. We implement finite element simulations of flows with varying Re and extraction height h (orifice height above a bottom bed). Numerical results are experimentally validated using particle image velocimetry measurements in a physical model for a representative flow case in the middle of the Re-h parameter space. We use two metrics to characterize the flow in space and time: regions of influence (ROIs), which describe the spatial extent of the flow field, and inhalation volumes, which describe the initial distribution of inhaled fluid. The transient response for all Re features an inviscid sinklike component at early times followed by a viscous diffusive component. At lower Re, diffusion entrains an increasing volume of fluid over time, enlarging the ROI indefinitely. In some geometries, these flows spatially bifurcate, with some fluid being inhaled through the orifice and some bypassing into recirculation. At higher Re, inward advection dominates outward viscous diffusion and the flow remains trapped in a sinklike state. Both ROIs and inhalation volumes are strongly dependent on Re and extraction height, suggesting that organisms or engineers could tune these parameters to achieve specific inhalation criteria.

Hydrodynamics of viscous inhalant flows.

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.

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

Odor attraction in walking  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.

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

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. 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.

Olfactory Navigation and the Receptor Nonlinearity.

Olfaction informs animal navigation for foraging, social interaction, and threat evasion. However, turbulent flow on the spatial scales of most animal navigation leads to intermittent odor information and presents a challenge to simple gradient-ascent navigation. Here we present two strategies for iterative gradient estimation and navigation via olfactory cues in 2D space: tropotaxis, spatial concentration comparison (i.e., instantaneous comparison between lateral olfactory sensors on a navigating animal) and klinotaxis, spatiotemporal concentration comparison (i.e., comparison between two subsequent concentration samples as the animal moves through space). We then construct a hybrid model that uses klinotaxis but utilizes tropotactic information to guide its spatial sampling strategy. We find that for certain body geometries in which bilateral sensors are closely-spaced (e.g., mammalian nares), klinotaxis outperforms tropotaxis; for widely-spaced sensors (e.g., arthropod antennae), tropotaxis outperforms klinotaxis. We find that both navigation strategies perform well on smooth odor gradients and are robust against noisy gradients represented by stochastic odor models and real turbulent flow data. In some parameter regimes, the hybrid model outperforms klinotaxis alone, but not tropotaxis.

Olfactory navigation in the real world: Simple local search strategies for turbulent environments.

Aerosols can transmit infectious diseases including SARS-CoV-2, influenza and norovirus. Flushed toilets emit aerosols that spread pathogens contained in feces, but little is known about the spatiotemporal evolution of these plumes or the velocity fields that transport them. Using laser light to illuminate ejected aerosols we quantify the kinematics of plumes emanating from a commercial flushometer-type toilet, and use the motion of aerosol particles to compute velocity fields of the associated flow. The toilet flush produces a strong chaotic jet with velocities exceeding 2 m/s; this jet transports aerosols to heights reaching 1.5 m within 8 seconds of initiating a flush. Quantifying toilet plumes and associated flow velocities provides a foundation for future design strategies to mitigate plume formation or to disinfect pathogens within it.

Commercial toilets emit energetic and rapidly spreading aerosol plumes.

In order to survive, animals often need to navigate a complex odor landscape where odors can exist in airborne plumes. Several odor plume properties change with distance from the odor source, providing potential navigational cues to searching animals. Here, we focus on odor intermittency, a temporal odor plume property that measures the fraction of time odor is above a threshold at a given point within the plume and decreases with increasing distance from the odor source. We sought to determine if mice can use changes in intermittency to locate an odor source. To do so, we trained mice on an intermittency discrimination task. We establish that mice can discriminate odor plume samples of low and high intermittency and that the neural responses in the olfactory bulb can account for task performance and support intermittency encoding. Modulation of sniffing, a behavioral parameter that is highly dynamic during odor-guided navigation, affects both behavioral outcome on the intermittency discrimination task and neural representation of intermittency. Together, this work demonstrates that intermittency is an odor plume property that can inform olfactory search and more broadly supports the notion that mammalian odor-based navigation can be guided by temporal odor plume properties.

Behavioral discrimination and olfactory bulb encoding of odor plume intermittency.

Two simple algorithms based on combining odor concentration differences across time and space along with information on the flow direction are tested for their ability to locate an odor source in four different odor landscapes. Image data taken from air plumes in three different regimes and a water plume are used as test environments for a bilateral ("stereo sampling") algorithm using concentration differences across two sensors and a "casting" algorithm that uses successive samples to decide orientation. Agents are started at random locations and orientations in the landscape and allowed to move until they reach the source of the odor (success) or leave the imaged area (failure). Parameters for the algorithm are chosen to optimize success and to minimize path length to the source. Success rates over 90% are consistently obtained with path lengths that can be as low as twice the starting distance from the source in air and four times the distance in the highly turbulent water plumes. We find that parameters that optimize success often lead to more exploratory pathways to the source. Information about the direction from which the odor is coming is necessary for successful navigation in the water plume and reduces the path length in the three tested air plumes.

Article	Year
Reaction enhancement of point sources due to vortex stirring. Physical review. E, Statistical, nonlinear, and soft matter physics\| PubMed ID: 16907191	2006
The role of structured stirring and mixing on gamete dispersal and aggregation in broadcast spawning. The Journal of experimental biology\| PubMed ID: 22357596	2012
The physics of broadcast spawning in benthic invertebrates. Annual review of marine science\| PubMed ID: 23957600	2014
Hydrodynamics of viscous inhalant flows. Physical review. E\| PubMed ID: 28618575	2017
Information-theoretic analysis of realistic odor plumes: What cues are useful for determining location? PLoS computational biology\| PubMed ID: 29990365	2018
Elementary sensory-motor transformations underlying olfactory navigation in walking fruit-flies. eLife\| PubMed ID: 30129438	2018
Olfactory Navigation and the Receptor Nonlinearity. The Journal of neuroscience : the official journal of the Society for Neuroscience\| PubMed ID: 30846614	2019
Olfactory navigation in the real world: Simple local search strategies for turbulent environments. Journal of theoretical biology\| PubMed ID: 33524405	2021
Commercial toilets emit energetic and rapidly spreading aerosol plumes. Scientific reports\| PubMed ID: 36481924	2022
Behavioral discrimination and olfactory bulb encoding of odor plume intermittency. eLife\| PubMed ID: 38441541	2024
Simple olfactory navigation in air and water. Journal of theoretical biology\| PubMed ID: 39260736	2024

John P. Crimaldi

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