Control of self-motion in dynamic fluids: fish do it differently from bees

To detect and avoid collisions, animals need to perceive and control the distance and the speed with which they are moving relative to obstacles. This is especially challenging for swimming and flying animals that must control movement in a dynamic fluid without reference from physical contact to the ground. Flying animals primarily rely on optic flow to control flight speed and distance to obstacles. Here, we investigate whether swimming animals use similar strategies for self-motion control to flying animals by directly comparing the trajectories of zebrafish (Danio rerio) and bumblebees (Bombus terrestris) moving through the same experimental tunnel. While moving through the tunnel, black and white patterns produced (i) strong horizontal optic flow cues on both walls, (ii) weak horizontal optic flow cues on both walls and (iii) strong optic flow cues on one wall and weak optic flow cues on the other. We find that the mean speed of zebrafish does not depend on the amount of optic flow perceived from the walls. We further show that zebrafish, unlike bumblebees, move closer to the wall that provides the strongest visual feedback. This unexpected preference for strong optic flow cues may reflect an adaptation for self-motion control in water or in environments where visibility is limited.     

Retinal illumination produces synaptic inhibition of a neurosecretory organ in the crayfish,pacifastacus leniusculus (Dana)

We have identified a cluster of neurosecretory cells in the crayfish eyestalk that possess dendrites in the second optic neuropil (Medulla) and project axons to the first optic neuropil (Lamina). Illumination of the ipsilateral retina produces a synaptic inhibition of these cells that is mimicked by iontophoresis of gamma-aminobutyric acid within the medullary neuropil. The neurosecretory nature of the cells, the efferent projection of their axons, and the strong inhibition of their spiking activity upon retinal illumination suggest that they may be involved in the feedback control of dark adaptation and/or circadian changes in visual sensitivity.     

Optic flow estimation on trajectories generated by bio-inspired closed-loop flight

We generated panoramic imagery by simulating a fly-like robot carrying an imaging sensor, moving in free flight through a virtual arena bounded by walls, and containing obstructions. Flight was conducted under closed-loop control by a bio-inspired algorithm for visual guidance with feedback signals corresponding to the true optic flow that would be induced on an imager (computed by known kinematics and position of the robot relative to the environment). The robot had dynamics representative of a housefly-sized organism, although simplified to two-degree-of-freedom flight to generate uniaxial (azimuthal) optic flow on the retina in the plane of travel. Surfaces in the environment contained images of natural and man-made scenes that were captured by the moving sensor. Two bio-inspired motion detection algorithms and two computational optic flow estimation algorithms were applied to sequences of image data, and their performance as optic flow estimators was evaluated by estimating the mutual information between outputs and true optic flow in an equatorial section of the visual field. Mutual information for individual estimators at particular locations within the visual field was surprisingly low (less than 1 bit in all cases) and considerably poorer for the bio-inspired algorithms that the man-made computational algorithms. However, mutual information between weighted sums of these signals and comparable sums of the true optic flow showed significant increases for the bio-inspired algorithms, whereas such improvement did not occur for the computational algorithms. Such summation is representative of the spatial integration performed by wide-field motion-sensitive neurons in the third optic ganglia of flies.     

Fly flight: a model for the neural control of complex behavior.

Flies exhibit a repertoire of aerial acrobatics unmatched in robustness and aerodynamic sophistication. The exquisite control of this complex behavior emerges from encoding intricate patterns of optic flow, and the translation of these visual signals into the mechanical language of the motor system. Recent advances in experimental design toward more naturalistic visual and mechanosensory stimuli have served to reinforce fly flight as a key model system for understanding how feedback from multiple sensory modalities is integrated to control complex and robust motor behaviors across taxa.     

A Bio-inspired Collision Avoidance Model Based on Spatial Information Derived from Motion Detectors Leads to Common Routes

Avoiding collisions is one of the most basic needs of any mobile agent, both biological and technical, when searching around or aiming toward a goal. We propose a model of collision avoidance inspired by behavioral experiments on insects and by properties of optic flow on a spherical eye experienced during translation, and test the interaction of this model with goal-driven behavior. Insects, such as flies and bees, actively separate the rotational and translational optic flow components via behavior, i.e. by employing a saccadic strategy of flight and gaze control. Optic flow experienced during translation, i.e. during intersaccadic phases, contains information on the depth-structure of the environment, but this information is entangled with that on self-motion. Here, we propose a simple model to extract the depth structure from translational optic flow by using local properties of a spherical eye. On this basis, a motion direction of the agent is computed that ensures collision avoidance. Flying insects are thought to measure optic flow by correlation-type elementary motion detectors. Their responses depend, in addition to velocity, on the texture and contrast of objects and, thus, do not measure the velocity of objects veridically. Therefore, we initially used geometrically determined optic flow as input to a collision avoidance algorithm to show that depth information inferred from optic flow is sufficient to account for collision avoidance under closed-loop conditions. Then, the collision avoidance algorithm was tested with bio-inspired correlation-type elementary motion detectors in its input. Even then, the algorithm led successfully to collision avoidance and, in addition, replicated the characteristics of collision avoidance behavior of insects. Finally, the collision avoidance algorithm was combined with a goal direction and tested in cluttered environments. The simulated agent then showed goal-directed behavior reminiscent of components of the navigation behavior of insects.     

Feedback from Horizontal Cells to Cones Mediates Color Induction and May Facilitate Color Constancy in Rainbow Trout

Color vision is most beneficial when the visual system is color constant and can correct the excitations of photoreceptors for differences in environmental irradiance. A phenomenon related to color constancy is color induction, where the color of an object shifts away from the color of its surroundings. These two phenomena depend on chromatic spatial integration, which was suggested to originate at the feedback synapse from horizontal cells (HC) to cones. However, the exact retinal site was never determined. Using the electroretinogram and compound action potential recordings, we estimated the spectral sensitivity of the photoresponse of cones, the output of cones, and the optic nerve in rainbow trout. Recordings were performed before and following pharmacological inhibition of HC-cone feedback, and were repeated under two colored backgrounds to estimate the efficiency of color induction. No color induction could be detected in the photoresponse of cones. However, the efficiency of color induction in the cone output and optic nerve was substantial, with the efficiency in the optic nerve being significantly higher than in the cone output. We found that the efficiency of color induction in the cone output and optic nerve decreased significantly with the inhibition of HC-cone feedback. Therefore, our findings suggest not only that color induction originates as a result of HC-cone feedback, but also that this effect of HC-cone feedback is further amplified at downstream retinal elements, possibly through feedback mechanisms at the inner plexiform layer. This study provides evidence for an important role of HC-cone feedback in mediating color induction, and therefore, likely also in mediating color constancy.     

Honeybees' speed depends on dorsal as well as lateral, ventral and frontal optic flows

Flying insects use the optic flow to navigate safely in unfamiliar environments, especially by adjusting their speed and their clearance from surrounding objects. It has not yet been established, however, which specific parts of the optical flow field insects use to control their speed. With a view to answering this question, freely flying honeybees were trained to fly along a specially designed tunnel including two successive tapering parts: the first part was tapered in the vertical plane and the second one, in the horizontal plane. The honeybees were found to adjust their speed on the basis of the optic flow they perceived not only in the lateral and ventral parts of their visual field, but also in the dorsal part. More specifically, the honeybees' speed varied monotonically, depending on the minimum cross-section of the tunnel, regardless of whether the narrowing occurred in the horizontal or vertical plane. The honeybees' speed decreased or increased whenever the minimum cross-section decreased or increased. In other words, the larger sum of the two opposite optic flows in the horizontal and vertical planes was kept practically constant thanks to the speed control performed by the honeybees upon encountering a narrowing of the tunnel. The previously described ALIS ("AutopiLot using an Insect-based vision System") model nicely matches the present behavioral findings. The ALIS model is based on a feedback control scheme that explains how honeybees may keep their speed proportional to the minimum local cross-section of a tunnel, based solely on optic flow processing, without any need for speedometers or rangefinders. The present behavioral findings suggest how flying insects may succeed in adjusting their speed in their complex foraging environments, while at the same time adjusting their distance not only from lateral and ventral objects but also from those located in their dorsal visual field.     

The effect of optic flow cues on honeybee flight control in wind

To minimize the risk of colliding with the ground or other obstacles, flying animals need to control both their ground speed and ground height. This task is particularly challenging in wind, where head winds require an animal to increase its airspeed to maintain a constant ground speed and tail winds may generate negative airspeeds, rendering flight more difficult to control. In this study, we investigate how head and tail winds affect flight control in the honeybee Apis mellifera, which is known to rely on the pattern of visual motion generated across the eye—known as optic flow—to maintain constant ground speeds and heights. We find that, when provided with both longitudinal and transverse optic flow cues (in or perpendicular to the direction of flight, respectively), honeybees maintain a constant ground speed but fly lower in head winds and higher in tail winds, a response that is also observed when longitudinal optic flow cues are minimized. When the transverse component of optic flow is minimized, or when all optic flow cues are minimized, the effect of wind on ground height is abolished. We propose that the regular sidewards oscillations that the bees make as they fly may be used to extract information about the distance to the ground, independently of the longitudinal optic flow that they use for ground speed control. This computationally simple strategy could have potential uses in the development of lightweight and robust systems for guiding autonomous flying vehicles in natural environments.     

Visual, auditory, and bimodal activity in the banks of the lateral suprasylvian sulcus in the cat

In addition to visually driven cells we found within the lateral suprasylvian visual cortex of cats a considerable number of auditory and/or bimodal cells. Most of the visually driven cells were direction and orientation selective with responses that were neither highly stimulus time locked nor very stable. Most of the auditory responses were also not very stable, had relatively high thresholds and were readily habituated. Previous studies have suggested that populations of cells within the lateral suprasylvian area are specialized for the analysis of optic flow fields. Given that a remarkable proportion of cells within this area can be also driven by auditory stimuli we hypothesize that the "optic flow" model may be extended to the bimodal domain rather than restricted to visual clues only. This, however, remains to be corroborated experimentally.     

Modeling boundary vector cell firing given optic flow as a cue

Boundary vector cells in entorhinal cortex fire when a rat is in locations at a specific distance from walls of an environment. This firing may originate from memory of the barrier location combined with path integration, or the firing may depend upon the apparent visual input image stream. The modeling work presented here investigates the role of optic flow, the apparent change of patterns of light on the retina, as input for boundary vector cell firing. Analytical spherical flow is used by a template model to segment walls from the ground, to estimate self-motion and the distance and allocentric direction of walls, and to detect drop-offs. Distance estimates of walls in an empty circular or rectangular box have a mean error of less than or equal to two centimeters. Integrating these estimates into a visually driven boundary vector cell model leads to the firing patterns characteristic for boundary vector cells. This suggests that optic flow can influence the firing of boundary vector cells.     

Feedback optimization of fed-batch fermentation

The problem of feedback optimization of the feed rate for fed-batch fermentation processes is formulated in the framework of singular control theory and switching hypersurfaces. Using four differential balance equations that describe a general class of fedbatch processes and a general objective function to be minimized, it is shown that under certain restrictions the feedback optimization of the feed rate can be realized as a nonlinear function of the state variables, such as the concentrations of cell mass, substrate and product, and the fermentor volume. The restrictions on the initial conditions, the fermentation kinetics and the objective function, that are needed for realization of the feedback optimization, are provided. Fed-batch fermentation models of lysine and alcohol are used to construct switching curves and to illustrate the feedback optimization of the feed flow rates.     

Angle of gaze and optic flow direction modulate body sway

Optic flow is a crucial signal in maintaining postural stability. We sought to investigate whether the activity of postural muscles and body sway was modulated by eye position during the view of radial optic flow stimuli. We manipulated the spatial distribution of dot speed and the fixation point position to simulate specific heading directions combined with different gaze positions. The experiments were performed using stabilometry and surface electromyography (EMG) on 24 right-handed young, healthy volunteers. Center of pressure (COP) signals were analyzed considering antero-posterior and medio-lateral oscillation, COP speed, COP area, and the prevalent direction of oscillation of body sway. We found a significant main effect of body side in all COP parameters, with the right body side showing greater oscillations. The different combinations of optic flow and eye position evoked a non-uniform direction of oscillations in females. The EMG analysis showed a significant main effect for muscle and body side. The results showed that the eye position modulated body sway without changing the activity of principal leg postural muscles, suggesting that the extraretinal input regarding the eye position is a crucial signal that needs to be integrated with perceptual optic flow processing in order to control body sway.     

Comparison of the glial investment of normal and regenerating fiber bundles in the optic nerve and optic tectum of the goldfish and the Crucian carp

Summary The architecture of normal and regenerating nerve fiber bundles in the optic nerve of the goldfish and the Crucian carp was compared to that of the axonal fascicles in the optic tectum of these teleost species with the use of ultrathin sections and freeze-fracture replicas. The fascicles in the optic nerve are clearly demarcated by astrocytic processes, in contrast to the fascicles in the tectum. No astrocytes could be identified in the tectum; in this region processes of astrocytes or of radial glial cells do not form channeling structures reminiscent of those in the optic nerve. Furthermore, tectal blood vessels lack complete investments of glial processes. It can be assumed that at least in lower vertebrates a framework of astrocytic processes might be important for growth of optic fibers over large distances, i.e., from the eye to the tectum, but may be dispensable in the target region itself.     

Optic flow representation in the optic lobes of Diptera: modeling innervation matrices onto collators and their evolutionary implications

A network model of optic flow processing, based on physiological and anatomical features of motion-processing neurons, is used to investigate the role of small-field motion detectors emulating T5 cells in producing optic flow selective properties in wide-field collator neurons. The imposition of different connectivities can mimic variations observed in comparative studies of lobula plate architecture across the Diptera. The results identify two features that are crucial for optic flow selectivity: the broadness of the spatial patterns of synaptic connections from motion detectors to collators, and the relative contributions of excitatory and inhibitory synaptic outputs. If these two aspects of the innervation matrix are balanced appropriately, the network's sensitivity to perturbations in physiological properties of the small-field motion detectors is dramatically reduced, suggesting that sensory systems can evolve robust mechanisms that do not rely upon precise control of network parameters. These results also suggest that alternative lobula plate architectures observed in insects are consistent in allowing optic flow selective properties in wide-field neurons. The implications for the evolution of optic flow selective neurons are discussed.     

Modeling the influence of optic flow on grid cell firing in the absence of other cues1

Information from the vestibular, sensorimotor, or visual systems can affect the firing of grid cells recorded in entorhinal cortex of rats. Optic flow provides information about the rat’s linear and rotational velocity and, thus, could influence the firing pattern of grid cells. To investigate this possible link, we model parts of the rat’s visual system and analyze their capability in estimating linear and rotational velocity. In our model a rat is simulated to move along trajectories recorded from rat’s foraging on a circular ground platform. Thus, we preserve the intrinsic statistics of real rats’ movements. Visual image motion is analytically computed for a spherical camera model and superimposed with noise in order to model the optic flow that would be available to the rat. This optic flow is fed into a template model to estimate the rat’s linear and rotational velocities, which in turn are fed into an oscillatory interference model of grid cell firing. Grid scores are reported while altering the flow noise, tilt angle of the optical axis with respect to the ground, the number of flow templates, and the frequency used in the oscillatory interference model. Activity patterns are compatible with those of grid cells, suggesting that optic flow can contribute to their firing.     

In vitro Studies on Differentiation of the Optic Stalk in the Chick Embryo

An orderly pattern of cell death accompanies growth of retinal ganglion cell axons through the optic stalk of the chick embryo. In order to determine ifthe cell death process in this adage is preprogrammed at earlier stages or if other factors play a role, we cultured optic stalk primordia at a stage prior to retinal differentiation, either alone or in the presence of head or limb bud mesenchyme. When optic stalk was alone, many cells differentiated into neurons. However, when mesenchyme cells of either head or limb bud origin were combined with the stalk, the stalk cells either degenerated, were unrecognizable in the mesenchyme mass, or retained their epithelial arrangement and became pigmented. Mesenchyme and/or neural crest which normally migrate around the stalk at the same time that ganglion cell axons penetrate this structure may therefore be involved in some aspect of the cell death process. Since many optic stalk cells in vitro differentiate into neurons, these cells may represent the population of cells which in situ would normally die.     

Spatial dynamics of feedback and feedforward regulation in cell lineages

Feedback mechanisms within cell lineages are thought to be important for maintaining tissue homeostasis. Mathematical models that assume well-mixed cell populations, together with experimental data, have suggested that negative feedback from differentiated cells on the stem cell self-renewal probability can maintain a stable equilibrium and hence homeostasis. Cell lineage dynamics, however, are characterized by spatial structure, which can lead to different properties. Here, we investigate these dynamics using spatially explicit computational models, including cell division, differentiation, death, and migration / diffusion processes. According to these models, the negative feedback loop on stem cell self-renewal fails to maintain homeostasis, both under the assumption of strong spatial restrictions and fast migration / diffusion. Although homeostasis cannot be maintained, this feedback can regulate cell density and promote the formation of spatial structures in the model. Tissue homeostasis, however, can be achieved if spatially restricted negative feedback on self-renewal is combined with an experimentally documented spatial feedforward loop, in which stem cells regulate the fate of transit amplifying cells. This indicates that the dynamics of feedback regulation in tissue cell lineages are more complex than previously thought, and that combinations of spatially explicit control mechanisms are likely instrumental.     

Nocturnal insects use optic flow for flight control

To avoid collisions when navigating through cluttered environments, flying insects must control their flight so that their sensory systems have time to detect obstacles and avoid them. To do this, day-active insects rely primarily on the pattern of apparent motion generated on the retina during flight (optic flow). However, many flying insects are active at night, when obtaining reliable visual information for flight control presents much more of a challenge. To assess whether nocturnal flying insects also rely on optic flow cues to control flight in dim light, we recorded flights of the nocturnal neotropical sweat bee, Megalopta genalis, flying along an experimental tunnel when: (i) the visual texture on each wall generated strong horizontal (front-to-back) optic flow cues, (ii) the texture on only one wall generated these cues, and (iii) horizontal optic flow cues were removed from both walls. We find that Megalopta increase their groundspeed when horizontal motion cues in the tunnel are reduced (conditions (ii) and (iii)). However, differences in the amount of horizontal optic flow on each wall of the tunnel (condition (ii)) do not affect the centred position of the bee within the flight tunnel. To better understand the behavioural response of Megalopta, we repeated the experiments on day-active bumble-bees (Bombus terrestris). Overall, our findings demonstrate that despite the limitations imposed by dim light, Megalopta-like their day-active relatives-rely heavily on vision to control flight, but that they use visual cues in a different manner from diurnal insects.     

Bayesian modeling of perceived surface slant from actively-generated and passively-observed optic flow

We measured perceived depth from the optic flow (a) when showing a stationary physical or virtual object to observers who moved their head at a normal or slower speed, and (b) when simulating the same optic flow on a computer and presenting it to stationary observers. Our results show that perceived surface slant is systematically distorted, for both the active and the passive viewing of physical or virtual surfaces. These distortions are modulated by head translation speed, with perceived slant increasing directly with the local velocity gradient of the optic flow. This empirical result allows us to determine the relative merits of two alternative approaches aimed at explaining perceived surface slant in active vision: an "inverse optics" model that takes head motion information into account, and a probabilistic model that ignores extra-retinal signals. We compare these two approaches within the framework of the bayesian theory. The "inverse optics" bayesian model produces veridical slant estimates if the optic flow and the head translation velocity are measured with no error; because of the influence of a "prior" for flatness, the slant estimates become systematically biased as the measurement errors increase. The bayesian model, which ignores the observer's motion, always produces distorted estimates of surface slant. Interestingly, the predictions of this second model, not those of the first one, are consistent with our empirical findings. The present results suggest that (a) in active vision perceived surface slant may be the product of probabilistic processes which do not guarantee the correct solution, and (b) extra-retinal signals may be mainly used for a better measurement of retinal information.