Eatai Roth

A comparative approach to closed-loop computation.

Neural computation is inescapably closed-loop: the nervous system processes sensory signals to shape motor output, and motor output consequently shapes sensory input. Technological advances have enabled neuroscientists to close, open, and alter feedback loops in a wide range of experimental preparations. The experimental capability of manipulating the topology-that is, how information can flow between subsystems-provides new opportunities to understand the mechanisms and computations underlying behavior. These experiments encompass a spectrum of approaches from fully open-loop, restrained preparations to the fully closed-loop character of free behavior. Control theory and system identification provide a clear computational framework for relating these experimental approaches. We describe recent progress and new directions for translating experiments at one level in this spectrum to predictions at another level. Operating across this spectrum can reveal new understanding of how low-level neural mechanisms relate to high-level function during closed-loop behavior.

Cellular mechanisms for integral feedback in visually guided behavior

Significance Visually driven behaviors of Drosophila have become a model system to study how neural circuits process sensory information. Here, we show that one of the computations performed by this system is temporal integration of visual motion. We provide evidence of how this computation might be performed by measuring the activity of identified visual interneurons during tethered flight that are thought to control the described behavior: Presynaptic calcium accumulation in these neurons mimics a leaky temporal integration of the visual motion signal as does the behavior. In the future, the genetic tools available in Drosophila will enable studying the precise mechanism of temporal integration in this model system, which could provide insights into general mechanisms of neuronal information processing. Sensory feedback is a ubiquitous feature of guidance systems in both animals and engineered vehicles. For example, a common strategy for moving along a straight path is to turn such that the measured rate of rotation is zero. This task can be accomplished by using a feedback signal that is proportional to the instantaneous value of the measured sensory signal. In such a system, the addition of an integral term depending on past values of the sensory input is needed to eliminate steady-state error [proportional-integral (PI) control]. However, the means by which nervous systems implement such a computation are poorly understood. Here, we show that the optomotor responses of flying Drosophila follow a time course consistent with temporal integration of horizontal motion input. To investigate the cellular basis of this effect, we performed whole-cell patch-clamp recordings from the set of identified visual interneurons [horizontal system (HS) cells] thought to control this reflex during tethered flight. At high stimulus speeds, HS cells exhibit steady-state responses during flight that are absent during quiescence, a state-dependent difference in physiology that is explained by changes in their presynaptic inputs. However, even during flight, the membrane potential of the large-field interneurons exhibits no evidence for integration that could explain the behavioral responses. However, using a genetically encoded indicator, we found that calcium accumulates in the terminals of the interneurons along a time course consistent with the behavior and propose that this accumulation provides a mechanism for temporal integration of sensory feedback consistent with PI control.

Feedback Control as a Framework for Understanding Tradeoffs in Biology

Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the stability (or change) of dynamical systems. It provides a framework for understanding any system with regulation via feedback, including biological ones such as regulatory gene networks, cellular metabolic systems, sensorimotor dynamics of moving animals, and even ecological or evolutionary dynamics of organisms and populations. Here, we focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organisms response to perturbations. We use examples from aquatic (two behaviors performed by electric fish), terrestrial (following of walls by cockroaches), and aerial environments (flight control by moths) to highlight how one can use control theory to understand the way feedback mechanisms interact with the physical dynamics of animals to determine their stability and response to sensory inputs and perturbations. Each case study is cast as a control problem with sensory input, neural processing, and motor dynamics, the output of which feeds back to the sensory inputs. Collectively, the interaction of these systems in a closed loop determines the behavior of the entire system.

Active sensing via movement shapes spatiotemporal patterns of sensory feedback.

SUMMARY Previous work has shown that animals alter their locomotor behavior to increase sensing volumes. However, an animal’s own movement also determines the spatial and temporal dynamics of sensory feedback. Because each sensory modality has unique spatiotemporal properties, movement has differential and potentially independent effects on each sensory system. Here we show that weakly electric fish dramatically adjust their locomotor behavior in relation to changes of modality-specific information in a task in which increasing sensory volume is irrelevant. We varied sensory information during a refuge-tracking task by changing illumination (vision) and conductivity (electroreception). The gain between refuge movement stimuli and fish tracking responses was functionally identical across all sensory conditions. However, there was a significant increase in the tracking error in the dark (no visual cues). This was a result of spontaneous whole-body oscillations (0.1 to 1 Hz) produced by the fish. These movements were costly: in the dark, fish swam over three times further when tracking and produced more net positive mechanical work. The magnitudes of these oscillations increased as electrosensory salience was degraded via increases in conductivity. In addition, tail bending (1.5 to 2.35 Hz), which has been reported to enhance electrosensory perception, occurred only during trials in the dark. These data show that both categories of movements – whole-body oscillations and tail bends – actively shape the spatiotemporal dynamics of electrosensory feedback.

Stimulus predictability mediates a switch in locomotor smooth pursuit performance for Eigenmannia virescens

SUMMARY The weakly electric glass knifefish, Eigenmannia virescens, will swim forward and backward, using propulsion from an anal ribbon fin, in response to motion of a computer-controlled moving refuge. Fish were recorded performing a refuge-tracking behavior for sinusoidal (predictable) and sum-of-sines (pseudo-random) refuge trajectories. For all trials, we observed high coherence between refuge and fish trajectories, suggesting linearity of the tracking dynamics. But superposition failed: we observed categorical differences in tracking between the predictable single-sine stimuli and the unpredictable sum-of-sines stimuli. This nonlinearity suggests a stimulus-mediated adaptation. At all frequencies tested, fish demonstrated reduced tracking error when tracking single-sine trajectories and this was typically accompanied by a reduction in overall movement. Most notably, fish demonstrated reduced phase lag when tracking single-sine trajectories. These data support the hypothesis that fish generate an internal dynamical model of the stimulus motion, hence improving tracking of predictable trajectories (relative to unpredictable ones) despite similar or reduced motor cost. Similar predictive mechanisms based on the dynamics of stimulus movement have been proposed recently, but almost exclusively for nonlocomotor tasks by humans, such as oculomotor target tracking and posture control. These data suggest that such mechanisms might be common across taxa and behaviors.

Synaptic Plasticity Can Produce and Enhance Direction Selectivity

The discrimination of the direction of movement of sensory images is critical to the control of many animal behaviors. We propose a parsimonious model of motion processing that generates direction selective responses using short-term synaptic depression and can reproduce salient features of direction selectivity found in a population of neurons in the midbrain of the weakly electric fish Eigenmannia virescens. The model achieves direction selectivity with an elementary Reichardt motion detector: information from spatially separated receptive fields converges onto a neuron via dynamically different pathways. In the model, these differences arise from convergence of information through distinct synapses that either exhibit or do not exhibit short-term synaptic depression—short-term depression produces phase-advances relative to nondepressing synapses. Short-term depression is modeled using two state-variables, a fast process with a time constant on the order of tens to hundreds of milliseconds, and a slow process with a time constant on the order of seconds to tens of seconds. These processes correspond to naturally occurring time constants observed at synapses that exhibit short-term depression. Inclusion of the fast process is sufficient for the generation of temporal disparities that are necessary for direction selectivity in the elementary Reichardt circuit. The addition of the slow process can enhance direction selectivity over time for stimuli that are sustained for periods of seconds or more. Transient (i.e., short-duration) stimuli do not evoke the slow process and therefore do not elicit enhanced direction selectivity. The addition of a sustained global, synchronous oscillation in the gamma frequency range can, however, drive the slow process and enhance direction selectivity to transient stimuli. This enhancement effect does not, however, occur for all combinations of model parameters. The ratio of depressing and nondepressing synapses determines the effects of the addition of the global synchronous oscillation on direction selectivity. These ingredients, short-term depression, spatial convergence, and gamma-band oscillations, are ubiquitous in sensory systems and may be used in Reichardt-style circuits for the generation and enhancement of a variety of biologically relevant spatiotemporal computations.

Mechanism of membrane fusion induced by vesicular stomatitis virus G protein

Significance Enveloped viruses—those with a lipid-bilayer membrane such as influenza, dengue, and human immunodeficiency viruses—enter cells by fusion of the viral membrane with a membrane of the cell. A viral surface glycoprotein, known as its “fusion protein,” facilitates this step. Previous work studying the kinetics of single virus particles fusing with a target membrane has outlined a mechanism by which conformational changes in the fusion protein accelerate merger of the two bilayers. In this paper, we extend that mechanism to a structurally distinct class of viral fusion proteins, providing strong evidence for its general applicability to all viral membrane fusion processes. The glycoproteins (G proteins) of vesicular stomatitis virus (VSV) and related rhabdoviruses (e.g., rabies virus) mediate both cell attachment and membrane fusion. The reversibility of their fusogenic conformational transitions differentiates them from many other low-pH-induced viral fusion proteins. We report single-virion fusion experiments, using methods developed in previous publications to probe fusion of influenza and West Nile viruses. We show that a three-stage model fits VSV single-particle fusion kinetics: (i) reversible, pH-dependent, G-protein conformational change from the known prefusion conformation to an extended, monomeric intermediate; (ii) reversible trimerization and clustering of the G-protein fusion loops, leading to an extended intermediate that inserts the fusion loops into the target-cell membrane; and (iii) folding back of a cluster of extended trimers into their postfusion conformations, bringing together the viral and cellular membranes. From simulations of the kinetic data, we conclude that the critical number of G-protein trimers required to overcome membrane resistance is 3 to 5, within a contact zone between the virus and the target membrane of 30 to 50 trimers. This sequence of conformational events is similar to those shown to describe fusion by influenza virus hemagglutinin (a “class I” fusogen) and West Nile virus envelope protein (“class II”). Our study of VSV now extends this description to “class III” viral fusion proteins, showing that reversibility of the low-pH-induced transition and architectural differences in the fusion proteins themselves do not change the basic mechanism by which they catalyze membrane fusion.

A task-level model for optomotor yaw regulation in drosophila melanogaster: A frequency-domain system identification approach

Fruit flies adeptly coordinate flight maneuvers to seek, avoid, or otherwise interact with salient objects in their environment. In the laboratory, tethered flies modulate yaw torque to steer towards a dark vertical visual stimulus. This stripe-fixation behavior is robust and repeatable, making it a powerful paradigm for the study of optomotor control in flies. In this work, we study stripe fixation through a series of closed-loop perturbation experiments; flies are observed stabilizing moving stripes oscillating over a range of frequencies. A system identification analysis of input-output data furnishes a frequency response function (FRF), a nonparametric description of the behavior. We parameterize this FRF description to hypothesize a Proportional-Integral-Derivative (PID) control model for the fixation behavior. Lastly, we revisit previous work in which discrepancies in open- and closed-loop performance in stripe fixation were used to support the reafference principle.We demonstrate that our hypothesized PID model (with a modest biologically plausible nonlinearity) provides a more parsimonious explanation for these previously reported discrepancies.

Integration of parallel mechanosensory and visual pathways resolved through sensory conflict

Significance Animals rely on information drawn from a host of sensory systems to control their movement as they navigate in and interact with their environment. How the nervous system consolidates and processes these channels of information to govern locomotion is a challenging reverse engineering problem. To address this issue, we asked how a hawkmoth feeding from a moving flower combines visual and mechanical (force) cues to follow the flower motion. Using experimental and theoretical approaches, we discover that the brain performs a remarkably simple summation of information from visual and mechanosensory pathways. Moreover, we reveal that the moth could perform the behavior with either visual or mechanical information alone, and this redundancy provides a robust strategy for movement control. The acquisition of information from parallel sensory pathways is a hallmark of coordinated movement in animals. Insect flight, for example, relies on both mechanosensory and visual pathways. Our challenge is to disentangle the relative contribution of each modality to the control of behavior. Toward this end, we show an experimental and analytical framework leveraging sensory conflict, a means for independently exciting and modeling separate sensory pathways within a multisensory behavior. As a model, we examine the hovering flower-feeding behavior in the hawkmoth Manduca sexta. In the laboratory, moths feed from a robotically actuated two-part artificial flower that allows independent presentation of visual and mechanosensory cues. Freely flying moths track lateral flower motion stimuli in an assay spanning both coupled motion, in which visual and mechanosensory cues follow the same motion trajectory, and sensory conflict, in which the two sensory modalities encode different motion stimuli. Applying a frequency-domain system identification analysis, we find that the tracking behavior is, in fact, multisensory and arises from a linear summation of visual and mechanosensory pathways. The response dynamics are highly preserved across individuals, providing a model for predicting the response to novel multimodal stimuli. Surprisingly, we find that each pathway in and of itself is sufficient for driving tracking behavior. When multiple sensory pathways elicit strong behavioral responses, this parallel architecture furnishes robustness via redundancy.

Honeybees in a virtual reality environment learn unique combinations of colour and shape

ABSTRACT Honeybees are well-known models for the study of visual learning and memory. Whereas most of our knowledge of learned responses comes from experiments using free-flying bees, a tethered preparation would allow fine-scale control of the visual stimuli as well as accurate characterization of the learned responses. Unfortunately, conditioning procedures using visual stimuli in tethered bees have been limited in their efficacy. In this study, using a novel virtual reality environment and a differential training protocol in tethered walking bees, we show that the majority of honeybees learn visual stimuli, and need only six paired training trials to learn the stimulus. We found that bees readily learn visual stimuli that differ in both shape and colour. However, bees learn certain components over others (colour versus shape), and visual stimuli are learned in a non-additive manner with the interaction of specific colour and shape combinations being crucial for learned responses. To better understand which components of the visual stimuli the bees learned, the shape–colour association of the stimuli was reversed either during or after training. Results showed that maintaining the visual stimuli in training and testing phases was necessary to elicit visual learning, suggesting that bees learn multiple components of the visual stimuli. Together, our results demonstrate a protocol for visual learning in restrained bees that provides a powerful tool for understanding how components of a visual stimulus elicit learned responses as well as elucidating how visual information is processed in the honeybee brain. Summary: A novel virtual reality environment and paradigm for visual training in walking honeybees shows that bees learn certain visual components over others (colour over shape), and interaction between components is crucial for visual learning in walking bees.