A comparative approach to closed-loop computation

Delay-Dependent Response in Weakly Electric Fish under Closed-Loop Pulse Stimulation

In this paper, we apply a real time activity-dependent protocol to study how freely swimming weakly electric fish produce and process the timing of their own electric signals. Specifically, we address this study in the elephant fish, Gnathonemus petersii, an animal that uses weak discharges to locate obstacles or food while navigating, as well as for electro-communication with conspecifics. To investigate how the inter pulse intervals vary in response to external stimuli, we compare the response to a simple closed-loop stimulation protocol and the signals generated without electrical stimulation. The activity-dependent stimulation protocol explores different stimulus delivery delays relative to the fish's own electric discharges. We show that there is a critical time delay in this closed-loop interaction, as the largest changes in inter pulse intervals occur when the stimulation delay is below 100 ms. We also discuss the implications of these findings in the context of information processing in weakly electric fish.

Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring

While the wing kinematics of many flapping insects have been well characterized, understanding the underlying sensory, neural, and physiological mechanisms that determine these kinematics is still a challenge. Two main difficulties in understanding the physiological mechanisms arise from the complexity of the interaction between a flapping wing and its own unsteady flow, as well as the intricate mechanics of the insect wing hinge, which is among the most complicated joints in the animal kingdom. These difficulties call for the application of reduced-order approaches. Here this strategy is used to model the torques exerted by the wing hinge along the wing-pitch axis of maneuvering fruit flies as a damped torsional spring with elastic and damping coefficients as well as a rest angle. Furthermore, we model the air flows using simplified quasistatic aerodynamics. Our findings suggest that flies take advantage of the passive coupling between aerodynamics and the damped torsional spring to indirectly control their wing-pitch kinematics by modulating the spring parameters. The damped torsional-spring model explains the changes measured in wing-pitch kinematics during roll correction maneuvers through modulation of the spring damping and elastic coefficients. These results, in conjunction with the previous literature, indicate that flies can accurately control their wing-pitch kinematics on a sub-wing-beat time scale by modulating all three effective spring parameters on longer time scales.

INSECT FLIGHT. Luminance-dependent visual processing enables moth flight in low light

Animals must operate under an enormous range of light intensities. Nocturnal and twilight flying insects are hypothesized to compensate for dim conditions by integrating light over longer times. This slowing of visual processing would increase light sensitivity but should also reduce movement response times. Using freely hovering moths tracking robotic moving flowers, we showed that the moth's visual processing does slow in dim light. These longer response times are consistent with models of how visual neurons enhance sensitivity at low light intensities, but they could pose a challenge for moths feeding from swaying flowers. Dusk-foraging moths avoid this sensorimotor tradeoff; their nervous systems slow down but not so much as to interfere with their ability to track the movements of real wind-blown flowers.

Intersegmental coupling and recovery from perturbations in freely running cockroaches

Cockroaches are remarkably stable runners, exhibiting rapid recovery from external perturbations. To uncover the mechanisms behind this important behavioral trait, we recorded leg kinematics of freely running animals in both undisturbed and perturbed trials. Functional coupling underlying inter-leg coordination was monitored before and during localized perturbations, which were applied to single legs via magnetic impulses. The resulting transient effects on all legs and the recovery times to normal pre-perturbation kinematics were studied. We estimated coupling architecture and strength by fitting experimental data to a six-leg-unit phase oscillator model. Using maximum-likelihood techniques, we found that a network with nearest-neighbor inter-leg coupling best fitted the data and that, although coupling strengths vary among preparations, the overall inputs entering each leg are approximately balanced and consistent. Simulations of models with different coupling strengths encountering perturbations suggest that the coupling schemes estimated from our experiments allow animals relatively fast and uniform recoveries from perturbations.

Pitch perfect: how fruit flies control their body pitch angle

Flapping insect flight is a complex and beautiful phenomenon that relies on fast, active control mechanisms to counter aerodynamic instability. To directly investigate how freely-flying D. melanogaster control their body pitch angle against such instability, we perturb them using impulsive mechanical torques and film their corrective maneuvers with high-speed video. Combining experimental observations and numerical simulation, we find that flies correct for pitch deflections of up to 40° in 29±8 ms by bilaterally modulating their wings' front-most stroke angle in a manner well-described by a linear proportional-integral (PI) controller. Flies initiate this corrective process only 10±2 ms after the perturbation onset, indicating that pitch stabilization involves a fast reflex response. Remarkably, flies can also correct for very large-amplitude pitch perturbations–greater than 150°–providing a regime in which to probe the limits of the linear-response framework. Together with previous studies regarding yaw and roll control, our results on pitch show that flies' stabilization of each of these body angles is consistent with PI control

Sensory processing within antenna enables rapid implementation of feedback control for high-speed running maneuvers

Animals are remarkably stable during high-speed maneuvers. As the speed of locomotion increases, neural bandwidth and processing delays can limit the ability to achieve and maintain stable control. Processing the information of sensory stimuli into a control signal within the sensor itself could enable rapid implementation of whole-body feedback control during high-speed locomotion. Here, we show that processing in antennal afferents is sufficient to act as control signal for a fast sensorimotor loop. American cockroaches Periplaneta americana use their antennae to mediate escape running by tracking vertical surfaces such as walls. A control theoretic model of wall following predicts that stable control is possible if the animal can compute wall position (P) and velocity, its derivative, (D). Previous whole-nerve recordings from the antenna during simulated turning experiments demonstrated a population response consistent with P and D encoding, and suggested that the response was synchronized with the timing of a turn executed while wall following. Here, we record extracellularly from individual mechanoreceptors distributed along the antenna and show that these receptors encode D and have distinct latencies and filtering properties. When summed, receptors transform the stimulus into a control signal that could control rapid steering maneuvers. The D encoding within the antenna in addition to the temporal filtering properties and P dependence of the population of afferents support a sensory encoding hypothesis from control theory. Our findings support the hypothesis that peripheral sensory processing can enable rapid implementation of whole-body feedback control during rapid running maneuvers.

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 organism's 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.

Predicting performance and plasticity in the development of respiratory structures and metabolic systems

The scaling laws governing metabolism suggest that we can predict metabolic rates across taxonomic scales that span large differences in mass. Yet, scaling relationships can vary with development, body region, and environment. Within species, there is variation in metabolic rate that is independent of mass and which may be explained by genetic variation, the environment or their interaction (i.e., metabolic plasticity). Additionally, some structures, such as the insect tracheal respiratory system, change throughout development and in response to the environment to match the changing functional requirements of the organism. We discuss how study of the development of respiratory function meets multiple challenges set forth by the NSF Grand Challenges Workshop. Development of the structure and function of respiratory and metabolic systems (1) is inherently stable and yet can respond dynamically to change, (2) is plastic and exhibits sensitivity to environments, and (3) can be examined across multiple scales in time and space. Predicting respiratory performance and plasticity requires quantitative models that integrate information across scales of function from the expression of metabolic genes and mitochondrial biogenesis to the building of respiratory structures. We present insect models where data are available on the development of the tracheal respiratory system and of metabolic physiology and suggest what is needed to develop predictive models. Incorporating quantitative genetic data will enable mapping of genetic and genetic-by-environment variation onto phenotypes, which is necessary to understand the evolution of respiratory and metabolic systems and their ability to enable respiratory homeostasis as organisms walk the tightrope between stability and change.

Tiger beetles pursue prey using a proportional control law with a delay of one half-stride

Tiger beetles are fast diurnal predators capable of chasing prey under closed-loop visual guidance. We investigated this control system using statistical analyses of high-speed digital recordings of beetles chasing a moving prey dummy in a laboratory arena. Correlation analyses reveal that the beetle uses a proportional control law in which the angular position of the prey relative to the beetle's body axis drives the beetle's angular velocity with a delay of about 28 ms. The proportionality coefficient or system gain, 12 s(-1), is just below critical damping. Pursuit simulations using the derived control law predict angular orientation during pursuits with a residual error of about 7°. This is of the same order of magnitude as the oscillation imposed by the beetle's alternating tripod gait, which was not factored into the control law. The system delay of 28 ms equals a half-stride period, i.e. the time between the touch down of alternating tripods. Based on these results, we propose a physical interpretation of the observed control law: to turn towards its prey, the beetle on average exerts a sideways force proportional to the angular position of the prey measured a half-stride earlier.

The receptive field is dead. Long live the receptive field?

Advances in experimental techniques, including behavioral paradigms using rich stimuli under closed loop conditions and the interfacing of neural systems with external inputs and outputs, reveal complex dynamics in the neural code and require a revisiting of standard concepts of representation. High-throughput recording and imaging methods along with the ability to observe and control neuronal subpopulations allow increasingly detailed access to the neural circuitry that subserves neural representations and the computations they support. How do we harness theory to build biologically grounded models of complex neural function?

Computational neuroscience: beyond the local circuit

Computational neuroscience has focused largely on the dynamics and function of local circuits of neuronal populations dedicated to a common task, such as processing a common sensory input, storing its features in working memory, choosing between a set of options dictated by controlled experimental settings or generating the appropriate actions. Most of current circuit models suggest mechanisms for computations that can be captured by networks of simplified neurons connected via simple synaptic weights. In this article I review the progress of this approach and its limitations. It is argued that new experimental techniques will yield data that might challenge the present paradigms in that they will (1) demonstrate the computational importance of microscopic structural and physiological complexity and specificity; (2) highlight the importance of models of large brain structures engaged in a variety of tasks; and (3) reveal the necessity of coupling the neuronal networks to chemical and environmental variables.

Mechanical processing via passive dynamic properties of the cockroach antenna can facilitate control during rapid running

The integration of information from dynamic sensory structures operating on a moving body is a challenge for locomoting animals and engineers seeking to design agile robots. As a tactile sensor is a physical linkage mediating mechanical interactions between body and environment, mechanical tuning of the sensor is critical for effective control. We determined the open-loop dynamics of a tactile sensor, specifically the antenna of the American cockroach, Periplaneta americana, an animal that escapes predators by using its antennae during rapid closed-loop tactilely mediated course control. Geometrical measurements and static bending experiments revealed an exponentially decreasing flexural stiffness (EI) from base to tip. Quasi-static experiments with a physical model support the hypothesis that a proximodistally decreasing EI can simplify control by increasing preview distance and allowing effective mapping to a putative control variable - body-to-wall distance - compared to an antenna with constant EI. We measured the free response at the tip of the antenna following step deflections and determined that the antenna rapidly damps large deflections: over 90% of the perturbation is rejected within the first cycle, corresponding to almost one stride period during high-speed running (~50 ms). An impulse-like perturbation near the tip revealed dynamics that were characteristic of an inelastic collision, keeping the antenna in contact with an object after impact. We contend that proximodistally decreasing stiffness, high damping, and inelasticity simplify control during high-speed tactile tasks by increasing preview distance, providing a one-dimensional map between antennal bending and body-to-wall distance, and increasing the reliability of tactile information.