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 feedback regulation, 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 (electric fish station keeping and jamming avoidance), terrestrial (cockroach wall following) and aerial environments (flight control in moths) to highlight how one can use control theory to understand how 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.Comment: Submitted to Integr Comp Bio

Cellular mechanisms for integral feedback in visually guided behavior

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

Mechanism of membrane fusion induced by vesicular stomatitis virus G protein

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

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