A model of the leech segmental swim central pattern generator

Excitation of the abdominal ganglion affects the electrophysiological activity of indirect flight muscles of the honeybee Apis mellifera

Our understanding of the nervous tissues that affect the wing flapping of insects mainly focuses on the brain, but wing flapping is a rhythmic movement related to the central pattern generator in the ventral nerve cord. To verify whether the neural activity of the abdominal ganglion of the honeybee (Apis mellifera) affects the flapping-wing flight, we profiled the response characteristics of indirect flight muscles to abdominal ganglion excitation. Strikingly, a change in the neural activity of ganglion 3 or ganglion 4 has a stronger effect on the electrophysiological activity of indirect flight muscles than that of ganglion 5. The electrophysiological activity of vertical indirect flight muscles is affected more by the change in neural activity of the abdominal ganglion than that of lateral indirect flight muscles. Moreover, the change in neural activity of the abdominal ganglion mainly causes the change in the muscular activity of indirect wing muscles, but the activity patterns change relatively little and there is little change in the complicated details. This work improves our understanding of the neuroregulatory mechanisms associated with the flapping-wing flight of honeybees.

An optimality principle for locomotor central pattern generators

Two types of neural circuits contribute to legged locomotion: central pattern generators (CPGs) that produce rhythmic motor commands (even in the absence of feedback, termed “fictive locomotion”), and reflex circuits driven by sensory feedback. Each circuit alone serves a clear purpose, and the two together are understood to cooperate during normal locomotion. The difficulty is in explaining their relative balance objectively within a control model, as there are infinite combinations that could produce the same nominal motor pattern. Here we propose that optimization in the presence of uncertainty can explain how the circuits should best be combined for locomotion. The key is to re-interpret the CPG in the context of state estimator-based control: an internal model of the limbs that predicts their state, using sensory feedback to optimally balance competing effects of environmental and sensory uncertainties. We demonstrate use of optimally predicted state to drive a simple model of bipedal, dynamic walking, which thus yields minimal energetic cost of transport and best stability. The internal model may be implemented with neural circuitry compatible with classic CPG models, except with neural parameters determined by optimal estimation principles. Fictive locomotion also emerges, but as a side effect of estimator dynamics rather than an explicit internal rhythm. Uncertainty could be key to shaping CPG behavior and governing optimal use of feedback.

Functionally asymmetric motor neurons contribute to coordinating locomotion of Caenorhabditis elegans

Locomotion circuits developed in simple animals, and circuit motifs further evolved in higher animals. To understand locomotion circuit motifs, they must be characterized in many models. The nematode Caenorhabditis elegans possesses one of the best-studied circuits for undulatory movement. Yet, for 1/6^th of the cholinergic motor neurons (MNs), the AS MNs, functional information is unavailable. Ventral nerve cord (VNC) MNs coordinate undulations, in small circuits of complementary neurons innervating opposing muscles. AS MNs differ, as they innervate muscles and other MNs asymmetrically, without complementary partners. We characterized AS MNs by optogenetic, behavioral and imaging analyses. They generate asymmetric muscle activation, enabling navigation, and contribute to coordination of dorso-ventral undulation as well as anterio-posterior bending wave propagation. AS MN activity correlated with forward and backward locomotion, and they functionally connect to premotor interneurons (PINs) for both locomotion regimes. Electrical feedback from AS MNs via gap junctions may affect only backward PINs.

Control strategies of 3-cell Central Pattern Generator via global stimuli

The study of the synchronization patterns of small neuron networks that control several biological processes has become an interesting growing discipline. Some of these synchronization patterns of individual neurons are related to some undesirable neurological diseases, and they are believed to play a crucial role in the emergence of pathological rhythmic brain activity in different diseases, like Parkinson’s disease. We show how, with a suitable combination of short and weak global inhibitory and excitatory stimuli over the whole network, we can switch between different stable bursting patterns in small neuron networks (in our case a 3-neuron network). We develop a systematic study showing and explaining the effects of applying the pulses at different moments. Moreover, we compare the technique on a completely symmetric network and on a slightly perturbed one (a much more realistic situation). The present approach of using global stimuli may allow to avoid undesirable synchronization patterns with nonaggressive stimuli.

Modelling Feedback Excitation, Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.

On exploration of geometrically constrained space by medicinal leeches Hirudo verbana

Leeches are fascinating creatures: they have simple modular nervous circuitry yet exhibit a rich spectrum of behavioural modes. Leeches could be ideal blue-prints for designing flexible soft robots which are modular, multi-functional, fault-tolerant, easy to control, capable for navigating using optical, mechanical and chemical sensorial inputs, have autonomous inter-segmental coordination and adaptive decision-making. With future designs of leech-robots in mind we study how leeches behave in geometrically constrained spaces. Core results of the paper deal with leeches exploring a row of rooms arranged along a narrow corridor. In laboratory experiments we find that rooms closer to ends of the corridor are explored by leeches more often than rooms in the middle of the corridor. Also, in series of scoping experiments, we evaluate leeches capabilities to navigating in mazes towards sources of vibration and chemo-attraction. We believe our results lay foundation for future developments of robots mimicking behaviour of leeches.

Multivariable harmonic balance analysis of the neuronal oscillator for leech swimming

Biological systems, and particularly neuronal circuits, embody a very high level of complexity. Mathematical modeling is therefore essential for understanding how large sets of neurons with complex multiple interconnections work as a functional system. With the increase in computing power, it is now possible to numerically integrate a model with many variables to simulate behavior. However, such analysis can be time-consuming and may not reveal the mechanisms underlying the observed phenomena. An alternative, complementary approach is mathematical analysis, which can demonstrate direct and explicit relationships between a property of interest and system parameters. This paper introduces a mathematical tool for analyzing neuronal oscillator circuits based on multivariable harmonic balance (MHB). The tool is applied to a model of the central pattern generator (CPG) for leech swimming, which comprises a chain of weakly coupled segmental oscillators. The results demonstrate the effectiveness of the MHB method and provide analytical explanations for some CPG properties. In particular, the intersegmental phase lag is estimated to be the sum of a nominal value and a perturbation, where the former depends on the structure and span of the neuronal connections and the latter is roughly proportional to the period gradient, communication delay, and the reciprocal of the intersegmental coupling strength.

Systems approach to modeling the neuronal CPG for leech swimming

This paper proposes a mathematical model of the neuronal central pattern generator (CPG) for leech swimming. The model is developed through the "systems approach" where dynamical components and their connections are first identified through input/output data from physiological experiments and then integrated into a chain of nonlinear oscillators. Our approach leads to a model of moderate complexity when compared with existing models developed through biophysical principles. We show through numerical simulations that our model can successfully reproduce the phase coordination observed in the isolated nerve cord of the leech CPG. As a byproduct, a prediction is obtained for the intrinsic period gradient along the nerve cord.

Systems-level modeling of neuronal circuits for leech swimming

This paper describes a mathematical model of the neuronal central pattern generator (CPG) that controls the rhythmic body motion of the swimming leech. The systems approach is employed to capture the neuronal dynamics essential for generating coordinated oscillations of cell membrane potentials by a simple CPG architecture with a minimal number of parameters. Based on input/output data from physiological experiments, dynamical components (neurons and synaptic interactions) are first modeled individually and then integrated into a chain of nonlinear oscillators to form a CPG. We show through numerical simulations that the values of a few parameters can be estimated within physiologically reasonable ranges to achieve good fit of the data with respect to the phase, amplitude, and period. This parameter estimation leads to predictions regarding the synaptic coupling strength and intrinsic period gradient along the nerve cord, the latter of which agrees qualitatively with experimental observations.

Neuronal control of leech behavior

The medicinal leech has served as an important experimental preparation for neuroscience research since the late 19th century. Initial anatomical and developmental studies dating back more than 100 years ago were followed by behavioral and electrophysiological investigations in the first half of the 20th century. More recently, intense studies of the neuronal mechanisms underlying leech movements have resulted in detailed descriptions of six behaviors described in this review; namely, heartbeat, local bending, shortening, swimming, crawling, and feeding. Neuroethological studies in leeches are particularly tractable because the CNS is distributed and metameric, with only 400 identifiable, mostly paired neurons in segmental ganglia. An interesting, yet limited, set of discrete movements allows students of leech behavior not only to describe the underlying neuronal circuits, but also interactions among circuits and behaviors. This review provides descriptions of six behaviors including their origins within neuronal circuits, their modification by feedback loops and neuromodulators, and interactions between circuits underlying with these behaviors.

A dye mixture (Neurobiotin and Alexa 488) reveals extensive dye-coupling among neurons in leeches; physiology confirms the connections

Although the neuronal circuits that generate leech movements have been studied for over 30 years, the list of interneurons (INs) in these circuits remains incomplete. Previous studies showed that some motor neurons (MNs) are electrically coupled to swim-related INs, e.g., rectifying junctions connect IN 28 to MN DI-1 (dorsal inhibitor), so we searched for additional neurons in these behavioral circuits by co-injecting Neurobiotin and Alexa Fluor 488 into segmental MNs DI-1, VI-2, DE-3 and VE-4. The high molecular weight Alexa dye is confined to the injected cell, whereas the smaller Neurobiotin molecules diffuse through gap junctions to reveal electrical coupling. We found that MNs were each dye-coupled to approximately 25 neurons, about half of which are likely to be INs. We also found that (1) dye-coupling was reliably correlated with physiologically confirmed electrical connections, (2) dye-coupling is unidirectional between MNs that are linked by rectifying connections, and (3) there are novel electrical connections between excitatory and inhibitory MNs, e.g. between excitatory MN VE-4 and inhibitory MN DI-1. The INs found in this study provide a pool of novel candidate neurons for future studies of behavioral circuits, including those underlying swimming, crawling, shortening, and bending movements.

Model for intersegmental coordination of leech swimming: central and sensory mechanisms

Sensory feedback as well as the coupling signals within the CNS are essential for leeches to produce intersegmental phase relationships in body movements appropriate for swimming behavior. To study the interactions between the central pattern generator (CPG) and peripheral feedback in controlling intersegmental coordination, we have constructed a computational model for the leech swimming system with physiologically realistic parameters. First, the leech swimming CPG is simulated by a chain of phase oscillators coupled by three channels of coordinating signals. The activity phase, the projection direction, and the phase response curve (PRC) of each channel are based on the identified intersegmental interneuron network. Output of this largely constrained model produces stable coordination in the simulated CPG with average phase lags of 8-10 degrees/segment in the period range from 0.5 to 1.5 s, similar to those observed in isolated nerve cords. The model also replicates the experimental finding that shorter chains of leech nerve cords have larger phase lags per segment. Sensory inputs, represented by stretch receptors, were subsequently incorporated into the CPG model. Each stretch receptor with its associated PRC, which was defined to mimic the experimental results of phase-dependent phase shifts of the central oscillator by the ventral stretch receptor, can alter the phase of the local central oscillator. Finally, mechanical interactions between the muscles from neighboring segments were simulated by PRCs linking adjacent stretch receptors. This model shows that interactions between neighboring muscles could globally increase the phase lags to the larger value required for the one-wavelength body form observed in freely swimming leeches. The full model also replicates the experimental observation that leeches with severed nerve cords have larger intersegmental phase lags than intact animals. The similarities between physiological and simulation results demonstrate that we have established a realistic model for the central and peripheral control of intersegmental coordination of leech swimming.

Analysis of oscillations in a reciprocally inhibitory network with synaptic depression

We present and analyze a model of a two-cell reciprocally inhibitory network that oscillates. The principal mechanism of oscillation is short-term synaptic depression. Using a simple model of depression and analyzing the system in certain limits, we can derive analytical expressions for various features of the oscillation, including the parameter regime in which stable oscillations occur, as well as the period and amplitude of these oscillations. These expressions are functions of three parameters: the time constant of depression, the synaptic strengths, and the amount of tonic excitation the cells receive. We compare our analytical results with the output of numerical simulations and obtain good agreement between the two. Based on our analysis, we conclude that the oscillations in our network are qualitatively different from those in networks that oscillate due to postinhibitory rebound, spike-frequency adaptation, or other intrinsic (rather than synaptic) adaptational mechanisms. In particular, our network can oscillate only via the synaptic escape mode of Skinner, Kopell, and Marder (1994).