Systems-level modeling of neuronal circuits for leech swimming

A tale of two leeches: Toward the understanding of the evolution and development of behavioral neural circuits

In the animal kingdom, behavioral traits encompass a broad spectrum of biological phenotypes that have critical roles in adaptive evolution, but an EvoDevo approach has not been broadly used to study behavior evolution. Here, we propose that, by integrating two leech model systems, each of which has already attained some success in its respective field, it is possible to take on behavioral traits with an EvoDevo approach. We first identify the developmental changes that may theoretically lead to behavioral evolution and explain why an EvoDevo study of behavior is challenging. Next, we discuss the pros and cons of the two leech model species, Hirudo, a classic model for invertebrate neurobiology, and Helobdella, an emerging model for clitellate developmental biology, as models for behavioral EvoDevo research. Given the limitations of each leech system, neither is particularly strong for behavioral EvoDevo. However, the two leech systems are complementary in their technical accessibilities, and they do exhibit some behavioral similarities and differences. By studying them in parallel and together with additional leech species such as Haementeria, it is possible to explore the different levels of behavioral development and evolution.

Distributed rhythm generators underlie Caenorhabditis elegans forward locomotion

Coordinated rhythmic movements are ubiquitous in animal behavior. In many organisms, chains of neural oscillators underlie the generation of these rhythms. In C. elegans, locomotor wave generation has been poorly understood; in particular, it is unclear where in the circuit rhythms are generated, and whether there exists more than one such generator. We used optogenetic and ablation experiments to probe the nature of rhythm generation in the locomotor circuit. We found that multiple sections of forward locomotor circuitry are capable of independently generating rhythms. By perturbing different components of the motor circuit, we localize the source of secondary rhythms to cholinergic motor neurons in the midbody. Using rhythmic optogenetic perturbation, we demonstrate bidirectional entrainment of oscillations between different body regions. These results show that, as in many other vertebrates and invertebrates, the C. elegans motor circuit contains multiple oscillators that coordinate activity to generate behavior.

A classic model animal in the 21st century: recent lessons from the leech nervous system

The medicinal leech (genus Hirudo) is a classic model animal in systems neuroscience. The leech has been central to many integrative studies that establish how properties of neurons and their interconnections give rise to the functioning of the animal at the behavioral level. Leeches exhibit several discrete behaviors (such as crawling, swimming and feeding) that are each relatively simple. Importantly, these behaviors can all be studied - at least at a basal level - in the isolated nervous system. The leech nervous system is particularly amenable to such studies because of its distributed nature; sensory processing and generation of behavior occur to a large degree in iterated segmental ganglia that each contain only ∼400 neurons. Furthermore, the neurons are relatively large and are arranged with stereotyped topography on the surface of the ganglion, which greatly facilitates their identification and accessibility. This Commentary provides an overview of recent work on the leech nervous system, with particular focus on circuits that underlie leech behavior. Studies that combine the unique features of the leech with modern optical and genetic techniques are also discussed. Thus, this Commentary aims to explain the continued appeal of the leech as an experimental animal in the 21st century.

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.

Biological clockwork underlying adaptive rhythmic movements

Owing to the complexity of neuronal circuits, precise mathematical descriptions of brain functions remain an elusive ambition. A more modest focus of many neuroscientists, central pattern generators, are more tractable neuronal circuits specialized to generate rhythmic movements, including locomotion. The relative simplicity and well-defined motor functions of these circuits provide an opportunity for uncovering fundamental principles of neuronal information processing. Here we present the culmination of mathematical analysis that captures the adaptive behaviors emerging from interactions between a central pattern generator, the body, and the physical environment during locomotion. The biologically realistic model describes the undulatory motions of swimming leeches with quantitative accuracy and, without further parameter tuning, predicts the sweeping changes in oscillation patterns of leeches undulating in air or swimming in high-viscosity fluid. The study demonstrates that central pattern generators are capable of adapting oscillations to the environment through sensory feedback, but without guidance from the brain.

Neural circuits for peristaltic wave propagation in crawling Drosophila larvae: analysis and modeling

Drosophila larvae crawl by peristaltic waves of muscle contractions, which propagate along the animal body and involve the simultaneous contraction of the left and right side of each segment. Coordinated propagation of contraction does not require sensory input, suggesting that movement is generated by a central pattern generator (CPG). We characterized crawling behavior of newly hatched Drosophila larvae by quantifying timing and duration of segmental boundary contractions. We developed a CPG network model that recapitulates these patterns based on segmentally repeated units of excitatory and inhibitory (EI) neuronal populations coupled with immediate neighboring segments. A single network with symmetric coupling between neighboring segments succeeded in generating both forward and backward propagation of activity. The CPG network was robust to changes in amplitude and variability of connectivity strength. Introducing sensory feedback via "stretch-sensitive" neurons improved wave propagation properties such as speed of propagation and segmental contraction duration as observed experimentally. Sensory feedback also restored propagating activity patterns when an inappropriately tuned CPG network failed to generate waves. Finally, in a two-sided CPG model we demonstrated that two types of connectivity could synchronize the activity of two independent networks: connections from excitatory neurons on one side to excitatory contralateral neurons (E to E), and connections from inhibitory neurons on one side to excitatory contralateral neurons (I to E). To our knowledge, such I to E connectivity has not yet been found in any experimental system; however, it provides the most robust mechanism to synchronize activity between contralateral CPGs in our model. Our model provides a general framework for studying the conditions under which a single locally coupled network generates bilaterally synchronized and longitudinally propagating waves in either direction.

Positive feedback loops sustain repeating bursts in neuronal circuits

Voluntary movements in animals are often episodic, with abrupt onset and termination. Elevated neuronal excitation is required to drive the neuronal circuits underlying such movements; however, the mechanisms that sustain this increased excitation are largely unknown. In the medicinal leech, an identified cascade of excitation has been traced from mechanosensory neurons to the swim oscillator circuit. Although this cascade explains the initiation of excitatory drive (and hence swim initiation), it cannot account for the prolonged excitation (10-100 s) that underlies swim episodes. We present results of physiological and theoretical investigations into the mechanisms that maintain swimming activity in the leech. Although intrasegmental mechanisms can prolong stimulus-evoked excitation for more than one second, maintained excitation and sustained swimming activity requires chains of several ganglia. Experimental and modeling studies suggest that mutually excitatory intersegmental interactions can drive bouts of swimming activity in leeches. Our model neuronal circuits, which incorporated mutually excitatory neurons whose activity was limited by impulse adaptation, also replicated the following major experimental findings: (1) swimming can be initiated and terminated by a single neuron, (2) swim duration decreases with experimental reduction in nerve cord length, and (3) swim duration decreases as the interval between swim episodes is reduced.

Mechanisms underlying rhythmic locomotion: interactions between activation, tension and body curvature waves

Undulatory animal locomotion arises from three closely related propagating waves that sweep rostrocaudally along the body: activation of segmental muscles by motoneurons (MNs), strain of the body wall, and muscle tension induced by activation and strain. Neuromechanical models that predict the relative propagation speeds of neural/muscle activation, muscle tension and body curvature can reveal crucial underlying control features of the central nervous system and the power-generating mechanisms of the muscle. We provide an analytical explanation of the relative speeds of these three waves based on a model of neuromuscular activation and a model of the body-fluid interactions for leech anguilliform-like swimming. First, we deduced the motoneuron spike frequencies that activate the muscle and the resulting muscle tension during swimming in intact leeches from muscle bending moments. Muscle bending moments were derived from our video-recorded kinematic motion data by our body-fluid interaction model. The phase relationships of neural activation and muscle tension in the strain cycle were then calculated. Our study predicts that the MN activation and body curvature waves have roughly the same speed (the ratio of curvature to MN activation speed ≈0.84), whereas the tension wave travels about twice as fast. The high speed of the tension wave resulting from slow MN activation is explained by the multiplicative effects of MN activation and muscle strain on tension development. That is, the product of two slower waves (activation and strain) with appropriate amplitude, bias and phase can generate a tension wave with twice the propagation speed of the factors. Our study predicts that (1) the bending moment required for swimming is achieved by minimal MN spike frequency, rather than by minimal muscle tension; (2) MN activity is greater in the mid-body than in the head and tail regions; (3) inhibitory MNs not only accelerate the muscle relaxation but also reduce the intrinsic tonus tension during one sector of the swim cycle; and (4) movements of the caudal end are passive during swimming. These predictions await verification or rejection through further experiments on swimming animals.

Mechanisms underlying rhythmic locomotion: dynamics of muscle activation

We have studied the dynamical properties of tension development in leech longitudinal muscle during swimming. A new method is proposed for modeling muscle properties under functionally relevant conditions where the muscle is subjected to both periodic activation and rhythmic length changes. The 'dual-sinusoid' experiments were conducted on preparations of leech nerve cord and body wall. The longitudinal muscle was activated periodically by injection of sinusoidal currents into an identified motoneuron. Simultaneously, sinusoidal length changes were imposed on the body wall with prescribed phase differences (12 values equally spaced over 2π radians) with respect to the current injection. Through the singular value decomposition of appropriately constructed tension data matrices, the leech muscle was found to have a multiplicative structure in which the tension was expressed as the product of activation and length factors. The time courses of activation and length factors were determined from the tension data and were used to develop component models. The proposed modeling method is a general one and is applicable to contractile elements for which the effects of series elasticity are negligible.

Mechanisms underlying rhythmic locomotion: body-fluid interaction in undulatory swimming

Swimming of fish and other animals results from interactions of rhythmic body movements with the surrounding fluid. This paper develops a model for the body-fluid interaction in undulatory swimming of leeches, where the body is represented by a chain of rigid links and the hydrodynamic force model is based on resistive and reactive force theories. The drag and added-mass coefficients for the fluid force model were determined from experimental data of kinematic variables during intact swimming, measured through video recording and image processing. Parameter optimizations to minimize errors in simulated model behaviors revealed that the resistive force is dominant, and a simple static function of relative velocity captures the essence of hydrodynamic forces acting on the body. The model thus developed, together with the experimental kinematic data, allows us to investigate temporal and spatial (along the body) distributions of muscle actuation, body curvature, hydrodynamic thrust and drag, muscle power supply and energy dissipation into the fluid. We have found that: (1) thrust is generated continuously along the body with increasing magnitude toward the tail, (2) drag is nearly constant along the body, (3) muscle actuation waves travel two or three times faster than the body curvature waves and (4) energy for swimming is supplied primarily by the mid-body muscles, transmitted through the body in the form of elastic energy, and dissipated into the water near the tail.

Neuronal control of swimming behavior: comparison of vertebrate and invertebrate model systems

Swimming movements in the leech and lamprey are highly analogous, and lack homology. Thus, similarities in mechanisms must arise from convergent evolution rather than from common ancestry. Despite over 40 years of parallel investigations into this annelid and primitive vertebrate, a close comparison of the approaches and results of this research is lacking. The present review evaluates the neural mechanisms underlying swimming in these two animals and describes the many similarities that provide intriguing examples of convergent evolution. Specifically, we discuss swim initiation, maintenance and termination, isolated nervous system preparations, neural-circuitry, central oscillators, intersegmental coupling, phase lags, cycle periods and sensory feedback. Comparative studies between species highlight mechanisms that optimize behavior and allow us a broader understanding of nervous system function.

Analysis of impulse adaptation in motoneurons

Animal locomotion results from muscle contraction and relaxation cycles that are generated within the central nervous system and then are relayed to the periphery by motoneurons. Thus, motoneuron function is an essential element for understanding control of animal locomotion. This paper presents motoneuron input-output relationships, including impulse adaptation, in the medicinal leech. We found that although frequency-current graphs generated by passing 1-s current pulses in neuron somata were non-linear, peak and steady-state graphs of frequency against membrane potential were linear, with slopes of 5.2 and 2.9 Hz/mV, respectively. Systems analysis of impulse frequency adaptation revealed a static threshold nonlinearity at -43 mV (impulse threshold) and a single time constant (tau = 88 ms). This simple model accurately predicts motoneuron impulse frequency when tested by intracellular injection of sinusoidal current. We investigated electrical coupling within motoneurons by modeling these as three-compartment structures. This model, combined with the membrane potential-impulse frequency relationship, accurately predicted motoneuron impulse frequency from intracellular records of soma potentials obtained during fictive swimming. A corollary result was that the product of soma-to-neurite and neurite-to-soma coupling coefficients in leech motoneurons is large, 0.85, implying that the soma and neurite are electrically compact.

Multivariable Harmonic Balance for Central Pattern Generators

The central pattern generator (CPG) is a nonlinear oscillator formed by a group of neurons, providing a fundamental control mechanism underlying rhythmic movements in animal locomotion. We consider a class of CPGs modeled by a set of interconnected identical neurons. Based on the idea of multivariable harmonic balance, we show how the oscillation profile is related to the connectivity matrix that specifies the architecture and strengths of the interconnections. Specifically, the frequency, amplitudes, and phases are essentially encoded in terms of a pair of eigenvalue and eigenvector. This basic principle is used to estimate the oscillation profile of a given CPG model. Moreover, a systematic method is proposed for designing a CPG-based nonlinear oscillator that achieves a prescribed oscillation profile.

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.

Dopamine activates the motor pattern for crawling in the medicinal leech

Locomotion in segmented animals is thought to be based on the coupling of "unit burst generators," but the biological nature of the unit burst generator has been revealed in only a few animal systems. We determined that dopamine (DA), a universal modulator of motor activity, is sufficient to activate fictive crawling in the medicinal leech, and can exert its actions within the smallest division of the animal's CNS, the segmental ganglion. In the entire isolated nerve cord or in the single ganglion, DA induced slow antiphasic bursting (approximately 15 s period) of motoneurons known to participate in the two-step elongation-contraction cycle underlying crawling behavior. During each cycle, the dorsal (DE-3) and ventral (VE-4) longitudinal excitor motoneurons fired approximately 180 degrees out of phase from the ventrolateral circular excitor motoneuron (CV), which marks the elongation phase. In many isolated whole nerve cords, DE-3 bursting progressed in an anterior to posterior direction with intersegmental phase delays appropriate for crawling. In the single ganglion, the dorsal (DI-1) and ventral (VI-2) inhibitory longitudinal motoneurons fired out of phase with each DE-3 burst, further confirming that the crawl unit burst generator exists in the single ganglion. All isolated ganglia of the CNS were competent to produce DA-induced robust fictive crawling, which typically lasted uninterrupted for 5-15 min. A quantitative analysis indicated that DA-induced crawling was not significantly different from electrically evoked or spontaneous crawling. We conclude that DA is sufficient to activate the full crawl motor program and that the kernel for crawling resides within each segmental ganglion.

Leech locomotion: swimming, crawling, and decisions

Research on the neuronal control of locomotion in leeches spans almost four decades. Recent advances reviewed here include discoveries that: (1) interactions between multiple hormones modulate initiation of swimming; (2) stretch receptors associated with longitudinal muscles interact with the central oscillator circuit via electrical junctions; (3) intersegmental interactions, according to theoretical analyses, must be relatively weak compared to oscillator interactions within ganglia; and (4) multiple interacting neurons control the expression of alternative modes of locomotion. The innovative techniques that facilitated these advances include optical recording of membrane potential changes, simultaneous intracellular injection of high and low molecular weight fluorescent dyes, and detailed modeling via an input-output systems engineering approach.

Formal analysis of resonance entrainment by central pattern generator

The neuronal circuit controlling the rhythmic movements in animal locomotion is called the central pattern generator (CPG). The biological control mechanism appears to exploit mechanical resonance to achieve efficient locomotion. The objective of this paper is to reveal the fundamental mechanism underlying entrainment of CPGs to resonance through sensory feedback. To uncover the essential principle, we consider the simplest setting where a pendulum is driven by the reciprocal inhibition oscillator. Existence and properties of stable oscillations are examined by the harmonic balance method, which enables approximate but insightful analysis. In particular, analytical conditions are obtained under which harmonic balance predicts existence of an oscillation at a frequency near the resonance frequency. Our result reveals that the resonance entrainment can be maintained robustly against parameter perturbations through two distinct mechanisms: negative integral feedback and positive rate feedback.

Spontaneous electrical activity and behavior in the leech hirudo medicinalis

In the absence of external stimuli, animals explore the environment by performing irregular movements, but the neuronal mechanisms underlying this arrhythmic motion are largely unknown. In this paper, we studied the relationship between the spontaneous neuronal activity in the leech (Hirudo medicinalis) and its behavior. We analyzed the electrical activity of isolated ganglia, chains of two connected ganglia, and semi-intact preparations. The spontaneous electrical activity in ganglia was characterized by the occurrence of irregular bursts of spikes with variable duration and size. Properties of these bursts were modified by synaptic inputs arriving from the neighboring ganglia and from the two primitive brains located in the head and tail. In fact, in semi-intact preparations, unusually large bursts of spikes occurring spontaneously were recorded and caused the leech to move even in the absence of any external sensory stimulation. These large bursts appear to act as internal triggers controlling the spontaneous leech behavior and determining the duration of stereotypical motor patterns.

Muscle function in animal movement: passive mechanical properties of leech muscle

We investigated passive properties of leech body wall as part of a larger project to understand better mechanisms that control locomotion and to establish mathematical models that predict such dynamical behavior. In tests of length-tension relationships in 2-segment-long preparations of body wall through step-stretch manipulations (step size = 1 mm), we discovered that these relationships are nonlinear, with significant hysteresis, even for the relatively small changes in length that occur during swimming. We developed a mathematical model comprising three nonlinear springs, two in series with nonlinear dashpots that describe well the tension statics and dynamics for step-stretch experiments. This model suggested that body wall dynamics are slow enough to be neglected when predicting the tension generated by imposed sinusoidal length changes (about +/-10% of nominal) at 1-3 Hz, mimicking swimming. We derived a static model, comprising one nonlinear spring, which predicts sinusoidal data accurately, even when preparations were exposed to serotonin (0.1-10 microM). Preparations bathed in saline-serotonin had significantly reduced steady-state and peak tensions, without alterations in tension dynamics. Anesthetizing preparations (8% ethanol) reduced body wall tension by 77%, indicating that passive tension in the obliquely striated longitudinal muscles of leeches results primarily from a resting tonus.