Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control

Like human walking, passive dynamic walking—i.e. walking down a slope with no actuation except gravity—is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG—i.e. the CPG’s eigenfrequency—is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.     

Altering cAMP levels within a central pattern generator modifies or disrupts rhythmic motor output

Cyclic AMP is a second messenger that has been implicated in the neuromodulation of rhythmically active motor patterns. Here, we tested whether manipulating cAMP affects swim motor pattern generation in the mollusc, Tritonia diomedea. Inhibiting adenylyl cyclase (AC) with 9-cyclopentyladenine (9-CPA) slowed or stopped the swim motor pattern. Inhibiting phosphodiesterase with 3-isobutyl-1-methylxanthine (IBMX) or applying dibutyryl-cAMP (dB-cAMP) disrupted the swim motor pattern, as did iontophoresing cAMP into the central pattern generator neuron C2. Additionally, during wash-in, IBMX sometimes temporarily produced extended or spontaneous swim motor patterns. Photolysis of caged cAMP in C2 after initiation of the swim motor pattern inhibited subsequent bursting. These results suggest that cAMP levels can dynamically modulate swim motor pattern generation, possibly shaping the output of the central pattern generator on a cycle-by-cycle basis.     

The brain can eat: Establishing the existence of a central pattern generator for feeding in third instar larvae of Drosophila virilis and Drosophila melanogaster

To establish the existence of a central pattern generator for feeding in the larval central nervous system of two Drosophila species, the gross anatomy of feeding related muscles and their innervation is described, the motor units of the muscles identified and rhythmic motor output recorded from the isolated CNS. The cibarial dilator muscles that mediate food ingestion are innervated by the frontal nerve. Their motor pathway projects from the brain through the antennal nerves, the frontal connectives and the frontal nerve junction. The mouth hook elevator and depressor system is innervated by side branches of the maxillary nerve. The motor units of the two muscle groups differ in amplitude: the elevator is always activated by a small unit, the depressor by a large one. The dorsal protractors span the cephalopharyngeal skeleton and the body wall hence mediating an extension of the CPS. These muscles are innervated by the prothoracic accessory nerve. Rhythmic motor output produced by the isolated central nervous system can simultaneously be recorded from all three nerves. The temporal pattern of the identified motor units resembles the sequence of muscle contractions deduced from natural feeding behavior and is therefore considered as fictive feeding. Phase diagrams show an almost identical fictive feeding pattern is in both species.     

The role of mechanical resonance in the neural control of swimming in fishes

The bodies of many fishes are flexible, elastic structures; if you bend them, they spring back. Therefore, they should have a resonant frequency: a bending frequency at which the output amplitude is maximized for a particular input. Previous groups have hypothesized that swimming at this resonant frequency could maximize efficiency, and that a neural circuit called the central pattern generator might be able to entrain to a mechanical resonance. However, fishes swim in water, which may potentially damp out many resonant effects. Additionally, their bodies are elongated, which means that bending can occur in complicated ways along the length of the body. We review previous studies of the mechanical properties of fish bodies, and then present new data that demonstrate complex bending properties of elongated fish bodies. Resonant peaks in amplitude exist, but there may be many of them depending on the body wavelength. Additionally, they may not correspond to the maximum swimming speed. Next, we describe experiments using a closed-loop preparation of the lamprey, in which a preparation of the spinal cord is linked to a real-time simulation of the muscle and body properties, allowing us to examine resonance entrainment as we vary the simulated resonant frequency. We find that resonance entrainment does occur, but is rare. Gain had a significant, though weak, effect, and a nonlinear muscle model produced resonance entrainment more often than a linear filter. We speculate that resonance may not be a critical effect for efficient swimming in elongate, anguilliform swimmers, though it may be more important for stiffer carangiform and thunniform fishes.     

Molecular mechanisms of homeostatic plasticity in central pattern generator networks

Central pattern generator (CPG) networks rely on a balance of intrinsic and network properties to produce reliable, repeatable activity patterns. This balance is maintained by homeostatic plasticity where alterations in neuronal properties dynamically maintain appropriate neural output in the face of changing environmental conditions and perturbations. However, it remains unclear just how these neurons and networks can both monitor their ongoing activity and use this information to elicit homeostatic physiological responses to ensure robustness of output over time. Evidence exists that CPG networks use a mixed strategy of activity‐dependent, activity‐independent, modulator‐dependent, and synaptically regulated homeostatic plasticity to achieve this critical stability. In this review, we focus on some of the current understanding of the molecular pathways and mechanisms responsible for this homeostatic plasticity in the context of central pattern generator function, with a special emphasis on some of the smaller invertebrate networks that have allowed for extensive cellular‐level analyses that have brought recent insights to these questions.     

A modeling comparison of projection neuron- and neuromodulator-elicited oscillations in a central pattern generating network

Many central pattern generating networks are influenced by synaptic input from modulatory projection neurons. The network response to a projection neuron is sometimes mimicked by bath applying the neuronally-released modulator, despite the absence of network interactions with the projection neuron. One interesting example occurs in the crab stomatogastric ganglion (STG), where bath applying the neuropeptide pyrokinin (PK) elicits a gastric mill rhythm which is similar to that elicited by the projection neuron modulatory commissural neuron 1 (MCN1), despite the absence of PK in MCN1 and the fact that MCN1 is not active during the PK-elicited rhythm. MCN1 terminals have fast and slow synaptic actions on the gastric mill network and are presynaptically inhibited by this network in the STG. These local connections are inactive in the PK-elicited rhythm, and the mechanism underlying this rhythm is unknown. We use mathematical and biophysically-realistic modeling to propose potential mechanisms by which PK can elicit a gastric mill rhythm that is similar to the MCN1-elicited rhythm. We analyze slow-wave network oscillations using simplified mathematical models and, in parallel, develop biophysically-realistic models that account for fast, action potential-driven oscillations and some spatial structure of the network neurons. Our results illustrate how the actions of bath-applied neuromodulators can mimic those of descending projection neurons through mathematically similar but physiologically distinct mechanisms.     

Modular neuromuscular control of human locomotion by central pattern generator

The central pattern generators (CPG) in the spinal cord are thought to be responsible for producing the rhythmic motor patterns during rhythmic activities. For locomotor tasks, this involves much complexity, due to a redundant system of muscle actuators with a large number of highly nonlinear muscles. This study proposes a reduced neural control strategy for the CPG, based on modular organization of the co-active muscles, i.e., muscle synergies. Four synergies were extracted from the EMG data of the major leg muscles of two subjects, during two gait trials each, using non-negative matrix factorization algorithm. A Matsuoka׳s four-neuron CPG model with mutual inhibition, was utilized to generate the rhythmic activation patterns of the muscle synergies, using the hip flexion angle and foot contact force information from the sensory afferents as inputs. The model parameters were tuned using the experimental data of one gait trial, which resulted in a good fitting accuracy (RMSEs between 0.0491 and 0.1399) between the simulation and experimental synergy activations. The model׳s performance was then assessed by comparing its predictions for the activation patterns of the individual leg muscles during locomotion with the relevant EMG data. Results indicated that the characteristic features of the complex activation patterns of the muscles were well reproduced by the model for different gait trials and subjects. In general, the CPG- and muscle synergy-based model was promising in view of its simple architecture, yet extensive potentials for neuromuscular control, e.g., resolving redundancies, distributed and fast control, and modulation of locomotion by simple control signals.     

Modulation of the feeding system by a radular mechanosensory neuron in the terrestrial slug,Incilaria fruhstorferi

We investigated the modulatory role of a radular mechanoreceptor (RM) in the feeding system of Incilaria. RM spiking induced by current injection evoked several cycles of rhythmic buccal motor activity in quiescent preparations, and this effect was also observed in preparations lacking the cerebral ganglia. The evoked rhythmic activity included sequential activation of the inframedian radular tensor, the supramedian radular tensor, and the buccal sphincter muscles in that order.In addition to the generation of rhythmic motor activity, RM spiking enhanced tonic activities in buccal nerve 1 as well as in the cerebrobuccal connective, showing a wide excitatory effect on buccal neurons. The excitatory effect was further examined in the supramedian radular tensor motoneuron. RM spiking evoked biphasic depolarization in the tensor motoneuron consisting of fast excitatory postsynaptic potentials and prolonged depolarization lasting after termination of RM spiking. These depolarizations also occurred in high divalent cation saline, suggesting that they were both monosynaptic.When RM spiking was evoked in the fictive rasp phase during food-induced buccal motor rhythm, the activity of the supramedian radular tensor muscle showed the greatest enhancement of the three muscles tested, while the rate of ongoing rhythmic motor activity showed no increase.Abbreviations CPG central pattern generator - EPSP excitatory postsynaptic potential - RBMA rhythmic buccal motor activity - RM radular mechanosensory neuron - SMT supramedian radular tensor neuron     

A computational model for motor pattern switching between taste-induced ingestion and rejection oromotor behaviors

The mechanism of switching activity patterns in a central pattern generator is fundamental to the generation of diverse motor behaviors. Based on what is known about a brainstem substrate mediating the oral components of ingestion and rejection, we use computational techniques to construct a hypothetical multifunctional network that switches between the motor outputs of ingestion (licking) and rejection (gaping). The network was constructed using single-compartment conductance-based models for individual neurons based on Hodgkin-Huxley formalism. Using a fast-slow reduction and geometric analysis we describe a mechanism for pattern switching between licks and gapes. The model supports the hypothesis that a single configuration of network connections can produce both activity patterns. It further predicts that prolonged inhibition of some network neurons could lead to a switch in network activity from licks to gapes. Action Editor: Frances K. Skinner     

Developmental stage‐dependent switching in the neuromodulation of vertebrate locomotor central pattern generator networks

Neuromodulation plays important and stage‐dependent roles in regulating locomotor central pattern (CPG) outputs during vertebrate motor system development. Dopamine, serotonin and nitric oxide are three neuromodulators that potently influence CPG outputs in the development of Xenopus frog tadpole locomotion. However, their roles switch from predominantly inhibitory early in development to mainly excitatory at later stages. In this review, we compare the stage‐dependent switching in neuromodulation in Xenopus with other vertebrate systems, notably the mouse and the zebrafish, and highlight features that appear to be phylogenetically conserved.     

Organization of the larval pre-ecdysis motor pattern in the tobacco hornworm,Manduca sexta

The tobacco hornworm, Manduca sexta, undergoes several larval molts before transforming into a pupa and then an adult moth. Each molt culminates in ecdysis, when the old cuticle is shed. Prior to each larval ecdysis, the old cuticle is loosened by pre-ecdysis behavior, which consists of rhythmic compressions that are synchronous along the abdomen and on both body sides, and rhythmic retractions of the abdominal prolegs. Both pre-ecdysis and ecdysis behaviors are triggered by a peptide, eclosion hormone. The aim of the present study was to investigate the neural circuitry underlying larval preecdysis behavior. The pre-ecdysis motor pattern was recorded in isolated nerve cords from eclosion hormone-treated larvae, and the effects of connective transections and ionic manipulations were tested. Our results suggest that the larval pre-ecdysis compression motor pattern is coordinated and maintained by interneurons in the terminal abdominal ganglion that ascend the nerve cord without chemical synaptic relays; these interneurons make bilateral, probably monosynaptic, excitatory connections with identified pre-ecdysis motor neurons throughout the abdominal nerve cord. This model of the organization of the larval pre-ecdysis motor pattern should facilitate identification of the relevant interneurons, allowing future investigation of the neural basis of the developmental weakening of the pre-ecdysis motor pattern that accompanies the larval-pupal transformation.Abbreviations A3, A4... abdominal ganglia 3, 4... - AT terminal abdominal ganglion - ALE anterior lateral external muscle - DN dorsal nerve - DN_A anterior branch of the dorsal nerve - DN_L lateral branch of the dorsal nerve - DN_P posterior branch of the dorsal nerve - EH eclosion hormone - TP tergopleural muscle - VN ventral nerve - VN_A anterior branch of the ventral nerve - VN_L lateral branch of the ventral nerve - VN_P posterior branch of the ventral nerve     

Fast axon activity and the motor pattern in cockroach legs during swimming

Abstract Electromyographic recordings were made from muscles that extend the trochanter/femur of each of the six legs of American cockroaches, Periplaneta americana (L.), while the insects swam in water. The recordings showed two novel features. (1) During swimming, muscle activity in different legs was coordinated in the alternating tripod pattern commonly seen during free walking on land, not in the pattern of synchronous leg pairs common to other large terrestrial insects in water. (2) Fast axons were usually recruited along with slow axons, even when the insect swam at a moderate pace. Fast axon activity always started after the middle of the slow axon burst in intact insects, but vanished from most bursts in the stump of the leg after amputation of the femur. The alternating tripod pattern was maintained even after amputation. Possible causes of fast axon recruitment are discussed.     

Topology selection by chaotic neurons of a pyloric central pattern generator

The pyloric Central Pattern Generator (CPG) in the lobster has an architecture in which every neuron receives at least one connection from another member of the CPG. We call this a "non-open" network topology. An "open" topology, where at least one neuron does not receive synapses from any other CPG member, is found neither in the pyloric nor in the gastric mill CPG. Here we investigate a possible reason for this topological structure using the ability to perform a biologically functional task as a measure of the efficacy of the network. When the CPG is composed of model neurons that exhibit regular membrane voltage oscillations, open topologies are as able to maximize this functionality as non-open topologies. When we replace these models by neurons which exhibit chaotic membrane voltage oscillations, the functional criterion selects non-open topologies. As isolated neurons from invertebrate CPGs are known in some cases to undergo chaotic oscillations, this suggests that there is a biological basis for the class of non-open network topologies that we observe.     

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.

Modulation of swimming speed in the pteropod mollusc,Clione limacina: Role of a compartmental serotonergic system

In locomotory systems, the central pattern generator and motoneuron output must be modulated in order to achieve variability in locomotory speed, particularly when speed changes are important components of different behavior acts. The swimming system of the pteropod molluscClione limacina is an excellent model system for investigating such modulation. In particular, a system of central serotonergic neurons has been shown to be intimately involved in regulating output of the locomotory pattern generator and motor system ofClione. There are approximately 27 pairs of serotonin-immunoreactive neurons in the central nervous system ofClione, with about 75% of these identified. The majority of these identified immunoreactive neurons are involved in various aspects of locomotory speed modulation. A symmetrical cluster of pedal serotonergic neurons serves to increase wing contractility without affecting wing-beat frequency or motoneuron activity. Two clusters of cerebral cells produce widespread responses that lead to an increase in pattern generator cycle frequency, recruitment of swim motoneurons, activation of the pedal serotonergic neurons and excitation of the heart excitor neuron. A pair of ventral cerebral neurons provides weak excitatory inputs to the swimming system, and strongly inhibits neurons of the competing whole-body withdrawal network. Overall, the serotonergic system inClione is compartmentalized so that each subsystem (usually neuron cluster) can act independently or in concert to produce variability in locomotory speed.     

Control of oscillation periods and phase durations in half-center central pattern generators: a comparative mechanistic analysis

Central pattern generators (CPGs) consisting of interacting groups of neurons drive a variety of repetitive, rhythmic behaviors in invertebrates and vertebrates, such as arise in locomotion, respiration, mastication, scratching, and so on. These CPGs are able to generate rhythmic activity in the absence of afferent feedback or rhythmic inputs. However, functionally relevant CPGs must adaptively respond to changing demands, manifested as changes in oscillation period or in relative phase durations in response to variations in non-patterned inputs or drives. Although many half-center CPG models, composed of symmetric units linked by reciprocal inhibition yet varying in their intrinsic cellular properties, have been proposed, the precise oscillatory mechanisms operating in most biological CPGs remain unknown. Using numerical simulations and phase-plane analysis, we comparatively investigated how the intrinsic cellular features incorporated in different CPG models, such as subthreshold activation based on a slowly inactivating persistent sodium current, adaptation based on slowly activating calcium-dependent potassium current, or post-inhibitory rebound excitation, can contribute to the control of oscillation period and phase durations in response to changes in excitatory external drive to one or both half-centers. Our analysis shows that both the sensitivity of oscillation period to alterations of excitatory drive and the degree to which the duration of each phase can be separately controlled depend strongly on the intrinsic cellular mechanisms involved in rhythm generation and phase transitions. In particular, the CPG formed from units incorporating a slowly inactivating persistent sodium current shows the greatest range of oscillation periods and the greatest degree of independence in phase duration control by asymmetric inputs. These results are explained based on geometric analysis of the phase plane structures corresponding to the dynamics for each CPG type, which in particular helps pinpoint the roles of escape and release from synaptic inhibition in the effects we find.     

北京市主城区城市森林景观格局特征分析

城市森林是城市生态文明建设的重要组成部分。该文以北京市五环内城市森林为研究对象,以2016年9月16日的GF-2遥感影像为数据源,依据景观和生态服务功能将城市森林划分为附属庭院美化林、道路河流防护林、城区公园休闲林和城市郊野游憩林四个类型,并运用面向对象法提取不同类型的城市森林数据信息,制作生成专题图,同时运用Fragstats 4.2软件对景观斑块数量和构成、破碎度指数、分维数、辛普森多样性指数、辛普森均匀度指数、聚合指数等指标进行计算。结果表明:高分影像在城市森林信息提取上具有优势,分类总体精度高达90.36%,Kappa系数达0.88;北京主城区城市森林总面积为22 514.79 hm 2 ,林木覆盖率为32.35%;城市森林斑块分布不均,大型、特大型斑块数量占总数比例13.62%,但面积占比高达73.20%,中小斑块的生态价值有待挖掘;不同城市森林类型特征存在差异,附属庭院美化林和道路河流防护林为优势景观类型,但两者破碎度高,聚合度差,分布零散,城区公园休闲林和城市郊野游憩林面积占比相对较小,南部城区公园建设薄弱;城市森林景观指数随城市拓展呈规律性变化,景观破碎度自市中心向外逐渐减小,二环内破碎度高达183.50。基于研究结果,建议北京市在城市森林建设中加强对中小斑块的资源整合,增建口袋公园;加强道路河流防护林建设,用以连接城区公园休闲林和城市郊野游憩林等大型斑块,同时加强南部城区公园建设;加强城市森林整体空间调控,对三环内老城区进行补植,对三环以外城市森林优化经营技术,提高整体城市森林覆盖度和质量。     

Dopamine and nicotine,but not serotonin,modulate the crustacean ventilatory pattern generator

Dopamine (DA) causes a dose-dependent increase in the frequency of motor neuron bursts [virtual ventilation (f_R)] produced by deafferented crab ventilatory pattern generators (CPG_v). Domperidone, a D₂-specific DA antagonist, by itself reversibly depresses f_R and also blocks the stimulatory effects of DA. Serotonin (5HT) has no direct effects on this CPG_v. Nicotine also causes dramatic dose-dependent increases in the frequency of motor bursts from the CPG_v. The action is triphasic, beginning with an initial reversal of burst pattern typical of reversed-mode ventilation, followed by a 2- to 3-min period of depression and then a long period of elevated burst rate. Acetylcholine chloride (ACh) alone is ineffective, but in the presence of eserine is moderately stimulatory. The inhibitory effects of nicotine are only partially blocked by curare. The excitatory action of nicotine is blocked by prior perfusion of domperidone, but not by SKF-83566.HCl, a D₁-specific DA antagonist. SKF-83566 had no effects on the ongoing pattern of firing. These observations support the hypothesis that dopaminergic pathways are involved in the maintenance of the CPG_v rhythm and that the acceleratory effects of nicotine may involve release of DA either directly or via stimulation of atypical ACh receptors at intraganglionic sites. © 1992 John Wiley & Sons, Inc.