Central Pattern Generators

Cheetahs and beetles run, dolphins and salmon swim, and bees and birds fly with grace and economy surpassing our technology. Evolution has shaped the breathtaking abilities of animals, leaving us the challenge of reconstructing their targets of control and mechanisms of dexterity. In this review we explore a corner of this fascinating world. We describe mathematical models for legged animal locomotion, focusing on rapidly running insects and highlighting past achievements and challenges that remain. Newtonian body-limb dynamics are most naturally formulated as piecewise-holonomic rigid body mechanical systems, whose constraints change as legs touch down or lift off. Central pattern generators and proprioceptive sensing require models of spiking neurons and simplified phase oscillator descriptions of ensembles of them. A full neuromechanical model of a running animal requires integration of these elements, along with proprioceptive feedback and models of goal-oriented sensing, planning, and learning. We outline relevant background material from biomechanics and neurobiology, explain key properties of the hybrid dynamical systems that underlie legged locomotion models, and provide numerous examples of such models, from the simplest, completely soluble "peg-leg walker" to complex neuromuscular subsystems that are yet to be assembled into models of behaving animals. This final integration in a tractable and illuminating model is an outstanding challenge.

The question of how the central nervous system coordinates muscle activity is central to an understanding
of motor control. The authors argue that motor programs may be considered as a characteristic timing of
muscle activations linked to specific kinematic events. In particular, muscle activity occurring during human
locomotion can be accounted for by five basic temporal components in a variety of locomotion conditions.
Spatiotemporal maps of spinal cord motoneuron activation also show discrete periods of activity. Furthermore,
the coordination of locomotion with voluntary tasks is accomplished through a superposition of motor
programs or activation timings that are separately associated with each task. As a consequence, the selection
of muscle synergies appears to be downstream from the processes that generate activation timings.

Motion of the upper limbs is often coupled to that of the lower limbs in human bipedal locomotion. It is unclear, however, whether the functional coupling between upper and lower limbs is bi-directional, i.e. whether arm movements can affect the lumbosacral locomotor circuitry. Here we tested the effects of voluntary rhythmic arm movements on the lower limbs. Participants lay horizontally on their side with each leg suspended in an unloading exoskeleton. They moved their arms on an overhead treadmill as if they walked on their hands. Hand-walking in the antero-posterior direction resulted in significant locomotor-like movements of the legs in 58% of the participants. We further investigated quantitatively the responses in a subset of the responsive subjects. We found that the electromyographic (EMG) activity of proximal leg muscles was modulated over each cycle with a timing similar to that of normal locomotion. The frequency of kinematic and EMG oscillations in the legs typically differed from that of arm oscillations. The effect of hand-walking was direction specific since medio-lateral arm movements did not evoke appreciably leg air-stepping. Using externally imposed trunk movements and biomechanical modelling, we ruled out that the leg movements associated with hand-walking were mainly due to the mechanical transmission of trunk oscillations. EMG activity in hamstring muscles associated with hand-walking often continued when the leg movements were transiently blocked by the experimenter or following the termination of arm movements. The present results reinforce the idea that there exists a functional neural coupling between arm and legs.

Controlling robots with multiple degrees of freedom (DOFs) is still an open and challenging issue, notably because planning complex, multidimensional trajectories in timevarying environments is a laborious and costly process. In this dissertation, we propose a control architecture where the planning consists in defining the key characteristics of the desired movement (e.g., the target for reaching), while the generation of the complete trajectory is based on predefined dynamics. More precisely, the generation of joint trajectories is decoupled from high-level planning (i.e., the definition of the task) through the use of a combination of discrete and rhythmic motor primitives, that is, movements with predefined dynamics.

Human locomotor movements exhibit considerable variability and are highly complex in terms of both neural activation and biomechanical output. The building blocks with which the central nervous system constructs these motor patterns can be preserved in patients with various sensory-motor disorders. In particular, several studies highlighted a modular burst-like organization of the muscle activity. Here we review and discuss this issue with a particular emphasis on the various examples of adaptation of locomotor patterns in patients (with large fiber neuropathy, amputees, stroke and spinal cord injury). The results highlight plasticity and different solutions to reorganize muscle patterns in both peripheral and central nervous system lesions. The findings are discussed in a general context of compensatory gait mechanisms, spatiotemporal architecture and modularity of the locomotor program.

An ability to produce rhythmic activity is ubiquitous for locomotor pattern generation and modulation. The role that the rhythmogenesis capacity of the spinal cord plays in injured populations has become an area of interest and systematic investigation among researchers in recent years, despite its importance being long recognized by neurophysiologists and clinicians. Given that each individual interneuron, as a rule, receives a broad convergence of various supraspinal and sensory inputs and may contribute to a vast repertoire of motor actions, the importance of assessing the functional state of the spinal locomotor circuits becomes increasingly evident. Air-stepping can be used as a unique and important model for investigating human rhythmogenesis since its manifestation is largely facilitated by a reduction of external resistance. This article aims to provide a review on current issues related to the " locomotor " state and interactions between spinal and supraspinal influences on the central pattern generator (CPG) circuitry in humans, which may be important for developing gait rehabilitation strategies in individuals with spinal cord and brain injuries.

• Air-stepping can be used as a model for investigating rhythmogenesis/CPG in humans. • We compared voluntary and non-voluntary (vibration-induced) stepping. • We examined MEPs in response to TMS of the motor cortex and H-reflex. • We found greater responsiveness to central/sensory inputs during voluntary stepping. • Findings support engagement of supraspinal motor areas in CPG-modulating therapies. a b s t r a c t Here, we compared motor evoked potentials (MEP) in response to transcranial magnetic stimulation of the motor cortex and the H-reflex during voluntary and vibration-induced air-stepping movements in humans. Both the MEPs (in mm biceps femoris, rectus femoris and tibialis anterior) and H-reflex (in m soleus) were significantly smaller during vibration-induced cyclic leg movements at matched amplitudes of angular motion and muscle activity. These findings highlight differences between voluntary and non-voluntary activation of the spinal pattern generator circuitry in humans, presumably due to an extra facilitatory effect of voluntary control/triggering of stepping on spinal motoneurons and interneurons. The results support the idea of active engagement of supraspinal motor areas in developing central pattern generator-modulating therapies.

The revealed secrets of nature always led humans to their aspiring achievements. The fastest animal on land is Cheetah and similar robot has developed by engineers so far to attain a record speed of 20mph among legged robots. But in nature there are some insects those are far ahead of cheetah in speed with a unit of body length per second. Insects are small in their body size with legs usually countable from 4 to 12 or more. With more legs they can have more stability and can adapt to different terrain faster while walking. Six legged robot (hexapod) is generally expect to attain higher speed in terms of body length per second, since the nature has proof for it. Bio-inspired Central Pattern Generator (CPG) is in use for so far in robotic world to mimic the locomotion patterns of insects and other animals. Currently the hybrid controller of CPG and reflex is going on and this paper suggests a new architecture for the system. Neural Network modeled CPG acts as the motor neuron for each joint of the leg. In each instant a neural network models the gait of the robot by learning procedure from the reflex system. This is like the Central Nervous System (CNS) selecting gait of an animal according to the terrain that travels. CNS takes sensory feedback from eyes, force on each leg and body balance from cochlea to adapt the gait for current terrain. This paper in first place tries to simulate the gait patterns for a hexapod.

Summary: Purpose: Nocturnal frontal lobe epilepsy (NFLE) is characterized by a wide spectrum of sleep-related motor manifestations of increasing complexity, ranging from major episodes to brief motor events (minor motor events, MMEs). NFLE patients may exhibit a large quantity of MMEs in the form of short-lasting stereotyped movements. Whereas major episodes are considered epileptiform manifestations, it remains unclear whether the MMEs are related to epileptiform discharges (EDs).Methods: To study the relation between EDs and the occurrence of MMEs, we report a detailed neurophysiolgical evaluation in NFLE subjects explored by using implanted electrodes.Results: The median value of ED-related movements was 71.8%. Motor expression in relation to epileptiform discharge was surprisingly variable; no peculiar expression of MMEs could be attributed to the presence of EDs.Conclusions: Our data suggest that ED-associated MMEs are extremely polymorphous, and no univocal relation to EDs can be identified. We hypothesize that MMEs are not a direct effect of epileptiform discharge (i.e., not epileptic in origin), but the result of aspecific disinhibition of innate motor patterns. We warn clinicians that the epileptic nature of minimal motor phenomena in NFLE cannot be established on the clinical phenomenology of the event.

Cheetahs and beetles run, dolphins and salmon swim, and bees and birds fly with grace and economy surpassing our technology. Evolution has shaped the breathtaking abilities of animals, leaving us the challenge of reconstructing their targets of control and mechanisms of dexterity. In this review we explore a corner of this fascinating world. We describe mathematical models for legged animal

Reorganizational Healing, (ROH), is an emerging wellness, growth and behavioral change paradigm. Through its three central elements (the Four Seasons of Wellbeing, the Triad of Change, and the Five Energetic Intelligences) Reorganizational Healing takes an approach to help create a map for individuals to self-assess and draw on strengths to create sustainable change. Reorganizational Healing gives individuals concrete tools to explore and use the meanings of their symptoms, problems, and life-stressors as catalysts to taking new and sustained action to create a more fulfilling and resilient life.

In this paper we study distributed online learning of locomotion gaits for modular robots. The learning is based on a stochastic approximation method, SPSA, which optimizes the parameters of coupled oscillators used to generate periodic actuation patterns. The strategy is implemented in a distributed fashion, based on a globally shared reward signal, but otherwise utilizing local communication only. In a physicsbased simulation of modular Roombots robots we experiment with online learning of gaits and study the effects of: module failures, different robot morphologies, and rough terrains. The experiments demonstrate fast online learning, typically 5-30 min. for convergence to high performing gaits (≈ 30 cm/sec), despite high numbers of open parameters (45-54). We conclude that the proposed approach is efficient, effective and a promising candidate for online learning on many other robotic platforms.

The plasticity of the nervous system during the processing of sensory information is of major interest to interdisciplinary neurobiology research. Here, we used an insect model system with stereotyped behavioral patterns for the investigation of how the nervous system can switch between two different motor outputs, walking and standing, despite having the same sensory input, in a computer simulation based on the known network structure. The strengths of 16 specific information pathways which integrate sensory information were permutated and the resulting database of more than 43 million network outputs was analyzed. Two independent analysis show that the same neural network can produce two different behaviors by specifically altering the weighting of several information pathways. We obtained specific combinations of pathway transmission levels that produced these behaviors. This means, that solely changing the strength with which a pathway transmits sensory information is sufficient to switch between different behaviors, like from standing to walking. The predictions that derive from our results can now be used in physiological experiments.

Objectives: This article explains the research on a unique spinal wave visibly observed in association with network spinal analysis care. Since 1997, the network wave has been studied using surface electromyography (sEMG), characterized mathematically, and determined to be a unique and repeatable phenomenon. Methods: The authors provide a narrative review of the research and a context for the network wave's development. Results: The sEMG research demonstrates that the movement of the musculature of the spine during the wave phenomenon is electromagnetic and mechanical. The changes running along the spine were characterized mathematically at three distinct levels of care. Additionally, the wave has the mathematical properties of a central pattern generator (CPG). Conclusions: The network wave may be the first CPG discovered in the spine unrelated to locomotion. The mathematical characterization of the signal also demonstrates coherence at a distance between the sacral to cervical spine. According to mathematical engineers, based on studies conducted a decade apart, the wave itself is a robust phenomenon and the detection methods for this coherence may represent a new measure for central nervous system health. This phenomenon has implications for recovery from spinal cord injury and for reorganizational healing development.

In 1911, Graham Brown 1 was the first to show the existence of neuronal networks within the thoracic spinal cord capable of producing repetitive rhythmic hind limb movements resembling locomotion. He reported that rhythmic alternating locomotorlike motor movements were observed in antagonistic muscles in each hind limb for a short time after experimental thoracic spinal cord transection in an animal model that had previously had its dorsal sensory roots sectioned. 1 These experiments unequivocally showed that neuronal aggregates in the spinal cord (deprived from sensory inputs and supraspinal influences) can generate a coordinated rhythmic motor movement.

An outstanding question in research of central pattern generators is whether CPGs can be used for whole body control of a robot. Given the spine’s important role in walking, including a robotic spine may be a prerequisite for answering this question, but most current robots use rigid torsos. Tensegrity offers exciting possibilities for future robotic structures, as their continuous tension networks automatically distribute forces. This property creates robust structures and shows the potential to improve torsos of legged robots, and may also provide mechanisms for distributed coordination of motor patterns and entrainment with oscillatory controllers such as CPGs. Our prior work with CPGs on tensegrity structures allowed for some adaptations in rough terrain, but without feedback success was limited with larger perturbations. This work demonstrates a CPG controlled tensegrity spine with locomotor capability on additional terrains by providing feedback to the CPG.

Recent studies have established and characterized the propagation of traveling electrical waves along the cat spinal cord during scratching, but the neuronal architecture that allows for the persistence of such waves even during periods of absence of bursts of motoneuron activity (deletions) is still unclear. Here we address this problem both theoretically and experimentally. Specifically, we monitored during long lasting periods of time the global electrical activity of spinal neurons during scratching. We found clear deletions of unaltered cycle in extensor activity without associated deletions of the traveling spinal wave. Furthermore, we also found deletions with a perturbed cycle associated with a concomitant absence of the traveling spinal wave. Numerical simulations of an asymmetric two-layer model of a central-pattern generator distributed longitudinally along the spinal cord qualitatively reproduce the sinusoidal traveling waves, and are able to replicate both classes of deletions. We believe these findings shed light into the longitudinal organization of the central-pattern generator networks in the spinal cord.

We present a general approach to design modular controllers for limit cycle locomotion over unperceived rough terrain. The control strategy uses a Central Pattern Generator (CPG) model implemented as coupled nonlinear oscillators as basis. Stumbling correction and leg extension reflexes are implemented as feedbacks for fast corrections, and model-based posture control mechanisms define feedbacks for continuous corrections. The control strategy is validated on a detailed physics-based simulated model of a compliant quadruped robot, the Oncilla robot. We demonstrate dynamic locomotion with a speed of more than 1.5 BodyLength/s over unperceived uneven terrains, steps, and slopes.

The effect of proprioceptive feedback on the control of posture and locomotion was studied in the crayfish Procambarus clarkii (Girard). Sensory and motor nerves of an isolated crayfish thoracic nerve cord were connected to a computational neuromechanical model of the crayfish thorax and leg. Recorded levator (Lev) and depressor (Dep) nerve activity drove the model Lev and Dep muscles to move the leg up and down. These movements released and stretched a model stretch receptor, the coxobasal chordotonal organ (CBCO). Model CBCO length changes drove identical changes in the real CBCO; CBCO afferent responses completed the feedback loop. In a quiescent preparation, imposed model leg lifts evoked resistance reflexes in the Dep motor neurons that drove the leg back down. A muscarinic agonist, oxotremorine, induced an active state in which spontaneous Lev/Dep burst pairs occurred and an imposed leg lift excited a Lev assistance reflex followed by a Lev/Dep burst pair. When the feedback lo...

We present a methodology enabled by the NASA Tensegrity Robotics Toolkit (NTRT) for the rapid structural design of tensegrity robots in simulation and an approach for developing control systems using central pattern generators, local impedance controllers, and parameter optimization techniques to determine effective locomotion strategies for the robot. Biomimetic tensegrity structures provide advantageous properties to robotic locomotion and manipulation tasks, such as their adaptability and force distribution properties, flexibility, energy efficiency, and access to extreme terrains. While strides have been made in designing insightful static biotensegrity structures, gaining a clear understanding of how a particular structure can efficiently move has been an open problem. The tools in the NTRT enable the rapid exploration of the dynamics of a given morphology, and the links between structure, controllability, and resulting gait efficiency. To highlight the effectiveness of the NTR...

We present a methodology enabled by the NASA Tensegrity Robotics Toolkit (NTRT) for the rapid structural design of tensegrity robots in simulation and an approach for developing control systems using central pattern generators, local impedance controllers, and parameter optimization techniques to determine effective locomotion strategies for the robot. Biomimetic tensegrity structures provide advantageous properties to robotic locomotion and manipulation tasks, such as their adaptability and force distribution properties, flexibility, energy efficiency, and access to extreme terrains. While strides have been made in designing insightful static biotensegrity structures, gaining a clear understanding of how a particular structure can efficiently move has been an open problem. The tools in the NTRT enable the rapid exploration of the dynamics of a given morphology, and the links between structure, controllability, and resulting gait efficiency. To highlight the effectiveness of the NTRT at this exploration of morphology and control, we will provide examples from the designs and locomotion of four different modular spine-like tensegrity robots.

The present discourse links the electrical and chemical properties of the brain with neurotransmitters and movement behaviors to further elucidate strategies to diagnose and treat brain disease. Neuromolecular imaging (NMI), based on electrochemical principles, is used to detect serotonin in nerve terminals (dorsal and ventral striata) and somatodendrites (ventral tegmentum) of reward/motor mesocorticolimbic and nigrostriatal brain circuits. Neuronal release of serotonin is detected at the same time and in the same animal, freely moving and unrestrained, while open-field behaviors are monitored via infrared photobeams. The purpose is to emphasize the unique ability of NMI and the BRODERICK PROBE® biosensors to empirically image a pattern of temporal synchrony, previously reported, for example, in Aplysia using central pattern generators (CPGs), serotonin and cerebral peptide-2. Temporal synchrony is reviewed within the context of the literature on central pattern generators, neurotr...

5-hydroxytryptamine, serotonin 5-HTP 5-hydroxytryptophan AB anterior burster CabTRP 1a Cancer borealis tachykinin-related peptide 1a CCAP crustacean cardioactive peptide GABA γ-aminobutyric acid I H hyperpolarization-activated inward current LP lateral pyloric MAOA monoamine oxidase A MCN1 modulatory commissural neuron 1 mGluR metabotropic glutamate receptor MPN modulatory proctolin neuron PD pyloric dilator STG stomatogastric ganglion Motor pattern generation Eve Marder

Reorganizational Healing, (ROH), is an emerging wellness, growth and behavioral change paradigm. Through its three central elements (the Four Seasons of Wellbeing, the Triad of Change, and the Five Energetic In-telligences) Reorganizational Healing takes an approach to help create a map for individuals to self-assess and draw on strengths to create sustainable change. Reorganizational Healing gives individuals concrete tools to explore and use the meanings of their symptoms, problems, and life-stressors as catalysts to taking new and sustained action to create a more fulfilling and resilient life.

Central pattern generators are neuron networks that produce vital rhythmic motor outputs such as those observed in mastication, walking and breathing. Their activity patterns depend on the tuning of their intrinsic ionic conductances, their synaptic interconnectivity and entrainment by extrinsic neurons. The influence of two commonly found synaptic connectivities--reciprocal inhibition and electrical coupling--are investigated here using a neuron model with subthreshold oscillation capability, in different firing and entrainment regimes. We study the dynamics displayed by a network of a pair of neurons with various firing regimes, coupled by either (i) only reciprocal inhibition or by (ii) electrical coupling first and then reciprocal inhibition. In both scenarios a range of coupling strengths for the reciprocal inhibition is tested, and in general the neuron with the lower firing rate stops spiking for strong enough inhibitory coupling, while the faster neuron remains active. Howev...

In this study we investigated the role of GABA and glycine receptors within the respiratory central pattern generator, i.e. the paratrigeminal respiratory group (pTRG), and the vagal motoneuron region of the lamprey. r Only GABA-mediated inhibition modulates the pTRG both during apnoea induced by blockade of glutamatergic transmission and under basal conditions. r Both GABA-and glycine-mediated inhibition within the vagal region are involved in the regulation of respiratory frequency via ascending excitatory projections to the pTRG. r Projecting neurons are retrogradely labelled from the pTRG, and intense GABA immunoreactivity is present within the pTRG and the vagal motoneuron region. r Inhibitory mechanisms, which appear to be evolutionarily conserved, regulate network excitability and may provide an important contribution to rhythmic activities, such as respiration and locomotion.

In recent years there has been a growing interest in the field of dynamic walking and bio-inspired robots. However, while walking and running on a flat surface have been studied extensively, walking dynamically over terrains with varying slope remains a challenge. Previously we developed an open loop controller based on a Central Pattern Generator (CPG). The controller applied predefined torque patterns to a compass-gait biped (CB), and achieved stable gaits over a limited range of slopes. In this work, this range is greatly extended by applying a once per cycle feedback to the CPG controller. The terrain's slope is measured and used to modify both the CPG frequency and the torque amplitude once per step. A multi-objective optimization algorithm was used to tune the controller parameters for a simulated CB model. The resulting controller successfully traverses terrains with slopes ranging from +7 • to-8 • , comparable to most slopes found in human constructed environments. Gait stability was verified by computing the linearized Poincaré Map both numerically and analytically.

How sensory information influences the dynamics of rhythm generation varies across systems, and general principles for understanding this aspect of motor control are lacking. Determining the origin of respiratory rhythm generation is challenging because the mechanisms in a central circuit considered in isolation may be different than those in the intact organism. We analyze a closed-loop respiratory control model incorporating a central pattern generator (CPG), the Butera-Rinzel-Smith (BRS) model, together with lung mechanics, oxygen handling, and chemosensory components. We show that: (1) Embedding the BRS model neuron in a control loop creates a bistable system; (2) Although closed-loop and open-loop (isolated) CPG systems both support eupnea-like bursting activity, they do so via distinct mechanisms; (3) Chemosensory feedback in the closed loop improves robustness to variable metabolic demand; (4) The BRS model conductances provide an autoresuscitation mechanism for recovery from...

We present for the first time direct electrophysiological evidence of the phenomenon of traveling electrical waves produced by populations of interneurons within the spinal cord. We show that, during a fictive rhythmic motor task, scratching, an electrical field potential of spinal interneurons takes the shape of a sinuous wave, "sweeping" the lumbosacral spinal cord rostrocaudally with a mean speed of ϳ0.3 m/s. We observed that traveling waves and scratching have the same cycle duration and that duration of the flexor phase, but not of the extensor phase, is highly correlated with the cycle duration of the traveling waves. Furthermore, we found that the interneurons from the deep dorsal horn and the intermediate nucleus can generate the spinal traveling waves, even in the absence of motoneuronal activity. These findings show that the sinusoidal field potentials generated during fictive scratching could be a powerful tool to disclose the organization of central pattern generator networks.

Stress alters adaptive behaviours such as learning and memory. Stressors can either enhance or diminish learning, memory formation and/or memory recall. We focus attention here on how environmentally relevant stressors alter learning, memory and forgetting in the pond snail, Lymnaea stagnalis. Operant conditioning of aerial respiration causes associative learning that may lead to long-term memory (LTM) formation. However, individual ecologically relevant stressors, combinations of stressors, and bio-active substances can alter whether or not learning occurs or memory forms. While the behavioural memory phenotype may be similar as a result of exposure to different stressors, how each stressor alters memory formation may occur differently. In addition, when a combination of stressors are presented it is difficult to predict ahead of time what the outcome will be regarding memory formation. Thus, how combinations of stressors act is an emergent property of how the snail perceives the stressors. . Survival characteristics of the mollusc Lymnaea stagnalis under constant culture conditions: effects of aging and disease. Mech. Ageing Dev. 42, 263-274. Kamardin, N. N., Shalanki, Y., Rozha, K. S. and Nozdrachev, A. D. (2001). Studies of chemoreceptor perception in mollusks. Neurosci. Behav. Physiol. 31, 227-235. Karnik, V., Braun, M. H., Dalesman, S. and Lukowiak, K. (2012a). Sensory input from the osphradium modulates the response to memory-enhancing stressors in Lymnaea stagnalis. J. Exp. Biol. 215, 536-542. Karnik, V., Dalesman, S. and Lukowiak, K. (2012b). Input from a chemosensory organ, the osphradium, does not mediate aerial respiration in Lymnaea stagnalis. Aquat. Biol. 15, 167-173. Kim, J. J. and Diamond, D. M. (2002). The stressed hippocampus, synaptic plasticity and lost memories. Nat. Rev. Neurosci. 3, 453-462.

The crustacean pyloric Central Pattern Generator (CPG) is a nervous circuit that endogenously provides periodic motor patterns. Even after about 40 years of intensive studies, the rhythm genesis is still not rigorously understood in this CPG, mainly because it is made of neurons with irregular intrinsic activity. Using mathematical models we addressed the question of using a network of irregularly behaving elements to generate periodic oscillations, and we show some advantages of using non-periodic neurons with intrinsic behavior in the transition from bursting to tonic spiking (as found in biological pyloric CPGs) as building components. We studied two-and three-neuron model CPGs built either with Hindmarsh-Rose or with conductance-based Hodgkin-Huxley-like model neurons. By changing a model's parameter we could span the neuron's intrinsic dynamical behavior from slow periodic bursting to fast tonic spiking, passing through a transition where irregular bursting was observed. Two-neuron CPG, half center oscillator (HCO), was obtained for each intrinsic behavior of the neurons by coupling them with mutual symmetric synaptic inhibition. Most of these HCOs presented regular antiphasic bursting activity and the changes of the bursting frequencies was studied as a function of the inhibitory synaptic strength. Among all HCOs, those made of intrinsic irregular neurons presented a wider burst frequency range while keeping a reliable regular oscillatory (bursting) behavior. HCOs of periodic neurons tended to be either hard to change their behavior with synaptic strength variations (slow periodic burster neurons) or unable to perform a physiologically meaningful rhythm (fast tonic spiking neurons). Moreover, 3-neuron CPGs with connectivity and output similar to those of the pyloric CPG presented the same results.

Neurons in cold-blooded animals remarkably maintain their function over a wide range of temperatures, even though the rates of many cellular processes increase twofold, threefold, or many-fold for each 10°C increase in temperature. Moreover, the kinetics of ion channels, maximal conductances, and Ca 2ϩ buffering each have independent temperature sensitivities, suggesting that the balance of biological parameters can be disturbed by even modest temperature changes. In stomatogastric ganglia of the crab Cancer borealis, the duty cycle of the bursting pacemaker kernel is highly robust between 7 and 23°C (Rinberg et al., 2013). We examined how this might be achieved in a detailed conductance-based model in which exponential temperature sensitivities were given by Q 10 parameters. We assessed the temperature robustness of this model across 125,000 random sets of Q 10 parameters. To examine how robustness might be achieved across a variable population of animals, we repeated this analysis across six sets of maximal conductance parameters that produced similar activity at 11°C. Many permissible combinations of maximal conductance and Q 10 parameters were found over broad regions of parameter space and relatively few correlations among Q 10 s were observed across successful parameter sets. A significant portion of Q 10 sets worked for at least 3 of the 6 maximal conductance sets (ϳ11.1%). Nonetheless, no Q 10 set produced robust function across all six maximal conductance sets, suggesting that maximal conductance parameters critically contribute to temperature robustness. Overall, these results provide insight into principles of temperature robustness in neuronal oscillators.