Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming.

Animal movements result from a complex balance of many different forces. Muscles produce force to move the body; the body has inertial, elastic, and damping properties that may aid or oppose the muscle force; and the environment produces reaction forces back on the body. The actual motion is an emergent property of these interactions. To examine the roles of body stiffness, muscle activation, and fluid environment for swimming animals, a computational model of a lamprey was developed. The model uses an immersed boundary framework that fully couples the Navier-Stokes equations of fluid dynamics with an actuated, elastic body model. This is the first model at a Reynolds number appropriate for a swimming fish that captures the complete fluid-structure interaction, in which the body deforms according to both internal muscular forces and external fluid forces. Results indicate that identical muscle activation patterns can produce different kinematics depending on body stiffness, and the optimal value of stiffness for maximum acceleration is different from that for maximum steady swimming speed. Additionally, negative muscle work, observed in many fishes, emerges at higher tail beat frequencies without sensory input and may contribute to energy efficiency. Swimming fishes that can tune their body stiffness by appropriately timed muscle contractions may therefore be able to optimize the passive dynamics of their bodies to maximize peak acceleration or swimming speed.

Wake structures behind a swimming robotic lamprey with a passively flexible tail.

A robotic lamprey, based on the silver lamprey, Ichthyomyzon unicuspis, was used to investigate the influence of passive tail flexibility on the wake structure and thrust production during anguilliform swimming. A programmable microcomputer actuated 11 servomotors that produce a traveling wave along the length of the lamprey body. The waveform was based on kinematic studies of living lamprey, and the shape of the tail was taken from a computer tomography scan of the silver lamprey. The tail was constructed of flexible PVC gel, and nylon inserts were used to change its degree of flexibility. Particle image velocimetry measurements using three different levels of passive flexibility show that the large-scale structure of the wake is dominated by the formation of two pairs of vortices per shedding cycle, as seen in the case of a tail that flexed actively according to a pre-defined kinematic pattern, and did not bend in response to fluid forces. When the tail is passively flexible, however, the large structures are composed of a number of smaller vortices, and the wake loses coherence as the degree of flexibility increases. Momentum balance calculations indicate that, at a given tailbeat frequency, increasing the tail flexibility yields less net force, but changing the cycle frequency to match the resonant frequency of the tail increases the force production.

On the derivation and tuning of phase oscillator models for lamprey central pattern generators.

Using phase response curves and averaging theory, we derive phase oscillator models for the lamprey central pattern generator from two biophysically-based segmental models. The first one relies on network dynamics within a segment to produce the rhythm, while the second contains bursting cells. We study intersegmental coordination and show that the former class of models shows more robust behavior over the animal's range of swimming frequencies. The network-based model can also easily produce approximately constant phase lags along the spinal cord, as observed experimentally. Precise control of phase lags in the network-based model is obtained by varying the relative strengths of its six different connection types with distance in a phase model with separate coupling functions for each connection type. The phase model also describes the effect of randomized connections, accurately predicting how quickly random network-based models approach the determinisitic model as the number of connections increases.

Phase-dependent effects of spinal cord stimulation on locomotor activity.

This paper examines how electrical stimulation of the spinal cord can modulate the output of the central pattern generator (CPG) for locomotion. Application of discrete current pulses to a single spinal segment was shown to affect multiple parameters of an ongoing locomotor pattern in an in vitro spinal cord. For any given stimulus, the effects on frequency, duration, and symmetry of locomotor output were strongly dependent on the phase at which stimulation was applied within the CPG cycle. Additionally, most stimuli had an immediate impact and evinced no effects on subsequent cycles. The most dramatic changes were seen when stimulation was applied during motor bursting: stimuli applied to the ipsilateral spinal hemicord increased the burst length, while stimuli applied to the contralateral spinal hemicord decreased the burst length. Smaller changes were observed when stimulating during delays between motor bursts. Thus, phasic stimulation was shown to influence the behavior of the CPG and spinal locomotion circuits on a cycle-by-cycle basis. This work represents the first step toward our ultimate goal of developing a neuroprosthetic device to restore locomotion after a severe spinal cord injury.

Changes in distribution of serotonin induced by spinal injury in larval lampreys: evidence from immunohistochemistry and HPLC.

Larval lampreys are known to successfully recover normal behavior following spinal cord injury. More recently, we showed temperature can influence functional recovery, with colder temperatures more likely producing behavioral abnormality despite the cold being the animals' normal temperature. Here we analyze the differences associated with temperature effects. We examine serotonergic expression along the spinal cord following midbody lesions considering time from injury, temperature during recovery and fiber location. We also examine the relationship between regeneration and locomotion, insofar as the pattern of muscle potentials during unrestrained swimming is normal or abnormal. At 26 weeks after spinal cord injury in all groups of animals, immunohistochemistry and HPLC for serotonin and serotonin expression above and below the lesion can be significantly changed in all regional sources of serotonin independent of the temperature animals recover from their injuries. Animals from warmer tanks recover serotonin expression in the segment immediately caudal to the lesion site with little further away from the lesion; animals from the cold room aquaria have significantly less recovery of expression caudal to the lesion and none further away. There was no apparent relationship between the distribution of serotonin and recovery. The changes suggest that some intraspinal reorganization has occurred. We propose a relationship between the observed results and functional recovery, but it remains conjectural. The fact that some animals recover normal function suggests plasticity must occur in animals successful in recovering normal function. Thus, the lamprey can be used as a model system to study the adaptive changes that permit or prevent functional recovery.

Phase locking asymmetries at flexor-extensor transitions during fictive locomotion.

The motor output for walking is produced by a network of neurons termed the spinal central pattern generator (CPG) for locomotion. The basic building block of this CPG is a half-center oscillator composed of two mutually inhibitory sets of interneurons, each controlling one of the two dominant phases of locomotion: flexion and extension. To investigate symmetry between the two components of this oscillator, we analyzed the statistics of natural variation in timing during fictive locomotion induced by stimulation of the midbrain locomotor region in the cat. As a complement to previously published analysis of these data focused on burst and cycle durations, we present a new analysis examining the strength of phase locking at the transitions between flexion and extension. Across our sample of nerve pairs, phase locking at the transition from extension to flexion (E to F) is stronger than at the transition from flexion to extension (F to E). This pattern did not reverse when considering bouts of fictive locomotion that were flexor vs. extensor dominated, demonstrating that asymmetric locking at the transitions between phases is dissociable from which phase dominates cycle duration. We also find that the strength of phase locking is correlated with the mean latency between burst offset and burst onset. These results are interpreted in the context of a hypothesis where network inhibition and intrinsic oscillatory mechanisms make distinct contributions to flexor-extensor alternation in half-center networks.

Mechanical properties of the lamprey spinal cord: uniaxial loading and physiological strain.

During spinal cord injury, nerves suffer a strain beyond their physiological limits which damages and disrupts their structure. Research has been done to measure the modulus of the spinal cord and surrounding tissue; however the relationship between strain and spinal cord fibers is still unclear. In this work, our objective is to measure the stress-strain response of the spinal cord in vivo and in vitro and model this response as a function of the number of fibers. We used the larvae lamprey (Petromyzon Marinus), a model for spinal cord regeneration and animal locomotion. We found that physiologically the spinal cord is pre-stressed to a longitudinal strain of 10% and this strain increases to 15% during swimming. Tensile measurements show that uniaxial, longitudinal loading is independent of the meninges. Stress values for uniaxial strains below 18%, are homogeneous through the length of the body. However, for higher uniaxial strains the Head section shows more resistance to longitudinal loading than the Tail. These data, together with the number of fibers obtained from histological sections were used in a composite-material model to obtain the properties of the spinal cord fibers (2.4 MPa) and matrix (0.017 MPa) to uniaxial longitudinal loading. This model allowed us to approximate the percentage of fibers in the spinal cord, establishing a relationship between uniaxial longitudinal strains and spinal cord composition. We showed that there is a proportional relationship between the number of fibers and the properties of the spinal cord at large uniaxial strains.

Regenerated synapses in lamprey spinal cord are sparse and small even after functional recovery from injury.

Despite the potential importance that synapse regeneration plays in restoring neuronal function after spinal cord injury (SCI), even the most basic questions about the morphology of regenerated synapses remain unanswered. Therefore, we set out to gain a better understanding of central synapse regeneration by examining the number, distribution, molecular composition, and ultrastructure of regenerated synapses under conditions in which behavioral recovery from SCI was robust. To do so, we used the giant reticulospinal (RS) neurons of lamprey spinal cord because they readily regenerate, are easily identifiable, and contain large synapses that serve as a classic model for vertebrate excitatory neurotransmission. Using a combination of light and electron microscopy, we found that regenerated giant RS synapses regained the basic structures and presynaptic organization observed at control giant RS synapses at a time when behavioral recovery was nearly complete. However, several obvious differences remained. Most strikingly, regenerated giant RS axons produced very few synapses. In addition, presynaptic sites within regenerated axons were less complex, had fewer vesicles, and had smaller active zones than normal. In contrast, the densities of presynapses and docked vesicles were nearly restored to control values. Thus, robust functional recovery from SCI can occur even when the structures of regenerated synapses are sparse and small, suggesting that functional recovery is due to a more complex set of compensatory changes throughout the spinal network.

Phase-based control of the central pattern generator for locomotion.

We have previously shown that the lamprey's central pattern generator (CPG) for locomotion can be manipulated by applying electrical stimuli to the spinal cord at precise phases within the CPG cycle. Here we demonstrate how these so-called phase dependent responses (PDR) can be used to repeatably and reliably manipulate individual parameters of locomotion in the lamprey. In particular, we show that: (1) the PDR for an arbitrary stimulus prescribes the phases at which to stimulate in order to effect specific modifications of the locomotor output; (2) ipsilateral and contralateral burst lengths can be controlled separately; and (3) the responses predicted by a single-cycle PDR plot remain stable over many cycles of stimulation. All of these properties suggest that phase-dependent stimulation may be an effective means of controlling the CPG in a future spinal locomotion neuroprosthesis.

Rostral versus caudal differences in mechanical entrainment of the lamprey central pattern generator for locomotion.

In fishes, undulatory swimming is produced by sets of spinal interneurons constituting a central pattern generator (CPG). The CPG generates waves of muscle activity that travel from head to tail, which then bend the body into wave shapes that also travel from head to tail. In many fishes, the wavelengths of the neural and mechanical waves are different, resulting in a rostral-to-caudal gradient in phase lag between muscle activity and bending. The neural basis of this phase gradient was investigated in the lamprey spinal cord using an isolated in vitro preparation. Fictive swimming was induced using d-glutamate and the output of the CPG was measured using suction electrodes placed on the ventral roots. The spinal cord was bent sinusoidally at various points along its length. First, the ranges of entrainment were estimated. Middle segments were able to entrain to frequencies approximately twice as high as those at end segments. Next, phase lags between centers of ventral root bursts and the stimulus were determined. Two halves of the cycle were identified: stretching and shortening of the edge of spinal cord on the same side as the electrode. Stimuli at rostral segments tended to entrain segmental bursting at the beginning of the stretch phase, almost 50% out of phase with previously measured in vivo electromyography data. Stimuli at caudal segments, in contrast, entrained segments at the end of stretch and the beginning of shortening, approximately the same phase as in vivo data.

Biologically inspired adaptive walking of a quadruped robot.

We describe here the efforts to induce a quadruped robot to walk with medium-walking speed on irregular terrain based on biological concepts. We propose the necessary conditions for stable dynamic walking on irregular terrain in general, and we design the mechanical and the neural systems by comparing biological concepts with those necessary conditions described in physical terms. PD-controller at joints constructs the virtual spring-damper system as the viscoelasticity model of a muscle. The neural system model consists of a central pattern generator (CPG), reflexes and responses. We validate the effectiveness of the proposed neural system model control using the quadruped robots called 'Tekken1&2'. MPEG footage of experiments can be seen at http://www.kimura.is.uec.ac.jp.

Temporal correlations in stochastic models of double bursting during simulated locomotion.

The output of the spinal central pattern generator for locomotion falls into two broad categories: alternation between antagonistic muscles and double bursting within muscles acting on multiple joints. We first model an alternating half-center and then present two different models of double bursting. The first double-bursting model consists of a central clock with an explicit one-to-one mapping between interneuron activity and model output. The second double-bursting model consists of a half-center with an added feedback neuron. Models are built using rate-coded leaky integrator neurons with slow self-inhibition. Structure-function relationships are explored by the addition of noise. The interaction of noise with the dynamics of each network creates a unique pattern of correlation between phases of the simulated cycle. The effects of noise can be explained by perturbation of deterministic versions of the networks. Three basic results were obtained: slow self-inhibitory currents lead to correlations between parts of the step cycle that are separated in time and network relative; model outputs are most sensitive to perturbations presented just before competitive switches in network activity, and clock-like models possess substantial symmetries within the correlation structure of burst durations, whereas the correlation structure of feedback models are asymmetric. Our models suggest that variability in burst length durations can be analyzed to make inferences about the structure of the spinal networks for locomotion. In particular, correlation patterns within double-bursting outputs may yield important clues regarding the interaction between more central, clock-like networks and feedback from more peripheral interneurons.

Dynamic control of the central pattern generator for locomotion.

We show that an ongoing locomotor pattern can be dynamically controlled by applying discrete pulses of electrical stimulation to the central pattern generator (CPG) for locomotion. Data are presented from a pair of experiments on biological (wetware) and electrical (hardware) models of the CPG demonstrating that stimulation causes brief deviations from the CPG's limit cycle activity. The exact characteristics of the deviation depend strongly on the phase of stimulation. Applications of this work are illustrated by examples showing how locomotion can be controlled by using a feedback loop to monitor CPG activity and applying stimuli at the appropriate times to modulate motor output. Eventually, this approach could lead to development of a neuroprosthetic device for restoring locomotion after paralysis.

The immune gene repertoire encoded in the purple sea urchin genome.

Echinoderms occupy a critical and largely unexplored phylogenetic vantage point from which to infer both the early evolution of bilaterian immunity and the underpinnings of the vertebrate adaptive immune system. Here we present an initial survey of the purple sea urchin genome for genes associated with immunity. An elaborate repertoire of potential immune receptors, regulators and effectors is present, including unprecedented expansions of innate pathogen recognition genes. These include a diverse array of 222 Toll-like receptor (TLR) genes and a coordinate expansion of directly associated signaling adaptors. Notably, a subset of sea urchin TLR genes encodes receptors with structural characteristics previously identified only in protostomes. A similarly expanded set of 203 NOD/NALP-like cytoplasmic recognition proteins is present. These genes have previously been identified only in vertebrates where they are represented in much lower numbers. Genes that mediate the alternative and lectin complement pathways are described, while gene homologues of the terminal pathway are not present. We have also identified several homologues of genes that function in jawed vertebrate adaptive immunity. The most striking of these is a gene cluster with similarity to the jawed vertebrate Recombination Activating Genes 1 and 2 (RAG1/2). Sea urchins are long-lived, complex organisms and these findings reveal an innate immune system of unprecedented complexity. Whether the presumably intense selective processes that molded these gene families also gave rise to novel immune mechanisms akin to adaptive systems remains to be seen. The genome sequence provides immediate opportunities to apply the advantages of the sea urchin model toward problems in developmental and evolutionary immunobiology.

Estimating the strength and direction of functional coupling in the lamprey spinal cord.

A method of estimating coupling strength between two neural oscillators based on their spikes trains (Kiemel and Cohen, J. Comput. Neurosci. 5: 267-284, 1998) is tested using simulated data and then applied to experimental data from the central pattern generator (CPG) for swimming in the lamprey. The method is tested using a model of two connectionist oscillators and a model of two endogenously bursting cells. For both models, the method provides useful estimates of the relative strength of coupling in each direction, as well as estimates of total strength. The method is applied to pairs of motor-nerve recordings from isolated 50-segment pieces of spinal cords from adult silver lampreys (Ichthyomyzon unicuspus). The strength and direction of coupling is estimated under control conditions and conditions in which intersegmental coupling between the two recording locations is weakened by hemisections of the spinal cords and/or chambers containing an inhibitory solution that blocks firing in postsynaptic cells. The relevance of these measures in constraining models of the CPG is discussed.

An in silico central pattern generator: silicon oscillator, coupling, entrainment, and physical computation.

In biological systems, the task of computing a gait trajectory is shared between the biomechanical and nervous systems. We take the perspective that both of these seemingly different computations are examples of physical computation. Here we describe the progress that has been made toward building a minimal biped system that illustrates this idea. We embed a significant portion of the computation in physical devices, such as capacitors and transistors, to underline the potential power of emphasizing the understanding of physical computation. We describe results in the exploitation of physical computation by (1) using a passive knee to assist in dynamics computation, (2) using an oscillator to drive a monoped mechanism based on the passive knee, (3) using sensory entrainment to coordinate the mechanics with the neural oscillator, (4) coupling two such systems together mechanically at the hip and computationally via the resulting two oscillators to create a biped mechanism, and (5) demonstrating the resulting gait generation in the biped mechanism.