Limb movements during locomotion: Tests of a model of an intersegmental coordinating circuit

The role of long-range coupling in crayfish swimmeret phase-locking

During forward swimming, crayfish and other long-tailed crustaceans rhythmically move four pairs of limbs called swimmerets to propel themselves through the water. This behavior is characterized by a particular stroke pattern in which the most posterior limb pair leads the rhythmic cycle and adjacent swimmerets paddle sequentially with a delay of roughly 25% of the period. The neural circuit underlying limb coordination consists of a chain of local modules, each of which controls a pair of limbs. All modules are directly coupled to one another, but the inter-module coupling strengths decrease with the distance of the connection. Prior modeling studies of the swimmeret neural circuit have included only the dominant nearest-neighbor coupling. Here, we investigate the potential modulatory role of long-range connections between modules. Numerical simulations and analytical arguments show that these connections cause decreases in the phase-differences between neighboring modules. Combined with previous results from a computational fluid dynamics model, we posit that this phenomenon might ensure that the resultant limb coordination lies within a range where propulsion is optimal. To further assess the effects of long-range coupling, we modify the model to reflect an experimental preparation where synaptic transmission from a middle module is blocked, and we generate predictions for the phase-locking properties in this system.

Profiling neurotransmitters in a crustacean neural circuit for locomotion

Locomotor systems are widely used to study rhythmically active neural networks. These networks have to be coordinated in order to produce meaningful behavior. The crayfish swimmeret system is well suited to investigate such coordination of distributed neural oscillators because the neurons and their connectivity for generating and especially for coordinating the motor output are identified. The system maintains a fixed phase lag between the segmental oscillators, independent of cycle period. To further the understanding of the system’s plasticity for keeping the phase lag fixed, we profiled the neurotransmitters used by the Coordinating Neurons, which are necessary and sufficient for coordination of the segmental oscillators. We used a combination of electrophysiological, immunohistochemical, and mass spectrometric methods. This arrangement of methods ensured that we could screen for several specific neurotransmitters, since a single method is often not suitable for all neurotransmitters of interest. In a first step, to preselect neurotransmitter candidates, we investigated the effect of substances known to be present in some swimmeret system neurons on the motor output and coordination. Subsequently, we demonstrated electrophysiologically that the identified synapse between the Coordinating Neurons and their target is mainly chemical, but neither glutamate antagonist nor γ-aminobutyric acid antagonist application affected this synapse. With immunohistochemical experiments, we provide strong evidence that the Coordinating Neurons are not serotonergic. Single-cell MALDI-TOF mass spectrometry with subsequent principal component analysis identified acetylcholine as the putative neurotransmitter for both types of Coordinating Neurons.

Neurobiology of the crustacean swimmeret system

The crustacean swimmeret system includes a distributed set of local circuits that individually control movements of one jointed limb. These modular local circuits occur in pairs in each segmental ganglion, and normally operate synchronously to produce smoothly coordinated cycles of limb movements on different body segments. The system presents exceptional opportunities for computational and experimental investigation of neural mechanisms of coordination because: (a) The system will express in vitro the periodic motor pattern that normally drives cycles of swimmeret movements during forward swimming. (b) The intersegmental neurons which encode information that is necessary and sufficient for normal coordination have been identified, and their activity can be recorded. (c) The local commissural neurons that integrate this coordinating information and tune the phase of each swimmeret are known. (d) The complete set of synaptic connections between coordinating neurons and these commissural neurons have been described. (e). The synaptic connections onto each local pattern-generating circuit through which coordinating information tunes the circuit's phase have been discovered. These factors make possible for the first time a detailed, comprehensive cellular and synaptic explanation of how this neural circuit produces an effective, behaviorally significant output. This paper is the first comprehensive review of the system's neuroanatomy and neurophysiology, its local and intersegmental circuitry, its transmitter pharmacology, its neuromodulatory control mechanisms, and its interactions with other motor systems. Each of these topics is covered in detail in an attempt to provide a complete review of the literature as a foundation for new research. The series of hypotheses that have been proposed to account for the system's properties are reviewed critically in the context of experimental tests of their validity.

State-changes in the swimmeret system: a neural circuit that drives locomotion

The crayfish swimmeret system undergoes transitions between a silent state and an active state. In the silent state, no patterned firing occurs in swimmeret motor neurons. In the active state, bursts of spikes in power stroke motor neurons alternate periodically with bursts of spikes in return stroke motor neurons. In preparations of the isolated crayfish central nervous system (CNS), the temporal structures of motor patterns expressed in the active state are similar to those expressed by the intact animal. These transitions can occur spontaneously, in response to stimulation of command neurons, or in response to application of neuromodulators and transmitter analogues. We used single-electrode voltage clamp of power-stroke exciter and return-stroke exciter motor neurons to study changes in membrane currents during spontaneous transitions and during transitions caused by bath-application of carbachol or octopamine (OA). Spontaneous transitions from silence to activity were marked by the appearance of a standing inward current and periodic outward currents in both types of motor neurons. Bath-application of carbachol also led to the development of these currents and activation of the system. Using low Ca(2+)-high Mg(2+) saline to block synaptic transmission, we found that the carbachol-induced inward current included a direct response by the motor neuron and an indirect component. Spontaneous transitions from activity to silence were marked by disappearance of the standing inward current and the periodic outward currents. Bath-application of OA led promptly to the disappearance of both currents, and silenced the system. OA also acted directly on both types of motor neurons to cause a hyperpolarizing outward current that would contribute to silencing the system.

Coding characteristics of spiking local interneurons during imposed limb movements in the locust

The performance of adaptive behavior relies on continuous sensory feedback to produce relevant modifications to central motor patterns. The femoral chordotonal organ (FeCO) of the legs of the desert locust monitors the movements of the tibia about the femoro-tibial joint. A ventral midline population of spiking local interneurons in the metathoracic ganglia integrates inputs from the FeCO. We used a Wiener kernel cross-correlation method combined with a Gaussian white noise stimulation of the FeCO to completely characterize and model the output dynamics of the ventral midline population of interneurons. A wide range of responses were observed, and interneurons could be classified into three broad groups that received excitatory and inhibitory or principally inhibitory or excitatory synaptic inputs from the FeCO. Interneurons that received mixed inputs also had the greatest linear responses but primarily responded to extension of the tibia and were mostly sensitive to stimulus velocity. Interneurons that received principally inhibitory inputs were sensitive to extension and to joint position. A small group of interneurons received purely excitatory synaptic inputs and were also sensitive to tibial extension. In addition to capturing the linear and nonlinear dynamics of this population of interneurons, first- and second-order Wiener kernels revealed that the dynamics of the interneurons in the population were graded and formed a spectrum of responses whereby the activity of many cells appeared to be required to adequately describe a particular stimulus characteristic, typical of population coding.

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.

Local and Intersegmental Interactions of Coordinating Neurons and Local Circuits in the Swimmeret System

During forward swimming, periodic movements of swimmerets on different segments of the crayfish abdomen progress from back to front with the same period. Information encoded as bursts of spikes by coordinating neurons in each segmental ganglion is necessary for this coherent organization. This information is conducted to targets in other ganglia. When an individual coordinating neuron is stimulated at different phases in the system's cycle of activity, the timing of motor output from other ganglia may be altered. In models of this coordinating circuit, we assumed that each coordinating neuron encodes information about the state of the local pattern-generating circuit in its home ganglion but is not part of that local circuit. We tested this assumption by stimulating individual coordinating neurons of two kinds—ASCE and DSC—at different phases under two conditions: with the target ganglion functional, and with the target ganglion silenced. Blocking a DSC neuron's target ganglion did not alter its negligible influence on the output from its home ganglion; the phase-response curves (PRC) remained flat. Blocking an ASCE neuron's target ganglion significantly affected its influence on the output from its home ganglion. We had predicted that ASCE's modest phase-dependent influence would disappear with the target silenced, but instead the amplitude of the PRCs increased significantly. Thus we have two different results: DSC neurons conformed to prediction based on the models’ assumptions, but ASCE neurons showed an unexpected property, one that is partially masked when the bidirectional flow of information between neighboring ganglia is operating normally.

Intersegmental coordination: influence of a single walking leg on the neighboring segments in the stick insect walking system

A key element of walking is the coordinated interplay of multiple limbs to achieve a stable locomotor pattern that is adapted to the environment. We investigated intersegmental coordination of walking in the stick insect, Carausius morosus by examining the influence a single stepping leg has on the motoneural activity of the other hemiganglia, and whether this influence changes with the walking direction. We used a reduced single leg walking preparation with only one intact front, middle, or hind leg. The intact leg performed stepping movements on a treadmill, thus providing intersegmental signals about its stepping to the other hemiganglia. The activity of coxal motoneurons was simultaneously recorded extracellularly in all other segments. Stepping sequences of any given single leg in either walking direction were accompanied by an increase in coxal motoneuron (MN) activity of all other segments, which was mostly modulated and slightly in phase with stance of the walking leg. In addition, forward stepping of the front leg and, to a lesser extent, backward stepping of the hind leg elicited alternating activity in mesothoracic coxal MNs. Forward and backward stepping of the middle leg did not elicit alternating activity in coxal MNs in any other hemiganglia, indicating that the influence of middle leg stepping is qualitatively different from that of forward front and backward hind leg stepping. Our results indicate that in an insect walking system individual segments differ with respect to their intersegmental influences and thus cannot be treated as similar within the chain of segmental walking pattern generators. Consequences for the current concepts on intersegmental coordination are discussed.

Not by spikes alone: responses of coordinating neurons and the swimmeret system to local differences in excitation

Swimmeret coordinating neurons in the crayfish CNS collectively encode a detailed cycle-by-cycle report on features of the motor output to each swimmeret. This information coordinates the motor output that drives swimmeret movements. To see how coordinating neurons responded to forced changes in intersegmental phase, we used a split-bath, repeated-measures experimental design to expose different regions of isolated abdominal nerve cords to different levels of excitation. We present a quantitative description of the firing of power-stroke (PS) motor units and two kinds of coordinating interneurons, ASC(E) and DSC, recorded simultaneously from each swimmeret ganglion under uniform and nonuniform excitation. When anterior and posterior ganglia were excited differently, several parameters of the swimmeret motor pattern were affected. Strengths of PS bursts in each ganglion were determined by local excitation. The phase of PS bursts in neighboring ganglia changed at the excitation boundary. Coordinating neurons from the two ganglia closest to the excitation boundary were most affected by nonuniform excitation. ASC(E) neurons tracked the timing and duration of each PS burst in their home ganglion, but did not follow changes in PS burst strength. DSC neurons changed the duration, phase, and number of spikes per burst. We propose two models to explain these results. First, the period expressed under nonuniform conditions is the sum of local intersegmental latencies and these latencies are determined by local excitation. Second, the phase change at the excitation boundary is determined by local modulation of the targets of the intersegmental coordinating neurons, not by modulation of the coordinating neurons themselves.

Neuronal network models of phase separation between limb CPGs of digging sand crabs

Ordinary differential equations are used to model a peculiar motor behaviour in the anomuran decapod crustacean Emerita analoga. Little is known about the neural circuitry that permits E. analoga to control the phase relationships between movements of the fourth legs and pair of uropods as it digs into sand, so mathematical models might aid in identifying features of the neural structures involved. The geometric arrangement of segmental ganglia controlling the movements of each limb provides an intuitive framework for modelling. Specifically, due to the rhythmic nature of movement, the network controlling the fourth legs and uropods is viewed as three coupled identical oscillators, one dedicated to the control of each fourth leg and one for the pair of uropods, which always move in bilateral synchrony. Systems of Morris-Lecar equations describe the voltage and ion channel dynamics of neurons. Each central pattern generator for a limb is first modelled as a single neuron and then, more realistically as a multi-neuron oscillator. This process results in high-dimensional systems of equations that are difficult to analyse. In either case, reduction to phase equations by averaging yields a two-dimensional system of equations where variables describe only each oscillator's phase along its limit cycle. The behaviour observed in the reduced equations approximates that of the original system. Results suggest that the phase response function in the two dimensional system, together with minimal input from asymmetric bilateral coupling parameters, is sufficient to account for the observed behaviour.

Invertebrate central pattern generation moves along

Central pattern generators (CPGs) are circuits that generate organized and repetitive motor patterns, such as those underlying feeding, locomotion and respiration. We summarize recent work on invertebrate CPGs which has provided new insights into how rhythmic motor patterns are produced and how they are controlled by higher-order command and modulatory interneurons.

Bursts of Information: Coordinating Interneurons Encode Multiple Parameters of a Periodic Motor Pattern

The limbs on different segments of the crayfish abdomen that drive forward swimming are directly controlled by modular pattern-generating circuits. These circuits are linked together by axons of identified coordinating interneurons. We described the distributions of these neurons in each abdominal ganglion and monitored their firing during expression of the swimming motor pattern. We analyzed the timing, the numbers of spikes, and the duration of each burst of spikes in these coordinating neurons. To see what information these neurons encoded, we correlated these parameters with the timing, durations, and strengths of bursts of spikes in motor axons from the same modules. During the power-stroke phase of each output cycle, the anterior-projecting neurons fired bursts of spikes that encoded information about the start-time, duration, and strength of each burst of spikes in power-stroke motor neurons from the same module. When the period and intensity of the motor output fluctuated, the bursts of spikes in these neurons tracked these fluctuations accurately. Each additional spike in these neurons signified an increase in the strength of the power-stroke burst. The posterior-projecting neurons that fired during the return-stroke phase encoded similar information about the return-stroke motor neurons. Although homologous neurons from different ganglia were qualitatively similar, neurons from posterior ganglia fired significantly more spikes per burst than those from more anterior ganglia, a segmental gradient that correlates with the normal posterior-to-anterior phase progression of limb movements. We propose that this gradient and a similar gradient in the durations of bursts in power-stroke motor neurons might reflect a hitherto-undetected difference in the excitation or intrinsic excitability of swimmeret modules in different segments.

A method to measure the strength of multi-unit bursts of action potentials

Both the numbers of neurons that are active during multi-unit bursts of spikes and the frequencies with which individual neurons fire in these bursts can vary in response to changes in excitation. Here is a digital-filtering method that measures the strength of a burst of spikes by calculating the area of a polygon derived from the squared voltages that record the burst, and dividing this area by the burst's duration. The method was developed in the SigmaPlot environment, and makes use of the Fast-Fourier Transform functions provided in the SigmaPlot transform language. To test the method's performance, I constructed multi-unit bursts of spikes with known structure and calculated the strengths of these known bursts. To demonstrate the method's usefulness, I applied it to a train of 23 bursts of spikes in motor axons recorded during a spontaneous bout of patterned motor output. The measured strengths of these bursts varied 30-fold, and were well-correlated with the differences in the original recording. The results demonstrate that the method effectively measures burst strength independent of burst duration.

Local commissural interneurons integrate information from intersegmental coordinating interneurons

The information that coordinates movements of swimmerets on different segments of the crayfish abdomen is conducted by interneurons that originate in each abdominal ganglion. These interneurons project axons to neighboring ganglia and beyond. To discover the anatomy of these axons in their target ganglia, we used Neurobiotin and dextran-Texas Red microelectrodes to fill them near their targets. Coordinating axons coursed through these target ganglia close to the midline and extended only a few short branches that did not approach the lateral neuropils. Two of the three types of coordinating axons made direct synaptic connections with a class of local commissural interneurons that relayed the information to targets in the swimmeret pattern-generating circuits. These commissural interneurons, named here ComInt 1 neurons, followed a particular route to cross the midline and reach their targets. ComInt 1 neurons were nonspiking; they received EPSPs from the coordinating axons near the midline and transmitted this information to their targets in the lateral neuropils using graded transmission. The output of each ComInt 1 was restricted to a single local circuit and had opposite effects on the power-stroke and return-stroke motor neurons driven by that circuit. ComInt 1 neurons were direct postsynaptic targets of both descending and ascending coordinating axons that originated in other anterior and posterior ganglia. Because of phase differences in the impulses in these different coordinating axons, their signals arrived simultaneously at each ComInt 1. We discuss these findings in the context of alternative models of the intersegmental coordinating circuit.

During fictive locomotion, graded synaptic currents drive bursts of impulses in swimmeret motor neurons

During forward swimming, motor neurons that innervate each crayfish swimmeret fire periodic coordinated bursts of impulses. These bursts occur simultaneously in neurons that are functional synergists but alternate with bursts in their antagonists. These impulses ride on periodic oscillations of membrane potential that occur simultaneously in neurons of each type. A model of the local circuit that generates this motor pattern has been proposed. In this model, each motor neuron is driven alternately by excitatory and inhibitory synaptic currents from nonspiking local interneurons. I tested this model by perturbing individual interneurons and recording synaptic currents and changes in input resistance from each class of motor neuron. I also simulated the synaptic currents that would be observed in a cell subject to different patterns of presynaptic input. When the CNS was actively expressing the swimming motor pattern, changes in the membrane potential of individual local interneurons controlled firing of whole sets of motor neurons. Membrane currents in these motor neurons oscillated in phase with the motor output from their own local circuit. The phases of these oscillations differed in different functional classes of motor neurons. In neurons that could be clamped at the reversal potential of their outward currents, the model predicted that large periodic inward currents would be recorded. I observed no signs of periodic inward currents, even when the outward currents clearly had reversed. These results permit a simplification of the cellular model. They are discussed in the context of neural control of locomotion in crustacea and insects.

Coordination of cellular pattern-generating circuits that control limb movements: the sources of stable differences in intersegmental phases

Neuronal mechanisms in nervous systems that keep intersegmental phase lags the same at different frequencies are not well understood. We investigated biophysical mechanisms that permit local pattern-generating circuits in neighboring segments to maintain stable phase differences. We use a modified version of an existing model of the crayfish swimmeret system that is based on three known coordinating neurons and hypothesized intersegmental synaptic connections. Weakly coupled oscillator theory was used to derive coupling functions that predict phase differences between neurons in neighboring segments. We show how features controlling the size of the lag under simplified network configurations combine to create realistic lags in the full network. Using insights from the coupled oscillator theory analysis, we identify an alternative intersegmental connection pattern producing realistic stable phase differences. We show that the persistence of a stable phase lag to changes in frequency can arise from complementary effects on the network with ascending-only or descending-only intersegmental connections. To corroborate the numerical results, we experimentally constructed phase-response curves (PRCs) for two different coordinating interneurons in the swimmeret system by perturbing the firing of individual interneurons at different points in the cycle of swimmeret movement. These curves provide information about the contribution of individual intersegmental connections to the stable phase lag. We also numerically constructed PRCs for individual connections in the model. Similarities between the experimental and numerical PRCs confirm the plausibility of the network configuration that has been proposed and suggest that the same stabilizing balance present in the model underlies the normal phase-constant behavior of the swimmeret system.

Sensory and central mechanisms control intersegmental coordination

Recent experiments on the sensory and central mechanisms that coordinate animal locomotory movements have advanced our understanding of the relative importance of these two components and overturned some previously held notions. In different experimental preparations, sensory inputs and central pattern generators have now been shown to play different roles in setting intersegmental phase lags.