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Insights from models of rhythmic motor systems Astrid A Prinz Computational models of rhythmic motor systems are valuable tools for the study of motor pattern generation and control. Recent modeling advances, together with experimental results, suggest that rhythmic behaviors, such as breathing or walking, are influenced by complex interactions among motor system components. Such interactions occur at all levels of organization, from the subcellular through to the cellular, synaptic, and network levels to the level of neuromuscular interactions and that of the whole organism. Simultaneously, safety mechanisms at all levels contribute to network stability and the generation of robust motor patterns. Addresses Emory University Department of Biology, Rollins Research Center, 1510 Clifton Road, Atlanta, GA 30322 USA Corresponding author: Prinz, Astrid A ([email protected]) Current Opinion in Neurobiology 2006, 16:615–620 This review comes from a themed issue on Motor systems Edited by Eve Marder and Peter L Strick Available online 23rd October 2006 0959-4388/$ – see front matter # 2006 Elsevier Ltd. All rights reserved. DOI 10.1016/j.conb.2006.10.001 systems function as tools for the integration of experimental results into a coherent picture of motor systems. Modeling generates predictions that inspire further experimentation to validate and refine the models and to derive new insights into rhythmic motor function. Furthermore, modeling of motor systems enables the computational manipulation of system parameters that might not be experimentally accessible and thus helps to elucidate the role of parameters such as neuronal or synaptic properties in motor control. Recent advances in modeling support two insights into rhythmic motor systems. First, that rhythmic behaviors are shaped by the interplay of complex mechanisms ranging from the subcellular through the neuromechanic to the organismal level, rather than arising from a one-way flow of information from the CPG through motor neurons to the muscles. And second, that rhythmic motor systems show robustness because of the multiple safety mechanisms at the cellular, synaptic and network levels. Here, I review motor system modeling efforts in invertebrate and vertebrate model systems, and focus on results that illustrate the two points described above. Because of this selection and its limited scope, this review is by no means a comprehensive account of recent advances in motor system modeling, but instead attempts to highlight trends in the field. Introduction The periphery is not so peripheral Many forms of animal behavior are rhythmic, including different types of locomotion such as walking, swimming, crawling and flying, and vital behaviors such as breathing and chewing. The rhythmic movements involved in these behaviors are governed by central pattern generators (CPGs), that is, neuronal circuits that generate rhythmic electrical activity patterns and that, directly or through intermediate motor neurons, cause the coordinated contraction of muscles that underlies rhythmic behavior. Rhythmic motor systems in various model organisms have been the subject of numerous experimental and theoretical studies, partly because they underlie basic and important behaviors but also because their function is clearly defined and often easily measurable. Our understanding of the mechanism of pattern generation and the control of rhythmic motor behaviors in the ‘simple’ motor systems of invertebrates is, therefore, fairly advanced [1], but significant progress has also been made in vertebrate motor systems [2]. One factor that makes a rhythmic motor system a good model system is that its motor pattern continues to be expressed when the neural circuitry is removed from the body and placed in vitro for experimental investigation. Much of our understanding of motor control comes from the study of such disembodied preparations, and accompanying computational models have, therefore, long focused on the CPG circuits that generate fictive movements without including the ‘periphery’, that is, the musculo-skeletal system that performs the movements in vivo. Although CPG models have provided many insights into the mechanisms of motor control, several recent studies are acknowledging that ‘‘the brain has a body’’ [3], and that interactions between the neuronal circuitry and the motor periphery can have significant influence on the motor pattern [4] (Figure 1). Computational modeling is an integral part of the effort to understand rhythmic motor control. Models of motor www.sciencedirect.com One pathway through which a body part can influence the CPG that governs it is through proprioceptive information. A recent model of stick insect walking [5,6] integrates a biomechanical model of the insect body with a model of the neural control system for walking, with the Current Opinion in Neurobiology 2006, 16:615–620 616 Motor systems Glossary Anterior burster neuron: Identified interneuron in the crustacean pyloric circuit that drives the pyloric rhythm with its periodic burst activity. Cable models: A model of a biological neuron in which the spatially extended axon and dendrites of the neuron are represented by leaky electrical cables. Cable models reproduce the signal decay and conduction delays along axons and dendrites of biological neurons. Coordinating interneurons: Neurons that connect and coordinate different pattern-generating circuits, for example the rhythmic circuits in different segments of a leech or the rhythmic circuits in both halves of the body in bilateral animals. Eupneic rhythm: The rhythmic respiratory activity associated with normal, unlabored breathing. Follower neurons: Neurons that are rhythmically active as part of a pattern-generating circuit in response to rhythmic synaptic inputs, but that do not generate rhythmic activity themselves when isolated from the circuit. Not intrinsically bursting neurons: Neurons that do not generate bursts of action potentials when isolated from synaptic inputs. Open-loop system: In an open-loop system, the flow of information is unidirectional, that is, from component A to component B without feedback from B to A. In an open-loop motor system, for example, the muscles would be controlled by neuronal commands from the brain, but would provide no sensory feedback about their actual movements to the brain. Pacemaker kernel: The subset of neurons in a pattern-generating circuit that drive the rhythmic activity, and that remain rhythmically active even when isolated from the rest of the circuit. Solution space: The region in the parameter space of a neuron or network model that generates a desired electrical activity pattern. Swimmeret: One of the paired abdominal appendages of certain aquatic crustaceans that function primarily for carrying the eggs in females and are usually adapted for swimming. biomechanical component providing proprioceptive information to the neural component of the model. The mutual entrainment of the oscillations of neural and mechanical components in such coupled locomotion models can have significant influence on the frequency of the motor pattern, which tends to deviate from the intrinsic oscillation frequency of the isolated neural circuit and to approach the natural frequency of the body part [7]. Furthermore, a closed loop between a neuronal oscillator and a mechanical system can lead to the emergence of modes of oscillation not present in open-loop systems (see glossary) [8]. An important parameter that influences the motor patterns generated by closed-loop locomotion models is the time delay incurred by signal transmission in the sensorimotor loop, which, therefore, is a sensitive parameter in such integrated models [9]. Including the periphery in models of motor control also enables the validation of CPG models, and was used with that intent in an integrated model of larval zebrafish swimming and escape [10]. This model confirms that the neural component of the model generates the expected behavior when used to control a hydrodynamic model of the animal. Similarly, respiratory CPG models have been integrated with a neurochemical feedback model of ventilation to demonstrate that they can reproduce various forms of periodic breathing [11]. Current Opinion in Neurobiology 2006, 16:615–620 Figure 1 Motor behavior arises from interactions between neural motor circuits and the body they control. (a) A more linear notion of information flow in the generation of motor behavior focuses on the role of the nervous system in processing incoming sensory information and responding with motor outputs that are then executed by the body. (b) Recent models of motor systems reviewed here have adopted a more integrated view of motor behaviour, in which the nervous system (NS) is perceived to be embedded within a body, which is in turn embedded in an environment, with interactions among these levels shaping motor behavior. Modified from [3] with permission. Modeling studies that examine the biomechanics of Aplysia californica feeding [12,13] demonstrate that passive mechanical forces can impose constraints on the movements possible in a motor system, and that neural control must take into account that the effect of activation of a muscle depends on its current biomechanical environment. How an Aplysia feeding muscle responds to neuronal commands is also influenced by neuromodulation (i.e. the modification of muscular properties by modulatory substances released onto the muscles), which enables the feeding apparatus to express a wide range of movements and effectively renders it ‘semi-autonomous’ [14]. Interactions among motor systems Pattern generation by a motor system can be affected not only through feedback from the periphery but also through interactions with other motor systems in the same animal. This is most obvious in the entrainment www.sciencedirect.com Insights from models of rhythmic motor systems Prinz 617 of respiration and locomotion that we experience when running. Locomotion can entrain respiration indirectly through somatic afferents, as demonstrated experimentally and in a model of the rat respiratory system [15], or directly through inhibitory connections from the locomotor to the respiratory CPG, as in a model of coordination between locomotion and respiration in the snail Lymnaea stagnalis [16]. Interactions between neuronal circuits involved in motor control — the pons and the medulla — have also recently been included in a model of respiratory pattern generation. This model suggests that the rhythmic activity produced by the reduced medullary preparations used in many studies of respiration might differ from the in vivo eupneic rhythm (see glossary) [17]. Influence of cellular properties on motor patterns In addition to neuromechanical influences, motor pattern generation can be influenced by the morphology and biophysical properties of the CPG interneurons and motor neurons. The often relatively simple neuron models used in models of rhythmic motor systems might, therefore, have to be replaced with more detailed and biophysically realistic model neurons to reproduce certain features of motor pattern generation accurately [18]. This is supported by a recent model of the leech heartbeat CPG [19], which showed that representing coordinating interneurons by complex multi-compartment cable models (see glossary) with realistic synaptic inputs, spike adaptation, and multiple spike initiation sites was necessary to capture the behavior of the system under different experimental conditions. In the same system, the detailed dynamical properties of the motor neurons driven by the CPG have been implicated in switching the motor pattern between two different states, peristaltic and synchronous heartbeat [20]. Similarly, comparison of different versions of a multi-compartment model of the leech heartbeat interneuron shows that the detailed morphological properties of the neuron can affect burst activity and lead to different mechanisms for burst generation [21,22]. In Xenopus laevis tadpoles, changes of the swimming motor pattern during development can be reproduced by a model of the swim CPG that incorporates the lengthening of motor neuron axons and the increasing complexity of the motor neuron dendritic trees that occurs during development. This model suggests that the changes in the motor pattern are partly due to changes in the morphological details of motor neurons [23]. Some motor patterns might even rely on subcellular phenomena. In the developing chick spinal cord, episodes of rhythmic discharges occur on a time-scale of minutes. A model of the underlying network with excitatory connections reproduces the episodic activity if slow, activity-dependent variations of the intracellular www.sciencedirect.com chloride concentration are incorporated [24], showing that network-level rhythmic behavior can arise from the dynamics of ion concentrations in the circuit neurons. Adding biophysical details to models of rhythmic motor systems thus can improve model performance. However, in some cases the opposite is true, such as in a recent study of crayfish swimming, in which simplifications of the model of a swimmeret (see glossary) circuit did not result in any decrease in model performance [25]. Furthermore, morphologically complex multi-compartment model neurons can often be reduced to simpler models with fewer compartments by grouping functionally similar compartments without dramatic effects on model behavior, as was recently demonstrated in a leech heart interneuron model [21]. Cellular and synaptic contributions to network robustness Rhythmic motor systems are robust, and function reliably throughout an animal’s life [26]. Several recent experimental and modeling studies have highlighted cellular and synaptic mechanisms that could potentially contribute to this robustness. Brute-force computational exploration of the parameter space of bursting neurons in the pyloric CPG of crustaceans has shown that bursting with physiologically meaningful characteristics can occur in pacemaker neurons with widely differing cellular properties [27]. This infers that pacemaker neurons need not be narrowly tuned to a unique ‘solution’ to function, but instead have an entire ‘solution space’ (see glossary) available to them, making pacemaker activity robust to parameter variations. A combination of experimental and modeling work [28] furthermore shows that pyloric CPG neurons use activityindependent homeostatic regulation to ensure a constant ratio of two antagonistic membrane currents, the transient potassium current IA and the hyperpolarization-activated cation current Ih. This regulation thus ensures that the effects of the two currents on CPG activity compensate each other, which again promotes robust pacemaking. IA also interacts with depressing pyloric synapses to ensure another robust property of pyloric circuits, phase constancy, meaning that the pyloric circuit is able to maintain constant phase relationships between the bursts of its component neurons over wide ranges of rhythm frequency [29,30]. In addition to these cellular contributions to CPG robustness, the dynamic properties of pyloric synapses also seem suited to ensure robust network performance. The only feedback synapse from the follower neurons in the pyloric circuit onto the pacemaker kernel (see glossary) shows dynamic properties that enable it to influence the pacemaker in a negative feedback loop to Current Opinion in Neurobiology 2006, 16:615–620 618 Motor systems counteract changes in pyloric frequency, thus stabilizing the rhythm period [31]. Furthermore, the synapses from one neuron in the circuit, the lateral pyloric neuron, onto different targets in the pyloric CPG have target-specific short-term dynamics that are tailored to the specific function of each synapse in ensuring proper circuit function [32]. Beyond the pyloric circuit, the effect of changes in the maximal conductance and activation time constant of Ih in leech heartbeat interneurons is independent of cycle period, suggesting that neuromodulation of Ih has robust effects in animals with different heart frequencies, such as juvenile leeches (fast heartbeat) versus adult leeches (slower heartbeat) [33]. Connectivity supports stability Besides cellular and synaptic contributions to network robustness, the connectivity of rhythmic motor circuits can also contribute to network stability. In the pyloric circuit, the anterior burster neuron that drives the rhythm is electrically coupled to two not intrinsically bursting neurons (see glossary) in a configuration that increases the dynamic range of the pacemaker [34]. Similarly, isolated hemisegments in the lamprey spinal cord can generate rhythmic swim activity, and reciprocal inhibition between the hemisegments functions to stabilize and coordinate that activity [35]. Excitatory connections can enable rhythmic activity to emerge as a network property in the absence of pacemaker neurons [36], or can lead to the coexistence of a cellular and a network rhythmogenic mechanism in the same circuit. This has been suggested to be the case for the pre-Bötzinger Complex (pBC) in the respiratory system [37] and for Xenopus tadpole brainstem circuits involved in swimming [38]. In addition to providing an extra rhythmogenic mechanism — and thus increasing the robustness of rhythm generation — excitatory coupling among oscillatory neurons also increases the parameter range over which robust bursting can occur in a model of the pBC [39]. The dynamic range of respiratory pattern generation also increases with the number of oscillatory neurons in a pBC model [11], suggesting that Figure 2 Similar network activity on the basis of different cellular and synaptic properties in a model of the crustacean pyloric CPG circuit. (a and b) Simulated voltage traces from two different versions of the pyloric CPG model. Both models generate functional tri-phasic activity. Scale bars are 0.5 s and 50 mV. (c and d) Cellular (top) and synaptic properties (bottom) of the same two network models. Bars in the top plots indicate the conductances of different membrane currents (ICaS, transient calcium current; IA, transient potassium current; IKCa, calcium-dependent potassium current; INa, fast sodium current; IH, hypolarization-activated cation current) in the circuit neurons AB/PD, LP, and PY. Bars in the bottom plots indicate the strength of different synapses in the circuit (AB-to-LP, AB-to-PY, etc.). Although the models produce similar activity, they do so on the basis of different network parameters. From [41] with permission. Abbreviations: AB/PD, anterior burster and pyloric dilator pacemaker kernel; LP, lateral pyloric neuron; PY, pyloric neuron. Current Opinion in Neurobiology 2006, 16:615–620 www.sciencedirect.com Insights from models of rhythmic motor systems Prinz 619 the large cell numbers in vertebrate CPG circuits also contribute to robustness. Connectivity patterns among CPG neurons can also support robustness by including seemingly redundant connections, such that the failure or loss of any given synapse can be compensated for by other connections [40]. Bruteforce exploration of millions of different combinations of synaptic conductances in a model of the pyloric circuit confirms this by showing that functional pyloric network activity can be generated on the basis of different synaptic connection patterns and strengths [41] (Figure 2). Similarly, a model of the zebrafish locomotor network generates stable oscillations with realistic frequencies for a wide range of synaptic connection strengths [42]. Rhythmic network activity in model networks with appropriate connectivity also appears to be largely independent of the cell type used in the model, suggesting robustness to variations in cellular properties [43]. Even irregular motor patterns, such as those governing feeding in Aplysia, can be adaptive in variable environments and provide a trial-and-error strategy that leads to overall — albeit not cycle-by-cycle — robust performance [14]. References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: of special interest of outstanding interest 1. Marder E, Bucher D, Schulz DJ, Taylor AL: Invertebrate central pattern generation moves along. Curr Biol 2005, 15:R685-R699. This review summarizes recent experimental results on invertebrate pattern generation, many of which have informed the computational models discussed here. 2. Grillner S: The motor infrastructure: From ion channels to neuronal networks. Nat Rev Neurosci 2003, 4:573-586. 3. Chiel HJ, Beer RD: The brain has a body: adaptive behavior emerges from interactions of nervous system, body and environment. Trends Neurosci 1997, 20:553-557. 4. Holmes P, Full RJ, Koditschek D, Guckenheimer J: The dynamics of legged locomotion: Models, analyses, and challenges. Siam Rev 2006, 48:207-304. A comprehensive review that describes recent efforts towards generating a full neuromechanical model of a running animal. Such a model would integrate models of central pattern generation, proprioception, and goaloriented sensing, planning, and learning. 5. Ekeberg O, Blumel M, Buschges A: Dynamic simulation of insect walking. Arthropod Structure & Development 2004, 33:287-300. 6. Akay T, Haehn S, Schmitz J, Buschges A: Signals from load sensors underlie interjoint coordination during stepping movements of the stick insect leg. J Neurophysiol 2004, 92:42-51. 7. Iwasaki T, Zheng M: Sensory feedback mechanism underlying entrainment of central pattern generator to mechanical resonance. Biol Cybern 2006, 94:245-261. 8. Sekerli M, Butera RJ: Oscillations in a simple neuromechanical system: Underlying mechanisms. J Comput Neurosci 2005, 19:181-197. 9. Ohgane K, Ei S, Kazutoshi K, Ohtsuki T: Emergence of adaptability to time delay in bipedal locomotion. Biol Cybern 2004, 90:125-132. Conclusions The recent models of rhythmic motor systems reviewed here support the notion that motor patterns can be shaped by complex interactions at all levels of circuit operation, ranging from the subcellular level through interactions between cellular and synaptic properties to network-level rhythmogenic mechanisms and interactions with the motor periphery. Depending on the purpose of the model in question, it might not be necessary to include biophysical details at all — or any — of these levels to achieve realistic model performance, but it seems advisable to keep in mind the possibility of influences on motor control from all of these levels when constructing models. This complexity of potential influences on the motor pattern endows motor networks with enormous flexibility, but can also make their analysis difficult [44]. Many different levels can influence motor pattern generation, but they can also contribute to its robustness. Modeling work from the past few years has provided several examples of contributions to network robustness from cellular, synaptic and network level sources. The role of rhythmic motor systems in important behaviors, such as respiration and locomotion, has obviously provided sufficient evolutionary pressure to install a variety of safety mechanisms in motor systems that ensure their reliable functioning throughout life. Acknowledgements Support from the Burroughs Wellcome Fund in the form of a Career Award at the Scientific Interface is gratefully acknowledged. www.sciencedirect.com 10. Kuo PD, Eliasmith C: Integrating behavioral and neural data in a model of zebrafish network interaction. 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Parker D: Complexities and uncertainties of neuronal network function. Philos Trans R Soc Lond B Biol Sci 2006, 361:81-99. The author uses the lamprey locomotor network to examine to what extent it is possible to claim detailed understanding of network function and plasticity. www.sciencedirect.com