Articles in PresS. J Neurophysiol (December 30, 2014). doi:10.1152/jn.00870.2014
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
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The effect of sensory feedback on
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crayfish posture and locomotion:
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II. Neuromechanical simulation of closing the loop
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Julien Bacqué-Cazenave1, Bryce Chung1, David Cofer1,
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Daniel Cattaert2, and Donald H. Edwards1
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Neuroscience Institute, Georgia State University, Atlanta, GA 30303
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Institute de Neurosciences Cognitives et Intégratives d’Aquitaine, Univ. of
Bordeaux 1, 33405, Talence Cedex, France
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Abbreviated title: Neuromechanical simulations of crayfish posture and
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locomotion
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Corresponding author: Dr. Donald H. Edwards Neuroscience Institute Georgia State University P.O. Box 5030 Atlanta, GA USA 30302-5030 e-mail:
[email protected] Tel: 404-312-6159 Tel: 404-413-5446
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Keywords: feedback, motor control, walking, crustacean, stretch receptor,
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proprioception, computational model, neuromechanics 1
Copyright © 2014 by the American Physiological Society.
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
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Abstract
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Neuromechanical simulation was used to determine whether proposed thoracic circuit
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mechanisms for the control of leg elevation and depression in crayfish could account for the
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responses of an experimental hybrid neuromechanical preparation when the proprioceptive
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feedback loop was open and closed. The hybrid neuromechanical preparation consisted of a
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computational model of the 5th crayfish leg driven in real time by the experimentally recorded
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activity of the levator and depressor nerves of an in vitro preparation of the crayfish thoracic
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nerve cord. Up and down movements of the model leg evoked by motor nerve activity released
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and stretched the model coxobasal chordotonal organ (CBCO); variations in the CBCO length
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were used to drive identical variations in the length of the live CBCO in the in vitro preparation.
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CBCO afferent responses provided proprioceptive feedback to affect the thoracic motor output.
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Experiments performed with this hybrid neuromechanical preparation were simulated with a
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neuromechanical model in which a computational circuit model represented the relevant thoracic
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circuitry. Model simulations were able to reproduce the hybrid neuromechanical experimental
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results to show that proposed circuit mechanisms with sensory feedback could account for
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resistance reflexes displayed in the quiescent state and for reflex reversal and spontaneous
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Lev/Dep bursting seen in the active state.
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Introduction
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The neural circuits for the control of movement are not well understood for any animal because
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they depend on the interaction of descending commands with sensory feedback and locally
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generated responses in lower motor centers. Here we provide a model of those circuit
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interactions for the crayfish, in which feedback from a leg stretch receptor organ provides reflex
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input to postural and locomotor circuits and substantially changes their outputs. The model is
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based on detailed circuit analysis (Cattaert and Le Ray, 2001) and on recent experimental results
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obtained with a hybrid neuromechanical preparation (Chung et al., 2014). Simulations of those
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hybrid experiments show that the transition from a quiescent postural state to an active
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locomotory state depends on neuromodulatory activation of a central pattern generator and an
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assistance reflex, and on inhibition of an antagonistic resistance reflex. The assistance reflex
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resets the CPG early in each cycle and thereby accelerates the intrinsic locomotor rhythm.
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The circuit mechanisms that control posture and locomotion are remarkably similar in legged
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vertebrates and arthropod invertebrates (Duysens et al. 2000). While an animal is standing
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stationary, negative feedback from resistance reflexes acts against imposed movements to
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stabilize and maintain a posture (Clarac et al. 2000). Resistance reflex pathways are often
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monosynaptic and activate antagonist muscles that oppose a movement. Once an animal is in
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motion, however, positive feedback from polysynaptic assistance reflexes acts to reinforce
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movements in coordination with central motor patterns and resistance reflexes. Together,
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resistance and assistance reflexes alternate during walking to help produce stance and swing
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movements for each leg (Ayers and Davis 1977b; Buschges et al. 2008). While many pathways
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that mediate those reflexes and central motor commands have been identified, it is not yet clear
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how they interact during the locomotor cycle of the active state or during the transition between
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the quiescent and active states.
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In the companion paper (Chung et al. 2014), we described how an in vitro crayfish ventral nerve
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cord preparation linked to a neuromechanical model of a crayfish leg produced a closed
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sensorimotor feedback loop that enabled these issues to be studied. Motor activity recorded from
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levator (Lev) and depressor (Dep) motor nerves excited model Lev and Dep leg muscles that
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moved the model leg up and down, and thereby released and stretched a model coxobasal 3
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chordotonal organ, or CBCO. Movement of the model CBCO drove a probe attached to the real
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CBCO and released and stretched it identically in real time. Release- and stretch-sensitive
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afferents from the real CBCO were excited by the model leg movements and projected back to
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the ventral nerve cord to complete the feedback loop (El Manira et al. 1991a).
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When the hybrid preparation was in the quiescent state, resistance reflexes reduced the
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perturbation of the leg caused by an imposed force. Exposure to oxotremorine, a muscarinic
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cholinergic agonist, induced an active state in which the same imposed force evoked an
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assistance reflex that triggered sequential opposing motor bursts (Ayers and Davis 1977b; Le
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Ray and Cattaert 1997). A brief force that lifted the leg excited levator motorneurons (Lev MNs)
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and triggered a burst of Lev MN activity that kept the leg elevated well after the force was
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removed. The Lev burst was immediately followed by a depressor (Dep) motor burst that moved
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the leg back down. Later in the active state, Lev/Dep burst pairs occurred spontaneously at a low
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frequency when the feedback loop was opened (viz., the motor nerve was disconnected from the
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model leg muscles). When the feedback loop was closed, the frequency of Lev/Dep burst pairs
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immediately increased to nearly three-times greater than in open loop and drove the leg
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rhythmically up and down in a manner similar to walking. The paper concluded that the closed
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loop increase in burst pair frequency resulted from the Lev assistance reflex that cut short the
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interval between Lev/Dep burst pairs and triggered a new burst pair that reset the burst pair
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rhythm. It showed that two aspects of the transition from quiescent to active states, reflex
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reversal and excitation of the Lev/Dep central pattern generator (CPG), were linked to produce a
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faster, feedback-dependent rhythm.
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A circuit mechanism for this transition in crayfish has been proposed where resistance reflexes
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present in quiescent preparations are reversed in active preparations to produce assistance
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reflexes (Cattaert and Le Ray 2001). In the quiescent crayfish, a leg elevation resistance reflex is
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excited when a vertical perturbation excites release-sensitive afferents from the CBCO. The
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afferents monosynaptically excite Dep motor neurons to resist the leg movement (El Manira et
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al. 1991a). In ventral nerve cord preparations exposed to the muscarinic cholinergic agonist
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oxotremorine, stimulated release-sensitive afferents excite the Assistance Reflex IN (ARIN),
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which then excites the Lev MNs (Le Ray and Cattaert 1997). The resistance reflex is blocked by 4
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presynaptic inhibition of the afferent terminals that excite Dep MNs (Cattaert et al. 1999), and by
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postsynaptic inhibition of the Dep MNs (Pearlstein et al. 1998). Finally, neurons that are part of
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the Lev/Dep CPG are disinhibited by oxotremorine block of a muscarine-sensitive outward
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current (Cattaert et al. 1995). This allows a rhythmic pattern of Lev/Dep activity to occur that is
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thought to drive walking (Ayers and Davis 1977a).
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Here we present a computational model of the neuromechanical control of elevation and
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depression movements of the crayfish leg (Fig. 1). The neural circuit portion of the model
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reflects current understanding of postural and locomotor circuits that control elevation and
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depression movements. The model expresses the mechanisms described above, and includes a
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central pattern generator (CPG), monosynaptic resistance reflexes, and polysynaptic assistance
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reflexes. The circuit model is linked to the neuromechanical leg model that was used in the
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hybrid preparation experiments to allow us to simulate those experiments (Chung et al. 2014).
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The motor output of the circuit model drives movements of the neuromechanical model, which
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then provides CBCO afferent feedback to the circuit model. Simulations of the hybrid
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preparation experiments with the model have shown that our current understanding of the
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postural and locomotor circuits for leg elevation and depression can account for our experimental
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results. They demonstrate how the system can shift from a quiescent state that controls posture to
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an active state that mediates locomotion through the interaction of a CPG and assistance reflexes.
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Materials and Methods
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Description of the model. A computational neuromechanical model of the hybrid experimental
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preparation was built in AnimatLab v1 (www.AnimatLab.com) based on descriptions of the
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known reflex circuitry (Cattaert and Le Ray, 2001) (Fig. 1). To build this model, the leg and
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body1 model used in the hybrid preparation experiments was connected to a simplified neuronal
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network model of the CPG and reflex circuitry. This neuronal network model replaced the live in
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vitro nerve cord preparation and hybrid interface used in the hybrid preparation experiments
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(Chung et al. 2014). (A list of parameter values used in the model is available in Supplemental
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Materials in Model Parameters Supplemental Material.xlx at
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https://www.dropbox.com/s/qzrjx19m3ug6vgg/Model%20Parameters%20Supplemental%20Mat
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erial.xlsx?dl=0. The equations used in the network model are listed in Equations.docx at
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https://www.dropbox.com/s/sbt9a9d16wtohq4/Equations.docx?dl=0.) The leg and body model
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contained Hill model muscles that were driven by the motor output of the neuronal network, as
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well as a model CBCO that was connected directly to model sensory afferents. All the parameter
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values and structural arrangements can be seen in the model file, “Crayfish hybrid simulation
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model”, which is available in Model DB (http://senselab.med.yale.edu/modeldb/default.asp. The
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ModelDB accession number for this model is 150698.)
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Model neurons were each represented by a single compartment integrate-and-fire model that had
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a resting potential of -70 mV with 0.1 mV of noise. Chemical synaptic transmission following a
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presynaptic spike was simulated by an exponentially decaying postsynaptic conductance
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triggered in a postsynaptic neuron after a synaptic delay of 0.5 ms. The postsynaptic
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conductance was in series with an appropriate reversal potential, so that the postsynaptic current
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equaled the product of the conductance and the difference between the membrane potential and
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the reversal potential. Electrical synapses were represented by electrical coupling resistances
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between neurons. Throughout the model, neuronal and synaptic properties were set so as to
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enable the network to replicate responses recorded from referenced experimental preparations.
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The names of items in the neuromechanical model are italicized to distinguish them from elements of the animal with the same name. 6
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Detection of stretch or release of the crayfish CBCO is mediated by afferents that are rate- and
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position-sensitive (Bush, 1965). The CBCO has approximately 20 afferents that respond to
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stretch or the rate of stretch and approximately 20 afferents that respond similarly to release (El
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Manira et al., 1991). In our model, we included three stretch-sensitive afferents: two identical
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rate-of-stretch units (Stretch Rate Resist Afferent and Stretch Rate Assist Afferent) and one whose
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response was proportional to the amount of stretch (Stretch Resist Afferent). Three corresponding
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release-sensitive afferents were also included: a Release Rate Resist Afferent, a Release Rate
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Assist Afferent, and a one Release Resist Afferent (Fig. 1). Transduction for the stretch- and
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release-rate afferents was mediated by linear current vs velocity functions with opposing slopes:
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1nA/mm/s for stretch and -1nA/mm/s for release. Similarly, transduction for stretch- and
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release-sensitive afferents was mediated by linear current vs length functions with opposing
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slopes: 30nA/mm for stretch and -30nA/mm for release.
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The sets of 12 depressor and 19 levator motor neurons (MNs) that innervate the leg (El Manira et
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al. 1991a; Hill and Cattaert 2008) were each represented by a pair of motor neurons, one tonic
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Dep or Lev MN and one phasic Dep or Lev MN. The tonic and phasic MNs were connected to
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the muscle models by conductance-based synapses that simulated the tonic and phasic
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neuromuscular junctions of the crayfish leg extensor muscle (Bradacs et al., 1997). A spike in a
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phasic MN produced a large, non-facilitating EPSP in all the phasic muscles, while a spike in a
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tonic MN produced a small, strongly facilitating EPSP in all the tonic muscles. A common
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inhibitor MN inhibited all muscles and was itself inhibited by Phasic Lev and Dep MNs (Wiens
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and Wolf 1993). Open loop conditions were created by disabling the connections between the
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MNs and the muscles.
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Resistance reflexes in the crayfish are mediated by monosynaptic connections between stretch-
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or release-sensitive afferents and the Lev or Dep MN pools, respectively (El Manira et al., 1991;
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Le Ray D. et al., 1997). Similar connections in the model enable stretch-sensitive resist afferents
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to mediate a resistance reflex triggered by leg depression, while the release-sensitive resist
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afferents mediate a resistance reflex triggered by leg elevation. Resistance reflexes also include
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disynaptic inhibitory pathways that inhibit antagonist motor neurons (Le Bon-Jego and Cattaert 7
Neuromechanical simulations of crayfish posture and locomotion
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2002). These are represented in the circuit model by a disynaptic pathway from CBCO stretch or
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release rate-sensitive afferents to either a Stretch or Release X Inhib neuron, which then inhibits
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the antagonist Dep or Lev MNs.
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Assistance reflexes in the crayfish are mediated by disynaptic pathways in which stretch- or
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release-sensitive afferents excite one or more assistance reflex interneurons (ARIN), and these
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excite units in the Dep or Lev MN pools, respectively (Le Ray and Cattaert, 1997). In the model,
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a leg depression assistance reflex was produced when a Stretch Rate Assist Afferent excited a
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Stretch Assistance Reflex Interneuron (Stretch ARIN), and that cell excited depressor MNs (Fig.
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1). The leg elevation assistance reflex was organized in a symmetrical fashion. Sensory afferents
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also excite an assistance reflex control interneuron (ARCIN) that controls the gain of the
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assistance reflex by inhibiting the ARIN (Le Ray and Cattaert 1997).
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The crayfish levator/depressor CPG includes two pools of electrically coupled neurons (half-
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centers) that are mutually inhibitory (Chrachri and Clarac, 1989;Pearlstein et al., 1998). The
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levator pool contains interneurons and a few of the 19 tonic and phasic Lev MNs, while the
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depressor pool includes interneurons and a few of the 12 tonic and phasic Dep MNs (Cattaert et
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al. 1994a; Cattaert and Le Ray 2001; Cattaert et al. 1995). The participating neurons are
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conditional bursters, depending on muscarinic cholinergic activation and depolarization. Our
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model contains a simplified Lev/Dep CPG (Fig. 1), in which the Lev and Dep half-centers each
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include three electrically coupled neurons: an interneuron (IN) and the phasic and tonic MNs.
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The Lev and Dep INs (but not the MNs) each have a slowly activating and a very slowly
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inactivating inward current that mediates rhythmic bursting. Mutual inhibition between the half-
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centers is mediated by three sets of inhibitory synapses: (i) mutual synaptic inhibition of the Lev
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and Dep INs; (ii) inhibition of the antagonist IN by the agonist Tonic MN; and (iii) inhibition of
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the antagonist Phasic and Tonic MNs by the agonist Phasic MN.
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Lev and Dep bursts in our experiments occurred in burst pairs, in which the Lev burst
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immediately preceded the Dep bursts (Chung et al. 2014); see below). Although the actual
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mechanisms of this functional asymmetry are unknown, the design of the model Lev/Dep CPG
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was asymmetric to favor this pattern. These asymmetries included: (i) a larger Lev IN inward 8
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current; (ii) stretch- and release-sensitive CBCO afferents that differed in their sensitivities to leg
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angle; and, (iii) stronger inhibition of Dep elements by Lev elements than vice versa.
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A muscarine-sensitive, persistent outward potassium current prevents bursting by Lev and Dep
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MNs in quiescent (tonically active) preparations (Cattaert et al., 1994a; Cattaert et al., 1995).
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This current is simulated in our model as a postsynaptic conductance-mediated outward current
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tonically produced in these neurons by a persistently depolarized presynaptic Outward Current
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neuron (Fig. 1). Tonic activity of the Outward Current neuron, like the outward current in the
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live preparation, keeps the CPG INs and the ARINs hyperpolarized and prevents both rhythmic
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bursting and assistance reflex responses during simulations of the tonically active preparation.
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In the crayfish, the outward current is blocked by activation of muscarinic acetylcholine
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receptors, thereby enabling the half-center cells to produce bursting activity (Cattaert et al.,
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1995). The action of oxotremorine in blocking the outward current was simulated in the model
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by synaptic inhibition of the Outward Current neuron by an OXO neuron. Application of
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oxotremorine to the preparation was simulated by application of a depolarizing stimulus current
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to the OXO neuron, which then inhibited the Outward Current neuron and reduced or stopped its
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inhibition of the Lev and Dep INs and the ARINs. Their depolarization allowed the Lev and Dep
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INs to begin bursting, and allowed the ARINs to mediate assistance reflexes.
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Enabling assistance reflexes is one part of reflex reversal, which also depends on the suppression
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of opposing resistance reflexes. Depolarizing inhibition of the primary afferent terminals (PAD)
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blocks the reflex excitation of motor neurons by the CBCO afferents when the opposing set of
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motor neurons is active (Cattaert et al. 2002; Cattaert and Le Ray 1998; Le Bon-Jego and
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Cattaert 2002). In the model, a pair of inhibitory interneurons, the Lev and Dep PADIs, are each
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excited by one set of motorneurons to inhibit the rate sensitive CBCO afferent that excites the
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other set.
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Simulation protocol. The duration of computational simulations for each condition was 60s and
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simulations for each condition were run 6 to 8 times. 0.1 mV noise applied separately to each
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neuron model made each simulation different. To simulate experimental tests of leg lift reflexes,
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a 1 N force was applied to the leg for 0.5 s and activity was recorded for further analysis.
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To reproduce open loop conditions in the hybrid experiment (Chung et al. 2014), connections
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between the motor neurons and leg muscles were disabled. Consequently, motor neuron activity
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did not result in muscle potentials or tension and there was no movement of the leg. Whether a
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simulation was run in open or closed loop, all neuron activity was recorded and saved for further
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analysis.
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Motor bursts were identified in each trial for comparison between conditions using the Poisson
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Surprise method in the data analysis software, DataView (see http://www.st-
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andrews.ac.uk/~wjh/dataview/). Once motor neuron bursts were identified separately for Lev and
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Dep motor neurons, Lev/Dep or Dep/Lev burst pairs were defined when one burst occurred
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immediately after the other. Non-parameteric statistics were used to determine whether different
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simulation conditions changed the system significantly. Statistics are reported as averages ±
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standard deviation.
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Results
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Quiescent state is characterized by tonic neuronal activity and resistance reflexes. The
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quiescent state of the preparation is characterized by the low-level tonic activity of sensory
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neurons, interneurons and motor neurons as well as resistance reflex responses to imposed leg
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movements. This state is maintained by a muscarine-sensitive tonic outward current that
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hyperpolarizes Lev and Dep motorneurons that, in crustaceans, are part of the CPG networks
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(Cattaert and Le Ray 2001; Hooper and DiCaprio 2004) and so prevents spontaneous rhythmic
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activity. The outward current is also likely to hyperpolarize as yet unidentified CPG interneurons
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and to prevent assistance reflex responses by hyperpolarizing the ARINs. In our model, the
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corresponding cells are quiet and a tonic outward current was evoked in CPGs and ARINs by
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hyperpolarizing conductance-based synapses from an “outward current” model neuron (Fig. 1).
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Resistance reflex response to leg lift: 0nA OXO stimulation. In the hybrid preparation
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experiments, reflex responses to imposed leg lifts were measured in a series of six 60 s trials in
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which a 0.5 s, 1 N upward force was applied to the model leg five times at 10 s intervals during
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each trial. The same protocol was followed in simulations of those experiments and similar
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responses were evoked. These are shown in 2 s post-stimulus time histograms of firing frequency
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responses in 20ms bins and averaged over the 30 responses to leg lifts (Fig. 2A).
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Each simulated upward force stimulus evoked a pair of chained resistance reflex responses that
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first resisted the imposed upward leg movement and then resisted the later downward movement
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(Fig. 2A, B). Each leg lift released (i.e., shortened) the CBCO (Fig. 2A, B marker 1), which
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transiently excited the CBCO Release Rate Resistance Afferent (marker 2). The Afferent
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monosynaptically excited both the Phasic and Tonic Dep MNs (marker 3), which excited the Dep
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muscles, but the applied upward force prevented the leg from depressing. The Dep MNs and
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Release X Inhib neuron inhibited the antagonist Lev MNs, while the Dep PADI inhibited the
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Stretch Rate Resistance Afferent. The CBCO Release Rate Assistance Afferent was also excited
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by the leg lift but evoked only subthreshold responses in the Release ARIN, which was
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hyperpolarized by the tonic Outward Current input. As a result, no disynaptic assistance reflex
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response of the Lev MNs occurred.
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When the upward force ended, gravity and the tension in the Dep muscles moved the leg
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downward. The downward leg movement (marker 4 in Fig. 2A and 2C) stretched the CBCO
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(marker 5) and strongly excited the Stretch Rate Assistance and Resistance Afferents (marker 6).
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The Stretch Rate Resistance Afferent excited the Tonic and Phasic Lev MNs, but failed to excite
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the Lev IN and the Lev ARIN, which were both hyperpolarized by the Outward Current. The Lev
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MN firing increased tension in the Lev muscles (marker 7), which slowed the downward
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movement of the leg (marker 8). The Lev MNs inhibited the Dep MNs and the Lev ARIN, and
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they excited the Lev PADI, which inhibited the Release Rate Resistance Afferent.
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OXO stimulation blocked the Outward Current neuron. The outward current that
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hyperpolarizes elements of the levator/depressor CPG is blocked by application of a muscarinic
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agonist, oxotremorine, which promotes transition of the thoracic circuitry from the quiescent
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state to an active state (Cattaert et al. 1994b). We simulated the effect of oxotremorine
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application in the model by stimulation of “OXO”, a model neuron that synaptically inhibits the
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Outward Current neuron (Fig. 3B, marker 1). To simulate other differences between the circuit
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in the active state and the circuit in the quiescent state, OXO also excites other cells, including
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the Dep and Lev PADIs, the Release and Stretch ARINs and ARCINs, and the Common Inhibitor
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MN (Fig. 1).
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Assistance reflex response to leg lift: 4.0 nA OXO stimulation. Upon depolarizing OXO with
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4 nA of current (Fig. 3B marker 1), the Outward Current was weakly inhibited and the ARINs
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and PADIs were weakly excited. The same leg lift evoked a weak resistance reflex and a strong
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assistance reflex in which a small burst of activity in Tonic Lev MNs helped to raise the leg (Fig.
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3A, green band). This occurred in response to 26 of the 30 leg lifts over the 6 trials; the four
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other leg lifts triggered full levator motor bursts. Fig. 3A shows the average response of each of
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the circuit elements to these 26 leg lifts. The leg lift (Fig. 3B marker 2) released the CBCO and
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excited Release-sensitive CBCO Afferents (marker 3). Depolarization by OXO enabled the
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Release ARIN (marker 4) to respond to the Release Rate Assistance Afferent (Fig. 3A) by
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inhibiting the Tonic Dep MN and exciting the Lev MNs (marker 5). The levator muscle
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contraction assisted the leg lift (marker 6).
328 329
The initial leg lift also excited the Release Rate Resistance Afferent that evoked a resistance
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reflex by monosynaptically exciting the Dep MNs. Both Tonic and Phasic Dep MNs fired a brief
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burst of spikes before being inhibited by the Release ARIN. The Tonic Lev MN also excited the
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Lev PADI, which then inhibited the Release Rate Resistance Afferent to prevent further
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resistance reflex responses.
334 335
When the leg fell at the end of the upward force (Fig. 3A, brown band; Fig 3A, C marker 7), the
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CBCO stretch excited stretch-sensitive afferents (marker 8). They continued to excite the Lev
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MNs (marker 9) in a resistance reflex that helped to slow the fall of the leg (marker 10). 12
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Reflex reversal and a Lev/Dep burst response to leg lift: 5.2 nA OXO stimulation. As the
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experimentally applied oxotremorine took effect, the levator assistance reflex response to an
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imposed leg lift often triggered a levator/depressor MN burst pair (Fig. 3B in Chung et al., 2014).
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The model network produced similar Lev/Dep burst pair responses (Fig. 4A) to leg lifts after the
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OXO stimulation was increased to 5.2nA (Fig. 4B marker 1). 8 of 30 leg lifts imposed over 6
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trials evoked Lev/Dep MN burst pairs; the other 22 leg lifts evoked resistance or assistance
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reflexes (Fig. 2A, 3A) or they occurred during or shortly after a spontaneous burst pair.
346 347
The OXO stimulation during each trial (Fig. 4B, marker 1) tonically excited the Lev and Dep
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PADIs (Fig. 4A), which largely suppressed the resistance reflexes by inhibiting the two CBCO
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resistance afferents, the Release Rate Resistance Afferent and the Stretch Rate Resistance
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Afferent. However, a leg lift (marker 2) evoked a robust assistance reflex through a pathway
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containing the Release Rate Assistance Afferent (marker 3), the Release ARIN (marker 4), and
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the Tonic Lev MN. This assistance reflex response helped to trigger bursts in the Lev IN and the
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Tonic and Phasic Lev MNs (marker 5) that maintained leg elevation long after the upward force
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stopped (marker 6). The leg began to fall immediately after the Lev burst stopped (Fig. 4A, C,
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marker 7). As before, the leg fall excited the Stretch Rate Assistance Afferent (marker 8), which
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then excited the Stretch ARIN (marker 9). Stretch ARIN excited the Dep MNs (marker 10) to fire
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a burst and both it and the Dep MNs inhibited the Lev MNs. The Dep MN burst drove the leg
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down (marker 11).
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Spontaneous Lev/Dep and Dep/Lev burst pairs: 5.7 nA OXO stimulation. Several minutes’
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exposure of an isolated crayfish nervous system to 50 μM oxotremorine induced spontaneous
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bursts in levator and depressor motor neurons (Cattaert et al. 1995). In the 6 hybrid preparation
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experiments, the bursting was organized as a low frequency (~1/25 s) series of 21
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levator/depressor (Lev/Dep) and 0 depressor/levator (Dep/Lev) burst pairs when the CBCO
365
feedback loop was open, and as a much higher frequency (~1/10 s) series of 75 Lev/Dep burst
366
pairs and 3 Dep/Lev burst pairs when the feedback loop was closed (Fig. 5A here and in Chung
367
et al., 2014). The model network produced the same set of phenomena when the OXO neuron
368
was stimulated with 5.7 nA (Fig. 5B). (A video of one closed loop simulation trial, Hybrid
369
simulation video.mpr, is available in Supplemental Materials at
370
https://www.dropbox.com/sh/kfbs96wmak2mlty/AACdqTm1hF5KRBajvcCW8mrva?dl=0.)
371 372
As in the hybrid preparation experiments (Fig. 1 in Chung et al., 2014), the feedback loop was
373
opened in our simulated experiments by disconnecting the model MNs from the model muscles
374
(Fig. 1), so the model was effectively paralyzed but could still respond to CBCO responses
375
evoked by imposed model leg movements. The model leg was kept in an initially stationary
376
horizontal position for 30 s at the beginning of each simulation trial to allow the effects of OXO
377
stimulation to reach a steady state before beginning the 60 s experimental period (Fig. 5B). At
378
that time, the leg was allowed to fall and stretch the CBCO, which excited the Stretch Rate
379
Afferent and the Tonic and Phasic Lev MNs in a resistance reflex. In this open loop
380
configuration, the leg fall triggered a Lev MN burst followed immediately by a Dep MN burst.
381
Subsequent burst pairs occurred at a frequency of 0.04 ± 0.003 Hz (Fig. 6B) and were nearly
382
equally likely to be a Dep/Lev pair (6 in six 60 s trials) as a Lev/Dep pair (8 in six 60s trials). The
383
interval between burst pairs was 23.1 ± 2.5 s (Fig. 6C), and the Lev/Dep burst pair duration was
384
3.6 ± 0.1 s (Fig. 6D).
385 386
When the loop was closed, the frequency of burst pairs increased significantly by a factor of 2.5
387
to 0.10 ± 0.01 Hz (P = 0.001); they were exclusively Lev/Dep pairs (Figs. 5B, 6B). The interval
388
between burst pairs was 7.7 ± 1.3 s, which was significantly (P = 0.001) shorter than in open
389
loop (Fig. 6C), as was the burst pair duration, which was 3.2 ± 0.1 s (P = 0.001) (Fig. 6C). In 14
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
390
both open loop and closed loop simulations, the durations of the Lev bursts were longer than the
391
durations of the Dep bursts (OL: P = 0.004, CL: P < 0.001) (Fig. 6E). In addition, Lev bursts in
392
closed loop were shorter than those in open loop (P = 0.051), whereas Dep bursts in closed loop
393
were similar to those in open loop (P = 0.181). Finally, the interval between Lev and Dep bursts
394
in the burst pairs was similar but less variable in closed loop than in open loop (Fig. 6F).
395 396
Burst pairs in closed loop differed significantly from burst pairs in open loop, largely because of
397
the role of the assistance reflex responses in triggering the closed loop bursts. These differences
398
are apparent in Fig. 7, which shows the membrane potential changes of the circuit elements
399
during Lev/Dep bursts in closed loop and open loop, and Fig. 8, which shows the changes in their
400
average firing rates. Under both conditions, OXO stimulation depolarized the Lev and Dep INs,
401
the Stretch and Release ARINs and the Lev and Dep PADIs, which fired tonically near 50 Hz
402
(Figs. 7, 8). In closed loop, the interval between Lev/Dep burst pairs ended when the Tonic Lev
403
MN began to fire more rapidly because of subthreshold input from the Lev IN (Fig. 7 closed
404
loop). The Lev IN and Tonic and Phasic Lev MNs are electrically coupled to each other (Fig. 1),
405
so that changes in the membrane potential of one affects the firing of the others. The Lev IN is
406
an endogenous burster because of a slowly activating, voltage-sensitive depolarizing
407
conductance, which gradually depolarized the Lev IN after it was inhibited by the previous Dep
408
IN burst. Electrical coupling allowed the depolarizing current to be driven from Lev IN into the
409
Lev Tonic MN, which has a low spiking threshold and so began to fire increasingly rapidly. This
410
Tonic Lev MN activity excited the Tonic Lev muscles and their contraction began to raise the leg.
411
(Fig. 7, Closed Loop; Fig. 8, Closed Loop). This movement released the CBCO and excited the
412
Release Rate Assist and Resist Afferents. The Assist Afferent excited the Release ARIN, which
413
then excited all three elements of the Lev half-center, the Lev IN, Lev Phasic and Lev Tonic MNs,
414
to complete a positive feedback loop (Fig. 1, Figs. 7 and 8, Closed Loop). This triggered a Lev
415
burst that raised the leg and inhibited the Dep half-center. The Lev MNs also excited the Lev
416
PADI, which inhibited the Release Rate Resistance Afferent to prevent resistance reflex
417
excitation of the Dep MNs.
418 419
Because the open loop simulation lacked the positive feedback mediated by the ARINs, the initial
420
Lev burst was triggered by the endogenous bursting Lev IN and its electrical coupling with the 15
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
421
Tonic and Phasic Lev MNs (Figs. 1, 7, 8 open loop). Instead of the abrupt onset characteristic of
422
closed loop bursts, the open loop bursts began more gradually (Fig. 7 open loop Lev/Dep, Fig. 8
423
open loop). The Dep/Lev burst was triggered similarly, with the endogenously bursting Dep IN
424
interacting with the Tonic and Phasic Dep MNs while inhibiting the Lev half-center (Fig 7, Open
425
Loop Dep/Lev).
426 427
Mutual inhibition between Lev and Dep half-centers (Fig. 1) ensured that the Dep IN and MNs
428
were inhibited during the Lev burst (Fig. 7). When the Lev MN burst ended, the Dep IN began to
429
depolarize, which excited the Tonic Dep MN. In closed loop, this caused the leg to begin to
430
depress, which stretched the CBCO and strongly excited the Stretch Rate Assist Afferent (Fig. 8).
431
This Assist Afferent excited the Stretch ARIN which then excited the Dep half-center. This
432
completed the positive feedback loop and excited the Dep burst and the Dep PADI, which
433
prevented interference from Lev resistance reflexes.
434 435
In open loop, the end of the Lev half-center burst removed inhibition of the Dep half-center,
436
which then produced a strong Dep burst (Fig. 8 Open Loop). The absence of feedback prevented
437
the initial increase in the Dep MN firing rates that the assistance reflex evoked in closed loop.
16
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
438 439
Blocking the ARINs. Both the hybrid experimental results (Chung et al. 2014) and our
440
simulations suggest that assistance reflexes played a critical role in mediating the higher
441
frequency of Lev/Dep bursting in closed loop. To test this, closed loop simulations were
442
repeated when ARINs were disabled. Under these conditions, only one Lev/Dep burst occurred in
443
six 60s trials (Fig. 5B, No ARINs). With the ARINs disabled and a high level of activity in the
444
PADIs evoked by OXO neuron stimulation, there was no sensory input to the MNs or to the Dep
445
or Lev INs. The Tonic Lev and Dep MNs, however, remained near their spiking thresholds and
446
the Lev IN and Dep IN were depolarized as a result of OXO stimulation. Consequently, a
447
combination of electrical coupling between each IN and its MNs and mutual inhibition between
448
Lev and Dep half centers resulted in irregular alternating activity between Lev and Dep MNs that
449
triggered the occasional burst pair when one half center happened to exceed burst threshold.
450 451
Discussion
452
The circuit model is a greatly simplified (See Materials and Methods) description of the crayfish
453
thoracic circuitry that mediates leg elevation and depression movements during posture and
454
walking (Cattaert and Le Ray 2001). We joined the circuit and leg models to create a model of
455
the hybrid experimental preparation, and used that model to simulate the experiments with the
456
hybrid preparation in both quiescent and active states and under open and closed loop conditions.
457
We found that our simulations could reproduce and account for the results of the hybrid
458
preparation experiments. In the absence of OXO stimulation, leg lifts evoked chained resistance
459
reflexes (Fig. 2) similar to those evoked in the quiescent hybrid preparations (Fig. 2 in Chung, et
460
al., 2014). Low levels of OXO stimulation reduced the resistance reflex and created an assistance
461
reflex (Fig. 3A), similar to the reflex changes experienced by the hybrid preparation soon after
462
exposure to oxotremorine (Fig. 3A in Chung et al., 2014). Higher levels of OXO stimulation
463
enabled the assistance reflexes to trigger a Lev/Dep burst pair (Fig. 4) that was similar to the
464
burst pair evoked in the hybrid preparation (Fig. 3B in Chung et al., 2014). A still higher level of
465
OXO stimulation induced spontaneous, low frequency burst pairs in open loop and higher
466
frequency burst pairs in closed loop (Fig. 5B). These were similar to the burst patterns produced
467
by the hybrid preparation under open and closed loop conditions (Fig. 5A).
468 17
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
469
The higher frequency of burst pairs in closed loop resulted from decreases in the interval
470
between the pairs, in the duration of the pairs, and in the interval between bursts in each pair
471
(Fig. 6C, D, F). These results agree with our hybrid experiment results (Fig. 5C, D, G in Chung
472
et al., 2014). Table 1 provides a comparison of the average values of the model and
473
experimental results taken from Fig. 6 in the present paper and from Fig. 5 in Chung et al., 2014.
474
In both simulations and experiments, the largest difference between bursting in closed and open
475
loop was the interval between burst pairs, which was 15 s, or three times, longer in open loop
476
simulations and nearly 26 s, or more than four times, longer in the open loop hybrid experiments.
477
The other open and closed loop differences were much smaller in absolute terms and somewhat
478
smaller in percentage terms, and they were of the same sign in both the experiments and the
479
simulations. The only exception to this is the relative durations of the Lev and Dep bursts in a
480
pair. In simulation, the Lev bursts were shorter than the Dep bursts, whereas with one exception,
481
the reverse was true of our experimental preparations.
482 483
Hypothesized mechanism of increased bursting frequency. During walking, many of the leg
484
reflexes present in the quiescent state that promote postural stability are modulated in the active
485
state to assist walking (Ayers and Davis 1977b; El Manira et al. 1991b). Results from the hybrid
486
preparation experiments showed that in the active state the assistance reflex responses to leg lift
487
could trigger Lev/Dep burst pairs. This capability appeared to account for the increased burst
488
pair frequency in closed loop. Small upward movements early in each interval between Lev/Dep
489
burst pairs evoked a levator assistance reflex that triggered an early Lev/Dep burst pair and reset
490
the Lev/Dep CPG.
491 492
Our simulations showed that leg elevation assistance reflexes mediated by the Release ARIN can
493
have this effect, and that the burst frequency fell to low levels when the ARINs were disabled.
494
The timing of ARIN excitations in each burst pair enabled them to produce positive feedback at
495
the transitions from swing to stance and stance to swing. Early upward movements of a
496
depressed leg excited the Release ARIN that, in turn, excited Lev MNs. Their responses increased
497
upward movement of the leg and helped to trigger the burst. The Stretch ARIN played a similar
498
role in downward movements of the raised leg.
18
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
499 500
A similar mechanism for leg promotion and remotion? Both resistance and assistance
501
reflexes are also active at the most proximal leg joint, the thoracic-coxa (TC) joint (Skorupski
502
and Sillar 1986), where they likely contribute to the locomotor rhythm. The assistance reflexes
503
are initiated by the rate-sensitive afferents of the thoracic-coxa muscle receptor organ (TCMRO)
504
and the thoracic-coxa chordotonal organ (TCCO), and they may help remote the leg during the
505
stance phase of forward walking and promote the leg during the swing phase (Skorupski et al.
506
1992).
507 508
Their similarity to the levator and depressor assistance reflexes suggests that the promotor and
509
remotor assistance reflexes may also increase the frequency of the walking rhythm when their
510
feedback loop is closed. During forward walking, leg elevation is coincident with leg promotion,
511
and leg depression is coincident with leg remotion (Cattaert and Le Ray 2001). The leg promotor
512
motor neurons are active at about the same time as the Lev MNs, and would excite a promotor
513
assistance reflex similar to the levator assistance reflex. Indeed, in both instances, rate-sensitive
514
afferents and the lower threshold motor neurons are the ones that participate in assistance
515
reflexes (Skorupski et al. 1992). Just as the levator assistance reflex helps excite a levator burst
516
to begin the swing phase of leg movement, the promotor assistance reflex may help trigger a
517
promotor burst at the same time. At the end of the swing phase, the fall of the leg would excite
518
the depressor assistance reflex while the first remotor spikes move the leg backwards and excite
519
the remotor assistance reflex. These assistance reflexes would trigger the depressor and remotor
520
bursts to produce the stance phase of the walking rhythm.
521 522
Reflex reversal in other animals. The assistance reflexes described here serve similar functions
523
to those described in insects and in mammals that promote locomotor phase transitions and load
524
compensation during locomotion (Duysens et al. 2000). A positive feedback reflex between
525
stress-sensitive afferents in the leg cuticle of cockroach legs and a leg depressor motor neuron
526
increased the power stroke output during walking when the animal was placed under load
527
(Pearson 1972). The femoral chorodotonal organ (FCO) in the stick insect mediates resistive
528
reflexes of the femoral-tibia joint to stabilize posture when the animal is resting, and assistive
529
reflexes during locomotion to aid in movement (Bässler 1976; Hellekes et al. 2012). 19
In cats, a
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
530
decrease in ankle extensor tension that occurs as the weight shifts off the leg helps to promote
531
the stance-to-swing transition (Ekeberg and Pearson 2005).
532 533
These individual reflex responses play definite roles within the context of specific movements,
534
where their timing and coordination with both the central commands and other reflexes are
535
critical. For example, the levator assistance reflex described here is both synergistic and co-
536
active with reflexes mediated by the TCCO and TCMRO and by the funnel canal organ on the
537
dactyl and the cuticular stress detectors near the CB joint (Clarac et al. 1991; El Manira et al.
538
1991b; Leibrock et al. 1996). However, which reflexes are synergistic and co-active will depend
539
on the movement and behavior; movements that are part of forward walking will require
540
different reflex synergies from those that contribute to backward walking or turning (Ayers and
541
Davis 1977b; El Manira et al. 1991b; Ting and Macpherson 2005). In cockroach and stick
542
insect, sets of campaniform sensilla in different leg segments of the leg encode forces during
543
walking to produce combinations of reflexes that are appropriate for distinct phases of movement
544
(Zill et al. 2010; Zill et al. 2012). In the cat, proprioceptive signals from the hip join those from
545
the ankle extensor tendon to help determine the timing of the stance to swing transition (Pearson
546
2008).
547 548
Understanding complex closed loop sensorimotor systems with the aid of computational
549
neuromechanical models. The complexity, variability and state-dependence of these reflexes
550
and their interactions with CPGs makes the underlying mechanisms difficult to understand with
551
unaided intuition.
552
loop systems, where the dynamic relationship between sensory feedback, motor output, and
553
behavior is broken, and emergent properties are hidden. Neuromechanical models like the one
554
described here can help reveal those closed loop dynamic relationships and explore their
555
consequences for motor control (Pearson et al. 2006). The neuromechanical model includes
556
explicit descriptions of the components of the system, including the different reflex pathways,
557
the CPG, the physical movement of the limbs under gravity, and the stimulation of
558
proprioceptors and exteroceptors by those movements. The model then can be asked how the
559
components might interact to reproduce the experimentally observed behavior of the animal, and
560
which components and processes should have the largest effects on that behavior. The model’s
Moreover, much of the experimental data comes from experiments on open
20
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
561
failures will help to identify faults in our understanding of the system or its components, while
562
its successes can provide a platform for extending our analysis to still more complex aspects of
563
the system.
564
21
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
565
Acknowledgements We would like to thank Drs. Franklin Krasne, William Heitler, Robert
566
Clewley and Ms. Katharine E. McCann for many helpful suggestions. Dr. Cofer’s current
567
address is NeuroRobotic Technologies, LLC, www.neurorobotictech.com,
568 569
Grants
570
This work was supported by NSF Research Grant IOS 1120291 and by a Brains & Behavior
571
Fellowship from Georgia State University.
572 573
Disclosures
574
The authors declare no competing financial interests.
575 576
22
Neuromechanical simulations of crayfish posture and locomotion 577
Bacqué-Cazenave, et al.
Figure Legends
578 579
Table 1. Comparison of measures of spontaneous Lev/Dep bursting in the model simulations
580
and hybrid preparation experiments under closed and open loop conditions. Average values are
581
shown. Abbreviations: “Freq.”, frequency; “Int.”, interval; “Dur.”, duration; “Hz”, hertz; “s”,
582
seconds.
583 584
Figure 1. Neuromechanical model of the crayfish thorax, leg, and thoracic circuitry for
585
elevating and depressing the leg. Crayfish leg and body model. Thorax and leg with an inset
586
showing the CB leg joint blown up and made transparent to show the phasic and tonic (blue and
587
light blue) levator muscles, phasic and tonic (red and pink) depressor muscles, the CBCO strand
588
(yellow). Leg elevation (blue arrow) and depression (red arrow) cause CBCO release (green
589
arrow) and stretch (brown arrow), respectively. Neural circuit model. Neurons are represented
590
by colored circles and rounded rectangles, synaptic connections by colored lines, excitatory
591
synapses by forks, inhibitory synapses by filled circles, and electrical synapses by resistance
592
symbols. The three cells of the depressor half-center of the depressor/levator CPG are within a
593
pink rectangle, the cells of the levator half-center are within a light blue rectangle. CBCO release
594
(green arrow) excites release-sensitive CBCO Afferents (green rounded rectangles within a light
595
green rectangle at top), CBCO stretch (brown arrow) excites stretch-sensitive CBCO Afferents
596
(brown rectangles within a yellow rectangle at bottom). Electrical stimulation of the OXO neuron
597
is symbolized by an electrode labeled “Stim”.
598 599
Figure 2. Resistance responses to leg lift. A. Time courses of responses to an upward 1 N force
600
applied to the leg at 0.5 s for 0.5 s. The top two traces (“physical”) display the change in the
601
angle of the CB joint (“Leg Angle”) and the CBCO length. The next two traces display the
602
membrane potential change of the Release Afferent and Stretch Afferent neurons. The remaining
603
traces display the average firing rates in 25 ms bins of individual neurons, as labeled, to five leg
604
lifts in each of six trials. The averages are taken from 30 responses obtained in 6 simulation
605
trials. Each trace is color-coded according to the color of the neuron in Fig. 1 and in B and C.
606
The pale green vertical stripe marks the depressor resistance reflex response to the leg lift; the
607
broader brown vertical stripe marks the levator resistance reflex response to the fall of the leg. 23
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
608
Numbered gold markers identify responses with events in B and C as explained in the text. B
609
and C. The circuit diagram of Fig. 1 is modified to show the active neurons during the depressor
610
(B) and levator (C) resistance reflexes in full color and the inactive or inhibited neurons in dim
611
or light colors. B. Depressor resistance reflex pathway. The green arrow represents the effect of
612
CBCO release on the release-sensitive afferents. The red arrow represents the effect of Dep MNs
613
on Dep muscles and leg depression. C. Levator resistance reflex pathway. The brown arrow
614
represents the effect of CBCO stretch on the stretch-sensitive afferents. The blue arrow
615
represents the effect of the Lev MNs on Lev muscles and the leg depression.
616 617
Figure 3. Assistance and resistance response to leg lift. The same figure layout as in Fig. 2, with
618
the same 1N upward leg stimulus applied during 4 nA OXO neuron stimulation. A. The
619
responses to leg lift. The average neuron firing rates are calculated from 25 responses obtained in
620
six trials. B and C. The circuit diagram of Fig. 1 is modified to show the active neurons during
621
the levator assistance (B) and levator resistance (C) reflexes in full color and the inactive or
622
inhibited neurons in dim or light colors. The numbered gold circles mark the responses
623
associated with the sequence of steps in B and C and are explained in the text. B. Levator
624
assistance reflex pathway. The green arrow marks the effect of CBCO release on release-
625
sensitive CBCO afferents; the blue arrow marks the effect of Lev MNs on levator muscles and leg
626
lift. C. Levator resistance reflex pathway. The brown arrow marks the effect of CBCO stretch on
627
stretch-sensitive CBCO afferents; the blue arrow marks the effect of Lev MNs on levator muscles
628
and leg lift.
629 630
Figure 4. Assistance reflexes trigger bursts. The same figure layout as in Fig. 2, with the same 1
631
N upward leg stimulus applied during 5.2 nA OXO neuron stimulation. A. The responses to leg
632
lift. B and C. The circuit diagram of Fig. 1 is modified to show the active neurons during the
633
levator (B) and depressor (C) assistance reflexes in full color and the inactive or inhibited
634
neurons in dim or light colors. The numbered gold circles mark the sequence of steps and their
635
responses and are explained in the text. B. Levator assistance reflex pathway. The green arrow
636
marks the effect of CBCO release on release-sensitive CBCO afferents; the blue arrow marks the
637
effect of Lev MNs on levator muscles and leg lift. C. Depressor assistance reflex pathway. The
24
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
638
brown arrow marks the effect of CBCO stretch on stretch-sensitive CBCO afferents; the red
639
arrow marks the effect of Dep MNs on depressor muscles and leg fall.
640 641
Figure 5. The effect of closing the feedback loop on burst pair frequency. A. Open and closed
642
loop responses of a hybrid experimental preparation under exposure to 50mM oxotremorine,
643
copied from Fig. 4 in Chung et al., 2014. B. Responses of the neuromechanical model during
644
stimulation of the OXO neuron with 5.7 nA when the CBCO feedback loop was open (left),
645
when it was closed (middle), and when it was closed and the ARINs were disabled (right).
646
Colors of the traces match the neuron colors in Fig. 1.
647 648
Figure 6. Identification and statistics of burst pair responses obtained from open and closed loop
649
trials under 5.7 nA OXO neuron stimulation. A. Top four traces show the Tonic Lev, Phasic
650
Lev, Tonic Dep, and Phasic Dep neuron responses during two Lev/Dep burst pairs. Dep/Lev
651
burst pairs were analyzed similarly. The pale blue vertical stripes mark the Lev phase; the pink
652
vertical stripes mark the Dep phase. The middle three traces show Dataview event markers for
653
each of the top traces, identifying the Lev burst (top), Dep burst (middle) and Lev/Dep burst pair
654
(bottom). The final five lines mark those bursts and burst pairs as well as the interval between
655
burst pairs and the interval between bursts. B-F. Simulation results of Lev/Dep burst pair
656
responses from 7 simulation trials run in closed loop, and Lev/Dep and Dep/Lev burst pairs from
657
6 simulation trials run in open loop, with the averages of individual simulation trials presented as
658
single data points, and box plots showing the median and 25th and 75th percentiles for each set of
659
simulation trials. Those found to be significantly different (see text) are identified with a double-
660
end bar and asterisk.
661 662
Figure 7. Single burst pairs under closed and open loop taken from one simulation trial. The
663
two top traces show the CB angle and CBCO length as in Figs. 2-5. The other traces display the
664
membrane potential changes of different model neurons in colors according to Fig. 1. Left:
665
Lev/Dep burst pair in closed loop; Middle: Lev/Dep burst pair in open loop; Right: Dep/Lev
666
burst pair in open loop.
667
25
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
668
Figure 8. Average post-stimulus time histograms (PSTH) of 39 Lev/Dep burst pairs from 7
669
closed loop trials (left) and 8 Lev/Dep burst pairs from 6 open loop trials, with OXO neuron
670
depolarized by 5.7 nA in both. The 6 Dep/Lev burst pairs recorded in those 6 open loop trials are
671
not included. Separate average PSTHs were plotted for the Lev and Dep burst portions of the
672
burst pairs. The onset of the Phasic Lev MN burst marked time 0 for the Lev portions of the
673
average PSTHs, while time 0 for the Dep portions of those plots was the onset of the Phasic Dep
674
MN burst.
675 676
26
Neuromechanical simulations of crayfish posture and locomotion
Bacqué-Cazenave, et al.
677
References
678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721
Ayers JL, and Davis WJ. Neuronal control of locomotion in the lobster, Homarus americanus. I. Motor programs for forward and backward walking. J. Comp. Physiol. [A] 115: 1-27, 1977a. Ayers JL, and Davis WJ. Neuronal control of locomotion in the lobster, Homarus americanus. II. Types of walking leg reflexes. J. Comp. Physiol.[A] 115: 29-46, 1977b. Bässler U. Reversal of a reflex to a single motoneuron in the stick insect Çarausius morosus. Biological Cybernetics 24: 47-49, 1976. Buschges A, Akay T, Gabriel JP, and Schmidt J. Organizing network action for locomotion: Insights from studying insect walking. Brain. Res. Rev. 57: 162-171, 2008. Cattaert D, Araque A, Buno W, and Clarac F. Motor neurones of the crayfish walking system possess TEA+-revealed regenerative electrical properties. J. Exp. Biol. 188: 339-345, 1994a. Cattaert D, Araque A, Buno W, and Clarac F. Nicotinic and muscarinic activation of motoneurons in the crayfish locomotor network. J. Neurophysiol. 72: 1622-1633, 1994b. Cattaert D, El MA, and Bevengut M. Presynaptic inhibition and antidromic discharges in crayfish primary afferents. J. Physiol. Paris 93: 349-358, 1999. Cattaert D, Le Bon M, and Le Ray D. Efferent controls in crustacean mechanoreceptors. Microsc. Res. Tech. 58: 312-324, 2002. Cattaert D, and Le Ray D. Adaptive motor control in crayfish. Prog. Neurobiol. 63: 199-240, 2001. Cattaert D, and Le Ray D. Direct glutamate-mediated presynaptic inhibition of sensory afferents by the postsynaptic motor neurons. Eur. J. Neurosci. 10: 3737-3746, 1998. Cattaert D, Pearlstein E, and Clarac F. Cholinergic control of the walking network in the crayfish Procambarus clarkii. J. Physiol. Paris 89: 209-220, 1995. Chung B, Bacque-Cazenave J, Cattaert D, and Edwards DH. The effect of sensory feedback on crayfish posture and locomotion: I. Experimental analysis of closing the loop J. Neurophysiol. 2014. Clarac F, Cattaert D, and Le Ray D. Central control components of a 'simple' stretch reflex. Trends Neurosci. 23: 199-208, 2000. Clarac F, Chrachri A, and Cattaert D. Interneuronal control of a walking leg reflex in an in vitro crayfish preparation. In: Locomotor Neural Mechanism in Arthropods and Vertebrates, edited by Armstrong DM, and Bush BMH. Manchester, U.K.: Manchester Univ. Press, 1991, p. 33-501. Duysens J, Clarac F, and Cruse H. Load-regulating mechanisms in gait and posture: Comparative Aspects. Physiol. Rev. 80: 83-133, 2000. Ekeberg O, and Pearson K. Computer simulation of stepping in the hind legs of the cat: an examination of mechanisms regulating the stance-to-swing transition. J. Neurophysiol. 94: 42564268, 2005. El Manira A, Cattaert D, and Clarac F. Monosynaptic connections mediate resistance reflex in crayfish (Procambarus clarkii) walking legs. J. Comp. Physiol. [A] 168: 1432-1351, 1991a. El Manira A, DiCaprio RA, Cattaert D, and Clarac F. Monosynaptic interjoint reflexes and their central modulation during fictive locomotion in crayfish. Eur. J. Neurosci. 3: 1219-1231, 1991b. Hellekes K, Blincow E, Hoffmann J, and Buschges A. Control of reflex reversal in stick insect walking: effects of intersegmental signals, changes in direction, and optomotor-induced turning. J. Neurophysiol. 107: 239-249, 2012.
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Neuromechanical simulations of crayfish posture and locomotion 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755
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Hill AAV, and Cattaert D. Recruitment in a heterogeneous population of motor neurons that innervates the depressor muscle of the crayfish walking leg muscle. J. Exp. Biol. 211: 613-629, 2008. Hooper SL, and DiCaprio RA. Crustacean motor pattern generator networks. Neurosignals 13: 50-69, 2004. Le Bon-Jego M, and Cattaert D. Inhibitory component of the resistance reflex in the locomotor network of the crayfish. J. Neurophysiol. 88: 2575-2588, 2002. Le Ray D, and Cattaert D. Neural mechanisms of reflex reversal in coxo-basipodite depressor motor neurons of the crayfish. J. Neurophysiol. 77: 1963-1978, 1997. Leibrock CS, Marchand AR, Barnes WJ, and Clarac F. Synaptic connections of the cuticular stress detectors in crayfish: mono- and polysynaptic reflexes and the entrainment of fictive locomotion in an in vitro preparation. J. Comp. Physiol. [A] 178: 711-725, 1996. Pearlstein E, Watson AH, Bqvengut M, and Cattaert D. Inhibitory connections between antagonistic motor neurones of the crayfish walking legs. J. Comp. Neurol. 399: 241-254, 1998. Pearson K, Ekeberg O, and Buschges A. Assessing sensory function in locomotor systems using neuro-mechanical simulations. Trends Neurosci. 29: 625-631, 2006. Pearson KG. Central programming and reflex control of walking in the cockroach. J. Exp. Biol. 56: 173-193, 1972. Pearson KG. Role of sensory feedback in the control of stance duration in walking cats. Brain Res. Rev. 57: 222-227, 2008. Skorupski P, Rawat BM, and Bush BM. Heterogeneity and central modulation of feedback reflexes in crayfish motor pool. J. Neurophysiol. 67: 648-663, 1992. Skorupski P, and Sillar KT. Phase-dependent reversal of reflexes mediated by the thoracocoxal muscle receptor organ in the crayfish, Pacifastacus Leniusculus. J. Neurophysiol. 55: 689-695, 1986. Ting LH, and Macpherson JM. A limited set of muscle synergies for force control during a postural task. J. Neurophysiol. 93: 609-613, 2005. Wiens TJ, and Wolf H. The inhibitory motoneurons of crayfish thoracic limbs: identification, structures, and homology with insect common inhibitors. J. Comp. Neurol. 336: 261-278, 1993. Zill SN, Keller BR, Chaudhry S, Duke ER, Neff D, Quinn R, and Flannigan C. Detecting substrate engagement: responses of tarsal campaniform sensilla in cockroaches. J. Comp. Physiol. [A] 196: 407-420, 2010. Zill SN, Schmitz J, Chaudhry S, and Buschges A. Force encoding in stick insect legs delineates a reference frame for motor control. J. Neurophysiol. 108: 1453-1472, 2012.
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Table 1 Closed Loop
Model Experiment
Burst Pair Freq. (Hz) 0.095 0.098
Burst Pair Int. (s) 7.76 7.77
Burst Pair Dur. (s) 3.19 6.73
Burst Int. (s) 0.43 0.64
Lev Burst Dur. (s) 1.55 2.070
Dep Burst Dur. (s) 1.21 3.90
1.73 3.72
1.27 2.73
Open Loop Model Experiment
0.039 0.044
23.05 33.64
3.57 9.95
0.57 3.46
757 758
Table 1. Comparison of measures of spontaneous Lev/Dep bursting in the model simulations
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and hybrid preparation experiments under closed and open loop conditions. Average values are
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shown. Abbreviations: “Freq.”, frequency; “Int.”, interval; “Dur.”, duration; “Hz”, hertz; “s”,
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seconds.
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Figure 1. Neuromechanical model of the crayfish thorax, leg, and thoracic circuitry for elevating and depressing the leg. Crayfish leg and body model. Thorax and leg with an inset showing the CB leg joint blown up and made transparent to show the phasic and tonic (blue and light blue) levator muscles, phasic and tonic (red and pink) depressor muscles, the CBCO strand (yellow). Leg elevation (blue arrow) and depression (red arrow) cause CBCO release (green arrow) and stretch (brown arrow), respectively. Neural circuit model. Neurons are represented by colored circles and rounded rectangles, synaptic connections by colored lines, excitatory synapses by forks, inhibitory synapses by filled circles, and electrical synapses by resistance symbols. The three cells of the depressor half-center of the
depressor/levator CPG are within a pink rectangle, the cells of the levator half-center are within a light blue rectangle. (green arrow) excites release-sensitive CBCOet al. Neuromechanical simulations of CBCO crayfishrelease posture and locomotion Bacqué-Cazenave, Afferents (green rounded rectangles within a light green rectangle at top), CBCO stretch (brown arrow) excites stretch-sensitive CBCO Afferents (brown rectangles within a yellow rectangle at bottom). Electrical stimulation of the OXO neuron is symbolized by an electrode labeled “Stim”.
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Figure 2. Resistance responses to leg lift. A. Time courses of responses to an upward 1 N force applied to the leg at 0.5 s for 0.5 s. The top two traces (“physical”) display the change in the angle of the CB joint (“Leg Angle”) and the CBCO length. The next two traces display the membrane potential change of the Release Afferent and Stretch Afferent neurons. The remaining traces display the average firing rates in 25 ms bins of individual neurons, as labeled, to five leg lifts in each of six trials. The averages are taken from 30 responses obtained in 6 simulation trials. Each trace is color-coded according to the color of the neuron in Fig. 1 and in B and C. The pale green vertical stripe marks the depressor resistance reflex response to the leg lift; the broader brown vertical stripe marks the levator resistance reflex response to the fall of the leg. Numbered gold markers identify responses with events in B and C as explained in the text. B and C. The circuit diagram of Fig. 1 is modified to show the active neurons during the depressor (B) and levator (C) resistance reflexes in full color and the inactive or inhibited neurons in dim or light colors. B. Depressor resistance reflex pathway. The green arrow represents the effect of CBCO release on the releasesensitive afferents. The red arrow represents the effect of Dep MNs on Dep muscles and leg depression. C. Levator resistance reflex pathway. The brown arrow represents the effect of CBCO stretch on the stretch-sensitive afferents. The blue arrow represents the effect of the Lev MNs on Lev muscles and the leg depression.
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Figure 3. Assistance and resistance response to leg lift. The same figure layout as in Fig. 2, with the same 1N upward leg stimulus applied during 4 nA OXO neuron stimulation. A. The responses to leg lift. The average neuron firing rates are calculated from 25 responses obtained in six trials. B and C. The circuit diagram of Fig. 1 is modified to show the active neurons during the levator assistance (B) and levator resistance (C) reflexes in full color and the inactive or inhibited neurons in dim or light colors. The numbered gold circles mark the responses associated with the sequence of steps in B and C and are explained in the text. B. Levator assistance reflex pathway. The green arrow marks the effect of CBCO release on release-sensitive CBCO afferents; the blue arrow marks the effect of Lev MNs on levator muscles and leg lift. C. Levator resistance reflex pathway. The brown arrow marks the effect of CBCO stretch on stretch-sensitive CBCO afferents; the blue arrow marks the effect of Lev MNs on levator muscles and leg lift.
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Figure 4. Assistance reflexes trigger bursts. The same figure layout as in Fig. 2, with the same 1 N upward leg stimulus applied during 5.2 nA OXO neuron stimulation. A. The responses to leg lift. B and C. The circuit diagram of Fig. 1 is modified to show the active neurons during the levator (B) and depressor (C) assistance reflexes in full color and the inactive or inhibited neurons in dim or light colors. The numbered gold circles mark the sequence of steps and their responses and are explained in the text. B. Levator assistance reflex pathway. The green arrow marks the effect of CBCO release on release-sensitive CBCO afferents; the blue arrow marks the effect of Lev MNs on levator muscles and leg lift. C. Depressor assistance reflex pathway. The brown arrow marks the effect of CBCO stretch on stretch-sensitive CBCO afferents; the red arrow marks the effect of Dep MNs on depressor muscles and leg fall.
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Figure 5. The effect of closing the feedback loop on burst pair frequency. A. Open and closed loop responses of a hybrid experimental preparation under exposure to 50mM oxotremorine, copied from Fig. 4 in Chung et al., 2014. B. Responses of the neuromechanical model during stimulation of the OXO neuron with 5.7 nA when the CBCO feedback loop was open (left), when it was closed (middle), and when it was closed and the ARINs were disabled (right). Colors of the traces match the neuron colors in Fig. 1.
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Figure 6. Identification and statistics of burst pair responses obtained from open and closed loop trials under 5.7 nA OXO neuron stimulation. A. Top four traces show the Tonic Lev, Phasic Lev, Tonic Dep, and Phasic Dep neuron responses during two Lev/Dep burst pairs. Dep/Lev burst pairs were analyzed similarly. The pale blue vertical stripes mark the Lev phase; the pink vertical stripes mark the Dep phase. The middle three traces show Dataview event markers for each of the top traces, identifying the Lev burst (top), Dep burst (middle) and Lev/Dep burst pair (bottom). The final five lines mark those bursts and burst pairs as well as the interval between burst pairs and the interval between bursts. B-F. Simulation results of Lev/Dep burst pair responses from 7 simulation trials run in closed loop, and Lev/Dep and Dep/Lev burst pairs from 6 simulation trials run in open loop, with the averages of individual simulation trials presented as single data points, and box plots showing the median and 25th and 75th percentiles for each set of simulation trials. Those found to be significantly different (see text) are identified with a double-end bar and asterisk. 1
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Figure 7. Single burst pairs under closed and open loop taken from one simulation trial. The two top traces show the CB angle and CBCO length as in Figs. 2-5. The other traces display the membrane potential changes of different model neurons in colors according to Fig. 1. Left: Lev/Dep burst pair in closed loop; Middle: Lev/Dep burst pair in open loop; Right: Dep/Lev burst pair in open loop.
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Figure 8. Average post-stimulus time histograms (PSTH) of 39 Lev/Dep burst pairs from 7 closed loop trials (left) and 8 Lev/Dep burst pairs from 6 open loop trials, with OXO neuron depolarized by 5.7 nA in both. The 6 Dep/Lev burst pairs recorded in those 6 open loop trials are not included. Separate average PSTHs were plotted for the Lev and Dep burst portions of the burst pairs. The onset of the Phasic Lev MN burst marked time 0 for the Lev portions of the average PSTHs, while time 0 for the Dep portions of those plots was the onset of the Phasic Dep MN burst.
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