The effect of sensory feedback on crayfish posture ... - Semantic Scholar

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.



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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



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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).

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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.

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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.

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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

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feedback loop was open, and as a much higher frequency (~1/10 s) series of 75 Lev/Dep burst

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pairs and 3 Dep/Lev burst pairs when the feedback loop was closed (Fig. 5A here and in Chung

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et al., 2014). The model network produced the same set of phenomena when the OXO neuron

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was stimulated with 5.7 nA (Fig. 5B). (A video of one closed loop simulation trial, Hybrid

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simulation video.mpr, is available in Supplemental Materials at

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https://www.dropbox.com/sh/kfbs96wmak2mlty/AACdqTm1hF5KRBajvcCW8mrva?dl=0.)

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As in the hybrid preparation experiments (Fig. 1 in Chung et al., 2014), the feedback loop was

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opened in our simulated experiments by disconnecting the model MNs from the model muscles

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(Fig. 1), so the model was effectively paralyzed but could still respond to CBCO responses

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evoked by imposed model leg movements. The model leg was kept in an initially stationary

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horizontal position for 30 s at the beginning of each simulation trial to allow the effects of OXO

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stimulation to reach a steady state before beginning the 60 s experimental period (Fig. 5B). At

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that time, the leg was allowed to fall and stretch the CBCO, which excited the Stretch Rate

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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



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



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



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



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



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



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



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



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


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



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



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



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



677

References

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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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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

759

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”,

761

seconds.

762

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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”.





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.



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



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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