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      The Metastability of the Double-Tripod Gait in Locust Locomotion

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          Summary

          Insect locomotion represents a fundamental example of neuronal oscillating circuits generating different motor patterns or gaits by controlling their phase coordination. Walking gaits are assumed to represent stable states of the system, often modeled as coupled oscillators. This view is challenged, however, by recent experimental observations, in which in vitro locust preparations consistently converged to synchronous rhythms (all legs oscillating as one), a locomotive pattern never seen in vivo. To reconcile this inconsistency, we developed a modeling framework to capture the trade-off between the two competing mechanisms: the endogenous neuronal circuitry, expressed in vitro, and the feedback mechanisms from sensory and descending inputs, active only in vivo. We show that the ubiquitously observed double-tripod walking gait emerges precisely from this balance. The outcome is a short-lived meta-stable double-tripod gait, which transitions and alternates with stable idling, thus recovering the observed intermittent bouts of locomotion, typical of many insects' locomotion behavior.

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          Highlights

          • Isolated in vitro locust preparations indicate that idling is a stable fictive gait

          • This is in contrast to the dominant in vivo locomotive pattern (i.e., double tripod)

          • Hence functional locomotion behavior is dependent on descending and sensory inputs

          • The presented model generates intermittent double-tripod bouts as seen empirically

          Abstract

          Entomology; Evolutionary Ecology; Biomechanics

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          Most cited references61

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          Central pattern generators and the control of rhythmic movements.

          Central pattern generators are neuronal circuits that when activated can produce rhythmic motor patterns such as walking, breathing, flying, and swimming in the absence of sensory or descending inputs that carry specific timing information. General principles of the organization of these circuits and their control by higher brain centers have come from the study of smaller circuits found in invertebrates. Recent work on vertebrates highlights the importance of neuro-modulatory control pathways in enabling spinal cord and brain stem circuits to generate meaningful motor patterns. Because rhythmic motor patterns are easily quantified and studied, central pattern generators will provide important testing grounds for understanding the effects of numerous genetic mutations on behavior. Moreover, further understanding of the modulation of spinal cord circuitry used in rhythmic behaviors should facilitate the development of new treatments to enhance recovery after spinal cord damage.
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            Critical branching captures activity in living neural networks and maximizes the number of metastable States.

            Recent experimental work has shown that activity in living neural networks can propagate as a critical branching process that revisits many metastable states. Neural network theory suggests that attracting states could store information, but little is known about how a branching process could form such states. Here we use a branching process to model actual data and to explore metastable states in the network. When we tune the branching parameter to the critical point, we find that metastable states are most numerous and that network dynamics are not attracting, but neutral.
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              The Dynamics of Legged Locomotion: Models, Analyses, and Challenges

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                Author and article information

                Contributors
                Journal
                iScience
                iScience
                iScience
                Elsevier
                2589-0042
                08 January 2019
                22 February 2019
                08 January 2019
                : 12
                : 53-65
                Affiliations
                [1 ]Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel
                [2 ]School of Zoology, Faculty of Life Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
                [3 ]Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv 69978, Israel
                Author notes
                []Corresponding author ayali@ 123456post.tau.ac.il
                [∗∗ ]Corresponding author baruchbarzel@ 123456gmail.com
                [4]

                Lead Contact

                Article
                S2589-0042(19)30002-1
                10.1016/j.isci.2019.01.002
                6352547
                30677739
                d72b8466-b90b-4ebe-91d4-9ffafbb1eed4
                © 2019 The Author(s)

                This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

                History
                : 4 July 2018
                : 27 November 2018
                : 2 January 2019
                Categories
                Article

                entomology,evolutionary ecology,biomechanics
                entomology, evolutionary ecology, biomechanics

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