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Avila B, Augusto P, Zimmer M, Serafino M, Makse HA. Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome. ARXIV 2024:arXiv:2305.19367v2. [PMID: 37396607 PMCID: PMC10312817] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Subscribe] [Scholar Register] [Indexed: 07/04/2023]
Abstract
Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.
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Affiliation(s)
- Bryant Avila
- Levich Institute, Physics Department, City College of New York, New York, NY, USA
| | - Pedro Augusto
- Vienna Biocenter PhD Program, Doctoral School of the University of Vienna and Medical University of Vienna, Vienna, Austria
- Department of Neuroscience and Developmental Biology, Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
| | - Manuel Zimmer
- Research Institute of Molecular Pathology (IMP), Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
- Department of Neuroscience and Developmental Biology, Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
| | - Matteo Serafino
- Levich Institute, Physics Department, City College of New York, New York, NY, USA
| | - Hernán A. Makse
- Levich Institute, Physics Department, City College of New York, New York, NY, USA
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2
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Avila B, Serafino M, Augusto P, Zimmer M, Makse HA. Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome. PLoS One 2024; 19:e0297669. [PMID: 38598455 PMCID: PMC11006206 DOI: 10.1371/journal.pone.0297669] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Accepted: 01/11/2024] [Indexed: 04/12/2024] Open
Abstract
Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.
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Affiliation(s)
- Bryant Avila
- Physics Department, Levich Institute, City College of New York, New York, NY, United Stated of America
| | - Matteo Serafino
- Physics Department, Levich Institute, City College of New York, New York, NY, United Stated of America
| | - Pedro Augusto
- Vienna Biocenter PhD Program, Doctoral School of the University of Vienna and Medical University of Vienna, Vienna, Austria
- Department of Neuroscience and Developmental Biology, Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
| | - Manuel Zimmer
- Research Institute of Molecular Pathology (IMP), Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
- Department of Neuroscience and Developmental Biology, Vienna Biocenter (VBC), University of Vienna, Vienna, Austria
| | - Hernán A. Makse
- Physics Department, Levich Institute, City College of New York, New York, NY, United Stated of America
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3
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Lanza E, Lucente V, Nicoletti M, Schwartz S, Cavallo IF, Caprini D, Connor CW, Saifuddin MFA, Miller JM, L’Etoile ND, Folli V. See Elegans: Simple-to-use, accurate, and automatic 3D detection of neural activity from densely packed neurons. PLoS One 2024; 19:e0300628. [PMID: 38517838 PMCID: PMC10959381 DOI: 10.1371/journal.pone.0300628] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Accepted: 02/29/2024] [Indexed: 03/24/2024] Open
Abstract
In the emerging field of whole-brain imaging at single-cell resolution, which represents one of the new frontiers to investigate the link between brain activity and behavior, the nematode Caenorhabditis elegans offers one of the most characterized models for systems neuroscience. Whole-brain recordings consist of 3D time series of volumes that need to be processed to obtain neuronal traces. Current solutions for this task are either computationally demanding or limited to specific acquisition setups. Here, we propose See Elegans, a direct programming algorithm that combines different techniques for automatic neuron segmentation and tracking without the need for the RFP channel, and we compare it with other available algorithms. While outperforming them in most cases, our solution offers a novel method to guide the identification of a subset of head neurons based on position and activity. The built-in interface allows the user to follow and manually curate each of the processing steps. See Elegans is thus a simple-to-use interface aimed at speeding up the post-processing of volumetric calcium imaging recordings while maintaining a high level of accuracy and low computational demands. (Contact: enrico.lanza@iit.it).
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Affiliation(s)
- Enrico Lanza
- Center for Life Nano- and Neuro-Science@Sapienza, Istituto Italiano di Tecnologia (IIT), Rome, Italy
| | - Valeria Lucente
- Center for Life Nano- and Neuro-Science@Sapienza, Istituto Italiano di Tecnologia (IIT), Rome, Italy
- D-tails s.r.l., Rome, Italy
| | - Martina Nicoletti
- Center for Life Nano- and Neuro-Science@Sapienza, Istituto Italiano di Tecnologia (IIT), Rome, Italy
- Department of Engineering, Campus Bio-Medico University, Rome, Italy
| | - Silvia Schwartz
- Center for Life Nano- and Neuro-Science@Sapienza, Istituto Italiano di Tecnologia (IIT), Rome, Italy
| | - Ilaria F. Cavallo
- Center for Life Nano- and Neuro-Science@Sapienza, Istituto Italiano di Tecnologia (IIT), Rome, Italy
- D-tails s.r.l., Rome, Italy
| | - Davide Caprini
- Center for Life Nano- and Neuro-Science@Sapienza, Istituto Italiano di Tecnologia (IIT), Rome, Italy
| | - Christopher W. Connor
- Department of Anesthesiology, Perioperative and Pain Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA, United States of America
| | - Mashel Fatema A. Saifuddin
- Department of Cell and Tissue Biology, University of California, San Francisco, San Francisco, CA, United States of America
| | - Julia M. Miller
- Department of Cell and Tissue Biology, University of California, San Francisco, San Francisco, CA, United States of America
| | - Noelle D. L’Etoile
- Department of Cell and Tissue Biology, University of California, San Francisco, San Francisco, CA, United States of America
| | - Viola Folli
- Center for Life Nano- and Neuro-Science@Sapienza, Istituto Italiano di Tecnologia (IIT), Rome, Italy
- D-tails s.r.l., Rome, Italy
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4
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Haspel G, Cohen N. Neurodevelopment: Maintaining function during circuit reconfiguration. Curr Biol 2022; 32:R1226-R1228. [DOI: 10.1016/j.cub.2022.09.051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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5
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Quillen AC, Peshkov A, Wright E, McGaffigan S. Metachronal waves in concentrations of swimming Turbatrix aceti nematodes and an oscillator chain model for their coordinated motions. Phys Rev E 2021; 104:014412. [PMID: 34412226 DOI: 10.1103/physreve.104.014412] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 05/14/2021] [Indexed: 01/23/2023]
Abstract
At high concentration, free swimming nematodes known as vinegar eels (Turbatrix aceti), collectively exhibit metachronal waves near a boundary. We find that the frequency of the collective traveling wave is lower than that of the freely swimming organisms. We explore models based on a chain of oscillators with nearest-neighbor interactions that inhibit oscillator phase velocity. The phase of each oscillator represents the phase of the motion of the eel's head back and forth about its mean position. A strongly interacting directed chain model mimicking steric repulsion between organisms robustly gives traveling wave states and can approximately match the observed wavelength and oscillation frequency of the observed traveling wave. We predict body shapes assuming that waves propagate down the eel body at a constant speed. The phase oscillator model that impedes eel head overlaps also reduces close interactions throughout the eel bodies.
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Affiliation(s)
- A C Quillen
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - A Peshkov
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - Esteban Wright
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - Sonia McGaffigan
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
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6
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Haspel G, Severi KE, Fauci LJ, Cohen N, Tytell ED, Morgan JR. Resilience of neural networks for locomotion. J Physiol 2021; 599:3825-3840. [PMID: 34187088 DOI: 10.1113/jp279214] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Accepted: 06/22/2021] [Indexed: 01/15/2023] Open
Abstract
Locomotion is an essential behaviour for the survival of all animals. The neural circuitry underlying locomotion is therefore highly robust to a wide variety of perturbations, including injury and abrupt changes in the environment. In the short term, fault tolerance in neural networks allows locomotion to persist immediately after mild to moderate injury. In the longer term, in many invertebrates and vertebrates, neural reorganization including anatomical regeneration can restore locomotion after severe perturbations that initially caused paralysis. Despite decades of research, very little is known about the mechanisms underlying locomotor resilience at the level of the underlying neural circuits and coordination of central pattern generators (CPGs). Undulatory locomotion is an ideal behaviour for exploring principles of circuit organization, neural control and resilience of locomotion, offering a number of unique advantages including experimental accessibility and modelling tractability. In comparing three well-characterized undulatory swimmers, lampreys, larval zebrafish and Caenorhabditis elegans, we find similarities in the manifestation of locomotor resilience. To advance our understanding, we propose a comparative approach, integrating experimental and modelling studies, that will allow the field to begin identifying shared and distinct solutions for overcoming perturbations to persist in orchestrating this essential behaviour.
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Affiliation(s)
- Gal Haspel
- Federated Department of Biological Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA
| | - Kristen E Severi
- Federated Department of Biological Sciences, New Jersey Institute of Technology, Newark, NJ, 07102, USA
| | - Lisa J Fauci
- Department of Mathematics, Tulane University, New Orleans, LA, 70118, USA
| | - Netta Cohen
- School of Computing, University of Leeds, Leeds, LS2 9JT, UK
| | - Eric D Tytell
- Department of Biology, Tufts University, Medford, MA, 02155, USA
| | - Jennifer R Morgan
- The Eugene Bell Center for Regenerative Biology and Tissue Engineering, Marine Biological Laboratory, Woods Hole, MA, 02543, USA
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Inhibition Underlies Fast Undulatory Locomotion in Caenorhabditis elegans. eNeuro 2021; 8:ENEURO.0241-20.2020. [PMID: 33361147 PMCID: PMC7986531 DOI: 10.1523/eneuro.0241-20.2020] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 10/20/2020] [Accepted: 12/01/2020] [Indexed: 12/21/2022] Open
Abstract
Inhibition plays important roles in modulating the neural activities of sensory and motor systems at different levels from synapses to brain regions. To achieve coordinated movement, motor systems produce alternating contractions of antagonist muscles, whether along the body axis or within and among limbs, which often involves direct or indirect cross-inhibitory pathways. In the nematode Caenorhabditis elegans, a small network involving excitatory cholinergic and inhibitory GABAergic motoneurons generates the dorsoventral alternation of body-wall muscles that supports undulatory locomotion. Inhibition has been suggested to be necessary for backward undulation because mutants that are defective in GABA transmission exhibit a shrinking phenotype in response to a harsh touch to the head, whereas wild-type animals produce a backward escape response. Here, we demonstrate that the shrinking phenotype is exhibited by wild-type as well as mutant animals in response to harsh touch to the head or tail, but only GABA transmission mutants show slow locomotion after stimulation. Impairment of GABA transmission, either genetically or optogenetically, induces lower undulation frequency and lower translocation speed during crawling and swimming in both directions. The activity patterns of GABAergic motoneurons are different during low-frequency and high-frequency undulation. During low-frequency undulation, GABAergic VD and DD motoneurons show correlated activity patterns, while during high-frequency undulation, their activity alternates. The experimental results suggest at least three non-mutually exclusive roles for inhibition that could underlie fast undulatory locomotion in C. elegans, which we tested with computational models: cross-inhibition or disinhibition of body-wall muscles, or neuronal reset.
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8
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Olivares E, Izquierdo EJ, Beer RD. A Neuromechanical Model of Multiple Network Rhythmic Pattern Generators for Forward Locomotion in C. elegans. Front Comput Neurosci 2021; 15:572339. [PMID: 33679357 PMCID: PMC7930337 DOI: 10.3389/fncom.2021.572339] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2020] [Accepted: 01/21/2021] [Indexed: 12/04/2022] Open
Abstract
Multiple mechanisms contribute to the generation, propagation, and coordination of the rhythmic patterns necessary for locomotion in Caenorhabditis elegans. Current experiments have focused on two possibilities: pacemaker neurons and stretch-receptor feedback. Here, we focus on whether it is possible that a chain of multiple network rhythmic pattern generators in the ventral nerve cord also contribute to locomotion. We use a simulation model to search for parameters of the anatomically constrained ventral nerve cord circuit that, when embodied and situated, can drive forward locomotion on agar, in the absence of pacemaker neurons or stretch-receptor feedback. Systematic exploration of the space of possible solutions reveals that there are multiple configurations that result in locomotion that is consistent with certain aspects of the kinematics of worm locomotion on agar. Analysis of the best solutions reveals that gap junctions between different classes of motorneurons in the ventral nerve cord can play key roles in coordinating the multiple rhythmic pattern generators.
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Affiliation(s)
- Erick Olivares
- Cognitive Science Program, Indiana University Bloomington, Bloomington, IN, United States
| | - Eduardo J. Izquierdo
- Cognitive Science Program, Indiana University Bloomington, Bloomington, IN, United States
- Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington, Bloomington, IN, United States
| | - Randall D. Beer
- Cognitive Science Program, Indiana University Bloomington, Bloomington, IN, United States
- Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington, Bloomington, IN, United States
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9
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Towlson EK, Barabási AL. Synthetic ablations in the C. elegans nervous system. Netw Neurosci 2020; 4:200-216. [PMID: 32166208 PMCID: PMC7055645 DOI: 10.1162/netn_a_00115] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2019] [Accepted: 11/12/2019] [Indexed: 01/03/2023] Open
Abstract
Synthetic lethality, the finding that the simultaneous knockout of two or more individually nonessential genes leads to cell or organism death, has offered a systematic framework to explore cellular function, and also offered therapeutic applications. Yet the concept lacks its parallel in neuroscience—a systematic knowledge base on the role of double or higher order ablations in the functioning of a neural system. Here, we use the framework of network control to systematically predict the effects of ablating neuron pairs and triplets on the gentle touch response. We find that surprisingly small sets of 58 pairs and 46 triplets can reduce muscle controllability in this context, and that these sets are localized in the nervous system in distinct groups. Further, they lead to highly specific experimentally testable predictions about mechanisms of loss of control, and which muscle cells are expected to experience this loss. “Synthetic lethality” in cell biology is an extreme example of the effects of higher order genetic interactions: The simultaneous knockout of two or more individually nonessential genes leads to cell death. We define a neural analog to this concept in relation to the locomotor response to gentle touch in C. elegans. Two or more neurons are synthetic essential if individually they are not required for this behavior, yet their combination is. We employ a network control approach to systematically assess all pairs and triplets of neurons by their effect on body wall muscle controllability, and find that only surprisingly small sets of neurons are synthetic essential. They are highly localized in the nervous system and predicted to affect control over specific sets of muscles.
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Affiliation(s)
- Emma K Towlson
- Network Science Institute and Department of Physics, Northeastern University, Boston, MA, USA
| | - Albert-László Barabási
- Network Science Institute and Department of Physics, Northeastern University, Boston, MA, USA
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10
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Pathak A, Chatterjee N, Sinha S. Developmental trajectory of Caenorhabditis elegans nervous system governs its structural organization. PLoS Comput Biol 2020; 16:e1007602. [PMID: 31895942 PMCID: PMC6959611 DOI: 10.1371/journal.pcbi.1007602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2019] [Revised: 01/14/2020] [Accepted: 12/11/2019] [Indexed: 11/22/2022] Open
Abstract
A central problem of neuroscience involves uncovering the principles governing the organization of nervous systems which ensure robustness in brain development. The nematode Caenorhabditis elegans provides us with a model organism for studying this question. In this paper, we focus on the invariant connection structure and spatial arrangement of the neurons comprising the somatic neuronal network of this organism to understand the key developmental constraints underlying its design. We observe that neurons with certain shared characteristics-such as, neural process lengths, birth time cohort, lineage and bilateral symmetry-exhibit a preference for connecting to each other. Recognizing the existence of such homophily and their relative degree of importance in determining connection probability within neurons (for example, in synapses, symmetric pairing is the most dominant factor followed by birth time cohort, process length and lineage) helps in connecting specific neuronal attributes to the topological organization of the network. Further, the functional identities of neurons appear to dictate the temporal hierarchy of their appearance during the course of development. Providing crucial insights into principles that may be common across many organisms, our study shows how the trajectory in the developmental landscape constrains the structural organization of a nervous system.
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Affiliation(s)
- Anand Pathak
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai, India
| | | | - Sitabhra Sinha
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai, India
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11
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Kim J, Leahy W, Shlizerman E. Neural Interactome: Interactive Simulation of a Neuronal System. Front Comput Neurosci 2019; 13:8. [PMID: 30930759 PMCID: PMC6425397 DOI: 10.3389/fncom.2019.00008] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Accepted: 01/30/2019] [Indexed: 01/14/2023] Open
Abstract
Connectivity and biophysical processes determine the functionality of neuronal networks. We, therefore, developed a real-time framework, called Neural Interactome,, to simultaneously visualize and interact with the structure and dynamics of such networks. Neural Interactome is a cross-platform framework, which combines graph visualization with the simulation of neural dynamics, or experimentally recorded multi neural time series, to allow application of stimuli to neurons to examine network responses. In addition, Neural Interactome supports structural changes, such as disconnection of neurons from the network (ablation feature). Neural dynamics can be explored on a single neuron level (using a zoom feature), back in time (using a review feature), and recorded (using presets feature). The development of the Neural Interactome was guided by generic concepts to be applicable to neuronal networks with different neural connectivity and dynamics. We implement the framework using a model of the nervous system of Caenorhabditis elegans (C. elegans) nematode, a model organism with resolved connectome and neural dynamics. We show that Neural Interactome assists in studying neural response patterns associated with locomotion and other stimuli. In particular, we demonstrate how stimulation and ablation help in identifying neurons that shape particular dynamics. We examine scenarios that were experimentally studied, such as touch response circuit, and explore new scenarios that did not undergo elaborate experimental studies.
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Affiliation(s)
- Jimin Kim
- Department of Electrical and Computer Engineering, University of Washington, Seattle, WA, United States
| | - William Leahy
- Department of Applied Mathematics, University of Washington, Seattle, WA, United States
| | - Eli Shlizerman
- Department of Electrical and Computer Engineering, University of Washington, Seattle, WA, United States.,Department of Applied Mathematics, University of Washington, Seattle, WA, United States
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12
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13
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Tolstenkov O, Van der Auwera P, Steuer Costa W, Bazhanova O, Gemeinhardt TM, Bergs AC, Gottschalk A. Functionally asymmetric motor neurons contribute to coordinating locomotion of Caenorhabditis elegans. eLife 2018; 7:34997. [PMID: 30204083 PMCID: PMC6173582 DOI: 10.7554/elife.34997] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2018] [Accepted: 09/09/2018] [Indexed: 12/11/2022] Open
Abstract
Locomotion circuits developed in simple animals, and circuit motifs further evolved in higher animals. To understand locomotion circuit motifs, they must be characterized in many models. The nematode Caenorhabditis elegans possesses one of the best-studied circuits for undulatory movement. Yet, for 1/6th of the cholinergic motor neurons (MNs), the AS MNs, functional information is unavailable. Ventral nerve cord (VNC) MNs coordinate undulations, in small circuits of complementary neurons innervating opposing muscles. AS MNs differ, as they innervate muscles and other MNs asymmetrically, without complementary partners. We characterized AS MNs by optogenetic, behavioral and imaging analyses. They generate asymmetric muscle activation, enabling navigation, and contribute to coordination of dorso-ventral undulation as well as anterio-posterior bending wave propagation. AS MN activity correlated with forward and backward locomotion, and they functionally connect to premotor interneurons (PINs) for both locomotion regimes. Electrical feedback from AS MNs via gap junctions may affect only backward PINs.
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Affiliation(s)
- Oleg Tolstenkov
- Buchmann Institute for Molecular Life Sciences, Goethe University, Frankfurt, Germany.,Institute for Biophysical Chemistry, Goethe University, Frankfurt, Germany.,Cluster of Excellence Frankfurt Macromolecular Complexes, Goethe University, Frankfurt, Germany
| | - Petrus Van der Auwera
- Buchmann Institute for Molecular Life Sciences, Goethe University, Frankfurt, Germany.,Institute for Biophysical Chemistry, Goethe University, Frankfurt, Germany.,Department of Biology, Functional Genomics and Proteomics Unit, Katholieke Universiteit Leuven, Leuven, Belgium
| | - Wagner Steuer Costa
- Buchmann Institute for Molecular Life Sciences, Goethe University, Frankfurt, Germany.,Institute for Biophysical Chemistry, Goethe University, Frankfurt, Germany
| | - Olga Bazhanova
- Buchmann Institute for Molecular Life Sciences, Goethe University, Frankfurt, Germany
| | - Tim M Gemeinhardt
- Buchmann Institute for Molecular Life Sciences, Goethe University, Frankfurt, Germany.,Institute for Biophysical Chemistry, Goethe University, Frankfurt, Germany
| | - Amelie Cf Bergs
- Buchmann Institute for Molecular Life Sciences, Goethe University, Frankfurt, Germany.,Institute for Biophysical Chemistry, Goethe University, Frankfurt, Germany.,International Max Planck Research School in Structure and Function of Biological Membranes, Frankfurt, Germany
| | - Alexander Gottschalk
- Buchmann Institute for Molecular Life Sciences, Goethe University, Frankfurt, Germany.,Institute for Biophysical Chemistry, Goethe University, Frankfurt, Germany.,Cluster of Excellence Frankfurt Macromolecular Complexes, Goethe University, Frankfurt, Germany
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14
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Izquierdo EJ, Beer RD. From head to tail: a neuromechanical model of forward locomotion in Caenorhabditis elegans. Philos Trans R Soc Lond B Biol Sci 2018; 373:20170374. [PMID: 30201838 PMCID: PMC6158225 DOI: 10.1098/rstb.2017.0374] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/21/2018] [Indexed: 12/16/2022] Open
Abstract
With 302 neurons and a near-complete reconstruction of the neural and muscle anatomy at the cellular level, Caenorhabditis elegans is an ideal candidate organism to study the neuromechanical basis of behaviour. Yet despite the breadth of knowledge about the neurobiology, anatomy and physics of C. elegans, there are still a number of unanswered questions about one of its most basic and fundamental behaviours: forward locomotion. How the rhythmic pattern is generated and propagated along the body is not yet well understood. We report on the development and analysis of a model of forward locomotion that integrates the neuroanatomy, neurophysiology and body mechanics of the worm. Our model is motivated by experimental analysis of the structure of the ventral cord circuitry and the effect of local body curvature on nearby motoneurons. We developed a neuroanatomically grounded model of the head motoneuron circuit and the ventral nerve cord circuit. We integrated the neural model with an existing biomechanical model of the worm's body, with updated musculature and stretch receptors. Unknown parameters were evolved using an evolutionary algorithm to match the speed of the worm on agar. We performed 100 evolutionary runs and consistently found electrophysiological configurations that reproduced realistic control of forward movement. The ensemble of successful solutions reproduced key experimental observations that they were not designed to fit, including the wavelength and frequency of the propagating wave. Analysis of the ensemble revealed that head motoneurons SMD and RMD are sufficient to drive dorsoventral undulations in the head and neck and that short-range posteriorly directed proprioceptive feedback is sufficient to propagate the wave along the rest of the body.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.
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Affiliation(s)
- Eduardo J Izquierdo
- Cognitive Science Program, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA
| | - Randall D Beer
- Cognitive Science Program, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA
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15
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Towlson EK, Vértes PE, Yan G, Chew YL, Walker DS, Schafer WR, Barabási AL. Caenorhabditis elegans and the network control framework-FAQs. Philos Trans R Soc Lond B Biol Sci 2018; 373:20170372. [PMID: 30201837 PMCID: PMC6158218 DOI: 10.1098/rstb.2017.0372] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/10/2018] [Indexed: 12/31/2022] Open
Abstract
Control is essential to the functioning of any neural system. Indeed, under healthy conditions the brain must be able to continuously maintain a tight functional control between the system's inputs and outputs. One may therefore hypothesize that the brain's wiring is predetermined by the need to maintain control across multiple scales, maintaining the stability of key internal variables, and producing behaviour in response to environmental cues. Recent advances in network control have offered a powerful mathematical framework to explore the structure-function relationship in complex biological, social and technological networks, and are beginning to yield important and precise insights on neuronal systems. The network control paradigm promises a predictive, quantitative framework to unite the distinct datasets necessary to fully describe a nervous system, and provide mechanistic explanations for the observed structure and function relationships. Here, we provide a thorough review of the network control framework as applied to Caenorhabditis elegans (Yan et al. 2017 Nature550, 519-523. (doi:10.1038/nature24056)), in the style of Frequently Asked Questions. We present the theoretical, computational and experimental aspects of network control, and discuss its current capabilities and limitations, together with the next likely advances and improvements. We further present the Python code to enable exploration of control principles in a manner specific to this prototypical organism.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.
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Affiliation(s)
- Emma K Towlson
- Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115, USA
| | - Petra E Vértes
- Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, UK
| | - Gang Yan
- Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115, USA
- School of Physics Science and Engineering, Tongji University, Shanghai 200092, People's Republic of China
| | - Yee Lian Chew
- Division of Neurobiology, MRC Laboratory of Molecular Biology, Cambridge Biomedical Campus, Francis Crick Avenue, Cambridge CB2 0QH, UK
| | - Denise S Walker
- Division of Neurobiology, MRC Laboratory of Molecular Biology, Cambridge Biomedical Campus, Francis Crick Avenue, Cambridge CB2 0QH, UK
| | - William R Schafer
- Division of Neurobiology, MRC Laboratory of Molecular Biology, Cambridge Biomedical Campus, Francis Crick Avenue, Cambridge CB2 0QH, UK
| | - Albert-László Barabási
- Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115, USA
- Center for Cancer Systems Biology, Dana Farber Cancer Institute, Boston, MA 02115, USA
- Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02115, USA
- Center for Network Science, Central European University, Budapest 1051, Hungary
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16
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Olivares EO, Izquierdo EJ, Beer RD. Potential role of a ventral nerve cord central pattern generator in forward and backward locomotion in Caenorhabditis elegans. Netw Neurosci 2018; 2:323-343. [PMID: 30294702 PMCID: PMC6145852 DOI: 10.1162/netn_a_00036] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2017] [Accepted: 11/06/2017] [Indexed: 01/03/2023] Open
Abstract
C. elegans locomotes in an undulatory fashion, generating thrust by propagating dorsoventral bends along its body. Although central pattern generators (CPGs) are typically involved in animal locomotion, their presence in C. elegans has been questioned, mainly because there has been no evident circuit that supports intrinsic network oscillations. With a fully reconstructed connectome, the question of whether it is possible to have a CPG in the ventral nerve cord (VNC) of C. elegans can be answered through computational models. We modeled a repeating neural unit based on segmentation analysis of the connectome. We then used an evolutionary algorithm to determine the unknown physiological parameters of each neuron so as to match the features of the neural traces of the worm during forward and backward locomotion. We performed 1,000 evolutionary runs and consistently found configurations of the neural circuit that produced oscillations matching the main characteristic observed in experimental recordings. In addition to providing an existence proof for the possibility of a CPG in the VNC, we suggest a series of testable hypotheses about its operation. More generally, we show the feasibility and fruitfulness of a methodology to study behavior based on a connectome, in the absence of complete neurophysiological details.
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Affiliation(s)
- Erick O Olivares
- Cognitive Science Program, Indiana University, Bloomington, IN, USA
| | | | - Randall D Beer
- Cognitive Science Program, Indiana University, Bloomington, IN, USA
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17
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The UBR-1 ubiquitin ligase regulates glutamate metabolism to generate coordinated motor pattern in Caenorhabditis elegans. PLoS Genet 2018; 14:e1007303. [PMID: 29649217 PMCID: PMC5931689 DOI: 10.1371/journal.pgen.1007303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Revised: 05/02/2018] [Accepted: 03/08/2018] [Indexed: 12/14/2022] Open
Abstract
UBR1 is an E3 ubiquitin ligase best known for its ability to target protein degradation by the N-end rule. The physiological functions of UBR family proteins, however, remain not fully understood. We found that the functional loss of C. elegans UBR-1 leads to a specific motor deficit: when adult animals generate reversal movements, A-class motor neurons exhibit synchronized activation, preventing body bending. This motor deficit is rescued by removing GOT-1, a transaminase that converts aspartate to glutamate. Both UBR-1 and GOT-1 are expressed and critically required in premotor interneurons of the reversal motor circuit to regulate the motor pattern. ubr-1 and got-1 mutants exhibit elevated and decreased glutamate level, respectively. These results raise an intriguing possibility that UBR proteins regulate glutamate metabolism, which is critical for neuronal development and signaling. Ubiquitin-mediated protein degradation is central to diverse biological processes. The selection of substrates for degradation is carried out by the E3 ubiquitin ligases, which target specific groups of proteins for ubiquitination. The human genome encodes hundreds of E3 ligases; many exhibit sequence conservation across animal species, including one such ligase called UBR1. Patients carrying mutations in UBR1 exhibit severe systemic defects, but the biology behinds UBR1’s physiological function remains elusive. Here we found that the C. elegans UBR-1 regulates glutamate level. When UBR-1 is defective, C. elegans exhibits increased glutamate; this leads to synchronization of motor neuron activity, hence defective locomotion when animals reach adulthood. UBR1-mediated glutamate metabolism may contribute to the physiological defects of UBR1 mutations.
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18
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Azulay A, Itskovits E, Zaslaver A. The C. elegans Connectome Consists of Homogenous Circuits with Defined Functional Roles. PLoS Comput Biol 2016; 12:e1005021. [PMID: 27606684 PMCID: PMC5015834 DOI: 10.1371/journal.pcbi.1005021] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2016] [Accepted: 06/15/2016] [Indexed: 12/15/2022] Open
Abstract
A major goal of systems neuroscience is to decipher the structure-function relationship in neural networks. Here we study network functionality in light of the common-neighbor-rule (CNR) in which a pair of neurons is more likely to be connected the more common neighbors it shares. Focusing on the fully-mapped neural network of C. elegans worms, we establish that the CNR is an emerging property in this connectome. Moreover, sets of common neighbors form homogenous structures that appear in defined layers of the network. Simulations of signal propagation reveal their potential functional roles: signal amplification and short-term memory at the sensory/inter-neuron layer, and synchronized activity at the motoneuron layer supporting coordinated movement. A coarse-grained view of the neural network based on homogenous connected sets alone reveals a simple modular network architecture that is intuitive to understand. These findings provide a novel framework for analyzing larger, more complex, connectomes once these become available.
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Affiliation(s)
- Aharon Azulay
- Department of Genetics, The Silberman Life Science Institute, Edmond J. Safra Campus, Hebrew University, Jerusalem, Israel
- Ph.D. Program in Brain Sciences, Edmond and Lily Safra Center for Brain Sciences, Hebrew University, Jerusalem, Israel
| | - Eyal Itskovits
- Department of Genetics, The Silberman Life Science Institute, Edmond J. Safra Campus, Hebrew University, Jerusalem, Israel
| | - Alon Zaslaver
- Department of Genetics, The Silberman Life Science Institute, Edmond J. Safra Campus, Hebrew University, Jerusalem, Israel
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19
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Bacik KA, Schaub MT, Beguerisse-Díaz M, Billeh YN, Barahona M. Flow-Based Network Analysis of the Caenorhabditis elegans Connectome. PLoS Comput Biol 2016; 12:e1005055. [PMID: 27494178 PMCID: PMC4975510 DOI: 10.1371/journal.pcbi.1005055] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2016] [Accepted: 07/12/2016] [Indexed: 11/18/2022] Open
Abstract
We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios. One of the goals of systems neuroscience is to elucidate the relationship between the structure of neuronal networks and the functional dynamics that they implement. An ideal model organism to study such interactions is the roundworm C. elegans, which not only has a fully mapped connectome, but has also been the object of extensive behavioural, genetic and neurophysiological experiments. Here we present an analysis of the neuronal network of C. elegans from a dynamical flow perspective. Our analysis reveals a multi-scale organisation of the signal flow in the network linked to anatomical and functional features of neurons, as well as identifying different neuronal roles in relation to signal propagation. We use our computational framework to explore biological input-response scenarios as well as exhaustive in silico ablations, which we relate to experimental findings reported in the literature.
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Affiliation(s)
- Karol A Bacik
- Department of Mathematics, Imperial College London, London, United Kingdom
| | - Michael T Schaub
- Department of Mathematics, Imperial College London, London, United Kingdom
- naXys & Department of Mathematics, University of Namur, Namur, Belgium
- ICTEAM, Université catholique de Louvain, Louvain-la-Neuve, Belgium
| | | | - Yazan N Billeh
- Computation and Neural Systems Program, California Institute of Technology, Pasadena, California, United States of America
| | - Mauricio Barahona
- Department of Mathematics, Imperial College London, London, United Kingdom
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20
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Izquierdo EJ, Beer RD. The whole worm: brain-body-environment models of C. elegans. Curr Opin Neurobiol 2016; 40:23-30. [PMID: 27336738 DOI: 10.1016/j.conb.2016.06.005] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2016] [Revised: 05/26/2016] [Accepted: 06/02/2016] [Indexed: 12/20/2022]
Abstract
Brain, body and environment are in continuous dynamical interaction, and it is becoming increasingly clear that an animal's behavior must be understood as a product not only of its nervous system, but also of the ongoing feedback of this neural activity through the biomechanics of its body and the ecology of its environment. Modeling has an essential integrative role to play in such an understanding. But successful whole-animal modeling requires an animal for which detailed behavioral, biomechanical and neural information is available and a modeling methodology which can gracefully cope with the constantly changing balance of known and unknown biological constraints. Here we review recent progress on both optogenetic techniques for imaging and manipulating neural activity and neuromechanical modeling in the nematode worm Caenorhabditis elegans. This work demonstrates both the feasibility and challenges of whole-animal modeling.
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Affiliation(s)
- Eduardo J Izquierdo
- Cognitive Science Program, Program in Neuroscience, School of Informatics and Computing, Indiana University, United States
| | - Randall D Beer
- Cognitive Science Program, Program in Neuroscience, School of Informatics and Computing, Indiana University, United States.
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21
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Brouilly N, Lecroisey C, Martin E, Pierson L, Mariol MC, Qadota H, Labouesse M, Streichenberger N, Mounier N, Gieseler K. Ultra-structural time-course study in the C. elegans model for Duchenne muscular dystrophy highlights a crucial role for sarcomere-anchoring structures and sarcolemma integrity in the earliest steps of the muscle degeneration process. Hum Mol Genet 2015; 24:6428-45. [PMID: 26358775 DOI: 10.1093/hmg/ddv353] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Accepted: 08/26/2015] [Indexed: 01/07/2023] Open
Abstract
Duchenne muscular dystrophy (DMD) is a genetic disease characterized by progressive muscle degeneration due to mutations in the dystrophin gene. In spite of great advances in the design of curative treatments, most patients currently receive palliative therapies with steroid molecules such as prednisone or deflazacort thought to act through their immunosuppressive properties. These molecules only slightly slow down the progression of the disease and lead to severe side effects. Fundamental research is still needed to reveal the mechanisms involved in the disease that could be exploited as therapeutic targets. By studying a Caenorhabditis elegans model for DMD, we show here that dystrophin-dependent muscle degeneration is likely to be cell autonomous and affects the muscle cells the most involved in locomotion. We demonstrate that muscle degeneration is dependent on exercise and force production. Exhaustive studies by electron microscopy allowed establishing for the first time the chronology of subcellular events occurring during the entire process of muscle degeneration. This chronology highlighted the crucial role for dystrophin in stabilizing sarcomeric anchoring structures and the sarcolemma. Our results suggest that the disruption of sarcomeric anchoring structures and sarcolemma integrity, observed at the onset of the muscle degeneration process, triggers subcellular consequences that lead to muscle cell death. An ultra-structural analysis of muscle biopsies from DMD patients suggested that the chronology of subcellular events established in C. elegans models the pathogenesis in human. Finally, we found that the loss of sarcolemma integrity was greatly reduced after prednisone treatment suggesting a role for this molecule in plasma membrane stabilization.
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Affiliation(s)
- Nicolas Brouilly
- Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre, 69622 Villeurbanne, France, Centre de Génétique et de Physiologie moléculaires et cellulaires, CNRS UMR 5534, 16 rue Dubois, 69622 Villeurbanne, France
| | - Claire Lecroisey
- Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre, 69622 Villeurbanne, France, Centre de Génétique et de Physiologie moléculaires et cellulaires, CNRS UMR 5534, 16 rue Dubois, 69622 Villeurbanne, France
| | - Edwige Martin
- Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre, 69622 Villeurbanne, France, Centre de Génétique et de Physiologie moléculaires et cellulaires, CNRS UMR 5534, 16 rue Dubois, 69622 Villeurbanne, France
| | - Laura Pierson
- Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre, 69622 Villeurbanne, France, Centre de Génétique et de Physiologie moléculaires et cellulaires, CNRS UMR 5534, 16 rue Dubois, 69622 Villeurbanne, France
| | - Marie-Christine Mariol
- Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre, 69622 Villeurbanne, France, Centre de Génétique et de Physiologie moléculaires et cellulaires, CNRS UMR 5534, 16 rue Dubois, 69622 Villeurbanne, France
| | - Hiroshi Qadota
- Department of Pathology, Emory University, 615 Michael Street, Whitehead 165, Atlanta, GA 30322, USA
| | - Michel Labouesse
- Intitut de Génétique et de Biologie Moléculaire et Cellulaire, CNRS UMR 7104 - Inserm U 964, 1 rue Laurent Fries, BP 10142, 67404 Illkirch CEDEX, France and
| | | | - Nicole Mounier
- Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre, 69622 Villeurbanne, France, Centre de Génétique et de Physiologie moléculaires et cellulaires, CNRS UMR 5534, 16 rue Dubois, 69622 Villeurbanne, France
| | - Kathrin Gieseler
- Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre, 69622 Villeurbanne, France, Centre de Génétique et de Physiologie moléculaires et cellulaires, CNRS UMR 5534, 16 rue Dubois, 69622 Villeurbanne, France,
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22
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Zhen M, Samuel ADT. C. elegans locomotion: small circuits, complex functions. Curr Opin Neurobiol 2015; 33:117-26. [PMID: 25845627 DOI: 10.1016/j.conb.2015.03.009] [Citation(s) in RCA: 111] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2015] [Revised: 03/18/2015] [Accepted: 03/18/2015] [Indexed: 12/20/2022]
Abstract
With 302 neurons in the adult Caenorhabditis elegans nervous system, it should be possible to build models of complex behaviors spanning sensory input to motor output. The logic of the motor circuit is an essential component of such models. Advances in physiological, anatomical, and neurogenetic analysis are revealing a surprisingly complex signaling network in the worm's small motor circuit. We are progressing towards a systems level dissection of the network of premotor interneurons, motor neurons, and muscle cells that move the animal forward and backward in its environment.
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Affiliation(s)
- Mei Zhen
- Lunenfeld-Tanenbaum Research Institute, Mount Sinai Hospital, Toronto, ON, Canada M5G 1X5; Department of Molecular Genetics, University of Toronto, Toronto, ON, Canada M5S 1A8; Department of Physiology, University of Toronto, Toronto, ON, Canada M5S 1A8.
| | - Aravinthan D T Samuel
- Center for Brain Science, Department of Physics, Harvard University, Cambridge, MA 02138, United States.
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23
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Pavlovic DM, Vértes PE, Bullmore ET, Schafer WR, Nichols TE. Stochastic blockmodeling of the modules and core of the Caenorhabditis elegans connectome. PLoS One 2014; 9:e97584. [PMID: 24988196 PMCID: PMC4079667 DOI: 10.1371/journal.pone.0097584] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2013] [Accepted: 04/21/2014] [Indexed: 02/02/2023] Open
Abstract
Recently, there has been much interest in the community structure or mesoscale organization of complex networks. This structure is characterised either as a set of sparsely inter-connected modules or as a highly connected core with a sparsely connected periphery. However, it is often difficult to disambiguate these two types of mesoscale structure or, indeed, to summarise the full network in terms of the relationships between its mesoscale constituents. Here, we estimate a community structure with a stochastic blockmodel approach, the Erdős-Rényi Mixture Model, and compare it to the much more widely used deterministic methods, such as the Louvain and Spectral algorithms. We used the Caenorhabditis elegans (C. elegans) nervous system (connectome) as a model system in which biological knowledge about each node or neuron can be used to validate the functional relevance of the communities obtained. The deterministic algorithms derived communities with 4-5 modules, defined by sparse inter-connectivity between all modules. In contrast, the stochastic Erdős-Rényi Mixture Model estimated a community with 9 blocks or groups which comprised a similar set of modules but also included a clearly defined core, made of 2 small groups. We show that the "core-in-modules" decomposition of the worm brain network, estimated by the Erdős-Rényi Mixture Model, is more compatible with prior biological knowledge about the C. elegans nervous system than the purely modular decomposition defined deterministically. We also show that the blockmodel can be used both to generate stochastic realisations (simulations) of the biological connectome, and to compress network into a small number of super-nodes and their connectivity. We expect that the Erdős-Rényi Mixture Model may be useful for investigating the complex community structures in other (nervous) systems.
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Affiliation(s)
- Dragana M. Pavlovic
- Department of Statistics and Warwick Manufacturing Group, University of Warwick, Coventry, United Kingdom
| | - Petra E. Vértes
- Brain Mapping Unit, Behavioural and Clinical Neuroscience Institute, Department of Psychiatry, University of Cambridge, Cambridge, United Kingdom
| | - Edward T. Bullmore
- Brain Mapping Unit, Behavioural and Clinical Neuroscience Institute, Department of Psychiatry, University of Cambridge, Cambridge, United Kingdom
- GlaxoSmithKline, Clinical Unit Cambridge, Addenbrooke's Hospital, Cambridge, United Kingdom
- Cambridgeshire and Peterborough NHS Foundation Trust, Cambridge, United Kingdom
| | - William R. Schafer
- Medical Research Council Laboratory of Molecular Biology, Cell Biology Division, Cambridge, United Kingdom
| | - Thomas E. Nichols
- Department of Statistics and Warwick Manufacturing Group, University of Warwick, Coventry, United Kingdom
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24
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Gjorgjieva J, Biron D, Haspel G. Neurobiology of Caenorhabditis elegans Locomotion: Where Do We Stand? Bioscience 2014; 64:476-486. [PMID: 26955070 PMCID: PMC4776678 DOI: 10.1093/biosci/biu058] [Citation(s) in RCA: 69] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Animals use a nervous system for locomotion in some stage of their life cycle. The nematode Caenorhabditis elegans, a major animal model for almost all fields of experimental biology, has long been used for detailed studies of genetic and physiological locomotion mechanisms. Of its 959 somatic cells, 302 are neurons that are identifiable by lineage, location, morphology, and neurochemistry in every adult hermaphrodite. Of those, 75 motoneurons innervate body wall muscles that provide the thrust during locomotion. In this Overview, we concentrate on the generation of either forward- or backward-directed motion during crawling and swimming. We describe locomotion behavior, the parts constituting the locomotion system, and the relevant neuronal connectivity. Because it is not yet fully understood how these components combine to generate locomotion, we discuss competing hypotheses and models.
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Affiliation(s)
- Julijana Gjorgjieva
- Julijana Gjorgjieva is a postdoctoral research fellow at the Center for Brain Science of Harvard University, in Cambridge, Massachusetts. She uses theoretical and numerical tools to understand how developing neural circuits wire to perform a particular function, from the mammalian visual system to the motor system of small invertebrates. David Biron is a physicist at the University of Chicago, Illinois. He studies the sleep of the roundworm Caenorhabditis elegans and related problems in biological physics. Gal Haspel ( ) is a neuroethologist at the New Jersey Institute of Technology, in Newark. He studies the activity, connectivity and recovery from injury of the neuronal network that underlie locomotion in the nematode Caenorhabditis elegans
| | - David Biron
- Julijana Gjorgjieva is a postdoctoral research fellow at the Center for Brain Science of Harvard University, in Cambridge, Massachusetts. She uses theoretical and numerical tools to understand how developing neural circuits wire to perform a particular function, from the mammalian visual system to the motor system of small invertebrates. David Biron is a physicist at the University of Chicago, Illinois. He studies the sleep of the roundworm Caenorhabditis elegans and related problems in biological physics. Gal Haspel ( ) is a neuroethologist at the New Jersey Institute of Technology, in Newark. He studies the activity, connectivity and recovery from injury of the neuronal network that underlie locomotion in the nematode Caenorhabditis elegans
| | - Gal Haspel
- Julijana Gjorgjieva is a postdoctoral research fellow at the Center for Brain Science of Harvard University, in Cambridge, Massachusetts. She uses theoretical and numerical tools to understand how developing neural circuits wire to perform a particular function, from the mammalian visual system to the motor system of small invertebrates. David Biron is a physicist at the University of Chicago, Illinois. He studies the sleep of the roundworm Caenorhabditis elegans and related problems in biological physics. Gal Haspel ( ) is a neuroethologist at the New Jersey Institute of Technology, in Newark. He studies the activity, connectivity and recovery from injury of the neuronal network that underlie locomotion in the nematode Caenorhabditis elegans
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25
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Cuellar C, Trejo A, Linares P, Delgado-Lezama R, Jiménez-Estrada I, Abyazova L, Baltina T, Manjarrez E. Spinal neurons bursting in phase with fictive scratching are not related to spontaneous cord dorsum potentials. Neuroscience 2014; 266:66-79. [DOI: 10.1016/j.neuroscience.2014.02.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2013] [Revised: 01/17/2014] [Accepted: 02/03/2014] [Indexed: 01/14/2023]
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26
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Can simple rules control development of a pioneer vertebrate neuronal network generating behavior? J Neurosci 2014; 34:608-21. [PMID: 24403159 DOI: 10.1523/jneurosci.3248-13.2014] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
How do the pioneer networks in the axial core of the vertebrate nervous system first develop? Fundamental to understanding any full-scale neuronal network is knowledge of the constituent neurons, their properties, synaptic interconnections, and normal activity. Our novel strategy uses basic developmental rules to generate model networks that retain individual neuron and synapse resolution and are capable of reproducing correct, whole animal responses. We apply our developmental strategy to young Xenopus tadpoles, whose brainstem and spinal cord share a core vertebrate plan, but at a tractable complexity. Following detailed anatomical and physiological measurements to complete a descriptive library of each type of spinal neuron, we build models of their axon growth controlled by simple chemical gradients and physical barriers. By adding dendrites and allowing probabilistic formation of synaptic connections, we reconstruct network connectivity among up to 2000 neurons. When the resulting "network" is populated by model neurons and synapses, with properties based on physiology, it can respond to sensory stimulation by mimicking tadpole swimming behavior. This functioning model represents the most complete reconstruction of a vertebrate neuronal network that can reproduce the complex, rhythmic behavior of a whole animal. The findings validate our novel developmental strategy for generating realistic networks with individual neuron- and synapse-level resolution. We use it to demonstrate how early functional neuronal connectivity and behavior may in life result from simple developmental "rules," which lay out a scaffold for the vertebrate CNS without specific neuron-to-neuron recognition.
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27
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Cohen N, Sanders T. Nematode locomotion: dissecting the neuronal-environmental loop. Curr Opin Neurobiol 2014; 25:99-106. [PMID: 24709607 DOI: 10.1016/j.conb.2013.12.003] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2013] [Revised: 11/01/2013] [Accepted: 12/05/2013] [Indexed: 10/25/2022]
Abstract
With a fully reconstructed and extensively characterized neural circuit, the nematode Caenorhabditis elegans is a promising model system for integrating our understanding of neuronal, circuit and whole-animal dynamics. Fundamental to addressing this challenge is the need to consider the tight neuronal-environmental coupling that allows the animal to survive and adapt to changing conditions. Locomotion behaviors are affected by environmental variables both at the biomechanical level and via adaptive sensory responses that drive and modulate premotor and motor circuits. Here we review significant advances in our understanding of proprioceptive control of locomotion, and more abstract models of spatial orientation and navigation. The growing evidence of the complexity of the underlying circuits suggests that the intuition gained is but the first step in elucidating the secrets of neural computation in this relatively simple system.
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Affiliation(s)
- Netta Cohen
- School of Computing, University of Leeds, Leeds LS2 9JT, United Kingdom.
| | - Tom Sanders
- School of Computing, University of Leeds, Leeds LS2 9JT, United Kingdom
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28
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Haspel G, O'Donovan MJ. A connectivity model for the locomotor network of Caenorhabditis elegans. WORM 2013; 1:125-8. [PMID: 24058836 PMCID: PMC3670228 DOI: 10.4161/worm.19392] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
Abstract
Recently, we described a new method for representing and analyzing the connectivity of a motoneuronal network. We used it to deduce a connectivity model for the neuromuscular network that generates locomotion in the nematode Caenorhabditis elegans. The network regulates muscle contraction and for this reason we used the location or function of body wall muscles to map every element (neuron or muscle cell) in a new framework, namely the peri-motor space. The previously published connectivity data for C. elegans locomotion network are incomplete; in particular, the connectivity of motoneurons in the posterior half of the animal is missing or partial. When we analyzed the connectivity data for motoneurons in the anterior half, we detected repeating patterns which we named iterativity. We analyzed the iterativity of each class of motoneuron and statistically validated that it is higher than expected by chance. We could then extrapolate the iteration into the posterior half. Here we will explain the new terms and elaborate on the process of analysis and the features of the new connectivity model.
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Affiliation(s)
- Gal Haspel
- Section on Developmental Neurobiology; National Institute of Neurological Disorders and Stroke; National Institutes of Health; Bethesda, MD USA
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29
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Nagy S, Wright C, Tramm N, Labello N, Burov S, Biron D. A longitudinal study of Caenorhabditis elegans larvae reveals a novel locomotion switch, regulated by G(αs) signaling. eLife 2013; 2:e00782. [PMID: 23840929 PMCID: PMC3699835 DOI: 10.7554/elife.00782] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2013] [Accepted: 05/28/2013] [Indexed: 11/25/2022] Open
Abstract
Despite their simplicity, longitudinal studies of invertebrate models are rare. We thus sought to characterize behavioral trends of Caenorhabditis elegans, from the mid fourth larval stage through the mid young adult stage. We found that, outside of lethargus, animals exhibited abrupt switching between two distinct behavioral states: active wakefulness and quiet wakefulness. The durations of epochs of active wakefulness exhibited non-Poisson statistics. Increased Gαs signaling stabilized the active wakefulness state before, during and after lethargus. In contrast, decreased Gαs signaling, decreased neuropeptide release, or decreased CREB activity destabilized active wakefulness outside of, but not during, lethargus. Taken together, our findings support a model in which protein kinase A (PKA) stabilizes active wakefulness, at least in part through two of its downstream targets: neuropeptide release and CREB. However, during lethargus, when active wakefulness is strongly suppressed, the native role of PKA signaling in modulating locomotion and quiescence may be minor. DOI:http://dx.doi.org/10.7554/eLife.00782.001 The roundworm C. elegans is a key model organism in neuroscience. It has a simple nervous system, made up of just 302 neurons, and was the first multicellular organism to have its genome fully sequenced. The lifecycle of C. elegans begins with an embryonic stage, followed by four larval stages and then adulthood, and worms can progress through this cycle in only three days. However, relatively little is known about how the behaviour of the worms varies across these distinct developmental phases. The body wall of C. elegans contains pairs of muscles that extend along its length, and when waves of muscle contraction travel along its body, the worm undergoes a sinusoidal pattern of movement. A signalling cascade involving a molecule called protein kinase A is thought to help control these movements, and upregulation of this cascade has been shown to increase locomotion. Now, Nagy et al. have analysed the movement of C. elegans during these different stages of development. This involved developing an image processing tool that can analyze the position and posture of a worm’s body in each of three million (or more) images per day. Using this tool, which is called PyCelegans, Nagy et al. identified two behavioral macro-states in one of the larval forms of C. elegans: these states, which can persist for hours, are referred to as active wakefulness and quiet wakefulness. During periods of active wakefulness, the worms spent most (but not all) of their time moving forwards; during quiet wakefulness, they remained largely still. The worms switched abruptly between these two states, and the transition seemed to be regulated by PKA signaling. By using PyCelegans to compare locomotion in worms with mutations in genes encoding various components of this pathway, Nagy et al. showed that mutants with increased PKA activity spent more time in a state of active wakefulness, while the opposite was true for worms with mutations that reduced PKA activity. In addition to providing new insights into the control of locomotion in C. elegans, this study has provided a new open-source PyCelegans suite of tools, which are available to be extended and adapted by other researchers for new uses. DOI:http://dx.doi.org/10.7554/eLife.00782.002
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Affiliation(s)
- Stanislav Nagy
- Institute for Biophysical Dynamics, University of Chicago , Chicago , United States
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Izquierdo EJ, Beer RD. Connecting a connectome to behavior: an ensemble of neuroanatomical models of C. elegans klinotaxis. PLoS Comput Biol 2013; 9:e1002890. [PMID: 23408877 PMCID: PMC3567170 DOI: 10.1371/journal.pcbi.1002890] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2012] [Accepted: 12/03/2012] [Indexed: 11/23/2022] Open
Abstract
Increased efforts in the assembly and analysis of connectome data are providing new insights into the principles underlying the connectivity of neural circuits. However, despite these considerable advances in connectomics, neuroanatomical data must be integrated with neurophysiological and behavioral data in order to obtain a complete picture of neural function. Due to its nearly complete wiring diagram and large behavioral repertoire, the nematode worm Caenorhaditis elegans is an ideal organism in which to explore in detail this link between neural connectivity and behavior. In this paper, we develop a neuroanatomically-grounded model of salt klinotaxis, a form of chemotaxis in which changes in orientation are directed towards the source through gradual continual adjustments. We identify a minimal klinotaxis circuit by systematically searching the C. elegans connectome for pathways linking chemosensory neurons to neck motor neurons, and prune the resulting network based on both experimental considerations and several simplifying assumptions. We then use an evolutionary algorithm to find possible values for the unknown electrophsyiological parameters in the network such that the behavioral performance of the entire model is optimized to match that of the animal. Multiple runs of the evolutionary algorithm produce an ensemble of such models. We analyze in some detail the mechanisms by which one of the best evolved circuits operates and characterize the similarities and differences between this mechanism and other solutions in the ensemble. Finally, we propose a series of experiments to determine which of these alternatives the worm may be using.
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Wen Q, Po MD, Hulme E, Chen S, Liu X, Kwok SW, Gershow M, Leifer AM, Butler V, Fang-Yen C, Kawano T, Schafer WR, Whitesides G, Wyart M, Chklovskii DB, Zhen M, Samuel ADT. Proprioceptive coupling within motor neurons drives C. elegans forward locomotion. Neuron 2012; 76:750-61. [PMID: 23177960 PMCID: PMC3508473 DOI: 10.1016/j.neuron.2012.08.039] [Citation(s) in RCA: 165] [Impact Index Per Article: 13.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/27/2012] [Indexed: 01/29/2023]
Abstract
Locomotion requires coordinated motor activity throughout an animal's body. In both vertebrates and invertebrates, chains of coupled central pattern generators (CPGs) are commonly evoked to explain local rhythmic behaviors. In C. elegans, we report that proprioception within the motor circuit is responsible for propagating and coordinating rhythmic undulatory waves from head to tail during forward movement. Proprioceptive coupling between adjacent body regions transduces rhythmic movement initiated near the head into bending waves driven along the body by a chain of reflexes. Using optogenetics and calcium imaging to manipulate and monitor motor circuit activity of moving C. elegans held in microfluidic devices, we found that the B-type cholinergic motor neurons transduce the proprioceptive signal. In C. elegans, a sensorimotor feedback loop operating within a specific type of motor neuron both drives and organizes body movement.
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Affiliation(s)
- Quan Wen
- Department of Physics and Center for Brain Science, Harvard University, Cambridge, MA 02138, USA.
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