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      Optimal synaptic signaling connectome for locomotory behavior in Caenorhabditis elegans: Design minimizing energy cost

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      1 , 2 , 3 , 4 , *
      PLoS Computational Biology
      Public Library of Science

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          Abstract

          The detailed knowledge of C. elegans connectome for 3 decades has not contributed dramatically to our understanding of worm’s behavior. One of main reasons for this situation has been the lack of data on the type of synaptic signaling between particular neurons in the worm’s connectome. The aim of this study was to determine synaptic polarities for each connection in a small pre-motor circuit controlling locomotion. Even in this compact network of just 7 neurons the space of all possible patterns of connection types (excitation vs. inhibition) is huge. To deal effectively with this combinatorial problem we devised a novel and relatively fast technique based on genetic algorithms and large-scale parallel computations, which we combined with detailed neurophysiological modeling of interneuron dynamics and compared the theory to the available behavioral data. As a result of these massive computations, we found that the optimal connectivity pattern that matches the best locomotory data is the one in which all interneuron connections are inhibitory, even those terminating on motor neurons. This finding is consistent with recent experimental data on cholinergic signaling in C. elegans, and it suggests that the system controlling locomotion is designed to save metabolic energy. Moreover, this result provides a solid basis for a more realistic modeling of neural control in these worms, and our novel powerful computational technique can in principle be applied (possibly with some modifications) to other small-scale functional circuits in C. elegans.

          Author summary

          Neural connectomes, i.e. neural connectivity maps, are important for understanding the design principles of nervous systems. However, they are not sufficient for understanding network dynamics, which in turn are related to animal’s behavior. To understand behavior, we need additionally to know the type of signaling mediated by neural connections, or simply their polarities (excitation or inhibition). But the determination of these polarities is generally challenging because of the large number of synapses in a typical network. The small nematode Caenorhabditis elegans with 302 neurons is the only animal with the known connectome on a level of single neurons. In this study, we use a powerful and fast computational technique to optimize intrinsic properties of C. elegans network controlling locomotion in order to determine the signaling signs of its connections. As a result, we find that all locomotory interneuron connections are inhibitory, which suggests that this network acts mainly via mutual suppression.

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          Most cited references42

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          Handbook of Stochastic Methods

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            Decision making in recurrent neuronal circuits.

            Decision making has recently emerged as a central theme in neurophysiological studies of cognition, and experimental and computational work has led to the proposal of a cortical circuit mechanism of elemental decision computations. This mechanism depends on slow recurrent synaptic excitation balanced by fast feedback inhibition, which not only instantiates attractor states for forming categorical choices but also long transients for gradually accumulating evidence in favor of or against alternative options. Such a circuit endowed with reward-dependent synaptic plasticity is able to produce adaptive choice behavior. While decision threshold is a core concept for reaction time tasks, it can be dissociated from a general decision rule. Moreover, perceptual decisions and value-based economic choices are described within a unified framework in which probabilistic choices result from irregular neuronal activity as well as iterative interactions of a decision maker with an uncertain environment or other unpredictable decision makers in a social group.
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              Wiring optimization can relate neuronal structure and function.

              We pursue the hypothesis that neuronal placement in animals minimizes wiring costs for given functional constraints, as specified by synaptic connectivity. Using a newly compiled version of the Caenorhabditis elegans wiring diagram, we solve for the optimal layout of 279 nonpharyngeal neurons. In the optimal layout, most neurons are located close to their actual positions, suggesting that wiring minimization is an important factor. Yet some neurons exhibit strong deviations from "optimal" position. We propose that biological factors relating to axonal guidance and command neuron functions contribute to these deviations. We capture these factors by proposing a modified wiring cost function.
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                Author and article information

                Contributors
                Role: Formal analysisRole: MethodologyRole: ResourcesRole: SoftwareRole: Visualization
                Role: ConceptualizationRole: Funding acquisitionRole: MethodologyRole: SupervisionRole: Writing – original draftRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, CA USA )
                1553-734X
                1553-7358
                November 2017
                20 November 2017
                : 13
                : 11
                : e1005834
                Affiliations
                [1 ] Interdisciplinary Centre for Mathematical and Computational Modeling, University of Warsaw, Warsaw, Poland
                [2 ] Mossakowski Medical Research Centre, Polish Academy of Sciences, Warsaw, Poland
                [3 ] Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland
                [4 ] Institute of Applied Mathematics and Mechanics, Department of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland
                Hamburg University, GERMANY
                Author notes

                The authors have declared that no competing interests exist.

                Author information
                http://orcid.org/0000-0001-5560-4723
                Article
                PCOMPBIOL-D-17-00653
                10.1371/journal.pcbi.1005834
                5714387
                29155814
                ed5a6449-c634-4ee3-8724-8430c809415d
                © 2017 Rakowski, Karbowski

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 24 April 2017
                : 19 October 2017
                Page count
                Figures: 14, Tables: 4, Pages: 28
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/501100004281, Narodowe Centrum Nauki;
                Award ID: 2015/17/B/NZ4/02600
                Award Recipient :
                The work was supported by the Polish National Science Centre (NCN) grant no. 2015/17/B/NZ4/02600 (JK). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology and Life Sciences
                Cell Biology
                Cellular Types
                Animal Cells
                Neurons
                Biology and Life Sciences
                Neuroscience
                Cellular Neuroscience
                Neurons
                Biology and Life Sciences
                Cell Biology
                Cellular Types
                Animal Cells
                Neurons
                Interneurons
                Biology and Life Sciences
                Neuroscience
                Cellular Neuroscience
                Neurons
                Interneurons
                Biology and Life Sciences
                Cell Biology
                Cellular Types
                Animal Cells
                Neurons
                Motor Neurons
                Biology and Life Sciences
                Neuroscience
                Cellular Neuroscience
                Neurons
                Motor Neurons
                Research and Analysis Methods
                Experimental Organism Systems
                Model Organisms
                Caenorhabditis Elegans
                Research and Analysis Methods
                Model Organisms
                Caenorhabditis Elegans
                Research and Analysis Methods
                Experimental Organism Systems
                Animal Models
                Caenorhabditis Elegans
                Biology and Life Sciences
                Organisms
                Eukaryota
                Animals
                Invertebrates
                Nematoda
                Caenorhabditis
                Caenorhabditis Elegans
                Biology and Life Sciences
                Neuroscience
                Brain Mapping
                Connectomics
                Biology and Life Sciences
                Anatomy
                Nervous System
                Neuroanatomy
                Connectomics
                Medicine and Health Sciences
                Anatomy
                Nervous System
                Neuroanatomy
                Connectomics
                Biology and Life Sciences
                Neuroscience
                Neuroanatomy
                Connectomics
                Biology and Life Sciences
                Physiology
                Biological Locomotion
                Medicine and Health Sciences
                Physiology
                Biological Locomotion
                Biology and Life Sciences
                Physiology
                Electrophysiology
                Neurophysiology
                Medicine and Health Sciences
                Physiology
                Electrophysiology
                Neurophysiology
                Biology and Life Sciences
                Neuroscience
                Neurophysiology
                Engineering and Technology
                Electrical Engineering
                Electrical Circuits
                Custom metadata
                vor-update-to-uncorrected-proof
                2017-12-04
                All relevant data are within the paper, its Supporting Information file, and are available from (Java code): https://github.com/hpdcj/elegans-simulation; https://github.com/hpdcj/evolutionary-algorithm; https://github.com/hpdcj/elegans-optimisation.

                Quantitative & Systems biology
                Quantitative & Systems biology

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