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Training sensory-motor behavior in the connectome of an artificial C. elegans

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Abstract

The C. elegans nematode worm is a small well-known creature, intensely studied for decades. Its entire morphology has been mapped cell-by-cell, including its 302 neuron connectome. The connectome is a synaptic wiring diagram that also specifies neurotransmitters and junction types. It does not however specify the synaptic connection strengths. It is believed that measuring these must be done in live specimens, requiring emerging or yet to be developed techniques. Without the connection strengths, it is not known how the nematode's nervous system produces behaviors. Discovering these strengths as a set of weights is a challenging and important problem: an artificial worm embodying the connectome and trained to perform a set of behaviors taken from measurements of the actual C. elegans would behave realistically in its environment. This is a crucial step toward creating a functional artificial creature. Indeed, knowing the artificial weights might cast light on the actual ones. In this project a genetic algorithm was used to train the entire connectome, a large space of 3680 synapse weights, to learn behaviors defined as sensory-motor sequences. It was found that utilizing the topology of the connectome for local optimization and crossover significantly boosts the performance of the genetic algorithm. Using a network of artificial neurons, random sequences involving the entire connectome were successfully trained. Additionally, for locomotion training, sinusoidal body postures were observed when sensory touch neurons were stimulated. Locomotion training was done using a Fourier Transform fitness function. Finally, using the NEURON tool to simulate a biologically higher fidelity network, the pharyngeal assembly of neurons was successfully trained.

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... The simulation of locomotion in C. elegans has been a common topic of research in recent years. The most common models are those based either on central pattern generators [7], oscillators [8] or artificial neural networks [9]- [12]. Previous research has considered chemosensory locomotion and behaviour, by either training a dynamic neural network to control muscle contraction in response to a chemical gradient [9], [11] or training an artificial neural network to produce the probability of forward motion, pirouette or rest [10]. ...
... To address the problem of unknown parameters, variables and modulation pathways, an evolutionary algorithm (EA) has been developed to estimate the values of the synaptic conductances and whether they produce an excitatory or inhibitory synapse. Although there are and have been previous attempts to use EAs to train the entire connectome to respond to specific stimuli [12] there is still no definitive answer into what are the parameters, and what might be missing, to fully simulate C. elegans behaviour. ...
... In this particular case, it is assumed that all neurons share the same spiking model. Even though C. elegans is thought to have no spiking neurons [33], if the output current that reaches the muscles is comparable to that produced by non-spiking models, the assumption of simpler neuron models is valid, as has been shown in similar work [12]. The Izhikevich neural model combines the biologically plausibility of ...
Article
For a considerable time, it has been the goal of computational neuroscientists to understand biological nervous systems. However, the vast complexity of such systems has made it very difficult to fully understand even basic functions such as movement. Because of its small neuron count, the C. elegans nematode offers the opportunity to study a fully described connectome and attempt to link neural network activity to behaviour. In this paper a simulation of the neural network in C. elegans that responds to chemical stimulus is presented and a consequent realistic head movement demonstrated. An evolutionary algorithm (EA) has been utilised to search for estimates of the values of the synaptic conductances and also to determine whether each synapse is excitatory or inhibitory in nature. The chemotaxis neural network was designed and implemented, using the parameterization obtained with the EA, on the Si elegans platform a state-of-the-art hardware emulation platform specially designed to emulate the C. elegans nematode.
... Modeling the nervous system of C. elegans involves two fundamental stages [59]: one relative to the modeling of the neuronal connectivity (connectome) and the other relative to the modeling of the neuronal dynamics. Nowadays, the vast majority of modeling works on C. elegans nervous system employ the well-established connectome but they do not take into account the specificities of the neuronal dynamics [59][60][61][62][63][64][65][66][67][68][69]. Typically, these works rather Table 4. Classification of the three types of non-spiking neurons in C. elegans, according to their current-voltage relationships. ...
... Actually, the connectome does not unveil such information [71]. To address that issue, some computational studies [60,62,64,[66][67][68] adopt an evolutionary approach in which the algorithm determines both the strength and nature of connections in order to obtain observable, realistic worm behavior. In such studies, the functional circuits studied are made up of identical neuron model parameters irrelevant to characterize the heterogeneity of C. elegans neurons and to represent acceptably their behavior (e.g. the homogeneous Izhikevich spiking model [72] is considered in [64,66], or the Hindmarsh-Rose spiking model in [68]). ...
... To address that issue, some computational studies [60,62,64,[66][67][68] adopt an evolutionary approach in which the algorithm determines both the strength and nature of connections in order to obtain observable, realistic worm behavior. In such studies, the functional circuits studied are made up of identical neuron model parameters irrelevant to characterize the heterogeneity of C. elegans neurons and to represent acceptably their behavior (e.g. the homogeneous Izhikevich spiking model [72] is considered in [64,66], or the Hindmarsh-Rose spiking model in [68]). Therefore, even if the macroscopic behavior of C. elegans is accurately reproduced, the results on the strength and nature of neuron connections may not be biologically adequate. ...
Article
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Unlike spiking neurons which compress continuous inputs into digital signals for transmitting information via action potentials, non-spiking neurons modulate analog signals through graded potential responses. Such neurons have been found in a large variety of nervous tissues in both vertebrate and invertebrate species, and have been proven to play a central role in neuronal information processing. If general and vast efforts have been made for many years to model spiking neurons using conductance-based models (CBMs), very few methods have been developed for non-spiking neurons. When a CBM is built to characterize the neuron behavior, it should be endowed with generalization capabilities ( i.e . the ability to predict acceptable neuronal responses to different novel stimuli not used during the model’s building). Yet, since CBMs contain a large number of parameters, they may typically suffer from a lack of such a capability. In this paper, we propose a new systematic approach based on multi-objective optimization which builds general non-spiking models with generalization capabilities. The proposed approach only requires macroscopic experimental data from which all the model parameters are simultaneously determined without compromise. Such an approach is applied on three non-spiking neurons of the nematode Caenorhabditis elegans ( C. elegans ), a well-known model organism in neuroscience that predominantly transmits information through non-spiking signals. These three neurons, arbitrarily labeled by convention as RIM, AIY and AFD, represent, to date, the three possible forms of non-spiking neuronal responses of C. elegans .
... Indeed, such information is not revealed by the connectome (Kopell et al., 2014) and is of crucial importance to understand the flow of information within the nematode's nervous system (Bargmann & Marder, 2013). Some computational works (Costalago-Meruelo et al., 2018;Lanza et al., 2021;Olivares et al., 2019;Portegys, 2015;Wicks et al., 1996) estimate the synaptic polarity using an evolutionary approach in which the algorithm determines both the nature and the strength of connections to obtain observable, realistic worm behavior. ...
... However, the networks studied are composed of neuron models that are not representative of the C. elegans neuron dynamics. For instance, Portegys (2015), Costalago-Meruelo et al. (2018) and Lanza et al. (2021) consider a homogeneous spiking model for the entire network although the C. elegans neurons are highly heterogeneous and contain non-spiking neurons (Goodman et al., 1998). Therefore, even if the macroscopic behavior of C. elegans is successfully reproduced, the results on the synaptic polarity and their strength may not be biologically adequate. ...
Article
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Due to the ubiquity of spiking neurons in neuronal processes, various simple spiking neuron models have been proposed as an alternative to conductance-based models (a.k.a. Hodgkin-Huxley–type models), known to be computationally expensive and difficult to treat mathematically. However, to the best of our knowledge, there is no equivalent in the literature of a simple and lightweight model for describing the voltage behavior of nonspiking neurons, which also are ubiquitous in a large variety of nervous tissues in both vertebrate and invertebrate species and play a central role in information processing. This letter proposes a simple model that reproduces the experimental qualitative behavior of known types of nonspiking neurons. The proposed model, which differs fundamentally from classic simple spiking models unable to characterize nonspiking dynamics due to their intrinsic structure, is derived from the bifurcation study of conductance-based models of nonspiking neurons. Since such neurons display a high sensitivity to noise, the model aims at capturing the experimental distribution of single-neuron responses rather than perfectly replicating a single given experimental voltage trace. We show that such a model can be used as a building block for realistic simulations of large nonspiking neuronal networks and is endowed with generalization capabilities, granted by design.
... À des fins de modélisation de ses circuits neuronaux, Kim et al. (2019) affirment la nécéssité de prendre en compte : (i) la connectivité biologique du ver, et (ii) la singularité et la richesse de la dynamique neuronale de C. elegans. Actuellement, la très grande majorité des travaux de modélisation prend en compte le connectome établit par ) ou Varshney et al. (2011 mais, à notre connaissance, aucun ne prend en compte la spécificité neuronale du ver (Wicks et al., 1996;Sakata et Shingai, 2004;Rakowski et al., 2013;Kunert et al., 2014;Portegys, 2015;Kunert et al., 2017;Costalago-Meruelo et al., 2018;Olivares et al., 2019;Kim et al., 2019;Lanza et al., 2021;Maertens et al., 2021). En effet, ces travaux considèrent, d'une part, un unique modèle de neurone pour l'ensemble du réseau (alors que les neurones de C. elegans exhibent, au contraire, une grande diversité de comportement) et, d'autre part, un modèle qui ne représente pas de façon adéquate le comportement neuronal observé expérimentalement (en considérant par exemple des modèles spikings). ...
... Or, de telles informations sont cruciales pour comprendre la manière dont le flot d'information circule à travers son cerveau (Bargmann et . En ce sens, et afin de les obtenir, de nombreux travaux computationnels (Wicks et al., 1996;Rakowski et al., 2013;Portegys, 2015;Costalago-Meruelo et al., 2018;Olivares et al., 2019;Lanza et al., 2021) 3.5. Des implications en modélisation procèdent comme suit : un réseau neuronal associé à un comportement est modélisé, i.e. qu'à chaque neurone est assigné un modèle mathématique, couplé aux autres selon le connectome biologique à travers des fonctions dites de couplage. ...
Thesis
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Cette thèse est consacrée à la modélisation et à l'étude de la dynamique des neurones non-spikings, en particulier du ver Caenorhabditis elegans (C. elegans). Ce ver présente l'avantage d'avoir un système nerveux relativement simple et un connectome parfaitement établit (302 neurones et environ 7000 connexions synaptiques).Une première partie est consacrée au développement de modèles à base de conductance (MBC) reproduisant le comportement des voltages expérimentaux de trois neurones (RIM, AIY et AFD) de C. elegans. Ces trois neurones sont représentatifs de la diversité neuronale non-spiking actuelle de C. elegans. De plus, une méthodologie est proposée permettant d'émettre des hypothèses sur l'existence et la nature des canaux ioniques présents dans chacun des neurones.Une deuxième partie propose une méthode d'optimisation multi-objectif dotant de façon systématique les MBCs d'une capacité de généralisation (i.e. la capacité du modèle à prédire des réponses neuronales associées à des stimuli qui n'ont pas été utilisés durant la construction du modèle). Cette méthode se base sur la structure de bifurcation des neurones non-spikings qui est alors mise en évidence et étudiée.Dans une troisième partie, nous présentons une équation générique pour les neurones de C. elegans. Cette équation permet la génération d'un ensemble de modèles aux caractéristiques électrophysiologiques différentes, adapté à un très grand nombre de neurones de C. elegans. Une étude mathématique de cette équation générique est réalisée à partir de laquelle des résultats sur la dynamique des neurones RIM, AIY et AFD sont déduits.Une quatrième partie propose la construction d'un modèle simple 1-D capable de reproduire les comportements qualitatifs de neurones non-spikings observés expérimentalement. Cette construction se base sur les structures de bifurcations que peuvent admettre les neurones non-spikings. Un tel modèle est montré pour être très peu coûteux en temps de construction et de simulation, offrant ainsi la possibilité de considérer la simulation et l'étude de réseaux de neurones de grandes tailles. De plus, une analyse mathématique de ses points d'équilibres et de ses bifurcations est réalisée.Enfin, une ouverture sur la mise en réseau des modèles construits dans les parties précédentes est présentée, ainsi que des résultats préliminaires concernant l'impact du réseau sur la dynamique intrinsèque d'un neurone non-spiking.
... Geliştirilen biyomekanik modellerden biri de gevşek bağlanmış yuvarlak parçacıkların normalde olandan daha fazla güce ve torka maruz kaldığı ortamda bulunan, lokomotif davranışı dönüşleriyle beraber, duyu ve davranış faktörlerini hesaba katmadan vurgulayan modeldir (13). Portegys sinir haritasının salınım yollarını araştırmaya yönelik bir evrimsel algoritma kullanmıştır (14). Kunert ve arkadaşları, salınımların bazı motor nöronlar uyarıldığında gerçekleştiğini gösteren nöral ağ modelini sunmuşlardır (15). ...
Article
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Neuroscience tries to understand the structure and functions of the human brain, which is made up of millions of neurons and billions of synapses. It is not possible to create and examine a model for such an advanced system in a laboratory environment. For more than two decades, Caernohabditis elegans (C. elegans) has come to the fore as a useful model for understanding the behavior of neural networks, due to its characteristics similar to the human nervous system and its easily observable structure. The created models facilitate quantitative analysis of behavior and neural activities and understanding the functioning of neural networks. Thus, research can be done at both the cell and the organism level. Since the purpose of neuroscience studies is to understand how the information transmitted from sensory neurons under the influence turns into an output response by motor neurons and to understand the role of the effect in making these responses a repetitive, consistent behavior; C. elegans, which has the advantage of being the first animal whose genome has been completely sequenced, is easy to observe with different techniques, and sheds light on the mammalian neural-behavioral pattern, has been used quite efficiently in these studies. In these researches, it is thought that there has been an increase after the 2000s, depending on the developments related to the medium and characterization. Research in this area has increased exponentially from the early 2000s until 2021. When neuroscience studies with C. elegans were examined by country, it was seen that countries such as America and Germany were the leading ones. While 67 of the 245 publications made in SCI-Expanded journals on this subject were neuroscience researches, 40 of them were made by researchers working in multidisciplinary fields. In this study, the general characteristics of C. elegans and its place in neuros-cience research will be mentioned and the distribution of these studies by years and countries will be evaluated. ÖZET Sinirbilim, milyonlarca nöron ve milyarlarca sinapstan oluşan insan beyninin yapı ve fonksiyonlarını anlamaya çalışır. Laboratuvar ortamında böylesine gelişmiş bir sistem için model oluşturmak ve incelemek mümkün değil-dir. Yirmi yılı aşkın süredir, insan sinir sistemine benzer özellikleri ve kolay incelenebilir yapısı nedeniyle Caerno-habditis elegans (C. elegans), nöral ağların davranışını anlamak için faydalı bir model olarak öne çıkmaktadır. Oluşturulan modeller, davranış ve nöral aktivitelerin nicel analizlerinin yapılmasını, sinir ağlarının işleyişinin anlaşılmasını kolaylaştırır. Böylece hem hücre hem de organizma düzeyinde araştırmalar yapılabilmektedir. Si-nirbilim çalışmalarının amacı, etki sonrası duyu nöronlarından aktarılan bilginin, motor nöronlar tarafından nasıl bir tepkiye dönüştüğünü anlamak; bu tepkilerin tekrarlı, tutarlı bir davranış haline gelmesinde etkinin rolünü kavramaktır. Genomu haritalandırılmış ilk hayvan olma avantajına sahip, farklı tekniklerle gözlenmesi mümkün ve kolay olan, memeli nöral-davranışsal örgüye ışık tutan C. elegans bu araştırmalarda oldukça verimli kullanılmaktadır. Bu araştırmalarda 2000'li yılların sonrasında, besi yeri ve karakterizasyona bağlı gelişmelere de bağlı olarak artış yaşandığı düşünülmektedir. Bu alandaki araştırmalar 2000'li yılların başından, 2021'e kadar katlanarak artmıştır. C. elegans ile yapılan sinirbilim araştırmaları ülkelere göre incelendiğinde, başı Amerika ve Almanya gibi ülkelerin çektiği görülmüştür. Bu konuda SCI-Expanded dergilerde yapılan 245 yayının 67'sini sinirbilim araştırmacıları oluştururken, 40'ını multidisipliner alanlarda çalışan araştırmacılar gerçekleş-tirmiştir. Bu çalışmada, C. elegans'ın genel özelliklerine ve sinirbilim araştırmalarındaki yerine değinilecek ve bu araştırmaların yıllara ve ülkelere göre dağılımları değerlendirilecektir.
... Neuroscientists are expending effort to solve the mysteries and even try to copy brain processes for artificial intelligence or create a brain in silico. The connectome for C. elegans is well studied which allows the simulation of its complete nervous system that consists of 302 neurons which are one third of all the cells in this organism (Portegys, 2015;Szigeti et al., 2014;White, 2005). More complex brains like those of reptiles, birds and mammals are far away to be completed and therefore simulated. ...
Article
One of the main goals in neuroscience is to understand the underlying neural circuit that governs behavior. Thanks to recent advances in experimental approaches and new technologies, we are a step closer to answering this question. One of the main promising approaches is to look directly into the brain in vivo. By using two-photon microscopy and genetically encoded calcium indicators, it is now possible to longitudinally observe the dynamics of neuronal networks in awake behaving animals under head-fixed conditions. Additionally mice can be exposed to a myriad of virtual realities that provides them with more realistic conditions in which they can control sensory stimuli. Neural recordings in head-restrained but behaving animals allow us to present controlled and realistic stimuli as well as simultaneous measurements of behavioral variables. Consequently this leads to better understanding of neural correlates of behavior and stimulus. In my thesis, I use a novel tactile virtual reality setup in which animals were freely running and whisking along a wall. I measured neural activity of different neural populations particularly in somatosensory cortex as well as hippocampus to understand how brain codes information under different motor states such as locomotion.
... This approach also works to characterize connectomics in small nervous systems such as that of the nematode Caenorhabditis elegans (302 neurons). In one case (Portegys, 2015), a hybrid genetic algorithm was used to weight synaptic connections in the C. elegans nervous system. There are over 3,000 synaptic connections between these neurons. ...
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The construction of an embryo from a single cell precursor is a highly complex process. Evolutionary emergence of the first embryos is even more complex, and involves both a transition to multicellularity along with the establishment of developmental mechanisms. We propose that embryogenesis relies on a community of cells conforming to a regulatory model of emergent multicellularity. This model draws together multiple threads in the scientific literature, from complexity theory to cybernetics, and from thermodynamic entropy to artificial life. All of these strands come together to inform a model of goal-oriented regulation for emergent structures in early life. This is an important step in the evolution of early life, as well as the emergence of complex life in the earliest habitats. Our model, called the cybernetic embryo, allows for a systems-level view of the embryogenetic process.
... Broadly, these efforts (i) attempt to model the generation of locomotion within the nervous system alone (e.g. [5,6,7,8,9,10,11,12]), (ii) model the biomechanics of the musculature/body alone [3,13,14,15,16,17,18,19], or (iii) build an integrated model for neural and bodily dynamics [20,21,22,23,24]. Most previous modeling efforts have focused on simulating the simple, sinusoidal bodily postures involved in forward locomotion. ...
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We develop a biophysically realistic model of the nematode C. elegans that includes: (i) its muscle structure and activation, (ii) key connectomic activation circuitry, and (iii) a weighted and time-dynamic propioception. In combination, we show that these model components can reproduce the complex waveforms exhibited in C. elegans locomotive behaviors, such as omega turns. We show that weighted, time-dependent synaptic dynamics are necessary for this complex behavior, ultimately revealing key functions that must be executed at the connectomic level. Such dynamics are biologically plausible due to the presence of many neuromodulators which have recently been experimentally implicated in complex behaviors such as omega turns. This is the first integrated neuromechanical model to reveal a mechanism capable of generating the complex waveforms observed in the behavior of C. elegans, thus providing a mathematical framework for understanding how control decisions must be executed at the connectome level in order to produce the full repertoire of observed behaviors.
... This approach also works to characterize connectomics in small nervous systems such as that of the nematode Caenorhabditis elegans (302 neurons). In one case (Portegys, 2015), a hybrid genetic algorithm was used to weight synaptic connections in the C. elegans nervous system. There are over 3,000 synaptic connections between these neurons. ...
Article
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The construction of an embryo from a single cell precursor is a highly complex process. Evolutionary emergence of the first embryos is even more complex, and involves both a transition to multicellularity along with the establishment of developmental mechanisms. In this chapter, we propose that embryogenesis relies on a community of cells conforming to a regulatory model of emergent multicellularity. This model draws together multiple threads in the scientific literature, from complexity theory to cybernetics, and from thermodynamic entropy to artificial life. All of these strands come together to inform a model of goal-oriented regulation for emergent structures in early life. This is an important step in the evolution of early life, as well as the emergence of complex life in the earliest habitats. Our model, called the cybernetic embryo, allows for a systems-level view of the embryogenetic process.
... Since then, diverse strategies for describing neural events that lead to postural change have been proposed of which only a few are mentioned. Among them are event-driven models consisting of an asynchronous system based on pulse modulation (Claverol et al 1999), compartmental conductancebased models exclusively for muscle cells (Boyle and Cohen 2008), a central pattern generator that drives the forward movement of a physics-based rigid body representation of the nematode (Mailler et al 2010) inspired by (Niebur and Erdös 1991), neuromuscular control systems that rely on a sensory feedback mechanism based on bistable dynamics without the need for a modulatory mechanism except for a proprioceptive response to the physical environment (Boyle et al 2012, Williamson 2012, dynamic neural networks based on a differential evolution algorithm in the head and body with a central pattern generator in between acting on a locomotion model with 12 multi-joint rigid links (Deng and Xu 2014), evolutionary algorithms for the identification of a minimal klinotaxis network (Izquierdo and Beer 2013) and genetic algorithms to train 3680 synaptic weights within the motor connectome to replicate behaviors based on sensorymotor sequences (Portegys 2015) as recently reviewed by (Gjorgjieva et al 2014) and (Izquierdo and Beer 2016). The lack of sufficient electrophysiological and biochemical data continues to fuel the connectome debate on whether the emergence of a certain behavior can be predicted solely from a network analysis (Jabr 2012, Seung 2012) featuring simplistic bistable neurons (Roberts et al 2016) or requires a more detailed description of neural events including other signaling modalities such as neuromodulators (Trojanowski and Raizen 2015) and proprioceptive (Butler et al 2015) or mechanosensory feedback (Bryden andCohen 2004, Karbowski et al 2008). ...
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The neural pathways for touch-induced movement in Caenorhabditis elegans contain six touch receptors, five pairs of interneurons, and 69 motor neurons. The synaptic relationships among these cells have been deduced from reconstructions from serial section electron micrographs, and the roles of the cells were assessed by examining the behavior of animals after selective killing of precursors of the cells by laser microsurgery. This analysis revealed that there are two pathways for touch-mediated movement for anterior touch (through the AVD and AVB interneurons) and a single pathway for posterior touch (via the PVC interneurons). The anterior touch circuitry changes in two ways as the animal matures. First, there is the formation of a neural network of touch cells as the three anterior touch cells become coupled by gap junctions. Second, there is the addition of the AVB pathway to the pre-existing AVD pathway. The touch cells also synapse onto many cells that are probably not involved in the generation of movement. Such synapses suggest that stimulation of these receptors may modify a number of behaviors.
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Living organisms have mechanisms to adapt to various conditions of external environments. If we can realize these mechanisms on the computer, it may be possible to apply methods of biological and biomimetic adaptation to the engineering of artificial machines. This paper focuses on the nematode Caenorhabditis elegans (C. elegans), which has a relatively simple structure and is one of the most studied multicellular organisms. We aim to develop its computer model, artificial C. elegans, to analyze control mechanisms with respect to motion. Although C. elegans processes many kinds of external stimuli, we focused on gentle touch stimulation. The proposed model consists of a neuronal circuit model for motor control that responds to gentle touch stimuli and a kinematic model of the body for movement. All parameters included in the neuronal circuit model are adjusted by using the real-coded genetic algorithm. Also, the neuronal oscillator model is employed in the body model to generate the sinusoidal movement. The motion velocity of the body model is controlled by the neuronal circuit model so as to correspond to the touch stimuli that are received in sensory neurons. The computer simulations confirmed that the proposed model is capable of realizing motor control similar to that of the actual organism qualitatively. By using the artificial organism it may be possible to clarify or predict some characteristics that cannot be measured in actual experiments. With the recent development of computer technology, such a computational analysis becomes a real possibility. The artificial C. elegans will contribute for studies in experimental biology in future, although it is still developing at present.
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Over the past four decades, one of the simplest nervous systems across the animal kingdom, that of the nematode worm Caenorhabditis elegans, has drawn increasing attention. This system is the subject of an intensive concerted effort to understand the behaviour of an entire living animal, from the bottom up and the top down. C. elegans locomotion, in particular, has been the subject of a number of models, but there is as yet no general agreement about the key (rhythm generating) elements. In this paper we investigate the role of one component of the locomotion subsystem, namely the body wall muscles, with a focus on the role of inter-muscular gap junctions. We construct a detailed electrophysiological model which suggests that these muscles function, to a first approximation, as mere actuators and have no obvious rhythm generating role. Furthermore, we show that within our model inter-muscular coupling is too weak to have a significant electrical effect. These results rule out muscles as key generators of locomotion, pointing instead to neural activity patterns. More specifically, the results imply that the reduced locomotion velocity observed in unc-9 mutants is likely to be due to reduced neuronal rather than inter-muscular coupling.
  • Q Wen
  • M D Po
  • E Hulme
  • S Chen
  • X Liu
  • S W Kwok
  • M Gershow
  • A M Leifer
  • V Butler
  • C Fang-Yen
  • T Kawano
  • W R Schafer
  • G Whitesides
  • M Wyart
  • D B Chklovskii
  • M Zhen
  • A D T Samuel
Q. Wen, M.D. Po, E. Hulme, S. Chen, X. Liu, S.W. Kwok, M. Gershow, A.M. Leifer, V. Butler, C. Fang-Yen, T. Kawano, W.R. Schafer, G. Whitesides, M. Wyart, D. B. Chklovskii, M. Zhen, A.D.T. Samuel, Proprioceptive coupling within motor neurons drives C. elegans forward locomotion, Neuron 76 (2012) 750-761.
The connectome debate: is mapping the mind of a worm worth it? Scientific American
  • F Jabr
F. Jabr, The connectome debate: is mapping the mind of a worm worth it? Scientific American, (October 2, 2012).
The Connectome Engine
  • T Busbice
T. Busbice, The Connectome Engine, (2014) 〈www.connectomeengine.com〉.
The connectome debate: is mapping the mind of a worm worth it?
  • F Jabr
F. Jabr, The connectome debate: is mapping the mind of a worm worth it? Scientific American, (October 2, 2012).
Nematode locomotion: dissecting the neuronalenvironmental loop
  • N Cohen
  • T Sanders
N. Cohen, T. Sanders, Nematode locomotion: dissecting the neuronalenvironmental loop, Current Opinion in Neurobiology, 25: pp. 99-106, Fairhall, A. and Sompolinsky, H. (Eds.) (2014) http://dx.doi.org/org/10.1016/j.conb. 2013.12.003.