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A Biologically Accurate 3D Model of the Locomotion of Caenorhabditis Elegans
Abstract and Figures
The nematode Caenorhabditis Elegans has become an important model organism for many areas of biological research including genetics, development, and neurobiology. It is the first organism to have its genome sequenced, complete cell ontogeny determined, and nervous system mapped. With all of the information that is available on this simple organism, C. elegans may also become the first organism to be accurately and completely modeled in silico. In this work we take a step toward this goal by presenting a biologically accurate, 3-dimensional model of C. elegans. This model takes into account many facets of the organism including size, shape, weight distribution, muscle placement, and muscle force. We also explicitly model the environment of the worm to include factors such as contact, friction, inertia, and gravity. We tuned and validated our model using video recordings taken of the worm and show that our model accurately depicts the physics of undulatory locomotion used to forward crawl on an agarose surface. We also present evidence that suggests that the forces applied by the nematode during locomotion are not uniform, but decrease as the wave is propagated from its head to its tail.
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... Previous models assigned the values of parameters by various means [11][12][13][14][24][25][26][27][28] , such as manually 10 or by using an evolutional algorithm 13,26 . However, the distribution of the assigned parameter values was not analyzed. ...
... However, these aspects of motion have already been extensively www.nature.com/scientificreports/ analyzed in previous models [11][12][13][14][24][25][26][27][28] . Incorporating body dynamics models 11,12,[28][29][30][31][32] is certainly required for the further analysis of complex movements such as an omega turn. ...
Caenorhabditis elegans (C. elegans) can produce various motion patterns despite having only 69 motor neurons and 95 muscle cells. Previous studies successfully elucidate the connectome and role of the respective motor neuron classes related to movement. However, these models have not analyzed the distribution of the synaptic and gap connection weights. In this study, we examined whether a motor neuron and muscle network can generate oscillations for both forward and backward movement and analyzed the distribution of the trained synaptic and gap connection weights through a machine learning approach. This paper presents a connectome-based neural network model consisting of motor neurons of classes A, B, D, AS, and muscle, considering both synaptic and gap connections. A supervised learning method called backpropagation through time was adapted to train the connection parameters by feeding teacher data composed of the command neuron input and muscle cell activation. Simulation results confirmed that the motor neuron circuit could generate oscillations with different phase patterns corresponding to forward and backward movement, and could be switched at arbitrary times according to the binary inputs simulating the output of command neurons. Subsequently, we confirmed that the trained synaptic and gap connection weights followed a Boltzmann-type distribution. It should be noted that the proposed model can be trained to reproduce the activity patterns measured for an animal (HRB4 strain). Therefore, the supervised learning approach adopted in this study may allow further analysis of complex activity patterns associated with movements.
... В настоящее время существует несколько теорий, объясняющих работу нейронных контуров управления локомоцией [3][4][5] и хемотаксисом [6][7] нематоды. В том числе предложено несколько компьютерных моделей, имитирующих движение нематоды, работу двигательного нейронного контура [4][5] и управление хемотаксисом [8][9][10][11]. ...
... В настоящее время существует несколько теорий, объясняющих работу нейронных контуров управления локомоцией [3][4][5] и хемотаксисом [6][7] нематоды. В том числе предложено несколько компьютерных моделей, имитирующих движение нематоды, работу двигательного нейронного контура [4][5] и управление хемотаксисом [8][9][10][11]. Однако существующие работы в большей степени сфокусированы на подборе параметров предлагаемых моделей с целью получения наиболее реалистичного поведения, в то время как возможность обучения и адаптации нейронного контура даже не рассматривается. ...
The C. Elegans nematode is currently the only organism, for which the structure of its nervous system is fully known, and the connectome is obtained in the first approximation. However, we still have not understood the working principles of such a simple nervous system. In this paper, we propose a learning control system, which models the work of neural circuits controlling chemotaxis of the C.Elegans nematode. A model of learning logical neurons has been proposed to create learning neural control circuits. Using the 3D-simulator of the nematode, we have conducted a series of successful experiments in training the proposed model. The control system can stably learn an optimal chemotaxis strategy in 1000 cycles on the average. At the same time, we observe a considerable visual likeness between the behavior of the model and the behavior of a real nematode. The results of experiments have shown that the movement function and associated orientation mechanisms of a nematode can be obtained by way of learning only in interaction with the environment. Practically, the results show that the proposed model can be successfully used to control complex objects.
... В настоящее время существует несколько теорий, объясняющих работу нейронного контура управления локомоцией нематоды [2][3][4]. В том числе предложено несколько компьютерных моделей, имитирующих движение нематоды и работу контура [3][4]. Однако существующие работы в большей степени сфокусированы на подборе параметров предлагаемых моделей с целью получения наиболее реалистичного движения, в то время как возможность обучения и адаптации нейронного контура даже не рассматривается. ...
... В настоящее время существует несколько теорий, объясняющих работу нейронного контура управления локомоцией нематоды [2][3][4]. В том числе предложено несколько компьютерных моделей, имитирующих движение нематоды и работу контура [3][4]. Однако существующие работы в большей степени сфокусированы на подборе параметров предлагаемых моделей с целью получения наиболее реалистичного движения, в то время как возможность обучения и адаптации нейронного контура даже не рассматривается. ...
In this paper we propose a learning model of neural circuit controlling locomotion of C. elegans nematode. Using realistic 3D simulator of the nematode, a number of successful computational experiments on proposed model’s learning were performed. It was shown that the control system was stably trained to produce effective undulatory way of forward movement within 100 cycles at average. At the same time significant visual similarity was observed between the way of movement found by a model and used by real biological nematode. Obtained results indicate that neural circuit controlling locomotion is able to learn complex undulatory form of nematode locomotion based only on experience of system’s inter-action with environment, and that proposed model of control system is quite effective and can be used for driving complex objects possessing multiple degrees of freedom.
... Given the importance of locomotion for the worm, there is a likelihood that the worm has multiple, redundant, and overlapping mechanisms for generating and coordinating rhythmic patterns. One of the mechanisms for which there is a growing consensus is proprioception (Tavernarakis et al., 1997;Mailler et al., 2010;Boyle et al., 2012;Cohen et al., 2012;Wen et al., 2012;Fieseler et al., 2018;Izquierdo and Beer, 2018). In this paper, we examined the possibility that multiple intrinsic network rhythmic pattern generators could coordinate through motorneuron gap junctions to produce a traveling wave along the body. ...
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.
... In recent years, there have been several efforts to model the locomotion of the worm in three dimensions. One of the simplest is reported in Mailler et al. (2010), where the worm is represented with a row of cylinders that are interconnected using joints. It is not very different from reported 2D approaches since the cylinders are completely rigid. ...
The Si elegans platform targets the complete virtualization of the nematode Caenorhabditis elegans, and its environment. This paper presents a suite of unified web-based Graphical User Interfaces (GUIs) as the main user interaction point, and discusses their underlying technologies and methods. The user-friendly features of this tool suite enable users to graphically create neuron and network models, and behavioral experiments, without requiring knowledge of domain-specific computer-science tools. The framework furthermore allows the graphical visualization of all simulation results using a worm locomotion and neural activity viewer. Models, experiment definitions and results can be exported in a machine-readable format, thereby facilitating reproducible and cross-platform execution of in silico C. elegans experiments in other simulation environments. This is made possible by a novel XML-based behavioral experiment definition encoding format, a NeuroML XML-based model generation and network configuration description language, and their associated GUIs. User survey data confirms the platform usability and functionality, and provides insights into future directions for web-based simulation GUIs of C. elegans and other living organisms. The tool suite is available online to the scientific community and its source code has been made available.
... The exact timing in the signals varies from model to model, largely due to differences in the timing of stimulation pulses. The works of Mailler et al. [19], Niebur et al. [20] and Bailey et al. [15,16] all agree on the underlying nature of propagating muscle signals and the resulting serpentine motion. These properties may be seen in both the muscle activation signals moving down the length of the animal and in the 3D model itself. ...
The scale of modern neural networks is growing rapidly, with direct hardware implementations providing significant speed and energy improvements over their software counterparts. However, these hardware implementations frequently assume global connectivity between neurons and thus suffer from communication bottlenecks. Such issues are not found in biological neural networks. It should therefore be possible to develop new architectures to reduce the dependence on global communications by considering the connectivity of biological networks. This paper introduces two reconfigurable locally-connected architectures for implementing biologically inspired neural networks in real time. Both proposed architectures are validated using the segmented locomotive model of the C. elegans, performing a demonstration of forwards, backwards serpentine motion and coiling behaviours. Local connectivity is discovered to offer up to a 17.5× speed improvement over hybrid systems that use combinations of local and global infrastructure. Furthermore, the concept of locality of connections is considered in more detail, highlighting the importance of dimensionality when designing neuromorphic architectures. Convolutional Neural Networks are shown to map poorly to locally connected architectures despite their apparent local structure, and both the locality and dimensionality of new neural processing systems is demonstrated as a critical component for matching the function and efficiency seen in biological networks.
Multiple mechanisms contribute to the generation, propagation, and coordination of 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 locomotion behavior can be produced by a chain of network oscillators in the ventral nerve cord. We use a simulation model to demonstrate that a repeating neural circuit identified in the worm's connectome can be chained together to drive forward locomotion on agar in a neuromechanical model of the nematode, 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 match the kinematics of the worm on agar. Analysis of the best solutions reveals that gap junctions between different classes of motoneurons are likely to play key roles in coordinating oscillations along the ventral nerve cord.
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.
One of the most tractable organisms for the study of nervous systems is the nematode Caenorhabditis elegans, whose locomotion in particular has been the subject of a number of models. In this paper we present a first integrated neuro-mechanical
model of forward locomotion. We find that a previous neural model is robust to the addition of a body with mechanical properties,
and that the integrated model produces oscillations with a more realistic frequency and waveform than the neural model alone.
We conclude that the body and environment are likely to be important components of the worm’s locomotion subsystem.
The nematode Caenorhabditis elegans (C elegans), a relatively simple organism in structure, is one of the most well-studied multicellular organisms. In this study, we develop a virtual C. elegans based on the actual nematode to analyze motor control which uses neuronal circuits and muscles. Although C. elegans processes many kinds of external stimuli, we focus on gentle touch stimulation. Virtual C. elegans consists of both a neuronal circuit model for touch-response and a dynamic body model, and is capable of reproducing a series of information processing from stimulation reception to generation of movement. The effectiveness of our model is discussed through simulation results
One of the most tractable organisms for the study of nervous
systems is the nematode Caenorhabditis elegans, whose locomotion in
particular has been the subject of a number of models. In this paper we
present a first integrated neuro-mechanical model of forward locomotion.
We find that a previous neural model is robust to the addition of a
body with mechanical properties, and that the integrated model produces
oscillations with a more realistic frequency and waveform than the neural
model alone. We conclude that the body and environment are likely to
be important components of the worm’s locomotion subsystem.
We develop a model of the undulatory locomotion of nematodes, in particular that of Caenorhabditis elegans, based on mechanics. The model takes into account the most important forces acting on a moving worm and allows the computer simulation of a creeping nematode. These forces are produced by the interior pressure in the liquid-filled body cavity, the elasticity of the cuticle, the excitation of certain sets of muscles and the friction between the body and its support.
We propose that muscle excitation patterns can be generated by stretch receptor control. By solving numerically the equations of motion of the model of the nematode, we demonstrate that these muscle excitation patterns are suitable for the propulsion of the animal.
The Ascaris motor nervous system contains about 90 motorneurons and interneurons. In order to understand its function, our strategy has been to start with an extensive morphological analysis of the wiring diagram, and then to use this information as a framework for the electrophysiological and biochemical analysis of cellular properties and interactions. In this article we discuss the signalling mechanisms, predominantly passive, used by this nervous system. We also discuss a model for nematode locomotion that emerges from our work.
