This article considers an inverse problem for a Cosserat rod where we are given only the position... more This article considers an inverse problem for a Cosserat rod where we are given only the position of the centreline of the rod and must solve for external forces and torques as well as the orientation of the cross sections of the centreline. We formulate the inverse problem as an optimal control problem using the position of the centreline as an objective function with the external force and torque as control variables, with meaningful regularisation of the orientations. A monolithic, implicit numerical scheme is proposed in the sense that primal and adjoint equations are solved in a fully-coupled manner and all the nonlinear coefficients of the governing partial differential equations are updated to the current state variables. The forward formulation, determining rod configuration from external forces and torques, is first validated by a numerical benchmark; the solvability and stability of the inverse problem are then tested using data from forward simulations. The proposed optim...
Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the... more Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the combined effects of internal neural control and mechanical forces. Here we use a computational model to identify effects of neural and mechanical modulation on undulatory forward locomotion of <i>Caenorhabditis elegans</i>, with a focus on proprioceptively driven neural control. We reveal a fundamental relationship between body elasticity and environmental drag in determining the dynamics of the body and demonstrate the manifestation of this relationship in the context of proprioceptively driven control. By considering characteristics unique to proprioceptive neurons, we predict the signatures of internal gait modulation that contrast with the known signatures of externally or biomechanically modulated gait. We further show that proprioceptive feedback can suppress neuromechanical phase lags during undulatory locomotion, contrasting with well studied advancing phase lags that have long been a signature of centrally generated, feed-forward control.This article is part of the theme issue 'Connectome to behaviour: modelling <i>C. elegans</i> at cellular resolution'.
Animal locomotion describes the coordinated self-propelled movement of a body, subject to the com... more Animal locomotion describes the coordinated self-propelled movement of a body, subject to the combined effects of internal muscle forcing and external forces. Here we use an integrated neuromechanical computational model to study the combined effects of neural modulation, mechanical modulation and modulation of the external environments on undulatory forward locomotion in the nematodeC. elegans. In particular we use a proprioceptively driven neural control circuit to consider the effects of proprioception, body elasticity and environmental drag on the waveform, frequency and speed of undulations. We find qualitative differences in the frequency-wavelength relationship obtained under extrinsic modulation of the environmental fluid or body elasticity versus intrinsic modulation due to changes in the sensorimotor control. We consider possible targets of modulation by the worm and implications of our results for our understanding of the neural control of locomotion in this system.
Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation... more Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation of waves along a body. As a mode of locomotion it is primitive and relatively simple, yet can be remarkably robust. No wonder then, that it is so prevalent across a range of biological scales from motile bacteria to gigantic prehistoric snakes. Key to understanding undulatory locomotion is the body's interplay with the physical environment, which the swimmer or crawler will exploit to generate propulsion, and in some cases, even to generate the underlying undulations. This review focuses by and large on undulators in the low Reynolds numbers regime, where the physics of the environment can be much more tractable. We review some key concepts and theoretical advances, as well as simulation tools and results applied to selected examples of biological swimmers. In particular, we extend the discussion to some simple cases of locomotion in non-Newtonian media as well as to small animals, ...
Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the... more Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the combined effects of internal neural control and mechanical forces. Here we use a computational model to identify effects of neural and mechanical modulation on undulatory forward locomotion of C. elegans, with a focus on proprioceptively driven neural control. We reveal a fundamental relationship between body elasticity and environmental drag in determining the dynamics of the body and demonstrate the manifestation of this relationship in the context of proprioceptively driven control. By considering characteristics unique to proprioceptive neurons, we predict the signatures of internal gait modulation that contrast with the known signatures of externally or biomechanically modulated gait. We further show that proprioceptive feedback can suppress neuromechanical phase lags during undulatory locomotion, contrasting with well studied advancing phase lags that have long been a signature of...
Over the past four decades, one of the simplest nervous systems across the animal kingdom, that o... more Over the past four decades, one of the simplest nervous systems across the animal kingdom, that of the nematode worm C. elegans, has drawn increasing attention. This system is the subject of an intensive concerted eort 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 eect. These results rule out muscles as key generat...
We study the effects of squeezed pump fluctuations in the degenerate parametric amplifier on sign... more We study the effects of squeezed pump fluctuations in the degenerate parametric amplifier on signal squeezing. We find, both through semiclassical calculations and through several detailed analytic methods, that pump squeezing is responsible for two competing processes: Reduced pump phase fluctuations improve limitations to squeezing; at the same time, increased pump intensity fluctuations can lead to a ``spillover'' of pump fluctuations onto negative pump phases and a consequent reduction in signal squeezing.
Hebbian learning has been implicated as a possible mech-anism in a wide range of learning and mem... more Hebbian learning has been implicated as a possible mech-anism in a wide range of learning and memory functions in the brain. A large body of theoretical studies and simu-lations has investigated its implications in the dynamics of single neuron as well as network models. For example, neural network models have been found to produce meaningful internal states when driven by structured external stimulation. These studies, however, typically lack a notion of a "desired output " in the form of a well specified pattern of network activity, corresponding to a relevant functional output. To impose a desired input-output relation, various forms of supervised learning (or at least reinforcement in the form of an external cue) are often invoked. Recently there has been increasing interest in computational models that involve a separation of
Noise is the stuff that life is made of. From the thermal fluctuations that drive conformational ... more Noise is the stuff that life is made of. From the thermal fluctuations that drive conformational changes in proteins, through the random interactions that occur due to the passive and active transport of finite species of molecules in the cellular and extra cellular environment, to the unpredictable nature of evolution, stochastic processes are responsible for the existence of the
Hebbian learning has been implicated as a possible mechanism in a wide range of learning and memo... more Hebbian learning has been implicated as a possible mechanism in a wide range of learning and memory functions in the brain. A large body of theoretical studies and simulations has investigated its implications in the dynamics of single neuron as well as network models. For example, neural network models have been found to produce meaningful internal states when driven by structured external stimulation. These studies, however, typically lack a notion of a "desired output " in the form of a well specified pattern of network activity, corresponding to a relevant functional output. To impose a desired inputoutput relation, various forms of supervised learning (or at least reinforcement in the form of an external cue) are often invoked. Recently there has been increasing interest in computational models that involve a separation of
A commentary on Shared strategies for behavioral switching: understanding how locomotor patterns ... more A commentary on Shared strategies for behavioral switching: understanding how locomotor patterns are turned on and off by Mesce, K. A., and Pierce-Shimomura, J.
Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation... more Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation of waves along a body. As a mode of locomotion it is primitive and relatively simple, yet can be remarkably robust. No wonder then, that it is so prevalent across a range of biological scales from motile bacteria to gigantic prehistoric snakes. Key to understanding undulatory locomotion is the body’s interplay with the physical environment, which the swimmer or crawler will exploit to generate propulsion, and in some cases, even to generate the underlying undulations. This review focuses by and large on undulators in the low Reynolds numbers regime, where the physics of the environment can be much more tractable. We review some key concepts and theoretical advances, as well as simulation tools and results applied to selected examples of biological swimmers. In particular, we extend the discussion to some simple cases of locomotion in non-Newtonian media as well as to small animals, in w...
An organism's ability to move freely is a fundamental behaviour in the animal kingdom. To und... more An organism's ability to move freely is a fundamental behaviour in the animal kingdom. To understand animal locomotion requires a characterisation of the material properties, as well as the biomechanics and physiology. We present a biomechanical model of C. elegans locomotion together with a novel finite element method. We formulate our model as a nonlinear initial-boundary value problem which allows the study of the dynamics of arbitrary body shapes, undulation gaits and the link between the animal's material properties and its performance across a range of environments. Our model replicates behaviours across a wide range of environments. It makes strong predictions on the viable range of the worm's Young's modulus and suggests that animals can control speed via the known mechanism of gait modulation that is observed across different media.
The survival of living cells crucially depends on the fidelity with which genetic information, st... more The survival of living cells crucially depends on the fidelity with which genetic information, stored in nucleotide sequence of DNA, is processed during cell division (DNA replication) and protein synthesis (DNA transcription and mRNA translation). However, thermodynamics introduces significant fluctuations which would incur massive error rates if efficient proofreading mechanisms were not in place [Hopfield (1974)].
Inhibition plays important roles in modulating the neural activities of sensory and motor systems... more 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 contraction of antagonist muscles, whether along the body axis or within and among limbs. In the nematode C. 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 stimula...
Inhibition plays important roles in modulating the neural activities of sensory and motor systems... more 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 hea...
This article considers an inverse problem for a Cosserat rod where we are given only the position... more This article considers an inverse problem for a Cosserat rod where we are given only the position of the centreline of the rod and must solve for external forces and torques as well as the orientation of the cross sections of the centreline. We formulate the inverse problem as an optimal control problem using the position of the centreline as an objective function with the external force and torque as control variables, with meaningful regularisation of the orientations. A monolithic, implicit numerical scheme is proposed in the sense that primal and adjoint equations are solved in a fully-coupled manner and all the nonlinear coefficients of the governing partial differential equations are updated to the current state variables. The forward formulation, determining rod configuration from external forces and torques, is first validated by a numerical benchmark; the solvability and stability of the inverse problem are then tested using data from forward simulations. The proposed optim...
Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the... more Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the combined effects of internal neural control and mechanical forces. Here we use a computational model to identify effects of neural and mechanical modulation on undulatory forward locomotion of <i>Caenorhabditis elegans</i>, with a focus on proprioceptively driven neural control. We reveal a fundamental relationship between body elasticity and environmental drag in determining the dynamics of the body and demonstrate the manifestation of this relationship in the context of proprioceptively driven control. By considering characteristics unique to proprioceptive neurons, we predict the signatures of internal gait modulation that contrast with the known signatures of externally or biomechanically modulated gait. We further show that proprioceptive feedback can suppress neuromechanical phase lags during undulatory locomotion, contrasting with well studied advancing phase lags that have long been a signature of centrally generated, feed-forward control.This article is part of the theme issue 'Connectome to behaviour: modelling <i>C. elegans</i> at cellular resolution'.
Animal locomotion describes the coordinated self-propelled movement of a body, subject to the com... more Animal locomotion describes the coordinated self-propelled movement of a body, subject to the combined effects of internal muscle forcing and external forces. Here we use an integrated neuromechanical computational model to study the combined effects of neural modulation, mechanical modulation and modulation of the external environments on undulatory forward locomotion in the nematodeC. elegans. In particular we use a proprioceptively driven neural control circuit to consider the effects of proprioception, body elasticity and environmental drag on the waveform, frequency and speed of undulations. We find qualitative differences in the frequency-wavelength relationship obtained under extrinsic modulation of the environmental fluid or body elasticity versus intrinsic modulation due to changes in the sensorimotor control. We consider possible targets of modulation by the worm and implications of our results for our understanding of the neural control of locomotion in this system.
Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation... more Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation of waves along a body. As a mode of locomotion it is primitive and relatively simple, yet can be remarkably robust. No wonder then, that it is so prevalent across a range of biological scales from motile bacteria to gigantic prehistoric snakes. Key to understanding undulatory locomotion is the body's interplay with the physical environment, which the swimmer or crawler will exploit to generate propulsion, and in some cases, even to generate the underlying undulations. This review focuses by and large on undulators in the low Reynolds numbers regime, where the physics of the environment can be much more tractable. We review some key concepts and theoretical advances, as well as simulation tools and results applied to selected examples of biological swimmers. In particular, we extend the discussion to some simple cases of locomotion in non-Newtonian media as well as to small animals, ...
Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the... more Animal neuromechanics describes the coordinated self-propelled movement of a body, subject to the combined effects of internal neural control and mechanical forces. Here we use a computational model to identify effects of neural and mechanical modulation on undulatory forward locomotion of C. elegans, with a focus on proprioceptively driven neural control. We reveal a fundamental relationship between body elasticity and environmental drag in determining the dynamics of the body and demonstrate the manifestation of this relationship in the context of proprioceptively driven control. By considering characteristics unique to proprioceptive neurons, we predict the signatures of internal gait modulation that contrast with the known signatures of externally or biomechanically modulated gait. We further show that proprioceptive feedback can suppress neuromechanical phase lags during undulatory locomotion, contrasting with well studied advancing phase lags that have long been a signature of...
Over the past four decades, one of the simplest nervous systems across the animal kingdom, that o... more Over the past four decades, one of the simplest nervous systems across the animal kingdom, that of the nematode worm C. elegans, has drawn increasing attention. This system is the subject of an intensive concerted eort 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 eect. These results rule out muscles as key generat...
We study the effects of squeezed pump fluctuations in the degenerate parametric amplifier on sign... more We study the effects of squeezed pump fluctuations in the degenerate parametric amplifier on signal squeezing. We find, both through semiclassical calculations and through several detailed analytic methods, that pump squeezing is responsible for two competing processes: Reduced pump phase fluctuations improve limitations to squeezing; at the same time, increased pump intensity fluctuations can lead to a ``spillover'' of pump fluctuations onto negative pump phases and a consequent reduction in signal squeezing.
Hebbian learning has been implicated as a possible mech-anism in a wide range of learning and mem... more Hebbian learning has been implicated as a possible mech-anism in a wide range of learning and memory functions in the brain. A large body of theoretical studies and simu-lations has investigated its implications in the dynamics of single neuron as well as network models. For example, neural network models have been found to produce meaningful internal states when driven by structured external stimulation. These studies, however, typically lack a notion of a "desired output " in the form of a well specified pattern of network activity, corresponding to a relevant functional output. To impose a desired input-output relation, various forms of supervised learning (or at least reinforcement in the form of an external cue) are often invoked. Recently there has been increasing interest in computational models that involve a separation of
Noise is the stuff that life is made of. From the thermal fluctuations that drive conformational ... more Noise is the stuff that life is made of. From the thermal fluctuations that drive conformational changes in proteins, through the random interactions that occur due to the passive and active transport of finite species of molecules in the cellular and extra cellular environment, to the unpredictable nature of evolution, stochastic processes are responsible for the existence of the
Hebbian learning has been implicated as a possible mechanism in a wide range of learning and memo... more Hebbian learning has been implicated as a possible mechanism in a wide range of learning and memory functions in the brain. A large body of theoretical studies and simulations has investigated its implications in the dynamics of single neuron as well as network models. For example, neural network models have been found to produce meaningful internal states when driven by structured external stimulation. These studies, however, typically lack a notion of a "desired output " in the form of a well specified pattern of network activity, corresponding to a relevant functional output. To impose a desired inputoutput relation, various forms of supervised learning (or at least reinforcement in the form of an external cue) are often invoked. Recently there has been increasing interest in computational models that involve a separation of
A commentary on Shared strategies for behavioral switching: understanding how locomotor patterns ... more A commentary on Shared strategies for behavioral switching: understanding how locomotor patterns are turned on and off by Mesce, K. A., and Pierce-Shimomura, J.
Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation... more Undulatory locomotion is a means of self-propulsion that relies on the generation and propagation of waves along a body. As a mode of locomotion it is primitive and relatively simple, yet can be remarkably robust. No wonder then, that it is so prevalent across a range of biological scales from motile bacteria to gigantic prehistoric snakes. Key to understanding undulatory locomotion is the body’s interplay with the physical environment, which the swimmer or crawler will exploit to generate propulsion, and in some cases, even to generate the underlying undulations. This review focuses by and large on undulators in the low Reynolds numbers regime, where the physics of the environment can be much more tractable. We review some key concepts and theoretical advances, as well as simulation tools and results applied to selected examples of biological swimmers. In particular, we extend the discussion to some simple cases of locomotion in non-Newtonian media as well as to small animals, in w...
An organism's ability to move freely is a fundamental behaviour in the animal kingdom. To und... more An organism's ability to move freely is a fundamental behaviour in the animal kingdom. To understand animal locomotion requires a characterisation of the material properties, as well as the biomechanics and physiology. We present a biomechanical model of C. elegans locomotion together with a novel finite element method. We formulate our model as a nonlinear initial-boundary value problem which allows the study of the dynamics of arbitrary body shapes, undulation gaits and the link between the animal's material properties and its performance across a range of environments. Our model replicates behaviours across a wide range of environments. It makes strong predictions on the viable range of the worm's Young's modulus and suggests that animals can control speed via the known mechanism of gait modulation that is observed across different media.
The survival of living cells crucially depends on the fidelity with which genetic information, st... more The survival of living cells crucially depends on the fidelity with which genetic information, stored in nucleotide sequence of DNA, is processed during cell division (DNA replication) and protein synthesis (DNA transcription and mRNA translation). However, thermodynamics introduces significant fluctuations which would incur massive error rates if efficient proofreading mechanisms were not in place [Hopfield (1974)].
Inhibition plays important roles in modulating the neural activities of sensory and motor systems... more 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 contraction of antagonist muscles, whether along the body axis or within and among limbs. In the nematode C. 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 stimula...
Inhibition plays important roles in modulating the neural activities of sensory and motor systems... more 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 hea...
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