📝 Original Info
- Title: Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics
- ArXiv ID: 0708.1794
- Date: 2008-06-10
- Authors: Researchers from original ArXiv paper
📝 Abstract
To establish the relationship between locomotory behavior and dynamics of neural circuits in the nematode C. elegans we combined molecular and theoretical approaches. In particular, we quantitatively analyzed the motion of C. elegans with defective synaptic GABA and acetylcholine transmission, defective muscle calcium signaling, and defective muscles and cuticle structures, and compared the data with our systems level circuit model. The major experimental findings are: (i) anterior-to-posterior gradients of body bending flex for almost all strains both for forward and backward motion, and for neuronal mutants, also analogous weak gradients of undulatory frequency, (ii) existence of some form of neuromuscular (stretch receptor) feedback, (iii) invariance of neuromuscular wavelength, (iv) biphasic dependence of frequency on synaptic signaling, and (v) decrease of frequency with increase of the muscle time constant. Based on (i) we hypothesize that the Central Pattern Generator (CPG) is located in the head both for forward and backward motion. Points (i) and (ii) are the starting assumptions for our theoretical model, whose dynamical patterns are qualitatively insensitive to the details of the CPG design if stretch receptor feedback is sufficiently strong and slow. The model reveals that stretch receptor coupling in the body wall is critical for generation of the neuromuscular wave. Our model agrees with our behavioral data(iii), (iv), and (v), and with other pertinent published data, e.g., that frequency is an increasing function of muscle gap-junction coupling.
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Deep Dive into Systems level circuit model of C. elegans undulatory locomotion: mathematical modeling and molecular genetics.
To establish the relationship between locomotory behavior and dynamics of neural circuits in the nematode C. elegans we combined molecular and theoretical approaches. In particular, we quantitatively analyzed the motion of C. elegans with defective synaptic GABA and acetylcholine transmission, defective muscle calcium signaling, and defective muscles and cuticle structures, and compared the data with our systems level circuit model. The major experimental findings are: (i) anterior-to-posterior gradients of body bending flex for almost all strains both for forward and backward motion, and for neuronal mutants, also analogous weak gradients of undulatory frequency, (ii) existence of some form of neuromuscular (stretch receptor) feedback, (iii) invariance of neuromuscular wavelength, (iv) biphasic dependence of frequency on synaptic signaling, and (v) decrease of frequency with increase of the muscle time constant. Based on (i) we hypothesize that the Central Pattern Generator (CPG) is l
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Caenorhabditis elegans nematode worms, with a small nervous system comprising only 302 neurons (White et al, 1986), move by generating an oscillatory neuromuscular wave that alternates dorsal and ventral muscles (Brenner, 1974;Chalfie et al, 1985;Karbowski et al, 2006). The molecular, cellular, and network mechanisms of this oscillatory spatio-temporal activity are virtually unknown. Their understanding may provide insight about the relationship between neuromuscular dynamics and how behavior is created in these extensively genetically studied animals (Bargmann, 1998;Hobert, 2003;de Bono and Maricq, 2005;Gray et al, 2005), and might be potentially relevant for other locomotory systems. It has proven difficult to address these questions using standard electrophysiological techniques in C. elegans because of its small neural sizes (Francis et al, 2003). In this paper, we use a combination of genetic perturbations, behavioral assays combined with a quantitative tracking system, and mathematical modeling to decipher dynamical properties of a detailed neuromuscular circuit relevant for C. elegans movement. By combining these approaches and building a mathematical circuit model we seek to bridge the gap between molecular/cellular and systems level understandings of undulatory locomotion (Fig. 1).
We investigate specific questions related to the mechanisms that control body undulations and coordination: (i) How do different elements in the C. elegans neuromuscular circuit interact to produce both body oscillations and neuromuscular wave? In particular, where is the primary oscillatory signal generated? (ii) How does mechanosensory feedback (stretch receptor coupling) affect locomotion? Does it play any role in generating a neuromuscular wave? If so, how does its strength affect the wavelength (intermuscle phase lag) of muscle contractions? (iii) How does synaptic coupling between neurons affect locomotory rhythm? Is there any qualitative difference between excitation and inhibition on oscillatory frequency? Are there optimal values for the synaptic couplings? (iv) How does gap-junction coupling between body-wall muscles and structural defects in muscles and cuticle affect movement?
To address these questions we employed a parallel approach of collecting experimental data and making model predictions in an iterative manner. In particular, we quantitatively analyzed the motion of different neuronal and non-neuronal mutants by measuring their kinematic parameters (Fig. 1B) and relating them to the dynamic properties of our circuit model. Investigated mutants included worms with decreased and increased synaptic GABA transmission, altered acetylcholine transmission, altered levels of calcium signaling in muscles, and worms with structural defects in muscles (myosin) and cuticle.
Description of analyzed mutants. We examined the locomotion of several C. elegans mutants with affected inhibitory synaptic transmission (GABA), excitatory synaptic transmission (acetylcholine), and muscular function (calcium channels and myosin).
We investigated mutants with both decreased and increased GABA function. For mutations effectively decreasing inhibition we studied: unc-25(e156), which encodes glutamic acid decarboxylase (GAD) -the biosynthetic enzyme for GABA production (Jin et al, 1999); unc-46(e177) (him-5(e1490) was in the background), which presumably plays a modulatory role in GABA packaging into vesicles (Schuske et al, 2004); and unc-18(e81) mutants carrying the syEx995 [cho-1::unc-18::yfp] transgene. unc-18 functions as a facilitator of vesicles docking at presynaptic neurons (Weimer et al, 2003) and is expressed in both cholinergic and GABAergic neurons (Gengyo-Ando et al, 1993). Therefore, in the unc-18(e81) strain carrying syEx995 [cho-1::unc-18::yfp] we have restored unc-18 function specifically to cholinergic neurons using the cho-1 promoter (Okuda et al, 2000), leaving the GABAergic neurons non-functional. For a mutation effectively increasing inhibition we studied slo-1(js118) mutants with extrachromosomal Pacr-2::slo-1(+) transgene. SLO-1 encodes a Ca 2+ activated K + channel that presumably counteracts quantal synaptic neurotransmission both in excitatory and inhibitory neurons (Wang et al, 2001), and removal of this channel (in slo-1 mutants) leads to an increased neurotransmission above wild-type level. slo-1(js118) worms with the Pacr-2::slo-1(+) transgenes (syEx996, syEx988, and syEx991) have elevated neurotransmitter release in inhibitory neurons, but they have restored wild-type release levels in excitatory neurons because Pacr-2::slo-1(+) drives expression of wild-type slo-1 in these neurons (Davies et al, 2003). We also studied three types of strains with presumably elevated acetylcholine (excitatory) synaptic signaling and wild-type level of GABA: slo-1(js118); Punc-25::slo-1, slo-1(js118); Punc-17::slo-1, and slo-1(js118); Pcho-1::slo-1.
For mutations affecting muscular calcium function, we studied u
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