Modelling the oscillatory component of forward locomotion in C. Elegans
Modelling the oscillatory component of forward locomotion in C. Elegans

Summary/Abstract: In this study we provide a simplified model of the forward oscillatory locomotion neural circuit of the worm C. Elegans. Based on available connectome but lacking electrophysiological data on neurons and synapses we fill this gap by fine-tuning the electrophysiological parameters of the model so that it achieves oscillations. We observe that without electrical synapses the motor neurons are not active synchronously, thus hindering movement patterns observed in live worms. After the introduction of electrical synapses into the model, motor neurons work in synchrony. Worm C. Elegans is still the only organism with a completely mapped connectome. This makes it a popular system for computational modelling. C. Elegans hermaphrodite has 302 neurons. The number of chemical and electrical synapses is in the thousands but is not yet definitively mapped. A seminal study by White et al.(1986) provided the first description of C. Elegans connectome and is continually updated. In spite of its relatively simple nervous system, C. Elegans is capable of a whole range of behaviours. The locomotory system of C. Elegans comprises of 95 wall muscles and 75 ventral cord motor neurons. Motor neurons are regulated by motor command interneurons. A worm moves by propagating bends along its body. C. Elegans is capable of moving forward and backward with differing speed. It can also realise U-turns to abruptly change the direction of its movement. Using Animatlab software we specified a set of neurons. We built two pairs of artificial motor neurons, representing VB and DB class and a single artificial neuron representing the PVC interneuron. Parameters of neurons and synapses were set by the software and fine-tuned by the authors to mimic processes described in theory. The first step was to build an oscillatory circuit that would enable the undulatory movement of the animal. We set up the PVC neuron with 100 nA tonic stimulus that would simulate incoming impulses that drive the forward movement. We also added 0.1 mV tonic noise to all neurons simulating noise inherent in neural systems. The initial threshold of the PVC neuron was -40mV; the resting potential was -60mV. Accommodation time constant was set to 10 ms, AHP conductance to 1 microS and AHP time constant to 3 ms. Relative accommodation was set to 0.3, relative size to 1 and time constant to 5 ms. We then set up DB1, DB2, VB1 and VB2 neurons with the same parameters: the initial threshold of neurons was -40mV, and the resting potential was -60mV. The accommodation time constant was set to 1 ms, the AHP conductance to 1 microS and the AHP time constant to 30 ms. The relative accommodation was set to 0.3, the relative size to 1 and the time constant to 5 ms. In the next step we introduced four depolarising IPSP synapses from PVC to DB and VB neurons. The equilibrium potential of each synapse was set to -30 mV, the decay rate to 10 ms and the facilitation decay to 100 ms. The relative facilitation was set to 1 and the synaptic conductance to 5 microS.

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