Our aim is to construct a neural model which quantitatively reproduces the experimental data and reliably predicts the neuronal dynamics in C. elegans. C. elegans shows various behaviors such as chemotaxis and thermotaxis. To understand these behaviors from the neurobiological viewpoint, the neuronal activity needs to be measured. The calcium imaging is a popular technique to visualize the neuronal activity. Since no evidence of Na+ current has been found in C. elegans, Ca2+ current is a key issue to the nervous system. Here quantity to be measured in the calcium imaging is not the intracellular Ca2+ concentration itself but the fluorescence intensity. In addition to the membrane potential, therefore, our model includes the concentrations of Ca2+, Ca2+-buffering protein, fluorescent protein and Ca2+-binding proteins as dynamical variables [Kuramochi & Iwasaki, 2010]. These concentrations are determined by chemical reaction equations. As ion channels, K+ channel, Ca2+ channel and SK channel are considered. A calcium pumping mechanism which carries Ca2+ out of the cell across the membrane is also considered. The fluorescence intensity is calculated from the concentration of Ca2+-binding fluorescent protein. The membrane potential and the fluorescence intensity are the observable variables which are comparable with the experimental data in C. elegans. On the basis of the neuronal model, we carry out computational studies on the nervous system of C. elegans. Firstly, we study the electrical properties of a single neuron (ASE chemosensory neurons) and find that our results agree well with the experimental data [Goodman et al., 1998]. Secondly, we study a neural circuit for NaCl chemotaxis [Iino & Yoshida, 2009]. In C. elegans, the main chemosensory neurons for NaCl are ASEL/R. Here ASEL/R neurons exhibit the left/right asymmetric activities [Suzuki et al., 2008]. In this work, the asymmetric stimulations are considered. The responses of the membrane potential, the Ca2+ concentration and the fluorescence intensity to the NaCl stimulus are simulated. We find that the neuronal activity measured by the fluorescence intensity shows quantitatively different behavior from that measured by the membrane potential. The difference comes from the threshold dynamics of Ca2+ current.

Affiliations:
- Department of Intelligent System Engineering, Ibaraki University, Hitachi, Ibaraki 316-8511, Japan
- Department of Chemistry and Bioengineering, Iwate University, Morioka, Iwate 020-8551, Japan
- Department of Biophysics and Biochemistry, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan