A mathematical and computational model of the calcium dynamics in Caenorhabditis elegans ASH sensory neuron

We propose a mathematical and computational model that captures the stimulus-generated Ca2+ transients in the C. elegans ASH sensory neuron. The rationale is to develop a tool that will enable a cross-talk between modeling and experiments, using modeling results to guide targeted experimental efforts. The model is built based on biophysical events and molecular cascades known to unfold as part of neurons' Ca2+ homeostasis mechanism, as well as on Ca2+ signaling events. The state of ion channels is described by their probability of being activated or inactivated, and the remaining molecular states are based on biochemically defined kinetic equations or known biochemical motifs. We estimate the parameters of the model using experimental data of hyperosmotic stimulus-evoked Ca2+ transients detected with a FRET sensor in young and aged worms, unstressed and exposed to oxidative stress. We use a hybrid optimization method composed of a multi-objective genetic algorithm and nonlinear least-squares to estimate the model parameters. We first obtain the model parameters for young unstressed worms. Next, we use these values of the parameters as a starting point to identify the model parameters for stressed and aged worms. We show that the model, in combination with experimental data, corroborates literature results. In addition, we demonstrate that our model can be used to predict ASH response to complex combinations of stimulation pulses. The proposed model includes for the first time the ASH Ca2+ dynamics observed during both "on" and "off" responses. This mathematical and computational effort is the first to propose a dynamic model of the Ca2+ transients' mechanism in C. elegans neurons, based on biochemical pathways of the cell's Ca2+ homeostasis machinery. We believe that the proposed model can be used to further elucidate the Ca2+ dynamics of a key C. elegans neuron, to guide future experiments on C. elegans neurobiology, and to pave the way for the development of more mathematical models for neuronal Ca2+ dynamics.