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

Abstract

We propose a mathematical and computational model that captures the stimulus-generated Ca2+ transients in the C. elegans ASH sensory neuron. 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 with phenomenological adjustments. 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 cells Ca2+ homeostasis machinery.\n\nSignificance StatementC. elegans is widely used as a model system for monitoring neuronal Ca2+ transients. The ASH neuron is the subject of several such studies, primarily due to its key importance as a polymodal nociceptor. However, despite its pivotal role in C. elegans biology, and the special characteristics of its stimulus-evoked Ca2+ transients (e.g., the \"off\" response), no mathematical or computational model has been developed to include special features of ASH Ca2+ dynamics, i.e. the \"off\" response. The model includes for the first time the ASH Ca2+ dynamics observed during both \"on\" and \"off\" responses, and is the first to propose a dynamical model of the C. elegans Ca2+ transients mechanism based on biochemical pathways of the cells Ca2+ homeostasis machinery.\n\nAbbreviations