Agonist Fluctuation Maintained Calcium Signaling in a Mesoscopic System

Background

Agonist influences the Ca²⁺ signaling through many pathways such as Ca²⁺-phosphatidylinositol (PI) pathway, NMDA receptor mediated synapses, derndritic calcium action potentials, and Ca²⁺ liberated by Ca²⁺ phenomena linked or not to the role of ryanodine receptors of the intracellular endoplasmic reticulum. Here, we employ the receptor-controlled model for intracellular Ca²⁺ signaling in hepatocytes proposed by Cuthbertson et al. (1991). In this model, the calcium signal (oscillation) is triggered by the binding of agonists (hormone or neurotransmitter) to their receptors, which is the basic signaling mechanism for most of the calcium signaling systems. The influence of agonist is expressed by its concentration. The system dynamics can be described by the following equations:

(1)

For simplicity, it is assumed that [DAG] and [IP₃] increase with the same rate, i.e., [DAG] = [IP₃]. [G_α-GDP] and [PLC] are determined by the relations: , in which G₀ and P₀ are the total concentration of G-proteins and PLC, respectively. Parameter k_g is proportional to the agonist concentration. l_d and l_c are “leak” terms of the signaling dynamics, which keeps the cell at its basal level of [DAG] and [Ca²⁺]_i, respectively, in the absence of external stimuli. k_p, h_p and k_d are supposed to take the form: where k_n = k_p,h_p,or k_d. Detailed information about the model can be found in Ref (Cuthbertson et al., 1991).