A study of feedback loop mechanisms regulating calcium, IP3 and dopamine in neurons

The present work primarily aims to explore the neuronal calcium (Ca2+), IP3, and dopamine (DA) signaling systems through a feedback loop model. To date, there has been no exploration of this feedback model in fractional-order dynamical systems. This feedback loop model incorporates several crucial mechanisms like the buffering process, IP3-receptor, ryanodine receptor, plasma membrane Ca2+ ATPase and sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pump, leak, sodium-calcium exchanger, voltage-gated Ca2+ channel, Orai channels, DA-dependent IP3 synthesis, and others. By incorporating these mechanisms, the model aims to provide a more comprehensive and realistic understanding of the system under investigation. The present model incorporates fractional-order dynamics along both spatial and temporal dimensions to examine the impacts of superdiffusion and memory showing Brownian motion of Ca2+, IP3, and DA signaling molecules. The bidirectional feedback between calcium and IP3 signaling systems, unidirectional feedback between calcium and dopamine signaling systems, and unidirectional feedback between IP3 and dopamine signaling systems have been incorporated into the present model. These feedback loops establish interactions among calcium, IP3, and dopamine signaling systems within neuronal cells. The numerical findings were obtained by using the Crank-Nicholson method with the Grunwald technique for fractional space derivatives and the L-1 method for fractional time derivatives in conjunction with the Gauss-Seidel Iterations. This research specifically investigates the implications of cell memory as well as superdiffusion on Ca2+, IP3, and DA dynamics in neuronal cells, which are interactive nonlinear systems. The superdiffusion process results in a reduction in Ca2+, IP3, and DA concentrations, while cellular memory leads to an increase in ion and molecule concentrations in neuronal cells during the initial time. The disruption of any given process can lead to imbalances in calcium, IP3, and DA systems, hence contributing to neurotoxicity and cellular demise.