Calcium Oscillation Model Based On Calcium Response Bell Curve

Calcium ion(Ca2+)is an important messenger that controls many cellular activities through the form of calcium oscillations.Thus,it is of great interest to investgate the mechanisms underlying such oscillations.Although Ca2+ oscillations have been modeled extensively,the concentration range of Ca2+ oscillations in the cytoplasm of most models is less than 3 ?M,and that in the endoplasmic reticulum is at most only a few tens of micromoles,which are far from the experimental data.In order to make the simulation results of the mathematical model reflect the experimental data better,the following two works are done in this paper:(1)improving the classical De Young-Keizer calcium oscillation model;(2)building a new calcium oscillation model based on bell-shaped calcium response curve.The model constructed by De Young and Keizer(abbreviated as DYK model)is one of the standard models in the field,and many models developed subsequently are based on it.In the first work,we proposed an improved DYK model by incorporating the role of cytoplasmic Ca2+ buffer into the classical DYK model.The results of bifurcation analysis show that the amplitudes of Ca2+ oscillations in the cytoplasm and endoplasmic reticulum are all consistent with the experimental observation.It is shown that by fine-tuning three parameters of the improved model,the calcium signal can be encoded in amplitude modulation,frequency modulation,or mixed modulation.This study not only helps people understand the mechanism and encoding modes of calcium oscillations from a theoretical perspective,but also provides a mathematical model that can truly reflect the experimental results and a theoretical framework for subsequent researches.The dynamic properties of IP3R(inositol 1,4,5-trisphosphate(IP3)receptor)located on the endoplasmic reticulum are crucial for the generation of Ca2+ oscillations.In the second work,by integrating recent experimental results,a new calcium oscillation model was constructed based onbell-shaped dependence of IP3 R gating on cytosolic calcium concentration([Ca2+]Cyt).The [Ca2+]Cyt and [Ca2+]ER obtained by the model are in line with the experimental results.In addition,the model can successfully reproduce many features described in experimental studies.After parameter sensitivity analysis of the model,the single-parameter bifurcation analysis is conducted to study the impact of two high-sensitivity parameters,i.e.,the total concentration of cytoplasmic Ca2+ buffer and IP3 R dissociation constant for activating Ca2+(K1)on Ca2+ oscillations.The results suggest that they have opposite effect on calcium signal.The result of two-parameter bifurcation analysis of IP3 concentration and K1 indicates that K1 plays a crucial role on the region of IP3 concentration that can generate Ca2+ oscillations and their amplitudes.This study not only helps to understand the mechanism of Ca2+oscillations,but also provides a framework for subsequent theoretical research.