Familial Alzheimer’s disease (FAD)-causing mutant presenilins (PS) interact with inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) Ca2+ release channels resulting in enhanced IP3R channel gating in an amyloid beta (Aβ) production-independent manner. This gain-of-function enhancement of IP3R activity is considered to be the main reason behind the upregulation of intracellular Ca2+ signaling in the presence of optimal and suboptimal stimuli and spontaneous Ca2+ signals observed in cells expressing mutant PS. In this paper, we employed computational modeling of single IP3R channel activity records obtained under optimal Ca2+ and multiple IP3 concentrations to gain deeper insights into the enhancement of IP3R function. We found that in addition to the high occupancy of the high-activity (H) mode and the low occupancy of the low-activity (L) mode, IP3R in FAD-causing mutant PS-expressing cells exhibits significantly longer mean life-time for the H mode and shorter life-time for the L mode, leading to shorter mean close-time and hence high open probability of the channel in comparison to IP3R in cells expressing wild-type PS. The model is then used to extrapolate the behavior of the channel to a wide range of IP3 and Ca2+ concentrations and quantify the sensitivity of IP3R to its two ligands. We show that the gain-of-function enhancement is sensitive to both IP3 and Ca2+ and that very small amount of IP3 is required to stimulate IP3R channels in the presence of FAD-causing mutant PS to the same level of activity as channels in control cells stimulated by significantly higher IP3 concentrations. We further demonstrate with simulations that the relatively longer time spent by IP3R in the H mode leads to the observed higher frequency of local Ca2+ signals, which can account for the more frequent global Ca2+ signals observed, while the enhanced activity of the channel at extremely low ligand concentrations will lead to spontaneous Ca2+ signals in cells expressing FAD-causing mutant PS.