Exploring the interplay of intrinsic fluctuation and complexity in intracellular calcium dynamics

The concentration of intracellular calcium ion (Ca2＋) exhibits complex oscillations, including bursting and chaos, as observed experimentally. These dynamics are influenced by inherent fluctuations within cells, which serve as crucial determinants in cellular decision-making processes and fate determination. In this study, we systematically explore the interplay between intrinsic fluctuation and the complexity of various dynamic states of intracellular cytosolic Ca2＋. To investigate this interplay, we employ complexity measures such as permutation entropy and statistical complexity. Using a stochastic chemical Langevin equation, we simulate the dynamics of cytosolic Ca2＋. Our findings reveal that permutation entropy and statistical complexity effectively characterize the diverse, dynamic states of cytosolic Ca2＋ and illustrate their interactions with intrinsic fluctuation. Permutation entropy analysis elucidates that the chaotic state is more sensitive to intrinsic fluctuation than the other periodic states. Furthermore, we identify distinct states of cytosolic Ca2＋ occupying specific locations within the theoretical bounds of the complexity–entropy causality plane. These locations indicate varying complexity and information content as intrinsic fluctuation varies. When adjusting the permutation order, the statistical complexity measure for the different periodic and chaotic states exhibits peaks in an intermediate range of intrinsic fluctuation values. Additionally, we identify scale-free or fractal patterns in this intermediate range, which are further corroborated by multifractal detrended fluctuation analysis. These high-complexity states likely correspond to optimal Ca2＋ dynamics with biological significance, revealing rich and complex dynamics shaped by the interplay of intrinsic fluctuation and complexity. Our investigation enhances our understanding of the intricate regulatory mechanisms governing intracellular Ca2＋ dynamics and how intrinsic fluctuation modulates the complexity of the various dynamics that play crucial roles in biological cells.