Fuzzy Recurrence Exponents of Subcellular-Nanostructure Dynamics in Time-Lapse Confocal Imaging

Studying the dynamics of nanostructures in the intracellular space is important because it allows gaining insights into the mechanism of complex biological functions of organelles. Understanding such dynamical processes can contribute to the development of nanomedicine for the diagnosis and treatment of many diseases caused by the interaction of multiple genes and environmental factors. Here a quantitative measure of spatial-temporal dynamics of nanostructures within a cell line in the context of nonlinear dynamics is introduced, where early endosomes, late endosomes, and lysosomes recorded by time-lapse confocal imaging are examined. The mathematical derivation of the proposed technique is based on the concept of recurrence dynamics and sequential rate of change over time. The quantification introduced as fuzzy recurrence exponents can be generalized for characterizing the dynamics of experimental evolutions in other nanostructures of living cells captured under the optical microscope.