Scaling laws of molecular residence time
Understanding the molecular residence autocorrelation function in liquid is of fundamental importance in physical and life science. Encoded in this function is not only the binding properties, but also the information of the liquid environment. Based on extensive in silico experiments and theoretical analysis, we reveal that power law residence scaling arises in both passive and active liquid, in contrast to the common sense of exponential decay. In simple homogeneous liquid, the scaling exponent depends solely on the system dimensionality. Such scaling law is robust against the superposition of diverse binding energies in single-phase liquid but can be breached if the system undergoes phase separation. Remarkably, in a dissipative system where phase separation is subject to non-equilibrium feedback controls, an anomalous power law emerges whose scaling exponent is in line with the puzzling residence scaling of transcription factors reported in recent experiments. Our results highlight the sensitivity of molecular residence to its surrounding liquid and suggest that active phase separation can serve as a scaling proofreading mechanism in gene regulation.