Conditional probability as found in nature: Facilitated diffusion

Search processes are ubiquitous in physical and biological phenomena, often involving the random motion of molecules. In particular, transcription factors (TFs) are proteins that regulate gene expression and need to find their DNA targets quickly-which is difficult to achieve with random motion alone. Nature came up with a remarkable solution known as facilitated diffusion, combining 1D diffusion along the DNA and "excursions" of diffusion in 3D that help the TF to quickly arrive at distant parts of the DNA. In this paper, we show that this process can be analyzed naturally using the concept of conditional probability, providing an alternative intuition to the effectiveness of this mechanism.