Molecular search for a target with a conformational change: First passage time approach

The process of a molecule search for its target is ubiquitous in Nature. During the process, the molecule is often moving in complex inhomogeneous environments with random transitions between different dynamic modes. A notable example is transcription factors searching for target sequences on a DNA. Here we study the search dynamics with stochastic transitions between two conformations in a one-dimensional lattice. Using the first passage time approach, we explicitly analyze the mean search time for arbitrary system parameters. We found that there are several dynamic regimes in the search dynamics, which are determined by the relative values of the relevant length scales in the system. Moreover, the search time can be minimized by the combination of two different modes. Intriguingly, a recent analysis of hOGG1 protein shows that the protein moves on a DNA in the optimal parameter range. Additionally, we construct a general dynamic phase diagram.