Discrete-State Kinetics Model for NMR-Based Analysis of Protein Translocation on DNA at Equilibrium

In the target DNA search process, sequence-specific DNA-binding proteins first nonspecifically bind to DNA and stochastically move from one site to another before reaching their targets. To rigorously assess how the translocation process influences NMR signals from proteins interacting with nonspecific DNA, we incorporated a discrete-state kinetic model for protein translocation on DNA into the McConnell equation. Using this equation, we simulated line shapes of NMR signals from proteins undergoing translocations on DNA through sliding, dissociation/reassociation, and intersegment transfer. Through this analysis, we validated an existing NMR approach for kinetic investigations of protein translocation on DNA, which utilizes NMR line shapes of two nonspecific DNA–protein complexes and their mixture. We found that, despite its use of simplistic two-state approximation neglecting the presence of many microscopic states, the previously proposed NMR approach provides accurate kinetic information on the intermolecular translocations of proteins between two DNA molecules. Interestingly, our results suggest that the same NMR approach can also provide qualitative information about the one-dimensional diffusion coefficient for proteins sliding on DNA.