We develop a theory for the rapid search of specific sites on DNA, via a mechanism in which a nonspecifically-bound protein can switch between two conformations. In the "inactive" conformation, the bound protein has favorable, nonspecific interactions with the DNA, but cannot be recognized by the target site. In the "active" conformation, the protein is recognized by the target site but has a very rugged energy surface elsewhere on the DNA. The rate constant for protein binding to the specific site is calculated by an approach in which the protein, after reaching the DNA surface via 3D diffusion, searches for the target site via 1D diffusion while being allowed to escape to the bulk solution. Mindful of the pitfalls of many previous approximate treatments, we validate our approach against a rigorous solution of the problem when the protein has a fixed conformation. In the 1D diffusion toward the specific site, a conformationally switchable protein predominantly adopts the inactive conformation due to the favorable nonspecific interactions with the DNA, thus maximizing the 1D diffusion constant and minimizing the chance of escape to the bulk solution. Once at the target site, a transition to the active conformation allows the protein to be captured. This induced-switch mechanism provides robust speedup of protein-DNA binding rates, and appears to be adopted by many transcription factors and DNA-modifying enzymes.conformational change | nonspecific binding | binding kinetics E ver since the first demonstration that proteins can bind to specific DNA sequences (1, 2), numerous studies have been carried out to address the question of how a protein can readily find a short specific site on a long . It is widely accepted that the search is accomplished by coupled 3D diffusion in the bulk solution and 1D diffusion, while specifically bound, along the DNA surface. Many theoretical models have focused on the 1D diffusion. Appealing terms such as hopping and jumping have been used to treat excursions into the bulk solution. However, the lack of rigor in previous treatments has led to conflicting results. In particular, whether 1D diffusion can play a significant rate-enhancement role under physiological conditions has been questioned (15). Here we present an approach for calculating the protein-DNA binding rate constant k a that allows for proper coupling between 3D and 1D diffusion. We use this approach to treat the conformational switch of a nonspecifically bound protein, and demonstrate that it provides a robust mechanism for speeding up the search of specific sites.The bimolecular rate constant k a can be rigorously determined from the equation governing the relative translational diffusion, rotational diffusion, and internal motions of the two binding molecules (21). This governing equation involves the potential of mean force in these degrees of freedom and parameters characterizing the external and internal dynamics, such as a position-dependent diffusion constant for the translational diffusion and transition rates...