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Proteins search along DNA for targets (e.g. transcription initiation sequences) through a combination of sliding, jumping, and intersegment transfers, wherein the sliding process proceeds until the protein-DNA complex dissociates. As such, we propose a diffusion-reaction model of the sliding phase of a total search process, and study the effect of varying reaction rate on the detailed search kinetics. With increasing dissociation rate, only the "fastest" proteins survive to explore downstream sequences, but at the price of increasing rarity, allowing for fluctuations to dominate the behavior at late times and long distances. Predictions of this model for the total search time agree with experimental estimates across an order of magnitude, providing bounds on dissociation rates that suggest a balance is established between maximizing downstream exploration of the DNA while minimizing the number of rare trajectories to guarantee the greatest chance of a successful search.