  Protein-DNA interactions are crucial for all biological processes. One of the
most important fundamental aspects of these interactions is the process of
protein searching and recognizing specific binding sites on DNA. A large number
of experimental and theoretical investigations have been devoted to uncovering
the molecular description of these phenomena, but many aspects of the
mechanisms of protein search for the targets on DNA remain not well understood.
One of the most intriguing problems is the role of multiple targets in protein
search dynamics. Using a recently developed theoretical framework we analyze
this question in detail. Our method is based on a discrete-state stochastic
approach that takes into account most relevant physical-chemical processes and
leads to fully analytical description of all dynamic properties. Specifically,
systems with two and three targets have been explicitly investigated. It is
found that multiple targets in most cases accelerate the search in comparison
with a single target situation. However, the acceleration is not always
proportional to the number of targets. Surprisingly, there are even situations
when it takes longer to find one of the multiple targets in comparison with the
single target. It depends on the spatial position of the targets, distances
between them, average scanning lengths of protein molecules on DNA, and the
total DNA lengths. Physical-chemical explanations of observed results are
presented. Our predictions are compared with experimental observations as well
as with results from a continuum theory for the protein search. Extensive Monte
Carlo computer simulations fully support our theoretical calculations.
