Kinetic Models of Translocation, Head-On Collision, and DNA Cleavage by Type I Restriction Endonucleases

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Abstract
Digestion of linear DNA by type I restriction endonucleases is generally activated following the head-on collision of two translocating enzymes. However, the resulting distributions of cleavage loci along the DNA vary with different enzymes; in some cases, cleavage is located in a discrete region midway between a pair of recognition sites while in other cases cleavage is broadly distributed and occurs at nearly every intervening locus. Statistical models for DNA translocation, collision, and cleavage are described that can account for these observations and that are generally applicable to other DNA-based motor proteins. If translocation is processive (stepping forward is significantly more likely than DNA dissociation), then the linear distribution of an ensemble of proteins can be described simply using a Poisson relationship. The pattern of cleavage sites resulting from collision between two processive type I enzymes over a distance d can then be described by a binomial distribution with a standard deviation 0.5·d1/2. Alternatively, if translocation is nonprocessive (stepping forward or dissociating become equally likely events), the linear distribution is described by a continuum of populated states and is thus extended. Comparisons of model data to the kinetics of DNA translocation and cleavage discount the nonprocessive model. Instead, the observed differences between enzymes are due to asynchronous events that occur upon collision. Therefore, type I restriction enzymes can be described as having processive DNA translocation but, in some cases, nonprocessive DNA cleavage.