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ABSTRACT
Recent single molecule experiments have determined the probability of loop formation in DNA as a function of the DNA contour length for different types of looping proteins. The optimal contour length for loop formation as well as the probability density functions have been found to be strongly dependent on the type of looping protein used. We show, using Monte Carlo simulations and analytical calculations, that these observations can be replicated using the wormlike-chain model for double-stranded DNA if we account for the nonzero size of the looping protein. The simulations have been performed in two dimensions so that bending is the only mode of deformation available to the DNA while the geometry of the looping protein enters through a single variable which is representative of its size. We observe two important effects that seem to directly depend on the size of the enzyme: 1), the overall propensity of loop formation at any given value of the DNA contour length increases with the size of the enzyme; and 2), the contour length corresponding to the first peak as well as the first well in the probability density functions increases with the size of the enzyme. Additionally, the eigenmodes of the fluctuating shape of the looped DNA calculated from simulations and theory are in excellent agreement, and reveal that most of the fluctuations in the DNA occur in regions of low curvature.
INTRODUCTION
Since its discovery in the 1980s, enzyme-mediated DNA looping has been implicated as the key to many important biological processes. For example, the activity of the lac, gal, and λ-operons in E. coli is known to be regulated by the formation of DNA loops mediated by their respective repressor proteins (1). Similarly, the functioning of many restriction enzymes is known to be controlled by the formation of loops in DNA (2). A subclass of these enzymes called two-site restriction endonucleases efficiently cleave double-stranded DNA only if they interact with the DNA at two distant sites. In fact, a majority of reactions on DNA that include transcription, replication and repair, site-specific recombination etc., are mediated by multimeric proteins that interact with DNA at multiple sites (2). As a result, the biochemistry and biophysics of these reactions have been the subject of many experimental,...