  We simulate long self-avoiding chains using a weighted-biased sampling
Monte-Carlo algorithm, and compute the probabilities for chain looping with and
without a protrusion. We find that a protrusion near one of the chain's termini
reduces the probability of looping, even for chains much longer than the
protrusion-chain-terminus distance. This effect increases with protrusion size,
and decreases with protrusion-terminus distance. We model the simulated results
theoretically by considering how the protrusion "eclipses" the chain terminus
closer to the protrusion from the more distant chain terminus. This eclipse
mechanism has implications for understanding the regulatory role of proteins
bound to DNA.
