We model the regulatory role of proteins bound to looped DNA using a simulation in which dsDNA is represented as a self-avoiding chain, and proteins as spherical protrusions. We simulate long self-avoiding chains using a sequential importance 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 chains 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. The reduced probability of looping can be explained via an eclipse-like model, which provides a novel inhibitory mechanism. We test the eclipse model on two possible transcription-factor occupancy states of the D. melanogaster eve 3/7 enhancer, and show that it provides a possible explanation for the experimentally-observed eve stripe 3 and 7 expression patterns.