Abstract
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 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. 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.
Highlights
Polymer looping is a phenomenon that is critical for the understanding of many chemical and biological processes
Using a biophysical model and a computer simulation that take dsDNA and transcription factor (TF) volumes into account, we identify a downregulatory mechanism which functions at large distances, whereby a TF bound within * 150 bp from an activator decreases the probability of looping-based interaction between the activator and the distant core promoter
We found that the regulatory effects are maximal for TFs bound at the center of the looping segment, and decrease as the looping segment length is increased
Summary
We model the DNA as a discrete semi-flexible chain made of N individual links of length l. A chain is described by the locations ri of its link ends, and a local coordinate system defined by three orthonormal vectors u^i, ^vi, ^ti at each link, where ^ti points along the direction of the ith link. We use the following notations for a specific chain configuration: θi, φi are the zenith and azimuthal angles of ^ti in local spherical coordinates of link i − 1, respectively. Joint i is the end-point of link i and joint 0 is the beginning terminus of the chain. Each chain joint is engulfed by a “hard-wall” spherical shell of diameter w. The total elastic energy associated with the polymer chain can be written as follows [29]: XN
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