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Quasi-genes : the many-body theory of gene regulation in the presence of decoys


During transcriptional regulation, transcription factor proteins bind to particular sites in the genome in order to switch genes on or off. The regulatory binding site intended for a transcription factor is just one out of millions of potential sites where the transcription factor can bind. Specificity of a binding motif determines whether less than one or up to tens of thousands of strong affinity binding sites can be expected by pure chance. The roles that these additional "decoy" binding sites play in the functioning of a cell are currently unknown. We incorporate decoys into traditional mass action and stochastic models of a simple gene network-the self- regulated gene-and use numerical and analytical techniques to quantify the effects that these extra sites have on altering gene expression properties. Counter-intuitively, we find that if bound transcription factors are protected from degradation, the mean steady state concentration of unbound transcription factors, , is insensitive to the addition of decoys. Many other gene expression properties do change as decoys are added. Decoys linearly increase the time necessary to reach steady state. Noise buffering by decoys occurs because of a coupling between the unbound proteomic environment and the reservoir of sites that can be very large, but the noise reduction is limited Poisson statistics because of the inherent noise resulting from binding and unbinding of transcription factors to DNA. This noise buffering is optimized for a given protein concentration when decoys have a 1/2 probability of being occupied. Decoys are able to preferentially stabilize one state of a bimodal system over the other, and exponentially increase the time to epigenetically switch between these states. In the limit that binding and unbinding rates are fast compared to the fluctuations in transcription factor copy number, we exploit timescale differences to collapse the model and derive analytical expressions that explain our numerical results. In analogy to traditional many-body systems, we derive effective parameters to describe a "quasi-gene" which can be used to approximate the influence of decoy binding sites on simple gene networks

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