Protein Copy Number Distributions for a Self-regulating Gene in the Presence of Decoy Bnding Sites

Abstract

A single transcription factor may interact with a multitude of targets onthe genome, some of which are at gene promoters, others being part of DNArepeat elements. Being sequestered at binding sites, protein molecules canbe prevented from partaking in other pathways, specically, from regulat-ing the expression of the very gene that encodes them. Acting as decoysat the expense of the autoregulatory loop, the binding sites can have aprofound impact on protein abundance | on its mean as well as on its cell-to-cell variability. In order to quantify this impact, we study in this papera mathematical model for pulsatile expression of a transcription factor thatautoregulates its expression and interacts with decoys. We determine theexact stationary distribution for protein abundance at the single-cell level,showing that in the case of non-cooperative positive autoregulation, the dis-tribution can be bimodal, possessing a basal expression mode and a distinct,up-regulated, mode. Bimodal protein distributions are more feasible if therate of degradation is the same irrespective of whether protein is bound ornot. Contrastingly, the presence of decoy binding sites which protect theprotein from degradation reduces the availability of the bimodal scenario.