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Effect of Promoter Architecture on the Cell-to-Cell Variability in Gene Expression

Figure 4

Repression by DNA looping.

(A) Kinetic mechanism of repression. and are the rates of repressor dissociation and association. The rate of loop formation is , where can be thought of as the local concentration of repressor in the vicinity of one operator when it is bound to the other operator. The rate of dissociation of the operator-repressor complex in the looped conformation is given by . The parameter c captures the rate of repressor dissociation in the looped state relative to the rate of dissociation in a non-looped state. (B) Effect of DNA looping on cell-to-cell variability. The Fano factor is plotted as a function of the fold-change in the mean expression level, in the absence (blue) and presence (black) of the auxiliary operator, and assuming that dissociation of the operator from Om is the same in the looped and the unlooped state (c = 1). The presence of the auxiliary operator, which enables repression by DNA looping, increases the cell-to-cell variability. The regions over which the state with two repressors bound, the state with one repressor bound, or the looped DNA state are dominant are indicated by the shading in the background. The noise is larger at intermediate repression levels, where only one repressor is found bound to the promoter region, simultaneously occupying the auxiliary and main operators through DNA looping. The rate of DNA loop formation is [33]. We also show the effect of DNA looping in the case where the kinetics of dissociation from the looped state are 100 times faster than the kinetics of dissociation from the unlooped state: (red). In this limit, the presence of the auxiliary operator leads to less gene expression noise. (C) Prediction for a library of P_lacUV5 promoter variants, harboring an O2 deletion, and with the position of O3 moved upstream by multiples of 11 bp while keeping its identity (red), or replaced by the operator by Oid (black). Parameters are taken from the analysis in [33] of the data in [98]. We assume a concentration of 50 Lac repressor tetramers per cell. The association rate of the tetrameric repressor to the operators is taken from Table 1. The lifetimes of the operator-repressor complex are given in the caption to Figure 2. The dependence of the rate of DNA looping on the inter-operator distance is taken from [33], and equal to: , where , , , . Note that the Fano factor is not plotted as a function of the mean, but as a function of the inter-operator distance D. In this case, as we change D, we vary both the mean and the Fano factor.

doi: https://doi.org/10.1371/journal.pcbi.1001100.g004