Biophysics of transcription regulation.

<p><b>A)</b> TFs bind to regulatory DNA regions (promoters and enhancers) in a sequence-specific manner to regulate transcriptional gene expression (mRNA production) level via different mechanisms, such as recruiting RNA polymerase (RNA-pol). <b>B)</b> A schematic of two types of mutational processes that we model: point mutations (left) and indel mutations (right). <b>C)</b> The mismatch binding model results in redundancy of genotype classes, with a binomial distribution (red) of genotypes in each mismatch class (some examples of degenerate sequences shown) <b>D)</b> The mapping from the TFBS regulatory sequence to gene expression level is determined by the thermodynamic occupancy (binding probability) of the binding site. If each of the <i>k</i> mismatches from the consensus sequence decreases the binding energy by <i>ϵ</i>, the occupancy of the binding site is <i>π</i>_TD(<i>k</i>) = (1 + <i>e</i>^{<i>β</i>(<i>ϵk</i>−<i>μ</i>))⁻¹}, where <i>μ</i> is the chemical potential (related to free TF concentration). A typical occupancy curve is shown in black (<i>ϵ</i> = 2 <i>k</i>_<i>B</i><i>T</i> and <i>μ</i> = 4 <i>k</i>_<i>B</i><i>T</i>); the gray curves show the effect of perturbation to these parameters (<i>ϵ</i> = 1 <i>k</i>_<i>B</i><i>T</i>, <i>ϵ</i> = 3 <i>k</i>_<i>B</i><i>T</i> and <i>μ</i> = 6 <i>k</i>_<i>B</i><i>T</i>); the orange curve illustrates the case of two cooperatively binding TFs (<i>k</i>_<i>c</i> = 0 and <i>E</i>_<i>c</i> = −3 <i>k</i>_<i>B</i><i>T</i>, see text for details). We pick two thresholds, shown in dashed lines, to define discrete binding classes: strong