Physical constraints determine the logic of bacterial promoter architectures

Abstract

Site-specific transcription factors (TFs) bind to their target sites on the DNA, where they regulate the rate at which genes are transcribed. Bacterial TFs undergo facilitated diffusion (a combination of 3D diffusion around and 1D random walk on the DNA) when searching for their target sites. Using computer simulations of this search process, we show that the organization of the binding sites, in conjunction with TF copy number and binding site affinity, plays an important role in determining not only the steady state of promoter occupancy, but also the order at which TFs bind. These effects can be captured by facilitated diffusion-based models, but not by standard thermodynamics. We show that the spacing of binding sites encodes complex logic, which can be derived from combinations of three basic building blocks: switches, barriers and clusters, whose response alone and in higher orders of organization we characterize in detail. Effective promoter organizations are commonly found in the E. coli genome and are highly conserved between strains. This will allow studies of gene regulation at a previously unprecedented level of detail, where our framework can create testable hypothesis of promoter logic.

Figure 1.

Distribution of promoter architectures in E. coli. We considered the binding sites in E. coli K-12, which were listed in RegulonDB (58). (A–C) plot histograms of the overlap or the distance between two sites that form a (A) switch, (B) barrier and (C) cluster. Next, we counted the number of (D) switches, (E) barriers and (F) clusters and found that these building blocks are frequently encountered in E. coli K-12 genome. For the barrier and cluster pairs, we consider binding sites that are <10 bp apart. In (G) and (H), we presented some examples of complex promoters: (G) double barrier and (H) double barrier cluster.

Figure 2.

Ratio of TF arrival times for switches and barriers. Here we show the density plot of the difference in arrival to the two target sites for (A) and (B) switches (overlapping sites by 5 bp) and (C), (D), (E) and (F) barriers (distances ). We considered an overlap of 5 bp because it is the average overlap between two adjacent binding sites; see Figure 1A. We simulated facilitated diffusion in (A–D), but only 3D diffusion in (E) and (F). The set of parameters for the TFs performing facilitated diffusion are listed in Supplementary Table S2, while the set of parameters for the system TFs performing only 3D diffusion are listed in Supplementary Table S3. In (A), (C) and (E) the two TF species have the same abundance (10 molecules), while in (B), (D) and (F) the second TF is 10 times more abundant than the first TF ( and ). Note that in (D) to emphasize the dependence of the arrival time on the distance we also plot the case of overlapping binding sites.

Figure 3.

Ratio of TF arrival times in clusters. We show the density plot of the difference in arrival to the two binding sites (distance between sites ) of the same TF, TF₁. In (A), TF₁ has low abundance (), and in (B), TF₁ has high abundance ().

Figure 4.

Heatmap of the ln of the first time all three sites are occupied in double sided barriers. We considered the promoter configuration ABA, where A is the target site of TF₁ and B is the target site of TF₂. The system consists of 10 molecules of TF₂ with a binding affinity scaling parameter of ; see ‘Materials and Methods’ section. The distance between adjacent binding sites is (A) 100 bp and (B) 0 bp. We vary the abundance and DNA binding affinity of TF₁.

Figure 5.

Impulse behaviour of AABAA. We show the number of simulations (out of 400) have only the central binding site bound, over time, for the AABAA configuration compared with (A) AA-B-AA and ABCDE and (B) ABA. For example, in the AABAA scenario, the y-axis represents the number of simulations out of the 400 in which the B site is bound and none of the A sites are bound. Note that we start the simulation with ‘naked’ DNA (no TFs bound).

Figure 6.

Differentialevolution of promoter components in E. coli. We compared (A) and (B) indel rates and (C) and (D) SNP rates between E. coli K-12 and other reference strains across different promoter regions. (B) and (D) display results of a paired-T-test with Holm corrections; significantly different promoter regions are red and insignificant pairs are blue (threshold: ). We considered the following five cases: (A) within binding sites (BSs), (B) between closely spaced binding sites (<100 bp spacers), (C) between binding sites farther than 100 bp (>100 bp spacers), (D) between TSS and first binding site (TSS to first BS) and (E) between the last binding site and the termination sequence (after last BS).