How the avidity of polymerase binding to the -35/-10 promoter sites affects gene expression

Abstract

Although the key promoter elements necessary to drive transcription in Escherichia coli have long been understood, we still cannot predict the behavior of arbitrary novel promoters, hampering our ability to characterize the myriad sequenced regulatory architectures as well as to design new synthetic circuits. This work builds upon a beautiful recent experiment by Urtecho et al. [G. Urtecho, et al, Biochemistry, 68, 1539-1551 (2019)] who measured the gene expression of over 10,000 promoters spanning all possible combinations of a small set of regulatory elements. Using these data, we demonstrate that a central claim in energy matrix models of gene expression-that each promoter element contributes independently and additively to gene expression-contradicts experimental measurements. We propose that a key missing ingredient from such models is the avidity between the -35 and -10 RNA polymerase binding sites and develop what we call a multivalent model that incorporates this effect and can successfully characterize the full suite of gene expression data. We explore several applications of this framework, namely, how multivalent binding at the -35 and -10 sites can buffer RNA polymerase (RNAP) kinetics against mutations and how promoters that bind overly tightly to RNA polymerase can inhibit gene expression. The success of our approach suggests that avidity represents a key physical principle governing the interaction of RNA polymerase to its promoter.

Keywords: avidity; statistical mechanics; transcription regulation.

Fig. 1.

The bivalent nature of RNAP–promoter binding. (A) Expression was measured for promoters comprising any combination of −35, −10, spacer, UP, and background (BG) elements. (B) Without an UP element, RNAP contacts the promoter at the −35 and −10 sites, giving rise to expression $r_0$ when unbound or partially bound and $r_{\text{max}}$ when fully bound. (C) Having two binding sites alters the dynamics of RNAP binding. $k_{\text{on}}$ represents the on-rate from unbound to partially bound RNAP, ${\tilde{k}}_{\text{on}}$ the analogous rate from partially to fully bound RNAP, and $k_{\text{off},j}$ denotes the unbinding rate from site $j$.

Fig. 2.

Expression of promoters with no UP element. Model predictions using (A) an energy matrix (Eq. 1) where the −35 and −10 elements independently contribute to RNAP binding and (B) a multivalent model (Eq. 3) where the two sites contribute cooperatively. (A, Inset) The epistasis-free nature of the energy matrix model makes sharp predictions about the gene expression of the consensus −35 and −10 sequences that markedly disagree with the data. Parameter values are given in SI Appendix, section B.

Fig. 3.

The interaction between RNAP and the UP element. (A) Possible mechanisms by which the RNAP C terminus can bind to the UP element (orange segments represent strong binding comparable to the −35 and −10 motifs; gray segments represent weak binding comparable to the spacer and background). The data support the Bottom schematic (SI Appendix, section D). (B) The corresponding characterization of 8,192 promoters identical to those shown in Fig. 2 but with one of two UP binding motifs. Red points represent promoters with a consensus −35 and −10. Data were fitted using the same parameters as in Fig. 2B and fitting the binding energies of the two UP elements (parameter values in SI Appendix, section B).

Fig. 4.

Gene expression is reduced when RNAP binds a promoter too tightly. Shown is measured expression vs. inferred promoter strength $-\mathrm{\Delta }{E}_{\text{RNAP}}$ (stronger promoters on the right). Expression decreases once the RNAP binding becomes comparable to the free energy of the transcription initiation state $-\mathrm{\Delta }{E}_{\text{trans}}=6.2\hspace{0.17em}{k}_{B}T$. The dashed line shows the prediction of the multivalent model.

Fig. 5.

The dissociation between RNAP and the promoter. Shown is RNAP binding to a promoter with a strong (solid lines, $K_{-35}=1\hspace{0.17em}\mathrm{\mu }\text{M}$) or weak (dashed lines, $K_{-35}\to \infty$) −35 sequence. $c_0$ represents the local concentration of singly bound RNAP.