Transcriptional regulation by the numbers: applications

Abstract

With the increasing amount of experimental data on gene expression and regulation, there is a growing need for quantitative models to describe the data and relate them to their respective context. Thermodynamic models provide a useful framework for the quantitative analysis of bacterial transcription regulation. This framework can facilitate the quantification of vastly different forms of gene expression from several well-characterized bacterial promoters that are regulated by one or two species of transcription factors; it is useful because it requires only a few parameters. As such, it provides a compact description useful for higher-level studies (e.g. of genetic networks) without the need to invoke the biochemical details of every component. Moreover, it can be used to generate hypotheses on the likely mechanisms of transcriptional control.

Figure 1

Simple activation. (a) Cis-regulatory architecture for transcriptional activation involving a single CRP operator, as found in the lac operon. The yellow box denotes the operator site and the blue box corresponds to the promoter. The DNA-binding affinity of the transcription factor for its operator is described by the in vivo dissociation constant K_A, which is the TF concentration at which the operator occupancy is half-maximal. The activator recruits RNAP through protein–protein interactions (schematically drawn as interacting protein subunits). (b) Log–log plot of the fold-change in gene expression as a function of the induced CRP dimer concentration, [CRP₂*]. The maximum log–log slope in the transition region, which is defined as the sensitivity (s), is highlighted with the dashed line and is equal to 0.75. This plot was generated using K_A = 5 nM, f = 50. These parameter values were estimated from experiments similar to those of Setty et al. [10], who measured β-galactosidase activity as a function of extra-cellular cAMP concentration in E. coli MG1655 cells, but with the additional deletion of the cyaA gene which encodes adenyl cyclase (T Kuhlman and T Hwa, unpublished). The enhancement factor obtained is consistent with that of others [41]. The estimated value of the effective dissociation constant K_A is dependent on the literature values for several biochemical parameters concerning cAMP binding and transport, and is not expected to be accurate to within a factor of 2. (For comparison, previous in vitro measurement of the CRP-operator affinity has ranged from 0.001 nM to 50 nM depending on the ionic strength of the assay [–44].)

Figure 2

Enhanced sensitivity by cooperative activation. (a) Cis-regulatory architecture for cooperative transcriptional activation in phage lambda P_RM promoter. Here, we are considering P_RM alone without the upstream P_R promoter [1^•] or the upstream P_L region, which affects P_RM activity through DNA looping [45]. We also neglect the operator O_R3, which has very weak affinity to cI in the absence of P_L [45]. The yellow boxes denote the operator sites O_R1, O_R2 and the blue box corresponds to the promoter. The DNA-binding affinity of cI₂ for O_R1 and O_R2 is described by the dissociation constants K_R1 and K_R2, respectively. The activator stimulates transcription and cI dimers interact with one another through intimate, cooperative interactions, both of which are indicated by overlapping protein–protein domains. (b) Log–log plot of the fold-change in gene expression as a function of cI₂ concentration for different ratios of K_R2/K_R1. The maximum log–log slopes (s) for the different curves are listed in the legend. The promoter with K_R2/K_R1 = 0 corresponds to a deletion of O_R1, and the regulation function for this case (thin solid line) is identical to the single operator case shown in Figure 1. If this promoter has a very small K_R1 (i.e. strong O_R1), then the onset of full activation will be shifted to smaller cI concentrations (dotted line). The latter corresponds effectively to a stronger O_R2 site, with dissociation constant K_R2/ω. These plots are generated using f ≈ 11 [46] and ω ≈ 100 [47] as extracted from in vitro biochemical studies. The absolute in vivo values of the K values are not known (which is why the concentration is expressed in terms of [cI₂] / K_R2). However, the ratio K_R2/K_R1 ≈ 25 (thick solid line) can be deduced from the in vitro results [47]. The transition region is steepest when ω ⪢ f and K_R2/K_R1 ≈ f. We note that the parameters for P_RM are nearly optimal for enhanced sensitivity.

Figure 3

Cooperative co-activation. (a) Cis-regulatory construct for co-activation by CRP and MelR. The figure shows the truncated JK15 version of melAB promoter studied by Wade et al. [16]. The full melAB promoter is more complicated due to the presence of multiple MelR operators. However, the co-activation pattern is similar to that of JK15 discussed here. The yellow boxes denote the operator sites O₁, O₂ and the blue box corresponds to the promoter. The DNA-binding affinity of CRP₂ for O₁ and MelR₂ for O₂ is described by the dissociation constant K₁ and K₂, respectively. MelR can recruit RNAP (drawn with protein–protein contacts) and cooperative interaction between MelR₂ and CRP₂ is indicated by interacting protein subunits. (b) Log–log plot of the fold-change in gene expression as a function of activated CRP dimer concentration [CRP₂*] for different activated MelR dimer concentrations [MelR₂*]. Since none of the parameters f, ω, and K values have been determined experimentally, the scales of the plot can only be expressed relative to these parameters. Nevertheless, the plot reveals important qualitative predictions by the thermodynamic model (e.g. the dependence of the maximal CRP-dependent fold-change on the MelR concentration). (c) Three-dimensional log–log plot of the fold-change in gene expression as a function of both CRP₂ and MelR₂. For different choices of `high' and `low' concentration (the four combinations of `high/low' for these two TFs form a rectangle), the same melAB promoter can serve as an OR function (solid circles) or an AND function (open circles).

Figure 4

Synergistic co-activation. (a) Cis-regulatory architecture for synergistic co-activation in synthetic promoters [21]. The yellow boxes denote the operator sites O₁, O₂ and the blue box corresponds to the promoter. The DNA-binding affinity of CRP₂ for O₁ and cI₂ for O₂ is described by the dissociation constants K₁ and K₂, respectively. Each activator can independently interact with RNAP and enhance transcription at different strengths f₁, f₂ (as shown with interacting protein–protein subunits). (b) Log–log plot of the fold-change in gene expression as a function of [CRP₂*] for different concentrations of [cI₂]. (c) Three-dimensional log–log plot of the fold-change in gene expression as a function of both CRP₂ and cI₂. Note that on log scale, the product appears as an additive shift.

Figure 5

Enhances sensitivity by synergistic activation. (a) To the left is the cis-regulatory architecture for synergistic activation by the same TF in synthetic promoters [19]. The yellow boxes denote the operator sites O₁, O₂ and the blue box corresponds to the promoter. The DNA-binding affinity of CRP₂ for O₁ and O₂ is described by the dissociation constants K₁ and K₂, respectively. Activators at each operator can recruit RNAP independently at different strengths f₁, f₂ (as shown with interacting protein–protein subunits). As illustrated to the right, the binding of CRP to proximal O₂ bends DNA and facilitates the `bent' interaction of RNAP to CRP bound at upstream O₁. (b) Log–log plot of the fold-change in gene expression as a function of [CRP₂*] for equal dissociation constants (K₁ = K₂). We have included the additional cooperativity ω that can occur when the binding of CRP to O₁ promotes the interaction of RNAP to CRP bound at O₂. The additional cooperativity simultaneously increases the maximal fold-change to ω · f₁ · f₂ and enhances the transcriptional sensitivity in the transition region.

Figure 6

Simple repression. (a) Cis-regulatory structure of the truncated lac promoter, with the main operator O_m (yellow box) located closely downstream of the core promoter (blue box). Repressor bound at O_m will block RNAP binding to the promoter, as denoted by the overlap (green box). The DNA-binding affinity of LacI₄ for O_m is described by the dissociation constant K_m. (b) Log–log plot of the fold-change in gene expression as a function of LacI₄. Here, the repressor concentration shown on the horizontal axis refers to the cellular LacI tetramers in the absence of inducers. The experiments of Oehler et al. [27] used the operator sequences O1, O2, O3 at position O_m and measured fold-repression at two different LacI concentrations (50 nM and 900 nM); the data are shown as circles. The expected form of the fold-changes are plotted as the solid, dotted and dashed lines as indicated in the legend. The value of K_m for each curve (see legend) is determined by fitting one of the two data points. The fact that the other data point lies closely on the curve supports the applicability of the thermodynamic model to this promoter.

Figure 7

Repression by DNA looping. (a) Cis-regulatory layout for looping and repression in the lac promoter experiments of Oehler et al. [27]. Yellow boxes are operators and the blue box is the promoter. LacI tetramer bound at the main operator O_m interferes with RNAP binding to the promoter, and this is indicated by the overlap (green box) between the promoter and the operator. This binding is further stabilized if the other two legs of the tetramer bind at O_a through DNA-looping. (b) Log–log plot of the fold-change in gene expression as a function of LacI₄ concentration for different constructs where O_m is replaced by O1, O2, or O3 and O_a is O2. The curves are generated by plotting Case 9 of Table 1 using the appropriate dissociation constants shown in Figure 6 for each pair of operators involved. Note that the six data points (shown with circles) can all be brought into agreement with the expected form (the lines) by the choice of a single parameter, the available LacI₄ concentration [L] due to looping. The best-fit value obtained is [L] ≈ 660 nM. (c) Log–linear plot of the transcriptional fold-change as a function of distance D between O1 (located at position O_m) and an auxiliary operator Oid located upstream of the promoter, for various repressor concentrations. The data of [34] (filled circles) are fitted to the transcriptional fold-changes expected for looping (solid line) using [LacI₄] = 50 nM and values of K₁ ≈ 0.27 nM and K_id 0.05 nM determined from the data of [27]. The fitting function is the dependence of the available concentration due to looping, [L], on the operator spacing D. We use the form [L] = exp(−a/D − b · ln(D) + c · D + e) motivated by the worm-like chain model of DNA bending [48]. The other lines correspond to the predicted gene expression of the same constructs at different LacI concentrations as indicated in the legend. (d) Log–linear plot of [L] versus D obtained from the fit described in (d), with a = 140.6, b = 2.52, c = 1.4 × 10⁻³, e = 19.9.

Figure 8

Enhanced sensitivity by dual repression. (a) Cis-regulatory architecture for cooperative transcriptional repression in phage lambda P_R promoter. The yellow boxes denote the operator sites O_R1, O_R2 and the blue box corresponds to the promoter. Repression is indicated by the overlap (green box) between the promoter and operator. The cooperative interaction between bound cI₂ at operators O_R1 and O_R2 is given by ω (protein–protein contacts). (b) Log–log plot of the fold-change in gene expression as a function of cI₂ concentration for two different values of K_R2/K_R1. At high repressor concentrations, the maximum log–log slope(s) for all the curves is equal to 2 with the exception of K_R2/K_R1 = 0 (i.e. deletion of O_R1) where the maximum log–log slope is equal to 1. The latter case corresponds to a single repressive site, O_R2 (see Figure 6). This plot was generated using ω ≈ 100, and K_R2/K_R1 ≈ 25 extracted from in vitro biochemical studies [47]. The absolute in vivo values of the K values are unknown, which is why our concentration is expressed in terms of [cI₂]/K_R2. (c) Cis-regulatory architecture for transcription repression in P_LtetO-1 promoter engineered by Lutz and Bujard [38]. Note that there is no cooperative interaction between the TetR dimers. The log–log plot of fold-change of P_LtetO-1 promoter is similar to that of phage lambda P_R with a maximum log–log slope equal to 2.