Aspects of protein-DNA interactions: a review of quantitative thermodynamic theory for modelling synthetic circuits utilising LacI and CI repressors, IPTG and the reporter gene lacZ

Abstract

Protein-DNA interactions are central to the control of gene expression across all forms of life. The development of approaches to rigorously model such interactions has often been hindered both by a lack of quantitative binding data and by the difficulty in accounting for parameters relevant to the intracellular situation, such as DNA looping and thermodynamic non-ideality. Here, we review these considerations by developing a thermodynamically based mathematical model that attempts to simulate the functioning of an Escherichia coli expression system incorporating two of the best characterised prokaryotic DNA binding proteins, Lac repressor and lambda CI repressor. The key aim was to reproduce experimentally observed reporter gene activities arising from the expression of either wild-type CI repressor or one of three positive-control CI mutants. The model considers the role of several potentially important, but sometimes neglected, biochemical features, including DNA looping, macromolecular crowding and non-specific binding, and allowed us to obtain association constants for the binding of CI and its variants to a specific operator sequence.

Keywords: Escherichia coli expression system; Lambda CI repressor; Mathematical model; Synthetic biology; lac repressor.

Fig. 1

The Escherichia coli expression/reporter system constructed by Kolkhof and Müller-Hill (1994). Expression of the cI gene on plasmid pSX 100cI occurs upon binding by RNA polymerase (RNAP) to promoter P_S. LacI represses expression of the cI gene by binding to operators adjacent to P_S; isopropyl β-D-1-thiogalactopyranoside (IPTG) induces cI expression by binding to LacI, greatly reducing LacI’s affinity for its operators (see Fig. 3). Expression of lacZ, the gene for the reporter enzyme β-galactosidase, occurs upon binding by RNAP to promoter P_RM on the E. coli chromosome. CI activates expression of lacZ when bound immediately adjacent to P_RM-bound RNAP (see Fig. 4)

Fig. 2

CI wild-type dimer bound to operator DNA [PDB ID: 3bdn (Stayrook et al. 2008)]. The positive-control (pc) mutants in the Kolkhof and Müller-Hill study (1994) arise from separate changes in three residues in the helix–turn–helix region of CI, namely: pc-1: G43R, pc-2: D38N and pc-3: E34K. Image of PDB ID: 3bdn (Stayrook et al. 2008) created with Protein Workshop (Moreland et al. 2005), http://www.pdb.org

Fig. 3

LacI repression of transcription from synthetic promoter P_S. Our modelling was based on the following proposed operation of the P_S control region: LacI, bound to operator O_id1 by its IPTG-free dimeric-half, sterically hinders RNAP from binding to P_S, and vice versa. LacI, bound to O_id2, reduces the initiation rate constant of RNAP by destabilising the elongating RNAP. LacI can form looped complexes by simultaneously binding to O_id3 and either O_id1 or O_id2, inhibiting RNAP from binding to the promoter. IPTG induces CI expression by binding LacI and effecting an allosteric transition that greatly reduces the ability of LacI to bind its operators. The midpoint of O_id3 is 83 base pairs upstream of the midpoint of O_id1, while O_id1 and O_id2 are separated by 24 bp, centre to centre

Fig. 4

CI control of transcription from promoter P_RM. Our modelling was based on the standard alternate pairwise mechanism of CI binding to the P_RM control region (Shea and Ackers ; Ptashne 2004), where CI dimers are bound cooperatively at operators O_R1 and O_R2, and a CI dimer bound at O_R2 activates transcription from P_RM. CI bound to O_R3 excludes RNAP from P_RM and vice versa. Note that, in the Kolkhof and Muller-Hill system, the LacZ reporter gene has been placed downstream of P_RM and that O_R3 (here named O_R3r) has two mutated base pairs (r3r1) which reduce CI binding (Kolkhof and Müller-Hill 1994)

Fig. 5

Fit of the effect of increasing amounts of wild-type CI on P_RM-lacZ activity. The solid line was obtained by setting K _IL = 0.48 μM⁻¹, and K _3r = 5.0 μM⁻¹, equal to K ₃. The dashed line was obtained by setting K _IL = 0.48 μM⁻¹ and K _3r = 1.0 μM⁻¹. Other parameters were as given in Table 1. The data points here and in subsequent figures are taken from Kolkhof and Müller-Hill (1994)

Fig. 6

Parameter sensitivity in fitting of wild-type CI data. The long dashed line shows the effect of halving K _PR (i.e. reduced from 0.65 to 0.325 nM⁻¹). The short dashed line shows the effect of reduction in K _IL from 0.48 to 0.38 μM⁻¹. The solid line is the original simulation, shown as coincident with the combined effect of halving K _PR and reducing K _IL from 0.48 to 0.38 μM⁻¹. Other parameters were as given in Table 1

Fig. 7

Fit of the effect of increasing amounts of the CI pc mutants on P_RM-lacZ activity. Note the change in scale of the ordinate axis here compared to Figs. 5 and 6. a CI pc-1. The solid line was obtained by setting α_CI = 1 and K _3r = 75 μM⁻¹. b CI pc-2. The solid line was obtained by setting α_CI = 1 and K _3r = 5.0 μM⁻¹. c CI pc-3. The solid line was obtained by setting α_CI = 1 and K _3r = 2.5 nM⁻¹. The dashed line illustrates the effect of also increasing K _ns, the CI-non-specific DNA binding constant, 100-fold. In a–c, other parameters were as given in Table 1