Theoretical analysis of inducer and operator binding for cyclic-AMP receptor protein mutants

Abstract

Allosteric transcription factors undergo binding events at inducer binding sites as well as at distinct DNA binding domains, and it is difficult to disentangle the structural and functional consequences of these two classes of interactions. We compare the ability of two statistical mechanical models-the Monod-Wyman-Changeux (MWC) and the Koshland-Némethy-Filmer (KNF) models of protein conformational change-to characterize the multi-step activation mechanism of the broadly acting cyclic-AMP receptor protein (CRP). We first consider the allosteric transition resulting from cyclic-AMP binding to CRP, then analyze how CRP binds to its operator, and finally investigate the ability of CRP to activate gene expression. We use these models to examine a beautiful recent experiment that created a single-chain version of the CRP homodimer, creating six mutants using all possible combinations of the wild type, D53H, and S62F subunits. We demonstrate that the MWC model can explain the behavior of all six mutants using a small, self-consistent set of parameters whose complexity scales with the number of subunits, providing a significant benefit over previous models. In comparison, the KNF model not only leads to a poorer characterization of the available data but also fails to generate parameter values in line with the available structural knowledge of CRP. In addition, we discuss how the conceptual framework developed here for CRP enables us to not merely analyze data retrospectively, but has the predictive power to determine how combinations of mutations will interact, how double mutants will behave, and how each construct would regulate gene expression.

Fig 1. Key parameters governing CRP function.

(A) Within the MWC and KNF models, each CRP subunit can assume either an active or an inactive conformation with a free energy difference ϵ between the two states. cAMP can bind to CRP (with a dissociation constant $M_D^A$ in the active state and $M_D^I$ in the inactive state) and promotes the active state ($M_D^A<M_D^I$ in the MWC model; $M_D^I\to \infty$ in the KNF model). Active CRP has a higher affinity for the operator ($L_D^A$) than the inactive state ($L_D^I$). When CRP is bound to DNA, it promotes RNA polymerase binding through an interaction energy ϵ_P, thereby enhancing gene expression. (B) Lanfranco et al. constructed a single-chain CRP molecule whose two subunits could be mutated independently. All possible dimers are shown using five mutant subunits: wild type (WT), D (D53H), S (S62F), G (G141Q), and L (L148R). Lanfranco et al. constructed the six mutants comprised of WT, D, and S (black and pink boxes) and analyzed each mutant independently.

Fig 2. Macroscopic states and Boltzmann weights for cAMP binding to CRP.

(A) Within the MWC model, cAMP (purple circles) may bind to a CRP subunit in either the active (dark green) or inactive (light green) state. $M_L^A$ and $M_L^I$ represent the dissociation constants of the left subunit in the active and inactive states, respectively, while $M_R^A$ and $M_R^I$ represent the analogous dissociation constants for the right subunit. [M] denotes the concentration of cAMP and ϵ represents the free energy difference between each subunit’s inactive and active states with $\beta =\frac{1}{k_{B}T}$. ${ϵ}_{\text{int}}^A$ and ${ϵ}_{\text{int}}^I$ represent a cooperative energy when two cAMP are bound to CRP in the active and inactive states, respectively. (B) The KNF model assumes that the two CRP subunits are inactive when unbound to cAMP and transition to the active state immediately upon binding to cAMP. The parameters have the same meaning as in the MWC model, but states where one subunit is active while the other is inactive are allowed.

Fig 3. cAMP binding for different CRP mutants.

In addition to the wild type CRP subunit (denoted WT), the mutation D53H (denoted D) and the mutation S62F (denoted S) can be applied to either subunit as indicated by the subscripts in the legend. (A) Curves were characterized using the MWC model, Eq (1). The D subunit increases CRP’s affinity for cAMP while the S subunit decreases this affinity. (B) Asymmetrically mutating the two subunits results in distinct cAMP binding curves. The data for the WT/D mutant lies between the WT/WT and D/D data in Panel A, and analogous statements apply for the WT/S and D/S mutants. (C) The fraction of CRP in the active state. Within the MWC model, mutants with an S subunit will be inactive even in the limit of saturating cAMP. (D) The symmetric and (E) asymmetric mutants can also be analyzed using the KNF model, Eq (6), resulting in curves that are similar to those found by the MWC model. (F) The KNF model predicts that all CRP mutants will be completely active in the limit of saturating cAMP. The (corrected) sample standard deviation $\sqrt{\frac{1}{n-1}{\sum }_{j=1}^n{(y_{\text{theory}}^{\left(j\right)}-y_{\text{data}}^{\left(j\right)})}^2}$ equals 0.03 for the MWC model and 0.05 for the KNF model, and the best-fit parameters for both models are given in Table 1. Data reproduced from Ref. [29].

Fig 4. States and weights for CRP binding to DNA.

The DNA unbound states from Fig 2 are shown together with the DNA bound states. The Boltzmann weight of each DNA bound state is proportional to the concentration [L] of CRP and inversely proportional to the CRP-DNA dissociation constants L_A or L_I for the active and inactive states, respectively.

Fig 5. The interaction between CRP and DNA.

Anisotropy of 32-bp fluorescein-labeled lac promoter binding to CRP_D/S at different concentrations of cAMP. An anisotropy of 1 corresponds to unbound DNA while higher values imply that DNA is bound to CRP. In the presence of cAMP, more CRP subunits will be active, and hence there will be greater anisotropy for any given concentration of CRP. The sample standard deviation $\sqrt{\frac{1}{n-1}{\sum }_{j=1}^n{(y_{\text{theory}}^{\left(j\right)}-y_{\text{data}}^{\left(j\right)})}^2}$ is 0.01, with the corresponding parameters given in Tables 1 and 2. Data reproduced from Ref. [29].

Fig 6. States and weights for a simple activation motif.

Binding of RNAP (blue) to a promoter is facilitated by the binding of the activator CRP. Simultaneous binding of RNAP and CRP is facilitated by an interaction energy ${ϵ}_{P,L_A}$ for active CRP (dark green) and ${ϵ}_{P,L_I}$ for inactive CRP (light green). cAMP (not drawn) influences the concentration of active and inactive CRP as shown in Fig 4.

Fig 7. Predicted gene expression profiles for a simple activation architecture.

(A) Gene expression for wild type CRP (green dots from Ref. [7]), where 1 Miller Unit (MU) represents a standardized amount of β-galactosidase activity. This data was used to determine the relevant parameters in Eq (14) for the promoter in the presence of [L] = 1.5 μM of CRP [45]. The predicted behavior of the CRP mutants is shown using their corresponding cAMP dissociation constants. (B) The spectrum of possible gene expression profiles can be categorized based upon the cAMP-CRP binding affinity in each subunit. In all cases, we assumed $M_L^A=M_R^A=3\times {10}^{-6}\text{M}$ and $e^{-\beta {ϵ}_{\text{int}}^A}=0$. The activation response (blue) was generated using $M_L^I=M_R^I=6\times {10}^{-6}\text{M}$. The repression response (orange) used $M_L^I=M_R^I={10}^{-7}\text{M}$. The peaked response (gold) used $M_L^I={10}^{-7}\text{M}$ and $M_R^I=300\times {10}^{-6}\text{M}$. The flat response used $M_L^I=M_R^I=3\times {10}^{-6}\text{M}$. The remaining parameters in both plots were $\frac{\left[P\right]}{P_D}=130\times {10}^{-6}$, $r_{\text{trans}}=5\times {10}^5\frac{\text{MU}}{\text{hr}}$, γ = 0.1, ${ϵ}_{P,L_A}=-3k_{B}T$, ${ϵ}_{P,L_I}=0k_{B}T$, ϵ = −3k_BT, and those shown in Tables 1 and 2.