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 in the active state and
in the inactive state) and promotes the active state (
in the MWC model;
in the KNF model). Active CRP has a higher affinity for the operator (
) than the inactive state (
). When CRP is bound to DNA, it promotes RNA polymerase binding through an interaction energy ϵP, 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. and
represent the dissociation constants of the left subunit in the active and inactive states, respectively, while
and
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
.
and
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 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].
Table 1.
Parameters for cAMP binding to CRP.
The data in Fig 3 can be characterized using a single set of dissociation constants for the WT, D, and S subunits whose values and standard errors are shown. To excise parameter degeneracy, the active-inactive free energy difference ϵ and the cAMP interaction energy in the active state are absorbed into the active state dissociation constants in the MWC model (Eqs (2) and (3)). Similarly, ϵ is absorbed into the KNF dissociation constants (Eqs (6) and (7)).
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 LA or LI 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 CRPD/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 is 0.01, with the corresponding parameters given in Tables 1 and 2. Data reproduced from Ref. [29].
Table 2.
Parameters for CRP binding to DNA.
The anisotropy data for CRPD/S characterized using Eq (9), as shown in Fig 5. Each value is given as a mean ± standard error. The uncertainty in the parameter (shown in Table 1) leads to a corresponding uncertainty in the active CRP dissociation constant LA.
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 for active CRP (dark green) and
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 and
. The activation response (blue) was generated using
. The repression response (orange) used
. The peaked response (gold) used
and
. The flat response used
. The remaining parameters in both plots were
,
, γ = 0.1,
,
, ϵ = −3kBT, and those shown in Tables 1 and 2.