Folding Thermodynamics of PagP Protein Mutants

The PagP samples for equilibrium folding and unfolding in DPC were prepared by 10-fold dilution of the respective protein stocks in various GdnHCl concentrations ranging from ∼0.7 to ∼6.6 m, at an increment of 0.1 m. This gave us a final protein concentration of 3 μm and DPC of 10 mm in each reaction. Samples were incubated at 25 °C, and fluorescence measurements were acquired on a microplate reader at the same temperature. We monitored the progress of the reactions using the decrease in tryptophan fluorescence emission intensity, with increase in GdnHCl concentration. Spectra were acquired using a λ_ex of 295 nm and λ_em of 320–400 nm. For PagP and its mutants, equilibrium for the reaction was achieved within 24 h.
From the fluorescence profiles, we calculated the unfolded fraction (f_U) for the 48-h data using the following equation.
$f_{\text{U}}=\frac{y_{\text{O}}-\left(y_{\text{F}}+m_{\text{F}}\left[D\right]\right)}{\left(y_{\text{U}}+m_{\text{U}}\left[D\right]\right)-\left(y_{\text{F}}+m_{\text{F}}\left[D\right]\right)}$ Here, y_O is the observed fluorescence at GdnHCl concentration [D], whereas y_F, m_F, y_U, and m_U are intercepts and slopes of the pre- and post-transition baselines, respectively.
We were able to explain the folding transitions for most of the mutants using the two-state equation (42 (link)).
$f_{\text{U}}=\frac{\exp \left(-\left(\Delta G+m\left[D\right]\right)/RT\right)}{1+\exp \left[-\left(\Delta G+m\left[D\right]\right)/RT\right]}$ This equation assumes that the protein folds in a cooperative manner from the unfolded (U) to the folded (F) state, without a detectable folding intermediate. We obtained the thermodynamic parameters ΔG⁰ (ΔG_F^0,H2O, folding free energy) and m value (change in ASA between U and F states) of folding from the fits. The midpoint of chemical denaturation (C_m) was calculated as C_m = ΔG/m.
The folding transition of some mutants could only be explained using a three-state equation (Equation 3), due to the occurrence of an intermediate (I) (7 (link)).
$f_{\text{U}}=\frac{\left(y_{\text{F}}+m_{\text{F}}\left[D\right]\right)+\left(\exp \left(-\frac{\Delta G_1+m_1\left[D\right]}{RT}\right)\left(y_{\text{I}}+m_{\text{I}}\left[D\right]\right)\right)+\left(\exp \left(-\frac{\Delta G_1+m_1\left[D\right]}{RT}\right)\exp \left(-\frac{\Delta G_2+m_2\left[D\right]}{RT}\right)\left(y_{\text{U}}+m_{\text{U}}\left[D\right]\right)\right)}{1+\exp \left(-\frac{\Delta G_1+m_1\left[D\right]}{RT}\right)+\exp \left(-\frac{\Delta G_1+m_1\left[D\right]}{RT}\right)\exp \left(-\frac{\Delta G_2+m_2\left[D\right]}{RT}\right)}$
Here, we obtained ΔG₁ and ΔG₂ and their corresponding m₁ and m₂ values for the change in free energy from the first (U → I) and second (I → N) transitions, respectively.
The PagP samples for folding in DLPC were prepared as described above. We used the same parameters for data acquisition in DLPC samples as for DPC. From the fluorescence profiles, we calculated the unfolded fraction (f_U) for the 48-h data using Equation 1. The data were fitted globally to Equation 2, assuming a common m value. Fits of the data to Equation 2 yielded the apparent thermodynamic parameters, namely the apparent change in free energy ΔG_app, apparent ASA change m_app, and C_m for each mutant.