Protein Folding
[1] Analyzing Urea Denaturation Curves
Protein X was denatured with urea at 25
oC. The raw data, spectroscopic signal as a function of urea concentration, are in the file
protXudc.txt. Using 100 as the signal for the folded protein Y
F, and 0 as the signal for the unfolded protein Y
U, calculate the conformational stability, ΔG
H2O, of protein X in units of kcal/mol. Remember that the value of R in those units is 0.001987 kcal/mol/K.
Show Answer
The conformational stability of protein X is 3.5 kcal/mol. The m value is 0.8 kcal/mol/M. From the raw data, ΔG is calculated at each point in the transition region using the equation:
$$\Delta G = {-RT\ln{{Y_F - Y} \over {Y - Y_U}}},$$
The values of ΔG calculated in the transition region (±1 kcal/mol) are shown below.
| [urea] (M) | Signal (Y) | ΔG (Kcal/mol) |
| 3.15 | 83.95 | 0.98 |
| 3.50 | 76.52 | 0.70 |
| 3.85 | 67.02 | 0.42 |
| 4.20 | 55.88 | 0.14 |
| 4.55 | 44.12 | -0.14 |
| 4.90 | 32.98 | -0.42 |
| 5.25 | 23.48 | -0.70 |
| 5.60 | 16.05 | -0.98 |
The values of ΔG from the transition region are plotted below as a function of urea concentration. The line is a linear fit to these data. The conformational stability, ΔGH2O, of protein X is the Y intercept of this plot, 3.5 kcal/mol.
[2] Analyzing Urea Denaturation Curves—Nonlinear Least–Squares Fitting
Protein Y was denatured with urea at 25
oC. The raw data, spectroscopic signal as a function of urea concentration, are in the file
protYudc.txt. Analyze these data using nonlinear least-squares fitting by fitting the equation
$$Y = {{(Y_F+m_F[urea]) + (Y_U+m_U[urea])e^{-({{\Delta G_{H_20} - m[urea]}\over {RT}})}}\over{1 + e^{-({{\Delta G_{H_2O} - m[urea]}\over {RT}})}}}$$
to your data. This fit will have six (6) parameters, YF and mF, the intercept and slope of the pre-transition baseline, YU and mU, the intercept and slope of the post-transition baseline, and ΔGH2O and m, the free energy difference between native and denatured states in water and the denaturant dependence of the free energy change, in units of Kcal/mol/M.
Show Answer
The values of interest from the fitting are ΔGH2O and m, in units of Kcal/mol and Kcal/mol/M, respectively. The slopes and intercepts of the baselines have no significant thermodynamic meaning. Below is an image of the best fit of the above equation to these data.
The figure below illustrates the design of the worksheet, with the translation of the above equation, used to fit these data. The numeric values of ΔGH2O and m are 5.4 Kcal/mol and 1.4 Kcal/mol/M.
