# Finding the thermodynamics of protein unfolding from temperature and absorbance using fluorescence spectroscopy?

I recently did an experiment on protein unfolding using a Perkin Elmer fluorescence spectrometer. The protein was $\alpha$-chymotrypsin. I was given this paper for my procedure. I am now trying to make sense of the data.

Increasing temperature was used as the denaturant. Temperature and absorbance were plotted, resulting in an essentially sigmoidal curve describing unfolding. The paper gives the following equation for determining an equilibrium constant for the experiment. $$K_u=\frac {X_N-X}{X-X_D}=\frac {[P_D]_{eq}}{[P_N]_{eq}}$$ Where $K_u$ is the equilibrium constant, $X_N$ is the absorbance for the native state, $X_D$ is the absorbance for the denatured state, and $X$ is any given absorbance. $P_D$ is the denatured protein and $P_N$ is the native protein.

The paper says that the free energy of unfolding can be described by the familiar equation: $$\Delta G = -RT\ln(K_u)$$ I'm fairly sure that I've calculated $K_u$ at each temperature recorded, but I'm not quite sure whether I use each $K_u$ as a point for another plot, or average them, or something else. If I use a Van't Hoff plot to graph each point of $\ln(K_u)$ vs. $\frac {1}{T}$, will the slope and intercept be $\frac{-\Delta H}{R}$ and $\frac{\Delta S}{R}$ respectively? I think so due to the rearrangement described here, and perhaps I've answered my own question as I attempted to ask it. Nevertheless, I would appreciate having my understanding of this calculation confirmed.

Update: I've plotted $\ln(K_u)$ vs. $\frac {1}{T}$ and the slope of $\ln(K_u)$ vs. $\frac{1}{T}$ is not linear as had been expected. Linear regression analysis gives a trendline with an $R^2$ value of 0.87. Should I separate the data so as to graph $\ln(K_u)$ vs. $\frac {1}{T}$ for points leading up to the sudden unfolding and also for points once unfolding becomes dramatic? This would give me two values for the enthalpy of unfolding--one before it unfolds much and the other for when unfolding is happening quickly. If I do so, will the difference between those enthalpies be the overall enthalpy of unfolding? I'm not sure what the significance of those two values would be.

• As I've looked more into the use of the Van't Hoff plot, it seems that only a maximum and minimum temperature are used. Should I pick these as the initial and final temperatures or the ones that are at the bounds of the steep part of the sigmoidal graph of absorbance vs. T? – Cohen_the_Librarian Dec 12 '14 at 7:44