Characterize protein stability curves as a function of temperature In the lectur
ID: 218668 • Letter: C
Question
Characterize protein stability curves as a function of temperature
In the lecture we derived an expression that describes the free energy of unfolding for proteins as a function of temperature. This expression uses the unfolding/melting temperature of the protein Tm, the enthalpy of unfolding ?uHº(Tm) at the melting temperature, and the difference in the heat capacities ?CP between the folded and unfolded proteins as parameters. These parameters can be obtained from a standard differential scanning calrimetry experiments, for example.
?uGº(T) = ?uHº(Tm) (1–T/Tm) +?CP [T–Tm–T ln(T/Tm)]
The main assumtpion underlying this expression is that ?CP can be considered as constant, i.e. indepdenent of the temperature.
Here, assume a protein with a melting/unfolding temperature of 78 ºC, an enhtalpy of unfolding ?uHº(Tm) of 400 kJ/mol and a ?CP of 9 kJ/(K mol).
Part A - Temperature of maximum stability
Calculate the temperature of maximum stability of the protein, i.e. the temperature for which the unfolding free energy reaches a maximum.
Provide your answer with 3 significant figures. The margin of error is 2%.
Part B - How many proteins are unfolded?
Estimate how many proteins per million will be statistically unfolded at the temperature of maximum stability.
Provide your answer with 3 significant figures. The margin of error is 2%.
Part C - Cold dentauration
We observed that the protein stability curve as described by the derived expression indicates that the native fold of proteins is only stable in a temperature window, i.e. that denaturation not only occurs at high temperatures, but also at low temperatures (although the latter typically lies below the freezing temperature of water). Estimate the cold denaturation temperature of the proteins in this example.
Note: Have a look into the Newton-Raphson method (https://en.wikipedia.org/wiki/Newton%27s_method) to numerically determine the roots xn of a function f(x), which satisy f(xn)=0. Choose a starting temperature lower than the temperature of maximum stability. 5-6 iterations should provide you with a converged numerical result.
Provide your answer with 3 significant figures. The margin of error is 10%.
Explanation / Answer
Differential scanning colorimetry is a thermoanalytical method to analyse the stability curve of the proteins as a function of temperature. It ia analysed in terms of free energy change to break the electrostatic interactions during melting of the protein. Now since the change in the heat capacities between the folded and unfolded form of protein is constant so ?CP is zero hence the equation becomes :
?uGº(T) = ?uHº(Tm) (1–T/Tm)
PART A : The temperature of maximum stability of the protein, means the temperature for which the unfolding free energy reaches a maximum, so ?uGº(T) is also maximum. Maximum ?uGº(T) can only be obtained when T is very low. So , the temp of maximum stability shall be almost equal to 351.5F (78 ºC).