We can use the principles of phase equilibrium to learn about the stability of proteins in biological systems. We consider the phase equilibrium of the protein lysozyme (/) between its

native phase,n, and its denatured phase, d, where unfolding occurs (native denatured), as shown in the Figure below. The following thermo chemical data are available. The heat capacity for each state is independent of temperature and is given by: \text { Denatured: } c_{P, d}=15.1 \frac{k J}{m o l, K} \quad \text { Native: } c_{P, n}=6.0 \frac{k J}{\operatorname{mol} K} At 25°C, the enthalpy and entropy differences between native and denatured states are given by: h_{d}-h_{n}=244 \frac{k J}{m o l} \quad s_{d}-s_{n}=624 \frac{J}{m o l . K} Answer the following questions: At 25°C, which phase is stable? Justify your answer. Using MS Excel or suitable tool, plot the difference in Gibbs energy from the native stateto the denatured state (ga – In) versus temperature, T. [50 points] Using the plot mentioned above, calculate and label the following: i. The heat-denaturation temperature, which is given as the temperature above which the native protein is no longer thermodynamically stable. [10 points] ii. The cold-denaturation temperature, which is given as the temperature below which thenative protein is no longer thermodynamically stable. [10 points] iii. The temperature that the native state is most stable. [10 points]