12. Protein stability is represented as

    Prior to development of sensitive calorimeters, thermodynamic parameters of processes were
    determined by following equation

    ΔH^O and ΔS^O are standard changes m enthalpy and entropy, respectively.

Which one of the following statements is correct for estimating ΔG, ΔH and ΔS?

(1) Determining the ratio of folded and unfolded protein at 37⁰C
(2) Plotting K_eq as a function of ΔH
(3) Plotting K_eq against ΔS
(4) Plotting K_eq against temperature

Introduction

Before the advent of sensitive calorimeters, thermodynamic parameters describing protein stability—such as Gibbs free energy change (ΔG), enthalpy change (ΔH), and entropy change (ΔS)—were estimated using equilibrium measurements between folded and unfolded states. These parameters are crucial to understanding protein folding, stability, and function.

This article explains the correct method for estimating ΔG, ΔH, and ΔS by analyzing the equilibrium constant (Keq) of protein unfolding as a function of temperature.

Protein Stability and Thermodynamics

Protein stability is often represented by the equilibrium between folded (N) and unfolded (D) states:

$$N\rightleftharpoons D$$

The equilibrium constant for unfolding is:

Keq=[D][N]Keq=[N][D]

From this, the standard Gibbs free energy change (ΔG°) can be calculated:

ΔG∘=−RTln⁡KeqΔG∘=−RTlnKeq

where $R$ is the gas constant and $T$ is the absolute temperature.

Estimating ΔG, ΔH, and ΔS

• ΔG° is temperature-dependent and relates to enthalpy (ΔH°) and entropy (ΔS°) changes by:

ΔG∘=ΔH∘−TΔS∘ΔG∘=ΔH∘−TΔS∘

• To determine ΔH° and ΔS°, the van ’t Hoff analysis is used by plotting ln⁡KeqlnKeq against $1/T$ (inverse temperature).

• The van ’t Hoff equation:

ln⁡Keq=−ΔH∘RT+ΔS∘RlnKeq=−RTΔH∘+RΔS∘

• From the slope and intercept of this plot, ΔH° and ΔS° can be derived.

Why Plotting Keq Against Temperature Is Correct

• Plotting KeqKeq or ln⁡KeqlnKeq against temperature or inverse temperature allows extraction of thermodynamic parameters.

• This method was standard before calorimetric techniques, relying on spectroscopic or other measurements to determine the fraction of folded/unfolded protein at various temperatures.

• The ratio of folded to unfolded protein at a single temperature (option 1) provides ΔG but not ΔH and ΔS.

• Plotting Keq against ΔH or ΔS (options 2 and 3) is not meaningful since ΔH and ΔS are derived parameters, not independent variables.

Summary of Options

Conclusion

The correct approach to estimate thermodynamic parameters ΔG, ΔH, and ΔS for protein stability prior to calorimetry is to plot the equilibrium constant (Keq) of unfolding against temperature (or inverse temperature) and analyze the data using the van ’t Hoff equation. This method enables accurate determination of enthalpy and entropy changes associated with protein folding and unfolding.

Keywords

protein stability, thermodynamics, Gibbs free energy, enthalpy, entropy, equilibrium constant, Keq, van ’t Hoff plot, protein unfolding, temperature dependence, pre-calorimeter methods

Final answer:
(4) Plotting Keq against temperature