Protein thermal denaturation — Interpreting the midpoint (Tm) of a temperature transition curve

Introduction:
Thermal unfolding of proteins is often monitored by spectroscopy or calorimetry and summarized by a sigmoidal temperature transition. The midpoint temperature, Tm, has precise thermodynamic meaning that connects populations and free energy.

Given Data / Assumptions:

• Two state unfolding model: Native ⇌ Unfolded.
• Definition of Tm as the temperature where the transition is halfway complete.
• Equilibrium constant Keq defined as [Unfolded] / [Native].

Concept / Approach:
At the midpoint of a two state transition, populations of the native and unfolded states are equal. Therefore Keq = 1, and ΔG = -RTln(Keq) equals zero. This also means that exactly half of the protein molecules are denatured in a macroscopic sense.

Step-by-Step Solution:

Verification / Alternative check:
Differential scanning calorimetry shows peak heat absorption near Tm. Although heat capacity changes can be nonzero across the transition, the free energy criterion at Tm remains ΔG = 0 for a two state system with Keq = 1.

Why Other Options Are Wrong:

• Individual statements (a), (b), and (c) are each correct; the combined answer that includes all of them is most complete.
• Heat capacity change is zero at Tm: not a general rule; ΔCp can be significant and does not necessarily vanish at Tm.

Common Pitfalls:
Assuming that half denatured means half of every molecule is unfolded. The interpretation is population based: about half the molecules are native and half unfolded.

Final Answer:
All of these.