Introduction

Differential scanning calorimetry (DSC) provides key thermodynamic parameters to characterize DNA thermal denaturation, including:

• Tm: Midpoint temperature of denaturation (°C or K)

• ΔHm: Enthalpy change at Tm (kcal/mole)

• ΔCp: Heat capacity change at constant pressure (kcal/mol·K)

Given these values, the Gibbs free energy change (ΔG) at any temperature T can be estimated using thermodynamic equations derived from the Gibbs-Helmholtz relation.

Given Data

• Tm = 75.5°C = 348.65 K

• ΔHm = 50.4 kcal/mole

• ΔCp = 0 (given)

• Temperature of interest: 37°C = 310 K

Thermodynamic Background

The Gibbs free energy change for DNA denaturation at temperature T (in Kelvin) can be approximated by:

ΔGD(T)=ΔHm(1−TTm)−ΔCp[(Tm−T)−Tln⁡TmT]ΔGD(T)=ΔHm(1−TmT)−ΔCp[(Tm−T)−TlnTTm]

Since ΔCp = 0, the equation simplifies to:

ΔGD(T)=ΔHm(1−TTm)ΔGD(T)=ΔHm(1−TmT)

Calculation Steps

1. Convert temperatures to Kelvin:

   • Tm=75.5+273.15=348.65 KTm=75.5+273.15=348.65K

   • $T=37+273.15=310.15K$

2. Calculate the ratio TTmTmT:

   310.15348.65≈0.889348.65310.15≈0.889

3. Calculate 1−TTm1−TmT:

   $$1-0.889=0.111$$

4. Calculate ΔG at 37°C:

   ΔGD(310 K)=50.4 kcal/mol×0.111=5.6 kcal/molΔGD(310K)=50.4kcal/mol×0.111=5.6kcal/mol

Interpretation

• A positive ΔG indicates that at 37°C, the DNA is predominantly in the double-stranded (folded) state, as denaturation is not spontaneous at this temperature.

• The calculated ΔG of approximately 5.6 kcal/mol aligns with typical DNA stability values near physiological temperature.

Summary Table of Options

Conclusion

Using the given DSC parameters and the simplified Gibbs-Helmholtz equation (with ΔCp = 0), the Gibbs free energy change for calf thymus DNA denaturation at 37°C is approximately 5.6 kcal/mole.

Keywords

Gibbs free energy DNA, DNA thermal denaturation, differential scanning calorimetry, ΔHm, Tm, ΔCp, Gibbs-Helmholtz equation, calf thymus DNA stability, DNA melting temperature, DNA folding thermodynamics

Final answer:
(4) 5.6 kcal/mole