WOLFRAM|DEMONSTRATIONS PROJECT

Two-State Protein Melting Curve (N, P, T Ensemble)

​
o
ΔH
T
m
This Demonstration illustrates the fraction (
Q
) of a two-state protein (or other biomolecule) that has melted at temperature
T
. The two states of the protein are denoted
N
(native or folded) and
D
(denatured or melted) and we consider the dynamic equilibrium
N⇌D
. The ratio of the two states' equilibrium concentrations is
[D]
[N]
=exp[-ΔG°/(RT)]
, where
ΔG°(=ΔH°-TΔS°
) is the standard state Gibbs free energy difference and
R
is the universal gas constant (8.314 J/mol-K). Melting occurs when
ΔG°=0
(i.e.,
[D]=[N]
).
Q≡
[D]
[N]+[D]
=
-1
1+
[N]
[D]
=
-1
(1+exp[ΔG°/(RT)])
=
-1
(1+exp[(ΔH°-TΔS°)/(RT)])
. The parameter
ΔH°
(standard state enthalpy difference) controls the steepness of the transition, but does not affect the location of the point where
Q=0.5
. The temperature (
T
) at which
Q=0.5
is
T
m
and
ΔS°=ΔH°/
T
m
.