Protein Folding Thermodynamics Calculator

Calculate protein folding stability ΔG, melting temperature Tm, and cooperativity from thermal denaturation data.

ΔH of unfolding (kJ/mol) (kJ/mol)

ΔS of unfolding (kJ/mol·K) (kJ/mol·K)

Temperature T (°C) (°C)

Melting temperature Tm (°C) (°C)

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Why Proteins Are Only Marginally Stable

Folding involves two very large opposing terms. Favourable interactions in the folded state are offset by the enormous entropy lost when a flexible chain adopts one conformation, and the difference between them is remarkably small.

ΔG_unfolding = ΔH − TΔS

Contribution	Magnitude
Favourable enthalpy and hydrophobic burial	Hundreds of kJ/mol
Conformational entropy loss	Hundreds of kJ/mol, opposing
Net stability	Typically 20–60 kJ/mol

Twenty to sixty kJ/mol is the energy of a few hydrogen bonds. A protein is a large difference of two larger numbers, which is why single point mutations can destabilise a fold completely and why proteins denature over a narrow temperature range.

Marginal stability appears to be selected rather than accidental — it permits the conformational flexibility that function requires, and allows regulated degradation.

The Two-State Assumption

The calculation assumes only folded and unfolded states are populated, with no intermediates. Small single-domain proteins approximate this well; larger ones frequently do not.

Test	What it shows
Coincident CD and fluorescence curves	Supports two-state
Non-coincident transitions	Intermediates present
van't Hoff ΔH = calorimetric ΔH	Supports two-state
van't Hoff < calorimetric	Multiple domains unfolding separately

The calorimetric comparison is the rigorous test. Secondary structure loss measured by CD and tertiary structure loss measured by fluorescence should occur together; when they separate, a molten globule or domain intermediate is populated.

Cold Denaturation

Because ΔC_p for unfolding is large and positive, stability is a curved function of temperature with a maximum, typically near 10–25°C. Proteins therefore unfold on cooling as well as heating.

Cold denaturation usually occurs below 0°C and is hard to observe without pressure or destabilising additives, but it is real and explains why the simple linear ΔH − TΔS treatment fails away from T_m.

Worked Examples

Example 1: Lysozyme: ΔH=400kJ, ΔS=1.2kJ/K at 25°C

ΔG=400-298×1.2=42.4kJ/mol

Result: Strongly stable — native fold preferred

Typical mesophilic protein stability 20-60kJ/mol

Example 2: At Tm: dG=0

Fraction folded=fraction unfolded=50%

Result: Tm is the midpoint of thermal transition

Two-state model for cooperative unfolding

Example 3: Detecting an intermediate

CD transition at 52°C, fluorescence at 58°C

Result: Not two-state

Secondary and tertiary structure are lost at different temperatures, indicating a molten globule intermediate between native and unfolded.

Example 4: Why stability is so small

Hundreds of kJ/mol favourable minus hundreds unfavourable

Result: Net 20–60 kJ/mol

A protein is a small difference between two large numbers, which is why single mutations can abolish folding entirely.

Common Mistakes

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Assuming two-state behaviour without testing

Multidomain proteins populate intermediates. Compare CD and fluorescence transitions, or van't Hoff against calorimetric enthalpy.

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Extrapolating linear ΔG far from T_m

The large positive ΔC_p makes stability curved in temperature. Linear extrapolation fails well away from the transition.

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Expecting large stability values

Typical net stability is 20–60 kJ/mol, equivalent to a few hydrogen bonds. Proteins are marginally stable by design.

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Forgetting that proteins cold-denature

Stability has a maximum near 10–25°C and falls at lower temperature too, though usually below the freezing point of water.

Frequently Asked Questions

Two-state model assumptions?

ΔGunfolding = ΔH - TΔS assumes only two states (folded and unfolded). Real proteins: may have intermediates (molten globule). Cooperative unfolding (Hill coefficient n): steep transition. Measured by CD, fluorescence, DSC (differential scanning calorimetry).

Thermophile vs mesophile?

Thermophile proteins: higher Tm (80-120°C), larger ΔH, more hydrophobic core, more salt bridges, shorter loops. ΔG at 25°C may be similar but more stable at high T. Engineering: disulfide bonds, helix capping, proline substitutions increase Tm.

Why are proteins only marginally stable?

Because large favourable interactions are nearly cancelled by conformational entropy loss. Net stability of 20–60 kJ/mol appears to be selected, allowing flexibility and regulated turnover.

How do I test the two-state assumption?

Compare CD and fluorescence melting curves — they should coincide. Rigorously, van't Hoff enthalpy should equal calorimetric enthalpy.

What happens at T_m?

Folded and unfolded states are equally populated, so ΔG is zero and the fraction folded is 50%.

Can proteins denature when cooled?

Yes. The large positive ΔC_p makes stability curved with a maximum near 10–25°C, so cold denaturation occurs — usually below 0°C.