 RNA melting log-odds plot

An RNA melting log-odds plot graphs the natural logarithm of the unfolded-to-folded population ratio against reciprocal absolute temperature. For $0<f_U<1$, let $y=\ln [f_U/(1-f_U)]$ and $x=1/T$. An ideal unimolecular two-state RNA melting model with temperature-independent unfolding enthalpy and entropy predictsThe slope is $-\Delta H_u/R$; the intercept is $\Delta S_u/R$. The equation is a testable model relation, not a reason to treat every transformed optical curve as linear.

For an original worked example, stipulate unfolded fractions 0.20 at $300\mathrm{K}$ and 0.50 at $320\mathrm{K}$. Their log-odds are $-\ln 4$ and 0, givingThe fitted enthalpy is approximately $55.3\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, and the model predicts $f_U\approx 0.773$ at $340\mathrm{K}$. A third measurement tests this prediction; two chosen points always determine a line.

The transformation also changes the noise. First-order uncertainty propagation gives an RNA melting log-odds uncertaintyFor the same small standard uncertainty $u_f=0.001$, this gives $u_y\approx 0.004$ at $f_U=0.5$, but approximately 0.101 at $f_U=0.01$. Thus equal uncertainty in population fractions produces heteroscedasticity in the transformed data; unweighted linear regression can overemphasize unreliable endpoint values. Exactly 0 or 1 cannot be transformed, and replacing them with arbitrary small offsets manufactures finite values.^[ref]

Fractions inferred from absorbance also inherit the fitted RNA melting baselines. Optical-melting thermodynamics depends on this modeling step.^[ref] Curvature may motivate testing baseline errors, additional states or changes in heat capacity; the plot alone does not identify which explanation is correct.