= RNA melting log-odds plot
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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> predicts
$$
y=-\frac{\Delta H_u}{R}x+\frac{\Delta S_u}{R}.
$$
The 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 $-\ln4$ and 0, giving
$$
\frac{\Delta H_u}{R}=\frac{\ln4}{1/300-1/320}\approx6654\,\mathrm K.
$$
The fitted <enthalpy> is approximately $55.3\,\mathrm{kJ\,mol^{-1}}$, and the model predicts $f_U\approx0.773$ 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 uncertainty>
$$
u_y\approx\frac{u_f}{f_U(1-f_U)}.
$$
For the same small <standard uncertainty> $u_f=0.001$, this gives $u_y\approx0.004$ 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.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[§5, first-order sensitivity-coefficient method; derivatives here are for the stated transformation.]{ref}
Fractions inferred from <absorbance> also inherit the fitted <RNA melting baselines>. Optical-melting thermodynamics depends on this modeling step.<Thermodynamic characterization of naturally occurring RNA tetraloops by Justin P. Sheehy and others>[Materials and Methods, optical curves and thermodynamic fitting.]{ref} Curvature may motivate testing baseline errors, additional states or changes in <heat capacity>; the plot alone does not identify which explanation is correct.
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