= RNA hairpin melting
{c}
\b[RNA hairpin melting] is the temperature-dependent loss of the folded <stem-loop> structure of an <RNA hairpin>. Here melting describes a molecular conformational transition in solution, rather than conversion of a solid sample into a liquid. Changing <temperature> shifts the relative populations of folded and unfolded <RNA>.
In optical measurements, a <spectrophotometer> tracks <absorbance> while the <RNA> solution is heated under controlled conditions. Changes in base stacking can alter ultraviolet <absorbance>, an effect associated with <RNA hyperchromicity>. In a 2010 tetraloop study, researchers recorded absorbance-versus-temperature curves, repeated measurements over an approximately 50-fold <RNA> concentration range, and observed concentration-independent transitions. That behavior supported intramolecular hairpin formation rather than association of separate strands.<Thermodynamic characterization of naturally occurring RNA tetraloops by Justin P. Sheehy and others>[Materials and Methods, Optical melting experiments and thermodynamics; repeated curves and concentration dependence.]{ref}
An explicit two-state model lets F and U denote folded and unfolded <RNA>. Define unfolding free energy $\Delta G_u=G_U-G_F$ and take temperature-independent unfolding parameters $\Delta H_u$ and $\Delta S_u$:
$$
\Delta G_u(T)=\Delta H_u-T\Delta S_u,\qquad
f_U(T)=\frac{1}{1+\exp[\Delta G_u(T)/(RT)]}.
$$
Here $T$ is absolute <temperature> and $R$ the <molar gas constant>. The <RNA melting temperature> satisfies $\Delta G_u(T_m)=0$, hence $T_m=\Delta H_u/\Delta S_u$ and $f_U(T_m)=1/2$ in this model.
For original stipulated values $\Delta H_u=120\,\mathrm{kJ\,mol^{-1}}$ and $T_m=330\,\mathrm K$, the predicted unfolded fractions at $300$, $330$ and $360\,\mathrm K$ are approximately $0.012$, $0.500$ and $0.975$. They are model calculations, not measurements from the cited study.
Raw <absorbance> is not automatically the unfolded fraction. Even in a two-state interpretation, folded and unfolded baselines can vary with <temperature>: $A(T)=[1-f_U(T)]A_F(T)+f_U(T)A_U(T)$. Baseline estimates, reversibility and alternative conformations affect the inference. A smooth single transition is useful evidence, but it does not independently prove that every <RNA> molecule follows one microscopic pathway.
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