= Concentration dependence of RNA melting
The <concentration dependence of RNA melting> is the change of an <RNA melting temperature> or population curve with total strand <molar concentration>, while other solution conditions are held fixed. It helps distinguish intramolecular <RNA hairpin melting> from association of separate strands, provided the system reaches <chemical equilibrium>.
For an ideal unimolecular folded-to-unfolded transition, $F\rightleftharpoons U$, the <equilibrium constant> is $K_u=[U]/[F]$. Multiplying both populations by the same amount leaves their ratio unchanged: the <two-state RNA melting model> has no total-concentration term. By contrast, consider <self-complementary RNA duplex melting>, with association $2S\rightleftharpoons D$. Let $c_T=[S]+2[D]$ count strands and let $c^\circ$ denote the reference <molar concentration> of the <standard state>. The dimensionless association <equilibrium constant> is
$$
K_a=\frac{[D]/c^\circ}{([S]/c^\circ)^2}.
$$
At the midpoint defined by half the strands belonging to duplexes, $[D]=c_T/4$ and $[S]=c_T/2$, giving \b[$K_a(T_m)=c^\circ/c_T$]. This factor follows from strand counting; a different reaction or midpoint convention requires its own derivation.
An original ideal calculation assumes constant association <enthalpy> $\Delta H_a=-200\,\mathrm{kJ\,mol^{-1}}$ and a midpoint $330\,\mathrm K$ at $1\,\mathrm{\mu M}$. Increasing strand <molar concentration> tenfold gives
$$
\frac1{T_{m,2}}=\frac1{330\,\mathrm K}-\frac{R\ln10}{200000\,\mathrm{J\,mol^{-1}}},
$$
or approximately $340.8\,\mathrm K$. Here $R$ is the molar gas constant. Greater strand availability favors association, so more heating is needed to reach the same strand-based midpoint.
Experimentally, one records <RNA optical melting> curves at several strand <molar concentrations>, with matched solvent conditions. A tetraloop study found concentration-independent transitions over approximately a 50-fold range, supporting intramolecular stem–loop formation.<Thermodynamic characterization of naturally occurring RNA tetraloops by Justin P. Sheehy and others>[Materials and Methods, Optical melting experiments and thermodynamics.]{ref} This test is conditional on reversibility: a kinetically trapped association can fail to show the expected equilibrium concentration response.
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