= Self-complementary RNA duplex melting
<Self-complementary RNA duplex melting> dissociates a duplex formed by two copies of the same <RNA> strand into separate strands. Self-complementarity means that the strand's <reverse complement> can match its own <nucleotide sequence>. The reaction has molecularity two in the association direction, unlike intramolecular <RNA hairpin melting>.
Use the ideal association model $2S\rightleftharpoons D$. Let total strand <molar concentration> be $c_T=[S]+2[D]$ and paired-strand fraction be $f=2[D]/c_T$. With reference <molar concentration> $c^\circ$, the dimensionless <equilibrium constant> is
$$
K_a=\frac{[D]c^\circ}{[S]^2}.
$$
Substituting $[S]=c_T(1-f)$ and $[D]=fc_T/2$ gives
$$
\alpha=\frac{K_ac_T}{c^\circ}=\frac{f}{2(1-f)^2},\qquad
f=\frac{4\alpha}{4\alpha+1+\sqrt{8\alpha+1}}.
$$
The final expression is the physical solution for a <self-complementary RNA duplex population>; the algebraically equivalent subtractive form loses numerical precision at small $\alpha$.
At $\alpha=1$, half the strands are paired. For an original $c_T=10\,\mathrm{\mu M}$ example, this means $[D]=2.5\,\mathrm{\mu M}$ and $[S]=5\,\mathrm{\mu M}$. Duplexes are only one-third of the independently diffusing molecular objects, $[D]/([D]+[S])=1/3$. Half the strands is not half the objects. At fixed <temperature> and $K_a$, increasing $c_T$ tenfold makes $\alpha=10$ and $f=0.8$.
Heating changes $K_a$ and thus the population. At the strand-based midpoint, $K_a(T_m)=c^\circ/c_T$, which explains the <concentration dependence of RNA melting>. A fit should state whether its constant describes association or dissociation and whether concentration counts strands or duplexes.
Real sequences can also form competing hairpins. A primary tetraloop study explicitly compared predicted hairpin and duplex equilibria when designing its optical-melting sequences.<Thermodynamic characterization of naturally occurring RNA tetraloops by Justin P. Sheehy and others>[Materials and Methods, Design of sequences for optical melting studies.]{ref} The equations above assume only separated strands and duplexes; they do not automatically cover competing folds or <RNA melting hysteresis>.
Back to article page
