= RNA melting relaxation time
{c}
An <RNA melting relaxation time> characterizes how quickly a perturbed <RNA> population approaches its new equilibrium. It belongs to a specified kinetic model, <temperature>, solution and measured signal. It is not an <RNA melting temperature> or, in general, the mean waiting time for an individual unfolding event.
For a reversible <two-state RNA melting model>, let $k_u$ be the first-order unfolding <rate constant> and $k_f$ the refolding <rate constant>. The unfolded fraction obeys
$$
\frac{df_U}{dt}=k_u(1-f_U)-k_ff_U.
$$
At fixed <temperature>,
$$
f_{U,\rm eq}=\frac{k_u}{k_u+k_f},\qquad
\tau=\frac1{k_u+k_f},\qquad
f_U(t)-f_{U,\rm eq}=[f_U(0)-f_{U,\rm eq}]e^{-t/\tau}.
$$
Both directions contribute to the return to equilibrium. For original stipulated values $k_u=20\,\mathrm{s^{-1}}$ and $k_f=80\,\mathrm{s^{-1}}$, $f_{U,\rm eq}=0.20$ and $\tau=10\,\mathrm{ms}$. The mean lifetime of an isolated folded state in this model is $1/k_u=50\,\mathrm{ms}$, which differs from the observed population <exponential decay> time.
A <temperature jump> shifts populations rapidly enough to reveal the subsequent motion. A primary study used 4-ns heating pulses, a 12-μm sample path and time-resolved <infrared spectroscopy> to follow melting and refolding of a UACG-containing <RNA hairpin>. Thin-cell cooling enabled direct observation of the return process. Its loop is UACG, not a <UUCG tetraloop>.<Measuring RNA UNCG Tetraloop Refolding Dynamics Using Temperature-Jump Drop Infrared Spectroscopy by C. P. Howe and others>[Printed pp.9171–9172, sequence and pump/probe apparatus; Abstract, melting and refolding dynamics.]{ref}
An <RNA relaxation instrument-response correction> may be needed if heating, detector response or cooling occur on comparable timescales. A changing sample <temperature> changes the equilibrium target during the measurement, invalidating a constant-temperature fit across the whole trace. Multiple kinetic states can also produce several decay components. One fitted exponential should therefore be identified as a model-dependent observed relaxation, rather than automatically assigned to a unique molecular step.
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