RNA melting relaxation time

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 obeysAt fixed temperature,Both directions contribute to the return to equilibrium. For original stipulated values $k_u=20{\mathrm{s}}^{-1}$ and $k_f=80{\mathrm{s}}^{-1}$, $f_{U,\mathrm{eq}}=0.20$ 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.^[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.

An RNA relaxation instrument-response correction accounts for the way an experiment's heating, detection and recording alter an underlying molecular transient. A measured RNA melting relaxation time can otherwise combine molecular kinetics with instrumental behavior. The response must be characterized for the actual apparatus and measurement conditions.

For an illustrative linear, time-invariant detector, let the normalized instrument response function be $h(t)={\tau }_I^{-1}{e}^{-t/{\tau }_I}$ for $t\ge 0$. Suppose the ideal molecular signal is $s(t)=A{e}^{-t/{\tau }_R}$ after excitation, and both vanish before it. Their convolution gives, for ${\tau }_R\ne {\tau }_I$,The recorded trace rises before decaying even though the assumed molecular transient begins at its maximum. Fitting the entire trace as one unblurred exponential would misdescribe the model.

An original example sets ${\tau }_R=10\mu \mathrm{s}$ and ${\tau }_I=5\mu \mathrm{s}$. The measured signal peaks at $10\ln 2\approx 6.93\mu \mathrm{s}$ with height $A/2$. Its normalized temporal centroid is ${\tau }_R+{\tau }_I=15\mu \mathrm{s}$, rather than 10. These different time summaries cannot be substituted for one another.

One useful approach predicts a molecular transient, convolves it with the characterized instrument response function, and fits that forward prediction to the data. Directly undoing a smoothing response can amplify measurement noise. Parameters that produce nearly indistinguishable recorded curves may remain difficult to determine separately.

Sample cooling is an additional physical process. A primary temperature jump study used a thin sample cell to accelerate cooling enough to observe RNA refolding, with separate infrared probe pulses following the transient.^[ref] If temperature changes during a trace, the molecular equilibrium and rate constants may change too; detector convolution alone does not account for that changing input. The two-exponential example is a stipulated teaching model, not a fit to that paper.