= RNA baseline extrapolation
{c}
<RNA baseline extrapolation> continues a fitted folded-state or unfolded-state <RNA melting baseline> from its observed temperature range into the transition region. It is necessary when estimating populations from <RNA optical melting>, because both hypothetical pure-state signals are needed at temperatures where the measured sample contains a mixture.
For a linear folded baseline, choose a reference $T_0$ and write
$$
A_F(T)=a+b(T-T_0).
$$
The reference merely changes parameterization. An original fit with $T_0=300\,\mathrm K$, $a=0.400$ and $b=0.001\,\mathrm{K^{-1}}$ predicts 0.420 at $320\,\mathrm K$ and 0.450 at $350\,\mathrm K$. The first prediction might interpolate within measured data; the second extrapolates if all folded-state observations were below $320\,\mathrm K$.
The inferred population depends on that continuation. At $350\,\mathrm K$, suppose measured <absorbance> is 0.600 and the unfolded <RNA melting baseline> is 0.700. The linear folded-baseline prediction gives
$$
f_U=\frac{0.600-0.450}{0.700-0.450}=0.600.
$$
If the actual pure folded-state response there were 0.490, the same optical-mixture equation would instead give $f_U\approx0.524$. A good fit in a limited low-temperature region does not rule out curvature beyond it.
<RNA baseline prediction covariance> is important even within the chosen linear model. With $x=T-T_0$,
$$
u^2(A_F(T))\approx u_a^2+x^2u_b^2+2x\operatorname{Cov}(a,b).
$$
For stipulated independent fit parameters $u_a=0.002$ and $u_b=0.0002\,\mathrm{K^{-1}}$, the prediction's <standard uncertainty> rises from 0.002 at $x=0$ to approximately 0.0102 at $x=50\,\mathrm K$. This is <uncertainty propagation> for estimated parameters; it does not include unmodeled curvature.<Evaluation of measurement data — Guide to the expression of uncertainty in measurement by JCGM>[§§5.1–5.2, linear sensitivities and correlated inputs.]{ref}
Optical-melting experiments fit signal curves to infer thermodynamics.<Thermodynamic characterization of naturally occurring RNA tetraloops by Justin P. Sheehy and others>[Materials and Methods, individual-curve thermodynamic fitting.]{ref} Report which regions constrain each <RNA melting baseline>, inspect residuals and compare plausible baseline forms. Confidence in the fitted parameters and confidence in the functional form are different parts of the inference.
Back to article page
