5.4.2 Prediction of melting temperatures

The aim of this section is to check how well the new thermodynamic values (see Table 5.3) work to predict the melting temperatures of oligonucleotides under various salt conditions. However, it has to be admitted that the confrontation of our results with the melting temperature of oligos is not the best way to show the reliability of the new NNBP energies. The reason is that most published sets of NNBP values obtained with different calorimetric or optical methods agree within 2$ ^\circ $C (in average), revealing that the melting temperature is not necessarily a very robust indicator. In fact, the fit of the melting temperatures in Eq. 5.4 provides a better estimation for the melting temperatures than for enthalpies and entropies, which are the relevant magnitudes. The melting temperature is probably not the best estimator, but we do not have any other experimental observable with which we can infer and compare our results. In the end, we are inferring the important magnitudes (enthalpies and entropies) by means of a derived magnitude (melting temperature) that is compatible with large variations of such important magnitudes (enthalpies and entropies).

Moreover, there seems to be a circular reasoning here. If our thermodynamics values (enthalpies and entropies) are obtained after fitting the melting temperatures, our thermodynamic values will obviously predict the melting temperatures well. However, our fit does not necessarily lead to good melting temperature predictions (i.e., within 2$ ^\circ $C). Indeed, our results might have led to a solution where the root mean squared error in Eq. 5.4 was much higher than the accepted experimental error in melting experiments (2$ ^\circ $C). Fortunately, this is not the case and our thermodynamic values predict the melting temperatures of ref. [143] with an average error of $ 1.90^\circ$C.

What is more, we have checked that if our found NNBP energies ( $ \epsilon _i$) increase only by $ 0.15$ kcal$ \cdot $mol$ ^{-1}$ (i.e., slightly beyond the standard error of the NNBP values) the standard deviation error for temperature melting prediction goes from 2$ ^\circ $C up to $ 5-6^\circ$C. So, if we had obtained the NNBP energies with a systematic error of $ 0.15$ kcal$ \cdot $mol$ ^{-1}$ we could never have predicted the melting temperatures within the 2$ ^\circ $C accuracy.

Once these preliminary issues have been addressed, let us focus on the prediction of the melting temperatures. Using our new thermodynamic values (Table 5.3 and Eq. 3.14), we calculate the melting temperatures of 92 oligos at 5 different salt conditions and compare our results with melting data taken from Owczarzy et al. [143]. Figure 5.14a illustrates how, in general, the UO values predict the melting temperatures better (average error of $ 1.53\,^\circ\mathrm{C}$) than our values (average error of $ 1.90\,^\circ\mathrm{C}$). The good news here is that our results are compatible and agree with the melting experiments. A deep look into the results reveals that our values work better for oligos longer than 15 bp (see Fig. 5.14b). Indeed, the UO prediction has an average error of $ 1.5\,^\circ\mathrm{C}$, while our values, $ 1.3\,^\circ\mathrm{C}$. All these results and their explanations will be discussed in the next section.

Figure 5.14: Prediction of melting temperatures. Comparison of melting temperatures for the 92 oligos ranging from 10 to 30 bp reported in ref. [143]. (a) Predicted versus experimentally measured melting temperatures at 5 salt conditions ( $ [\textrm {Na}^+] = 69, 119, 220, 621, 1020$ mM). The values obtained from unzipping have less error at higher temperatures (corresponding to longer oligos). (b) Prediction at 69 mM [NaCl] (left panel) and 1.02 M [NaCl] (right panel). Black lines are the experimentally measured melting temperatures, green line is the UO prediction and red line our prediction from unzipping data. Note that unzipping experiments predict the melting temperatures better above 15 bp, while the UO prediction works fine below this length.

JM Huguet 2014-02-12