3.3.3 Salt dependence

The prediction of melting temperatures is commonly done at standard conditions, which means that the concentration of salt is [NaCl]=1 M. However, this prediction can be extended when the hybridization reaction is performed at a different concentration of salt. According to the studies of calorimetry, the entropy is the only thermodynamic magnitude that depends on the salt due to rearrangements of the cloud of counterions along the DNA. This is deduced from the melting experiments performed on oligos, in which the enthalpy is directly obtained from the slope of the van't Hoff equation [120]. The results for several molecules show no significant enthalpic differences at different salt concentrations [121], meaning that the enthalpy is salt-independent. So, the salt correction only affects the entropy. The values of $ \Delta s^0_i$ that enter in Eq. 3.3 must be substituted by $ \Delta s_i$ according to

$\displaystyle \Delta s_i([\textrm{Na}^+])=\Delta s^0_i+\frac{m_i(T)}{T} \ln [\textrm{Na}^+]$ (3.13)

where $ \Delta s_i([\textrm{Na}^+])$ is the formation entropy of motif $ i$ at a salt concentration of [Na$ ^+$], $ T$ is the temperature and $ m_i(T)$ is a pre-factor that corrects for the salt and it is temperature-dependent. Although $ m_i$ depends on $ T$, the whole prefactor $ m_i(T)/T$ is temperature independent. Therefore, $ m_i(T)$ is linear with $ T$.

In general, the values of $ m_i$ do not need to be identical for all the NN motifs. However, in the studies of calorimetry they are taken to be all the same at first approach, and their value is $ m_i=0.114$ kcal$ \cdot $mol $ ^{-1}\cdot $K$ ^{-1}$ at $ T=310$ K [28]. On the other hand, the salt correction does not apply to the initiation term ( $ \Delta S_\mathrm{init}$) of Eq. 3.3. After introducing the salt correction, Eq. 3.12 can be rewritten as

$\displaystyle T_m=\frac{\Delta H^0}{\Delta S^0 + \sum_{i=1}^{N-1} \frac{m_i(T)}{T} \ln[\textrm{Na}^+]+ R\ln[c_T/4]}$ (3.14)

where the new term in the denominator is a summation that rolls over all the bases of the sequence. Strictly speaking, the summation should be done for the number of phosphates of the DNA, divided by two [28]. In our case, it is identical to the number of base pairs of the molecular construct. Again, the prefactor $ m_i(T)/T$ is temperature independent and the value of $ T$ at which it is measured is not important.

JM Huguet 2014-02-12