5.3.2 Independence of initial conditions

The optimization algorithm gives the same solution within 0.05 kcal$ \cdot $mol$ ^{-1}$ when the initial conditions are modified. A detailed study of the optimization algorithm has been carried out in order to check that the final solution does not depend on the initial conditions given to the algorithm.

An ensemble of initial conditions have been selected from the values of the different labs that were unified by SantaLucia [28] (see Fig. 5.10a). The FDCs predicted by the different energy values are depicted in Fig. 5.10c. Here we can observe how an overestimation (underestimation) in the absolute value of the NNBP energies leads to an overestimation (underestimation) of the mean unzipping force. The same elastic properties (ssDNA, handles and optical trap) have been used in all cases. Figure 5.10b shows the optimal values of the NNBP energies for the ensemble of initial conditions. All the NNBP energies have an error smaller than 0.1 kcal$ \cdot $mol$ ^{-1}$.

The optimization algorithm converges to essentially the same solution when starting from various initial conditions because the error bars of the different solutions obtained for each initial condition overlap with each other. Figure 5.10d shows the final theoretically predicted FDCs obtained when using the optimal values of the NNBP energies obtained for each initial condition. The different FDCs are indistinguishable and they reproduce quantitatively the experimental FDC.

Figure 5.10: Dependence on initial conditions taken from bulk measurements [28]. (a) Ensemble of initial conditions that we tested. Data was obtained from SantaLucia [28] and it was corrected according to temperature (298 K) and salt conditions (1 M [NaCl]) of our experiments. Cyan points, values of Benight; red points, values of Blake; green points, values of Breslauer; blue points, values of Gotoh; orange points, values of SantaLucia; magenta points, values of Sugimoto; yellow points, values of Vologodskii; black curve, our fit values. (b) Solutions found after the fitting algorithm for the different initial conditions. Same color code as in panel a. The heterogeneous ensemble of initial conditions has converged to similar values for all the NNBP energies that differ by less than 0.1 kcal$ \cdot $mol$ ^{-1}$. (c) FDCs obtained using the NNBP energies from the different initial conditions. The color code is the same as in panel a. The black curve shows our fit FDC. Some of the initial conditions (Gotoh and SantaLucia) are compatible with the experimental FDC. (d) FDCs obtained using the optimal NNBP energies obtained for each initial condition. Experimental and optimal FDCs differ by less than 0.1 pN throughout the molecule.
\includegraphics[width=\textwidth]{figs/chapter5/initcond.eps}

JM Huguet 2014-02-12