5. Salt dependence of nearest-neighbor base-pair free energies

Doutez toujours de vous-mêmes,
jusqu'à ce que les données ne
laissent aucun doute.

Louis Pasteur (1822-1895)

Nowadays, many biological applications require an accurate calculation of the free energy of formation of nucleic acids. The prediction of secondary structures is important in a wide range of fields such as self-assembled structures in DNA origami [128,129]; achievement of high selectivity in the hybridization of synthetic DNAs [130]; antigene targeting and siRNA design [131]; characterization of translocating motion of enzymes that mechanically disrupt nucleic acids [102]; prediction of non-native states (e.g., RNA misfolding) [132]; and DNA guided crystallization of colloids [133].

The Nearest-Neighbor (NN) model for DNA thermodynamics described in Sec. 3.3 was developed in the early 1960's [26]. Since then, this model has been successfully applied to predict the free energy of secondary structures in nucleic acids. The main premise of the model is simple: the total free energy change to form a double helix can be written as the sum of the base-pair interactions (which depend on the base-pair itself and on the nearest-neighbor). This means that two fragments of DNA that have different sequences will generally have different free energies of formation. It is important to note that the model does not include the energetic values of the NN interactions. The values of these energies are called Nearest-Neighbor Base-Pair (NNBP) energies and they must be determined from experiments.

The estimates of the NNBP energies have been traditionally obtained from thermal denaturation experiments of DNA oligonucleotides [134,135]. These experiments consist on heating a sample of a DNA oligo, measuring the melting temperature and inferring the thermodynamic properties of the molecules (enthalpy and entropy). In 1998, John SantaLucia Jr. gathered the experimental data from several labs (including his own) and provided a set of unified NNBP energies that best fit all the results [28]. Since then, these Unified Oligonucleotide (UO) energies have been considered the most reliable estimates and have been widely used as a reference. What is more, the validity of the NN model and the UO energies have exceeded the boundaries of melting experiments and they have been tested in single-molecule techniques. During the first decade of the 21st century, most of the works done on force denaturation experiments of nucleic acids used these values with satisfactory results [49,24,116,136,113]. Indeed, the UO values have become a referent to model the single-molecule experiments (see Sec. 3.4) because they reproduce quite well the force vs. extension curves of unfolding/refolding experiments of DNA and RNA molecules.

The UO energies are given at standard conditions (25$ ^\circ $C and 1 M [NaCl]) and a few correction formulas are available to extend the values of the energies to other experimental conditions (temperature and salt concentration). However, some discrepancies appear when comparing the UO predictions with the single-molecule pulling experiments at different salt concentrations. For instance, at low salt concentration (10 mM [NaCl]), the measured mean unzipping force is $ \sim$12 pN, while the force predicted by the UO energies is $ \sim$13 pN. This is a significant discrepancy since the force resolution of the instrument is 0.1 pN.

The origin of this discrepancy is attributed to the differences in the assumptions and the treatment of data in both types of experiments. In melting experiments, the DNA duplexes are assumed to melt in a two-state fashion (all or none; hybridized or denaturated). This is acceptable for short oligos (less than $ \sim20$ bp) but the two-state assumption fails as the length of the duplex increases. So, the longer oligos exhibit intermediate states where the DNA duplex is partially melted. This is the reason why there are two sets of NNBP energies inferred from melting experiments: one for the oligomers and one for the polymers [28]. The description of the unzipping experiments on DNA also has its own assumptions (elasticity of ssDNA, linearity of the optical trap, etc.). Nevertheless, unzipping experiments do not distinguish between the unfolding of oligonucleotides and polynucleotides. This is a useful feature because the NNBP energies are unique for all the DNAs of any length. The key point here is that single-molecule techniques allow one to control and monitor the denaturated state of the molecule along a full reaction coordinate, without having to rely on a two-state model.

Up to now, we know that the NNBP energies given by the melting experiments are not capable of reproducing the unzipping experiments. Here emerges an interesting question. What are the values of the NNBP energies that quantitatively describe the DNA unzipping experiments? Can we extract them from our own experimental data? Since we have the data and we have the model, in order to extract the energies, we just need to tune the parameters to make the model fit the data.

This chapter describes how to infer the NNBP energies of DNA from unzipping experiments performed on optical tweezers. Here we develop the mathematical tool that allows us to reach this goal. The strategy consists in: 1) measuring the FDC of unzipping; 2) determining the elastic response of the ssDNA; 3) using the model described in Sec. 3.4 to compute the theoretical FDC; and 4) fit the experimental FDC to the theoretical one to obtain the NNBP parameters. The advantage of this technique is that it and can extended to a wide variety of conditions (salt concentration, pH, temperature) and molecules (RNA, proteins such as helical repeats like the leucine zipper [137]).

JM Huguet 2014-02-12