Aiming at absolute force calibration of optical tweezers, following a critical review of proposed theoretical models, we present and test the results of Mie-Debye-spherical aberration (MDSA) theory, an extension of a previous (MD) model, taking account of spherical aberration at the glass-water interface. This first-principles theory is formulated entirely in terms of experimentally accessible parameters (none adjustable). Careful experimental tests of the MDSA theory, undertaken at two laboratories, with very different setups, are described. A detailed description is given of the procedures employed to measure laser beam waist, local beam power at the transparent microspheres trapped by the tweezers, microsphere radius, and the trap transverse stiffness, as a function of radius and height in the (inverted microscope) sample chamber. We find generally very good agreement with MDSA theory predictions, for a wide size range, from the Rayleigh domain to large radii, including the values most often employed in practice, and at different chamber heights, both with objective overfilling and underfilling. The results asymptotically approach geometrical optics in the mean over size intervals, as they should, and this already happens for size parameters not much larger than unity. MDSA predictions for the trapping threshold, position of stiffness peak, stiffness variation with height, multiple equilibrium points, and “hopping” effects among them are verified. Remaining discrepancies are ascribed to focus degradation, possibly arising from objective aberrations in the infrared, not yet included in MDSA theory.

In this review we focus on the idea of establishing connections between the mechanical properties of DNA–ligand complexes and the physical chemistry of DNA–ligand interactions.

We use optical tweezers to perform stretching experiments on DNA molecules when interacting with the drugs daunomycin and ethidium bromide, which intercalate the DNA molecule. Our results show that the persistence length of the DNA-drug complexes increases strongly as the drug concentration increases up to some critical value. Above this critical value, the persistence length decreases abruptly and remains approximately constant for larger drug concentrations, at least in the concentration range used in our experiments. Measured intercalators critical concentrations for the persistence length transition coincide with the reported values for the helix-coil transition of DNA-drug complexes obtained from sedimentation experiments. The contour length of the molecules increases monotonically and saturates as the drug concentration increases. The neighbor exclusion model fits to our results for the total drug concentration as a function of the relative increase of the contour length.

Binding of ligands to DNA can be studied by measuring the change of the persistence length of the complex formed, in single-molecule assays. We propose a methodology for persistence length data analysis based on a quenched disorder statistical model and describing the binding isotherm by a Hill-type equation. We obtain an expression for the effective persistence length as a function of the total ligand concentration, which we apply to our data of the DNA-cationic $\beta${}-cyclodextrin and to the DNA-HU protein data available in the literature, determining the values of the local persistence lengths, the dissociation constant, and the degree of cooperativity for each set of data. In both cases the persistence length behaves nonmonotonically as a function of ligand concentration and based on the results obtained we discuss some physical aspects of the interplay between DNA elasticity and cooperative binding of ligands.