Josep Maria Huguet

Single-molecule derivation of salt dependent base-pair free energies in DNA

Accurate knowledge of the thermodynamic properties of nucleic acids is crucial to predicting their structure and stability. To date most measurements of base-pair free energies in DNA are obtained in thermal denaturation experiments, which depend on several assumptions. Here we report measurements of the DNA base-pair free energies based on a simplified system, the mechanical unzipping of single DNA molecules. By combining experimental data with a physical model and an optimization algorithm for analysis, we measure the 10 unique nearest-neighbor base-pair free energies with 0.1 kcal mol-1 precision over two orders of magnitude of monovalent salt concentration. We find an improved set of standard energy values compared with Unified Oligonucleotide energies and a unique set of 10 base-pair-specific salt-correction values. The latter are found to be strongest for AA/TT and weakest for CC/GG. Our unique energy values and salt corrections improve predictions of DNA unzipping forces and are fully compatible with melting temperatures for oligos. The method should make it possible to obtain free energies, enthalpies, and entropies in conditions not accessible by bulk methodologies.

Improving Signal/Noise Resolution in Single-Molecule Experiments Using Molecular Constructs with Short Handles

We investigate unfolding/folding force kinetics in DNA hairpins exhibiting two and three states with newly designed short dsDNA handles (29 bp) using optical tweezers. We show how the higher stiffness of the molecular setup moderately enhances the signal/noise ratio (SNR) in hopping experiments as compared to conventional long-handled constructs (≅700 bp). The shorter construct results in a signal of higher SNR and slower folding/unfolding kinetics, thereby facilitating the detection of otherwise fast structural transitions. A novel analysis, as far as we are aware, of the elastic properties of the molecular setup, based on high-bandwidth measurements of force fluctuations along the folded branch, reveals that the highest SNR that can be achieved with short handles is potentially limited by the marked reduction of the effective persistence length and stretch modulus of the short linker complex.

Dynamic force spectroscopy of DNA hairpins: I. Force kinetics and free energy landscapes

We investigate the thermodynamics and kinetics of DNA hairpins that fold/unfold under the action of applied mechanical force. We introduce the concept of the molecular free energy landscape and derive simplified expressions for the force dependent Kramers–Bell rates. To test the theory we have designed a specific DNA hairpin sequence that shows two-state cooperative folding under mechanical tension and carried out pulling experiments using optical tweezers. We show how we can determine the parameters that characterize the molecular free energy landscape of such sequences from rupture force kinetic studies. Finally we combine such kinetic studies with experimental investigations of the Crooks fluctuation relation to derive the free energy of formation of the hairpin at zero force.

Measurement of work in single-molecule pulling experiments

A main goal of single-molecule experiments is to evaluate equilibrium free energy differences by applying fluctuation relations to repeated work measurements along irreversible processes. We quantify the error that is made in a free energy estimate by means of the Jarzynski equality when the accumulated work expended on the whole system (including the instrument) is erroneously replaced by the work transferred to the subsystem consisting of the sole molecular construct. We find that the error may be as large as 100%, depending on the number of experiments and on the bandwidth of the data acquisition apparatus. Our theoretical estimate is validated by numerical simulations and pulling experiments on DNA hairpins using optical tweezers.

Dynamic force spectroscopy of DNA hairpins: II. Irreversibility and dissipation

We investigate irreversibility and dissipation in single molecules that cooperatively fold/unfold in a two-state manner under the action of mechanical force. We apply path thermodynamics to derive analytical expressions for the average dissipated work and the average hopping number in two-state systems. It is shown how these quantities only depend on two parameters that characterize the folding/unfolding kinetics of the molecule: the fragility and the coexistence hopping rate. The latter has to be rescaled to take into account the appropriate experimental set-up. Finally we carry out pulling experiments with optical tweezers in a specifically designed DNA hairpin that shows two-state cooperative folding. We then use these experimental results to validate our theoretical predictions.

Single-Molecule Stochastic Resonance

Stochastic resonance (SR) is a well known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively folding/unfolding transitions under the action of an applied oscillating mechanical force with optical tweezers. By varying the frequency of the force oscillation, we investigated the folding/unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measured several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that the signal-to-noise ratio (SNR) of the spectral density of measured fluctuations in molecular extension of the DNA hairpins is a good quantifier of the SR. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance matching condition. Finally, we carried out experiments in short hairpins that show how SR might be useful to enhance the detection of conformational molecular transitions of low SNR.

Investigating the thermodynamics of small biosystems with optical tweezers

We present two examples of how single-molecule experimental techniques applied to biological systems can give insight into problems within the scope of equilibrium and nonequilibrium mesoscopic thermodynamics. The first example is the mapping of the free energy landscape of a macromolecule, the second the experimental verification of Crooks’ fluctuation theorem. In both cases the experimental setup comprises optical tweezers and DNA molecules.

Derivation of nearest-neighbor DNA parameters in magnesium from single molecule experiments

Abstract DNA hybridization is an essential molecular reaction in biology with many applications. The nearest-neighbor (NN) model for nucleic acids predicts DNA thermodynamics using energy values for the different base pair motifs. These values have been derived from melting experiments in monovalent and divalent salt and applied to predict melting temperatures of oligos within a few degrees. However, an improved determination of the NN energy values and their salt dependencies in magnesium is still needed for current biotechnological applications seeking high selectivity in the hybridization of synthetic DNAs. We developed a methodology based on single molecule unzipping experiments to derive accurate NN energy values and initiation factors for DNA. A new set of values in magnesium is derived, which reproduces unzipping data and improves melting temperature predictions for all available oligo lengths, in a range of temperature and salt conditions where correlation effects between the magnesium bound ions are weak. The NN salt correction parameters are shown to correlate to the GC content of the NN motifs. Our study shows the power of single-molecule force spectroscopy assays to unravel novel features of nucleic acids such as sequence-dependent salt corrections.

Work distributions in the T=0 random field Ising model.

We perform a numerical study of the three-dimensional random-field Ising model at T=0. We compare work distributions along metastable trajectories obtained with the single-spin flip dynamics with the distribution of the internal energy change along equilibrium trajectories. The goal is to investigate the possibility of extending the Crooks fluctuation theorem [G. E. Crooks, Phys. Rev. E. 60, 2721 (1999)] to zero temperature when, instead of the standard ensemble statistics, one considers the ensemble generated by the quenched disorder. We show that a simple extension of Crooks fails close to the disordered induced equilibrium phase transition due to the fact that work and internal energy distributions are very asymmetric.