Statistical properties of metastable intermediates in DNA unzipping

Stochastic resonance in a model of a periodically driven DNA: Multiple transitions, scaling, and sequence dependence

We numerically study stochastic resonance in the unzipping of a model double-stranded DNA by a periodic force. We observe multiple peaks in stochastic resonance in the output signal as the driving force frequency is varied for different force amplitudes, temperature, chain length, and chain heterogeneity. Multiple peaks point to the existence of multiple stable and metastable states, which correspond to dynamical states of partially zipped and unzipped conformations and transitions between them. We quantify such transitions by looking at the time evolution of the fraction of bound base pairs. We obtain phase diagrams in the force amplitude-temperature plane both in the resonance frequency of the primary peak and the output signal at the peak value. We further obtain an excellent scaling behavior of the output signal for changing lengths of the DNA. Resonance behavior is also affected by chain heterogeneity as it depends strongly on which base pair the periodic forcing is applied.

Experimental Test of Sinai's Model in DNA Unzipping

The experimental measurement of correlation functions and critical exponents in disordered systems is key to testing renormalization group (RG) predictions. We mechanically unzip single DNA hairpins with optical tweezers, an experimental realization of the diffusive motion of a particle in a one-dimensional random force field, known as the Sinai model. We measure the unzipping forces F_{w} as a function of the trap position w in equilibrium and calculate the force-force correlator Δ_{m}(w), its amplitude, and correlation length, finding agreement with theoretical predictions. We study the universal scaling properties since the effective trap stiffness m^{2} decreases upon unzipping. Fluctuations of the position of the base pair at the unzipping junction u scales as u∼m^{-ζ}, with a roughness exponent ζ=1.34±0.06, in agreement with the analytical prediction ζ=4/3. Our study provides a single-molecule test of the functional RG approach for disordered elastic systems in equilibrium.

Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles

Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modeled as an elastic system subject to quenched disorder. The ensuing field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group (RG) flow involves a function, the disorder correlator Δ(w), and is therefore termed the functional RG. Δ(w) is a physical observable, the auto-correlation function of the center of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of the mappings between these systems requires specific techniques, which we develop, including modeling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and non-linear surface growth with additional Kardar-Parisi-Zhang (KPZ) terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random-field magnets. Emphasis is given to numerical and experimental tests of the theory.

Stem-loop formation drives RNA folding in mechanical unzipping experiments

Accurate knowledge of RNA hybridization is essential for understanding RNA structure and function. Here we mechanically unzip and rezip a 2-kbp RNA hairpin and derive the 10 nearest-neighbor base pair (NNBP) RNA free energies in sodium and magnesium with 0.1 kcal/mol precision using optical tweezers. Notably, force-distance curves (FDCs) exhibit strong irreversible effects with hysteresis and several intermediates, precluding the extraction of the NNBP energies with currently available methods. The combination of a suitable RNA synthesis with a tailored pulling protocol allowed us to obtain the fully reversible FDCs necessary to derive the NNBP energies. We demonstrate the equivalence of sodium and magnesium free-energy salt corrections at the level of individual NNBP. To characterize the irreversibility of the unzipping-rezipping process, we introduce a barrier energy landscape of the stem-loop structures forming along the complementary strands, which compete against the formation of the native hairpin. This landscape correlates with the hysteresis observed along the FDCs. RNA sequence analysis shows that base stacking and base pairing stabilize the stem-loops that kinetically trap the long-lived intermediates observed in the FDC. Stem-loops formation appears as a general mechanism to explain a wide range of behaviors observed in RNA folding.

Probability distribution for heat exchange in plastic deformation

Fluctuation theorems allow one to obtain equilibrium information from nonequilibrium experiments. The probability distribution function of the relevant magnitude measured along the irreversible nonequilibrium trajectories is an essential ingredient of fluctuation theorems. In small systems, where fluctuations can be larger than average values, probability distribution functions often deviate from being Gaussian, showing long tails, mostly exponential, and usually strongly asymmetric. Recently, the probability distribution function of the van Hove correlation function of the relevant magnitude was calculated, instead of that of the magnitude itself. The resulting probability distribution function is highly symmetric, obscuring the application of fluctuation theorems. Here, the discussion is illustrated with the help of results for the heat exchanged during plastic deformation of aluminum nanowires, obtained from molecular dynamics calculations. We find that the probability distribution function for the heat exchanged is centrally Gaussian, with asymmetric exponential tails further out. By calculating the symmetry function we show that this distribution is consistent with fluctuation theorems relating the differences between two equilibrium states to an infinite number of nonequilibrium paths connecting those two states.

Direct detection of molecular intermediates from first-passage times

All natural phenomena are governed by energy landscapes. However, the direct measurement of this fundamental quantity remains challenging, particularly in complex systems involving intermediate states. Here, we uncover key details of the energy landscapes that underpin a range of experimental systems through quantitative analysis of first-passage time distributions. By combined study of colloidal dynamics in confinement, transport through a biological pore, and the folding kinetics of DNA hairpins, we demonstrate conclusively how a short-time, power-law regime of the first-passage time distribution reflects the number of intermediate states associated with each of these processes, despite their differing length scales, time scales, and interactions. We thereby establish a powerful method for investigating the underlying mechanisms of complex molecular processes.

Detection of single DNA mismatches by force spectroscopy in short DNA hairpins

Identification of defective DNA structures is a difficult task, since small differences in base-pair bonding are hidden in the local structural variability of a generally random base-pair sequence. Defects, such as base mismatches, missing bases, crosslinks, and so on, occur in DNA with high frequency and must be efficiently identified and repaired to avoid dire consequences such as genetic mutations. Here, we focus on the detection of base mismatches, which is local deviations from the ideal Watson-Crick pairing rule, which may typically originate from DNA replication process, foreign chemical attack, or ionizing radiation. Experimental detection of a mismatch defect demands the ability to measure slight deviations in the free energy and molecular structure. We introduce different mismatches in short DNA hairpins (10 or 20 base pairs plus a 4-base loop) sandwiched between dsDNA handles to be used in single-molecule force spectroscopy with optical tweezers. We perform both hopping and force-pulling experiments to measure the excess free energies and deduce the characteristic kinetic signatures of the mismatch from the force-distance curves. All-atom molecular dynamics simulations lend support to the detailed interpretation of the experimental data. Such measurements, at the lowest sensitivity limits of this experimental technique, demonstrate the capability of identifying the presence of mismatches in a random complementary dsDNA sequence and provide lower bounds for the ability to distinguish different structural defects.

Possible scenarios of DNA double-helix unzipping process in single-molecule manipulation experiments

Single-molecule experiments on DNA unzipping are analyzed on the basis of the mobility of nucleic bases in complementary pairs. Two possible scenarios of DNA double-helix unzipping are proposed and studied, using the atom-atom potential function method. According to the first scenario, the base pairs transit into a 'preopened' metastable state and then fully open along the 'stretch' pathway. In this case, the DNA unzipping takes place slowly and as an equilibrium process, with the opening energies being similar to the energies obtained in thermodynamic experiments on DNA melting. The second scenario is characterized by higher opening forces. In this case, the DNA base pairs open directly along the 'stretch' pathway. It follows from our calculations that, in this scenario, the enthalpy difference between the A[Formula: see text]T and G[Formula: see text]C base pairs is much higher than in the first case. The features of the first unzipping scenario show that it can play a key role during the process of DNA genetic information transfer in vivo. It follows from our study that a peculiarity of the second scenario is that it can be used for the development of faster methods for reading genetic information in vitro.

Evolutionary advantage of directional symmetry breaking in self-replicating polymers

Due to the asymmetric nature of the nucleotides, the extant informational biomolecule, DNA, is constrained to replicate unidirectionally on a template. As a product of molecular evolution that sought to maximize replicative potential, DNA's unidirectional replication poses a mystery since symmetric bidirectional self-replicators obviously would replicate faster than unidirectional self-replicators and hence would have been evolutionarily more successful. Here we carefully examine the physico-chemical requirements for evolutionarily successful primordial self-replicators and theoretically show that at low monomer concentrations that possibly prevailed in the primordial oceans, asymmetric unidirectional self-replicators would have an evolutionary advantage over bidirectional self-replicators. The competing requirements of low and high kinetic barriers for formation and long lifetime of inter-strand bonds respectively are simultaneously satisfied through asymmetric kinetic influence of inter-strand bonds, resulting in evolutionarily successful unidirectional self-replicators. Within our model, circular strands, the configuration prefered by primitive life forms, have higher replicative potential compared to linear strands.

Opening of DNA chain due to force applied on different locations

We consider a homogeneous DNA molecule and investigate the effect of random force applied on the unzipping profile of the molecule. How the critical force varies as a function of the chain length or number of base pairs is the objective of this study. In general, the ratio of the critical forces that is applied on the middle of the chain to that which is applied on one of the ends is two. Our study shows that this ratio depends on the length of the chain. This means that the force which is applied to a point can be experienced by a section of the chain. Beyond a length, the base pairs have no information about the applied force. In the case when the chain length is shorter than this length, this ratio may vary. Only in the case when the chain length exceeds a critical length, this ratio is found to be two. Based on the de Gennes formulation, we developed a method to calculate these forces at zero temperature. The exact results at zero temperature match numerical calculations.

Control of force through feedback in small driven systems

Controlling a time-dependent force applied to single molecules or colloidal particles is crucial for many types of experiments. Since in optical tweezers the primary controlled variable is the position of the trap, imposing a target force requires an active feedback process. We analyze this feedback process for the paradigmatic case of a nonequilibrium steady state generated by a dichotomous force protocol, first theoretically for a colloidal particle in a harmonic trap and then with both simulations and experiments for a long DNA hairpin. For the first setup, we find there is an optimal feedback gain separating monotonic from oscillatory response, whereas a too strong feedback leads to an instability. For the DNA molecule, reaching the target force requires substantial feedback gain since weak feedback cannot overcome the tendency to relax towards the equilibrium force.

Single-molecule kinetics and footprinting of DNA bis-intercalation: the paradigmatic case of Thiocoraline

DNA bis-intercalators are widely used in molecular biology with applications ranging from DNA imaging to anticancer pharmacology. Two fundamental aspects of these ligands are the lifetime of the bis-intercalated complexes and their sequence selectivity. Here, we perform single-molecule optical tweezers experiments with the peptide Thiocoraline showing, for the first time, that bis-intercalation is driven by a very slow off-rate that steeply decreases with applied force. This feature reveals the existence of a long-lived (minutes) mono-intercalated intermediate that contributes to the extremely long lifetime of the complex (hours). We further exploit this particularly slow kinetics to determine the thermodynamics of binding and persistence length of bis-intercalated DNA for a given fraction of bound ligand, a measurement inaccessible in previous studies of faster intercalating agents. We also develop a novel single-molecule footprinting technique based on DNA unzipping and determine the preferred binding sites of Thiocoraline with one base-pair resolution. This fast and radiolabelling-free footprinting technique provides direct access to the binding sites of small ligands to nucleic acids without the need of cleavage agents. Overall, our results provide new insights into the binding pathway of bis-intercalators and the reported selectivity might be of relevance for this and other anticancer drugs interfering with DNA replication and transcription in carcinogenic cell lines.

Extracting physical chemistry from mechanics: a new approach to investigate DNA interactions with drugs and proteins in single molecule experiments

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.

Unfolding kinetics of periodic DNA hairpins

DNA hairpin molecules with periodic base sequences can be expected to exhibit a regular coarse-grained free energy landscape (FEL) as a function of the number of open base pairs and applied mechanical force. Using a commonly employed model, we first analyze for which types of sequences a particularly simple landscape structure is predicted, where forward and backward energy barriers between partly unfolded states are decreasing linearly with force. Stochastic unfolding trajectories for such molecules with simple FEL are subsequently generated by kinetic Monte Carlo simulations. Introducing probabilities that can be sampled from these trajectories, it is shown how the parameters characterizing the FEL can be estimated. Already 300 trajectories, as typically generated in experiments, provide faithful results for the FEL parameters.

Electrostatic binding and hydrophobic collapse of peptide-nucleic acid aggregates quantified using force spectroscopy

Knowledge of the mechanisms of interaction between self-aggregating peptides and nucleic acids or other polyanions is key to the understanding of many aggregation processes underlying several human diseases (e.g., Alzheimer's and Parkinson's diseases). Determining the affinity and kinetic steps of such interactions is challenging due to the competition between hydrophobic self-aggregating forces and electrostatic binding forces. Kahalalide F (KF) is an anticancer hydrophobic peptide that contains a single positive charge that confers strong aggregative properties with polyanions. This makes KF an ideal model to elucidate the mechanisms by which self-aggregation competes with binding to a strongly charged polyelectrolyte such as DNA. We use optical tweezers to apply mechanical forces to single DNA molecules and show that KF and DNA interact in a two-step kinetic process promoted by the electrostatic binding of DNA to the aggregate surface followed by the stabilization of the complex due to hydrophobic interactions. From the measured pulling curves we determine the spectrum of binding affinities, kinetic barriers, and lengths of DNA segments sequestered within the KF-DNA complex. We find there is a capture distance beyond which the complex collapses into compact aggregates stabilized by strong hydrophobic forces and discuss how the bending rigidity of the nucleic acid affects this process. We hypothesize that within an in vivo context, the enhanced electrostatic interaction of KF due to its aggregation might mediate the binding to other polyanions. The proposed methodology should be useful to quantitatively characterize other compounds or proteins in which the formation of aggregates is relevant.

Spin-oscillator model for the unzipping of biomolecules by mechanical force

A spin-oscillator system models unzipping of biomolecules (such as DNA, RNA, or proteins) subject to an external force. The system comprises a macroscopic degree of freedom, represented by a one-dimensional oscillator, and internal degrees of freedom, represented by Glauber spins with nearest-neighbor interaction and a coupling constant proportional to the oscillator position. At a critical value F(c) of an applied external force F, the oscillator rest position (order parameter) changes abruptly and the system undergoes a first-order phase transition. When the external force is cycled at different rates, the extension given by the oscillator position exhibits a hysteresis cycle at high loading rates, whereas it moves reversibly over the equilibrium force-extension curve at very low loading rates. Under constant force, the logarithm of the residence time at the stable and metastable oscillator rest position is proportional to F-F(c) as in an Arrhenius law.