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.

Force feedback effects on single molecule hopping and pulling experiments.

Single-molecule experiments with optical tweezers have become an important tool to study the properties and mechanisms of biological systems, such as cells and nucleic acids. In particular, force unzipping experiments have been used to extract the thermodynamics and kinetics of folding and unfolding reactions. In hopping experiments, a molecule executes transitions between the unfolded and folded states at a preset value of the force [constant force mode (CFM) under force feedback] or trap position [passive mode (PM) without feedback] and the force-dependent kinetic rates extracted from the lifetime of each state (CFM) and the rupture force distributions (PM) using the Bell-Evans model. However, hopping experiments in the CFM are known to overestimate molecular distances and folding free energies for fast transitions compared to the response time of the feedback. In contrast, kinetic rate measurements from pulling experiments have been mostly done in the PM while the CFM is seldom implemented in pulling protocols. Here, we carry out hopping and pulling experiments in a short DNA hairpin in the PM and CFM at three different temperatures (6 °C, 25 °C, and 45 °C) exhibiting largely varying kinetic rates. As expected, we find that equilibrium hopping experiments in the CFM and PM perform well at 6 °C (where kinetics are slow), whereas the CFM overestimates molecular parameters at 45 °C (where kinetics are fast). In contrast, nonequilibrium pulling experiments perform well in both modes at all temperatures. This demonstrates that the same kind of feedback algorithm in the CFM leads to more reliable determination of the folding reaction parameters in irreversible pulling experiments.

Non-specific binding of Na+ and Mg2+ to RNA determined by force spectroscopy methods.

RNA duplex stability depends strongly on ionic conditions, and inside cells RNAs are exposed to both monovalent and multivalent ions. Despite recent advances, we do not have general methods to quantitatively account for the effects of monovalent and multivalent ions on RNA stability, and the thermodynamic parameters for secondary structure prediction have only been derived at 1M [Na(+)]. Here, by mechanically unfolding and folding a 20 bp RNA hairpin using optical tweezers, we study the RNA thermodynamics and kinetics at different monovalent and mixed monovalent/Mg(2+) salt conditions. We measure the unfolding and folding rupture forces and apply Kramers theory to extract accurate information about the hairpin free energy landscape under tension at a wide range of ionic conditions. We obtain non-specific corrections for the free energy of formation of the RNA hairpin and measure how the distance of the transition state to the folded state changes with force and ionic strength. We experimentally validate the Tightly Bound Ion model and obtain values for the persistence length of ssRNA. Finally, we test the approximate rule by which the non-specific binding affinity of divalent cations at a given concentration is equivalent to that of monovalent cations taken at 100-fold concentration for small molecular constructs.

Variance sum rule for entropy production.

Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.

Massively parallel analysis of single-molecule dynamics on next-generation sequencing chips.

Single-molecule techniques are ideally poised to characterize complex dynamics but are typically limited to investigating a small number of different samples. However, a large sequence or chemical space often needs to be explored to derive a comprehensive understanding of complex biological processes. Here we describe multiplexed single-molecule characterization at the library scale (MUSCLE), a method that combines single-molecule fluorescence microscopy with next-generation sequencing to enable highly multiplexed observations of complex dynamics. We comprehensively profiled the sequence dependence of DNA hairpin properties and Cas9-induced target DNA unwinding-rewinding dynamics. The ability to explore a large sequence space for Cas9 allowed us to identify a number of target sequences with unexpected behaviors. We envision that MUSCLE will enable the mechanistic exploration of many fundamental biological processes.

Fluctuation relation for weakly ergodic aging systems.

A fluctuation relation for aging systems is introduced and verified by extensive numerical simulations. It is based on the hypothesis of partial equilibration over phase-space regions in a scenario of entropy-driven relaxation. The relation provides a simple alternative method, amenable of experimental implementation, to measure replica symmetry breaking parameters in aging systems. The connection with the effective temperatures obtained from the fluctuation-dissipation theorem is discussed.

Force spectroscopy with dual-trap optical tweezers: molecular stiffness measurements and coupled fluctuations analysis.

Dual-trap optical tweezers are often used in high-resolution measurements in single-molecule biophysics. Such measurements can be hindered by the presence of extraneous noise sources, the most prominent of which is the coupling of fluctuations along different spatial directions, which may affect any optical tweezers setup. In this article, we analyze, both from the theoretical and the experimental points of view, the most common source for these couplings in dual-trap optical-tweezers setups: the misalignment of traps and tether. We give criteria to distinguish different kinds of misalignment, to estimate their quantitative relevance and to include them in the data analysis. The experimental data is obtained in a, to our knowledge, novel dual-trap optical-tweezers setup that directly measures forces. In the case in which misalignment is negligible, we provide a method to measure the stiffness of traps and tether based on variance analysis. This method can be seen as a calibration technique valid beyond the linear trap region. Our analysis is then employed to measure the persistence length of dsDNA tethers of three different lengths spanning two orders of magnitude. The effective persistence length of such tethers is shown to decrease with the contour length, in accordance with previous studies.

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.

Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies.

Atomic force microscopes and optical tweezers are widely used to probe the mechanical properties of individual molecules and molecular interactions, by exerting mechanical forces that induce transitions such as unfolding or dissociation. These transitions often occur under nonequilibrium conditions and are associated with hysteresis effects-features usually taken to preclude the extraction of equilibrium information from the experimental data. But fluctuation theorems allow us to relate the work along nonequilibrium trajectories to thermodynamic free-energy differences. They have been shown to be applicable to single-molecule force measurements and have already provided information on the folding free energy of a RNA hairpin. Here we show that the Crooks fluctuation theorem can be used to determine folding free energies for folding and unfolding processes occurring in weak as well as strong nonequilibrium regimes, thereby providing a test of its validity under such conditions. We use optical tweezers to measure repeatedly the mechanical work associated with the unfolding and refolding of a small RNA hairpin and an RNA three-helix junction. The resultant work distributions are then analysed according to the theorem and allow us to determine the difference in folding free energy between an RNA molecule and a mutant differing only by one base pair, and the thermodynamic stabilizing effect of magnesium ions on the RNA structure.

Statistical properties of metastable intermediates in DNA unzipping.

We unzip DNA molecules using optical tweezers and determine the sizes of the cooperatively unzipping and zipping regions separating consecutive metastable intermediates along the unzipping pathway. Sizes are found to be distributed following a power law, ranging from one base pair up to more than a hundred base pairs. We find that a large fraction of unzipping regions smaller than 10 bp are seldom detected because of the high compliance of the released single stranded DNA. We show how the compliance of a single nucleotide sets a limit value around 0.1 N/m for the stiffness of any local force probe aiming to discriminate one base pair at a time in DNA unzipping experiments.

Negative fluctuation-dissipation ratios in the backgammon model.

We analyze fluctuation-dissipation relations in the backgammon model: a system that displays glassy behavior at zero temperature due to the existence of entropy barriers. We study local and global fluctuation relations for the different observables in the model. For the case of a global perturbation we find a unique negative fluctuation-dissipation ratio that is independent of the observable and which diverges linearly with the waiting time. This result suggests that a negative effective temperature can be observed in glassy systems even in the absence of thermally activated processes.

Thermal activation and ATP dependence of the cytoskeleton remodeling dynamics.

The cytoskeleton (CSK) is a nonequilibrium polymer network that uses hydrolyzable sources of free energy such as adenosine triphosphate (ATP) to remodel its internal structure. As in inert nonequilibrium soft materials, CSK remodeling has been associated with structural rearrangements driven by energy-activated processes. We carry out particle tracking and traction microscopy measurements of alveolar epithelial cells at various temperatures and ATP concentrations. We provide the first experimental evidence that the remodeling dynamics of the CSK is driven by structural rearrangements over free-energy barriers induced by thermally activated forces mediated by ATP. The measured activation energy of these forces is approximately 40k_{B}T_{r} ( k_{B} being the Boltzmann constant and T_{r} being the room temperature). Our experiments provide clues to understand the analogy between the dynamics of the living CSK and that of inert nonequilibrium soft materials.

Experimental evidence of symmetry breaking of transition-path times.

While thermal rates of state transitions in classical systems have been studied for almost a century, associated transition-path times have only recently received attention. Uphill and downhill transition paths between states at different free energies should be statistically indistinguishable. Here, we systematically investigate transition-path-time symmetry and report evidence of its breakdown on the molecular- and meso-scale out of equilibrium. In automated Brownian dynamics experiments, we establish first-passage-time symmetries of colloids driven by femtoNewton forces in holographically-created optical landscapes confined within microchannels. Conversely, we show that transitions which couple in a path-dependent manner to fluctuating forces exhibit asymmetry. We reproduce this asymmetry in folding transitions of DNA-hairpins driven out of equilibrium and suggest a topological mechanism of symmetry breakdown. Our results are relevant to measurements that capture a single coordinate in a multidimensional free energy landscape, as encountered in electrophysiology and single-molecule fluorescence experiments.

Force-induced misfolding in RNA.

RNA folding is a kinetic process governed by the competition of a large number of structures stabilized by the transient formation of base pairs that may induce complex folding pathways and the formation of misfolded structures. Despite its importance in modern biophysics, the current understanding of RNA folding kinetics is limited by the complex interplay between the weak base pair interactions that stabilize the native structure and the disordering effect of thermal forces. The possibility of mechanically pulling individual molecules offers a new perspective to understand the folding of nucleic acids. Here we investigate the folding and misfolding mechanism in RNA secondary structures pulled by mechanical forces. We introduce a model based on the identification of the minimal set of structures that reproduce the patterns of force-extension curves obtained in single molecule experiments. The model requires only two fitting parameters: the attempt frequency at the level of individual base pairs and a parameter associated to a free-energy correction that accounts for the configurational entropy of an exponentially large number of neglected secondary structures. We apply the model to interpret results recently obtained in pulling experiments in the three-helix junction S15 RNA molecule (RNAS15). We show that RNAS15 undergoes force-induced misfolding where force favors the formation of a stable non-native hairpin. The model reproduces the pattern of unfolding and refolding force-extension curves, the distribution of breakage forces, and the misfolding probability obtained in the experiments.

Derivation of the spin-glass order parameter from stochastic thermodynamics.

A fluctuation relation is derived to extract the order parameter function q(x) in weakly ergodic systems. The relation is based on measuring and classifying entropy production fluctuations according to the value of the overlap q between configurations. For a fixed value of q, entropy production fluctuations are Gaussian distributed allowing us to derive the quasi-FDT so characteristic of aging systems. The theory is validated by extracting the q(x) in various types of glassy models. It might be generally applicable to other nonequilibrium systems and experimental small systems.

Single-molecule experiments in biological physics: methods and applications.

I review single-molecule experiments (SMEs) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SMEs it is possible to manipulate molecules one at a time and measure distributions describing molecular properties, characterize the kinetics of biomolecular reactions and detect molecular intermediates. SMEs provide additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SMEs it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level, emphasizing the importance of SMEs to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SMEs from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOTs), magnetic tweezers (MTs), biomembrane force probes (BFPs) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation) and proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SMEs to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.

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.

Resonant nonequilibrium temperatures.

In this paper, we investigate nonequilibrium temperatures in a two-state system driven to a nonequilibrium steady state by the action of an oscillatory field. The nonequilibrium temperature is determined by coupling a small cavity or probe to the nonequilibrium system and studying the fluctuating noise in the cavity, as has been proposed in the context of glassy systems. We show the presence of resonant effects in the nonequilibrium temperature and discuss the existence of a constitutive steady-state equation in such nonequilibrium conditions. We propose this simple model as an excellent system to carry out experimental measurements of nonequilibrium temperatures. This may help to better understand the physical meaning of such an elusive concept.

Mode-dependent nonequilibrium temperature in aging systems.

We introduce an exactly solvable model for glassy dynamics with many relaxational modes, each one characterized by a different relaxational time scale. Analytical solution of the aging dynamics at low temperatures shows that a nonequilibrium or effective temperature can be associated to each time scale or mode. The spectrum of effective temperatures shows two regions that are separated by an age-dependent boundary threshold. Region I is characterized by partially equilibrated modes that relax faster than the modes at the threshold boundary. Thermal fluctuations and time correlations for modes in region I show that those modes are in mutual thermal equilibrium at a unique age-dependent effective temperature theta(s). In contrast, modes with relaxational time scales longer than that of modes at the threshold (region II) show diffusive properties and do not share the common temperature theta(s). The shift of the threshold toward lower energy modes as the system ages, and the progressive shrinking of region II, determines how the full spectrum of modes equilibrates. As is usually done in experiments, we have defined a frequency-dependent effective temperature and we have found that all modes in region I are mutually equilibrated at the temperature theta(s) independently of the probing frequency. The present model aims to explain transport anomalies observed in supercooled liquids in terms of a collection of structurally disordered and cooperative rearranging mesoscopic regions.

Universality of fluctuation-dissipation ratios: the ferromagnetic model.

We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising ferromagnets quenched to criticality, both for the long-range model and its short-range analog in the limit of large dimension. Our exact solution shows that, for both models, if the system is unmagnetized while if the initial magnetization is nonzero. This indicates that two different classes of critical coarsening dynamics need to be distinguished depending on the initial conditions, each with its own nontrivial FDR. We also analyze the dependence of the FDR on whether local and global observables are used. These results clarify how a proper local FDR (and the corresponding effective temperature) should be defined in long-range models in order to avoid spurious inconsistencies and maintain the expected correspondence between local and global results; global observables turn out to be far more robust tools for detecting nonequilibrium FDRs.