DNA Hairpin Folding Research Articles

Quantifying the Properties of Nonproductive Attempts at Thermally Activated Energy-Barrier Crossing through Direct Observation

Thermally activated energy-barrier crossing is ubiquitous in physical, chemical, and biological processes. Most barrier-crossing attempts have insufficient energy to overcome the barrier; hence, productive transition paths that successfully cross the barrier are very rare compared to nonproductive fluctuations that enter the barrier region but return without crossing it. Recent experimental advances have yielded important insights into transition paths, but nonproductive attempts remain little studied experimentally or theoretically, even though they can reveal information about parts of the reaction energy landscape not visited during transition paths. Observing the diffusive dynamics of a bead hopping between bistable optical traps as a model system, we measured the duration, maximum position along the reaction coordinate, and occupancy statistics of unsuccessful crossing attempts. Experimental results agreed quantitatively with expectations of an analytical framework we derived from committor theory. Applying these analyses to a more complex example, DNA hairpin folding under tension, we found that some properties differed from those of transition paths, such as the asymmetric occupancies for folding and unfolding attempts, whereas others were similar, such as the diffusion coefficient reflecting landscape roughness. These results show how nonproductive crossing attempts can be detected and analyzed rigorously, enabling characterization of the full dynamics within the transition region. Published by the American Physical Society 2024

Conformational Dynamics of Poly(T) Single-Stranded DNA at the Single-Molecule Level.

The conformational dynamics of single-stranded DNA (ss-DNA) are implicated in the mechanisms of several key biological processes such as DNA replication and damage repair and have been modeled with those of semiflexible or flexible polymer. The high flexibility and customizability of ss-DNA also make it an excellent polymeric material for materials engineering. Polythymidine (poly(T)) is an excellent model ss-DNA as a flexible polymer since it does not form any secondary structure. However, only limited experimental results have been reported of poly(T) conformational dynamics with a very short length that is not relevant to the aforementioned processes and applications. Here, we provide the first experimental results of the conformational dynamics of poly(T) with lengths in the range of 130-170 nucleotides at the single-molecule level. Our experiments are based on single-molecule FRET and a DNA hairpin structure of which the folding kinetics are governed by the conformational dynamics of poly(T). We found that the folding kinetics deviate far from those of a flexible polymer model with a harmonic bending potential. To this end, we derived a simple model for the kinetics of DNA hairpin folding from the self-avoiding-walk (SAW). Our model describes the conformational dynamics of poly(T) very well and enables estimation of the conformational dimensionality. The estimated dimensionalities suggest that ss-DNA is completely flexible at 100 mM or a higher NaCl concentration, but not at 50 mM. These results will help understand the conformational dynamics of ss-DNA implicated in several key biological processes and maximize the utility of ss-DNA for materials engineering. Also, our system and model provide an excellent platform to investigate the conformational dynamics of ss-DNA.

Correlative Single-Molecule Force-FRET Measurements of DNA Hairpin Conformational Dynamics

The biological function of many macromolecules such as proteins and nucleic acids is tightly coupled to their conformation and their conformational dynamics. Therefore, studying how macromolecules fold and undergo conformational changes is crucial to understand the underlying mechanisms of biological processes. In particular DNA/RNA hairpins play essential regulatory roles in vivo, since they can regulate the interaction with nucleic acid processing proteins in processes such as transcription, recombination or replication. Therefore, understanding the principles of their structure formation is important for elucidating those biological roles. Single-molecule force spectroscopy represents an ideal tool for such studies because of its unique capability to isolate individual biomolecules and observe conformational transitions in real-time, while providing the control over the population distribution as opposed to approaches in solution. Here we report a study on FRET-labelled DNA hairpin folding transitions using high-resolution optical tweezers combined with fluorescence microscopy. We present equilibrium measurements at unprecedent trap distance stability, which allows to measure conformational state distributions over hours without altering the energy landscape. Measuring over longer time periods while keeping the trap distance within nanometer precision is crucial to capture the rare conformational states that might be overlooked in measurements over a timescale that is limited by instrumental drift. These measurements were enabled by integrating trap-distance and temperature stabilization feedback loops to achieve the ultimate stability in distance between the traps. Kinetic, energetic and structural properties of these states could be determined quantitatively from a correlative information source – force and fluorescence data, thereby providing new insights into folding pathways and energy landscape. This study shows how correlating force spectroscopy measurements with fluorescence microscopy could complement the investigation of the prevalence and energy landscape of certain conformational states with extra three-dimensional structural information of the macromolecule of interest.

Memory Effects in Single-Molecule Force Spectroscopy Measurements of Biomolecular Folding

Folding is generally assumed to be a Markov process, without memory. When the molecular motion is coupled to that of a probe as in single-molecule force spectroscopy (SMFS) experiments, however, theory predicts that the coupling to a second Markov process should induce memory when monitoring a projection of the full multi-dimensional motion onto a reduced coordinate. We developed a method to evaluate the time constant of the induced memory from its effects on the autocorrelation function, which can be readily determined from experimental data. Applying this method to both simulated SMFS measurements and experimental trajectories of DNA hairpin folding measured by optical tweezers, we validated the prediction that the linker induces memory. For these measurements, the timescale of the induced memory was found to be similar to the time required for the force probe to respond to changes in the molecule, and in the regime where the experimentally observed dynamics were not significantly perturbed by probe-molecule coupling artifacts. Memory effects are thus a general feature of SMFS measurements induced by the mechanical connection between the molecule and force probe that should be considered when interpreting experimental data.

Tension propagation during DNA hairpin folding

Characterization of DNA/RNA folding dynamics is an interesting problem involving the complex force balance between the relaxation of the growing duplex and the stretched single-stranded segments. In a previous paper, we reported that the helicity plays an important role in determining the folding time for a chain of size N, where is the Flory exponent. Here we analyze this process in further detail by using molecular dynamics, with particular emphasis on tension propagation along a single strand on the unfolded segment. We directly observe that the single-strand segments are always stretched during the folding process by the tension induced by base pair formation, propagating ahead of the y -junction. Our molecular dynamics simulations verify the existence of a stem-flower structure in the unfolded segments, with a power-law dependence of the stem length Ns on the duplex length n. For the longest hairpin structures considered, we also find that the power-law regime terminates before the first half of the folding is completed. We demonstrate that the structure’s helicity is an integral aspect of the folding dynamics by comparing our findings with those obtained from a hypothetical non-helical model.

Super-Resolution Optical Lithography with DNA.

We developed an efficient, versatile, and accessible super-resolution microscopy method to construct a nanoparticle assembly at a spatial resolution below the optical diffraction limit. The method utilizes DNA and a photoactivated DNA cross-linker. Super-resolution optical techniques have been used only as a means to make measurements below the light diffraction limit. Furthermore, no optical technique is currently available to construct nanoparticle assemblies with a precisely designed shape and internal structure at a resolution of a few tens of nanometers (nm). Here we demonstrate that we can fulfill this deficiency by utilizing spontaneous structural dynamics of DNA hairpins combined with single-molecule fluorescence resonance energy transfer (smFRET) microscopy and a photoactivated DNA cross-linker. The stochastic fluorescence blinking due to the spontaneous folding and unfolding motions of DNA hairpins enables us to precisely localize a folded hairpin and solidify it only when it is within a predesigned target area whose size is below the diffraction limit. As the method is based on an optical microscope and an easily clickable DNA cross-linking reagent, it will provide an efficient means to create large nanoparticle assemblies with a shape and internal structure at an optical super-resolution, opening a wide window of opportunities toward investigating their photophysical and optoelectronic properties and developing novel devices.

Measuring the average shape of transition paths during the folding of a single biological molecule

Transition paths represent the parts of a reaction where the energy barrier separating products and reactants is crossed. They are essential to understanding reaction mechanisms, yet many of their properties remain unstudied. Here, we report measurements of the average shape of transition paths, studying the folding of DNA hairpins as a model system for folding reactions. Individual transition paths were detected in the folding trajectories of hairpins with different sequences held under tension in optical tweezers, and path shapes were computed by averaging all transitions in the time domain, 〈t(x)〉, or by averaging transitions of a given duration in the extension domain, 〈x(t|τ)〉 τ Whereas 〈t(x)〉 was close to straight, with only a subtle curvature, 〈x(t|τ)〉 τ had more pronounced curvature that fit well to theoretical expectations for the dominant transition path, returning diffusion coefficients similar to values obtained previously from independent methods. Simulations suggested that 〈t(x)〉 provided a less reliable representation of the path shape than 〈x(t|τ)〉 τ , because it was far more sensitive to the effects of coupling the molecule to the experimental force probe. Intriguingly, the path shape variance was larger for some hairpins than others, indicating sequence-dependent changes in the diversity of transition paths reflective of differences in the character of the energy barriers, such as the width of the barrier saddle-point or the presence of parallel paths through multiple barriers between the folded and unfolded states. These studies of average path shapes point the way forward for probing the rich information contained in path shape fluctuations.

Using a system’s equilibrium behavior to reduce its energy dissipation in nonequilibrium processes

Cells must operate far from equilibrium, utilizing and dissipating energy continuously to maintain their organization and to avoid stasis and death. However, they must also avoid unnecessary waste of energy. Recent studies have revealed that molecular machines are extremely efficient thermodynamically compared with their macroscopic counterparts. However, the principles governing the efficient out-of-equilibrium operation of molecular machines remain a mystery. A theoretical framework has been recently formulated in which a generalized friction coefficient quantifies the energetic efficiency in nonequilibrium processes. Moreover, it posits that, to minimize energy dissipation, external control should drive the system along the reaction coordinate with a speed inversely proportional to the square root of that friction coefficient. Here, we demonstrate the utility of this theory for designing and understanding energetically efficient nonequilibrium processes through the unfolding and folding of single DNA hairpins.

Using Equilibrium Behavior to Reduce Energy Dissipation in Non-Equilibrium Biomolecular Processes

Cells must operate far from equilibrium, utilizing and dissipating energy continuously to maintain their organization and to avoid stasis and death. However, they must also avoid unnecessary waste of energy. Recent studies have revealed that molecular machines are extremely efficient thermodynamically when compared to their macroscopic counterparts. However, the principles governing the efficient out-of-equilibrium operation of molecular machines remain a mystery. A theoretical framework has been recently formulated in which a generalized friction coefficient quantifies the energetic efficiency in non-equilibrium processes. Moreover, it posits that to minimize energy dissipation, external control should drive the system along the reaction coordinate with a speed inversely proportional to the square root of that friction coefficient. Here, we demonstrate the utility of this theory for designing and understanding energetically efficient non-equilibrium processes through the unfolding and folding of single DNA hairpins.

Three-State DNA Hairpin Conformational Dynamics Revealed by Higher-Order Fluorescence Correlation Spectroscopy.

Previous fluorescence correlation spectroscopy (FCS) measurements of DNA hairpin folding dynamics revealed at least three conformational states of the DNA are present, distinguished by the brightness of fluorescent dye-quencher labels. Rapid fluctuations between two of the states occurred on time scales observable by FCS. A third state that was static on the FCS time scale was also observed. In this study, we investigate these conformational states using newly developed higher-order FCS techniques. It is shown that conventional FCS alone cannot uniquely distinguish the conformational states or assign their roles in the observed mechanism. The additional information offered by higher-order FCS makes it possible (i) to uniquely identify the static and rapidly fluctuating states and (ii) to directly measure the brightnesses and populations of all three observed states. The rapid fluctuations occurring on the FCS time scale are due to a reversible reaction between the two lowest brightness levels, attributed to the folded and random-coil conformations of the DNA. Evidence is presented that the third state, which is the brightest, may be associated with spatially extended unfolded conformations that are isolated from the more compact conformations by a substantial barrier. These conformations attain a maximum equilibrium population of nearly 10% near physiological temperatures and salt concentrations.

Memory effects in single-molecule force spectroscopy measurements of biomolecular folding.

Folding is generally assumed to be a Markov process, without memory. When the molecular motion is coupled to that of a probe as in single-molecule force spectroscopy (SMFS) experiments, however, theory predicts that the coupling to a second Markov process should induce memory when monitoring a projection of the full multi-dimensional motion onto a reduced coordinate. We developed a method to evaluate the time constant of the induced memory from its effects on the autocorrelation function, which can be readily determined from experimental data. Applying this method to both simulated SMFS measurements and experimental trajectories of DNA hairpin folding measured by optical tweezers as a model system, we validated the prediction that the linker induces memory. For these measurements, the timescale of the induced memory was found to be similar to the time required for the force probe to respond to changes in the molecule, and in the regime where the experimentally observed dynamics were not significantly perturbed by probe-molecule coupling artifacts. Memory effects are thus a general feature of SMFS measurements induced by the mechanical connection between the molecule and force probe that should be considered when interpreting experimental data.

Role of Helicity in DNA Hairpin Folding Dynamics.

We study hairpin folding dynamics by means of extensive molecular dynamics simulations, with particular attention paid to the influence of helicity on the folding time. We find that the dynamical exponent α in the anomalous scaling n(t)∼t^{1/α} of the hairpin length n with time changes from 1.6 (≃1+ν, where ν is the Flory exponent) to 1.2 (≃2ν) in three dimensions, when duplex helicity is removed. The relation α=2ν in rotationless hairpin folding is further verified in two dimensions (ν=0.75) and for a ghost chain (ν=0.5). Our findings suggest that the folding dynamics in long helical chains is governed by the duplex dynamics, contrasting the earlier understanding based on the stem-flower picture of unpaired segments. We propose a scaling argument for α=1+ν in helical chains, assuming that duplex relaxation required for orientational positioning of the next pair of bases is the rate-limiting process.

Measuring the Local Velocity along Transition Paths during the Folding of Single Biological Molecules

Transition paths are the most interesting part of folding reactions but remain little studied. We measured the local velocity along transition paths in DNA hairpin folding using optical tweezers. The velocity distribution agreed well with diffusive theories, yielding the diffusion coefficient. We used the average velocity to calculate the transmission factor in transition-state theory (TST), finding observed rates that were ∼10^{5}-fold slower than predicted by TST. This work quantifies the importance of barrier recrossing events and highlights the effectiveness of the diffusive model of folding.

Probing Position-Dependent Diffusion in Folding Reactions Using Single-Molecule Force Spectroscopy

Folding of proteins and nucleic acids involves a diffusive search over a multidimensional conformational energy landscape for the minimal-energy structure. When examining the projection of conformational motions onto a one-dimensional reaction coordinate, as done in most experiments, the diffusion coefficient D is generally position dependent. However, it has proven challenging to measure such position-dependence experimentally. We investigated the position-dependence of D in the folding of DNA hairpins as a simple model system in two ways: first, by analyzing the round-trip time to return to a given extension in constant-force extension trajectories measured by force spectroscopy, and second, by analyzing the fall time required to reach a given extension in force jump measurements. These methods yielded conflicting results: the fall time implied a fairly constant D, but the round-trip time implied variations of over an order of magnitude. Comparison of experiments with computational simulations revealed that both methods were strongly affected by experimental artifacts inherent to force spectroscopy measurements, which obscured the intrinsic position-dependence of D. Lastly, we applied Kramers’s theory to the kinetics of hairpins with energy barriers located at different positions along the hairpin stem, as a crude probe of D at different stem positions, and we found that D did not vary much as the barrier was moved along the reaction coordinate. This work underlines the difficulties faced when trying to deduce position-dependent diffusion coefficients from experimental folding trajectories.

Improved data analysis method of single-molecule experiments based on probability optimization**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474237 and 11574310) and the 111 Project, China (Grant No. B16029).

To extract the dynamic parameters from single molecule manipulation experiments, usually lots of data at different forces need to be recorded. But the measuring time of a single molecule is limited due to breakage of the tether or degradation of the molecule. Here we propose a data analysis method based on probability maximization of the recorded time trace to extract the dynamic parameters from a single measurement. The feasibility of this method was verified by dealing with the simulation data of a two-state system. We also applied this method to estimate the parameters of DNA hairpin folding and unfolding dynamics measured by a magnetic tweezers experiment.

Scanning Single-Molecule Fluorescence Correlation Spectroscopy Enables Kinetics Study of DNA Hairpin Folding with a Time Window from Microseconds to Seconds.

Single-molecule fluorescence measurements have been widely used to explore kinetics and dynamics of biological systems. Among them, single-molecule imaging (SMI) is good at tracking processes slower than tens of milliseconds, whereas fluorescence correlation spectroscopy (FCS) is good at probing processes faster than submilliseconds. However, there is still shortage of simple yet effective single-molecule fluorescence method to cover the time-scale between submilliseconds and tens of milliseconds. To effectively bridge this millisecond gap, we developed a single-molecule fluorescence correlation spectroscopy (smFCS) method that works on surface-immobilized single molecules through surface scanning. We validated it by monitoring the classical DNA hairpin folding process. With a wide time window from microseconds to seconds, the experimental data are well fitted to the two-state folding model. All relevant molecular parameters, including the relative fluorescence brightness, equilibrium constant, and reaction rate constants, were uniquely determined.

Single Molecule Fluorescence Studies of Transition Paths in DNA Hairpin Folding

DNA hairpins are the simplest structures for investigating fundamental aspects of nucleic acid folding mechanisms. For hairpins exhibiting two-state behavior, all of the mechanistic information on how the hairpin folds is contained in the transition path, the rare event in single molecule trajectories when the free energy barrier between folded and unfolded states is actually crossed. In the only experimental study of transition paths in nucleic acids to date, Woodside and coworkers measured an upper bound of 50 μs for the average transition path times (TPT) of several nucleic acids, limited by the time resolution of their optical tweezer experiments (Neupane et al. Phys. Rev. Lett. 2012). Neupane et al. also reconstructed the free energy surface for an indirect determination of average transition path times from Szabo's analytical theory for diffusive barrier crossing. We used confocal single molecule FRET to study a DNA hairpin with 4 base pairs in the stem and 21 T's in the loop and that has a folding time of 310 μs in 500mM NaCl at 22oC. Maximum likelihood analysis of 780 transitions in photon trajectories yielded an upper bound of 2.5 μs for the average transition path time (Truex et al., Phys. Rev. Lett. 2015), compared to the value of ∼4 μs predicted by Neupane et al. from hairpins with 9-30 base pair stems and 4 T's in the loop, providing an important test of energy landscape theory. Current experiments are aimed at reducing blinking, a major obstacle to measuring transition path times, and at eventually characterizing structural changes during transition paths, which will provide a very demanding test of mechanisms predicted by both theoretical models and simulations.

Hairpins under tension: RNA versus DNA.

We use optical tweezers to control the folding and unfolding of individual DNA and RNA hairpins by force. Four hairpin molecules are studied in comparison: two DNA and two RNA ones. We observe that the conformational dynamics is slower for the RNA hairpins than for their DNA counterparts. Our results indicate that structures made of RNA are dynamically more stable. This difference might contribute to the fact that DNA and RNA play fundamentally different biological roles in spite of chemical similarity.

Refinement of Generalized Born Implicit Solvation Parameters for Nucleic Acids and Their Complexes with Proteins.

The Generalized Born (GB) implicit solvent model has undergone significant improvements in accuracy for modeling of proteins and small molecules. However, GB still remains a less widely explored option for nucleic acid simulations, in part because fast GB models are often unable to maintain stable nucleic acid structures or they introduce structural bias in proteins, leading to difficulty in application of GB models in simulations of protein-nucleic acid complexes. Recently, GB-neck2 was developed to improve the behavior of protein simulations. In an effort to create a more accurate model for nucleic acids, a similar procedure to the development of GB-neck2 is described here for nucleic acids. The resulting parameter set significantly reduces absolute and relative energy error relative to Poisson-Boltzmann for both nucleic acids and nucleic acid-protein complexes, when compared to its predecessor GB-neck model. This improvement in solvation energy calculation translates to increased structural stability for simulations of DNA and RNA duplexes, quadruplexes, and protein-nucleic acid complexes. The GB-neck2 model also enables successful folding of small DNA and RNA hairpins to near native structures as determined from comparison with experiment. The functional form and all required parameters are provided here and also implemented in the AMBER software.

Testing Landscape Theory for Biomolecular Processes with Single Molecule Fluorescence Spectroscopy.

Although Kramers' theory for diffusive barrier crossing on a 1D free energy profile plays a central role in landscape theory for complex biomolecular processes, it has not yet been rigorously tested by experiment. Here we test this 1D diffusion scenario with single molecule fluorescence measurements of DNA hairpin folding. We find an upper bound of 2.5 μs for the average transition path time, consistent with the predictions by theory with parameters determined from optical tweezer measurements.