Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins

RNA adapts its flexibility to efficiently fold and resist unfolding

Recent studies have demonstrated that the mechanisms through which biopolymers like RNA interconvert between multiple folded structures are critical for their cellular functions. A major obstacle to elucidating these mechanisms is the lack of experimental approaches that can resolve these interconversions between functionally relevant biomolecular structures. Here, using a nano-electronic device with microsecond time resolution, we dissect the complete set of structural rearrangements executed by an ultra-stable RNA, the UUCG stem-loop, at the single-molecule level. We show that the stem-loop samples at least four conformations along two folding pathways leading to two distinct folded structures, only one of which has been previously observed. By modulating its flexibility, the stem-loop can adaptively select between these pathways, enabling it to both fold rapidly and resist unfolding. This paradigm of stabilization through compensatory changes in flexibility broadens our understanding of stable RNA structures and is expected to serve as a general strategy employed by all biopolymers.

Sequence-Dependent Melting and Refolding Dynamics of RNA UNCG Tetraloops Using Temperature-Jump/Drop Infrared Spectroscopy

Time-resolved temperature-jump/drop infrared (IR) spectroscopy has been used to measure the impact of stem base sequence on the melting and refolding dynamics of ribonucleic acid (RNA) tetraloops. A series of three 12-nucleotide RNA hairpin sequences were studied, each featuring a UACG tetraloop motif and a double-stranded stem containing four base pairs. In each case, the stem comprised three GC pairs plus a single AU base pair inserted at the closing point of the loop (RNA_loop), in the middle of the stem (RNA_mid), or at the stem terminus (RNA_end). Results from analogous DNA tetraloop (TACG) sequences were also obtained. Inclusion of AU or AT base pairs in the stem leads to faster melting of the stem-loop structure compared to a stem sequence featuring four GC base pairs while refolding times were found to be slower, consistent with a general reduction in stem-loop stability caused by the AU/AT pair. Independent measurement of the dynamic timescales for melting and refolding of ring vibrational modes of guanine (G_R) and adenine (A_R) provided position-specific insight into hairpin dynamics. The G_R-derived data showed that DNA sequences melted more quickly (0.5 ± 0.1 to 0.7 ± 0.1 μs at 70 °C) than analogous RNA sequences (4.3 ± 0.4 to 4.4 ± 0.3 μs at 70 °C). Position-sensitive data from the A_R modes suggests that DNA hairpins begin melting from the terminal end of the stem toward the loop while RNA sequences begin melting from the loop. Refolding timescales for both RNA and DNA hairpins were found to be similar (250 ± 50 μs at 70 °C) except for RNA_end and DNA_loop which refolded much more slowly (746 ± 36 and 430 ± 31 μs, respectively), showing that the refolding pathway is significantly impaired by the placement of AU/AT pairs at different points in the stem. We conclude that conformational changes of analogous pairs of RNA and DNA tetraloops proceed by different mechanisms.

Measuring RNA UNCG Tetraloop Refolding Dynamics Using Temperature-Jump/Drop Infrared Spectroscopy

Determining the structural dynamics of RNA and DNA is essential to understanding their cellular function, but direct measurement of strand association or folding remains experimentally challenging. Here we illustrate a temperature-jump/drop method able to reveal refolding dynamics. Time-resolved temperature-jump/drop infrared spectroscopy is used to measure the melting and refolding dynamics of a 12-nucleotide RNA sequence comprising a UACG tetraloop and a four-base-pair double-stranded GC stem, comparing them to an equivalent DNA (TACG) sequence. Stem-loop melting occurred an order of magnitude more slowly in RNA than DNA (6.0 ± 0.1 μs versus 0.8 ± 0.1 μs at 70 °C). In contrast, the refolding dynamics of both sequences occurred on similar time scales (200 μs). While the melting and refolding dynamics of RNA and DNA hairpins both followed Arrhenius temperature dependences, refolding was characterized by an apparent negative activation energy, consistent with a mechanism involving multiple misfolded intermediates prior to zipping of the stem base pairs.

Millisecond Time-Resolved Solid-State NMR Initiated by Rapid Inverse Temperature Jumps

Elucidation of the detailed mechanisms by which biological macromolecules undergo major structural conversions, such as folding, complex formation, and self-assembly, is a central concern of biophysical chemistry that will benefit from new experimental methods. We describe a simple technique for initiating a structural conversion process by a rapid decrease in the temperature of a solution, i.e., a rapid inverse temperature jump. By pumping solutions through copper capillary tubes that are thermally anchored to heated and cooled blocks, solution temperatures can be switched from 95 to 30 °C (or lower) in about 0.8 ms. For time-resolved solid-state nuclear magnetic resonance (ssNMR), solutions can then be frozen rapidly by spraying into cold isopentane after a variable structural evolution time τ_e. As an initial demonstration, we use this "inverse T-jump" technique to characterize the kinetics and mechanism by which the 26-residue peptide melittin converts from its primarily disordered, monomeric state at 95 °C to its α-helical, tetrameric state at 30 °C. One- and two-dimensional ssNMR spectra of frozen solutions with various values of τ_e, recorded at 25 K with signal enhancements from dynamic nuclear polarization, show that both helical secondary structure and intermolecular contacts develop on the same time scale of about 6 ms. The dependences on τ_e of both intraresidue crosspeak patterns and inter-residue crosspeak volumes in two-dimensional spectra can be fit with a unidirectional dimerization model, consistent with dimerization being the rate-limiting step for melittin tetramer formation.

Can one detect intermediate denaturation states of DNA sequences by following the equilibrium open-close dynamic fluctuations of a single base pair?

Melting of DNA sequences may occur through a few major intermediate states, whose influence on the melting curve has been discussed previously, while their effect on the kinetics has not been explored thoroughly. Here, we chose a simple DNA sequence, forming a hairpin in its native (zipped) state, and study it using molecular dynamic (MD) simulations and a model integrating the Gaussian network model with bond-binding energies-the Gaussian binding energy (GBE) model. We find two major partial denaturation states, a bubble state and a partial unzipping state. We demonstrate the influence of these two states on the closing-opening base pair dynamics, as probed by a tagged bond auto-correlation function (ACF). We argue that the latter is measured by fluorescence correlation spectroscopy experiments, in which one base of the pair is linked to a fluorescent dye, while the complementary base is linked to a quencher, similar to the experiment reported by Altan-Bonnet et al. [Phys. Rev. Lett. 90, 138101 (2003)]. We find that tagging certain base pairs at temperatures around the melting temperature results in a multi-step relaxation of the ACF, while tagging other base pairs leads to an effectively single-step relaxation, albeit non-exponential. Only the latter type of relaxation has been observed experimentally, and we suggest which of the other base pairs should be tagged in order to observe multi-step relaxation. We demonstrate that this behavior can be observed with other sequences and argue that the GBE can reliably predict these dynamics for very long sequences, where MD simulations might be limited.

Insights into the free energy landscape and salt-controlled mechanism of the conformational conversions between human telomeric G-quadruplex structures

G-quadruplexes have become attractive drug targets in cancer therapy. However, due to the polymorphism of G-quadruplex structures, it is difficult to experimentally verify the relevant structures of multiple intermediates and transition states in dynamic equilibrium. Hence, understanding the mechanism by which structural conversions of G-quadruplexes occur is still challenging. We conducted targeted molecular dynamics simulation with umbrella sampling to investigate how salt affects the conformational conversion of human telomeric G-quadruplex. Our results explore a unique view into the structures and energy barrier of the intermediates and transition states in the interconversion process. The pathway of G-quadruplex conformational interconversion was mapped out by a free energy landscape, consisting of branched parallel pathways with multiple energy basins. We propose a salt-controlled mechanism that as the salt concentration increases, the conformational conversion mechanism switches from multi-pathway folding to sequential folding pathways. The hybrid-I and hybrid-II structures are intermediates in the basket-propeller transformation. In high-salt solutions, the conformational conversion upon K⁺ binding is more feasible than upon Na⁺ binding. The free energy barrier for conformational conversions ranges from 1.6 to 4.6 kcal/mol. Our work will be beneficial in developing anticancer agents.

Massively Parallelized Molecular Force Manipulation with On-Demand Thermal and Optical Control

In single-molecule force spectroscopy (SMFS), a tethered molecule is stretched using a specialized instrument to study how macromolecules extend under force. One problem in SMFS is the serial and slow nature of the measurements, performed one molecule at a time. To address this long-standing challenge, we report on the origami polymer force clamp (OPFC) which enables parallelized manipulation of the mechanical forces experienced by molecules without the need for dedicated SMFS instruments or surface tethering. The OPFC positions target molecules between a rigid nanoscale DNA origami beam and a responsive polymer particle that shrinks on demand. As a proof-of-concept, we record the steady state and time-resolved mechanical unfolding dynamics of DNA hairpins using the fluorescence signal from ensembles of molecules and confirm our conclusion using modeling.

Microsecond Equilibrium Dynamics of Hairpin-Forming Oligonucleotides Quantified by Two-Color Two-Dimensional Fluorescence Lifetime Correlation Spectroscopy

RNA and DNA play distinct roles in biological systems. However, the underlying physicochemical difference has been poorly understood, in particular, that in dynamical aspects. In this paper, we report on a comparative study of the formation-dissociation dynamics of a hairpin structure of RNA and DNA with development of two-color two-dimensional fluorescence lifetime correlation spectroscopy (two-color 2D FLCS). In this extension of 2D FLCS, we newly introduce the two-color detection scheme to analyze not only donor fluorescence photons but also acceptor fluorescence photons from a doubly labeled Förster resonance energy transfer (FRET) pair. This new 2D FLCS is utilized to resolve multiple species present in an equilibrated condition with a microsecond time resolution and enhanced sensitivity, and the combined use with the filtered fluorescence correlation spectroscopy (FCS) method enables a quantitative discussion on microsecond structural dynamics occurring in the equilibrium. This integrated approach is applied to FRET-labeled RNA/DNA oligonucleotides having analogous hairpin-forming sequences, and it was revealed that the hairpin dissociation rate of RNA is an order of magnitude slower than that of DNA while their hairpin-forming rates are comparable. This marked difference is attributable to the distinct duplex structure of RNA and DNA. The present study demonstrates that the integrated approach combining two-color 2D FLCS and filtered FCS has a high potential for quantifying microsecond kinetics at the single-molecule level, which allows us to experimentally construct a free energy landscape.

Validation of DBFOLD: An efficient algorithm for computing folding pathways of complex proteins

Atomistic simulations can provide valuable, experimentally-verifiable insights into protein folding mechanisms, but existing ab initio simulation methods are restricted to only the smallest proteins due to severe computational speed limits. The folding of larger proteins has been studied using native-centric potential functions, but such models omit the potentially crucial role of non-native interactions. Here, we present an algorithm, entitled DBFOLD, which can predict folding pathways for a wide range of proteins while accounting for the effects of non-native contacts. In addition, DBFOLD can predict the relative rates of different transitions within a protein’s folding pathway. To accomplish this, rather than directly simulating folding, our method combines equilibrium Monte-Carlo simulations, which deploy enhanced sampling, with unfolding simulations at high temperatures. We show that under certain conditions, trajectories from these two types of simulations can be jointly analyzed to compute unknown folding rates from detailed balance. This requires inferring free energies from the equilibrium simulations, and extrapolating transition rates from the unfolding simulations to lower, physiologically-reasonable temperatures at which the native state is marginally stable. As a proof of principle, we show that our method can accurately predict folding pathways and Monte-Carlo rates for the well-characterized Streptococcal protein G. We then show that our method significantly reduces the amount of computation time required to compute the folding pathways of large, misfolding-prone proteins that lie beyond the reach of existing direct simulation. Our algorithm, which is available online, can generate detailed atomistic models of protein folding mechanisms while shedding light on the role of non-native intermediates which may crucially affect organismal fitness and are frequently implicated in disease.

Many proteins must adopt a specific structure in order to function. Computational simulations have been used to shed light on the mechanisms of protein folding, but unfortunately, realistic simulations can typically only be run for small proteins, due to severe limits in computational speed. Here, we present a method to solve this problem, whereby instead of directly simulating folding from an unfolded state, we run simulations that allow for computation of equilibrium folding free energies, alongside high temperature simulations to compute unfolding rates. From these quantities, folding rates can be computed using detailed balance. Importantly, our method can account for the effects of nonnative contacts which transiently form during folding and must be broken prior to adoption of the native state. Such contacts, which are often excluded from simple models of folding, may crucially affect real protein folding pathways and are often observed in folding intermediates implicated in disease.

Temperature-Jump 2D IR Spectroscopy with Intensity-Modulated CW Optical Heating

Pulsed temperature-jump (T-jump) spectroscopy with infrared (IR) detection has been widely used to study biophysical processes occurring from nanoseconds to ∼1 ms with structural sensitivity. However, many systems exhibit structural dynamics on time scales longer than the millisecond barrier that is set by the time scale for thermal relaxation of the sample. We developed a linear and nonlinear infrared spectrometer coupled to an intensity-modulated continuous wave (CW) laser to probe T-jump-initiated chemical reactions from <1 ms to seconds. Time-dependent modulation of the CW laser leads to a <1 ms heating time as well as a constant final temperature (±3%) for the duration of the heating time. Temperature changes of up to 75 °C in D₂O are demonstrated, allowing for nonequilibrium measurements inaccessible to standard pulsed optical T-jump setups. T-jump linear absorption, pump-probe, and two-dimensional IR (2D IR) spectroscopy are applied to the unfolding and refolding of ubiquitin and a model intercalated motif (i-motif) DNA sequence, and analysis of the observed signals is used to demonstrate the limits and utility of each method. Overall, the ability to probe temperature-induced chemical processes from <1 ms to many seconds with 2D IR spectroscopy provides multiple new avenues for time-dependent spectroscopy in chemistry and biophysics.

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.

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.

Length-Dependent Melting Kinetics of Short DNA Oligonucleotides Using Temperature-Jump IR Spectroscopy

In this work, we utilize Fourier transform infrared and temperature-jump (T-jump) infrared (IR) spectroscopy to investigate the melting thermodynamics and kinetics of a series of five DNA sequences ranging from 6 to 14 base pairs long. IR spectroscopy is well suited for the study of DNA because of its ability to distinguish base-specific information, and the nanosecond time resolution of the T-jump apparatus can access the relevant range of kinetics. Eyring analysis of a two-state model examines both the activation enthalpy and entropy, providing new insights into the energetic driving forces and physical processes behind the association and dissociation while also helping to clarify the commonly observed negative activation energy. Global analysis of the thermodynamic and kinetic data applying a linear dependence of activation barriers on oligo length provides a holistic result by producing reasonable agreement between our data and existing nearest-neighbor (NN) thermodynamic parameters blending the experimental results with established predictive models. By studying the trends in the thermodynamics and kinetics as a function of length, this work demonstrates a direct correlation between the effects additional dinucleotides have on the kinetics and the NN parameters for those dinucleotides. This result further supports the development of a kinetic analogue to the thermodynamic NN parameters.

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.

Transition-path properties for folding reactions in the limit of small barriers

Transition paths are of great interest because they encapsulate information about the mechanisms of barrier-crossing reactions. Analysis of experiments measuring biomolecular folding reactions has relied on expressions for properties of transition paths such as transition-path times and velocities that hold in the limit of large harmonic barriers, but real molecules often have relatively small barriers. Recent theoretical work presented more general expressions for transition-path properties. Here we extend this work, deriving expressions from the general case that can be applied to small harmonic barriers. We first compared the performance of small-barrier, large-barrier, and general solutions when applied to simulated transitions, focusing on improvements in estimates of the diffusion coefficient determined from transition times and velocities. We then applied these expressions to experimental data from force spectroscopy measurements of DNA hairpins. We found that the low-barrier approximation and exact solution reduced or resolved the small but systematic inconsistencies that had arisen from assuming large harmonic barriers, demonstrating the practical utility of the new equations for analyzing experimental data.

Dynamics of physiologically relevant noncanonical DNA structures: an overview from experimental and theoretical studies

DNA is a complex molecule with phenomenal inherent plasticity and the ability to form different hydrogen bonding patterns of varying stabilities. These properties enable DNA to attain a variety of structural and conformational polymorphic forms. Structurally, DNA can exist in single-stranded form or as higher-order structures, which include the canonical double helix as well as the noncanonical duplex, triplex and quadruplex species. Each of these structural forms in turn encompasses an ensemble of dynamically heterogeneous conformers depending on the sequence composition and environmental context. In vivo, the widely populated canonical B-DNA attains these noncanonical polymorphs during important cellular processes. While several investigations have focused on the structure of these noncanonical DNA, studying their dynamics has remained nontrivial. Here, we outline findings from some recent advanced experimental and molecular simulation techniques that have significantly contributed toward understanding the complex dynamics of physiologically relevant noncanonical forms of DNA.

Monovalent ions modulate the flux through multiple folding pathways of an RNA pseudoknot

The assembly mechanism of RNA, vital to describing its functions, depends on both the sequence and the metal ion concentration. How the latter influences the folding trajectories remains an important unsolved problem. Here, we examine the folding pathways of an RNA pseudoknot (PK) with key functional roles in transcription and translation, using a combination of experiments and simulations. We demonstrate that the PK, consisting of two hairpins with differing stabilities, folds by parallel pathways. Surprisingly, the flux between them is modulated by monovalent salt concentration. Our work shows that the order of assembly of PKs is determined by the relative stability of the hairpins, implying that the folding landscape can be controlled by sequence and ion concentration.

The functions of RNA pseudoknots (PKs), which are minimal tertiary structural motifs and an integral part of several ribozymes and ribonucleoprotein complexes, are determined by their structure, stability, and dynamics. Therefore, it is important to elucidate the general principles governing their thermodynamics/folding mechanisms. Here, we combine laser temperature-jump experiments and coarse-grained simulations to determine the folding/unfolding pathways of VPK, a variant of the mouse mammary tumor virus (MMTV) PK involved in ribosomal frameshifting. Fluorescent nucleotide analogs (2-aminopurine and pyrrolocytidine) placed at different stem/loop positions in the PK serve as local probes allowing us to monitor the order of assembly of VPK that has two constituent hairpins with different intrinsic stabilities. We show that at 50 mM KCl, the dominant folding pathway populates only the more stable hairpin intermediate; as the salt concentration is increased, a parallel folding pathway emerges involving the less stable hairpin as an alternate intermediate. Notably, the flux between the pathways is modulated by the ionic strength. Our findings support the principle that the order of PK structure formation is determined by the relative stabilities of the hairpins, which can be altered by sequence variations or salt concentrations. The experimental results of salt effects on the partitioning between the two folding pathways are in remarkable agreement with simulations that were performed with no adjustable parameters. Our study not only unambiguously demonstrates that VPK folds by parallel pathways but also showcases the power of combining experiments and simulations for a more enriched description of RNA self-assembly.

Sequence-Dependent Three Interaction Site Model for Single- and Double-Stranded DNA

We develop a robust coarse-grained model for single- and double-stranded DNA by representing each nucleotide by three interaction sites (TIS) located at the centers of mass of sugar, phosphate, and base. The resulting TIS model includes base-stacking, hydrogen bond, and electrostatic interactions as well as bond-stretching and bond angle potentials that account for the polymeric nature of DNA. The choices of force constants for stretching and the bending potentials were guided by a Boltzmann inversion procedure using a large representative set of DNA structures extracted from the Protein Data Bank. Some of the parameters in the stacking interactions were calculated using a learning procedure, which ensured that the experimentally measured melting temperatures of dimers are faithfully reproduced. Without any further adjustments, the calculations based on the TIS model reproduce the experimentally measured salt and sequence-dependence of the size of single-stranded DNA (ssDNA), as well as the persistence lengths of poly(dA) and poly(dT) chains. Interestingly, upon application of mechanical force, the extension of poly(dA) exhibits a plateau, which we trace to the formation of stacked helical domains. In contrast, the force-extension curve (FEC) of poly(dT) is entropic in origin and could be described by a standard polymer model. We also show that the persistence length of double-stranded DNA, formed from two complementary ssDNAs, is consistent with the prediction based on the worm-like chain. The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific trends. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting profiles of dimers, attests to the transferability and robustness of the TIS model for ssDNA and dsDNA.

Improving the mesoscopic modeling of DNA denaturation dynamics

Although previously developed mesoscopic DNA models have successfully reproduced thermodynamic denaturation data, recent studies show that these overestimate the rate of denaturation by orders of magnitude. Using adapted Peyrard-Bishop-Dauxois (PBD) models, we have calculated the denaturation rates of several DNA hairpins and made comparison with experimental data. We show that the addition of a barrier at the onsite potential of the PBD model gives a more accurate description of the unzipping dynamics of short DNA sequences. The new models provide a refined theoretical insight on the dynamical mechanisms of unzipping which can have implications for the understanding of transcription and replication processes. Still, this class of adapted PBD models seems to have a fundamental limitation which implies that it is not possible to get agreement with available experimental results on the dynamics of long DNA sequences and at the same time maintain the good agreement regarding its thermodynamics. The reason for this is that the denaturation rate of long DNA chains is not dramatically lowered by the additional barrier-as the base-pairs that open are more likely to remain open, facilitating the opening of the full DNA molecule. Some care has to be taken, since experimental techniques suitable to the study of denaturation rates of long sequences seem not to agree with other experimental data on short DNA sequences. Further research, both theoretical and experimental, is therefore needed to resolve these inconsistencies-which will be a starting point for new minimalistic models that are able to describe both thermodynamics and dynamics at a predictive level.

Direct Observation of Activated Kinetics and Downhill Dynamics in DNA Dehybridization

We have studied two model DNA oligonucleotide sequences that display contrasting degrees of heterogeneous melting using an optical temperature jump to trigger dehybridization and a nonlinear infrared (IR) spectroscopy probe to track the response of the helix ensemble. This approach offers base-sensitive structural insight through the unique vibrational fingerprint characteristic of each nucleobase as well as time resolution capable of following unfolding across nanoseconds to milliseconds. We observe predissociation unzipping of the helical termini, loss of final dimer contacts, and rehybridization of the dissociated strands all in a single measurement. Complete dissociation of the dimer is found to be well described by Arrhenius kinetics for both sequences, with dissociation barriers in the range of 160-190 kJ/mol. A sequence with terminal adenine-thymine (AT) base pairs and a guanine-cytosine core returns a large-amplitude fast response ranging from 70 to 170 ns, originating only from the AT base pairs. Variable temperature jump ( T-jump) experiments in which the final temperature ( T_f) is fixed and the initial temperature ( T_i) is varied such that different starting ensembles all evolve on the same final free-energy surface were employed to explore the features of the underlying potential that dictates hybridization. These experiments reveal that the unzipping of the AT termini is an essentially barrierless process and that both activated and downhill events are necessary to describe the dehybridization mechanism. Although our results are largely consistent with the classic nucleation-zipper picture, new insights regarding the nature of base pair zippering refine the mechanistic details of the fastest DNA hybridization dynamics.

The collective behavior of spring-like motifs tethered to a DNA origami nanostructure

Dynamic DNA nanotechnology relies on the integration of small switchable motifs at suitable positions of DNA nanostructures, thus enabling the manipulation of matter with nanometer spatial accuracy in a trigger-dependent fashion. Typical examples of such motifs are hairpins, whose elongation into duplexes can be used to perform long-range, translational movements. In this work, we used temperature-dependent FRET spectroscopy to determine the thermal stabilities of distinct sets of hairpins integrated into the central seam of a DNA origami structure. We then developed a hybrid spring model to describe the energy landscape of the tethered hairpins, combining the thermodynamic nearest-neighbor energy of duplex DNA with the entropic free energy of single-stranded DNA estimated using a worm-like chain approximation. We show that the organized scaffolding of multiple hairpins enhances the thermal stability of the device and that the coordinated action of the tethered motors can be used to mechanically unfold a G-quadruplex motif bound to the inner cavity of the origami structure, thus surpassing the operational capabilities of freely diffusing motors. Finally, we increased the complexity of device functionality through the insertion of two sets of parallel hairpins, resulting in four distinct states and in the reversible localization of desired molecules within the reconfigurable regions of the origami architecture.

Direct measurement of sequence-dependent transition path times and conformational diffusion in DNA duplex formation

The conformational diffusion coefficient, D, sets the timescale for microscopic structural changes during folding transitions in biomolecules like nucleic acids and proteins. D encodes significant information about the folding dynamics such as the roughness of the energy landscape governing the folding and the level of internal friction in the molecule, but it is challenging to measure. The most sensitive measure of D is the time required to cross the energy barrier that dominates folding kinetics, known as the transition path time. To investigate the sequence dependence of D in DNA duplex formation, we measured individual transition paths from equilibrium folding trajectories of single DNA hairpins held under tension in high-resolution optical tweezers. Studying hairpins with the same helix length but with G:C base-pair content varying from 0 to 100%, we determined both the average time to cross the transition paths, τ_tp, and the distribution of individual transit times, P_TP(t). We then estimated D from both τ_tp and P_TP(t) from theories assuming one-dimensional diffusive motion over a harmonic barrier. τ_tp decreased roughly linearly with the G:C content of the hairpin helix, being 50% longer for hairpins with only A:T base pairs than for those with only G:C base pairs. Conversely, D increased linearly with helix G:C content, roughly doubling as the G:C content increased from 0 to 100%. These results reveal that G:C base pairs form faster than A:T base pairs because of faster conformational diffusion, possibly reflecting lower torsional barriers, and demonstrate the power of transition path measurements for elucidating the microscopic determinants of folding.

Enhancing pairwise state-transition weights: A new weighting scheme in simulated tempering that can minimize transition time between a pair of conformational states

Simulated tempering (ST) is a widely used enhancing sampling method for Molecular Dynamics simulations. As one expanded ensemble method, ST is a combination of canonical ensembles at different temperatures and the acceptance probability of cross-temperature transitions is determined by both the temperature difference and the weights of each temperature. One popular way to obtain the weights is to adopt the free energy of each canonical ensemble, which achieves uniform sampling among temperature space. However, this uniform distribution in temperature space may not be optimal since high temperatures do not always speed up the conformational transitions of interest, as anti-Arrhenius kinetics are prevalent in protein and RNA folding. Here, we propose a new method: Enhancing Pairwise State-transition Weights (EPSW), to obtain the optimal weights by minimizing the round-trip time for transitions among different metastable states at the temperature of interest in ST. The novelty of the EPSW algorithm lies in explicitly considering the kinetics of conformation transitions when optimizing the weights of different temperatures. We further demonstrate the power of EPSW in three different systems: a simple two-temperature model, a two-dimensional model for protein folding with anti-Arrhenius kinetics, and the alanine dipeptide. The results from these three systems showed that the new algorithm can substantially accelerate the transitions between conformational states of interest in the ST expanded ensemble and further facilitate the convergence of thermodynamics compared to the widely used free energy weights. We anticipate that this algorithm is particularly useful for studying functional conformational changes of biological systems where the initial and final states are often known from structural biology experiments.

Understanding the kinetic mechanism of RNA single base pair formation

RNA functions are intrinsically tied to folding kinetics. The most elementary step in RNA folding is the closing and opening of a base pair. Understanding this elementary rate process is the basis for RNA folding kinetics studies. Previous studies mostly focused on the unfolding of base pairs. Here, based on a hybrid approach, we investigate the folding process at level of single base pairing/stacking. The study, which integrates molecular dynamics simulation, kinetic Monte Carlo simulation, and master equation methods, uncovers two alternative dominant pathways: Starting from the unfolded state, the nucleotide backbone first folds to the native conformation, followed by subsequent adjustment of the base conformation. During the base conformational rearrangement, the backbone either retains the native conformation or switches to nonnative conformations in order to lower the kinetic barrier for base rearrangement. The method enables quantification of kinetic partitioning among the different pathways. Moreover, the simulation reveals several intriguing ion binding/dissociation signatures for the conformational changes. Our approach may be useful for developing a base pair opening/closing rate model.

Hairpins participating in folding of human telomeric sequence quadruplexes studied by standard and T-REMD simulations

DNA G-hairpins are potential key structures participating in folding of human telomeric guanine quadruplexes (GQ). We examined their properties by standard MD simulations starting from the folded state and long T-REMD starting from the unfolded state, accumulating ∼130 μs of atomistic simulations. Antiparallel G-hairpins should spontaneously form in all stages of the folding to support lateral and diagonal loops, with sub-μs scale rearrangements between them. We found no clear predisposition for direct folding into specific GQ topologies with specific syn/anti patterns. Our key prediction stemming from the T-REMD is that an ideal unfolded ensemble of the full GQ sequence populates all 4096 syn/anti combinations of its four G-stretches. The simulations can propose idealized folding pathways but we explain that such few-state pathways may be misleading. In the context of the available experimental data, the simulations strongly suggest that the GQ folding could be best understood by the kinetic partitioning mechanism with a set of deep competing minima on the folding landscape, with only a small fraction of molecules directly folding to the native fold. The landscape should further include non-specific collapse processes where the molecules move via diffusion and consecutive random rare transitions, which could, e.g. structure the propeller loops.

Determining intrachain diffusion coefficients for biopolymer dynamics from single-molecule force spectroscopy measurements

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.

De novo design of heat-repressible RNA thermosensors in E. coli

RNA-based temperature sensing is common in bacteria that live in fluctuating environments. Most naturally-occurring RNA thermosensors are heat-inducible, have long sequences, and function by sequestering the ribosome binding site in a hairpin structure at lower temperatures. Here, we demonstrate the de novo design of short, heat-repressible RNA thermosensors. These thermosensors contain a cleavage site for RNase E, an enzyme native to Escherichia coli and many other organisms, in the 5′ untranslated region of the target gene. At low temperatures, the cleavage site is sequestered in a stem–loop, and gene expression is unobstructed. At high temperatures, the stem–loop unfolds, allowing for mRNA degradation and turning off expression. We demonstrated that these thermosensors respond specifically to temperature and provided experimental support for the central role of RNase E in the mechanism. We also demonstrated the modularity of these RNA thermosensors by constructing a three-input composite circuit that utilizes transcriptional, post-transcriptional, and post-translational regulation. A thorough analysis of the 24 thermosensors allowed for the development of design guidelines for systematic construction of similar thermosensors in future applications. These short, modular RNA thermosensors can be applied to the construction of complex genetic circuits, facilitating rational reprogramming of cellular processes for synthetic biology applications.

Effect of loop composition on the stability and folding kinetics of RNA hairpins with large loops

RNA hairpins are ubiquitous structural elements in biological RNAs, where they have the potential to regulate RNA folding and interactions with other molecules. There are established methods for predicting the thermodynamic stability of an RNA hairpin, but there are still relatively few detailed examinations of the kinetics of folding. Nonetheless, several recent studies indicate that hairpin folding does not proceed via a simple two-state model. Here, we monitor fluorescence from hairpins constructed as molecular beacons in ensemble, fluorescence correlation spectroscopy, and stopped-flow experiments to describe the folding of RNA hairpins with long (15 nucleotide) loops. Our results show that folding of these hairpins occurs through more than two states and that the mechanism of folding includes a fast intermediate phase observed on the tens of microseconds time scale and a slow phase, attributed to formation of the native folded hairpin loop and stem, observed on the milliseconds time scale. The composition of the RNA loop determines the time scale of intermediate and native folded states. Hairpins with a polyuracil loop sequence exhibit slower relaxation of the intermediate state and faster relaxation of the native folded state when compared to that of hairpins with cytosine or adenine in the loop. We hypothesize this composition dependence could be attributed to nucleobase stacking in cytosine and adenine containing regions of the loop, which would be absent in hairpins containing polyuracil loops. Such base stacking could destabilize the intermediate folds, thereby speeding the relaxation of the intermediate relative to similar sized hairpins with no base stacking in the loop. Likewise, the lower intermediate stability could prolong the relaxation of the native folded state.

RNA folding: structure prediction, folding kinetics and ion electrostatics

Beyond the "traditional" functions such as gene storage, transport and protein synthesis, recent discoveries reveal that RNAs have important "new" biological functions including the RNA silence and gene regulation of riboswitch. Such functions of noncoding RNAs are strongly coupled to the RNA structures and proper structure change, which naturally leads to the RNA folding problem including structure prediction and folding kinetics. Due to the polyanionic nature of RNAs, RNA folding structure, stability and kinetics are strongly coupled to the ion condition of solution. The main focus of this chapter is to review the recent progress in the three major aspects in RNA folding problem: structure prediction, folding kinetics and ion electrostatics. This chapter will introduce both the recent experimental and theoretical progress, while emphasize the theoretical modelling on the three aspects in RNA folding.

Structure and dynamics of oligonucleotides in the gas phase

By combining ion-mobility mass spectrometry experiments with sub-millisecond classical and ab initio molecular dynamics we fully characterized, for the first time, the dynamic ensemble of a model nucleic acid in the gas phase under electrospray ionization conditions. The studied oligonucleotide unfolds upon vaporization, loses memory of the solution structure, and explores true gas-phase conformational space. Contrary to our original expectations, the oligonucleotide shows very rich dynamics in three different timescales (multi-picosecond, nanosecond, and sub-millisecond). The shorter timescale dynamics has a quantum mechanical nature and leads to changes in the covalent structure, whereas the other two are of classical origin. Overall, this study suggests that a re-evaluation on our view of the physics of nucleic acids upon vaporization is needed.

Single-molecule FRET studies of HIV TAR-DNA hairpin unfolding dynamics

We directly measure the dynamics of the HIV trans-activation response (TAR)-DNA hairpin with multiple loops using single-molecule Förster resonance energy transfer (smFRET) methods. Multiple FRET states are identified that correspond to intermediate melting states of the hairpin. The stability of each intermediate state is calculated from the smFRET data. The results indicate that hairpin unfolding obeys a "fraying and peeling" mechanism, and evidence for the collapse of the ends of the hairpin during folding is observed. These results suggest a possible biological function for hairpin loops serving as additional fraying centers to increase unfolding rates in otherwise stable systems. The experimental and analytical approaches developed in this article provide useful tools for studying the mechanism of multistate DNA hairpin dynamics and of other general systems with multiple parallel pathways of chemical reactions.

Structure and properties of DNA in apolar solvents

The study of nucleic acids in low-polarity environments paves the way for novel biotechnological applications of DNA. Here, we use a repertoire of atomistic molecular simulation tools to study the nature of DNA when placed in a highly apolar environment and when transferred from aqueous to apolar solvent. Our results show that DNA becomes stiffer in apolar solvents and suggest that highly negatively charged states, which are the most prevalent in water, are strongly disfavored in apolar solvents and neutral states with conformations not far from the aqueous ones are the dominant forms. Transfer from water to an apolar solvent such as CCl₄ is unlikely to occur, but our results suggest that if forced, the DNA would migrate surrounded by a small shell of water (the higher the DNA charge, the larger the number of water molecules in this shell). Even the neutral form (predicted to be the dominant one in apolar solvents) would surround itself by a small number of highly stable water molecules when moved from water to a highly apolar environment. Neutralization of DNA charges seems a crucial requirement for transfer of DNA to apolar media, and the most likely mechanism to achieve good transfer properties.

Folding and unfolding pathways of the human telomeric G-quadruplex

Sequence analogs of human telomeric DNA such as d[AGGG(TTAGGG)3] (Tel22) fold into monomeric quadruplex structures in the presence of a suitable cation. To investigate the pathway for unimolecular quadruplex formation, we monitored the kinetics of K(+)-induced folding of Tel22 by circular dichroism (CD), intrinsic 2-aminopurine fluorescence, and fluorescence resonance energy transfer (FRET). The results are consistent with a four-step pathway U ↔ I1 ↔ I2 ↔ I3 ↔ F where U and F represent unfolded and folded conformational ensembles and I1, I2, and I3 are intermediates. Previous kinetic studies have shown that I1 is formed in a rapid pre-equilibrium and may consist of an ensemble of "prefolded" hairpin structures brought about by cation-induced electrostatic collapse of the DNA. The current study shows that I1 converts to I2 with a relaxation time τ1=0.1s at 25 °C in 25 mM KCl. The CD spectrum of I2 is characteristic of an antiparallel quadruplex that could form as a result of intramolecular fold-over of the I1 hairpins. I3 is relatively slowly formed (τ2≈3700s) and has CD and FRET properties consistent with those expected of a triplex structure as previously observed in equilibrium melting studies. I3 converts to F with τ3≈750s. Identical pathways with different kinetic constants involving a rapidly formed antiparallel intermediate were observed with oligonucleotides forming mixed parallel/antiparallel hybrid-1 and hybrid-2 topologies {e.g. d[TTGGG(TTAGGG)3A] and d[TAGGG(TTAGGG)3TT]}. Aspects of the kinetics of unfolding were also monitored by the spectroscopic methods listed above and by time-resolved fluorescence lifetime measurements using a complementary strand trap assay. These experiments reveal a slow, rate-limiting step along the unfolding pathway.

Impact of bulge loop size on DNA triplet repeat domains: Implications for DNA repair and expansion

Repetitive DNA sequences exhibit complex structural and energy landscapes, populated by metastable, noncanonical states, that favor expansion and deletion events correlated with disease phenotypes. To probe the origins of such genotype-phenotype linkages, we report the impact of sequence and repeat number on properties of (CNG) repeat bulge loops. We find the stability of duplexes with a repeat bulge loop is controlled by two opposing effects; a loop junction-dependent destabilization of the underlying double helix, and a self-structure dependent stabilization of the repeat bulge loop. For small bulge loops, destabilization of the underlying double helix overwhelms any favorable contribution from loop self-structure. As bulge loop size increases, the stabilizing loop structure contribution dominates. The role of sequence on repeat loop stability can be understood in terms of its impact on the opposing influences of junction formation and loop structure. The nature of the bulge loop affects the thermodynamics of these two contributions differently, resulting in unique differences in repeat size-dependent minima in the overall enthalpy, entropy, and free energy changes. Our results define factors that control repeat bulge loop formation; knowledge required to understand how this helix imperfection is linked to DNA expansion, deletion, and disease phenotypes.

Aripiprazole-montmorillonite: a new organic-inorganic nanohybrid material for biomedical applications

Poor aqueous solubility and the unpleasant taste of aripiprazole (APZ) have been recurring problems, owing to its low bioavailability and low patient tolerance, respectively. Herein, we prepared a nanohybrid system that was based on a bentonite clay material, montmorillonite (MMT), which could both mask the taste and enhance the solubility of APZ (i.e., APZ-MMT). To further improve the efficacy of this taste masking and drug solubility, APZ-MMT was also coated with a cationic polymer, polyvinylacetal diethylamino acetate (AEA). In vitro dissolution tests at neutral pH showed that the amount of drug that was released from the AEA-coated APZ-MMT was greatly suppressed (<1%) for the first 3 min, thus suggesting that AEA-coated APZ-MMT has strong potential for the taste masking of APZ. Notably, in simulated gastric juice at pH 1.2, the total percentage of APZ that was released within the first 2 h increased up to 95% for AEA-coated APZ-MMT. Furthermore, this in vitro release profile was also similar to that of Abilify®, a commercially available medication. In vivo experiments by using Sprague-Dawley rats were also performed to compare the pharmacokinetics of AEA-coated APZ-MMT and Abilify®. AEA-coated APZ-MMT exhibited about 20% higher systemic exposure of APZ and its metabolite, dehydro-APZ, compared with Abilify®. Therefore, a new MMT-based nanovehicle, which is coated with a cationic polymer, can act as a promising delivery system for both taste masking and for enhancing the bioavailability of APZ.

Transition path times for nucleic Acid folding determined from energy-landscape analysis of single-molecule trajectories

The duration of structural transitions in biopolymers is only a fraction of the time spent searching diffusively over the configurational energy landscape. We found the transition time, τ(TP), and the diffusion constant, D, for DNA and RNA folding using energy landscapes obtained from single-molecule trajectories under tension in optical traps. DNA hairpins, RNA pseudoknots, and a riboswitch all had τ(TP)~10 μs and D~10(-13-14) m(2)/s, despite widely differing unfolding rates. These results show how energy-landscape analysis can be harnessed to characterize brief but critical events during folding reactions.

Kinetic mechanism of conformational switch between bistable RNA hairpins

Transitions between the different conformational states play a critical role in many RNA catalytic and regulatory functions. In this study, we use the Kinetic Monte Carlo method to investigate the kinetic mechanism for the conformational switches between bistable RNA hairpins. We find three types of conformational switch pathways for RNA hairpins: refolding after complete unfolding, folding through basepair-exchange pathways and through pseudoknot-assisted pathways, respectively. The result of the competition between the three types of pathways depends mainly on the location of the rate-limiting base stacks (such as the GC base stacks) in the structures. Depending on the structural relationships between the two bistable hairpins, the conformational switch can follow single or multiple dominant pathways. The predicted folding pathways are supported by the activation energy results derived from the Arrhenius plot as well as the NMR spectroscopy data.

Laser temperature-jump spectroscopy of intrinsically disordered proteins

Laser temperature-jump methods allow an experimenter to study the kinetics and dynamics of very rapid solution-phase processes, including conformational dynamics of biomolecules on time scales of nanoseconds and microseconds. The combination of laser temperature-jump (T-jump) excitation and appropriate optical detection techniques such as fluorescence energy transfer allows the study of intramolecular and intermolecular conformational changes and interactions that occur during protein folding and binding. This article describes the application of the laser temperature-jump method to UV-visible fluorescence studies of the coupled folding and binding of intrinsically disordered proteins. We emphasize the practical aspects of instrument alignment and optimization, sample preparation, and data collection using fluorescently labeled peptides with UV laser excitation.

Frontiers in molecular dynamics simulations of DNA

It has been known for decades that DNA is extremely flexible and polymorphic, but our knowledge of its accessible conformational space remains limited. Structural data, primarily from X-ray diffraction studies, is sparse in comparison to the manifold configurations possible, and direct experimental examinations of DNA's flexibility still suffer from many limitations. In the face of these shortcomings, molecular dynamics (MD) is now an essential tool in the study of DNA. It affords detailed structural and dynamical insights, which explains its recent transition from a small number of highly specialized laboratories to a large variety of groups dealing with challenging biological problems. MD is now making an irreversible journey to the mainstream of research in biology, with the attendant opportunities and challenges. But given the speed with which MD studies of DNA have spread, the roots remain somewhat shallow: in many cases, there is a lack of deep knowledge about the foundations, strengths, and limits of the technique. In this Account, we discuss how MD has become the most important source of structural and flexibility data on DNA, focusing on advances since 2007 of atomistic MD in the description of DNA under near-physiological conditions and highlighting the possibilities and shortcomings of the technique. The evolution in the field over the past four years is a prelude to the ongoing revolution. The technique has gained in robustness and predictive power, which when coupled with the spectacular improvements in software and hardware has enabled the tackling of systems of increasing complexity. Simulation times of microseconds have now been achieved, with even longer times when specialized hardware is used. As a result, we have seen the first real-time simulation of large conformational transitions, including folding and unfolding of short DNA duplexes. Noteworthy advances have also been made in the study of DNA-ligand interactions, and we predict that a global thermodynamic and kinetic picture of the binding landscape of DNA will become available in a few years. MD will become a crucial tool in areas such as biomolecular engineering and synthetic biology. MD has also been shown to be an excellent source of parameters for mesoscopic models of DNA flexibility. Such models can be refined through atomistic MD simulations on small duplexes and then applied to the study of entire chromosomes. Recent evidence suggests that MD-derived elastic models can successfully predict the position of regulatory regions in DNA and can help advance our understanding of nucleosome positioning and chromatin plasticity. If these results are confirmed, MD simulations can become the ultimate tool to decipher a physical code that can contribute to gene regulation. We are entering the golden age of MD simulations of DNA. Undoubtedly, the expectations are high, but the challenges are also enormous. These include the need for more accurate potential energy functionals and for longer and more complex simulations in more realistic systems. The joint research effort of several groups will be crucial for adapting the technique to the requirements of the coming decade.