Single-molecule methods for ligand counting: linking ion uptake to DNA hairpin folding

Quantify the combined effects of temperature and force on the stability of DNA hairpin

OxDNA, as a successful coarse-grain model, has been applied to reproduce the thermodynamic and mechanical properties of both single- and double-stranded DNA. In current simulation, oxDNA is extended to explore the combined effects of temperature and force on the stability of DNA hairpin and its free energy landscape. Simulations were carried out at different forces and temperatures, at each temperature, a 18-base-pair DNA hairpin dynamically transited between folded state and unfolded state, and the separation between two states is consistent with the full contour length of single-stranded DNA in the unfolded state. Two methods were used to identify the critical force of DNA hairpin at each temperature and the critical forces obtained from two methods were consistent with each other and gradually decreased with the increasing temperature from 300 K to 326 K. The critical force at 300 K is reasonably consistent with the single molecule result of DNA hairpin with the same stem length. The two-state free energy landscape can be elucidated from the probability distribution of DNA hairpin extension and its dependence on the force and temperature is totally different. The increasing temperature not only reduces the free energy barrier, but also alters the position of transition point along the extension coordinate, resulting in the reduction of folding distance and the extension of unfolding distance, but their sum is not obviously dependent on the temperature. Generally, an assumption that the location of transition state in two-state energy landscape is independent of the stretching force is used to analyze the data of the single molecule experiment, but current simulation results indicate that effects of stretching forces on the location of transition state in two-state energy landscape are dependent on temperature. At relatively high temperature, stretching force can also change the location of transition state in the free energy landscape.

Using Magnetic Tweezers to Unravel the Mechanism of the G-quadruplex Binding and Unwinding Activities of DHX36 Helicase

Single-molecule manipulation methods are useful techniques to probe the interactions of proteins and nucleic acid structures. Here, we describe the magnetic tweezers-based single-molecule investigation of the binding of helicases to G-quadruplex structures and their ATP-dependent unwinding activity, using DHX36 (also known as RHAU and G4R1) helicase and a DNA G-quadruplex structure for an example. We specifically emphasize on the principle and method to probe the interactions between DHX36 and the DNA G-quadruplex in different intermediate states during an ATPase cycle of DHX36, based on detecting the DHX36-induced changes in the lifetime of the DNA G-quadruplex under tension. The principle of the measurement can be broadly extended to the studies of other DNA or RNA G-quadruplex helicases.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

Molecular Simulations of Ion Effects on the Thermodynamics of RNA Folding

How ions affect RNA folding thermodynamics and kinetics is an important but a vexing problem that remains unsolved. Experiments have shown that the free-energy change, Δ G( c), of RNA upon folding varies with the salt concentration ( c) as, Δ G( c) = k _c ln  c + const, where the coefficient k _c is proportional to the difference in the ion preferential coefficient, ΔΓ. We performed simulations of a coarse-grained model, by modeling electrostatic interactions implicitly and with explicit representation of ions, to elucidate the molecular underpinnings of the relationship between Δ G and ΔΓ. The simulations quantitatively reproduce the heat capacity for a pseudoknot, thus validating the model. We show that Δ G( c), calculated directly from ΔΓ, varies linearly with ln  c ( c < 0.2 M), for a hairpin and the pseudoknot, demonstrating a molecular link between the two quantities. Explicit ion simulations also show the linear dependence of Δ G( c) on ln  c at all c with k _c = 2 k_B T, except that Δ G( c) values are shifted by ∼2 kcal/mol higher than experiments. The discrepancy is due to an underestimation of Γ for both the folded and unfolded states while giving accurate values for ΔΓ. The predictions for the salt dependence of ΔΓ are amenable to test using single-molecule pulling experiments. The framework provided here can be used to obtain accurate thermodynamics for other RNA molecules as well.

Counting the ions surrounding nucleic acids

Nucleic acids are strongly negatively charged, and thus electrostatic interactions—screened by ions in solution—play an important role in governing their ability to fold and participate in biomolecular interactions. The negative charge creates a region, known as the ion atmosphere, in which cation and anion concentrations are perturbed from their bulk values. Ion counting experiments quantify the ion atmosphere by measuring the preferential ion interaction coefficient: the net total number of excess ions above, or below, the number expected due to the bulk concentration. The results of such studies provide important constraints on theories, which typically predict the full three-dimensional distribution of the screening cloud. This article reviews the state of nucleic acid ion counting measurements and critically analyzes their ability to test both analytical and simulation-based models.

Single molecule high-throughput footprinting of small and large DNA ligands

Most DNA processes are governed by molecular interactions that take place in a sequence-specific manner. Determining the sequence selectivity of DNA ligands is still a challenge, particularly for small drugs where labeling or sequencing methods do not perform well. Here, we present a fast and accurate method based on parallelized single molecule magnetic tweezers to detect the sequence selectivity and characterize the thermodynamics and kinetics of binding in a single assay. Mechanical manipulation of DNA hairpins with an engineered sequence is used to detect ligand binding as blocking events during DNA unzipping, allowing determination of ligand selectivity both for small drugs and large proteins with nearly base-pair resolution in an unbiased fashion. The assay allows investigation of subtle details such as the effect of flanking sequences or binding cooperativity. Unzipping assays on hairpin substrates with an optimized flat free energy landscape containing all binding motifs allows determination of the ligand mechanical footprint, recognition site, and binding orientation.

Mapping the sequence specificity of DNA ligands remains a challenge, particularly for small drugs. Here the authors develop a parallelized single molecule magnetic tweezers approach using engineered DNA hairpins that can detect sequence selectivity, thermodynamics and kinetics of binding for small drugs and large proteins.

High Spatiotemporal-Resolution Magnetic Tweezers: Calibration and Applications for DNA Dynamics

The observation of biological processes at the molecular scale in real time requires high spatial and temporal resolution. Magnetic tweezers are straightforward to implement, free of radiation or photodamage, and provide ample multiplexing capability, but their spatiotemporal resolution has lagged behind that of other single-molecule manipulation techniques, notably optical tweezers and AFM. Here, we present, to our knowledge, a new high-resolution magnetic tweezers apparatus. We systematically characterize the achievable spatiotemporal resolution for both incoherent and coherent light sources, different types and sizes of beads, and different types and lengths of tethered molecules. Using a bright coherent laser source for illumination and tracking at 6 kHz, we resolve 3 Å steps with a 1 s period for surface-melted beads and 5 Å steps with a 0.5 s period for double-stranded-dsDNA-tethered beads, in good agreement with a model of stochastic bead motion in the magnetic tweezers. We demonstrate how this instrument can be used to monitor the opening and closing of a DNA hairpin on millisecond timescales in real time, together with attendant changes in the hairpin dynamics upon the addition of deoxythymidine triphosphate. Our approach opens up the possibility of observing biological events at submillisecond timescales with subnanometer resolution using camera-based detection.

Magnetic tweezers force calibration for molecules that exhibit conformational switching

High spatial and temporal resolution magnetic tweezers experiments allow for the direct calibration of pulling forces applied to short biomolecules. In one class of experiments, a force is applied to a structured RNA or protein to induce an unfolding transition; when the force is maintained at particular values, the molecule can exhibit conformational switching between the folded and unfolded states or between intermediate states. Here, we analyze the degree to which common force calibration approaches, involving the fitting of model functions to the Allan variance or power spectral density of the bead trajectory, are biased by this conformational switching. We find significant effects in two limits: that of large molecular extension changes between the two states, in which alternative fitting functions must be used, and that of very fast switching kinetics, in which the force calibration cannot be recovered due to the slow diffusion time of the magnetic bead. We use simulations and high-resolution RNA hairpin data to show that most biophysical experiments do not occur in either of these limits.

Salt Effects on the Thermodynamics of a Frameshifting RNA Pseudoknot under Tension

Because of the potential link between -1 programmed ribosomal frameshifting and response of a pseudoknot (PK) RNA to force, a number of single-molecule pulling experiments have been performed on PKs to decipher the mechanism of programmed ribosomal frameshifting. Motivated in part by these experiments, we performed simulations using a coarse-grained model of RNA to describe the response of a PK over a range of mechanical forces (fs) and monovalent salt concentrations (Cs). The coarse-grained simulations quantitatively reproduce the multistep thermal melting observed in experiments, thus validating our model. The free energy changes obtained in simulations are in excellent agreement with experiments. By varying f and C, we calculated the phase diagram that shows a sequence of structural transitions, populating distinct intermediate states. As f and C are changed, the stem-loop tertiary interactions rupture first, followed by unfolding of the 3'-end hairpin (I⇌F). Finally, the 5'-end hairpin unravels, producing an extended state (E⇌I). A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as (logCm)(α) with α=1(0.5) for E⇌I (I⇌F) transition. This relation is used to obtain the preferential ion-RNA interaction coefficient, which can be quantitatively measured in single-molecule experiments, as done previously for DNA hairpins. A by-product of our work is the suggestion that the frameshift efficiency is likely determined by the stability of the 5'-end hairpin that the ribosome first encounters during translation.

Quantifying the ion atmosphere of unfolded, single-stranded nucleic acids using equilibrium dialysis and single-molecule methods

To form secondary structure, nucleic acids (NAs) must overcome electrostatic strand–strand repulsion, which is moderated by the surrounding atmosphere of screening ions. The free energy of NA folding therefore depends on the interactions of this ion atmosphere with both the folded and unfolded states. We quantify such interactions using the preferential ion interaction coefficient or ion excess: the number of ions present near the NA in excess of the bulk concentration. The ion excess of the folded, double-helical state has been extensively studied; however, much less is known about the salt-dependent ion excess of the unfolded, single-stranded state. We measure this quantity using three complementary approaches: a direct approach of Donnan equilibrium dialysis read out by atomic emission spectroscopy and two indirect approaches involving either single-molecule force spectroscopy or existing thermal denaturation data. The results of these three approaches, each involving an independent experimental technique, are in good agreement. Even though the single-stranded NAs are flexible polymers that are expected to adopt random-coil configurations, we find that their ion atmosphere is quantitatively described by rod-like models that neglect large-scale conformational freedom, an effect that we explain in terms of the competition between the relevant structural and electrostatic length scales.

Ranking of Molecular Biomarker Interaction with Targeted DNA Nucleobases via Full Atomistic Molecular Dynamics

DNA-based sensors can detect disease biomarkers, including acetone and ethanol for diabetes and H2S for cardiovascular diseases. Before experimenting on thousands of potential DNA segments, we conduct full atomistic steered molecular dynamics (SMD) simulations to screen the interactions between different DNA sequences with targeted molecules to rank the nucleobase sensing performance. We study and rank the strength of interaction between four single DNA nucleotides (Adenine (A), Guanine (G), Cytosine (C), and Thymine (T)) on single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA) with acetone, ethanol, H2S and HCl. By sampling forward and reverse interaction paths, we compute the free-energy profiles of eight systems for the four targeted molecules. We find that dsDNA react differently than ssDNA to the targeted molecules, requiring more energy to move the molecule close to DNA as indicated by the potential of mean force (PMF). Comparing the PMF values of different systems, we obtain a relative ranking of DNA base for the detection of each molecule. Via the same procedure, we could generate a library of DNA sequences for the detection of a wide range of chemicals. A DNA sensor array built with selected sequences differentiating many disease biomarkers can be used in disease diagnosis and monitoring.

A thin permeable-membrane device for single-molecule manipulation

Single-molecule manipulation instruments have unparalleled abilities to interrogate the structure and elasticity of single biomolecules. Key insights are derived by measuring the system response in varying solution conditions; yet, typical solution control strategies require imposing a direct fluid flow on the measured biomolecule that perturbs the high-sensitivity measurement and/or removes interacting molecules by advection. An alternate approach is to fabricate devices that permit solution changes by diffusion of the introduced species through permeable membranes, rather than by direct solution flow through the sensing region. Prior implementations of permeable-membrane devices are relatively thick, disallowing their use in apparatus that require the simultaneous close approach of external instrumentation from two sides, as occurs in single-molecule manipulation devices like the magnetic tweezer. Here, we describe the construction and use of a thin microfluidic device appropriate for single-molecule studies. We create a flow cell of only ∼500 μm total thickness by sandwiching glass coverslips around a thin plastic gasket and then create permeable walls between laterally separated channels in situ through photo-induced cross-linking of poly(ethylene glycol) diacrylate hydrogels. We show that these membranes permit passage of ions and small molecules (thus permitting solution equilibration in the absence of direct flow), but the membranes block the passage of larger biomolecules (thus retaining precious samples). Finally, we demonstrate the suitability of the device for high-resolution magnetic-tweezer experiments by measuring the salt-dependent folding of a single RNA hairpin under force.

General Differential Contact Identities for Macromolecules

We discuss general Maxwell identities relating a macromolecule's charge, the forces acting at its surface, and the osmotic pressure of the solution in which it sits. The identities are closely related to the contact value relations that hold for certain special geometries, but are more general. In particular, the Maxwell identities can be applied to any macromolecule geometry, and they hold both within and outside of mean-field theory. Examples illustrate that combining the identities with approximate treatments of screening can often return simple, accurate osmotic pressure estimates.

Measuring the differential stoichiometry and energetics of ligand binding to macromolecules by single-molecule force spectroscopy: an extended theory

Many chemical techniques exist for measuring the stoichiometry of ligand binding to a macromolecule; however, these techniques are often specific to certain ligands or require the presumption of specific binding models. Here, we further develop a previously reported, general, thermodynamic method for extracting the change in number of ligands bound to a macromolecule as that macromolecule undergoes a conformational transition driven by mechanical stretching, for example, by magnetic tweezers or optical trapping. We extend the theory of this method to consider systems with many ligands, experiments conducted in different thermodynamic ensembles (e.g., constant-force, constant-extension), and experiments in which the system is not at equilibrium. Further, we show that analysis of the same single-molecule mechanical manipulation data yields a measure of the differential free energy of stabilization due to ligand binding, that is, the free energy contribution by which ligand binding favors one conformation of the macromolecule over another. We interpret an existing data set measuring ion binding to RNA and DNA in terms of this free energy.