A semiflexible polymer model applied to loop formation in DNA hairpins

A statistical mechanical "zipper" model is applied to describe the equilibrium melting of short DNA hairpins with poly(dT) loops ranging from 4 to 12 bases in the loop. The free energy of loop formation is expressed in terms of the persistence length of the chain. This method provides a new measurement of the persistence length of single-stranded DNA, which is found to be approximately 1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of the hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of > or = 7, much larger than the exponent of approximately 1.5-1.8 expected from considerations of loop entropy alone. This result indicates a strong dependence of the excess stability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arising from favorable hydrophobic interactions among the bases in tight loops and which diminish as the loops get larger. Free energy profiles along a generalized reaction coordinate are calculated from the equilibrium zipper model. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a lower enthalpy than the random coil state. The equilibrium model predicts apparent activation energy of approximately -11 kcal/mol for the hairpin closing step, in remarkable agreement with the value obtained from kinetics measurements.     

Looping charged elastic rods: applications to protein-induced DNA loop formation

We analyze looping of thin charged elastic filaments under applied torques and end forces, using the solution of linear elasticity theory equations. In application to DNA, we account for its polyelectrolyte character and charge renormalization, calculating electrostatic energies stored in the loops. We argue that the standard theory of electrostatic persistence is only valid when the loop’s radius of curvature and close-contact distance are much larger than the Debye screening length. We predict that larger twist rates are required to trigger looping of charged rods as compared with neutral ones. We then analyze loop shapes formed on charged filaments of finite length, mimicking DNA looping by proteins with two DNA-binding domains. We find optimal loop shapes at different salt amounts, minimizing the sum of DNA elastic, DNA electrostatic, and protein elastic energies. We implement a simple model where intercharge repulsions do not affect the loop shape directly but can choose the energy-optimized shape from the allowed loop types. At low salt concentrations more open loops are favored due to enhanced repulsion of DNA charges, consistent with the results of computer simulations on formation of DNA loops by lac repressor. Then, we model the precise geometry of DNA binding by the lac tetramer and explore loop shapes, varying the confined DNA length and protein opening angle. The characteristics of complexes obtained, such as the total loop energy, stretching forces required to maintain its shape, and the reduction of electrostatic energy with increment of salt, are in good agreement with the outcomes of more elaborate numerical calculations for lac-repressor-induced DNA looping.     

Probing single-stranded DNA conformational flexibility using fluorescence spectroscopy

Single-stranded DNA (ssDNA) is an essential intermediate in various DNA metabolic processes and interacts with a large number of proteins. Due to its flexibility, the conformations of ssDNA in solution can only be described using statistical approaches, such as flexibly jointed or worm-like chain models. However, there is limited data available to assess such models quantitatively, especially for describing the flexibility of short ssDNA and RNA. To address this issue, we performed FRET studies of a series of oligodeoxythymidylates, (dT)N, over a wide range of salt concentrations and chain lengths (10 < or = N < or = 70 nucleotides), which provide systematic constraints for testing theoretical models. Unlike in mechanical studies where available ssDNA conformations are averaged out during the time it takes to perform measurements, fluorescence lifetimes may act here as an internal clock that influences fluorescence signals depending on how fast the ssDNA conformations fluctuate. A reasonably good agreement could be obtained between our data and the worm-like chain model provided that limited relaxations of the ssDNA conformations occur within the fluorescence lifetime of the donor. The persistence length thus estimated ranges from 1.5 nm in 2 M NaCl to 3 nm in 25 mM NaCl.     

T7 DNA helicase: a molecular motor that processively and unidirectionally translocates along single-stranded DNA

DNA helicases are molecular motors that use the energy from NTP hydrolysis to drive the process of duplex DNA strand separation. Here, we measure the translocation and energy coupling efficiency of a replicative DNA helicase from bacteriophage T7 that is a member of a class of helicases that assembles into ring-shaped hexamers. Presteady state kinetics of DNA-stimulated dTTP hydrolysis activity of T7 helicase were measured using a real time assay as a function of ssDNA length, which provided evidence for unidirectional translocation of T7 helicase along ssDNA. Global fitting of the kinetic data provided an average translocation rate of 132 bases per second per hexamer at 18 degrees C. While translocating along ssDNA, T7 helicase hydrolyzes dTTP at a rate of 49 dTTP per second per hexamer, which indicates that the energy from hydrolysis of one dTTP drives unidirectional movement of T7 helicase along two to three bases of ssDNA. One of the features that distinguishes this ring helicase is its processivity, which was determined to be 0.99996, which indicated that T7 helicase travels on an average about 75kb of ssDNA before dissociating. We propose that the ability of T7 helicase to translocate unidirectionally along ssDNA in an efficient manner plays a crucial role in DNA unwinding.     

Radius of gyration of plasmid DNA isoforms from static light scattering

Despite the extensive interest in applications of plasmid DNA, there have been few direct measurements of the root mean square radius of gyration, R_G, of different plasmid isoforms over a broad range of plasmid size. Static light scattering data were obtained using supercoiled, open‐circular, and linear isoforms of 5.76, 9.80, and 16.8 kbp plasmids. The results from this study extend the range of R_G values available in the literature to plasmid sizes typically used for gene therapy and DNA vaccines. The experimental data were compared with available theoretical expressions based on the worm‐like chain model, with the best‐fit value of the apparent persistence length for both the linear and open‐circular isoforms being statistically identical at 46 nm. A new expression was developed for the radius of gyration of the supercoiled plasmid based on a model for linear DNA using an effective contour length that is equal to a fraction of the total contour length. These results should facilitate the development of micro/nano‐fluidic devices for DNA manipulation and size‐based separation processes for plasmid DNA purification. Biotechnol. Bioeng. 2010;107: 134–142. © 2010 Wiley Periodicals, Inc.     

Single-strand stacking free energy from DNA beacon kinetics

DNA beacons are short single-stranded chains which can form closed hairpin shapes through complementary base pairing at their ends. Contrary to the common polymer theory assumption that only their loop length matters, experiments show that their closing kinetics depend on the loop composition. We have modeled the closing kinetics and in so doing have obtained stacking enthalpies and entropies for single-stranded nucleic acids. The resulting change of persistence length with temperature effects the dynamics. With a Monte Carlo study, we answer another polymer question of how the closing time scales with chain length, finding tau approximately N(2.44+/-0.02). There is a significant crossover for shorter chains, bringing the effective exponent into good agreement with experiment.     

Ultrasonic wave spectroscopy study of sugar oligomers and polysaccharides in aqueous solutions: the hydration length concept

The determination of apparent persistence length and radius of gyration of maltodextrins in water is achievable through high-resolution ultrasonic spectroscopy measurements. Classical hydration number for those carbohydrates is characteristic of an apparent persistence degree of polymerisation of the polymer. A force-field based molecular modeling of a 10DP malto-oligomer allows measurement of the corresponding length for the lowest energetic conformation in solution. A good agreement between the apparent radii of gyration determined by this technique and the freely rotating polymer chain model is found with radii of gyration calculated from the intrinsic viscosity.     

A Monte-Carlo estimate of DNA loop formation

The ends of rather short double-helical DNA segments (approximately two persistence lengths) can be enzymatically joined to form closed circles. Such covalent closure into circles is a measure of the likelihood of the two ends of the DNA coming into close contact. There is a length of DNA for which loop formation is most likely to occur. We have determined the chain-length dependence of loop formation for stiff chains using computer-generated chains of cylinders. The distribution from which the values for the angles between cylinders were chosen relates the chain parameters to a given chain persistence. Our results are compared with those of other theories, including a statistical wormlike chain model, and with the experimental measurements for ring closure of DNA restriction fragments.     

Modulating the chemo-mechanical response of structured DNA assemblies through binding molecules

Recent advances in DNA nanotechnology led the fabrication and utilization of various DNA assemblies, but the development of a method to control their global shapes and mechanical flexibilities with high efficiency and repeatability is one of the remaining challenges for the realization of the molecular machines with on-demand functionalities. DNA-binding molecules with intercalation and groove binding modes are known to induce the perturbation on the geometrical and mechanical characteristics of DNA at the strand level, which might be effective in structured DNA assemblies as well. Here, we demonstrate that the chemo-mechanical response of DNA strands with binding ligands can change the global shape and stiffness of DNA origami nanostructures, thereby enabling the systematic modulation of them by selecting a proper ligand and its concentration. Multiple DNA-binding drugs and fluorophores were applied to straight and curved DNA origami bundles, which demonstrated a fast, recoverable, and controllable alteration of the bending persistence length and the radius of curvature of DNA nanostructures. This chemo-mechanical modulation of DNA nanostructures would provide a powerful tool for reconfigurable and dynamic actuation of DNA machineries.     

Determination of the elastic properties of short ssDNA molecules by mechanically folding and unfolding DNA hairpins

The characterization of elastic properties of biopolymers is crucial to understand many molecular reactions determined by conformational bending fluctuations of the polymer. Direct measurement of such elastic properties using single‐molecule methods is usually hindered by the intrinsic tendency of such biopolymers to form high‐order molecular structures. For example, single‐stranded deoxyribonucleic acids (ssDNA) tend to form secondary structures such as local double helices that prevent the direct measurement of the ideal elastic response of the ssDNA. In this work, we show how to extract the ideal elastic response in the entropic regime of short ssDNA molecules by mechanically pulling two‐state DNA hairpins of different contour lengths. This is achieved by measuring the force dependence of the molecular extension and stiffness on mechanically folding and unfolding the DNA hairpin. Both quantities are fit to the worm‐like chain elastic model giving values for the persistence length and the interphosphate distance. This method can be used to unravel the elastic properties of short ssDNA and RNA sequences and, more generally, any biopolymer that can exhibit a cooperative two‐state transition between mechanically folded and unfolded states (such as proteins). © 2014 Wiley Periodicals, Inc. Biopolymers 101: 1193–1199, 2014.     

Coarse-grained modeling reveals the impact of supercoiling and loop length in DNA looping kinetics

Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model’s ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.     

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. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 1–12, 2014.     

Thermodynamics of DNA packaging inside a viral capsid: the role of DNA intrinsic thickness

We characterize the equilibrium thermodynamics of a thick polymer confined in a spherical region of space. This is used to gain insight into the DNA packaging process. The experimental reference system for the present study is the recent characterization of the loading process of the genome inside the phi29 bacteriophage capsid. Our emphasis is on the modelling of double-stranded DNA as a flexible thick polymer (tube) instead of a beads-and-springs chain. By using finite-size scaling to extrapolate our results to genome lengths appropriate for phi29, we find that the thickness-induced force may account for up to half the one measured experimentally at high packing densities. An analogous agreement is found for the total work that has to be spent in the packaging process. Remarkably, such agreement can be obtained in the absence of any tunable parameters and is a mere consequence of the DNA thickness. Furthermore, we provide a quantitative estimate of how the persistence length of a polymer depends on its thickness. The expression accounts for the significant difference in the persistence lengths of single and double-stranded DNA (again with the sole input of their respective sections and natural nucleotide/base-pair spacing).     

Computer simulation of hydrodynamic properties of semiflexible macromolecules: randomly broken chains, wormlike chains, and analysis of properties of DNA

The translational and rotational diffusion coefficients and the intrinsic viscosity of semiflexible, randomly broken, and wormlike chains have been obtained by Monte Carlo simulation in the context of the rigid-body treatment. Both approximate and rigorous rigid-body hydrodynamics are used, so that the error introduced by the approximate methods can be evaluated. A randomly broken chain and a wormlike chain having the same contour length and persistence length have the same radius of gyration but different values for any of the hydrodynamic properties. The two types of chains are compared in this regard. Considering that the cross section of the chain is represented by a cylinder better than by a string of spheres, we devise a cylindrical correction to be applied to the results simulated for chains of beads. Application is made to the analysis of experimental data for the translational and rotational coefficients of DNA fragments with up to 10(3) base pairs, obtaining the persistence length for each model. The values for the wormlike chain agree well with model-independent values obtained from radii of gyration and with other literature data at varying ionic strength. The randomly broken chain is equally able to reproduce the experimental length dependence of the properties, but the resulting persistence length may be too high.     

Persistence length of titin from rabbit skeletal muscles measured with scattering and microrheology techniques

The persistence length of titin from rabbit skeletal muscles was measured using a combination of static and dynamic light scattering, and neutron small angle scattering. Values of persistence length in the range 9-16 nm were found for titin-II, which corresponds to mainly physiologically inelastic A-band part of the protein, and for a proteolytic fragment with 100-nm contour length from the physiologically elastic I-band part. The ratio of the hydrodynamic radius to the static radius of gyration indicates that the proteins obey Gaussian statistics typical of a flexible polymer in a -solvent. Furthermore, measurements of the flexibility as a function of temperature demonstrate that titin-II and the I-band titin fragment experience a similar denaturation process; unfolding begins at 318 K and proceeds in two stages: an initial gradual 50% change in persistence length is followed by a sharp unwinding transition at 338 K. Complementary microrheology (video particle tracking) measurements indicate that the viscoelasticity in dilute solution behaves according to the Flory/Fox model, providing a value of the radius of gyration for titin-II (63 +/- 1 nm) in agreement with static light scattering and small angle neutron scattering results.