Probing the Elasticity of DNA on Short Length Scales by Modeling Supercoiling under Tension

The wormlike-chain (WLC) model is widely used to describe the energetics of DNA bending. Motivated by recent experiments, alternative, so-called subelastic chain models were proposed that predict a lower elastic energy of highly bent DNA conformations. Until now, no unambiguous verification of these models has been obtained because probing the elasticity of DNA on short length scales remains challenging. Here we investigate the limits of the WLC model using coarse-grained Monte Carlo simulations to model the supercoiling of linear DNA molecules under tension. At a critical supercoiling density, the DNA extension decreases abruptly due to the sudden formation of a plectonemic structure. This buckling transition is caused by the large energy required to form the tightly bent end-loop of the plectoneme and should therefore provide a sensitive benchmark for model evaluation. Although simulations based on the WLC energetics could quantitatively reproduce the buckling measured in magnetic tweezers experiments, the buckling almost disappears for the tested linear subelastic chain model. Thus, our data support the validity of a harmonic bending potential even for small bending radii down to 3.5 nm.     

Analysis of the intrinsic bend in the M13 origin of replication by atomic force microscopy

Atomic force microscopy (AFM) has been used to image a 471-bp bent DNA restriction fragment derived from the M13 origin of replication in plasmid LITMUS 28, and a 476-bp normal, unbent fragment from plasmid pUC19. The most probable angle of curvature of the 471-bp DNA fragment is 40-50 degrees, in reasonably good agreement with the bend angle determined by transient electric birefringence, 38 degrees +/- 7 degrees. The normal 476-bp DNA fragment exhibited a Gaussian distribution of bend angles centered at 0 degrees, indicating that this fragment does not contain an intrinsic bend. The persistence length, P, was estimated to be 60 +/- 8 and 62 +/- 8 nm for the 471- and 476-bp fragments, respectively, from the observed mean-square end-to-end distances in the AFM images. Since the P-values of the normal and bent fragments are close to each other, the overall flexibility of DNA fragments of this size is only marginally affected by the presence of a stable bend. The close agreement of AFM and transient electric birefringence results validates the suitability of both methods for characterizing DNA bending and flexibility.     

Probing a label-free local bend in DNA by single molecule tethered particle motion

Being capable of characterizing DNA local bending is essential to understand thoroughly many biological processes because they involve a local bending of the double helix axis, either intrinsic to the sequence or induced by the binding of proteins. Developing a method to measure DNA bend angles that does not perturb the conformation of the DNA itself or the DNA-protein complex is a challenging task. Here, we propose a joint theory-experiment high-throughput approach to rigorously measure such bend angles using the Tethered Particle Motion (TPM) technique. By carefully modeling the TPM geometry, we propose a simple formula based on a kinked Worm-Like Chain model to extract the bend angle from TPM measurements. Using constructs made of 575 base-pair DNAs with in-phase assemblies of one to seven 6A-tracts, we find that the sequence CA₆CGG induces a bend angle of 19° ± 4°. Our method is successfully compared to more theoretically complex or experimentally invasive ones such as cyclization, NMR, FRET or AFM. We further apply our procedure to TPM measurements from the literature and demonstrate that the angles of bends induced by proteins, such as Integration Host Factor (IHF) can be reliably evaluated as well.     

Contour and persistence length of Corynebacterium diphtheriae pili by atomic force microscopy

Many bacteria are characterized by nanoscale ultrastructures, for example S-layers, flagella, fimbriae, or pili. The last two are especially important for attachment to different abiotic and biotic surfaces and for host-pathogen interactions. In this study, we investigated the geometric and elastic properties of pili of different Corynebacterium diphtheriae strains by atomic force microscopy (AFM). We performed quantitative contour-length analysis of bacterial pili and found that the visible contour length of the pili can be described by a log-normal distribution. Our data revealed significant strain-specific variations in the mean visible contour length of the pili, ranging from 260 to 1,590 nm. To estimate their full contour length, which is not directly accessible from the AFM images, we developed a simple correction model. Using this model, we determined the mean full contour length as 510-2,060 nm. To obtain the persistence length we used two different methods of analysis, one based on the end-to-end distance of the pili and one based on the bending angles of short segments. In comparison, the bending angle analysis proved to be more precise and resulted in persistence lengths in the narrow range of 220-280 nm, with no significant strain-specific variations. This is small compared with some other bacterial polymers, for example type IV pili, F-pili, or flagella.     

The Snakelike Chain Character of Unstructured RNA

In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod “wormlike chain” (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a “snakelike chain,” characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation.     

Anisotropic flexibility of DNA depends on the base sequence. Conformation calculations of double-stranded tetranucleotides AAAA:TTTT, (AATT)2, (TTAA)2, GGGG:CCCC, (GGCC)2, (CCGG)2

The bending flexibility of six tetramers was studied in an assumption that they were extended in the both directions by regular double helices. The bends of B-DNA in different directions were considered. The stiffness of the B-DNA double helix when bent into the both grooves proved to be less pronounced than in the perpendicular direction by the order of magnitude. Such an anisotropy is a feature of the sugar-phosphate backbone structure. The calculated fluctuations of the DNA bending along the dyad axis, 5-7 degrees, are in agreement with the experimental value of DNA persistence length. Anisotropy of the double helix is sequence-dependent: most easily bent into the minor groove are the tetramers with purine-pyrimidine dimer (RY) in the middle. In contrast, YR dinucleotides prefer bending into the major groove, moreover, they have an equilibrium bend of 6-12 degrees into this groove. The above inequality is caused by the stacking interaction of the bases. The bend in the central dimers is distributed to some extent between the adjacent links, though the main fraction of the bend remains within the central link. Variation of the sugar-phosphate geometry in the bent helix is unessential, so that DNA remains within the limits of the B-family of forms: namely, when the helical axis is bent by 20 degrees the backbone dihedral angles vary by no more than 15 degrees. The obtained results are in accord with the X-ray structure of B-DNA dodecamer; they further substantiate our earlier model of DNA wrapping in the nucleosome by means of "mini-kinks" separated by a half-pitch of the double helix, i.e. by 5-6 b. p. Sequence-dependent anisotropy of DNA presumably dictates the three-dimensional structure of DNA in solution as well. We have found that nonrandom allocation of YR dimers leads to the systematic bends in the equilibrium structure of certain DNA fragments. To the four "Calladine rules" two more can be added: the minor-groove steric clash of purines in the YR sequences are avoided by: (1) bending of the helix into the major groove; (2) increasing the distance between the base pairs (stretching the double helix).     

Sequence-dependent anisotropic flexibility of B-DNA. A conformational study

Bending flexibility of the six tetrameric duplexes was investigated d(AAAA):d(TTTT), d(AATT)2, d(TTAA)2, d(GGGG):d(CCCC), d(GGCC)2 and d(CCGG)2,. The tetramers were extended in the both directions by regular double helices. The stiffness of the B-DNA double helix when bent into the both grooves proved to be less than that in the perpendicular direction by an order of magnitude. Such an anisotropy is a property of the sugar-phosphate backbone structure. The calculated fluctuations of the DNA bending along the dyad axis, 5-7 degree, are in agreement with experimental value of the DNA persistence length. Anisotropy of the double helix is sequence-dependent: most easily bent into the minor groove are the tetramers with purine-pyrimidine dimer (RY) in the middle. In contrast, YR dinucleotides prefer bending into the major groove. Moreover, they have an equilibrium bend of 6-12 degree into this groove. The above inequality is caused by stacking interaction of the bases. The bend in the central dimer is distributed to some extent between the adjacent links, though the main fraction of the bend remains within the central link. Variation of the sugar-phosphate geometry in the bent helix is inessential, so that DNA remains within the B-family of forms: namely, when the helical axis is bent by 20 degree. the backbone dihedral angles vary by no more than 15 degree. The obtained results are in accord with x-ray structure of the B-DNA dodecamer; they further substantiate our early model of DNA wrapping in the nucleosome by means of "mini-kinks" separated by a half-pitch of the double helix, i.e. by 5-6 b.p. Sequence-dependent anisotropy of DNA presumably dictates the three-dimensional structure of DNA in solution as well. We have found that nonrandom allocation of YR dimers leads to the systematic bends in equilibrium structure of certain DNA fragments.     

The Snakelike Chain Character of Unstructured RNA

In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod “wormlike chain” (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a “snakelike chain,” characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation.     

Sequence-Dependent Anisotropic Flexibility of B-DNA A Conformational Study

Abstract

Bending flexibility of the six tetrameric duplexes was investigated d(AAAA):d(TTTT), d(AATT)₂, d(TTAA) ₂, d(GGGG):d(CCCC), d(GGCC) ₂ and d(CCGG) ₂. The tetramers were extended in the both directions by regular double helices. The stiffness of the B-DNA double helix when bent into the both grooves proved to be less than that in the perpendicular direction by an order of magnitude. Such an anisotropy is a property of the sugar-phosphate backbone structure. The calculated fluctuations of the DNA bending along the dyad axis, 5–7°, are in agreement with experimental value of the DNA persistence length.

Anisotropy of the double helix is sequence-dependent: most easily bent into the minor groove are the tetramers with purine-pyrimidine dimer (RY) in the middle. In contrast, YR dinucleotides prefer bending into the major groove. Moreover, they have an equilibrium bend of 6–12° into this groove. The above inequality is caused by stacking interaction of the bases.

The bend in the central dimer is distributed to some extent between the adjacent links, though the main fraction of the bend remains within the central link. Variation of the sugar-phosphate geometry in the bent helix is inessential, so that DNA remains within the B-family of forms: namely, when the helical axis is bent by 20°, the backbone dihedral angles vary by no more than 15°.

The obtained results are in accord with x-ray structure of the B-DNA dodecamer; they further substantiate our early model of DNA wrapping in the nucleosome by means of “mini-kinks” separated by a half-pitch of the double helix, i.e. by 5–6 b.p. Sequence-dependent anisotropy of DNA presumably dictates the three-dimentional structure of DNA in solution as well. We have found that nonrandom allocation of YR dimers leads to the systematic bends in equilibrium structure of certain DNA fragments.     

Helical phasing between DNA bends and the determination of bend direction.

The presence and location of bends in DNA can be inferred from the anomalous mobility of DNA fragments or protein-DNA complexes during electrophoresis in polyacrylamide gels. Direction of bending is not so easily determined. We show here that a protein-induced bend, when linked to a protein-independent DNA bend by a segment of variable length, exhibits an electrophoretic mobility that varies in a sinusoidal manner with the length of the linker. Mobility minima occur once for each addition to the linker of one helical turn of DNA. Since minima should occur when two bends reinforce one another, the direction of one bend relative to the other can be determined from the distances between the two centers of bending at which minima occur. Our results strongly support the idea that the A5-6 tracts in kinetoplast DNA bend towards the minor groove while the bend at the recombination site of the gamma delta resolvase (binding site I of the gamma delta res site) bends towards the major groove.     

Electric dichroism and bending amplitudes of DNA fragments according to a simple orientation function for weakly bent rods

The linear dichroism is calculated for DNA fragments in their thermal bending equilibrium. These calculations are given for relatively short fragments, where bent molecules can be described by an arc model. Using the measured value of 350 A for the persistence length, the limit dichroism (corresponding to complete alignment) decreases due to thermal bending, e.g., for a fragment with 100 base pairs to 80% of the value expected for straight molecules. Thermal bending should lead to a strong continuous decrease of the dichroism with increasing chain length, which is not observed, however, in electric dichroism experiments due to electric stretching. The influence of the electric field on the bending equilibrium is described by a contribution to the bending energy, which is calculated from the movement of charge equivalents against the potential gradient upon bending. The charge equivalents, which are assigned to the helix ends, are derived from the dipole moments causing the stationary degree of orientation. By this procedure the energy term inducing DNA stretching is given for induced, permanent, and saturating induced dipole models without introduction of any additional parameter. The stationary dichroism at a given electric field strength is then calculated according to an arc model by integration over all angles of orientation of helix axes or chords with respect to the field vector, and at each of these angles the contribution to the dichroism is calculated by integration over all helices with different degrees of bending. Orientation functions obtained by this procedure are fitted to dichroism data measured for various restriction fragments. Optimal fits are found for an induced dipole model with saturation of the polarizability. The difference between orientation functions with and without electric stretching is used to evaluate dichroism bending amplitudes. Both chain length and field strength dependence of bending amplitudes are consistent with experimental amplitudes derived from the dichroism decay in low salt buffers containing multivalent ions like Mg2+, spermine, or [CoNH3)6]3+. Bending amplitudes can be used to evaluate the persistence length from electrooptical data obtained for a single DNA restriction fragment. Bending and stretching effects are considerable already at relatively low chain length, and thus should not be neglected in any quantitative evaluation of experimental data.     

Atomic force microscopy imaging of double stranded DNA and RNA.

A procedure for imaging long DNA and double stranded RNA (dsRNA) molecules using Atomic Force Microscopy (AFM) is described. Stable binding of double stranded DNA molecules to the flat mica surface is achieved by chemical modification of freshly cleaved mica under mild conditions with 3-aminopropyltriethoxy silane. We have obtained striking images of intact lambda DNA, Hind III restriction fragments of lambda DNA and dsRNA from reovirus. These images are stable under repeated scanning and measured contour lengths are accurate to within a few percent. This procedure leads to strong DNA attachment, allowing imaging under water. The widths of the DNA images lie in the range of 20 to 80nm for data obtained in air with commercially available probes. The work demonstrates that AFM is now a routine tool for simple measurements such as a length distribution. Improvement of substrate and sample preparation methods are needed to achieve yet higher resolution.     

Direct measurement of DNA bending by type IIA topoisomerases: implications for non-equilibrium topology simplification

Type IIA topoisomerases modify DNA topology by passing one segment of duplex DNA (transfer or T–segment) through a transient double-strand break in a second segment of DNA (gate or G–segment) in an ATP-dependent reaction. Type IIA topoisomerases decatenate, unknot and relax supercoiled DNA to levels below equilibrium, resulting in global topology simplification. The mechanism underlying this non-equilibrium topology simplification remains speculative. The bend angle model postulates that non-equilibrium topology simplification scales with the bend angle imposed on the G–segment DNA by the binding of a type IIA topoisomerase. To test this bend angle model, we used atomic force microscopy and single-molecule Förster resonance energy transfer to measure the extent of bending imposed on DNA by three type IIA topoisomerases that span the range of topology simplification activity. We found that Escherichia coli topoisomerase IV, yeast topoisomerase II and human topoisomerase IIα each bend DNA to a similar degree. These data suggest that DNA bending is not the sole determinant of non-equilibrium topology simplification. Rather, they suggest a fundamental and conserved role for DNA bending in the enzymatic cycle of type IIA topoisomerases.     

Atomic Force Microscopy Imaging of Double Stranded DNA and RNA

Abstract

A procedure for imaging long DNA and double stranded RNA (dsRNA) molecules using Atomic Force Microscopy (AFM) is described. Stable binding of double stranded DNA molecules to the flat mica surface is achieved by chemical modification of freshly cleaved mica under mild conditions with 3-aminopropyltriethoxy silane. We have obtained striking images of intact lambda DNA, Hind III restriction fragments of lambda DNA and dsRNA from reovirus. These images are stable under repeated scanning and measured contour lengths are accurate to within a few percent. This procedure leads to strong DNA attachment, allowing imaging under water. The widths of the DNA images lie in the range of 20 to 80nm for data obtained in air with commercially available probes. The work demonstrates that AFM is now a routine tool for simple measurements such as a length distribution. Improvement of substrate and sample preparation methods are needed to achieve yet higher resolution.     

Stretching short DNAs in electrolytes

This paper is aimed at a combined theoretical and numerical study of the force-extension relation of a short DNA molecule stretched in an electrolyte. A theoretical formula based on a recent discrete wormlike chain (WLC) model of Kierfeld et al. (Eur Phys. J. E, Vol. 14, pp.17-34, 2004) and the classical OSF mean-field theory on electrostatic stiffening of a charged polymer is numerically verified by a set of Brownian dynamics simulations based on a generalized bead-rod (GBR) model incorporating long-ranged electrostatic interactions via the Debye-Hueckel potential (DH). The analysis indicates that the stretching of a short DNA can be well described as a WLC with a constant effective persistent length. This contrasts the behavior of long DNA chains that are known to exhibit variable persistent lengths depending on the ion concentration levels and force magnitudes.