Effect of Genomic Long-Range Correlations on DNA Persistence Length: From Theory to Single Molecule Experiments

Approaches for Determining DNA Persistence Length Using Atomic Force Microscopy

Atomic force microscopy (AFM) is widely used to image and study biological molecules. As an example, we have utilized AFM to investigate how the mechanical properties of DNA polymers depend on electrostatics and the strength of DNA base stacking by studying double-stranded DNA molecules incorporating several different neutral and charged base modifications. Here we describe ten complementary approaches for determining DNA persistence length by AFM imaging. The combination of different approaches provides increased confidence and statistical reliability over existing methods utilizing only a single approach.

Environment-Dependent Stability and Mechanical Properties of DNA Origami Six-Helix Bundles with Different Crossover Spacings

The internal design of DNA nanostructures defines how they behave in different environmental conditions, such as endonuclease-rich or low-Mg²⁺ solutions. Notably, the inter-helical crossovers that form the core of such DNA objects have a major impact on their mechanical properties and stability. Importantly, crossover design can be used to optimize DNA nanostructures for target applications, especially when developing them for biomedical environments. To elucidate this, two otherwise identical DNA origami designs are presented that have a different number of staple crossovers between neighboring helices, spaced at 42- and 21- basepair (bp) intervals, respectively. The behavior of these structures is then compared in various buffer conditions, as well as when they are exposed to enzymatic digestion by DNase I. The results show that an increased number of crossovers significantly improves the nuclease resistance of the DNA origami by making it less accessible to digestion enzymes but simultaneously lowers its stability under Mg²⁺ -free conditions by reducing the malleability of the structures. Therefore, these results represent an important step toward rational, application-specific DNA nanostructure design.

Semiflexible Polymers Interacting With Planar Surfaces: Weak versus Strong Adsorption

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness κ as well as the strength of the adsorption potential ϵwall are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter η) and the mean square gyration radius parallel, 〈Rg2〉||, and perpendicular, 〈Rg2〉⊥, to the wall. While for strongly adsorbed chains EV has negligible effect on f and η, we find that 〈Rg2〉|| is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that f,η, and 〈Rg2〉⊥ converge to their asymptotic values with 1/N corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.

Linear Dimensions of Adsorbed Semiflexible Polymers: What Can Be Learned about Their Persistence Length?

Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length L, chain stiffness, κ, and the strength of the adsorption potential over a wide range. Molecular dynamics simulations show that partially adsorbed chains (with "tails," surface attached "trains," and "loops") are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value (ℓ_{p}) to the enhanced value in two dimensions (2ℓ_{p}) is analyzed, and excluded volume effects are identified for L≫ℓ_{p}. Consequences for the interpretation of experiments are suggested. We verify the prediction that the adsorption threshold scales as ℓ_{p}^{-1/3}.

Approaches for Determining DNA Persistence Length Using Atomic Force Microscopy

Atomic force microscopy (AFM) is widely used to image and study biological molecules. As an example, we have utilized AFM to investigate how the mechanical properties of DNA polymers depend on electrostatics and the strength of DNA base stacking by studying double-stranded DNA molecules incorporating several different neutral and charged base modifications. Here, we describe ten complementary approaches for determining DNA persistence length by AFM imaging. The combination of different approaches provides increased confidence and statistical reliability over existing methods utilizing only a single approach.

Semiflexible macromolecules in quasi-one-dimensional confinement: Discrete versus continuous bond angles

The conformations of semiflexible polymers in two dimensions confined in a strip of width D are studied by computer simulations, investigating two different models for the mechanism by which chain stiffness is realized. One model (studied by molecular dynamics) is a bead-spring model in the continuum, where stiffness is controlled by a bond angle potential allowing for arbitrary bond angles. The other model (studied by Monte Carlo) is a self-avoiding walk chain on the square lattice, where only discrete bond angles (0° and ±90°) are possible, and the bond angle potential then controls the density of kinks along the chain contour. The first model is a crude description of DNA-like biopolymers, while the second model (roughly) describes synthetic polymers like alkane chains. It is first demonstrated that in the bulk the crossover from rods to self-avoiding walks for both models is very similar, when one studies average chain linear dimensions, transverse fluctuations, etc., despite their differences in local conformations. However, in quasi-one-dimensional confinement two significant differences between both models occur: (i) The persistence length (extracted from the average cosine of the bond angle) gets renormalized for the lattice model when D gets less than the bulk persistence length, while in the continuum model it stays unchanged. (ii) The monomer density near the repulsive walls for semiflexible polymers is compatible with a power law predicted for the Kratky-Porod model in the case of the bead-spring model, while for the lattice case it tends to a nonzero constant across the strip. However, for the density of chain ends, such a constant behavior seems to occur for both models, unlike the power law observed for flexible polymers. In the regime where the bulk persistence length ℓp is comparable to D, hairpin conformations are detected, and the chain linear dimensions are discussed in terms of a crossover from the Daoud/De Gennes "string of blobs"-picture to the flexible rod picture when D decreases and/or the chain stiffness increases. Introducing a suitable further coarse-graining of the chain contours of the continuum model, direct estimates for the deflection length and its distribution could be obtained.

The persistence length of adsorbed dendronized polymers

The persistence length of cationic dendronized polymers adsorbed onto oppositely charged substrates was studied by atomic force microscopy (AFM) and quantitative image analysis. One can find that a decrease in the ionic strength leads to an increase of the persistence length, but the nature of the substrate and of the generation of the side dendrons influence the persistence length substantially. The strongest effects as the ionic strength is being changed are observed for the fourth generation polymer adsorbed on mica, which is a hydrophilic and highly charged substrate. However, the observed dependence on the ionic strength is much weaker than the one predicted by the Odijk, Skolnik, and Fixman (OSF) theory for semi-flexible chains. Low-generation polymers show a variation with the ionic strength that resembles the one observed for simple and flexible polyelectrolytes in solution. For high-generation polymers, this dependence is weaker. Similar dependencies are found for silica and gold substrates. The observed behavior is probably caused by different extents of screening of the charged groups, which is modified by the polymer generation, and to a lesser extent, the nature of the substrate. For highly ordered pyrolytic graphite (HOPG), which is a hydrophobic and weakly charged substrate, the electrostatic contribution to the persistence length is much smaller. In the latter case, we suspect that specific interactions between the polymer and the substrate also play an important role.

Mechanical properties of base-modified DNA are not strictly determined by base stacking or electrostatic interactions

This work probes the mystery of what balance of forces creates the extraordinary mechanical stiffness of DNA to bending and twisting. Here we explore the relationship between base stacking, functional group occupancy of the DNA minor and major grooves, and DNA mechanical properties. We study double-helical DNA molecules substituting either inosine for guanosine or 2,6-diaminopurine for adenine. These DNA variants, respectively, remove or add an amino group from the DNA minor groove, with corresponding changes in hydrogen-bonding and base stacking energy. Using the techniques of ligase-catalyzed cyclization kinetics, atomic force microscopy, and force spectroscopy with optical tweezers, we show that these DNA variants have bending persistence lengths within the range of values reported for sequence-dependent variation of the natural DNA bases. Comparison with seven additional DNA variants that modify the DNA major groove reveals that DNA bending stiffness is not correlated with base stacking energy or groove occupancy. Data from circular dichroism spectroscopy indicate that base analog substitution can alter DNA helical geometry, suggesting a complex relationship among base stacking, groove occupancy, helical structure, and DNA bend stiffness.

Symmetric curvature descriptors for label-free analysis of DNA

High-resolution microscopy techniques such as electron microscopy, scanning tunnelling microscopy and atomic force microscopy represent well-established, powerful tools for the structural characterization of adsorbed DNA molecules at the nanoscale. Notably, the analysis of DNA contours allows mapping intrinsic curvature and flexibility along the molecular backbone. This is particularly suited to address the impact of the base-pairs sequence on the local conformation of the strands and plays a pivotal role for investigations relating the inherent DNA shape and flexibility to other functional properties. Here, we introduce novel chain descriptors aimed to characterize the local intrinsic curvature and flexibility of adsorbed DNA molecules with unknown orientation. They consist of stochastic functions that couple the curvatures of two nanosized segments, symmetrically placed on the DNA contour. We show that the fine mapping of the ensemble-averaged functions along the molecular backbone generates characteristic patterns of variation that highlight all pairs of tracts with large intrinsic curvature or enhanced flexibility. We demonstrate the practical applicability of the method for DNA chains imaged by atomic force microscopy. Our approach paves the way for the label-free comparative analysis of duplexes, aimed to detect nanoscale conformational changes of physical or biological relevance in large sample numbers.

DNA Bending through Roll Angles Is Independent of Adjacent Base Pairs

We have studied DNA bending for a wide range of DNA sequences by two-dimensional adaptive umbrella sampling simulations on adjacent roll angles. Calculated free energy surfaces are largely additive and can be well approximated by the sum of the one-dimensional free energy surfaces. Cooperativity between adjacent roll angles was found to be negligible: less than 1.0 kcal/mol and a small fraction of the overall bending energy. Our calculations validate the assumptions underlying many popular coarse-grained models for DNA bending, and demonstrate their theoretical validity for investigating DNA bending.

Structure and stability of the complex formed by oligonucleotides

Polycations and cationic lipids have been widely used as non-viral vectors for the delivery of plasmid DNA, siRNA and anti-sense oligonucleotides. To demonstrate that one polycation can form a complex with several types of DNA, we conducted a comparative study on the complexation of poly(L-lysine) (PLL) with 2000 bp salmon testes DNA (dsDNA), 21 bp double-stranded oligonucleotides (ds-oligo), and 21 nt single-stranded oligonucleotides (ss-oligo) in PBS buffer. The complexes are prepared by a titration method and the process is monitored by laser light scattering. It was found that in most cases, ss-oligo and ds-oligo form complexes with higher molecular weights than the complex formed by dsDNA at the same +/- ratio immediately after mixing. More importantly, the complexes formed by oligonucleotides are not stable, the scattered intensity gradually decreases to the level of the solvent in weeks. Atomic force microscopy measurements also indicate that the freshly prepared complex is subject to environmental changes and could dissociate very quickly. The behaviour of oligonucleotides cannot be predicted by the classical polyelectrolyte theories.

Label-free, atomic force microscopy-based mapping of DNA intrinsic curvature for the nanoscale comparative analysis of bent duplexes

We propose a method for the characterization of the local intrinsic curvature of adsorbed DNA molecules. It relies on a novel statistical chain descriptor, namely the ensemble averaged product of curvatures for two nanosized segments, symmetrically placed on the contour of atomic force microscopy imaged chains. We demonstrate by theoretical arguments and experimental investigation of representative samples that the fine mapping of the average product along the molecular backbone generates a characteristic pattern of variation that effectively highlights all pairs of DNA tracts with large intrinsic curvature. The centrosymmetric character of the chain descriptor enables targetting strands with unknown orientation. This overcomes a remarkable limitation of the current experimental strategies that estimate curvature maps solely from the trajectories of end-labeled molecules or palindromes. As a consequence our approach paves the way for a reliable, unbiased, label-free comparative analysis of bent duplexes, aimed to detect local conformational changes of physical or biological relevance in large sample numbers. Notably, such an assay is virtually inaccessible to the automated intrinsic curvature computation algorithms proposed so far. We foresee several challenging applications, including the validation of DNA adsorption and bending models by experiments and the discrimination of specimens for genetic screening purposes.

Revisiting polymer statistical physics to account for the presence of long-range-correlated structural disorder in 2D DNA chains

We elaborate on a generalization of the 2D wormlike chain (WLC) model that accounts for the presence of long-range correlations (LRC) in the intrinsic curvature distribution of eukaryotic DNA. This model predicts some decrease of the DNA persistence length resulting from some large-scale intrinsic curvature induced by sequence-dependent persistent random distribution of local bending sites. When assisting exact analytical calculations by numerical DNA simulations, we show that the conjugated contributions of i) the thermal curvature fluctuations characterized by the "dynamic" persistence length ℓ(p)(d) = 2A, where A is the elastic bending modulus, and ii) the intrinsic LRC curvature disorder of amplitude σ(o) and Hurst exponent H > 1/2, characterized by a "static" persistence length ℓ(p)(H) = A(1/2H)σ(o)(-1/H) Γ(1/2H + 1), can be described by a continuum of generalized WLC (GWLC) models parametrized by the LRC exponent H. We use perturbation analysis to investigate the two limiting cases of weak static disorder (w(H) << 1 and weak dynamical fluctuations (1/w (H) << 1), where w(H) = l(p)(d)/l(p)(H) is a dimensionless parameter. From a quantitative point of view, our study demonstrates that even for a small value of the LRC (H approximately equal 0.6-0.8) static disorder amplitude σ(o) ~ 10(-2), as previously reported for genomic DNA, the decrease of the persistence length from the WLC prediction l(p)(d) can be very significant, up to twofold. The implications of these results on the first steps of compaction of DNA in eukaryotic cells are discussed.

Mechanical properties of high-G.C content DNA with a-type base-stacking

The sequence of a DNA molecule is known to influence its secondary structure and flexibility. Using a combination of bulk and single-molecule techniques, we measure the structural and mechanical properties of two DNAs which differ in both sequence and base-stacking arrangement in aqueous buffer, as revealed by circular dichroism: one with 50% G·C content and B-form and the other with 70% G·C content and A-form. Atomic force microscopy measurements reveal that the local A-form structure of the high-G·C DNA does not lead to a global contour-length decrease with respect to that of the molecule in B-form although it affects its persistence length. In the presence of force, however, the stiffness of high-G·C content DNA is similar to that of balanced-G·C DNA as magnetic and optical tweezers measured typical values for the persistence length of both DNA substrates. This indicates that sequence-induced local distortions from the B-form are compromised under tension. Finally, high-G·C DNA is significantly harder to stretch than 50%-G·C DNA as manifested by a larger stretch modulus. Our results show that a local, basepair configuration of DNA induced by high-G·C content influences the stretching elasticity of the polymer but that it does not affect the global, double-helix arrangement.

Mechanics of the IL2RA gene activation revealed by modeling and atomic force microscopy

Transcription implies recruitment of RNA polymerase II and transcription factors (TFs) by DNA melting near transcription start site (TSS). Combining atomic force microscopy and computer modeling, we investigate the structural and dynamical properties of the IL2RA promoter and identify an intrinsically negative supercoil in the PRRII region (containing Elf-1 and HMGA1 binding sites), located upstream of a curved DNA region encompassing TSS. Conformational changes, evidenced by time-lapse studies, result in the progressive positioning of curvature apex towards the TSS, likely facilitating local DNA melting. In vitro assays confirm specific binding of the General Transcription Factors (GTFs) TBP and TFIIB over TATA-TSS position, where an inhibitory nucleosome prevented preinitiation complex (PIC) formation and uncontrolled DNA melting. These findings represent a substantial advance showing, first, that the structural properties of the IL2RA promoter are encoded in the DNA sequence and second, that during the initiation process DNA conformation is dynamic and not static.