An introduction to the mechanics of DNA

Strongly Bent Double-Stranded DNA: Reconciling Theory and Experiment

The strong bending of polymers is poorly understood. We propose a general quantitative framework of polymer bending that includes both the weak and strong bending regimes on the same footing, based on a single general physical principle. As the bending deformation increases beyond a certain (polymer-specific) point, the change in the convexity properties of the effective bending energy of the polymer makes the harmonic deformation energetically unfavorable: in this strong bending regime the energy of the polymer varies linearly with the average bending angle as the system follows the convex hull of the deformation energy function. For double-stranded DNA, the effective bending deformation energy becomes non-convex for bends greater than ~ 2° per base-pair, equivalent to the curvature of a closed circular loop of ~ 160 base pairs. A simple equation is derived for the polymer loop energy that covers both the weak and strong bending regimes. The theory shows quantitative agreement with recent DNA cyclization experiments on short DNA fragments, while maintaining the expected agreement with experiment in the weak bending regime. Counter-intuitively, cyclization probability (j-factor) of very short DNA loops is predicted to increase with decreasing loop length; the j-factor reaches its minimum for loops of ≃ 45 base pairs. Atomistic simulations reveal that the attractive component of the short-range Lennard-Jones interaction between the backbone atoms can explain the underlying non-convexity of the DNA effective bending energy, leading to the linear bending regime. Applicability of the theory to protein-DNA complexes, including the nucleosome, is discussed.

Nanomechanics of Diaminopurine-Substituted DNA

2,6-diaminopurine (DAP) is a nucleobase analog of adenine. When incorporated into double-stranded DNA (dsDNA), it forms three hydrogen bonds with thymine. Rare in nature, DAP substitution alters the physical characteristics of a DNA molecule without sacrificing sequence specificity. Here, we show that in addition to stabilizing double-strand hybridization, DAP substitution also changes the mechanical and conformational properties of dsDNA. Thermal melting experiments reveal that DAP substitution raises melting temperatures without diminishing sequence-dependent effects. Using a combination of atomic force microscopy (AFM), magnetic tweezer (MT) nanomechanical assays, and circular dichroism spectroscopy, we demonstrate that DAP substitution increases the flexural rigidity of dsDNA yet also facilitates conformational shifts, which manifest as changes in molecule length. DAP substitution increases both the static and dynamic persistence length of DNA (measured by AFM and MT, respectively). In the static case (AFM), in which tension is not applied to the molecule, the contour length of DAP-DNA appears shorter than wild-type (WT)-DNA; under tension (MT), they have similar dynamic contour lengths. At tensions above 60 pN, WT-DNA undergoes characteristic overstretching because of strand separation (tension-induced melting) and spontaneous adoption of a conformation termed S-DNA. Cyclic overstretching and relaxation of WT-DNA at near-zero loading rates typically yields hysteresis, indicative of tension-induced melting; conversely, cyclic stretching of DAP-DNA showed little or no hysteresis, consistent with the adoption of the S-form, similar to what has been reported for GC-rich sequences. However, DAP-DNA overstretching is distinct from GC-rich overstretching in that it happens at a significantly lower tension. In physiological salt conditions, evenly mixed AT/GC DNA typically overstretches around 60 pN. GC-rich sequences overstretch at similar if not slightly higher tensions. Here, we show that DAP-DNA overstretches at 52 pN. In summary, DAP substitution decreases the overall stability of the B-form double helix, biasing toward non-B-form DNA helix conformations at zero tension and facilitating the B-to-S transition at high tension.

Twist-stretch profiles of DNA chains

Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs configurations. The method selects, for any applied force, the average twist angle which minimizes the molecule's free energy. It is found that the chains generally over-twist under an applied stretching and the over-twisting is physically associated to the contraction of the average helix diameter, i.e. to the damping of the base pair fluctuations. Instead, assuming that the maximum amplitude of the bending fluctuations may decrease against the external load, the DNA molecule first over-twists for weak applied forces and then untwists above a characteristic force value. Our results are discussed in relation to available experimental information albeit for kilo-base long molecules.

An elastic rod model to evaluate effects of ionic concentration on equilibrium configuration of DNA in salt solution

As a coarse-gained model, a super-thin elastic rod subjected to interfacial interactions is used to investigate the condensation of DNA in a multivalent salt solution. The interfacial traction between the rod and the solution environment is determined in terms of the Young-Laplace equation. Kirchhoff's theory of elastic rod is used to analyze the equilibrium configuration of a DNA chain under the action of the interfacial traction. Two models are established to characterize the change of the interfacial traction and elastic modulus of DNA with the ionic concentration of the salt solution, respectively. The influences of the ionic concentration on the equilibrium configuration of DNA are discussed. The results show that the condensation of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of forces that drive DNA condensation. With the change of concentration, the DNA segments will undergo a series of alteration from the original configuration to the condensed configuration, and the spiral-shape appearing in the condensed configuration of DNA is independent of the original configuration.

Concluding remarks: Cum grano salis

Hofmeister effects are part of a larger story--one in which the devil is perhaps in the details, but which promises to give us a much deeper understanding of how the solvent is a part of cell and molecular biology.

DNA information: from digital code to analogue structure

The digital linear coding carried by the base pairs in the DNA double helix is now known to have an important component that acts by altering, along its length, the natural shape and stiffness of the molecule. In this way, one region of DNA is structurally distinguished from another, constituting an additional form of encoded information manifest in three-dimensional space. These shape and stiffness variations help in guiding and facilitating the DNA during its three-dimensional spatial interactions. Such interactions with itself allow communication between genes and enhanced wrapping and histone-octamer binding within the nucleosome core particle. Meanwhile, interactions with proteins can have a reduced entropic binding penalty owing to advantageous sequence-dependent bending anisotropy. Sequence periodicity within the DNA, giving a corresponding structural periodicity of shape and stiffness, also influences the supercoiling of the molecule, which, in turn, plays an important facilitating role. In effect, the super-helical density acts as an analogue regulatory mode in contrast to the more commonly acknowledged purely digital mode. Many of these ideas are still poorly understood, and represent a fundamental and outstanding biological question. This review gives an overview of very recent developments, and hopefully identifies promising future lines of enquiry.

Helical post-buckling of a rod in a cylinder: with applications to drill-strings

The helical buckling and post-buckling of an elastic rod within a cylindrical casing arises in many disciplines, but is particularly important in the petroleum industry. Here, a drill-string, subjected to an end twisting moment combined with axial tension or compression, is particularly prone to buckling within its bore-hole—with potentially serious results. In this paper, we make a detailed theoretical study of this type of instability, deriving precise new results for the advanced post-buckling stage when the rod is in continuous contact with the cylinder. Results, including rigorous stability analyses and contact pressure assessments, are presented as equilibrium surfaces to facilitate comparisons with experimental results. Two approximate solutions give insight, universal graphs and parameters, for the practically relevant case of small angles, and highlight the existence of a critical cylinder diameter. Excellent agreement with experiments is achieved.

Supramolecular systems based on novel mono- and dicationic pyrimidinic amphiphiles and oligonucleotides: a self-organization and complexation study

Novel mono- and dicationic pyrimidinic surfactants are synthesized and their aggregation behavior is studied by methods of tensiometry and nuclear magnetic resonance (NMR) self-diffusion. To estimate their potentiality as gene delivery agents, the complexation with oligonucleotides (ONus) is explored by dynamic light scattering (DLS) and zeta-potential titration methods and ethidium bromide exclusion experiments. Bola-type pyrimidinic amphiphile (BPM) demonstrates rather a weak affinity to ONus. Although it induces mixed associations with ONus, only slight charge compensation changes occur at a large excess of bola, with no recharging reached. Similarly, the ethydium bromide exclusion study reveals a slow increase in the binding capacity toward an ONu with an increment in BPM concentration. The monocationic pyrimidinic surfactant (MPM) and its gemini analogue (GPM-1) are ranked as intermediates in both their aggregative activity and complexing properties toward ONus. They both form mixed associates with ONus well below the critical micelle concentrations (cmcs) of 2 and 15 mM respectively. However, GPM-1 has a much lower isoelectric point at the molar ratio surfactant/ONu r~1 compared to r~3 for MPM. This probably indicates a larger electrostatic contribution to the ONu complexation in the case of GPM-1. The most hydrophobic pyrimidinic surfactant (GPM-2), bearing three alkyl tails, demonstrates enhanced aggregative activity and binding capacity toward ONus as compared to former pyrimidinic surfactants. Due to effective aggregative (low cmc of 0.04 mM) plus binding properties (fraction of bound ONu β=0.76 at r=2.5), GPM-2 may be ranked as a promising agent for wider biological applications.

Modulating DNA configuration by interfacial traction: an elastic rod model to characterize DNA folding and unfolding

As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the equilibrium configuration of DNA in intracellular solution. The interfacial traction between the rod and the solution environment is derived in detail. Kirchhoff's theory of elastic rods is used to analyze the equilibrium configuration of a DNA segment under the action of the interfacial traction. The influences of the interfacial energy factor and bending stiffness on the toroidal spool formation of the DNA segment are discussed. The results show that the equilibrium configuration of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of the forces that drives DNA folding and unfolding.

Epigenetic events associated with breast cancer and their prevention by dietary components targeting the epigenome

Aberrant epigenetic alterations in the genome such as DNA methylation and chromatin remodeling play a significant role in breast cancer development. Since epigenetic alterations are considered to be more easily reversible compared to genetic changes, epigenetic therapy is potentially very useful in reversing some of these defects. Methylation of CpG islands is an important component of the epigenetic code, and a number of genes become abnormally methylated in breast cancer patients. Currently, several epigenetic-based synthetic drugs that can reduce DNA hypermethylation and histone deacetylation are undergoing preclinical and clinical trials. However, these chemicals are generally very toxic and do not have gene specificity. Epidemiological studies have shown that Asian women are less prone to breast cancer due to their high consumption of soy food than the Caucasian women of western countries. Moreover, complementary/and or alternative medicines are commonly used by Asian populations which are rich in bioactive ingredients known to be chemopreventive against tumorigenesis in general. Examples of such agents include dietary polyphenols, (-)-epigallocatechin-3-gallate (EGCG) from green tea, genistein from soybean, isothiocyanates from plant foods, curcumin from turmeric, resveratrol from grapes, and sulforaphane from cruciferous vegetables. These bioactive components are able to modulate epigenetic events, and their epigenetic targets are known to be associated with breast cancer prevention and therapy. This approach could facilitate the discovery and development of novel drugs for the treatment of breast cancer. In this brief review, we will summarize the epigenetic events associated with breast cancer and the potential of some of these bioactive dietary components to modulate these events and thus afford new therapeutic or preventive approaches.

Predicting nucleosome positioning in genomes: physical and bioinformatic approaches

In eukaryotic genomes, nucleosomes are responsible for packaging DNA and controlling gene expression. For this reason, an increasing interest is arising on computational methods capable of predicting the nucleosome positioning along genomes. In this review we describe and compare bioinformatic and physical approaches adopted to predict nucleosome occupancy along genomes. Computational analyses attempt at decoding the experimental nucleosome maps of genomes in terms of certain dinucleotide step periodicity observed along DNA. Such investigations show that highly significant information about the occurrence of a nucleosome along DNA is intrinsic in certain features of the sequence suggesting that DNA of eukaryotic genomes encodes nucleosome organization. Besides the bioinformatic approaches, physical models were proposed based on the sequence dependent conformational features of the DNA chain, which govern the free energy needed to transform recurrent DNA tracts along the genome into the nucleosomal shape.

DNA double-strand break repair and the evolution of intron density

The density of introns is both an important feature of genome architecture and a highly variable trait across eukaryotes. This heterogeneity has posed an evolutionary puzzle for the last 30 years. Recent evidence is consistent with novel introns being the outcome of the error-prone repair of DNA double-stranded breaks (DSBs) via non-homologous end joining (NHEJ). Here we suggest that deletion of pre-existing introns could occur via the same pathway. We propose a novel framework in which species-specific differences in the activity of NHEJ and homologous recombination (HR) during the repair of DSBs underlie changes in intron density.

The role of histone modifications and variants in regulating gene expression in breast cancer

The role of epigenetic phenomena in cancer biology is increasingly being recognized. Here we focus on the mechanisms and enzymes involved in regulating histone methylation and acetylation, and the modulation of histone variant expression and deposition. Implications of these epigenetic marks for tumor development, progression and invasiveness are discussed with a particular emphasis on breast cancer progression.

Twist-stretch coupling and phase transition during DNA supercoiling

As a single DNA molecule is positively supercoiled under constant tension, its extension initially increases due to a negative twist-stretch coupling. The subsequent attainment of an extension maximum has previously been assumed to be indicative of the onset of a phase transition from B- to scP-DNA. Here we show that an extension maximum in fact does not coincide with the onset of a phase transition. This transition is evidenced by a direct observation of a torque plateau using an angular optical trap. Instead we find that the shape of the extension curve can be well explained with a theory that incorporates both DNA twist-stretch coupling and bending fluctuations. This theory also provides a more accurate method of determining the value of the twist-stretch coupling modulus, which has possibly been underestimated in previous studies that did not take into consideration the bending fluctuations. Our study demonstrates the importance of torque detection in the correct identification of phase transitions as well as the contribution of the twist-stretch coupling and bending fluctuations to DNA extension.

Structural properties of polymeric DNA from molecular dynamics simulations

Most of the reported DNA structural studies are based on oligonucleotide structures, which have artifacts due to unstable terminal base pairs (bps). We have carried out molecular dynamics simulation of DNA oligonucleotides in such a manner that gives rise to properties of polymeric DNA of infinite length. Molecular dynamics simulation studies of six homo- and heteropolymeric DNA sequences are reported here to understand structural features of all ten unique dinucleotide sequences. We observe that each of these dinucleotide sequences has unique features in agreement with Calladine's rule [C. R. Calladine, J. Mol. Biol. 161, 343 (1982)]. We noticed significant structural alternation between B(I) and B(II) forms for d(CA).d(TG) dinucleotide, where one of the strands showed frequent transitions between usual and unusual epsilon and zeta torsion angles associated with bp stacking geometry. In terms of the calculated bending rigidity and persistence length, pyrimidine-purine bp steps, namely, d(TA).d(TA), d(CA).d(TG), and d(CG).d(CG) are the most flexible dinucleotide bp steps. We estimated the major groove widths from our simulations. We did not observe much variation in major and minor groove widths depending on the base sequence. However, the distribution of water molecules in the minor groove shows sensitivity to the DNA sequence.

Single-molecule magnetic tweezer tests on DNA: bounds on topoisomerase relaxation

Biomedical researchers regularly stretch and twist single DNA molecules in magnetic tweezer experiments. By making the molecule writhe into a plectoneme (ply) and plotting its load–extension curves, key DNA parameters, such as effective radius, can be estimated. Adding untangling enzymes (topoisomerases) to the DNA's environment, their individual cuts are detected as jumps in extension.

Sufficient information is now known about the topoisomerases for us to make good idealizations about their kinematics and mechanics. The novelty of this paper is to study their actions in the context of accurate ply solutions from the theory of elastic rods. To do this, we define an extended rod-plus-tension system that allows us to determine the stored energies from areas in the conventional link versus writhe plane.

After a cut, the molecule relaxes dynamically to a new equilibrium state, and often there will be two or more alternative stable configurations onto which it might settle. Knowing the energy levels allows us to identify which states can and cannot be reached over the unstable mountain passes, and which of the accessible states offer the greatest energy relaxation. Strict energy bounds on behaviour are established.

This knowledge has medical value because topoisomerase inhibitors, lethal for cells, are used as antibiotics and in chemotherapy for cancer.

B-DNA under stress: over- and untwisting of DNA during molecular dynamics simulations

The twist flexibility of DNA is central to its many biological functions. Explicit solvent molecular dynamics simulations in combination with an umbrella sampling restraining potential have been employed to study induced twist deformations in DNA. Simulations allowed us to extract free energy profiles for twist deformations and were performed on six DNA dodecamer duplexes to cover all 10 possible DNA basepair steps. The shape of the free energy curves was similar for all duplexes. The calculated twist deformability was in good agreement with experiment and showed only modest variation for the complete duplexes. However, the response of the various basepair steps on twist stress was highly nonuniform. In particular, pyrimidine/purine steps were much more flexible than purine/purine steps followed by purine/pyrimidine steps. It was also possible to extract correlations of twist changes and other helical as well as global parameters of the DNA molecules. Twist deformations were found to significantly alter the local as well as global shape of the DNA modulating the accessibility for proteins and other ligands. Severe untwisting of DNA below an average of 25 degrees per basepair step resulted in the onset of a global structural transition with a significantly smaller twist at one end of the DNA compared to the other.

DNA overwinds when stretched

DNA is often modelled as an isotropic rod, but its chiral structure suggests the possible importance of anisotropic mechanical properties, including coupling between twisting and stretching degrees of freedom. Simple physical intuition predicts that DNA should unwind under tension, as it is pulled towards a denatured structure. We used rotor bead tracking to directly measure twist-stretch coupling in single DNA molecules. Here we show that for small distortions, contrary to intuition, DNA overwinds under tension, reaching a maximum twist at a tension of approximately 30 pN. As tension is increased above this critical value, the DNA begins to unwind. The observed twist-stretch coupling predicts that DNA should also lengthen when overwound under constant tension, an effect that we quantitatively confirm. We present a simple model that explains these unusual mechanical properties, and also suggests a possible origin for the anomalously large torsional rigidity of DNA. Our results have implications for the action of DNA-binding proteins that must stretch and twist DNA to compensate for variability in the lengths of their binding sites. The requisite coupled DNA distortions are favoured by the intrinsic mechanical properties of the double helix reported here.

Modeling DNA loops using the theory of elasticity

An elastic rod model of a protein-bound DNA loop is adapted for application in multi-scale simulations of protein-DNA complexes. The classical Kirchhoff system of equations which describes the equilibrium structure of the elastic loop is modified to account for the intrinsic twist and curvature, anisotropic bending properties, and electrostatic charge of DNA. The effects of bending anisotropy and electrostatics are studied for the DNA loop clamped by the lac repressor protein. For two possible lengths of the loop, several topologically different conformations are predicted and extensively analyzed over the broad range of model parameters describing DNA bending and electrostatic properties. The scope and applications of the model in already accomplished and in future multi-scale studies of protein-DNA complexes are discussed.

Docking, triggering, and biological activity of dynemicin A in DNA: a computational study

The triggering and biological activity of the naturally occurring enediyne dynemicin A (1) was investigated, both inside and outside the minor groove of the duplex 10-mer B-DNA sequence d(CTACTACTGG).d(CCAGTAGTAG), using density functional theory (B3LYP with the 3-21G and 6-31G(d) basis set), BD(T)/cc-pVDZ (Brueckner doubles with a perturbative treatment of triple excitations), and the ONIOM approach. Enediyne 1 is triggered by NADPH in a strongly exothermic reaction (-88 kcal/mol), which involves a number of intermediate steps. Untriggered 1 has a high barrier for the Bergman cyclization (52 kcal/mol) that is lowered after triggering to 16.7 kcal/mol due to an epoxide opening and the accompanying strain relief. The Bergman reaction of triggered 1 is slightly exothermic by 2.8 kcal/mol. The singlet biradical formed in this reaction is kinetically stable (activation enthalpies of 19.5 and 21.8 kcal/mol for retro-Bergman reactions) and is as reactive as para-benzyne. The activity-relevant docking mode is an edge-on insertion into the minor groove, whereas the intercalation between base pairs, although leading to larger binding energies, excludes a triggering of 1 and the development of its biological activity. Therefore, an insertion-intercalation model is developed, which can explain all known experimental observations made for 1. On the basis of the insertion-intercalation model it is explained why large intercalation energies suppress the biological activity of dynemicin and why double-strand scission can be achieved only in a two-step mechanism that involves two enediyne molecules, explaining thus the high ratio of single-strand to double-strand scission observed for 1.

Solenoids and plectonemes in stretched and twisted elastomeric filaments

We study the behavior of a naturally straight highly extensible elastic filament subjected to large extensional and twisting strains. We find that two different phases can coexist for a range of parameter values: the plectoneme and the solenoid. A simple theory based on a neo-Hookean model for the material of the filament and accounting for the slender geometry suffices to explain these observations, and leads to a phase diagram that is consistent with observations. Extension and relaxation experiments on these phases show the presence of large hysteresis loops and sawtooth-like force-displacement curves which are different for the plectoneme and the solenoid.

The complexity of anatomical systems

BACKGROUND

The conception of anatomical entities as a hierarchy of infinitely graduated forms and the increase in the number of observed anatomical sub-entities and structural variables has generated a growing complexity, thus highlighting new properties of organised biological matter.

RESULTS

(1) Complexity is so pervasive in the anatomical world that it has come to be considered as a primary characteristic of anatomical systems. (2) Anatomical entities, when viewed at microscopic as well as macroscopic level of observation, show a different degree of complexity. (3) Complexity can reside in the structure of the anatomical system (having many diverse parts with varying interactions or an intricate architecture) or in its behaviour. Often complexity in structure and behaviour go together. (4) Complex systems admit many descriptions (ways of looking at the system) each of which is only partially true. Each way of looking at a complex system requires its own description, its own mode of analysis and its own breaking down of the system in different parts; (5) Almost all the anatomical entities display hierarchical forms: their component structures at different spatial scales or their process at different time scales are related to each other.

CONCLUSION

The need to find a new way of observing and measuring anatomical entities, and objectively quantifying their different structural changes, prompted us to investigate the non-Euclidean geometries and the theories of complexity, and to apply their concepts to human anatomy. This attempt has led us to reflect upon the complex significance of the shape of an observed anatomical entity. Its changes have been defined in relation to variations in its status: from a normal (i.e. natural) to a pathological or altered state introducing the concepts of kinematics and dynamics of anatomical forms, speed of their changes, and that of scale of their observation.

Influence of DNA stiffness in protein–DNA recognition

Protein-DNA recognition plays an essential role in the regulation of gene expression. The protein-DNA binding specificity is based on direct atomic contacts between protein and DNA and/or the conformational properties of DNA. In this work, we have analyzed the influence of DNA stiffness (E) to the specificity of protein-DNA complexes. The average DNA stiffness parameters for several protein-DNA complexes have been computed using the structure based sequence dependent stiffness scale. The relationship between DNA stiffness and experimental protein-DNA binding specificity has been brought out. We have investigated the importance of DNA stiffness with the aid of experimental free energy changes (DeltaDeltaG) due to binding in several protein-DNA complexes, such as, ETS proteins, 434, lambda, Mnt and trp repressors, 434 cro protein, EcoRV endonuclease V and zinc fingers. We found a correlation in the range 0.65-0.97 between DeltaDeltaG and E in these examples. Further, we have qualitatively analyzed the effect of mutations in the target sequence of lambda repressor and we observed that the DNA stiffness could correctly identify 70% of the correct bases among the considered nine positions.