On the compact form of linear duplex DNA: globular states of the uniform elastic (persistent) macromolecule

A theory of collapse of DNA considered as unifilar homopolymer is suggested. The collapse is interpreted as the coil-globule transition. Three reasons of the collapse such as the confinement in a microcavity, the influence of poor low-molecular-weight solvent and the influence of polymeric solvent were studied. The results are summed up by the stage diagrams in variables: DNA length versus the characteristics of the compaction factor (the cavity volume, the energy of attraction of DNA segments in poor low-molecular-weight solvent and the concentration of polymer added). It is shown that a sufficiently long DNA forms the spherical compact particle while the relatively short DNA forms the toroidal one. More delicate features of the tertiary structure are determined by the relative role of the bending stiffness and steric repulsions in preventing further collapse. As the compaction occurs in polymeric solvent almost all added polymer is forced out from the globule. Thus, the internal structure of the compact DNA particle in polymeric solvent is similar to that in the model of microcavity.     

Transition between two regimes describing internal fluctuation of DNA in a nanochannel

We measure the thermal fluctuation of the internal segments of a piece of DNA confined in a nanochannel about 50-100 nm wide. This local thermodynamic property is key to accurate measurement of distances in genomic analysis. For DNA in ~100 nm channels, we observe a critical length scale ~10 m for the mean extension of internal segments, below which the de Gennes' theory describes the fluctuations with no fitting parameters, and above which the fluctuation data falls into Odijk's deflection theory regime. By analyzing the probability distributions of the extensions of the internal segments, we infer that folded structures of length 150-250 nm, separated by ~10 m exist in the confined DNA during the transition between the two regimes. For ~50 nm channels we find that the fluctuation is significantly reduced since the Odijk regime appears earlier. This is critical for genomic analysis. We further propose a more detailed theory based on small fluctuations and incorporating the effects of confinement to explicitly calculate the statistical properties of the internal fluctuations. Our theory is applicable to polymers with heterogeneous mechanical properties confined in non-uniform channels. We show that existing theories for the end-to-end extension/fluctuation of polymers can be used to study the internal fluctuations only when the contour length of the polymer is many times larger than its persistence length. Finally, our results suggest that introducing nicks in the DNA will not change its fluctuation behavior when the nick density is below 1 nick per kbp DNA.     

DNA Motion Capture Reveals the Mechanical Properties of DNA at the Mesoscale

Single-molecule studies probing the end-to-end extension of long DNAs have established that the mechanical properties of DNA are well described by a wormlike chain force law, a polymer model where persistence length is the only adjustable parameter. We present a DNA motion-capture technique in which DNA molecules are labeled with fluorescent quantum dots at specific sites along the DNA contour and their positions are imaged. Tracking these positions in time allows us to characterize how segments within a long DNA are extended by flow and how fluctuations within the molecule are correlated. Utilizing a linear response theory of small fluctuations, we extract elastic forces for the different, ∼2-μm-long segments along the DNA backbone. We find that the average force-extension behavior of the segments can be well described by a wormlike chain force law with an anomalously small persistence length.     

Structure of collapsed persistent macromolecule: Toroid vs. spherical globule

We studied theoretically the behavior of a collapsed persistent macromolecule in poor solvent as a model of collapse transition of single double-stranded DNA chain, and constructed the diagram of states in the variables with contour length of a macromolecule and quality of the solvent. We found that the state of toroidal globule exists as an intermediate state between the states of elongated coil state and the spherical globule. Our theoretical result suggests that a single linear macromolecule with a high degree of polymerization can form a toroidal globule. However, the range in which the toroidal structure is stable decreases as the macromolecule length increases. Experimental observation with transmission electron microscopy has been performed to study the globular structure of single DNA chain (bacteriophage T4 DNA, λ-DNA) collapsed by hexammine cobalt (III) at different concentrations. We found that an extremely long chain of T4 DNA (166 kbp), with a contour length of 56 μm, actually forms a toroidal globule, and that isotropic spherical globule appears at higher hexammine cobalt concentration. © 1997 John Wiley & Sons, Inc.     

Theory of the toroidal compact form of DNA in a polymer solution

A diagram of the states of single long rigid DNA macromolecule in solution of short flexible polymer was plotted. It has been shown that the compacting effect of the polymer solvent on DNA can be interpreted as hydrostatic pressure of coils gas on impermeable "walls" of the DNA globule. Conditions were found for the existence of compact (globular) states in the form of a sphere (stable for a very long DNA) and tore (for a relatively short one). Possibility of intramolecular liquidcrystalline orderliness of DNA segments in a globule was analyzed. Regions of realization of both regimes were studied: when compression with an added polymer was equalized by the forces of steric repulsion of DNA segments and when it was balanced by the elasticity of the DNA chain bendings.     

Dielectric control of counterion-induced single-chain folding transition of DNA

In the presence of condensing agents, single chains of giant double-stranded DNA undergo a first-order phase transition between an elongated coil state and a folded compact state. To connect this like-charged attraction phenomenon to counterion condensation, we performed a series of single-chain experiments on aqueous solutions of DNA, where we varied the extent of counterion condensation by varying the relative dielectric constant epsilon(r) from 80 to 170. Single-chain observations of changes in the conformation of giant DNA were performed by transmission electron microscopy and fluorescence microscopy, with tetravalent spermine (SPM(4+)) as a condensing agent. At a fixed dielectric constant, single DNA chains fold into a compact state upon the addition of spermine, whereas at a constant spermine concentration single DNA chains unfold with an increase in epsilon(r). In both cases, the transition is largely discrete at the level of single chains. We found that the critical concentration of spermine necessary to induce the single-chain folding transition increases exponentially as the dielectric constant increases, corresponding to 87-88% of the DNA charge neutralized at the onset of the transition. We also observed that the toroidal morphology of compact DNA partially unfolds when epsilon(r) is increased.     

Structural analysis of hyperperiodic DNA from Caenorhabditis elegans

Several bioinformatics studies have identified an unexpected but remarkably prevalent ~10 bp periodicity of AA/TT dinucleotides (hyperperiodicity) in certain regions of the Caenorhabditis elegans genome. Although the relevant C.elegans DNA segments share certain sequence characteristics with bent DNAs from other sources (e.g. trypanosome mitochondria), the nematode sequences exhibit a much more extensive and defined hyperperiodicity. Given the presence of hyperperiodic structures in a number of critical C.elegans genes, the physical characteristics of hyperperiodic DNA are of considerable interest. In this work, we demonstrate that several hyperperiodic DNA segments from C.elegans exhibit structural anomalies using high-resolution atomic force microscopy (AFM) and gel electrophoresis. Our quantitative analysis of AFM images reveals that hyperperiodic DNA adopts a significantly smaller mean square end-to-end distance, hence a more compact coil structure, compared with non-periodic DNA of similar length. While molecules remain capable of adopting both bent and straight (rod-like) configurations, indicating that their flexibility is still retained, examination of the local curvatures along the DNA contour length reveals that the decreased mean square end-to-end distance can be attributed to the presence of long-scale intrinsic bending in hyperperiodic DNA. Such bending is not detected in non-periodic DNA. Similar studies of shorter, nucleosome-length DNAs that survived micrococcal nuclease digestion show that sequence hyperperiodicity in short segments can likewise induce strong intrinsic bending. It appears, therefore, that regions of the C.elegans genome display a significant correlation between DNA sequence and unusual mechanical properties.     

Structural stability and buckling analysis of a series of carbon nanotorus using molecular dynamics simulations

Based on molecular dynamics (MD) simulations, the buckling analysis of a perfect carbon nanotorus is presented herein. First of all, the minimum length of single-walled carbon nanotubes (SWCNTs) with different radii is determined at which perfect toroidal CNTs can be formed without any ripple at the inner side of the rings. According to the results, by increasing the radius of SWCNT (r), the radius of its corresponding perfect nanotorus (R) increases. Also, for SWCNTs with various lengths, it is found that the buckling force and strain of related carbon nanotoruses increase by increasing R/r. In addition, as the perfect toroidal CNTs are arranged vertically in a column form in accordance with two different schemes, the effects of increasing the radius (R) and the number of carbon nanotoruses (the height of the column made by nanotoruses) on the buckling force and strain are investigated. Based on the results, as a fixed number of carbon nanotoruses with the same radius are arranged vertically in the column form, the buckling force and strain increase by increasing R/r. By contrast, increasing the height of the column made by carbon nanotoruses with similar radius leads to the reduction of buckling force and strain.     

X-ray diffraction studies on cation-collapsed DNA

The polyamines spermidine, spermine and putrescine are now known to induce tertiary collapse of DNA. In this collapsed state DNA assumes a compact toroidal conformation. However, the structural details of DNA in these compact particles and the forces that stabilize the collapsed state are not clear. We show here that the structural arrangement of DNA in this tertiary conformation is determined by the chemical structure of the agent used to collapse. We have used aliphatic triamines (NH₃⁺-(CH₂)₃-NH₂⁺-(CH₂)_n-NH₃⁺ with n = 3, 4, 5 and 8) and diamines (NH₃⁺-(CH₂)_x-NH₃⁺ with x = 2, 3, 4 and 6) to collapse DNA. We find that the Bragg spacing and the calculated interhelical spacing for a hexagonal packing model vary systematically with the length of the methylene bridge. We also find that the ionic strength of the solution has no effect on the Bragg spacing. This observation suggests that the arrangement of DNA strands in the complexes is determined by the structure of the polycation, and argues against suggestions that the structure of the collapsed state is maintained by the balance of long-range electrostatic repulsive and attractive forces. Instead we propose that DNA helices form a hexagonal array with counterions in the interstices between the helices resulting in a stable three-dimensional phase with high structural order. Arguments are presented favoring such a model in terms of stabilizing and destabilizing thermodynamic forces.     

Single molecule studies of DNA-protamine interactions

Single molecule studies of protamine-DNA interactions have characterized the kinetics of protamine binding to DNA and the morphology of the toroidal subunits that comprise sperm chromatin. The results provided by these studies are reviewed, the advantage of using single molecule techniques is discussed, and the implications of the results to the structure, kinetics of toroid formation, and stability of the DNA-protamine complex are described. New measurements of DNA condensation forces induced by the binding of protamine to DNA are also presented. These forces induce a significant tension in constrained segments of DNA and may contribute to the reduction in volume and shaping of the maturing spermatid cell nucleus.     

Torsional and bending rigidity of the double helix from data on small DNA rings

We have calculated the variance of equilibrium distribution of a circular wormlike polymer chain over the writhing number, [Wr)2), as a function of the number of Kuhn statistical segments, n. For large n these data splice well with our earlier results obtained for a circular freely jointed polymer chain. Assuming that [delta Lk)2) = [delta Tw)2) we have compared our results with experimental data on the chain length dependence of the [delta Lk)2) value recently obtained by Horowitz and Wang for small DNA rings. This comparison has shown an excellent agreement between theory and experiment and yielded a reliable estimate of the torsional and bending rigidity parameters. Namely, the torsional rigidity constant is C = 3.0.10(-19) erg cm, and the bending rigidity as expressed in terms of the DNA persistence length is a = 500 A. The obtained value of C agrees well with earlier estimates by Shore and Baldwin as well as by Horowitz and Wang whereas the a value is in accord with the data of Hagerman. We have found the data of Shore and Baldwin on the chain length dependence of the [delta Lk)2) value to be entirely inconsistent with our theorectical results.     

Visualizing the Formation and Collapse of DNA Toroids

In living organisms, DNA is generally confined into very small volumes. In most viruses, positively charged multivalent ions assist the condensation of DNA into tightly packed toroidal structures. Interestingly, such cations can also induce the spontaneous formation of DNA toroids in vitro. To resolve the condensation dynamics and stability of DNA toroids, we use a combination of optical tweezers and fluorescence imaging to visualize in real-time spermine-induced (de)condensation in single DNA molecules. By actively controlling the DNA extension, we are able to follow (de)condensation under tension with high temporal and spatial resolution. We show that both processes occur in a quantized manner, caused by individual DNA loops added onto or removed from a toroidal condensate that is much smaller than previously observed in similar experiments. Finally, we present an analytical model that qualitatively captures the experimentally observed features, including an apparent force plateau.     

On the theory of Ψ-condensation

We suggest a theory of Ψ-condensation, based on the assumption that a compact DNA particle is a globule, and specifically that a polymer solution is a strongly fluctuating system and that double-stranded DNA is a stiff homopolymer single-stranded chain. We show the DNA globule as it appears in a dilute poly(ethylene oxide) (PEO) solution. The corresponding phase transition is investigated in detail. Growth of the PEO concentration should lead to a decrease in the size of the compact particle and to an increase in its optical rotatory power. Conditions are defined at which drastic compaction of DNA takes place, accompanied by the loss of its optic rotatory power, in regions of high PEO concentrations.     

Scaling theory of polymer translocation into confined regions

We examine the voltage-driven polymer translocation from a spacious region into a confined region imposed by two parallel planes, so that the entry is impeded by the entropic confinement but aided by the electric field inside the confined region. Two modes of entry are examined: linear translocation where a chain enters the confined region with chain ends, and hairpin translocation where a chain enters the confined region by forming a hairpin. Our calculation shows that translocation time increases with polymer length for linear entries but decreases with polymer length for hairpin entries. Applying to electrophoresis of DNA molecules through periodic spacious and confined regions, our theory shows that the dominance of hairpin translocations leads to the experimentally observed faster migration of longer DNA molecules. Our theory predicts experimental conditions for the validity of this law in terms of polymer length, size of the confined region, and solution conditions.     

Double-stranded DNA organization in bacteriophage heads: an alternative toroid-based model.

Studies of the organization of double-stranded DNA within bacteriophage heads during the past four decades have produced a wealth of data. However, despite the presentation of numerous models, the true organization of DNA within phage heads remains unresolved. The observations of toroidal DNA structures in electron micrographs of phage lysates have long been cited as support for the organization of DNA in a spool-like fashion. This particular model, like all other models, has not been found to be consistent will all available data. Recently we proposed that DNA within toroidal condensates produced in vitro is organized in a manner significantly different from that suggested by the spool model. This new toroid model has allowed the development of an alternative model for DNA organization within bacteriophage heads that is consistent with a wide range of biophysical data. Here we propose that bacteriophage DNA is packaged in a toroid that is folded into a highly compact structure.     

The inactive form of recA protein: the 'compact' structure.

When recA protein is enzymatically inactive in vitro, it adopts a more compact helical polymer form than that of the active protein polymerized onto DNA in the presence of ATP. Here we describe some aspects of this structure. By cryo-electron microscopy, a pitch of 76 A is found for both the self-polymer and the inactive complex with ssDNA. A smaller pitch of 64 A is observed in conventional electron micrographs. The contour length of complexes with ssDNA was used to estimate the binding stoichiometry in the compact complex, 6 +/- 1 nt/recA. In addition, the compact structure was observed in vivo in Escherichia coli: inclusion bodies produced upon induction of recA expression in an overproducing strain have a fibrous morphology with the structural parameters of the compact polymer.     

Cooperative chiral order in the B-Z transition in random sequences of DNA.

We present a theory for cooperative chiral order in the transition between right-handed B-DNA and left-handed Z-DNA. This theory, based on the random-field Ising model, predicts the characteristic length scale of Z-DNA segments. This length scale depends on whether the DNA is a homopolymer or a random sequence: it is approximately 4000 nucleotides in a homopolymer but only approximately 25 nucleotides in a random sequence. These theoretical results are consistent with experiments on DNA homopolymers and random sequences.     

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.     

Topological defects and the optimum size of DNA condensates.

Under a wide variety of conditions, the addition of condensing agents to dilute solutions of random-coil DNA gives rise to highly compact particles that are toroidal in shape. The size of these condensates is remarkably constant and is largely independent of DNA molecular weight and basepair sequence, and of the nature of condensing agent (e.g., multivalent cation, polymers, or added cosolvent). We show how this optimum size is determined by the interactions between topological defects, which unavoidably strain the circumferentially wound DNA strands in the torus.