Interplay of ion binding and attraction in DNA condensed by multivalent cations

We have measured forces generated by multivalent cation-induced DNA condensation using single-molecule magnetic tweezers. In the presence of cobalt hexammine, spermidine, or spermine, stretched DNA exhibits an abrupt configurational change from extended to condensed. This occurs at a well-defined condensation force that is nearly equal to the condensation free energy per unit length. The multivalent cation concentration dependence for this condensation force gives the apparent number of multivalent cations that bind DNA upon condensation. The measurements show that the lower critical concentration for cobalt hexammine as compared to spermidine is due to a difference in ion binding, not a difference in the electrostatic energy of the condensed state as previously thought. We also show that the resolubilization of condensed DNA can be described using a traditional Manning–Oosawa cation adsorption model, provided that cation–anion pairing at high electrolyte concentrations is taken into account. Neither overcharging nor significant alterations in the condensed state are required to describe the resolubilization of condensed DNA. The same model also describes the spermidine³⁺/Na⁺ phase diagram measured previously.     

Salt dependence of the elasticity and overstretching transition of single DNA molecules

As double-stranded DNA is stretched to its B-form contour length, models of polymer elasticity can describe the dramatic increase in measured force. When the molecule is stretched beyond this contour length, it shows a highly cooperative overstretching transition. We have measured the elasticity and overstretching transition as a function of monovalent salt concentration by stretching single DNA molecules in an optical tweezers apparatus. As the sodium ion concentration was decreased from 1000 to 2.57 mM, the persistence length of DNA increased from 46 to 59 nm, while the elastic stretch modulus remained approximately constant. These results are consistent with the model of Podgornik, et al. (2000, J. Chem. Phys. 113:9343-9350) using an effective DNA length per charge of 0.67 nm. As the monovalent salt concentration was decreased over the same range, the overstretching transition force decreased from 68 to 52 pN. This reduction in force is attributed to a decrease in the stability of the DNA double helix with decreasing salt concentration. Although, as was shown previously, the hydrogen bonds holding DNA strands in a helical conformation break as DNA is overstretched, these data indicate that both DNA strands remain close together during the transition.     

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.     

Stretching DNA with optical tweezers.

Force-extension (F-x) relationships were measured for single molecules of DNA under a variety of buffer conditions, using an optical trapping interferometer modified to incorporate feedback control. One end of a single DNA molecule was fixed to a coverglass surface by means of a stalled RNA polymerase complex. The other end was linked to a microscopic bead, which was captured and held in an optical trap. The DNA was subsequently stretched by moving the coverglass with respect to the trap using a piezo-driven stage, while the position of the bead was recorded at nanometer-scale resolution. An electronic feedback circuit was activated to prevent bead movement beyond a preset clamping point by modulating the light intensity, altering the trap stiffness dynamically. This arrangement permits rapid determination of the F-x relationship for individual DNA molecules as short as -1 micron with unprecedented accuracy, subjected to both low (approximately 0.1 pN) and high (approximately 50 pN) loads: complete data sets are acquired in under a minute. Experimental F-x relationships were fit over much of their range by entropic elasticity theories based on worm-like chain models. Fits yielded a persistence length, Lp, of approximately 47 nm in a buffer containing 10 mM Na1. Multivalent cations, such as Mg2+ or spermidine 3+, reduced Lp to approximately 40 nm. Although multivalent ions shield most of the negative charges on the DNA backbone, they did not further reduce Lp significantly, suggesting that the intrinsic persistence length remains close to 40 nm. An elasticity theory incorporating both enthalpic and entropic contributions to stiffness fit the experimental results extremely well throughout the full range of extensions and returned an elastic modulus of approximately 1100 pN.     

Optical tweezers reveal force plateau and internal friction in PEG-induced DNA condensation

The simplified artificial environments in which highly complex biological systems are studied do not represent the crowded, dense, salty, and dynamic environment inside the living cell. Consequently, it is important to investigate the effect of crowding agents on DNA. We used a dual-trap optical tweezers instrument to perform force spectroscopy experiments at pull speeds ranging from 0.3 to 270 μm/s on single dsDNA molecules in the presence of poly(ethylene glycol) (PEG) and monovalent salt. PEG of sizes 1,500 and 4,000 Da condensed DNA, and force–extension data contained a force plateau at approximately 1 pN. The level of the force plateau increased with increasing pull speed. During slow pulling the dissipated work increased linearly with pull speed. The calculated friction coefficient did not depend on amount of DNA incorporated in the condensate, indicating internal friction is independent of the condensate size. PEG300 had no effect on the dsDNA force–extension curve. The force plateau implies that condensation induced by crowding agents resembles condensation induced by multivalent cations.     

Improved resolution of tertiary structure elasticity in muscle protein

Rearrangement of tertiary structure in response to mechanical force (termed tertiary structure elasticity) in the tandem Ig chain is the first mode of elastic response for muscle protein titin. Tertiary structure elasticity occurs at low stretching forces (few tens of pN), and was described at atomic resolution in a recent molecular dynamics study, in which an originally crescent-shaped six-Ig chain was stretched into a linear chain. However, the force-extension profile that resulted from this explicit solvent simulation was dominated by the hydrodynamic drag force, and effects of tertiary structure elasticity only manifested for stretching forces above 20 pN. Here we report a slow pulling 100-ns simulation (along with other auxiliary simulations), in which hydrodynamic drag force is seen to reduce to near 0 pN, such that tertiary structure elasticity could be characterized over a 0–200 pN range. Statistical mechanical analysis showed that the stretching velocity was sufficiently low such that the protein remained significantly relaxed during the major part of its extension.     

DNA stretching on functionalized gold surfaces.

We describe a method for anchoring bacteriophage lambda DNA by one end to gold by Au-biotin-streptavidin-biotin-DNA bonds. DNA anchored to a microfabricated Au line could be aligned and stretched in flow and electric fields. The anchor was shown to resist a force of at least 11 pN, a linkage strong enough to allow DNA molecules of chromosome size to be stretched and aligned.     

Ligand-induced DNA condensation: choosing the model

We test and compare different models for ligand-induced DNA condensation. Using 14C-labeled spermidine3+, we measure the binding to condensed DNA at micromolar to molar polyamine concentrations. DNA aggregates at a critical polyamine concentration. Spermidine3+ binding becomes highly cooperative at the onset of aggregation. At higher concentrations, spermidine3+ binding to condensed DNA reaches a plateau with the degree of binding equal to 0.7 (NH(4+)/PO3-). Condensed DNA exists in a wide range of spermidine concentrations with the roughly constant degree of ligand binding. At greater concentrations, the degree of binding increases again. Further spermidine penetration between the double helices causes DNA resolubilization. We show that a simple two-state model without ligand-ligand interactions qualitatively predicts the reentrant aggregation-resolubilization behavior and the dependence on the ligand, Na+, and DNA concentrations. However, such models are inconsistent with the cooperative ligand binding to condensed DNA. Including the contact or long-range ligand-ligand interactions improves the coincidence with the experiments, if binding to condensed DNA is slightly more cooperative than to the starting DNA. For example, in the contact interaction model it is equivalent to an additional McGhee-von Hippel cooperativity parameter of approximately 2. Possible physical mechanisms for the observed cooperativity of ligand binding are discussed.     

Structure of viral φ29 DNA condensed by simple triamines: A light-scattering and electron-microscopy study

The structures of viral φ29 DNA condensed by triamines, principally spermidine, in 10^?3M NaCl were investigated by static and dynamic light scattering and electron microscopy. All of the results for DNA condensed in 30 μM spermidine at neutral pH are quantitatively consistent with a toroidal structure with a mean outer diameter of 1850 Å. At pH 10.2, however, condensed structures of a completely different size and shape are observed for the first time. These structures are also more irregular in shape and more polydisperse than those at neutral pH. This conformational change is believed to result from a change in the mode of spermidine binding that is coupled to, or associated with, the (premature) titration of protons on the base-ring nitrogens of guanine and thymine. Besides spermidine, certain homologs of spermidine, in which the butyl moiety of spermidine was replaced by longer pentyl through octyl moieties, were also studied. Though all of the triamines condensed the DNA at 30 μM, aggregation became a more prevalent occurrence as the length of the end chain increased. This suggests that crosslinking may play an important role in the condensation process. Finally, these aggregates are dissociated to a considerable extent at pH 10.2, and the resulting compact structures appear to be quite similar, independent of the triamine used to condense the DNA. The observed partial breakdown of aggregates is also consistent with the hypothesis of a change in mode of triamine binding at pH 10.2.     

Inhibition of cation-induced DNA condensation by intercalating dyes

Several intercalating dyes are shown to inhibit the cation-induced condensation of λ-DNA when Co³⁺(NH₃)₆ is the condensing agent. The dyes that have been studied are ethidium, propidium, proflavin, quinacrine, and actinomycin D. Earlier work has shown that intercalating dyes inhibit ψ-DNA condensation. [Lerman, L. S. (1971) Prog. Mol. Subcell. Biol. 2 , 382–391; Cheng, S. & Mohr, S. C. (1975) Biopolymers 14 , 663–674.] Dye-induced decondensation of intramolecularly condensed DNA has been studied by making use of conditions in which Co³⁺(NH₃)₆ produces intramolecular condensation without significant aggregation. Some aggregation is caused, however, during dye-induced decondensation. Dye titration curves of DNA decondensation have been measured by excess light scattering to monitor decondensation and by fluorescence to monitor intercalation. All of the dyes studied act as competing cations in displacing the condensing cation Co³⁺(NH₃)₆ from the DNA. Competition occurs both in and below the transition zone for condensation. The effectiveness of a dye as a competing cation increases with its net positive charge. Before decondensation begins, no intercalated dye can be detected, suggesting that intercalation might be incompatible with the proper helix packing needed for cation-induced DNA condensation. To test this last point, methidium–spermine was synthesized: it contains an intercalating methidium head group combined with a polyamine tail. Methidium–spermine is found to cause λ-DNA condensation, but aggregation accompanies condensation, as has been found earlier for spermine and spermidine. Fluorescence and absorption spectra indicate that the methidium group is intercalated when the DNA is condensed, indicating that intercalation need not be incompatible with DNA condensation. The presence of aggregates among the condensed DNA molecules makes this last conclusion tentative.     

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.     

B-S transition in short oligonucleotides

Stretching experiments with long double-stranded DNA molecules in physiological ambient revealed a force-induced transition at a force of 65 pN. During this transition between B-DNA and highly overstretched S-DNA the DNA lengthens by a factor of 1.7 of its B-form contour length. Here, we report the occurrence of this so-called B-S transition in short duplexes consisting of 30 basepairs. We employed atomic-force-microscope-based single molecule force spectroscopy to explore the unbinding mechanism of two short duplexes containing 30 or 20 basepairs by pulling at the opposite 5' termini. For a 30-basepair-long DNA duplex the B-S transition is expected to cause a length increase of 6.3 nm and should therefore be detectable. Indeed 30% of the measured force-extension curves exhibit a region of constant force (plateau) at 65 pN, which corresponds to the B-S transition. The observed plateaus show a length between 3 and 7 nm. This plateau length distribution indicates that the dissociation of a 30-basepair duplex mainly occurs during the B-S transition. In contrast, the measured force-extension curves for a 20-basepair DNA duplex exhibited rupture forces below 65 pN and did not show any evidence of a B-S transition.     

Modeling AFM-induced PEVK extension and the reversible unfolding of Ig/FNIII domains in single and multiple titin molecules

Molecular elasticity is associated with a select number of polypeptides and proteins, such as titin, Lustrin A, silk fibroin, and spider silk dragline protein. In the case of titin, the globular (Ig) and non-globular (PEVK) regions act as extensible springs under stretch; however, their unfolding behavior and force extension characteristics are different. Using our time-dependent macroscopic method for simulating AFM-induced titin Ig domain unfolding and refolding, we simulate the extension and relaxation of hypothetical titin chains containing Ig domains and a PEVK region. Two different models are explored: 1) a series-linked WLC expression that treats the PEVK region as a distinct entropic spring, and 2) a summation of N single WLC expressions that simulates the extension and release of a discrete number of parallel titin chains containing constant or variable amounts of PEVK. In addition to these simulations, we also modeled the extension of a hypothetical PEVK domain using a linear Hooke's spring model to account for "enthalpic" contributions to PEVK elasticity. We find that the modified WLC simulations feature chain length compensation, Ig domain unfolding/refolding, and force-extension behavior that more closely approximate AFM, laser tweezer, and immunolocalization experimental data. In addition, our simulations reveal the following: 1) PEVK extension overlaps with the onset of Ig domain unfolding, and 2) variations in PEVK content within a titin chain ensemble lead to elastic diversity within that ensemble.     

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 DNA condensation and the electrostatic zipper

Sequence-dependent configuration changes and condensation of double-stranded poly(dG-dC).(dG-dC) (GC-DNA) and ds poly(dA-dT).(dA-dT) (AT-DNA) were observed by atomic force microscopy in the presence of Ni(II). Less condensing agent was required to generate configuration changes in GC-DNA as compared to AT-DNA. In the presence of Ni(II) cations, GC-DNA adopted a Z-type conformation and underwent a stepwise condensation, starting with partial intramolecular folding, followed by intermolecular condensation of two to several molecules and ending with the formation of toroids, rods, and jumbles. GC-DNA condensates were unusual in that the most highly condensed regions were surrounded by loops of ds GC-DNA. In contrast, AT-DNA retained its B-type conformation and displayed only minor condensation even at high Ni(II) concentrations. The Ni(II)-dependent differences in condensation between GC-DNA and AT-DNA are predicted by an extension of the electrostatic zipper motif proposed by Kornyshev and Leikin, in which we account for shorter than Debye screening length surface separations between the DNA molecules and for the Ni(II)-induced conformation change of GC-DNA to Z-DNA.     

Why double-stranded RNA resists condensation

The addition of small amounts of multivalent cations to solutions containing double-stranded DNA leads to inter-DNA attraction and eventual condensation. Surprisingly, the condensation is suppressed in double-stranded RNA, which carries the same negative charge as DNA, but assumes a different double helical form. Here, we combine experiment and atomistic simulations to propose a mechanism that explains the variations in condensation of short (25 base-pairs) nucleic acid (NA) duplexes, from B-like form of homopolymeric DNA, to mixed sequence DNA, to DNA:RNA hybrid, to A-like RNA. Circular dichroism measurements suggest that duplex helical geometry is not the fundamental property that ultimately determines the observed differences in condensation. Instead, these differences are governed by the spatial variation of cobalt hexammine (CoHex) binding to NA. There are two major NA-CoHex binding modes—internal and external—distinguished by the proximity of bound CoHex to the helical axis. We find a significant difference, up to 5-fold, in the fraction of ions bound to the external surfaces of the different NA constructs studied. NA condensation propensity is determined by the fraction of CoHex ions in the external binding mode.     

The structural transition of DNA-Tris(1,10-phenanthroline) cobalt(III) complexes in ethanol-water solution

The interaction of DNA with Tris(1,10-phenanthroline) cobalt(III) was studied by means of atomic force microscopy. Changes in the morphologies of DNA complex in the presence of ethanol may well indicate the crucial role of electrostatic force in causing DNA condensation. With the increase of the concentration of ethanol, electrostatic interaction is enhanced corresponding to a lower dielectric constant. Counterions condense along the sugar phosphate backbone of DNA when epsilon is lowered and the phosphate charge density can thus be neutralized to the level of DNA condensation. Electroanalytical measurement of DNA condensed with Co(phen)(3)(3+) in ethanol solution indicated that intercalating reaction remains existing. According to both the microscopic and spectroscopic results, it can be found that no secondary structure transition occurs upon DNA condensing. B-A conformation transition takes place at more than 60% ethanol solution.