Incomplete ion dissociation underlies the weakened attraction between DNA helices at high spermidine concentrations

Treatment of peri-implant mucositis using spermidine and calcium chloride as local adjunctive delivery to non-surgical mechanical debridement: a double-blind randomized controlled clinical trial

OBJECTIVES

To evaluate the effects of non-surgical mechanical debridement with or without adjunctive application of a gel with spermidine and sodium hyaluronate associated to a sealing gel (i.e. calcium chloride) in the treatment of peri-implant mucositis (PiM).

MATERIALS AND METHODS

Forty patients with one implant with PiM were randomly allocated in test and control groups. Test implants were treated with non-surgical mechanical debridement and local unique application of spermidine and calcium chloride gel while control implants were treated using non-surgical mechanical debridement alone. The primary outcome was BOP change. FMPS, FMBS and PD were also assessed. For an Implant the presence of a single bleeding spot (1 site/implant without a continuous line or profuse bleeding) was considered as complete disease resolution.

RESULTS

After 3 months, a statistically significant improvement of all parameters were recorded in each group (p < 0.05). However, no statistically significant differences were found between test and control procedures (p > 0.05). At 3 months, 85% of test implants and 70% of control implants resulted in disease resolution. Residual implants with PiM in control group displayed a greater number of BOP-positive sites when compared with those of test group (p < 0.05).

CONCLUSIONS

Whitin the limitations of the present study, results indicate that the clinical parameters improved following non-surgical mechanical debridement regardless the adjunct of spermidine and calcium chloride gel. Nevertheless complete resolution of PiM was not obtained in both experimental groups.

CLINICAL RELEVANCE

Although no statistically significant differences were found between test and control procedures, the adjunctive application of spermidine and calcium chloride gel to non-surgical mechanical debridement may be considered in order to reduce the number of sites with BOP-positive.

Lifting Hofmeister's Curse: Impact of Cations on Diffusion, Hydrogen Bonding, and Clustering of Water

Water plays a role in the stability, reactivity, and dynamics of the solutes that it contains. The presence of ions alters this capacity by changing the dynamics and structure of water. However, our understanding of how and to what extent this occurs is still incomplete. Here, a study of the low-frequency Raman spectra of aqueous solutions of various cations by using optical Kerr-effect spectroscopy is presented. This technique allows for the measurement of the changes that ions cause in both the diffusive dynamics and the vibrations of the hydrogen-bond structure of water. It is found that when salts are added, some of the water molecules become part of the ion solvation layers, while the rest retain the same diffusional properties as those of pure water. The slowing of the dynamics of the water molecules in the solvation shell of each ion was found to depend on its charge density at infinite dilution conditions and on its position in the Hofmeister series at higher concentrations. It is also observed that all cations weaken the hydrogen-bond structure of the solution and that this weakening depends only on the size of the cation. Finally, evidence is found that ions tend to form amorphous aggregates, even at very dilute concentrations. This work provides a novel approach to water dynamics that can be used to better study the mechanisms of solute nucleation and crystallization, the structural stability of biomolecules, and the dynamic properties of complex solutions, such as water-in-salt electrolytes.

Structure-guided DNA-DNA attraction mediated by divalent cations

Probing the role of surface structure in electrostatic interactions, we report the first observation of sequence-dependent dsDNA condensation by divalent alkaline earth metal cations. Disparate behaviors were found between two repeating sequences with 100% AT content, a poly(A)-poly(T) duplex (AA-TT) and a poly(AT)-poly(TA) duplex (AT-TA). While AT-TA exhibits non-distinguishable behaviors from random-sequence genomic DNA, AA-TT condenses in all alkaline earth metal ions. We characterized these interactions experimentally and investigated the underlying principles using computer simulations. Both experiments and simulations demonstrate that AA-TT condensation is driven by non-specific ion–DNA interactions. Detailed analyses reveal sequence-enhanced major groove binding (SEGB) of point-charged alkali ions as the major difference between AA-TT and AT-TA, which originates from the continuous and close stacking of nucleobase partial charges. These SEGB cations elicit attraction via spatial juxtaposition with the phosphate backbone of neighboring helices, resulting in an azimuthal angular shift between apposing helices. Our study thus presents a distinct mechanism in which, sequence-directed surface motifs act with cations non-specifically to enact sequence-dependent behaviors. This physical insight allows a renewed understanding of the role of repeating sequences in genome organization and regulation and offers a facile approach for DNA technology to control the assembly process of nanostructures.

Influence of Microscopic Interactions on the Flexible Mechanical Properties of Viral DNA

During the packaging and ejection of viral DNA, its mechanical properties play an essential role in viral infection. Some of these mechanical properties originate from different microscopic interactions of the encapsulated DNA in the capsid. Based on an updated mesoscopic model of the interaction potential by Parsegian et al., an alternative continuum elastic model of the free energy of the confined DNA in the capsid is developed in this work. With this model, we not only quantitatively identify the respective contributions from hydration repulsion, electrostatic repulsion, entropy and elastic bending but also predict the ionic effect of viral DNA's mechanical properties during the packaging and ejection. The relevant predictions are quantitively or qualitatively consistent with the existing experimental results. Furthermore, the nonmonotonous or monotonous changes in the respective contributions of microscopic interactions to the ejection force and free energy at different ejection stages are revealed systematically. Among these, the nonmonotonicity in the entropic contribution implies a transition of viral DNA structure from order to disorder during the ejection.

The Mixing Counterion Effect on DNA Compaction and Charge Neutralization at Low Ionic Strength

DNA compaction and charge neutralization in a mixing counterion solution involves competitive and cooperative electrostatic binding, and sometimes counterion complexation. At normal ionic strength, it has been found that the charge neutralization of DNA by the multivalent counterion is suppressed when being added extra mono- and di-valent counterions. Here, we explore the effect mixing counterion on DNA compaction and charge neutralization under the condition of low ionic strength. Being quite different from normal ionic strength, the electrophoretic mobility of DNA in multivalent counterion solution (octalysine, spermine) increases the presence of mono- and di-valent cations, such as sodium and magnesium ions. It means that the charge neutralization of DNA by the multivalent counterion is promoted rather than suppressed when introducing extra mono- and di-valent counterions into solution. This conclusion is also supported by the measurement of condensing and unraveling forces of DNA condensates under the same condition by single molecular magnetic tweezers. This mixing effect can be attributed to the cooperative electrostatic binding of counterions to DNA when the concentration of counterions in solution is below a critical concentration.

Order and interactions in DNA arrays: Multiscale molecular dynamics simulation

While densely packed DNA arrays are known to exhibit hexagonal and orthorhombic local packings, the detailed mechanism governing the associated phase transition remains rather elusive. Furthermore, at high densities the atomistic resolution is paramount to properly account for fine details, encompassing the DNA molecular order, the contingent ordering of counterions and the induced molecular ordering of the bathing solvent, bringing together electrostatic, steric, thermal and direct hydrogen-bonding interactions, resulting in the observed osmotic equation of state. We perform a multiscale simulation of dense DNA arrays by enclosing a set of 16 atomistically resolved DNA molecules within a semi-permeable membrane, allowing the passage of water and salt ions, and thus mimicking the behavior of DNA arrays subjected to external osmotic stress in a bathing solution of monovalent salt and multivalent counterions. By varying the DNA density, local packing symmetry, and counterion type, we obtain osmotic equation of state together with the hexagonal-orthorhombic phase transition, and full structural characterization of the DNA subphase in terms of its positional and angular orientational fluctuations, counterion distributions, and the solvent local dielectric response profile with its order parameters that allow us to identify the hydration force as the primary interaction mechanism at high DNA densities.

The effect of pH on charge inversion and condensation of DNA

Charge inversion and condensation of DNA in solutions of trivalent and quadrivalent counterions are significantly influenced by the pH value of the solution. We systematically investigated the condensation and charge compensation of DNA by spermidine, hexammine cobalt(iii) (cohex, [Co(NH3)6](3+)) and spermine in solutions of a wide range of pH values from 3 to 9.3 by dynamic light scattering, magnetic tweezers, and atomic force microscopy. In trivalent counterion solution, we found that there is a critical concentration (0.75 mM for cohex and 0.5 mM for spermidine), under which the electrophoresis mobility of DNA initially increases, reaches a maximum, and finally decreases when the pH value is decreased. In contrast, above the critical concentration, the electrophoretic mobility of DNA increases monotonously with decreasing pH value of the solution. The corresponding condensing force has the same dependence on the pH value. However, for the case of quadrivalent counterions, the electrophoretic mobility of DNA is monotonously promoted by lowering the pH value of the solution at any concentration of counterions in which charge inversion of DNA may occur. In atomic force microscopy images and force spectroscopy of magnetic tweezers, we found that maximal charge neutralization and condensation force correspond to the most compact DNA condensation. We propose a mechanism of promoting DNA charge neutralization: small and highly mobile hydrogen ions tend to attach to the DNA-counterion complex to further neutralize its remaining charge, which is related to the surface area of the complex. Therefore, this further neutralization is prominent when the complex is toroidal which corresponds to the case of mild ion concentration while it is less prominent for more compact globules or rod complexes at high counterion concentration.

Ionic switch controls the DNA state in phage λ

We have recently found that DNA packaged in phage λ undergoes a disordering transition triggered by temperature, which results in increased genome mobility. This solid-to-fluid like DNA transition markedly increases the number of infectious λ particles facilitating infection. However, the structural transition strongly depends on temperature and ionic conditions in the surrounding medium. Using titration microcalorimetry combined with solution X-ray scattering, we mapped both energetic and structural changes associated with transition of the encapsidated λ-DNA. Packaged DNA needs to reach a critical stress level in order for transition to occur. We varied the stress on DNA in the capsid by changing the temperature, packaged DNA length and ionic conditions. We found striking evidence that the intracapsid DNA transition is 'switched on' at the ionic conditions mimicking those in vivo and also at the physiologic temperature of infection at 37°C. This ion regulated on-off switch of packaged DNA mobility in turn affects viral replication. These results suggest a remarkable adaptation of phage λ to the environment of its host bacteria in the human gut. The metastable DNA state in the capsid provides a new paradigm for the physical evolution of viruses.

DNA under Force: Mechanics, Electrostatics, and Hydration

Quantifying the basic intra- and inter-molecular forces of DNA has helped us to better understand and further predict the behavior of DNA. Single molecule technique elucidates the mechanics of DNA under applied external forces, sometimes under extreme forces. On the other hand, ensemble studies of DNA molecular force allow us to extend our understanding of DNA molecules under other forces such as electrostatic and hydration forces. Using a variety of techniques, we can have a comprehensive understanding of DNA molecular forces, which is crucial in unraveling the complex DNA functions in living cells as well as in designing a system that utilizes the unique properties of DNA in nanotechnology.

Multivalent ion screening of charged glass surface studied by streaming potential measurements

We used streaming potential technique to measure ζ potentials for glass as a function of Co(NH3)6Cl3 concentration, KCl concentration, and pH. Charge inversion was observed only at high surface charge densities and was inhibited by increased KCl concentration. Measured ζ potentials were compared with predictions from a recent theory by dos Santos et al. [J. Chem. Phys. 132, 104105 (2010)] that models multivalent ions adsorbed to the charged surface as a strong coupled liquid (SCL). The location of shear plane was determined independent of the SCL theory, allowing a rigorous experimental test of the theory with no fitting parameters. We found that SCL predictions agree quantitatively with our experimental data.

Ion competition in condensed DNA arrays in the attractive regime

Physical origin of DNA condensation by multivalent cations remains unsettled. Here, we report quantitative studies of how one DNA-condensing ion (Cobalt(3+) Hexammine, or Co(3+)Hex) and one nonDNA-condensing ion (Mg(2+)) compete within the interstitial space in spontaneously condensed DNA arrays. As the ion concentrations in the bath solution are systematically varied, the ion contents and DNA-DNA spacings of the DNA arrays are determined by atomic emission spectroscopy and x-ray diffraction, respectively. To gain quantitative insights, we first compare the experimentally determined ion contents with predictions from exact numerical calculations based on nonlinear Poisson-Boltzmann equations. Such calculations are shown to significantly underestimate the number of Co(3+)Hex ions, consistent with the deficiencies of nonlinear Poisson-Boltzmann approaches in describing multivalent cations. Upon increasing the concentration of Mg(2+), the Co(3+)Hex-condensed DNA array expands and eventually redissolves as a result of ion competition weakening DNA-DNA attraction. Although the DNA-DNA spacing depends on both Mg(2+) and Co(3+)Hex concentrations in the bath solution, it is observed that the spacing is largely determined by a single parameter of the DNA array, the fraction of DNA charges neutralized by Co(3+)Hex. It is also observed that only ∼20% DNA charge neutralization by Co(3+)Hex is necessary for spontaneous DNA condensation. We then show that the bath ion conditions can be reduced to one variable with a simplistic ion binding model, which is able to describe the variations of both ion contents and DNA-DNA spacings reasonably well. Finally, we discuss the implications on the nature of interstitial ions and cation-mediated DNA-DNA interactions.

Reentrant condensation, liquid–liquid phase separation and crystallization in protein solutions induced by multivalent metal ions

We briefly summarize the recent progress in tuning protein interactions as well as phase behavior in protein solutions using multivalent metal ions. We focus on the influence of control parameters and the mechanism of reentrant condensation, the metastable liquid–liquid phase separation and classical vs. non-classical pathways of protein crystallization.

Intermolecular forces between low generation PAMAM dendrimer condensed DNA helices: role of cation architecture

In recent years, dendriplexes, complexes of cationic dendrimers with DNA, have become attractive DNA delivery vehicles due to their well-defined chemistries. To better understand the nature of the forces condensing dendriplexes, we studied low generation poly(amidoamine) (PAMAM) dendrimer-DNA complexes and compared them to comparably charged linear arginine peptides. Using osmotic stress coupled with X-ray scattering, we have investigated the effect of molecular chain architecture on DNA-DNA intermolecular forces that determine the net attraction and equilibrium interhelical distance within these polycation condensed DNA arrays. In order to compact DNA, linear cations are believed to bind in DNA grooves and to interact with the phosphate backbone of apposing helices. We have previously shown a length dependent attraction resulting in higher packaging densities with increasing charge for linear cations. Hyperbranched polycations, such as polycationic dendrimers, presumably would not be able to bind to DNA and correlate their charges in the same manner as linear cations. We show that attractive and repulsive force amplitudes in PAMAM-DNA assemblies display significantly different trends than comparably charged linear arginines resulting in lower DNA packaging densities with increasing PAMAM generation. The salt and pH dependencies of packaging in PAMAM dendrimer-DNA and linear arginine-DNA complexes were also investigated. Significant differences in the force curve behaviour and salt and pH sensitivities suggest that different binding modes may be present in DNA condensed by dendrimers when compared to linear polycations.

A comparison of DNA compaction by arginine and lysine peptides: a physical basis for arginine rich protamines

Protamines are small, highly positively charged peptides used to package DNA at very high densities in sperm nuclei. Tight DNA packing is considered essential for the minimization of DNA damage by mutagens and reactive oxidizing species. A striking and general feature of protamines is the almost exclusive use of arginine over lysine for the positive charge to neutralize DNA. We have investigated whether this preference for arginine might arise from a difference in DNA condensation by arginine and lysine peptides. The forces underlying DNA compaction by arginine, lysine, and ornithine peptides are measured using the osmotic stress technique coupled with X-ray scattering. The equilibrium spacings between DNA helices condensed by lysine and ornithine peptides are significantly larger than the interhelical distances with comparable arginine peptides. The DNA surface-to-surface separation, for example, is some 50% larger with polylysine than with polyarginine. DNA packing by lysine rich peptides in sperm nuclei would allow much greater accessibility to small molecules that could damage DNA. The larger spacing with lysine peptides is caused by both a weaker attraction and a stronger short-range repulsion relative to that of the arginine peptides. A previously proposed model for binding of polyarginine and protamine to DNA provides a convenient framework for understanding the differences between the ability of lysine and arginine peptides to assemble DNA.

DNA bending-induced phase transition of encapsidated genome in phage λ

The DNA structure in phage capsids is determined by DNA-DNA interactions and bending energy. The effects of repulsive interactions on DNA interaxial distance were previously investigated, but not the effect of DNA bending on its structure in viral capsids. By varying packaged DNA length and through addition of spermine ions, we transform the interaction energy from net repulsive to net attractive. This allowed us to isolate the effect of bending on the resulting DNA structure. We used single particle cryo-electron microscopy reconstruction analysis to determine the interstrand spacing of double-stranded DNA encapsidated in phage λ capsids. The data reveal that stress and packing defects, both resulting from DNA bending in the capsid, are able to induce a long-range phase transition in the encapsidated DNA genome from a hexagonal to a cholesteric packing structure. This structural observation suggests significant changes in genome fluidity as a result of a phase transition affecting the rates of viral DNA ejection and packaging.

Evidence for water structuring forces between surfaces

Structured water on apposing surfaces can generate significant energies due to reorganization and displacement of water as the surfaces encounter each other. Force measurements on a multitude of biological structures using the osmotic stress technique have elucidated commonalities that point toward an underlying hydration force. In this review, the forces of two contrasting systems are considered in detail: highly charged DNA and nonpolar, uncharged hydroxypropyl cellulose. Conditions for both net repulsion and attraction, along with the measured exclusion of chemically different solutes from these macromolecular surfaces, are explored and demonstrate common features consistent with a hydration force origin. Specifically, the observed interaction forces can be reduced to the effects of perturbing structured surface water.

Salt effects on condensed protamine-DNA assemblies: anion binding and weakening of attraction

Using osmotic stress coupled with X-ray scattering, we have directly examined the salt sensitivity of the intermolecular forces between helices in condensed protamine-DNA arrays. Thermodynamic forces are measured from the dependence of DNA helical interaxial spacings on external salt concentration or the osmotic pressure applied by neutral polymer solutions in equilibrium with the condensed phase. Force curves of salmon protamine-DNA condensates are highly dependent on salt species and concentration, indicating salt binding to protamine-DNA complexes. This dependence of the forces on salt species follows the Hofmeister series for anions. Chaotropic anions bind more tightly to protamine-DNA arrays than kosmotropic anions, thus more greatly disrupting the attractive thermodynamic forces. Variations with cation type are small compared with those observed for anions. Further, osmotic stress is used to estimate the number of ions bound in the condensed phase through a Gibbs-Duhem relationship. We estimate that at equilibrium, ∼1 Br(-) is bound per protamine molecule at 200 mM NaBr concentration. Remarkably, this one bound anion results in a change of ∼12% in the surface-to-surface distance between DNA helices. Potential biological implications of this attractive force salt sensitivity are discussed.

Salt has a biphasic effect on the higher-order structure of a DNA-protamine complex

We observed single DNA molecules by fluorescence microscopy to clarify the effect of protamine on their higher-order structure. With an increase in the protamine concentration, the conformation of DNA molecules changes from an elongated coil state to a compact state through an intermediate state. Furthermore, the long-axis length of DNA gradually decreases while maintaining a distribution profile with a single peak. Such behavior is markedly different from the conformational transition of DNA induced by small polyamines such as spermidine and spermine, where individual DNA molecules exhibit an all-or-none transition from a coil to a globule state and the size distribution is characterized by twin peaks around the transition region. Next, we examined the effect of salt on the conformation of the DNA-protamine complex. Interestingly, at a fixed concentration of protamine, DNA tends to shrink with an increase in the NaCl concentration up to 300 mM, and then swells with a further increase in the NaCl concentration, that is, biphasic behavior is generated depending on the salt concentration. For comparison, we examined the effect of salt on DNA compaction induced by the trivalent polyamine spermidine. We confirmed that salt always has an inhibitory effect on spermine-induced compaction. To clarify this biphasic effect of salt on protamine-induced DNA compaction, we performed a numerical simulation on a negatively charged semiflexible polyelectrolyte in the presence of polycations with relatively large numbers of positive charges by taking into account the effect of salt at different concentrations. The results showed that salt promotes compaction up to a certain concentration and then tends to unfold the polyelectrolyte chain, which reproduced the experimental observation in a semiquantitative manner. This biphasic effect is discussed in relation to the specific shielding effect that depends on the salt concentration.

Physics of DNA: unravelling hidden abilities encoded in the structure of ‘the most important molecule’

A comprehensive article “Structure and Interactions of Biological Helices”, published in 2007 in Reviews of Modern Physics, overviewed various aspects of the effect of DNA structure on DNA–DNA interactions in solution and related phenomena, with a thorough analysis of the theory of these effects. Here, an updated qualitative account of this area is presented without any sophisticated ‘algebra’. It overviews the basic principles of the structure-specific interactions between double-stranded DNA and focuses on the physics behind several related properties encoded in the structure of DNA. Among them are (i) DNA condensation and aptitude to pack into small compartments of cells or viral capcids, (ii) the structure of DNA mesophases, and (iii) the ability of homologous genes to recognize each other prior to recombination from a distance. Highlighted are some of latest developments of the theory, including the shape of the ‘recognition well’. The article ends with a brief discussion of the first experimental evidence of the protein-free homology recognition in a ‘test tube’.

Cation charge dependence of the forces driving DNA assembly

Understanding the strength and specificity of interactions among biologically important macromolecules that control cellular functions requires quantitative knowledge of intermolecular forces. Controlled DNA condensation and assembly are particularly critical for biology, with separate repulsive and attractive intermolecular forces determining the extent of DNA compaction. How these forces depend on the charge of the condensing ion has not been determined, but such knowledge is fundamental for understanding the basis of DNA-DNA interactions. Here, we measure DNA force-distance curves for a homologous set of arginine peptides. All forces are well fit as the sum of two exponentials with 2.4- and 4.8-Å decay lengths. The shorter-decay-length force is always repulsive, with an amplitude that varies slightly with length or charge. The longer-decay-length force varies strongly with cation charge, changing from repulsion with Arg¹ to attraction with Arg². Force curves for a series of homologous polyamines and the heterogeneous protein protamine are quite similar, demonstrating the universality of these forces for DNA assembly. Repulsive amplitudes of the shorter-decay-length force are species-dependent but nearly independent of charge within each species. A striking observation was that the attractive force amplitudes for all samples collapse to a single curve, varying linearly with the inverse of the cation charge.

Salt-dependent DNA-DNA spacings in intact bacteriophage λ reflect relative importance of DNA self-repulsion and bending energies

Using solution synchrotron x-ray scattering, we measure the variation of DNA-DNA d spacings in bacteriophage λ with mono-, di-, and polyvalent salt concentrations, for wild-type [48.5×10(3) base pairs (bp)] and short-genome-mutant (37.8 kbp) strains. From the decrease in d spacings with increasing salt, we deduce the relative contributions of DNA self-repulsion and bending to the energetics of packaged phage genomes. We quantify the DNA-DNA interaction energies within the intact phage by combining the measured d spacings in the capsid with measurements of osmotic pressure in DNA assemblies under the same salt conditions in bulk solution. In the commonly used Tris-Mg buffer, the DNA-DNA interaction energies inside the phage capsids are shown to be about 1kT/bp, an order of magnitude larger than the bending energies.

Universality of protein reentrant condensation in solution induced by multivalent metal ions

The effective interactions and phase behavior of protein solutions under strong electrostatic coupling conditions are difficult to understand due to the complex charge pattern and irregular geometry of protein surfaces. This distinguishes them from related systems such as DNA or conventional colloids. In this work, we discuss the question of universality of the reentrant condensation (RC) of proteins in solution induced by multivalent counterions, i.e., redissolution on adding further salts after phase separation, as recently discovered (Zhang et al., Phys Rev Lett 2008; 101:148101). The discussion is based on a systematic investigation of five different proteins with different charge patterns and five different multivalent counterions. Zeta potential measurements confirm the effective charge inversion of proteins in the reentrant regime via binding of multivalent counterions, which is supported by Monte Carlo simulations. Charge inversion by trivalent cations requires an overall negative net charge of the protein. Statistical analysis of a representative set of protein sequences reveals that, in theory, this effect could be possible for about half of all proteins. Our results can be exploited for the control of the phase behavior of proteins, in particular facilitating protein crystallization.

Undulations enhance the effect of helical structure on DNA interactions

During the past decade, theory and experiments have provided clear evidence that specific helical patterns of charged groups and adsorbed (condensed) counterions on the DNA surface are responsible for many important features of DNA-DNA interactions in hydrated aggregates. The effects of helical structure on DNA-DNA interactions result from a preferential juxtaposition of the negatively charged sugar phosphate backbone with counterions bound within the grooves of the opposing molecule. Analysis of X-ray diffraction experiments confirmed the mutual alignment of parallel molecules in hydrated aggregates required for such juxtaposition. However, it remained unclear how this alignment and molecular interactions might be affected by intrinsic and thermal fluctuations, which cause structural deviations away from an ideal double helical conformation. We previously argued that the torsional flexibility of DNA allows the molecules to adapt their structure to accommodate a more electrostatically favorable alignment between molecules, partially compensating disruptive fluctuation effects. In the present work, we develop a more comprehensive theory, incorporating also stretching and bending fluctuations of DNA. We found the effects of stretching to be qualitatively and quantitatively similar to those of twisting fluctuations. However, this theory predicts more dramatic and surprising effects of bending. Undulations of DNA in hydrated aggregates strongly amplify rather than weaken the helical structure effects. They enhance the structural adaptation, leading to better alignment of neighboring molecules and pushing the geometry of the DNA backbone closer to that of an ideal helix. These predictions are supported by a quantitative comparison of the calculated and measured osmotic pressures in DNA.

Condensed DNA: condensing the concepts

DNA is stored in vivo in a highly compact, so-called condensed phase, where gene regulatory processes are governed by the intricate interplay between different states of DNA compaction. These systems often have surprising properties, which one would not predict from classical concepts of dilute solutions. The mechanistic details of DNA packing are essential for its functioning, as revealed by the recent developments coming from biochemistry, electrostatics, statistical mechanics, and molecular and cell biology. Different aspects of condensed DNA behavior are linked to each other, but the links are often hidden in the bulk of experimental and theoretical details. Here we try to condense some of these concepts and provide interconnections between the different fields. After a brief description of main experimental features of DNA condensation inside viruses, bacteria, eukaryotes and the test tube, main theoretical approaches for the description of these systems are presented. We end up with an extended discussion of the role of DNA condensation in the context of gene regulation and mention potential applications of DNA condensation in gene therapy and biotechnology.

Electrostatics of strongly charged biological polymers: ion-mediated interactions and self-organization in nucleic acids and proteins

Charges on biological polymers in physiologically relevant solution conditions are strongly screened by water and salt solutions containing counter-ions. However, the entropy of these counterions can result in surprisingly strong interactions between charged objects in water despite short screening lengths, via coupling between osmotic and electrostatic interactions. Widespread work in theory, experiment, and computation has been carried out to gain a fundamental understanding of the rich, yet sometimes counterintuitive, behavior of these polyelectrolyte systems. Examples of polyelectrolyte association in biology include DNA packaging and RNA folding, as well as aggregation and self-organization phenomena in different disease states.

A molecular simulation probing of structure and interaction for supramolecular sodium dodecyl sulfate/single-wall carbon nanotube assemblies

Here we report a larger-scale atomic-level molecular dynamics (MD) simulation for the self-assembly of sodium dodecyl sulfate (SDS) surfactant on single-walled carbon nanotube (SWNT) surfaces and the interaction between supramolecular SDS/SWNT aggregates. We make an effort to address several important problems in regard to carbon nanotube dispersion/separation. At first, the simulation provides comprehensive direct evidence for SDS self-assembly structures on carbon nanotube surfaces, which can help to clarify the relevant debate over the exact adsorption structure. We also, for the first time, simulated the potential of mean force (PMF) between two SWNTs embedded in SDS surfactant micelles. A novel unified PMF approach has been applied to reveal various cooperative interactions between the SDS/SWNT aggregates, which is different from the previous electrostatic repulsion explanation. The unique role of sodium ions revealed here provides a new microscopic understanding of the recent experiments in the electrolyte tuning of the interfacial forces on the selective fractionation of SDS surrounding SWNTs.

DNA stretching and multivalent-cation-induced condensation

Motivated by measurements on stretched double-stranded DNA in the presence of multivalent cations, we develop a statistical mechanical model for the compaction of an insoluble semiflexible polymer under tension. Using a mean-field approach, we determine the order of the extended-to-compact transition and provide an interpretation for the magnitude and interval of tensions over which compaction takes place. In the simplest thermodynamic limit of an infinitely long homogeneous polymer, compaction is a first-order transition that occurs at a single value of tension. For finite length chains or for heterogeneous polymers, the transition progresses over an interval of tension. Our theory provides an interpretation for the result of single-molecule experiments in terms of microscopic parameters such as persistence length and free energy of condensation.

Abrupt transition from a free, repulsive to a condensed, attractive DNA phase, induced by multivalent polyamine cations

We have investigated the energetics of DNA condensation by multivalent polyamine cations. Solution small angle x-ray scattering was used to monitor interactions between short 25 base pair dsDNA strands in the free supernatant DNA phase that coexists with the condensed DNA phase. Interestingly, when tetravalent spermine is used, significant inter-DNA repulsion is observed in the free phase, in contrast with the presumed inter-DNA attraction in the coexisting condensed phase. DNA condensation thus appears to be a discrete, first-order-like, transition from a repulsive gaseous to an attractive condensed solid phase, in accord with the reported all-or-none condensation of giant DNA. We further quantify the electrostatic repulsive potentials in the free DNA phase and estimate the number of additional spermine cations that bind to DNA upon condensation.

DNA attraction in monovalent and divalent electrolytes

The dependence of the effective force on the distance between two DNA molecules was directly computed from a set of extensive all-atom molecular dynamics simulations. The simulations revealed that in a monovalent electrolyte the effective force is repulsive at short and long distances but can be attractive in the intermediate range. This attractive force is, however, too weak (approximately 5 pN per turn of a DNA helix) to induce DNA condensation in the presence of thermal fluctuations. In divalent electrolytes, DNA molecules were observed to form a bound state, where Mg(2+) ions bridged minor groves of DNA. The effective force in divalent electrolytes was predominantly attractive, reaching a maximum of 42 pN per one turn of a DNA helix.

Mono- and trivalent ions around DNA: a small-angle scattering study of competition and interactions

The presence of small numbers of multivalent ions in DNA-containing solutions results in strong attractive forces between DNA strands. Despite the biological importance of this interaction, e.g., DNA condensation, its physical origin remains elusive. We carried out a series of experiments to probe interactions between short DNA strands as small numbers of trivalent ions are included in a solution containing DNA and monovalent ions. Using resonant (anomalous) and nonresonant small angle x-ray scattering, we coordinated measurements of the number and distribution of each ion species around the DNA with the onset of attractive forces between DNA strands. DNA-DNA interactions occur as the number of trivalent ions increases. Surprisingly good agreement is found between data and size-corrected numerical Poisson-Boltzmann predictions of ion competition for non- and weakly interacting DNAs. We also obtained an estimate for the minimum number of trivalent ions needed to initiate DNA-DNA attraction.

Attractive forces between cation condensed DNA double helices

By combining single-molecule magnetic tweezers and osmotic stress on DNA assemblies, we separate attractive and repulsive components of the total intermolecular interaction between multivalent cation condensed DNA. Based on measurements of several different cations, we identify two invariant properties of multivalent cation-mediated DNA interactions: repulsive forces decay exponentially with a 2.3 +/- 0.1 A characteristic decay length and the attractive component of the free energy is always 2.3 +/- 0.2 times larger than the repulsive component of the free energy at force-balance equilibrium. These empirical constraints are not consistent with current theories that attribute DNA-DNA attractions to a correlated lattice of counterions. The empirical constraints are consistent with theories for Debye-Hückel interactions between helical line charges and with the order-parameter formalism for hydration forces. Each of these theories posits exponentially decaying attractions and, if we assume this form, our measurements indicate a cation-independent, 4.8 +/- 0.5 A characteristic decay length for intermolecular attractions between condensed DNA molecules.

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.

Effects of salt concentrations and bending energy on the extent of ejection of phage genomes

Recent work has shown that pressures inside dsDNA phage capsids can be as high as many tens of atmospheres; it is this pressure that is responsible for initiation of the delivery of phage genomes to host cells. The forces driving ejection of the genome have been shown to decrease monotonically as ejection proceeds, and hence to be strongly dependent on the genome length. Here we investigate the effects of ambient salts on the pressures inside phage-lambda, for the cases of mono-, di-, and tetravalent cations, and measure how the extent of ejection against a fixed osmotic pressure (mimicking the bacterial cytoplasm) varies with cation concentration. We find, for example, that the ejection fraction is halved in 30 mM Mg(2+) and is decreased by a factor of 10 upon addition of 1 mM spermine. These effects are calculated from a simple model of genome packaging, using DNA-DNA repulsion energies as determined independently from x-ray diffraction measurements on bulk DNA solutions. By comparing the measured ejection fractions with values implied from the bulk DNA solution data, we predict that the bending energy makes the d-spacings inside the capsid larger than those for bulk DNA at the same osmotic pressure.

Aggregation and adsorption at the air-water interface of bacteriophage phiX174 single-stranded DNA

We study the phase behavior of phage phiX174 single-stranded DNA in very dilute solutions in the presence of monovalent and multivalent salts, in both water (H(2)O) and heavy water (D(2)O). DNA solubility depends on the nature of the salts, their concentrations, and the nature of the solvent. The appearance of attractive interactions between the monomers of the DNA chains in the bulk of the solution is correlated with an adsorption of the chains at the air-water interface. We characterize this correlation in two types of aggregation processes: the condensation of DNA induced by the trivalent cation spermidine and its salting out in the presence of high concentrations (molar and above) of monovalent (sodium) cations, both in water and in heavy water. The overall solubility of single-stranded DNA is decreased in D(2)O compared to H(2)O, pointing to a role of DNA hydration in addition to electrostatic factors in the observed phase separations. DNA adsorption involves attractive van der Waals forces, and these forces are also operating in the bulk aggregation process.

Electrostatic free energy landscapes for nucleic acid helix assembly

Metal ions are crucial for nucleic acid folding. From the free energy landscapes, we investigate the detailed mechanism for ion-induced collapse for a paradigm system: loop-tethered short DNA helices. We find that Na+ and Mg2+ play distinctive roles in helix-helix assembly. High [Na+] (>0.3 M) causes a reduced helix-helix electrostatic repulsion and a subsequent disordered packing of helices. In contrast, Mg2+ of concentration >1 mM is predicted to induce helix-helix attraction and results in a more compact and ordered helix-helix packing. Mg2+ is much more efficient in causing nucleic acid compaction. In addition, the free energy landscape shows that the tethering loops between the helices also play a significant role. A flexible loop, such as a neutral loop or a polynucleotide loop in high salt concentration, enhances the close approach of the helices in order to gain the loop entropy. On the other hand, a rigid loop, such as a polynucleotide loop in low salt concentration, tends to de-compact the helices. Therefore, a polynucleotide loop significantly enhances the sharpness of the ion-induced compaction transition. Moreover, we find that a larger number of helices in the system or a smaller radius of the divalent ions can cause a more abrupt compaction transition and a more compact state at high ion concentration, and the ion size effect becomes more pronounced as the number of helices is increased.

Charge inversion at high ionic strength studied by streaming currents

We report charge inversion, the sign reversal of the effective surface charge in the presence of multivalent counterions, for the biologically relevant regimes of divalent ions and mixtures of monovalent and multivalent ions. Using streaming currents, the pressure-driven transport of countercharges in the diffuse layer, we find that charge inversion occurs in rectangular silica nanochannels at high concentrations of divalent ions. Strong monovalent screening is found to cancel charge inversion, restoring the original surface charge polarity. An analytical model based on ion correlations successfully describes our observations.

Overview of the structure of all-AT oligonucleotides: organization in helices and packing interactions

We present the crystalline organization of 33 all-AT deoxyoligonucleotide duplexes, studied by x-ray diffraction. Most of them have very similar structures, with Watson-Crick basepairs and a standard average twist close to 36 degrees. The molecules are organized as parallel columns of stacked duplexes in a helical arrangement. Such organization of duplexes is very regular and repetitive: all sequences show the same pattern. It is mainly determined by the stacking of the terminal basepairs, so that the twist in the virtual TA base step between neighbor duplexes is always negative, approximately -22 degrees. The distance between the axes of parallel columns is practically identical in all cases, approximately 26 A. Interestingly, it coincides with that found in DNA viruses and fibers in their hexagonal phase. It appears to be a characteristic distance for ordered parallel DNA molecules. This feature is due to the absence of short range intermolecular forces, which are usually due to the presence of CG basepairs at the end of the oligonucleotide sequence. The duplexes apparently interact only through their diffuse ionic atmospheres. The results obtained can thus be considered as intermediate between liquid crystals, fibers, and standard crystal structures. They provide new information on medium range DNA-DNA interactions.

Ion-mediated nucleic acid helix-helix interactions

Salt ions are essential for the folding of nucleic acids. We use the tightly bound ion (TBI) model, which can account for the correlations and fluctuations for the ions bound to the nucleic acids, to investigate the electrostatic free-energy landscape for two parallel nucleic acid helices in the solution of added salt. The theory is based on realistic atomic structures of the helices. In monovalent salt, the helices are predicted to repel each other. For divalent salt, while the mean-field Poisson-Boltzmann theory predicts only the repulsion, the TBI theory predicts an effective attraction between the helices. The helices are predicted to be stabilized at an interhelix distance approximately 26-36 A, and the strength of the attractive force can reach -0.37 k(B)T/bp for helix length in the range of 9-12 bp. Both the stable helix-helix distance and the strength of the attraction are strongly dependent on the salt concentration and ion size. With the increase of the salt concentration, the helix-helix attraction becomes stronger and the most stable helix-helix separation distance becomes smaller. For divalent ions, at very high ion concentration, further addition of ions leads to the weakening of the attraction. Smaller ion size causes stronger helix-helix attraction and stabilizes the helices at a shorter distance. In addition, the TBI model shows that a decrease in the solvent dielectric constant would enhance the ion-mediated attraction. The theoretical findings from the TBI theory agree with the experimental measurements on the osmotic pressure of DNA array as well as the results from the computer simulations.