Attraction between DNA molecules mediated by multivalent ions

Ion correlation-driven like-charge attraction in multivalent salt solutions

The electrostatic double layer force is key to determining the stability and self-assembly of charged colloids and many other soft matter systems. Fully understanding the attractive force between two like-charged surfaces remains a great challenge. Here, we apply the modified Gaussian renormalized fluctuation theory to study ion correlation-driven like-charge attraction in multivalent salt solutions. The effects of spatially varying ion correlations on the structure of overlapping double layers and their free energy are self-consistently accounted for. In the presence of multivalent salts, increasing surface charge or counterion valency leads to a short-range attraction. We demonstrate that although both overcharging and like-charge attraction are outcomes of ion correlation, there is no causal relationship between them. Our theory also captures the non-monotonic dependence of like-charge attraction on multivalent salt concentration. The reduction of attraction at high salt concentrations could be a contributing factor toward the reentrant stability of charged colloidal suspensions. Our theoretical predictions are consistent with the observations reported in experiments and simulations.

Structural correlations in highly asymmetric binary charged colloidal mixtures

We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles.

Effect of mono- and multi-valent ionic environments on the in-lattice nanoparticle-grafted single-stranded DNA

Polyelectrolyte (PE) chains respond in a complex manner to multivalent salt environments, and this behavior depends on pH, temperature, and the presence of specific counter ions. Although much work has been done to understand the behaviour of free PE chains, it is important to reveal their behaviour on a nanoparticle's surface, where surface constraints, particle geometry, and multi-chain environment can affect their behaviour and contribute to particles' assembly states. Our work investigates, using in situ small-angle X-ray scattering (SAXS), the morphology of PE (single-stranded DNA) chains grafted onto the surface of spherical gold nanoparticles assembled in a lattice in the presence of monovalent, divalent and trivalent salts. For divalent salts, the DNA brush length was found to decrease at a faster rate with salt concentration than in the monovalent salt environment, while trivalent salts led to chain collapse. Using a power law analysis and the modified Daoud-Cotton model, we have obtained insight into the mechanism of a nanoparticle-grafted chain's response to ionic environments. Our analysis suggests that the decrease in brush length is due to the conventional electrostatic screening for monovalent systems, whereas for divalent systems both electrostatic screening and divalent ion bridging must be considered.

Dendritic polyelectrolytes with monovalent and divalent counterions: the charge regulation effect and counterion release

The charge regulation and the release of counterions are extremely important and substantial in determining the charge state of polyelectrolytes and the interaction between polyelectrolytes and proteins. Going beyond monovalent to multivalent cations, it is well-known that the effects of ions are qualitatively different. Therefore, the well-accepted descriptions of the charge regulation and the counterion release based on monovalent ions do not immediately apply to systems with multivalent ions. Here, we study the key structural and electrostatic features of charged dendrimers at hand of the pharmaceutically important dendritic polyglycerol sulfate (dPGS) macromolecule equilibrated with monovalent and divalent salts by molecular dynamics (MD) simulations. Following a simple but accurate scheme to determine its effective radius, the counterion condensed layer of the dPGS is determined with high accuracy and we observe the sequential replacement of condensed monovalent cations (MCs) to divalent cations (DCs) rendering a smaller dPGS effective charge versus the DC concentration. We resolve and track the release of counterions on the dPGS along its binding pathway with the plasma protein Human Serum Albumin (HSA). We find that the release of MCs remains favorable for the complexation leading to a considerable amount of release entropy as the driving force for complexation. The release of DCs only occurs above a certain DC concentration with a comparably smaller number of released ions than MCs. Its contribution to the binding free energy is small indicating a subtle cancellation between the entropy gain in releasing DCs and the enthalpy penalty from dissociating DCs from the dendrimer.

Multivalent counterions induced attraction between DNA polyelectrolytes

In this paper we study the electrostatic attraction between two parallel rodlike DNA polyelectrolytes induced by neutralizing multivalent counterions at the zero temperature limit. The counterions crystallize on the charged surfaces of DNA so that we can handle the system by using the Wigner crystal lattice model. We derived the 3D ground state configuration of counterions with minimized energy by use of the gradient descent method, and calculated the interaction between two DNA cylinders with divalent or trivalent counterions when they approach. The results show that the complex ground state configuration of counterions plays a key role in determining the caused attraction. The counterions form three-dimensional Wigner crystals on each cylinder at large separation. When the cylinders are brought together, some counterion lines will move towards the inner region and lead to strong attraction. The calculated interaction from our model is in good agreement with the simulation result, however, the single particle approximation considerably overestimates the attraction.

Counterions in the ground state partially condense in the intervening region of two approaching DNA cylinders and result in attraction.

Band gap, dielectric constant, and susceptibility of DNA layers as controlled by vanadium ion concentration

Deoxyribonucleic acid (DNA) doped with transition metal ions shows great versatility for molecular-based biosensors and bioelectronics. Methodologies for developing DNA lattices (formed by synthetic double-crossover tiles) and DNA layers (used by natural salmon) doped with vanadium ions (V3+), as well as an understanding of the physical characteristics of V3+-doped DNA nanostructures, are essential in practical applications in interdisciplinary research fields. Here, DNA lattices and layers doped with V3+ are constructed through substrate-assisted growth and drop-casting methods. In addition, enhanced physical characteristics such as the band gap energy, work function, dielectric constant, and susceptibility of V3+-doped DNA nanostructures with varying V3+ concentration ([V 3+ ]) are investigated. The critical concentration ([V 3+ ]C ) at a given amount of DNA was predicted based on an analysis of the phase transition of DNA lattices from crystalline to amorphous with specific [V 3+ ]. Generally, the [V 3+ ]C provided crucial information on the structural stability and extremum physical characteristics of V3+-doped DNA nanostructures due to the optimum incorporation of V3+ into DNA. We obtained the optical absorption spectra for energy band gap estimation; Raman spectra for identifying the preferential coordination sites of V3+ in DNA; x-ray photoelectron spectra to examine the chemical state, chemical composition, and functional groups; and ultraviolet photoelectron spectra to estimate the work function. In addition, we addressed the electrical properties (i.e. current, capacitance, dielectric constant, and storage energy) and magnetic properties (magnetic field-dependent and temperature-dependent magnetizations and susceptibility) of DNA layers in the presence of V3+. The development of biocompatible materials with specific optical, electrical, and magnetic properties is required for future applications because they must have designated functionality, high efficiency, and affordability.

Current Enhancement in Solid-State Nanopores Depends on Three-Dimensional DNA Structure

The translocation of double-stranded DNA through a solid-state nanopore may either decrease or increase the ionic current depending on the ionic concentration of the surrounding solution. Below a certain crossover ionic concentration, the current change inverts from a current blockade to current enhancement. In this paper, we show that the crossover concentration for bundled DNA nanostructures composed of multiple connected DNA double-helices is lower than that of double-stranded DNA. Our measurements suggest that counterion mobility in the vicinity of DNA is reduced depending on the three-dimensional structure of the molecule. We further demonstrate that introducing neutral polymers such as polyethylene glycol into the measurement solution reduces electroosmotic outflow from the nanopore, allowing translocation of large DNA structures at low salt concentrations. Our experiments contribute to an improved understanding of ion transport in confined DNA environments, which is critical for the development of nanopore sensing techniques as well as synthetic membrane channels. Our salt-dependent measurements of model DNA nanostructures will guide the development of computational models of DNA translocation through nanopores.

Simple ions control the elasticity of calcite gels via interparticle forces

Suspensions of calcite in water are employed in many industrial fields such as paper filling, pharmaceutics or heritage conservation. Whereas organics are generally used to tune the rheological properties of the paste, we also expect simple ions to be able to control the suspension rheology via the interparticle forces. We have thus investigated the impact of calcium, sodium and hydroxide ions on the elasticity of a colloidal gel of nanocalcite. We confront our macroscopic measurements to DLVO interaction potentials, based on chemical speciation and measurements of the zeta potential. Upon addition of calcium hydroxide, we observe a minimum in shear modulus, correlated to a maximum in the DLVO energy barrier, due to two competing effects: Calcium adsorption onto calcite surface rises the zeta potential, while increasing salt concentration induces stronger electrostatic screening. We also demonstrate that the addition of sodium hydroxide completely screens the surface charge and leads to a more rigid paste. A second important result is that carbonation of the calcite suspensions by the atmospheric CO₂ leads to a convergent high elasticity of the colloidal gels, whatever their initial value, also well rationalized by DLVO theory and resulting from a decrease in zeta potential.

"End-to-end" stacking of small dsRNA

PELDOR (pulsed electron-electron double resonance) is an established method to study intramolecular distances and can give evidence for conformational changes and flexibilities. However, it can also be used to study intermolecular interactions as for example oligerimization. Here, we used PELDOR to study the "end-to-end" stacking of small double-stranded (ds) RNAs. For this study, the dsRNA molecules were only singly labeled with the spin label TPA to avoid multispin effects and to measure only the intermolecular stacking interactions. It can be shown that small dsRNAs tend to assemble to rod-like structures due to π-π interactions between the base pairs at the end of the strands. On the one hand, these interactions can influence or complicate measurements aimed at the determining of the structure and dynamics of the dsRNA molecule itself. On the other hand, it can be interesting to study such intermolecular stacking interactions in more detail, as for example their dependence on ion concentration. We quantitatively determined the stacking probability as a function of the monovalent NaCl salt and the dsRNA concentration. From these data, the dissociation constant K_d was deduced and found to depend on the ratio between the NaCl salt and dsRNA concentrations. Additionally, the distances and distance distributions obtained predict a model for the stacking geometry of dsRNAs. Introducing a nucleotide overhangs at one end of the dsRNA molecule restricts the stacking to the other end, leading only to dimer formations. Introducing such an overhang at both ends of the dsRNA molecule fully suppresses stacking, as we demonstrate by PELDOR experiments quantitatively.

The promotion and suppression of DNA charge neutralization by the cosolute ectoine

Ectoine, a cosolute and osmolyte, is used by extremophilic microorganisms to maintain an osmotic equilibrium of cells with their surrounding medium under conditions of extreme salinity or thermal and pressure stresses. It is also considered a protectant of biomolecules such as protein and DNA in cells. In the present study, we investigate its influence on DNA charge neutralization and compaction through dynamic light scattering (DLS), atomic force microscopy (AFM) and single molecular magnetic tweezers (MT). We found that ectoine can promote DNA charge neutralization induced by multivalent cations at mild cosolute concentration in solution. When the concentration of ectoine is high enough, however, a mixed effect of promotion and suppression can be found under the same ionic conditions. In this case, the electrophoretic mobility (EM) of DNA is promoted in the region of low cation concentration, while suppressed in the region of high counterionic concentration. The charge neutralization of DNA by ectoine is also related to DNA compaction. The promotion and suppression of DNA compaction by ectoine was observed by AFM imaging. The condensed structure of DNA becomes more compact and then loose once more with the increasing concentration of ectoine. Meanwhile, the condensing forces of DNA measured by magnetic tweezers shows the same trend as does the DNA EM. We explained the experimental findings through the combined effect of two intrinsic features of ectoine, preferential exclusion and enhancement of the dielectric constant of the medium.

Ectoine can promote DNA charge neutralization at mild cosolute concentration in solution. When the concentration of ectoine is high enough, however, a mixing effect of promotion and suppression can be found in the same ionic condition.

Direct Demonstration of DNA Compaction Mediated by Divalent Counterions

We unambiguously demonstrated DNA attraction and its regulation mediated by divalent cations Mg²⁺ and Ca²⁺ by tethering a DNA single chain at various pH solutions. It is found that DNA is compacted when the pH of the solution containing these divalent counterions is decreased below 5. When the pH of the medium is ∼4, DNA is in an unstable transition state, being able to switch between compact and extensible states. We can also regulate the DNA attraction through a cyclic process of DNA compaction and unraveling by alternating the pH of the solution between 3 and 8. The corresponding change of morphology of DNA modulated by pH is also confirmed by atomic force microscopy (AFM). In the theoretical aspect, the present experimental finding is consistent with the coarse-grained simulation of Langevin dynamics on the effect of pH on DNA in a solution of divalent counterions.

Open-Boundary Molecular Dynamics of a DNA Molecule in a Hybrid Explicit/Implicit Salt Solution

The composition and electrolyte concentration of the aqueous bathing environment have important consequences for many biological processes and can profoundly affect the behavior of biomolecules. Nevertheless, because of computational limitations, many molecular simulations of biophysical systems can be performed only at specific ionic conditions: either at nominally zero salt concentration, i.e., including only counterions enforcing the system's electroneutrality, or at excessive salt concentrations. Here, we introduce an efficient molecular dynamics simulation approach for an atomistic DNA molecule at realistic physiological ionic conditions. The simulations are performed by employing the open-boundary molecular dynamics method that allows for simulation of open systems that can exchange mass and linear momentum with the environment. In our open-boundary molecular dynamics approach, the computational burden is drastically alleviated by embedding the DNA molecule in a mixed explicit/implicit salt-bathing solution. In the explicit domain, the water molecules and ions are both overtly present in the system, whereas in the implicit water domain, only the ions are explicitly present and the water is described as a continuous dielectric medium. Water molecules are inserted and deleted into/from the system in the intermediate buffer domain that acts as a water reservoir to the explicit domain, with both water molecules and ions free to enter or leave the explicit domain. Our approach is general and allows for efficient molecular simulations of biomolecules solvated in bathing salt solutions at any ionic strength condition.

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 tilt-dependent potential of mean force of a pair of DNA oligomers from all-atom molecular dynamics simulations

Electrostatic interactions between DNA molecules have been extensively studied experimentally and theoretically, but several aspects (e.g. its role in determining the pitch of the cholesteric DNA phase) still remain unclear. Here, we performed large-scale all-atom molecular dynamics simulations in explicit water and 150 mM sodium chloride, to reconstruct the potential of mean force (PMF) of two DNA oligomers 24 base pairs long as a function of their interaxial angle and intermolecular distance. We find that the potential of mean force is dominated by total DNA charge, and not by the helical geometry of its charged groups. The theory of homogeneously charged cylinders fits well all our simulation data, and the fit yields the optimal value of the total compensated charge on DNA to  ≈65% of its total fixed charge (arising from the phosphorous atoms), close to the value expected from Manning's theory of ion condensation. The PMF calculated from our simulations does not show a significant dependence on the handedness of the angle between the two DNA molecules, or its size is on the order of [Formula: see text]. Thermal noise for molecules of the studied length seems to mask the effect of detailed helical charge patterns of DNA. The fact that in monovalent salt the effective interaction between two DNA molecules is independent on the handedness of the tilt may suggest that alternative mechanisms are required to understand the cholesteric phase of DNA.

Morphological and Optoelectronic Characteristics of Double and Triple Lanthanide Ion-Doped DNA Thin Films

Double and triple lanthanide ion (Ln(3+))-doped synthetic double crossover (DX) DNA lattices and natural salmon DNA (SDNA) thin films are fabricated by the substrate assisted growth and drop-casting methods on given substrates. We employed three combinations of double Ln(3+)-dopant pairs (Tb(3+)-Tm(3+), Tb(3+)-Eu(3+), and Tm(3+)-Eu(3+)) and a triple Ln(3+)-dopant pair (Tb(3+)-Tm(3+)-Eu(3+)) with different types of Ln(3+), (i.e., Tb(3+) chosen for green emission, Tm(3+) for blue, and Eu(3+) for red), as well as various concentrations of Ln(3+) for enhancement of specific functionalities. We estimate the optimum concentration of Ln(3+) ([Ln(3+)]O) wherein the phase transition of Ln(3+)-doped DX DNA lattices occurs from crystalline to amorphous. The phase change of DX DNA lattices at [Ln(3+)]O and a phase diagram controlled by combinations of [Ln(3+)] were verified by atomic force microscope measurement. We also developed a theoretical method to obtain a phase diagram by identifying a simple relationship between [Ln(3+)] and [Ln(3+)]O that in practice was found to be in agreement with experimental results. Finally, we address significance of physical characteristics-current for evaluating [Ln(3+)]O, absorption for understanding the modes of Ln(3+) binding, and photoluminescence for studying energy transfer mechanisms-of double and triple Ln(3+)-doped SDNA thin films. Current and photoluminescence in the visible region increased as the varying [Ln(3+)] increased up to a certain [Ln(3+)]O, then decreased with further increases in [Ln(3+)]. In contrast, the absorbance peak intensity at 260 nm showed the opposite trend, as compared with current and photoluminescence behaviors as a function of varying [Ln(3+)]. A DNA thin film with varying combinations of [Ln(3+)] might provide immense potential for the development of efficient devices or sensors with increasingly complex functionality.

Multi-shell model of ion-induced nucleic acid condensation

We present a semi-quantitative model of condensation of short nucleic acid (NA) duplexes induced by trivalent cobalt(iii) hexammine (CoHex) ions. The model is based on partitioning of bound counterion distribution around single NA duplex into "external" and "internal" ion binding shells distinguished by the proximity to duplex helical axis. In the aggregated phase the shells overlap, which leads to significantly increased attraction of CoHex ions in these overlaps with the neighboring duplexes. The duplex aggregationfree energy is decomposed into attractive and repulsive components in such a way that they can be represented by simple analytical expressions with parameters derived from molecular dynamic simulations and numerical solutions of Poisson equation. The attractive term depends on the fractions of bound ions in the overlapping shells and affinity of CoHex to the "external" shell of nearly neutralized duplex. The repulsive components of the free energy are duplex configurational entropy loss upon the aggregation and the electrostatic repulsion of the duplexes that remains after neutralization by bound CoHex ions. The estimates of the aggregationfree energy are consistent with the experimental range of NA duplex condensation propensities, including the unusually poor condensation of RNA structures and subtle sequence effects upon DNAcondensation. The model predicts that, in contrast to DNA, RNA duplexes may condense into tighter packed aggregates with a higher degree of duplex neutralization. An appreciable CoHex mediated RNA-RNA attraction requires closer inter-duplex separation to engage CoHex ions (bound mostly in the "internal" shell of RNA) into short-range attractive interactions. The model also predicts that longer NA fragments will condense more readily than shorter ones. The ability of this model to explain experimentally observed trends in NAcondensation lends support to proposed NAcondensation picture based on the multivalent "ion binding shells."

Multivalent ion-mediated nucleic acid helix-helix interactions: RNA versus DNA

Ion-mediated interaction is critical to the structure and stability of nucleic acids. Recent experiments suggest that the multivalent ion-induced aggregation of double-stranded (ds) RNAs and DNAs may strongly depend on the topological nature of helices, while there is still lack of an understanding on the relevant ion-mediated interactions at atomistic level. In this work, we have directly calculated the potentials of mean force (PMF) between two dsRNAs and between two dsDNAs in Co(NH3)6 (3+) (Co-Hex) solutions by the atomistic molecular dynamics simulations. Our calculations show that at low [Co-Hex], the PMFs between B-DNAs and between A-RNAs are both (strongly) repulsive. However, at high [Co-Hex], the PMF between B-DNAs is strongly attractive, while those between A-RNAs and between A-DNAs are still (weakly) repulsive. The microscopic analyses show that for A-form helices, Co-Hex would become 'internal binding' into the deep major groove and consequently cannot form the evident ion-bridge between adjacent helices, while for B-form helices without deep grooves, Co-Hex would exhibit 'external binding' to strongly bridge adjacent helices. In addition, our further calculations show that, the PMF between A-RNAs could become strongly attractive either at very high [Co-Hex] or when the bottom of deep major groove is fixed with a layer of water.

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.

Conformation-dependent DNA attraction

Understanding how DNA molecules interact with other biomolecules is related to how they utilize their functions and is therefore critical for understanding their structure-function relationships. For a long time, the existence of Z-form DNA (a left-handed double helical version of DNA, instead of the common right-handed B-form) has puzzled the scientists, and the definitive biological significance of Z-DNA has not yet been clarified. In this study, the effects of DNA conformation in DNA-DNA interactions are explored by molecular dynamics simulations. Using umbrella sampling, we find that for both B- and Z-form DNA, surrounding Mg(2+) ions always exert themselves to screen the Coulomb repulsion between DNA phosphates, resulting in very weak attractive force. On the contrary, a tight and stable bound state is discovered for Z-DNA in the presence of Mg(2+) or Na(+), benefiting from their hydrophobic nature. Based on the contact surface and a dewetting process analysis, a two-stage binding process of Z-DNA is outlined: two Z-DNA first attract each other through charge screening and Mg(2+) bridges to phosphate groups in the same way as that of B-DNA, after which hydrophobic contacts of the deoxyribose groups are formed via a dewetting effect, resulting in stable attraction between two Z-DNA molecules. The highlighted hydrophobic nature of Z-DNA interaction from the current study may help to understand the biological functions of Z-DNA in gene transcription.

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.

Competition between Na⁺ and Rb⁺ in the minor groove of DNA

The competition between Na⁺ and Rb⁺ ions in the minor groove of a synthetic B-DNA dodecamer d (CGCGAATTCGCG) is studied using molecular dynamics simulations as the ratio of these two ions changing from 9:1 to 1:9 with the DNA merged into the solvent of water molecule at 298 K. When the concentration of Rb⁺ ions increases, from minority to majority, Na⁺ ions are gradually released from the A tract, and the binding sites in the minor groove are occupied by Rb⁺ ions, extending from the A tract to the whole minor groove. Comparing Na⁺ with Rb⁺ ions, the conformation of the minor groove is influenced strongly by Na⁺ ions.

A universal description for the experimental behavior of salt-(in)dependent oligocation-induced DNA condensation

We report a systematic study of the condensation of plasmid DNA by oligocations with variation of the charge, Z, from +3 to +31. The oligocations include a series of synthetic linear ε-oligo(L-lysines), (denoted εKn, n = 3–10, 31; n is the number of lysines with the ligand charge Z = n+1) and branched α-substituted homologues of εK10: εYK10, εLK10 (Z = +11); εRK10, εYRK10 and εLYRK10 (Z = +21). Data were obtained by light scattering, UV absorption monitored precipitation assay and isothermal titration calorimetry in a wide range concentrations of DNA and monovalent salt (KCl, CKCl). The dependence of EC50 (ligand concentration at the midpoint of DNA condensation) on C(KCl) shows the existence of a salt-independent regime at low C(KCl) and a salt-dependent regime with a steep rise of EC50 with increase of C(KCl). Increase of the ligand charge shifts the transition from the salt-independent to salt-dependent regime to higher C(KCl). A novel and simple relationship describing the EC50 dependence on DNA concentration, charge of the ligand and the salt-dependent dissociation constant of the ligand–DNA complex is derived. For the ε-oligolysines εK6–εK10, the experimental dependencies of EC50 on C(KCl) and Z are well-described by an equation with a common set of parameters. Implications from our findings for understanding DNA condensation in chromatin are discussed.

Effective solvent mediated potentials of Na+ and Cl- ions in aqueous solution: temperature dependence

The effective solvent-mediated potentials for Na(+) and Cl(-) ions in aqueous solution were calculated in a wide range of temperatures from 0 to 100 °C. The potentials have been determined using the inverse Monte Carlo approach, from the ion-ion radial distribution functions computed in 50 ns molecular dynamics simulations of ions and explicit water molecules. We further separated the effective potentials into a short-range part and an electrostatic long-range part represented by a coulombic potential with some dielectric permittivity. We adjusted the value of the dielectric permittivity to provide the fastest possible decay of the short-range potentials at larger distances. The obtained temperature dependence of the dielectric permittivity follows well the experimental data. We show also that the largest part of the temperature dependence of the effective potentials can be attributed to the temperature-dependent dielectric permittivity.

Comparing the Predictions of the Nonlinear Poisson-Boltzmann Equation and the Ion Size-Modified Poisson-Boltzmann Equation for a Low-Dielectric Charged Spherical Cavity in an Aqueous Salt Solution

The ion size-modified Poisson Boltzmann equation (SMPBE) is applied to the simple model problem of a low-dielectric spherical cavity containing a central charge, in an aqueous salt solution to investigate the finite ion size effect upon the electrostatic free energy and its sensitivity to changes in salt concentration. The SMPBE is shown to predict a very different electrostatic free energy than the nonlinear Poisson-Boltzmann equation (NLPBE) due to the additional entropic cost of placing ions in solution. Although the energy predictions of the SMPBE can be reproduced by fitting an appropriatelysized Stern layer, or ion-exclusion layer to the NLPBE calculations, the size of the Stern layer is difficult to estimate a priori. The SMPBE also produces a saturation layer when the central charge becomes sufficiently large. Ion-competition effects on various integrated quantities such the total number of ions predicted by the SMPBE are qualitatively similar to those given by the NLPBE and those found in available experimental results.

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.

Modulation effects within the mean-field theory of electrolyte solutions

The consequences of source charge and surface modulation are studied within the framework of the Poisson-Boltzmann theory of electrolyte solutions. Through a consideration of various examples, it is found that inherent modulation can lead to both like-charge attraction and overcharging effects.

Symmetry of electrostatic interaction between pyrophosphate DNA molecules

We study chiral electrostatic interaction between artificial ideal homopolymer DNA-like molecules in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential U of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of the potential U indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by the potential U . The symmetries form a non-commutative group of 8th order, S . Using the group S we suggest a classification of liquid crystalline phases of the DNA, which allows several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the role played by charges in their liquid crystalline phases, and open experimental research, important for nano-technological and bio-medical applications.

A universal description for the experimental behavior of salt-(in)dependent oligocation-induced DNA condensation

We report a systematic study of the condensation of plasmid DNA by oligocations with variation of the charge, Z, from +3 to +31. The oligocations include a series of synthetic linear epsilon-oligo(l-lysines), (denoted epsilonKn, n = 3-10, 31; n is the number of lysines equal to the ligand charge) and branched alpha-substituted homologues of epsilonK10: epsilonYK10, epsilonLK10 (Z = +10); epsilonRK10, epsilonYRK10 and epsilonLYRK10 (Z = +20). Data were obtained by light scattering, UV absorption monitored precipitation assay and isothermal titration calorimetry in a wide range concentrations of DNA and monovalent salt (KCl, C(KCl)). The dependence of EC(50) (ligand concentration at the midpoint of DNA condensation) on C(KCl) shows the existence of a salt-independent regime at low C(KCl) and a salt-dependent regime with a steep rise of EC(50) with increase of C(KCl). Increase of the ligand charge shifts the transition from the salt-independent to salt-dependent regime to higher C(KCl). A novel and simple relationship describing the EC(50) dependence on DNA concentration, charge of the ligand and the salt-dependent dissociation constant of the ligand-DNA complex is derived. For the epsilon-oligolysines epsilonK3-epsilonK10, the experimental dependencies of EC(50) on C(KCl) and Z are well-described by an equation with a common set of parameters. Implications from our findings for understanding DNA condensation in chromatin are discussed.

Nonadditivity in the effective interactions of binary charged colloidal suspensions

Based on primitive model computer simulations with explicit microions, we calculate the effective interactions in a binary mixture of charged colloids with species A and B for different size and charge ratios. An optimal pairwise interaction is obtained by fitting the many-body effective forces. This interaction is close to a Yukawa (or Derjaguin-Landau-Verwey-Overbeek (DLVO)) pair potential but the AB cross-interaction is different from the geometric mean of the two direct AA and BB interactions. As a function of charge asymmetry, the corresponding nonadditivity parameter is first positive, then significantly negative and is then positive again. We finally show that an inclusion of nonadditivity within an optimal effective Yukawa model gives better predictions for the fluid pair structure than DLVO theory.

Multilayered crystals of macroions under slit confinement

The crystalline ground state of macroions confined between two neutral parallel plates in the presence of their homogeneously spread counterions is calculated by lattice sum minimization of candidate phases involving up to six layers. For increasing macroion density, a cascade of solid-solid transitions is found involving various multilayered crystals. The cascade includes triangular monolayer and buckled bilayer as well as rhombic, squared and triangular phase structures.

Mediating role of multivalent cations in DNA electrostatics: an epsilon-modified Poisson-Boltzmann study of B-DNA-B-DNA interactions in mixture of NaCl and MgCl2 solutions

Potentials of mean force acting between two ions in SPC/E water have been determined via molecular dynamics simulations using the spherical cavity approach ( J. Phys. Chem. B 2006 , 110 , 10878 ). The potentials were obtained for Me(2+)-Me(+) pairs, where Me(2+) means cations Mg(2+) and Ca(2+) and Me(+) denotes monovalent ions Li(+), Na(+), and K(+). The hard-core interaction distance for effective Me(2+)-Me(+) potentials appears to be of about 5 A that looks like a sum of the effective radii of a Me(2+) ion (3 A) and of an alkali metal ion Me(+) (about 2 A). These ion-ion interaction parameters were used in the epsilon-Modified Poisson-Boltzmann (epsilon-MPB) calculations ( J. Phys. Chem. B 2007 , 111 , 5264 ) of ionic distributions around DNA generalized for the arbitrary mixture of different ion species. Ionic distributions around an all-atom geometry model of B-DNA in solution of a mixture of NaCl and MgCl(2) were obtained. It was found that even a small fraction of ions Mg(2+) led to sharp condensation of Mg(2+) near the phosphate groups of DNA due to polarization deficiency of cluster [Mg(H(2)O)(6)](2+) in an external field. The epsilon-MPB calculations of the B-DNA-B-DNA interaction energies suggest that adding 1 mM of Mg(2+) to 50 mM solution of NaCl notably affects the force acting between the two macromolecules. Being compared to Poisson-Boltzmann results and to MPB calculations for the primitive model of ions, the epsilon-MPB results also indicate an important contribution of dielectric saturation effects to the mediating role of divalent cations in the DNA-DNA interaction energies.

A mesoscale model of DNA and its renaturation

A mesoscale model of DNA is presented (3SPN.1), extending the scheme previously developed by our group. Each nucleotide is mapped onto three interaction sites. Solvent is accounted for implicitly through a medium-effective dielectric constant and electrostatic interactions are treated at the level of Debye-Hückel theory. The force field includes a weak, solvent-induced attraction, which helps mediate the renaturation of DNA. Model parameterization is accomplished through replica exchange molecular dynamics simulations of short oligonucleotide sequences over a range of composition and chain length. The model describes the melting temperature of DNA as a function of composition as well as ionic strength, and is consistent with heat capacity profiles from experiments. The dependence of persistence length on ionic strength is also captured by the force field. The proposed model is used to examine the renaturation of DNA. It is found that a typical renaturation event occurs through a nucleation step, whereby an interplay between repulsive electrostatic interactions and colloidal-like attractions allows the system to undergo a series of rearrangements before complete molecular reassociation occurs.

Nonmonotonic density dependence of the diffusion of DNA fragments in low-salt suspensions

The high linear charge density of 20-base-pair oligomers of DNA is shown to lead to a striking nonmonotonic dependence of the long-time self-diffusion on the concentration of DNA in low-salt conditions. This generic nonmonotonic behavior results from the strong coupling between the electrostatic and solvent-mediated hydrodynamic interactions, from the renormalization of these electrostatic interactions at large separations, and specifically from the dominance of the far-field hydrodynamic interactions caused by the strong repulsion between the DNA fragments.

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.

Electrostatics of B-DNA in NaCl and CaCl2 solutions: ion size, interionic correlation, and solvent dielectric saturation effects

The epsilon-modified Poisson-Boltzmann (-MPB) equations ( J. Phys. Chem. B, 2007, 111, 5264) have been solved on a three-dimensional grid for an all-atom geometry model of B-DNA. The approach is based on the implicit solvent model including finite sizes of hydrated ions and a dielectric approximation of the ion hydration shell. Results were obtained for the detailed geometry model of B-DNA in dilute and moderately concentrated solutions of NaCl and CaCl(2). All -MPB parameters of ions and dielectric medium were extracted from published results of all-atom molecular dynamics simulations. The study allows evaluations of the ion size, interionic correlation, and the solvent dielectric saturation effects on the ion distributions around DNA. It unambiguously suggests that the difference between the -MPB and Poisson-Boltzmann distributions of ions is low for Na(+) counterions. Such a difference in the case of divalent counterions Ca(2+) is dramatic: the dielectric saturation of the ion hydration shell leads to point-like adsorption of Ca(2+) on the phosphate groups of DNA. The -MPB equations were also applied to calculate the energy of interaction between two B-DNA molecules. Results agree with previously published simulations and experimental data. Some aspects of ion specificity of polyelectrolyte properties are discussed.

Computer simulation study of probe-target hybridization in model DNA microarrays: effect of probe surface density and target concentration

We use lattice Monte Carlo simulations to study the thermodynamics of hybridization of single-stranded "target" genes in solution with complementary "probe" DNA molecules immobilized on a microarray surface. The target molecules in our system contain 48 segments and the probes tethered on a hard surface contain 8-24 segments. The segments on the probe and target are distinct, with each segment representing a sequence of nucleotides that interacts exclusively with its unique complementary target segment with a single hybridization energy; all other interactions are zero. We examine how surface density (number of probes per unit surface area) and concentration of target molecules affect the extent of hybridization. For short probe lengths, as the surface density increases, the probability of binding long stretches of target segments increases at low surface density, reaches a maximum at an intermediate surface density, and then decreases at high surface density. Furthermore, as the surface density increases, the target is less likely to bind completely to one probe; instead, it binds simultaneously to multiple probes. At short probe lengths, as the target concentration increases, the fraction of targets binding completely to the probes (specificity) decreases. At long probe lengths, varying the target concentration does not affect the specificity. At all target concentrations as the probe length increases, the fraction of target molecules bound to the probes by at least one segment (sensitivity) increases while the fraction of target molecules completely bound to the probes (specificity) decreases. This work provides general guidelines to maximizing microarray sensitivity and specificity. Our results suggest that the sensitivity and specificity can be maximized by using probes 130-180 nucleotides long at a surface density in the range of 7 x 10(-5)- 3 x 10(-4) probe molecules per nm(2).

Interaction of the alternating double stranded copolymer poly(dA-dT) x poly(dA-dT) with NiCl(2) and CdCl(2): solution behavior

The thermal denaturation of the synthetic high molecular weight double stranded polynucleotide poly(dA-dT) x poly(dA-dT) has been studied in aqueous buffered solution (Tris 1.0 mM; pH 7.8+/-0.2) in the presence of increasing concentrations of either Ni(2+) (borderline cation) or Cd(2+) (soft cation) at four different constant ionic strength values (NaCl), making use of UV and circular dichroism (CD) spectroscopies. The experimental results show that the B-type double helix of the polymer is stabilized against thermal denaturation in the presence of both cations at low concentrations, relative to the systems where only NaCl is present, in the same conditions of ionic strength and pH. The effect is more pronounced for Ni(2+) than for Cd(2+). At higher concentrations, both cations start to destabilize the double helix, with Cd cations inducing larger variations of T(m). In many cases, when denaturation starts, interstrand cross-linking occurs with formation of aggregates that precipitate.