Monte Carlo Simulation Study of DNA Polyelectrolyte Properties in the Presence of Multivalent Polyamine Ions

Direct Measurement of Interhelical DNA Repulsion and Attraction by Quantitative Cross-Linking

To better understand the forces that mediate nucleic acid compaction in biology, we developed the disulfide cross-linking approach xHEED (X-linking of Helices to measure Electrostatic Effects at Distance) to measure the distance-dependent encounter frequency of two DNA helices in solution. Using xHEED, we determined the distance that the electrostatic potential extends from DNA helices, the dependence of this distance on ionic conditions, and the magnitude of repulsion when two helices approach one another. Across all conditions tested, the potential falls to that of the bulk solution within 15 Å of the major groove surface. For separations of ∼30 Å, we measured a repulsion of 1.8 kcal/mol in low monovalent ion concentration (30 mM Na+), with higher Na+ concentrations ameliorating this repulsion, and 2 M Na+ or 100 mM Mg2+ eliminating it. Strikingly, we found full screening at very low Co3+ concentrations and net attraction at higher concentrations, without the higher-order DNA condensation that typically complicates studies of helical attraction. Our measurements define the relevant distances for electrostatic interactions of nucleic-acid helices in biology and introduce a new method to propel further understanding of how these forces impact biological processes.

Recent Advances in Hybrid Biomimetic Polymer-Based Films: from Assembly to Applications

Biological membranes, in addition to being a cell boundary, can host a variety of proteins that are involved in different biological functions, including selective nutrient transport, signal transduction, inter- and intra-cellular communication, and cell-cell recognition. Due to their extreme complexity, there has been an increasing interest in developing model membrane systems of controlled properties based on combinations of polymers and different biomacromolecules, i.e., polymer-based hybrid films. In this review, we have highlighted recent advances in the development and applications of hybrid biomimetic planar systems based on different polymeric species. We have focused in particular on hybrid films based on (i) polyelectrolytes, (ii) polymer brushes, as well as (iii) tethers and cushions formed from synthetic polymers, and (iv) block copolymers and their combinations with biomacromolecules, such as lipids, proteins, enzymes, biopolymers, and chosen nanoparticles. In this respect, multiple approaches to the synthesis, characterization, and processing of such hybrid films have been presented. The review has further exemplified their bioengineering, biomedical, and environmental applications, in dependence on the composition and properties of the respective hybrids. We believed that this comprehensive review would be of interest to both the specialists in the field of biomimicry as well as persons entering the field.

Photosensitive Cationic Azobenzene Surfactants: Thermodynamics of Hydration and the Complex Formation with Poly(methacrylic acid)

In this computational work, we investigate the photosensitive cationic surfactants with the trimethylammonium or polyamine hydrophilic head and the azobenzene-containing hydrophobic tail. The azobenzene-based molecules are known to undergo a reversible trans-cis-trans isomerization reaction when subjected to UV-visible light irradiation. Combining the density functional theory and the all-atom molecular dynamics simulations, the structural and the hydration properties of the trans- and the cis-isomers and their interaction with the oppositely charged poly(methacrylic acid) in aqueous solution are investigated. We establish and quantify the correlations of the molecular structure and the isomerization state of the surfactants and their hydrophilicity/hydrophobicity and the self-assembling altered by light. For this reason, we compare the hydration free energies of the trans- and the cis-isomers. Moreover, the investigations of the interaction strength between the azobenzene molecules and the polyanion provide additional elucidations of the recent experimental and theoretical studies on the light triggered reversible deformation behavior of the microgels and the polymer brushes loaded with azobenzene surfactants.

Bundling in semiflexible polymers: A theoretical overview

Supramolecular assemblies of polymers are key modules to sustain the structure of cells and their function. The main elements of these assemblies are charged semiflexible polymers (polyelectrolytes) generally interacting via a long(er)-range repulsion and a short(er)-range attraction. The most common supramolecular structure formed by these polymers is the bundle. In the present paper, we critically review some recent theoretical and computational advances on the problem of bundle formation, and point a few promising directions for future work.

Multiscale coarse-grained modelling of chromatin components: DNA and the nucleosome

To model large biomolecular systems, such as cell and organelles an atomistic description is not currently achievable and is not generally practical. Therefore, simplified coarse-grained (CG) modelling becomes a necessity. One of the most important cellular components is chromatin, a large DNA-protein complex where DNA is highly compacted. Recent progress in coarse graining modelling of the major chromatin components, double helical DNA and the nucleosome core particle (NCP) is presented. First, general principles and approaches allowing rigorous bottom-to-top generation of interaction potentials in the CG models are presented. Then, recent CG models of DNA are reviewed and their adequacy is benchmarked against experimental data on the salt dependence of DNA flexibility (persistence length). Furthermore, a few recent CG models of the NCP are described and their application for studying salt-dependent NCP-NCP interaction is discussed. An example of a multiscale approach to CG modelling of chromatin is presented where interactions and self-assembly of thousands of NCPs in solution are observed.

The structure and intermolecular forces of DNA condensates

Spontaneous assembly of DNA molecules into compact structures is ubiquitous in biological systems. Experiment has shown that polycations can turn electrostatic self-repulsion of DNA into attraction, yet the physical mechanism of DNA condensation has remained elusive. Here, we report the results of atomistic molecular dynamics simulations that elucidated the microscopic structure of dense DNA assemblies and the physics of interactions that makes such assemblies possible. Reproducing the setup of the DNA condensation experiments, we measured the internal pressure of DNA arrays as a function of the DNA–DNA distance, showing a quantitative agreement between the results of our simulations and the experimental data. Analysis of the MD trajectories determined the DNA–DNA force in a DNA condensate to be pairwise, the DNA condensation to be driven by electrostatics of polycations and not hydration, and the concentration of bridging cations, not adsorbed cations, to determine the magnitude and the sign of the DNA–DNA force. Finally, our simulations quantitatively characterized the orientational correlations of DNA in DNA arrays as well as diffusive motion of DNA and cations.

Strong-coupling electrostatic theory of polymer counterions close to planar charges

Strong-coupling phenomena, such as like-charge macroion attraction, opposite-charged macroion repulsion, charge renormalization, and charge inversion, are known to be mediated by multivalent counterions. Most theories treat the counterions as point charges and describe the system by a single coupling parameter that measures the strength of the Coulomb interactions. In many biological systems, the counterions are highly charged and have finite sizes and can be well-described by polyelectrolytes. The shapes and orientations of these polymer counterions play a major role in the thermodynamics of these systems. In this work we apply a field-theoretic description in the strong-coupling regime to the polymer counterions in the presence of a fixed charge distribution. We work out the special cases of rodlike polymer counterions confined by one, and two charged walls, respectively. The effects of the geometry of the rodlike counterions and the excluded volume of the walls on the density, pressure, and free energy of the rodlike counterions are discussed.

Coarse-Grained Ions for Nucleic Acid Modeling

We present a general coarse-grained model of sodium, magnesium, spermidine, and chlorine in implicit solvent. The effective potentials between ions are systematically parametrized using a relative entropy coarse-graining approach [Carmichael, S. P. and M. S. Shell, J. Phys. Chem. B, 116, 8383-93 (2012)] that maximizes the information retained in a coarse-grained model. We describe the local distribution of ions in the vicinity of a recently published coarse-grained DNA model and demonstrate a dependence of persistence length on ionic strength that differs from that predicted by Odijk-Skolnick-Fixman theory. Consistent with experimental observations, we show that spermidine induces DNA condensation whereas magnesium and sodium do not. This model can be used alongside any coarse-grained DNA model that has explicit charges and an accurate reproduction of the excluded volume of dsDNA.

An experimentally-informed coarse-grained 3-Site-Per-Nucleotide model of DNA: structure, thermodynamics, and dynamics of hybridization

A new 3-Site-Per-Nucleotide coarse-grained model for DNA is presented. The model includes anisotropic potentials between bases involved in base stacking and base pair interactions that enable the description of relevant structural properties, including the major and minor grooves. In an improvement over available coarse-grained models, the correct persistence length is recovered for both ssDNA and dsDNA, allowing for simulation of non-canonical structures such as hairpins. DNA melting temperatures, measured for duplexes and hairpins by integrating over free energy surfaces generated using metadynamics simulations, are shown to be in quantitative agreement with experiment for a variety of sequences and conditions. Hybridization rate constants, calculated using forward-flux sampling, are also shown to be in good agreement with experiment. The coarse-grained model presented here is suitable for use in biological and engineering applications, including nucleosome positioning and DNA-templated engineering.

Reduced atomic pair-interaction design (RAPID) model for simulations of proteins

Increasingly, theoretical studies of proteins focus on large systems. This trend demands the development of computational models that are fast, to overcome the growing complexity, and accurate, to capture the physically relevant features. To address this demand, we introduce a protein model that uses all-atom architecture to ensure the highest level of chemical detail while employing effective pair potentials to represent the effect of solvent to achieve the maximum speed. The effective potentials are derived for amino acid residues based on the condition that the solvent-free model matches the relevant pair-distribution functions observed in explicit solvent simulations. As a test, the model is applied to alanine polypeptides. For the chain with 10 amino acid residues, the model is found to reproduce properly the native state and its population. Small discrepancies are observed for other folding properties and can be attributed to the approximations inherent in the model. The transferability of the generated effective potentials is investigated in simulations of a longer peptide with 25 residues. A minimal set of potentials is identified that leads to qualitatively correct results in comparison with the explicit solvent simulations. Further tests, conducted for multiple peptide chains, show that the transferable model correctly reproduces the experimentally observed tendency of polyalanines to aggregate into β-sheets more strongly with the growing length of the peptide chain. Taken together, the reported results suggest that the proposed model could be used to succesfully simulate folding and aggregation of small peptides in atomic detail. Further tests are needed to assess the strengths and limitations of the model more thoroughly.

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.

Electrostatic origin of salt-induced nucleosome array compaction

The physical mechanism of the folding and unfolding of chromatin is fundamentally related to transcription but is incompletely characterized and not fully understood. We experimentally and theoretically studied chromatin compaction by investigating the salt-mediated folding of an array made of 12 positioning nucleosomes with 177 bp repeat length. Sedimentation velocity measurements were performed to monitor the folding provoked by addition of cations Na(+), K(+), Mg(2+), Ca(2+), spermidine(3+), Co(NH(3))(6)(3+), and spermine(4+). We found typical polyelectrolyte behavior, with the critical concentration of cation needed to bring about maximal folding covering a range of almost five orders of magnitude (from 2 μM for spermine(4+) to 100 mM for Na(+)). A coarse-grained model of the nucleosome array based on a continuum dielectric description and including the explicit presence of mobile ions and charged flexible histone tails was used in computer simulations to investigate the cation-mediated compaction. The results of the simulations with explicit ions are in general agreement with the experimental data, whereas simple Debye-Hückel models are intrinsically incapable of describing chromatin array folding by multivalent cations. We conclude that the theoretical description of the salt-induced chromatin folding must incorporate explicit mobile ions that include ion correlation and ion competition effects.

Charge state of the globular histone core controls stability of the nucleosome

Presented here is a quantitative model of the wrapping and unwrapping of the DNA around the histone core of the nucleosome that suggests a mechanism by which this transition can be controlled: alteration of the charge state of the globular histone core. The mechanism is relevant to several classes of posttranslational modifications such as histone acetylation and phosphorylation; several specific scenarios consistent with recent in vivo experiments are considered. The model integrates a description based on an idealized geometry with one based on the atomistic structure of the nucleosome, and the model consistently accounts for both the electrostatic and nonelectrostatic contributions to the nucleosome free energy. Under physiological conditions, isolated nucleosomes are predicted to be very stable (38 +/- 7 kcal/mol). However, a decrease in the charge of the globular histone core by one unit charge, for example due to acetylation of a single lysine residue, can lead to a significant decrease in the strength of association with its DNA. In contrast to the globular histone core, comparable changes in the charge state of the histone tail regions have relatively little effect on the nucleosome's stability. The combination of high stability and sensitivity explains how the nucleosome is able to satisfy the seemingly contradictory requirements for thermodynamic stability while allowing quick access to its DNA informational content when needed by specific cellular processes such as transcription.

Cation-induced polyelectrolyte-polyelectrolyte attraction in solutions of DNA and nucleosome core particles

The paper reviews our current studies on the experimentally induced cation compaction and aggregation in solutions of DNA and nucleosome core particles and the theoretical modelling of these processes using coarse-grained continuum models with explicit mobile ions and with all-atom molecular dynamics (MD) simulations. Recent experimental results on DNA condensation by cationic oligopeptides and the effects of added salt are presented. The results of MD simulations modelling DNA-DNA attraction due to the presence of multivalent ions including the polyamine spermidine and fragments of histone tails, which exhibit bridging between adjacent DNA molecules, are discussed. Experimental data on NCP aggregation, using recombinantly prepared systems are summarized. Literature data and our results of studying of the NCP solutions are compared with predictions of coarse-grained MD simulations, including the important ion correlation as well as bridging mechanisms. The importance of the results to chromatin folding and aggregation is discussed.

Polyelectrolyte condensation in bulk, at surfaces, and under confinement

In this review we discuss recent results from computer simulations based on coarse-grained polyion models representing aqueous solutions of polyelectrolytes. The focus will be directed to the conformation of the polyions and, in particular, their condensation in bulk, induced by multivalent ions and oppositely charged polyelectrolytes, at responsive surfaces and under confinement.

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 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.

Binding mechanisms in supramolecular complexes

Supramolecular chemistry has expanded dramatically in recent years both in terms of potential applications and in its relevance to analogous biological systems. The formation and function of supramolecular complexes occur through a multiplicity of often difficult to differentiate noncovalent forces. The aim of this Review is to describe the crucial interaction mechanisms in context, and thus classify the entire subject. In most cases, organic host-guest complexes have been selected as examples, but biologically relevant problems are also considered. An understanding and quantification of intermolecular interactions is of importance both for the rational planning of new supramolecular systems, including intelligent materials, as well as for developing new biologically active agents.

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.

Interactions of like-charged rods at low temperatures: analytical theory vs. simulations

We investigate a system consisting of two like-charged infinitely long rods and neutralizing counterions at low temperatures, using both analytic theory and simulations. With some reasonable approximations we can analytically solve for several ground-state structures of the model, starting with states where all counterions are lined up in the gap between the rods, over planar configurations, where the counterions are divided up into a fraction which resides between the rods, and counterions which are located on the outer surfaces, up to configurations which cover the full rod surfaces. Using parallel tempering simulations, we are able to study the system over a wide range of temperatures. At low temperatures we find good agreement with our T = 0 results. At higher temperatures, the strong coupling (SC) theory delivers qualitatively better results. We furthermore demonstrate that for the SC theory and our ground-state approximations to yield quantitative agreement, three parameters are required to be large, the strong-coupling parameter, the Rouzina-Bloomfield parameter, and the ratio of the average distance of the counterions to the radius of the rods. In the case of the latter ratio being small, our T = 0 results show better agreement with the simulation data at very low temperatures.

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).

Charge structure and counterion distribution in hexagonal DNA liquid crystal

A hexagonal liquid crystal of DNA fragments (double-stranded, 150 basepairs) with tetramethylammonium (TMA) counterions was investigated with small angle neutron scattering (SANS). We obtained the structure factors pertaining to the DNA and counterion density correlations with contrast matching in the water. Molecular dynamics (MD) computer simulation of a hexagonal assembly of nine DNA molecules showed that the inter-DNA distance fluctuates with a correlation time around 2 ns and a standard deviation of 8.5% of the interaxial spacing. The MD simulation also showed a minimal effect of the fluctuations in inter-DNA distance on the radial counterion density profile and significant penetration of the grooves by TMA. The radial density profile of the counterions was also obtained from a Monte Carlo (MC) computer simulation of a hexagonal array of charged rods with fixed interaxial spacing. Strong ordering of the counterions between the DNA molecules and the absence of charge fluctuations at longer wavelengths was shown by the SANS number and charge structure factors. The DNA-counterion and counterion structure factors are interpreted with the correlation functions derived from the Poisson-Boltzmann equation, MD, and MC simulation. Best agreement is observed between the experimental structure factors and the prediction based on the Poisson-Boltzmann equation and/or MC simulation. The SANS results show that TMA is too large to penetrate the grooves to a significant extent, in contrast to what is shown by MD simulation.

Computer simulation study of molecular recognition in model DNA microarrays

DNA microarrays have been widely adopted by the scientific community for a variety of applications. To improve the performance of microarrays there is a need for a fundamental understanding of the interplay between the various factors that affect microarray sensitivity and specificity. We use lattice Monte Carlo simulations to study the thermodynamics and kinetics 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 and each segment represents a sequence of nucleotides ( approximately 11 nucleotides). Each probe segment interacts exclusively with its unique complementary target segment with a single hybridization energy; all other interactions are zero. We examine how the probe length, temperature, or hybridization energy, and the stretch along the target that the probe segments complement, affect the extent of hybridization. For systems containing single probe and single target molecules, we observe that as the probe length increases, the probability of binding all probe segments to the target decreases, implying that the specificity decreases. We observe that probes 12-16 segments ( approximately 132-176 nucleotides) long gave the highest specificity and sensitivity. This agrees with the experimental results obtained by another research group, who found an optimal probe length of 150 nucleotides. As the hybridization energy increases, the longer probes are able to bind all their segments to the target, thus improving their specificity. The hybridization kinetics reveals that the segments at the ends of the probe are most likely to start the hybridization. The segments toward the center of the probe remain bound to the target for a longer time than the segments at the ends of the probe.

Line of charges in electrolyte solution near a half-space

The effect of a half-space on counterion condensation around a line of charges in electrolyte solution is examined in the framework of Debye-Hückel electrostatics. The half-space substrate is allowed to be a conductor, a dielectric, or a semiconductor. Counterions are predicted to be released completely as the line of charges approaches a conducting substrate. When it approaches a dielectric substrate, depending on the ratio of solvent to substrate dielectric constant, there are three possibilities: (1) epsilon(sol)/epsilon(sub) < 1; the counterions are partially (or completely) released; (2) epsilon(sol)/epsilon(sub) = 1; the amount of condensation remains unchanged; and (3) epsilon(sol)/epsilon(sub) > 1; more counterions condense. Depending on the relative magnitude of screening lengths in the semiconductor and in the solution, its effect on condensation follows either that of a metal or that of a dielectric. For the case of a moderately doped silicon substrate, condensation is predicted to be similar to that for a dielectric.

Counterions between charged polymers exhibit liquid-like organization and dynamics

Current understanding of electrostatics in water is based on mean-field theories like the Poisson-Boltzmann formalism and its approximations, which are routinely used in colloid science and computational biology. This approach, however, breaks down for highly charged systems, which exhibit counterintuitive phenomena such as overcharging and like-charge attraction. Models of counterion correlations have been proposed as possible explanations, but no experimental comparisons are available. Here, collective dynamics of counterions that mediate like-charge attraction between F-actin filaments have been directly observed in aqueous solution using high-resolution inelastic x-ray scattering down to molecular length-scales. We find a previously undescribed acoustic-like phonon mode associated with correlated counterions. The excitation spectra at high wave-vector Q reveal unexpected dynamics due to ions interacting with their "cages" of nearest neighbors. We examine this behavior in the context of intrinsic charge density variations on F-actin. The measured speed of sound and collective relaxation rates in this liquid agree surprisingly well with simple model calculations.

Condensation of DNA-actin polyelectrolyte mixtures driven by ions of different valences

Multivalent ions can induce condensation of like-charged polyelectrolytes into compact states, a process that requires different ion valences for different polyelectrolyte species. In this work we examine the condensation behavior in binary anionic polyelectrolyte mixtures consisting of DNA coils and F-actin rods in the presence of monovalent, divalent, and trivalent ions. As expected, monovalent ions do not condense either component and divalent ions selectively condense F-actin rods out of the polyelectrolyte mixture. For trivalent ions, however, we observe a microphase separation between the two polyelectrolytes into coexisting finite-sized F-actin bundles and DNA toroids. Further, by increasing the DNA volume fraction in the mixture, condensed F-actin bundles can be completely destabilized, leading to only DNA condensation within the mixture. We examine a number of possible causes and propose a model based on polyelectrolyte competition for ions.

Polyelectrolytes in solutions with multivalent salt. Effects of flexibility and contour length

It has been experimentally observed that trivalent ions are capable of promoting compaction of semi-flexible polyelectrolyte chains. In this work we perform Monte Carlo simulations on single chain model systems with varying chain size and stiffness and evaluate the action of multivalent salt on the chain conformation. It is observed that longer chains tend to achieve relatively more compact conformations than shorter ones, and the dimensions of the collapsed structures do not significantly vary with contour length. The influence of contour length and intrinsic stiffness in the process of ion condensation is studied by analysis of the ion-ion nearest-neighbor distribution. The general trend is an increase of the degree of ion condensation as the chain length increases, in accordance with experimental evidence. A decreased importance of end-effects and, especially, larger volume charge densities are responsible for such behavior. The influence of chain stiffness is nontrivial, and depends on salt concentration. The results emphasize the complex nature of ion-correlation phenomena in flexible or semi-flexible chains and call for the development of more sophisticated analytical theories.

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

We have investigated the salt sensitivity of the hexagonal-to-cholesteric phase transition of spermidine-condensed DNA. This transition precedes the resolubilization of precipitated DNA that occurs at high spermidine concentration. The sensitivity of the critical spermidine concentration at the transition point to the anion species and the NaCl concentration indicates that ion pairing of this trivalent ion underlies this unusual transition. Osmotic pressure measurements of spermidine salt solutions are consistent with this interpretation. Spermidine salts are not fully dissociated at higher concentrations. The competition for DNA binding among the fully charged trivalent ion and the lesser charged complex species at higher concentrations significantly weakens attraction between DNA helices in the condensed state. This is contrary to the suggestion that the binding of spermidine at higher concentrations causes DNA overcharging and consequent electrostatic repulsion.

Direct observation of counterion organization in F-actin polyelectrolyte bundles

Attractions between like-charged polyelectrolytes have been observed in a variety of systems (W.M. Gelbart, R.F. Bruinsma, P.A. Pincus, V.A. Parsegian, Phys. Today 53, September issue, 38 (2000)). Recent biological examples include DNA, filamentous viruses, and F-actin. Theoretical investigations on idealized systems indicate that counterion correlations play a central role, but no experiments that specifically probe such correlations have been performed. Using synchrotron X-ray diffraction, we have directly observed the organization of multivalent ions on cytoskeletal filamentous actin (a well-defined biological polyelectrolyte) and found an unanticipated symmetry-breaking collective counterion mechanism for generating attractions. Surprisingly, the counterions do not form a lattice that simply follows actin's helical symmetry; rather, the counterions organize into "frozen" ripples parallel to the actin filaments and form structures reminiscent of charge density waves. Moreover, these 1D counterion charge density waves form a coupled mode with twist deformations of the oppositely charged actin filaments. This counterion organization is not sensitive to thermal fluctuations in temperature range accessible to protein-based polyelectrolyte systems. Moreover, the counterion density waves are "pinned" to the spatial periodicity of charges on the actin filament even if the global filament charge density is varied, indicating the importance of charge periodicity on the polyelectrolyte substrate.

"Like-charge attraction" between anionic polyelectrolytes: molecular dynamics simulations

"Like-charge attraction" is a phenomenon found in many biological systems containing DNA or proteins, as well as in polyelectrolyte systems of industrial importance. "Like-charge attraction" between polyanions is observed in the presence of mobile multivalent cations. At a certain limiting concentration of cations, the negatively charged macroions cease to repel each other and even an attractive force between the anions is found. With classical molecular dynamics simulations it is possible to elucidate the processes that govern the attractive behavior with atomistic resolution. As an industrially relevant example we study the interaction of negatively charged carboxylate groups of sodium polyacrylate molecules with divalent cationic Ca2+ counterions. Here we show that Ca2+ ions initially associate with single chains of polyacrylates and strongly influence sodium ion distribution; shielded polyanions approach each other and eventually "stick" together (precipitate), contrary to the assumption that precipitation is initially induced by intermolecular Ca2+ bridging.

Monte Carlo simulation of an inhomogeneous dielectric continuum model for B-DNA

Thermodynamic and structural properties of the counterion atmosphere surrounding B-DNA are calculated by Monte Carlo simulation in a spatially inhomogeneous, but piecewise uniform, dielectric continuum cell model - the "barbarous" model. A boundary element formulation is implemented to study the sensitivity of these properties with respect to perturbations in the location of discontinuous dielectric boundaries relative to fixed and mobile charges. High concentrations are considered corresponding to the liquid crystalline hexagonally ordered phase of DNA. Primitive model results are verified against other simulation reports and a comparison of barbarous model predictions with experimental data is discussed. The internal energy, osmotic coefficient, radial distributions and the population ratio of counterions in the geometrically resolved major and minor grooves are all found to strongly depend on the dielectric boundary position. This suggests that a self-consistent development of the model should consider a free surface problem where the boundary is not specified a priori.

Thermodynamic behaviors of polyampholytes at low temperatures

The thermodynamic properties of 6-mer polyampholyte chains were simulated with the multicanonical Monte Carlo method in a three-dimensional off-lattice model. The results demonstrate that the number of the charged monomers on the chain and the sequence significantly affect the transition behaviors of polyampholyte chains. In the case of the random distribution of the charged monomers, two oppositely charged monomers act as two stickers during a collapse process, due to which the movement of monomers is suppressed and the chains can more directly reach their solid state. Interestingly, in a proper arrangement of the charged monomers, the chains may have a proteinlike nondegenerate state, i.e., the chain is designable. The transition of such polyampholyte chains appears to be of a two-state, all-or-none type.

Interhelical spacing in liquid crystalline spermine and spermidine-DNA precipitates

The structure of polyamines-DNA precipitates was studied by x-ray diffraction. Precise measurements of the interhelix distance a(H) were obtained at different NaCl, polyamine, and DNA concentrations. Most of the results were obtained using spermine and few others using spermidine. The precipitates are liquid crystalline, either hexagonal and/or cholesteric, with an interhelical spacing that depends on the ionic concentrations and on the polyamine type. In our experimental conditions, the spacing varies from 28.15 to 33.4 angstroms. This variation is interpreted in terms of different ionic components that are present inside the precipitates and that are thought to regulate the value of the cohesive energy of DNA. These results are discussed in relation to the biological processes requiring a closeness of double helices and to the role played by polyamine analogs in cancer therapy.

Exclusion of alcohols from spermidine-DNA assemblies: probing the physical basis of preferential hydration

The interaction of the alcohols 2-methyl-2,4-pentanediol (MPD) and 2-propanol and of glycerol with condensed spermidine(3+)-DNA arrays are investigated with direct force measurements using osmotic stress coupled with X-ray scattering. Thermodynamic forces between DNA helices are measured from the dependence of helical interaxial spacings on the osmotic pressure applied by poly(ethylene glycol) solutions in equilibrium with the DNA phase. The sensitivity of these forces to solute concentration can be transformed into a change in the number of excess or deficit solutes or waters in the DNA phase by applying the Gibbs-Duhem equation. The alcohols examined are excluded from the condensed DNA array and strongly affect the osmotic stress force curves. DNA is preferentially hydrated. MPD is significantly more excluded than 2-propanol. The exclusion of these alcohols, however, is not due to a steric repulsion since glycerol that is intermediate in size between MPD and 2-propanol does not observably affect DNA force curves. As the distance between DNA helices varies, the change in the number of excess waters is independent of alcohol concentration for each alcohol. These solutes are acting osmotically on the condensed array. The distance dependence of exclusion indicates that repulsive water structuring forces dominate the interaction of alcohols with the DNA surface. The exclusion measured for these condensed arrays can quantitatively account for the effect of these alcohols on the precipitation of DNA from dilute solution by spermidine(3+).

Onset of DNA aggregation in presence of monovalent and multivalent counterions

We address theoretically aggregation of DNA segments by multivalent polyamines such as spermine and spermidine. In experiments, the aggregation occurs above a certain threshold concentration of multivalent ions. We demonstrate that the dependence of this threshold on the concentration of DNA has a simple form. When the DNA concentration c(DNA) is smaller than the monovalent salt concentration, the threshold multivalent ion concentration depends linearly on c(DNA), having the form alphac(DNA) + beta. The coefficients alpha and beta are related to the density profile of multivalent counterions around isolated DNA chains, at the onset of their aggregation. This analysis agrees extremely well with recent detailed measurements on DNA aggregation in the presence of spermine. From the fit to the experimental data, the number of condensed multivalent counterions per DNA chain can be deduced. A few other conclusions can then be reached: 1), the number of condensed spermine ions at the onset of aggregation decreases with the addition of monovalent salt; 2), the Poisson-Boltzmann theory overestimates the number of condensed multivalent ions at high monovalent salt concentrations; and 3), our analysis of the data indicates that the DNA charge is not overcompensated by spermine at the onset of aggregation.