Electrostatic interaction between long, rigid helical macromolecules at all interaxial angles

Nucleosome-induced homology recognition in chromatin

One of the least understood properties of chromatin is the ability of its similar regions to recognize each other through weak interactions. Theories based on electrostatic interactions between helical macromolecules suggest that the ability to recognize sequence homology is an innate property of the non-ideal helical structure of DNA. However, this theory does not account for the nucleosomal packing of DNA. Can homologous DNA sequences recognize each other while wrapped up in the nucleosomes? Can structural homology arise at the level of nucleosome arrays? Here, we present a theoretical model for the recognition potential well between chromatin fibres sliding against each other. This well is different from the one predicted for bare DNA; the minima in energy do not correspond to literal juxtaposition, but are shifted by approximately half the nucleosome repeat length. The presence of this potential well suggests that nucleosome positioning may induce mutual sequence recognition between chromatin fibres and facilitate the formation of chromatin nanodomains. This has implications for nucleosome arrays enclosed between CTCF-cohesin boundaries, which may form stiffer stem-like structures instead of flexible entropically favourable loops. We also consider switches between chromatin states, e.g. through acetylation/deacetylation of histones, and discuss nucleosome-induced recognition as a precursory stage of genetic recombination.

Anomalous Laterally Stressed Kinetically Trapped DNA Surface Conformations

DNA kinking is inevitable for the highly anisotropic 1D-1D electrostatic interaction with the one-dimensionally periodically charged surface. The double helical structure of the DNA kinetically trapped on positively charged monomolecular films comprising the lamellar templates is strongly laterally stressed and extremely perturbed at the nanometer scale. The DNA kinetic trapping is not a smooth 3D-> 2D conformational flattening but is a complex nonlinear in-plane mechanical response (bending, tensile and unzipping) driven by the physics beyond the scope of the applicability of the linear worm-like chain approximation. Up to now, the DNA molecule adsorbed on a surface was believed to always preserve its native structure. This belief implies a negligible contribution of lateral surface forces during and after DNA adsorption although their impact has never been elucidated. High-resolution atomic force microscopy was used to observe that stiff DNA molecules kinetically trapped on monomolecular films comprising one-dimensional periodically charged lamellar templates as a single layer or as a sublayer are oversaturated by sharp discontinuous kinks and can also be locally melted and supercoiled. We argue that kink/anti-kink pairs are induced by an overcritical lateral bending stress (> 30 pNnm) inevitable for the highly anisotropic 1D-1D electrostatic interaction of DNA and underlying rows of positive surface charges. In addition, the unexpected kink-inducing mechanical instability in the shape of the template-directed DNA confined between the positively charged lamellar sides is observed indicating the strong impact of helicity. The previously reported anomalously low values of the persistence length of the surface-adsorbed DNA are explained by the impact of the surface-induced low-scale bending. The sites of the local melting and supercoiling are convincingly introduced as other lateral stress-induced structural DNA anomalies by establishing a link with DNA high-force mechanics. The results open up the study in the completely unexplored area of the principally anomalous kinetically trapped DNA surface conformations in which the DNA local mechanical response to the surface-induced spatially modulated lateral electrostatic stress is essentially nonlinear. The underlying rich and complex in-plane nonlinear physics acts at the nanoscale beyond the scope of applicability of the worm-like chain approximation.

Ion-mediated interactions between like-charged polyelectrolytes with bending flexibility

Ion-mediated interactions between polyelectrolytes (PEs) are crucial to the properties of flexible biopolymers such as nucleic acids and proteins but the effect of PE flexibility on such interactions has not been explicitly addressed until now. In this work, the potentials of mean force (PMFs) between like-charged PEs with different bending flexibility have been investigated by Monte Carlo simulations and a cylindrical confinement around each PE was involved to model two PEs in an array. We found that in the absence of trivalent salt, the PMFs between like-charged PEs in an array are apparently repulsive while the bending flexibility can visibly decrease the repulsive PMFs. With the addition of high trivalent salt, the PMFs become significantly attractive whereas the attractive PMFs can be apparently weakened by the bending flexibility. Our analyses reveal that the effect of bending flexibility is attributed to the increased PE conformational space, which allows the PEs to fluctuate away to decrease the monovalent ion-mediated repulsion or to weaken the trivalent ion-mediated attraction through disrupting trivalent ion-bridging configuration. Additionally, our further calculations show that the effect of bending flexibility on the ion-mediated interactions is less apparent for PEs without cylindrical confinement.

Ionic liquids-mediated interactions between nanorods

Surface forces mediated by room-temperature ionic liquids (RTILs) play an essential role in diverse applications including self-assembly, lubrication, and electrochemical energy storage. Therefore, their fundamental understanding is critical. Using molecular simulations, we study the interactions between two nanorods immersed in model RTILs at rod-rod separations where both structural and double layer forces are important. The interaction force between neutral rods oscillates as the two rods approach each other, similar to the classical structural forces. Such oscillatory force originates from the density oscillation of RTILs near each rod and is affected by the packing constraints imposed by the neighboring rods. The oscillation period and decay length of the oscillatory force are mainly dictated by the ion density distribution near isolated nanorods. When charges are introduced on the rods, the interaction force remains short-range and oscillatory, similar to the interactions between planar walls mediated by some protic RTILs reported earlier. Nevertheless, introducing net charges to the rods greatly changes the rod-rod interactions, e.g., by delaying the appearance of the first force trough and increasing the oscillation period and decay length of the interaction force. The oscillation period and decay length of the oscillatory force and free energy are commensurate with those of the space charge density near an isolated, charged rod. The free energy of rod-rod interactions reaches local minima (maxima) at rod-rod separations when the space charges near the two rods interfere constructively (destructively). The insight on the short-range interactions between nanorods in RTILs helps guide the design of novel materials, e.g., ionic composites based on rigid-rod polyanions and RTILs.

Divalent Ion-Mediated DNA-DNA Interactions: A Comparative Study of Triplex and Duplex

Ion-mediated interaction between DNAs is essential for DNA condensation, and it is generally believed that monovalent and nonspecifically binding divalent cations cannot induce the aggregation of double-stranded (ds) DNAs. Interestingly, recent experiments found that alkaline earth metal ions such as Mg²⁺ can induce the aggregation of triple-stranded (ts) DNAs, although there is still a lack of deep understanding of the surprising findings at the microscopic level. In this work, we employed all-atom dynamic simulations to directly calculate the potentials of mean force (PMFs) between tsDNAs, between dsDNAs, and between tsDNA and dsDNA in Mg²⁺ solutions. Our calculations show that the PMF between tsDNAs is apparently attractive and becomes more strongly attractive at higher [Mg²⁺], although the PMF between dsDNAs cannot become apparently attractive even at high [Mg²⁺]. Our analyses show that Mg²⁺ internally binds into grooves and externally binds to phosphate groups for both tsDNA and dsDNA, whereas the external binding of Mg²⁺ is much stronger for tsDNA. Such stronger external binding of Mg²⁺ for tsDNA favors more apparent ion-bridging between helices than for dsDNA. Furthermore, our analyses illustrate that bridging ions, as a special part of external binding ions, are tightly and positively coupled to ion-mediated attraction between DNAs.

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.

Texture formation in DNA films with alkali metal chlorides

The formation of textures in DNA films with LiCl, NaCl, KCl, RbCl, and CsCl salts has been studied. The films are prepared by evaporation of water solution with highly polymerized calf thymus DNA and excess salt of specific type. For DNA solution with 10 mM concentration of NaCl, KCl, and RbCl the films with dendritic textures have been obtained, whereas in case of CsCl the textures in the films appear only at 30 mM concentration of excess salt in the initial solution. In the solution with LiCl, the textures in DNA films have not been observed within the whole range of concentration of excess salt under consideration. The analysis of parameters of DNA films with different salts has showed that evaporation of solution leads to crystallization of salt ions on DNA macromolecule and formation of DNA-salt complexes. Electrostatic energy of the system of crystalline ordered ions and charges of DNA chains has been estimated to study the stability of DNA-salt complexes. The results obtained for different salts have been showed that the presence of DNA macromolecule enhances crystallization as compared with solution without DNA. The property of excess salt to form the crystalline structures has been found to decrease in the following order: KCl > NaCl > RbCl > CsCl > LiCl. The results of estimation are in good agreement with the experimentally observed dependence of texture formation on excess salt type.

Rod Packing in Chiral Nematic Cellulose Nanocrystal Dispersions Studied by Small-Angle X-ray Scattering and Laser Diffraction

The packing of cellulose nanocrystals (CNC) in the anisotropic chiral nematic phase has been investigated over a wide concentration range by small-angle X-ray scattering (SAXS) and laser diffraction. The average separation distance between the CNCs and the average pitch of the chiral nematic phase have been determined over the entire isotropic-anisotropic biphasic region. The average separation distances range from 51 nm, at the onset of the anisotropic phase formation, to 25 nm above 6 vol % (fully liquid crystalline phase) whereas the average pitch varies from ≈15 μm down to ≈2 μm as ϕ increases from 2.5 up to 6.5 vol %. Using the cholesteric order, we determine that the twist angle between neighboring CNCs increases from about 1° up to 4° as ϕ increases from 2.5 up to 6.5 vol %. The dependence of the twisting on the volume fraction was related to the increase in the magnitude of the repulsive interactions between the charged rods as the average separation distance decreases.

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.

Physical theory of ionomer aggregation in water

This article presents a physical theory for the aggregation of ionomer molecules in aqueous solution. To study this phenomenon, we consider a system of charged rigid rods with uniform surface charge immersed in water. The free-energy functional derived for this system consists of hydrophobic and direct electrostatic contributions as well as entropic terms. Energy minimization gives the stable aggregation number as a function of surface charge density, surface tension, geometric parameters, and density of rods in solution. We provide configuration diagrams of the system, which display the impact of the hydrophobic and electrostatic interaction strengths on the stabilization of finite-size bundles.

Torsional deformation of double helix in interaction and aggregation of DNA

We incorporate sequence-dependent twisting between adjacent base pairs and torsional elasticity of double helix into the theory of DNA-DNA interaction. The results show that pairing and counterion-induced-aggregation of nonhomologous DNA are accompanied by considerable torsional deformation. The deformation tunes negatively charged phosphate strands and positively charged grooves on opposing molecules to stay "in register", substantially reducing nonideality of the helical structure of DNA. Its cost, however, makes interaction between nonhomologous DNA less energetically favorable. In particular, interaction between double helical DNA may result in sequence homology recognition and selective pairing of homologous fragments containing more than 100-200 base pairs. We also find a weak, but potentially measurable, increase in the expected counterion concentration required for aggregation of nonhomologous DNA and slightly higher solubility of such DNA above the critical concentration.

Chiral electrostatics breaks the mirror symmetry of DNA supercoiling

DNA supercoiling plays a fundamental role in regulating cellular activity and in the packaging of genetic material. In this communication, we analyse the effect of attractive chiral forces on the conformation of a closed circular DNA molecule, arising due to the helical patterns of charges on the DNA. We propose a model for closed loop DNA which uses the results of the recent theory of electrostatic interactions of a braid of two free-ended DNA molecules. Our model reproduces the known features of DNA supercoiling in an environment of low ionic strength. In high salt conditions, and in the presence of counterions that have high affinity to the DNA grooves, helix-specific forces significantly affect the conformation of the molecule by favouring a state characterized by a central left-handed braided section where there is close contact between distant portions of the loop. In such an environment we predict a previously unexplored possibility that nicked or topologically relaxed DNA molecules adopt a writhed state. This prediction suggests an alternative explanation for experiments in which it was assumed that the most stable topoisomer is always an open circle. Our results also give the first plausible explanation for the occurrence of tightly interwound molecules observed in cryo-electron microscopy and atomic force microscopy in a high ionic strength environment. We suggest several new experiments to test the predictions of this theory.

Electrostatic braiding and homologous pairing of DNA double helices

Homologous pairing and braiding (supercoiling) have crucial effects on genome organization, maintenance, and evolution. Generally, the pairing and braiding processes are discussed in different contexts, independently of each other. However, analysis of electrostatic interactions between DNA double helices suggests that in some situations these processes may be related. Here we present a theory of DNA braiding that accounts for the elastic energy of DNA double helices as well as for the chiral nature of the discrete helical patterns of DNA charges. This theory shows that DNA braiding may be affected, stabilized, or even driven by chiral electrostatic interactions. For example, electrostatically driven braiding may explain the surprising recent observation of stable pairing of homologous double-stranded DNA in solutions containing only monovalent salt. Electrostatic stabilization of left-handed braids may stand behind the chiral selectivity of type II topoisomerases and positive plasmid supercoiling in hyperthermophilic bacteria and archea.

Correlation forces between helical macro-ions in the weak coupling limit

When correlation effects are relatively weak, electrostatic interaction forces between cylindrical macro-ions may be divided into two contributions (Lee 2010 J. Phys.: Condens. Matter 22 414101). Firstly, there is a mean field contribution, described by the theory of Kornyshev and Leikin (1997 J. Chem. Phys. 107 3656) at large separations. Secondly, we have correlation forces, which we analyze by performing an expansion in the number density of condensed ions. We see three distinct contributions, for which analytical expressions are given for both general and helical contributions. Firstly, there is a term (of leading order in the expansion) that is a change in the solvation energies of uncondensed counter-ions due to two macro-molecular interfaces. Secondly, we have a contribution that comes from fluctuations in the condensed ion charge density being repelled by their 'images' in the other molecule. Both of these contributions are repulsive. Lastly, there exists an attractive Oosawa contribution that arises from fluctuations in the condensed ions about one molecule correlating with those about the other molecule. The first two forces do not depend on the orientation of the molecules about their long axes. However, the Oosawa force may do so, depending on the pattern of bound and fixed charges. For a DNA like charge distribution, we see that the strength of this dependence is governed by the relative proportion of bound ions, between two positions that represent the DNA groove centers. We see that, at a Debye screening length equivalent to physiological salt concentrations, the correlation forces can be neglected for univalent ions. For divalent ions, they contribute a small, albeit significant, correction. Our calculations suggest that increasing the salt concentration reduces the size of these forces.

Cholesteric and nematic liquid crystalline phase behavior of double-stranded DNA stabilized single-walled carbon nanotube dispersions

The first lyotropic cholesteric single-walled carbon nanotube (SWNT) liquid crystal phase was obtained by dispersing SWNTs in an aqueous solution of double-stranded DNA (dsDNA). Depending on the dispersion methodology, the polydomain nematic phase previously reported for other lyotropic carbon nanotube dispersions could also be obtained. The phase behavior and dispersion microstructure were affected by the relative concentrations of dsDNA and SWNT and whether small bundles were removed prior to concentrating the dispersions. This readily controlled phase behavior opens new routes for producing SWNT films with controlled morphology.

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

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

A geometrical model for DNA organization in bacteria

Recent experimental studies have revealed that bacteria, such as C. crescentus, show a remarkable spatial ordering of their chromosome. A strong linear correlation has been found between the position of genes on the chromosomal map and their spatial position in the cellular volume. We show that this correlation can be explained by a purely geometrical model. Namely, self-avoidance of DNA, specific positioning of one or few DNA loci (such as origin or terminus) together with the action of DNA compaction proteins (that organize the chromosome into topological domains) are sufficient to get a linear arrangement of the chromosome along the cell axis. We develop a Monte-Carlo method that allows us to test our model numerically and to analyze the dependence of the spatial ordering on various physiologically relevant parameters. We show that the proposed geometrical ordering mechanism is robust and universal (i.e. does not depend on specific bacterial details). The geometrical mechanism should work in all bacteria that have compacted chromosomes with spatially fixed regions. We use our model to make specific and experimentally testable predictions about the spatial arrangement of the chromosome in mutants of C. crescentus and the growth-stage dependent ordering in E. coli.

Charge renormalization of helical macromolecules

Some time ago a theory of electrostatic interaction between helical macromolecules was proposed (Kornyshev and Leikin 1997 J. Chem. Phys. 107 3656): the Kornyshev-Leikin (KL) theory. We place this theory on a more rigorous statistical mechanical grounding, starting from the free energy that can be derived from a grand partition function. We see that the long range behaviour of the force is indeed given by the KL theory, no matter whether the distributions of 'condensed' ionic charge are at the surface of the macromolecule or extend away from it. Thus, for the limiting behaviour, we need only self-consistently calculate the distribution of the condensed fraction of ions for a single macro-ion. This distribution can be related back to interaction parameters: KL parameters. Furthermore, we are able to see within the formalism where corrections due to the hard core radius of the ion enter. For the adjustment of the 'condensed' ions, we show an expression for the leading order contribution, as well as relevant decay lengths. As a demonstration of the theoretical 'machinery', as well as a study of qualitative effects, we calculate the KL parameters in one instance. We use a DNA-like surface charge distribution, where a fraction of the ions are assumed to be bound in the grooves at the surface of a DNA molecule, whereas the rest of the charge distribution is calculated self-consistently. Also, the electrostatic contribution to the counter-ion binding potentials that ions experience within the grooves can be calculated.

Homology recognition funnel

The recognition of homologous sequences of DNA before strand exchange is considered to be the most puzzling stage of homologous recombination. A mechanism for two homologous dsDNAs to recognize each other from a distance in electrolytic solution without unzipping had been proposed in an earlier paper [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 366 (2001)]. In that work, the difference in the electrostatic interaction energy between homologous duplexes and between nonhomologous duplexes, termed the recognition energy, has been calculated. That calculation was later extended in a series of papers to account for torsional elasticity of the molecules. A recent paper [A. A. Kornyshev and A. Wynveen, Proc. Natl. Acad. Sci. U.S.A. 106, 4683 (2009)] investigated the form of the potential well that homologous DNA molecules may feel when sliding along each other. A simple formula for the shape of the well was obtained. However, this latter study was performed under the approximation that the sliding molecules are torsionally rigid. Following on from this work, in the present article we investigate the effect of torsional flexibility of the molecules on the shape of the well. A variational approach to this problem results in a transcendental equation that is easily solved numerically. Its solutions show that at large interaxial separations the recognition well becomes wider and shallower, whereas at closer distances further unexpected features arise related to an abrupt change in the mean azimuthal alignment of the molecules. The energy surface as a function of interaxial separation and the axial shift defines what we call the recognition funnel. We show that it depends dramatically on the patterns of adsorption of counterions on DNA.

Right-handed double-helix ultrashort DNA yields chiral nematic phases with both right- and left-handed director twist

Concentrated solutions of duplex-forming DNA oligomers organize into various mesophases among which is the nematic (N(∗)), which exhibits a macroscopic chiral helical precession of molecular orientation because of the chirality of the DNA molecule. Using a quantitative analysis of the transmission spectra in polarized optical microscopy, we have determined the handedness and pitch of this chiral nematic helix for a large number of sequences ranging from 8 to 20 bases. The B-DNA molecule exhibits a right-handed molecular double-helix structure that, for long molecules, always yields N(∗) phases with left-handed pitch in the μm range. We report here that ultrashort oligomeric duplexes show an extremely diverse behavior, with both left- and right-handed N(∗) helices and pitches ranging from macroscopic down to 0.3 μm. The behavior depends on the length and the sequence of the oligomers, and on the nature of the end-to-end interactions between helices. In particular, the N(∗) handedness strongly correlates with the oligomer length and concentration. Right-handed phases are found only for oligomers shorter than 14 base pairs, and for the sequences having the transition to the N(∗) phase at concentration larger than 620 mg/mL. Our findings indicate that in short DNA, the intermolecular double-helical interactions switch the preferred liquid crystal handedness when the columns of stacked duplexes are forced at high concentrations to separations comparable to the DNA double-helix pitch, a regime still to be theoretically described.

Undulations enhance the effect of helical structure on DNA interactions

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

Nanoscale measurements of the assembly of collagen to fibrils

Observing the self-assembly of collagen from single collagen monomers to higher order fibrils and fibers provides a bottom-up approach to engineering its ultrastructure in comparison to structural studies of already formed collagen fibers. This approach can be used for the fabrication of controlled collagen-based biomaterials with varying mechanical properties. Here, we investigate the time-dependent self-assembly of collagen into single fibrils in vitro through high resolution imaging of collagen type 1 prior to fibrillogenesis. This was confirmed by comparing persistence length and diameter in controlled experiments and studying the morphology and mechanical properties of nanoscale collagen fibrils through AFM nanoindentation measurements. The Young's modulus of these collagen fibrils was estimated to be around 1GPa in the dehydrated state. The stability and mechanical characteristics of collagen obtained in these experiments indicate the hierarchical assembly occurs at both a structural and mechanical level.

Correlation effects, image charge effects and finite size in the macro-ion-electrolyte system: a field-theoretic approach

We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function. For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations. Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions. This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical formula for the interaction of two charged cylinders.

DNA cholesteric phases: the role of DNA molecular chirality and DNA-DNA electrostatic interactions

DNA molecules form dense liquid-crystalline twisted phases both in vivo and in vitro. How the microscopic DNA chirality is transferred into intermolecular twist in these mesophases and what is the role of chiral DNA-DNA electrostatic interactions is still not completely clear. In this paper, we first give an extended overview of experimental observations on DNA cholesteric phases and discuss the factors affecting their stability. Then, we consider the effects of steric and electrostatic interactions of grooved helical molecules on the sign of cholesteric twist. We present some theoretical results on the strength of DNA-DNA chiral electrostatic interactions, on DNA-DNA azimuthal correlations in cholesteric phases, on the value of DNA cholesteric pitch, and on the regions of existence of DNA chiral phases stabilized by electrostatic interactions. We suggest for instance that 146 bp long DNA fragments with stronger affinities for the nucleosome formation can form less chiral cholesteric phases, with a larger left-handed cholesteric pitch. Also, the value of left-handed pitch formed in assemblies of homologous DNA fragments is predicted to be smaller than that of randomly sequenced DNAs. We expect also the cholesteric assemblies of several-kbp-long DNAs to require higher external osmotic pressures for their stability than twisted phases of short nucleosomal DNA fragments at the same DNA lattice density.

Electrostatic free energy landscapes for nucleic acid helix assembly

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

On the physical nature of mesophases of guanosine gels

The unusual columnar aqueous mesophases of self-assembled guanosine stacks, such as 2'-deoxyguanosine 5'-monophosphate and 2'-deoxyguanosine 3'-monophosphate, are analyzed in terms of a general theory of azimuthal correlations between the charged helices. This theory considers forces, specific to the helical structure of each macromolecule, which depend on the azimuthal orientations of the molecules about their long axes. More specifically, in determining the magnitudes and decay lengths of these helix specific forces we utilize the Kornyshev-Leikin theory of electrostatic interaction between helical macromolecules and quantitatively fit experimental data. Together with explaining a number of the observed features of these mesophases, several new effects are predicted. Possible limitations and developments of our theoretical model are discussed, as well as new experiments to test the implications of the theory.

DNA cholesteric pitch as a function of density and ionic strength

The nature of chiral interactions among chiral biopolymers, such as DNA, protein alpha-helices, and rodlike virus particles, remains elusive. In particular, a satisfactory model connecting molecular chiral interactions and the pitch of the resulting chiral mesophases is lacking. We report the measurement of short-fragment (146-bp) DNA cholesteric spherulite pitch as a function of osmotic pressure, average DNA interaxial spacing, and salt concentration. We determined cholesteric pitch and interaxial spacing by polarizing optical microscopy and x-ray scattering, respectively, from which the twist-angle between DNA molecules can be calculated. Surprisingly, we found that decreasing ionic strength resulted in weaker chiral interactions between DNA chains, as evidenced by the decrease in the twist-angle, and consequent increase in the cholesteric pitch, for a fixed interaxial spacing. We propose that this behavior can be explained by increased smearing-out of the helical charge pattern along DNA as the Debye screening length is increased.

Structure and stability of chiral β-tapes: A computational coarse-grained approach

We present two coarse-grained models of different levels of detail for the description of beta-sheet tapes obtained from equilibrium self-assembly of short rationally designed oligopeptides in solution. Here we only consider the case of the homopolymer oligopeptides with the identical sidegroups attached, in which the tapes have a helicoid surface with two equivalent sides. The influence of the chirality parameter on the geometrical characteristics, namely the diameter, interstrand distance, and pitch, of the tapes has been investigated. The two models are found to produce equivalent results suggesting a considerable degree of universality in conformations of the tapes.

Statistical mechanics of columnar DNA assemblies

Many physical systems can be mapped onto solved or "solvable" models of magnetism. In this work, we have mapped the statistical mechanics of columnar phases of ideally helical rigid DNA--subject to the earlier found unusual, frustrated pair potential (A.A. Kornyshev, S. Leikin, J. Chem. Phys. 107, 3656 (1997))--onto an exotic, unknown variant of the XY model on a fixed or restructurable lattice. Here, the role of the "spin" is played by the azimuthal orientation of the molecules. We have solved this model using a Hartree-Fock approximation, ground-state calculations, and finite-temperature Monte Carlo simulations. We have found peculiar spin order transitions, which may also be accompanied by positional restructuring, from hexagonal to rhombohedric lattices. Some of these have been experimentally observed in dense columnar aggregates. Note that DNA columnar phases are of great interest in biophysical research, not only because they are a useful in vitro tool for the study of DNA condensation, but also since these structures have been detected in living matter. Within the approximations made, our study provides insight into the statistical mechanics of these systems.

From the double-stranded helix to the chiral nematic phase of B-DNA: A molecular model

B-DNA solutions of suitable concentration form left-handed chiral nematic phases (cholesterics). Such phases have also been observed in solutions of other stiff or semiflexible chiral polymers; magnitude and handedness of the cholesteric pitch are uniquely related to the molecular features. In this work we present a theoretical method and a numerical procedure which, starting from the structure of polyelectrolytes, lead to the prediction of the cholesteric pitch. Molecular expressions for the free energy of the system are obtained on the basis of steric and electrostatic interactions between polymers; the former are described in terms of excluded volume, while a mean field approximation is used for the latter. Calculations have been performed for 130 base pair fragments of B-DNA. The theoretical predictions provide an explanation for the experimental behavior, by showing the counteracting role played by shape and charge chirality of the molecule.

DNA-DNA interaction beyond the ground state

The electrostatic interaction potential between DNA duplexes in solution is a basis for the statistical mechanics of columnar DNA assemblies. It may also play an important role in recombination of homologous genes. We develop a theory of this interaction that includes thermal torsional fluctuations of DNA using field-theoretical methods and Monte Carlo simulations. The theory extends and rationalizes the earlier suggested variational approach which was developed in the context of a ground state theory of interaction of nonhomologous duplexes. It shows that the heuristic variational theory is equivalent to the Hartree self-consistent field approximation. By comparison of the Hartree approximation with an exact solution based on the QM analogy of path integrals, as well as Monte Carlo simulations, we show that this easily analytically-tractable approximation works very well in most cases. Thermal fluctuations do not remove the ability of DNA molecules to attract each other at favorable azimuthal conformations, neither do they wash out the possibility of electrostatic "snap-shot" recognition of homologous sequences, considered earlier on the basis of ground state calculations. At short distances DNA molecules undergo a "torsional alignment transition," which is first order for nonhomologous DNA and weaker order for homologous sequences.

Using Hydrogen Bonds to Direct the Assembly of Crowded Aromatics

This Minireview details the design, synthesis, and self-assembly of a new class of crowded aromatics that form columnar superstructures. The assembly of these subunits produces helical and polar stacks, whose assembly can be directed with electric fields. In concentrated solutions, these self-assembled helical rods exhibit superhelical arrangements that reflect circularly polarized light at visible wavelengths. Depending on the side chains employed, spin-cast films yield either polar monolayers or isolated strands of molecules that can be visualized with scanning probe microscopy. Also detailed herein are methods to link these mesogens together to produce monodisperse oligomers that fold into defined secondary conformations.

Theory of polyelectrolytes in solvents

Using a continuum description, we account for fluctuations in the ionic solvent surrounding a Gaussian, charged chain and derive an effective short-ranged potential between the charges on the chain. This potential is repulsive at short separations and attractive at longer distances. The chemical potential can be derived from this potential. When the chemical potential is positive, it leads to a meltlike state. For a vanishingly low concentration of segments, this state exhibits scaling behavior for long chains. The Flory exponent characterizing the radius of gyration for long chains is calculated to be approximately 0.63, close to the classical value obtained for second order phase transitions. For short chains, the radius of gyration varies linearly with N, the chain length, and is sensitive to the parameters in the interaction potential. The linear dependence on the chain length N indicates a stiff behavior. The chemical potential associated with this interaction changes sign, when the screening length in the ionic solvent exceeds a critical value. This leads to condensation when the chemical potential is negative. In this state, it is shown using the mean-field approximation that spherical and toroidal condensed shapes can be obtained. The thickness of the toroidal polyelectrolyte is studied as a function of the parameters of the model, such as the ionic screening length. The predictions of this theory should be amenable to experimental verification.

Effective interaction between helical biomolecules

The effective interaction between two parallel strands of helical biomolecules, such as deoxyribose nucleic acids (DNA), is calculated using computer simulations of the "primitive" model of electrolytes. In particular we study a simple model for B-DNA incorporating explicitly its charge pattern as a double-helix structure. The effective force and the effective torque exerted onto the molecules depend on the central distance and on the relative orientation. The contributions of nonlinear screening by monovalent counterions to these forces and torques are analyzed and calculated for different salt concentrations. As a result, we find that the sign of the force depends sensitively on the relative orientation. For intermolecular distances smaller than 6 A it can be both attractive and repulsive. Furthermore, we report a nonmonotonic behavior of the effective force for increasing salt concentration. Both features cannot be described within linear screening theories. For large distances, on the other hand, the results agree with linear screening theories provided the charge of the biomolecules is suitably renormalized.