Ising models of charge storage in multifile metallic nanopores.

Ising type models of charging of conductive nanopores with ions have already been proposed and investigated for single file cylindrical or single layer slit nanopores. In such pores, the state of ions, the coulombic interactions of which are exponentially screened by their images in pore walls, was named superionic. In the present work we extend the analysis of the superionic state to nanopores that can accommodate multiple rows of ions. By grouping multiple charges in the same row into 'supercharges', we map the arrangement of ions in polarised electrodes on a multi-row Ising model in an external field. We investigate one-, two- and three-row cases, which we solve exactly, using a purpose-built semi-numerical transfer matrix method. For pores of different radii, which can accommodate the corresponding number of ion rows, we calculate the dependence of the electrical capacitance and stored energy density on electrode potential. As in charging the single file pores, we find that in narrower pores higher energy densities can be achieved at low applied potentials, while wider pores perform better as the voltage is increased.

Monitoring plasmon coupling and SERS enhancement through in situ nanoparticle spacing modulation.

Self-assembled nanoparticle (NP) arrays at liquid interfaces provide a unique optical response which has opened the door to new tuneable metamaterials for sensing and optical applications. NPs can spontaneously assemble at a liquid-liquid interface, forming an ordered, self-healing, low-defect 2D film. The close proximity of the NPs at the interface results in collective plasmonic modes with a spectral response dependent on the distance between the NPs and induces large field enhancements within the gaps. In this study, we assembled spherical and rod-shaped gold NPs with the aim of improving our understanding of NP assembly processes at liquid interfaces, working towards finely controlling their structure and producing tailored optical and enhanced Raman signals. We systematically tuned the assembly and spacing between NPs through increasing or decreasing the degree of electrostatic screening with the addition of electrolyte or pH adjustment. The in situ modulation of the nanoparticle position on the same sample allowed us to monitor plasmon coupling and the resulting SERS enhancement processes in real time, with sub-nm precision.

Evidence of protein-free homology recognition in magnetic bead force-extension experiments.

Earlier theoretical studies have proposed that the homology-dependent pairing of large tracts of dsDNA may be due to physical interactions between homologous regions. Such interactions could contribute to the sequence-dependent pairing of chromosome regions that may occur in the presence or the absence of double-strand breaks. Several experiments have indicated the recognition of homologous sequences in pure electrolytic solutions without proteins. Here, we report single-molecule force experiments with a designed 60 kb long dsDNA construct; one end attached to a solid surface and the other end to a magnetic bead. The 60 kb constructs contain two 10 kb long homologous tracts oriented head to head, so that their sequences match if the two tracts fold on each other. The distance between the bead and the surface is measured as a function of the force applied to the bead. At low forces, the construct molecules extend substantially less than normal, control dsDNA, indicating the existence of preferential interaction between the homologous regions. The force increase causes no abrupt but continuous unfolding of the paired homologous regions. Simple semi-phenomenological models of the unfolding mechanics are proposed, and their predictions are compared with the data.

Electrotunable lubricity with ionic liquid nanoscale films.

One of the main challenges in tribology is finding the way for an in situ control of friction without changing the lubricant. One of the ways for such control is via the application of electric fields. In this respect a promising new class of lubricants is ionic liquids, which are solvent-free electrolytes, and their properties should be most strongly affected by applied voltage. Based on a minimal physical model, our study elucidates the connection between the voltage effect on the structure of the ionic liquid layers and their lubricating properties. It reveals two mechanisms of variation of the friction force with the surface charge density, consistent with recent AFM measurements, namely via the (i) charge effect on normal and in-plane ordering in the film and (ii) swapping between anion and cation layers at the surfaces. We formulate conditions that would warrant low friction coefficients and prevent wear by resisting "squeezing-out" of the liquid under compression. These results give a background for controllable variation of friction.

Voltage-dependent capacitance of metallic nanoparticles at a liquid/liquid interface.

A theoretical model is described for the voltage-dependent capacitance across the interface between two immiscible electrolytic solutions that is partially or completely covered with nanoparticles. The model is based on the description of competitive contributions of electrical double layers at the free interface and around nanoparticles. The effect of different system parameters is rationalised, and theoretical predictions are shown to be in agreement with available experimental data. The model provides a route for the characterisation of nanoparticle layers at liquid/liquid interfaces using capacitance measurements.

Signatures of DNA flexibility, interactions and sequence-related structural variations in classical X-ray diffraction patterns.

The theory of X-ray diffraction from ideal, rigid helices allowed Watson and Crick to unravel the DNA structure, thereby elucidating functions encoded in it. Yet, as we know now, the DNA double helix is neither ideal nor rigid. Its structure varies with the base pair sequence. Its flexibility leads to thermal fluctuations and allows molecules to adapt their structure to optimize their intermolecular interactions. In addition to the double helix symmetry revealed by Watson and Crick, classical X-ray diffraction patterns of DNA contain information about the flexibility, interactions and sequence-related variations encoded within the helical structure. To extract this information, we have developed a new diffraction theory that accounts for these effects. We show how double helix non-ideality and fluctuations broaden the diffraction peaks. Meridional intensity profiles of the peaks at the first three helical layer lines reveal information about structural adaptation and intermolecular interactions. The meridional width of the fifth layer line peaks is inversely proportional to the helical coherence length that characterizes sequence-related and thermal variations in the double helix structure. Analysis of measured fiber diffraction patterns based on this theory yields important parameters that control DNA structure, packing and function.

A superionic state in nano-porous double-layer capacitors: insights from Monte Carlo simulations.

Recently observed anomalous properties of ionic-liquid-based nanoporous supercapacitors [C. Largot et al., J. Am. Chem. Soc., 2008, 130, 2730-2731] have attracted much attention. Here we present Monte Carlo simulations of a model ionic liquid in slit-like metallic nanopores. We show that exponential screening of the electrostatic interactions of ions inside a pore, as well as the image-charge attraction of ions to the pore surface, lead to the 'anomalous' increase of the capacitance with decreasing the pore width. The simulation results are in good agreement with the experimental data. The capacitance as a function of voltage is almost constant for low voltages and vanishes above a certain threshold voltage. For very narrow pores, these two regions are separated by a peak. With increase of the pore size the peak turns into a bump and disappears for wide pores. This effect, related to a specific character of the voltage-induced filling of nanopores with counterions at high densities, is yet to be verified experimentally.

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.

Nanoparticles at electrified liquid--liquid interfaces: new options for electro-optics.

We describe the results of a theoretical analysis of the localization of functionalized metal or semiconductor nanoparticles at the interface of two immiscible electrolytic solutions and discuss various options that this interface may offer for a new kind of self-assembled, electro-optic devices.

Giant Stark effect in quantum dots at liquid/liquid interfaces: a new option for tunable optical filters.

Control of the fundamental absorption edge of a quantum dot with an applied electric field has been limited by the breakdown fields of the solid-state material surrounding the dot. However, much larger fields can be applied at the interface of two immiscible electrolytic solutions (ITIES) in an electrochemical cell. These electric fields also localize the quantum dots at the ITIES. Our analysis shows that semiconductor nanocrystals localized at the ITIES should have electric-field-tunable optical properties across much of the visible spectrum. The transparency of the liquids in such cells indicates that this configuration would be well suited for electrically tunable optical filters with wide-angle acceptance.

Protein--DNA interactions: reaching and recognizing the targets.

Protein searching and recognizing the targets on DNA was the subject of many experimental and theoretical studies. It is often argued that some proteins are capable of finding their targets 10-100 times faster than predicted by the three-dimensional diffusion rate. However, recent single-molecule experiments showed that the diffusion constants of the protein motion along DNA are usually small. This controversy pushed us to revisit this problem. We present a theoretical approach that describes some physical-chemical aspects of the target search and recognition. We consider the search process as a sequence of cycles, with each cycle consisting of three-dimensional and one-dimensional tracks. It is argued that the search time contains three terms: for the motion on three-dimensional and one-dimensional segments, and the correlation term. Our analysis shows that the acceleration in the search time is achieved at some intermediate strength of the protein-DNA binding energy and it is partially "apparent" because it is in fact reached by parallel scanning for the target by many proteins. We also show how the complementarity of the charge patterns on a target DNA sequence and on the protein may result in electrostatic recognition of a specific track on DNA and subsequent protein pinning. Within the scope of a model, we obtain an analytical expression for the capturing well. We estimate the depth and width of such a potential well and the typical time that a protein spends in it.

Simple theory of current fluctuations and noise in bridge-mediated nano-junctions.

We develop a simplified, model theory of noise caused by highly damped oscillating conformational fluctuations of a chain molecule mediating a nano-junction. Considering the most 'primitive' approximation of direct tunneling of electrons and barrier coupling with collective coordinates that describe internal conformations of the chain molecule, we derive approximate analytical formulas for the temporary current correlation function, noise power, and Fano factor. We analyze the role of different cumulative parameters of the model that affect the noise, as well as the effect of the temperature and of the number of groups in the chain. We present this analysis in expectation of experiments on this type of noise and in an attempt to trigger such experiments.

Double-tunnel nanoscale switch with a redox mediator: operational principles and tunneling spectroscopy.

A description of the physical mechanism and operation of a novel nanometric electronic switch [D.I. Gittins et al., Nature 2000 408, 67] is presented. New options for controlling the properties of this device are suggested and analyzed.

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.

DNA melting in aggregates: impeded or facilitated?

How does DNA melt in columnar aggregate relative to its melting in diluted solution? Is the melting temperature increased or decreased with the aggregate density? Have DNA-DNA interactions, predominantly of electrostatic nature, an effect on the character of the melting transition? In attempt to answer these questions, we have incorporated the theory of electrostatic interactions between DNA duplexes into the simplest model of DNA melting. The analysis shows that the effect of aggregate density is very different for aggregates built of homologous (or identical) DNA fragments relative to the case of DNA with random base pair sequences. The putative attraction between homologous DNA helices hampers their melting and increases the melting temperature and can even dramatically change the character of the transition. In the aggregate of nonhomologous DNAs, the pattern of electrostatic interactions is more complicated, and their effect could be opposite; in some cases we may even expect electrostatically induced melting. These findings define new directions for melting experiments in dense DNA assemblies.

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.

Nonlinear effects in the torsional adjustment of interacting DNA.

DNA molecules in solution, having negatively charged phosphates and countercations readsorbed on its surface, possess a distinct charge separation motif to interact electrostatically. If their double-helical structure were ideal, duplexes in parallel juxtaposition could choose azimuthal alignment providing attraction, or at least a reduction of repulsion, between them. But duplexes are not perfect staircases and the distortions of their helical structure correlate with their base pair texts. If the patterns of distortions on the opposing molecules are uncorrelated, the mismatch will accumulate as a random walk and attraction vanishes. Based on this idea, a model of recognition of homologous sequences has been proposed [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 3666 (2001)]. But DNA has torsional elasticity. How will this help to relax a mismatch between the charge distributions on two nonhomologous DNA's? In the same work, the solution of this problem has been mapped onto a frustrated sine Gordon equation in a nonlocal random field (where the latter represents a pattern of twist angle distortions on the opposing molecules), but the results had been obtained in the limit of torsionally rigid molecules. In the present paper, by solving this equation numerically, we find a strongly nonlinear relaxation mechanism which utilizes static kink-soliton modes triggered by the "random field." In the range of parameters where the solitons do not emerge, we find good agreement with the results of a variational study [A. G. Cherstvy, A. A. Kornyshev, and S. Leikin, J. Phys. Chem. B (to be published)]. We reproduce the first-order transitions in the interaxial separation dependence, but detect also second-order or weak first-order transitions for shorter duplexes. The recognition energy between two nonhomologous DNA sequences is calculated as a function of interaxial separation and the length of juxtaposition. The soliton-caused kinky length dependence is discussed in connection with plots of recombination frequency as a function of the length of homology.

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.

Phase behavior of columnar DNA assemblies.

The interaction between two stiff parallel DNA molecules depends not only on the distance between their axes but also on their azimuthal orientation. The positional and orientational order in columnar B-DNA assemblies in solution is investigated, on the basis of the electrostatic pair potential that takes into account DNA helical symmetry and the amount and distribution of adsorbed counterions. A phase diagram obtained by lattice sums predicts a variety of positionally and azimuthally ordered phases and bundling transitions strongly depending on the counterion adsorption patterns.

Sequence recognition in the pairing of DNA duplexes.

Pairing of DNA fragments with homologous sequences occurs in gene shuffling, DNA repair, and other vital processes. While chemical individuality of base pairs is hidden inside the double helix, x ray and NMR revealed sequence-dependent modulation of the structure of DNA backbone. Here we show that the resulting modulation of the DNA surface charge pattern enables duplexes longer than approximately 50 base pairs to recognize sequence homology electrostatically at a distance of up to several water layers. This may explain the local recognition observed in pairing of homologous chromosomes and the observed length dependence of homologous recombination.