Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators.

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and stability of coupled driven-damped Helmholtz-Duffing oscillators in bi-stability regimes. We find that despite the fact that the system parameters and the driving force are identical, the stability of the two states to spatially non-uniform perturbations is very different. Moreover, the final stable states, resulting from these spatial perturbations, are not solely dictated by the wavelength of the perturbing mode and take different spatial configurations in terms of the coupled oscillator phases.

Describing nonequilibrium soft matter with mean field game theory.

We demonstrate that combining an emerging approach to game theory with self-consistent mean field theory provides realistic treatments of diblock copolymer phase evolution. We especially examine order-order phase transformations upon quenched temperature change involving hexagonal cylinders, lamellae, and the gyroid. Our findings demonstrate that (i) the game theoretical dynamics produce realistic trajectories for the evolution of the local compositions, (ii) the predicted small-angle scattering follows experimentally observed trends, (iii) nucleation and growth is active when the system is quenched far from the critical point, and (iv) epitaxial growth is manifest. To our knowledge, the methodology presented provides the first merger of mean field game theory and statistical mechanics for soft matter systems, giving a new inroad to studying polymer dynamics.

The self-assembly of particles with isotropic interactions.

A generic field-theoretic model for the self-assembly of particles with isotropic interactions, motivated by ideas in DNA-mediated colloidal assembly, is presented. A simplest possible system of colloids in explicit solvent is examined to determine the ability of non-connected particles to form complex nanometre or micron scale equilibrium structures in the absence of confounding kinetic effects. It is found that non-trivial morphologies are possible and that, for this effectively one component system, these parallel the phases of diblock copolymer melts for certain parameter choices, despite the absence of connectivity or packing frustration in the model. An explanation for the morphological similarity between these architecturally disparate systems is given. For other parameter choices, it is found that meta-stable and defected phases become more common, and that similarity with block copolymer morphologies decreases.

Anharmonic dynamics of intramolecular hydrogen bonds driven by DNA breathing.

We study the effects of the anharmonic strand-separation dynamics of double-stranded DNA on the infrared spectra of the intramolecular base-pairing hydrogen bonds. Using the extended Peyrard-Bishop-Dauxois model for the DNA breathing dynamics coupled with the Lippincott-Schroeder potential for N-H· · ·N and N-H· · ·O hydrogen bonding, we identify a high-frequency (~96 THz) feature in the infrared spectra. We show that this sharp peak arises as a result of the anharmonic base-pair breathing dynamics of DNA. In addition, we study the effects of friction on the infrared spectra. For higher temperatures (~300 K), where the anharmonicity of DNA dynamics is pronounced, the high-frequency peak is always present irrespective of the friction strength.

Promoter polymorphisms in two overlapping 6p25 genes implicate mitochondrial proteins in cognitive deficit in schizophrenia.

In a previous study, we detected a 6p25-p24 region linked to schizophrenia in families with high composite cognitive deficit (CD) scores, a quantitative trait integrating multiple cognitive measures. Association mapping of a 10 Mb interval identified a 260 kb region with a cluster of single-nucleotide polymorphisms (SNPs) significantly associated with CD scores and memory performance. The region contains two colocalising genes, LYRM4 and FARS2, both encoding mitochondrial proteins. The two tagging SNPs with strongest evidence of association were located around the overlapping putative promoters, with rs2224391 predicted to alter a transcription factor binding site (TFBS). Sequencing the promoter region identified 22 SNPs, many predicted to affect TFBSs, in a tight linkage disequilibrium block. Luciferase reporter assays confirmed promoter activity in the predicted promoter region, and demonstrated marked downregulation of expression in the LYRM4 direction under the haplotype comprising the minor alleles of promoter SNPs, which however is not driven by rs2224391. Experimental evidence from LYRM4 expression in lymphoblasts, gel-shift assays and modelling of DNA breathing dynamics pointed to two adjacent promoter SNPs, rs7752203-rs4141761, as the functional variants affecting expression. Their C-G alleles were associated with higher transcriptional activity and preferential binding of nuclear proteins, whereas the G-A combination had opposite effects and was associated with poor memory and high CD scores. LYRM4 is a eukaryote-specific component of the mitochondrial biogenesis of Fe-S clusters, essential cofactors in multiple processes, including oxidative phosphorylation. LYRM4 downregulation may be one of the mechanisms involved in inefficient oxidative phosphorylation and oxidative stress, increasingly recognised as contributors to schizophrenia pathogenesis.

Feigenbaum cascade of discrete breathers in a model of DNA.

We demonstrate that period-doubled discrete breathers appear from the anticontinuum limit of the driven Peyrard-Bishop-Dauxois model of DNA. These novel breathers result from a stability overlap between subharmonic solutions of the driven Morse oscillator. Subharmonic breathers exist whenever a stability overlap is present within the Feigenbaum cascade to chaos and therefore an entire cascade of such breathers exists. This phenomenon is present in any driven lattice where the on-site potential admits subharmonic solutions. In DNA these breathers may have ramifications for cellular gene expression.

DNA Breathing Dynamics in the Presence of a Terahertz Field.

We consider the influence of a terahertz field on the breathing dynamics of double-stranded DNA. We model the spontaneous formation of spatially localized openings of a damped and driven DNA chain, and find that linear instabilities lead to dynamic dimerization, while true local strand separations require a threshold amplitude mechanism. Based on our results we argue that a specific terahertz radiation exposure may significantly affect the natural dynamics of DNA, and thereby influence intricate molecular processes involved in gene expression and DNA replication.

Dendrimers as synthetic gene vectors: cell membrane attachment.

We present molecular-level simulations of dendrimer/DNA complexes in the presence of a model cell membrane. We determine the required conditions for the complex to arrive intact at the membrane, and the lifetime of the complex as it resides attached to the membrane. Our simulations directly pertain to critical issues arising in emerging gene delivery therapeutic applications, where a molecular carrier is required to deliver DNA segments to the interior of living cells.

Stress distributions in diblock copolymers.

We demonstrate how a generalized self-consistent field theory for polymer melts that includes elastic stress and strain fields can be applied to the study of AB diblock copolymers melts. By obtaining the stress distributions for volume conserving strain loadings where lamellar and hexagonal morphologies are stable, we show that the local stress is reduced at the domain interface but slightly enhanced in the immediate vicinity of the interface. The overall stress profile is the result of the combined effects of chain connectivity across the interface, which yields a positive contribution, and the immiscible nature of the monomers, which leads to a stress reduction because of interfacial tension.

Probing the mechanical unzipping of DNA.

A study of the micromechanical unzipping of DNA in the framework of the Peyrard-Bishop-Dauxois model is presented. We introduce a Monte Carlo technique that allows accurate determination of the dependence of the unzipping forces on unzipping speed and temperature. Our findings agree quantitatively with experimental results for homogeneous DNA, and for lamda-phage DNA we reproduce the recently obtained experimental force-temperature phase diagram. Finally, we argue that there may be fundamental differences between in vivo and in vitro DNA unzipping.

Sequencing DNA by dynamic force spectroscopy: limitations and prospects.

Using a well established model, we systematically analyze fundamental limitations on the viability of using mechanical unzipping of DNA as a fast and inexpensive sequencing method. Standard unzipping techniques, where double-stranded DNA is unzipped through the application of a force at one end of the molecule, are shown to be inadequate. Emerging techniques that unzip DNA by local force application are more promising, and we establish the necessary experimental requirements that must be met for these techniques to succeed as single molecule sequencing tools.

Healing length and bubble formation in DNA.

It has been suggested that thermally induced separations ("bubbles") of the DNA double-strand may play a role in the initiation of gene transcription, and an accurate understanding of the sequence dependence of thermal strand separation is therefore desirable. Based on the Peyrard-Bishop-Dauxois model, we show here that the bubble forming ability of DNA can be quantified in terms of a healing length L(n), defined as the length (number of base-pairs) over which a base-pair defect affects bubbles involving n consecutive base-pairs. The probability for a bubble of size n is demonstrated to be proportional to the number of adenine-thymine base-pairs found within this length. The method for calculating bubble probabilities in a given sequence derived from this notion requires several order of magnitude less numerical effort than direct evaluation.

Bubble statistics and dynamics in double-stranded DNA.

The dynamical properties of double-stranded DNA are studied in the framework of the Peyrard-Bishop-Dauxois model using Langevin dynamics. Our simulations are analyzed in terms of two distribution functions describing localized separations ("bubbles") of the double strand. The result that the bubble distributions are more sharply peaked at the active sites than thermodynamically obtained distributions is ascribed to the fact that the bubble lifetimes affect the distributions. Certain base-pair sequences are found to promote long-lived bubbles, and we argue that this is a result of length scale competition between the nonlinearity and disorder present in the system.

ac conductivity in a DNA charge transport model.

We present the ac response of a DNA charge transport model, where the charge in the pi-stack interacts with the base-pair opening dynamics of the double strand. The calculated ac conductivity exhibits prominent peaks at polaron normal modes with electronic character, while weaker response appears at lower frequencies in the vibrational part of the polaron normal mode spectrum. Examples of the former, strong peaks, show redshifts as the amplitude of the ac field increases.

Bubble nucleation and cooperativity in DNA melting.

The onset of intermediate states (denaturation bubbles) and their role during the melting transition of DNA are studied using the Peyrard-Bishop-Dauxois model by Monte Carlo simulations with no adjustable parameters. Comparison is made with previously published experimental results finding excellent agreement. Melting curves, critical DNA segment length for stability of bubbles, and the possibility of a two-state transition are studied.

Multipeaked polarons in soft potentials.

We consider a minimal coupled charge / excitation-lattice model capturing a competition between linear polaronic self-trapping and the self-focusing effects of a soft nonlinear on-site potential. The standard single-humped polaron ceases to exist above a critical value of the coupling strength, closely related to the inflection point in the nonlinear potential. For couplings beyond this critical value, we find that successive multihumped polaronic solutions correspond to the lowest-energy stationary states of the system, which may admit interesting quantum resonance behavior.

Improved convergence in block copolymer self-consistent field theory by Anderson mixing.

A modification to real space polymeric self-consistent field theory algorithms that greatly improves the convergence properties is presented. The method is based on Anderson mixing [D. G. Anderson, J. Assoc. Comput. Mach. 12, 547 (1965)], and each iteration computed takes negligibly longer to perform than with other methods, but the number of iterations required to reach a high accuracy solution is greatly reduced. No a priori knowledge of possible phases is required to apply this method. We apply our approach to a standard diblock copolymer melt, and demonstrate iteration reductions of more than a factor of 5 in some cases.

Elastic moduli of multiblock copolymers in the lamellar phase.

We study the linear elastic response of multiblock copolymer melts in the lamellar phase, where the molecules are composed of tethered symmetric AB diblock copolymers. We use a self-consistent field theory method, and introduce a real space approach to calculate the tensile and shear moduli as a function of block number. The former is found to be in qualitative agreement with experiment. We find that the increase in bridging fraction with block number, that follows the increase in modulus, is not responsible for the increase in modulus. It is demonstrated that the change in modulus is due to an increase in mixing of repulsive A and B monomers. Under extension, this increase originates from a widening of the interface, and more molecules pulled free of the interface. Under compression, only the second of these two processes acts to increase the modulus.

Localization in physical systems described by discrete nonlinear Schrodinger-type equations.

Following a short introduction on localized modes in a model system, namely the discrete nonlinear Schrodinger equation, we present explicit results pertaining to three different physical systems described by similar equations. The applications range from the Raman scattering spectra of a complex electronic material through intrinsic localized vibrational modes, to the manifestation of an abrupt and irreversible delocalizing transition of Bose-Einstein condensates trapped in two-dimensional optical lattices, and to the instabilities of localized modes in coupled arrays of optical waveguides.