A nonlinear journey from structural phase transitions to quantum annealing

Motivated by an exact mapping between equilibrium properties of a one-dimensional chain of quantum Ising spins in a transverse field (the transverse field Ising (TFI) model) and a two-dimensional classical array of particles in double-well potentials (the "ϕ4 model") with weak inter-chain coupling, we explore connections between the driven variants of the two systems. We argue that coupling between the fundamental topological solitary waves in the form of kinks between neighboring chains in the classical ϕ4 system is the analog of the competing effect of the transverse field on spin flips in the quantum TFI model. As an example application, we mimic simplified measurement protocols in a closed quantum model system by studying the classical ϕ4 model subjected to periodic perturbations. This reveals memory/loss of memory and coherence/decoherence regimes, whose quantum analogs are essential in annealing phenomena. In particular, we examine regimes where the topological excitations control the thermal equilibration following perturbations. This paves the way for further explorations of the analogy between lower-dimensional linear quantum and higher-dimensional classical nonlinear systems.

Advancing Transcription Factor Binding Site Prediction Using DNA Breathing Dynamics and Sequence Transformers via Cross Attention

Understanding the impact of genomic variants on transcription factor binding and gene regulation remains a key area of research, with implications for unraveling the complex mechanisms underlying various functional effects. Our study delves into the role of DNA's biophysical properties, including thermodynamic stability, shape, and flexibility in transcription factor (TF) binding. We developed a multi-modal deep learning model integrating these properties with DNA sequence data. Trained on ChIP-Seq (chromatin immunoprecipitation sequencing) data in vivo involving 690 TF-DNA binding events in human genome, our model significantly improves prediction performance in over 660 binding events, with up to 9.6% increase in AUROC metric compared to the baseline model when using no DNA biophysical properties explicitly. Further, we expanded our analysis to in vitro high-throughput Systematic Evolution of Ligands by Exponential enrichment (SELEX) and Protein Binding Microarray (PBM) datasets, comparing our model with established frameworks. The inclusion of DNA breathing features consistently improved TF binding predictions across different cell lines in these datasets. Notably, for complex ChIP-Seq datasets, integrating DNABERT2 with a cross-attention mechanism provided greater predictive capabilities and insights into the mechanisms of disease-related non-coding variants found in genome-wide association studies. This work highlights the importance of DNA biophysical characteristics in TF binding and the effectiveness of multi-modal deep learning models in gene regulation studies.

Examining DNA breathing with pyDNA-EPBD

MOTIVATION

The two strands of the DNA double helix locally and spontaneously separate and recombine in living cells due to the inherent thermal DNA motion. This dynamics results in transient openings in the double helix and is referred to as "DNA breathing" or "DNA bubbles." The propensity to form local transient openings is important in a wide range of biological processes, such as transcription, replication, and transcription factors binding. However, the modeling and computer simulation of these phenomena, have remained a challenge due to the complex interplay of numerous factors, such as, temperature, salt content, DNA sequence, hydrogen bonding, base stacking, and others.

RESULTS

We present pyDNA-EPBD, a parallel software implementation of the Extended Peyrard-Bishop-Dauxois (EPBD) nonlinear DNA model that allows us to describe some features of DNA dynamics in detail. The pyDNA-EPBD generates genomic scale profiles of average base-pair openings, base flipping probability, DNA bubble probability, and calculations of the characteristically dynamic length indicating the number of base pairs statistically significantly affected by a single point mutation using the Markov Chain Monte Carlo algorithm.

AVAILABILITY AND IMPLEMENTATION

pyDNA-EPBD is supported across most operating systems and is freely available at https://github.com/lanl/pyDNA_EPBD. Extensive documentation can be found at https://lanl.github.io/pyDNA_EPBD/.

Examining DNA Breathing with pyDNA-EPBD

Motivation

The two strands of the DNA double helix locally and spontaneously separate and recombine in living cells due to the inherent thermal DNA motion.This dynamics results in transient openings in the double helix and is referred to as "DNA breathing" or "DNA bubbles." The propensity to form local transient openings is important in a wide range of biological processes, such as transcription, replication, and transcription factors binding. However, the modeling and computer simulation of these phenomena, have remained a challenge due to the complex interplay of numerous factors, such as, temperature, salt content, DNA sequence, hydrogen bonding, base stacking, and others.

Results

We present pyDNA-EPBD, a parallel software implementation of the Extended Peyrard-Bishop- Dauxois (EPBD) nonlinear DNA model that allows us to describe some features of DNA dynamics in detail. The pyDNA-EPBD generates genomic scale profiles of average base-pair openings, base flipping probability, DNA bubble probability, and calculations of the characteristically dynamic length indicating the number of base pairs statistically significantly affected by a single point mutation using the Markov Chain Monte Carlo (MCMC) algorithm.

Measurement and memory in the periodically driven complex Ginzburg-Landau equation

In the present work we illustrate that classical but nonlinear systems may possess features reminiscent of quantum ones, such as memory, upon suitable external perturbation. As our prototypical example, we use the two-dimensional complex Ginzburg-Landau equation in its vortex glass regime. We impose an external drive as a perturbation mimicking a quantum measurement protocol, with a given "measurement rate" (the rate of repetition of the drive) and "mixing rate" (characterized by the intensity of the drive). Using a variety of measures, we find that the system may or may not retain its coherence, statistically retrieving its original glass state, depending on the strength and periodicity of the perturbing field. The corresponding parametric regimes and the associated energy cascade mechanisms involving the dynamics of vortex waveforms and domain boundaries are discussed.

Bubble lifetimes in DNA gene promoters and their mutations affecting transcription

Relative lifetimes of inherent double stranded DNA openings with lengths up to ten base pairs are presented for different gene promoters and corresponding mutants that either increase or decrease transcriptional activity in the framework of the Peyrard-Bishop-Dauxois model. Extensive microcanonical simulations are used with energies corresponding to physiological temperature. The bubble lifetime profiles along the DNA sequences demonstrate a significant reduction of the average lifetime at the mutation sites when the mutated promoter decreases transcription, while a corresponding enhancement of the bubble lifetime is observed in the case of mutations leading to increased transcription. The relative difference in bubble lifetimes between the mutated and wild type promoters at the position of mutation varies from 20% to more than 30% as the bubble length decreases.

Distributions of bubble lifetimes and bubble lengths in DNA

We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-Bishop-Dauxois (PBD) model, as well as an extended version (ePBD) having a sequence-dependent stacking interaction, emphasizing the effect of the sequences' guanine-cytosine (GC)/adenine-thymine (AT) content on these distributions. For both models we find that base pair-dependent (GC vs AT) thresholds for considering complementary nucleotides to be separated are able to reproduce the observed dependence of the melting temperature on the GC content of the DNA sequence. Using these thresholds for base pair openings, we obtain bubble lifetime distributions for bubbles of lengths up to ten base pairs as the GC content of the sequences is varied, which are accurately fitted with stretched exponential functions. We find that for both models the average bubble lifetime decreases with increasing either the bubble length or the GC content. In addition, the obtained bubble length distributions are also fitted by appropriate stretched exponential functions and our results show that short bubbles have similar likelihoods for any GC content, but longer ones are substantially more likely to occur in AT-rich sequences. We also show that the ePBD model permits more, longer-lived, bubbles than the PBD system.

Multiscale Patterning from Competing Interactions and Length Scales

We live in a research era marked by impressive new tools powering the scientific method to accelerate the discovery, prediction, and control of increasingly complex systems. In common with many disciplines and societal challenges and opportunities, materials and condensed matter sciences are beneficiaries. The volume and fidelity of experimental, computational, and visualization data available, and tools to rapidly interpret them, are remarkable. Conceptual frameworks, including multiscale, multiphysics modeling of this complexity, are fueled by the data and, in turn, guide directions for future experimental and computational strategies. In this spirit, I discuss the importance of competing interactions, length scales, and constraints as pervasive sources of spatiotemporal complexity. I use representative examples drawn from materials and condensed matter, including the important role of elasticity in some technologically important quantum materials. Expected final online publication date for the Annual Review of Materials Research, Volume 50 is July 1, 2020. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Metabolomics and the pig model reveal aberrant cardiac energy metabolism in metabolic syndrome

Although metabolic syndrome (MS) is a significant risk of cardiovascular disease (CVD), the cardiac response (MR) to MS remains unclear due to traditional MS models' narrow scope around a limited number of cell-cycle regulation biomarkers and drawbacks of limited human tissue samples. To date, we developed the most comprehensive platform studying MR to MS in a pig model tightly related to human MS criteria. By incorporating comparative metabolomic, transcriptomic, functional analyses, and unsupervised machine learning (UML), we can discover unknown metabolic pathways connections and links on numerous biomarkers across the MS-associated issues in the heart. For the first time, we show severely diminished availability of glycolytic and citric acid cycle (CAC) pathways metabolites, altered expression, GlcNAcylation, and activity of involved enzymes. A notable exception, however, is the excessive succinate accumulation despite reduced succinate dehydrogenase complex iron-sulfur subunit b (SDHB) expression and decreased content of precursor metabolites. Finally, the expression of metabolites and enzymes from the GABA-glutamate, GABA-putrescine, and the glyoxylate pathways significantly increase, suggesting an alternative cardiac means to replenish succinate and malate in MS. Our platform discovers potential therapeutic targets for MS-associated CVD within pathways that were previously unknown to corelate with the disease.

Speed-of-light pulses in the massless nonlinear Dirac equation with a potential

We consider the massless nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction g^{2}/2(Ψ[over ¯]Ψ)^{2} in the presence of three external electromagnetic real potentials V(x), a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find different scenarios depending on initial conditions, namely, propagation of the initial pulse along one direction, splitting of the initial pulse into two pulses traveling in opposite directions, and focusing of two initial pulses followed by a splitting. For all considered cases, the final waves travel with the speed of light and are solutions of the massless linear Dirac equation. During these processes the charge and the energy are conserved, whereas the momentum is conserved when the solutions possess specific symmetries. For the case of the constant potential, we derive exact analytical solutions of the massless NLD equation that are also solutions of the massless linearized Dirac equation. Decay or growth of the initial pulse is also predicted from the evolution of the charge for the case of a non-zero imaginary part of the potential.

Evaluating the role of coherent delocalized phonon-like modes in DNA cyclization

The innate flexibility of a DNA sequence is quantified by the Jacobson-Stockmayer's J-factor, which measures the propensity for DNA loop formation. Recent studies of ultra-short DNA sequences revealed a discrepancy of up to six orders of magnitude between experimentally measured and theoretically predicted J-factors. These large differences suggest that, in addition to the elastic moduli of the double helix, other factors contribute to loop formation. Here, we develop a new theoretical model that explores how coherent delocalized phonon-like modes in DNA provide single-stranded "flexible hinges" to assist in loop formation. We combine the Czapla-Swigon-Olson structural model of DNA with our extended Peyrard-Bishop-Dauxois model and, without changing any of the parameters of the two models, apply this new computational framework to 86 experimentally characterized DNA sequences. Our results demonstrate that the new computational framework can predict J-factors within an order of magnitude of experimental measurements for most ultra-short DNA sequences, while continuing to accurately describe the J-factors of longer sequences. Further, we demonstrate that our computational framework can be used to describe the cyclization of DNA sequences that contain a base pair mismatch. Overall, our results support the conclusion that coherent delocalized phonon-like modes play an important role in DNA cyclization.

Variational approach to studying solitary waves in the nonlinear Schrödinger equation with complex potentials

We discuss the behavior of solitary wave solutions of the nonlinear Schrödinger equation (NLSE) as they interact with complex potentials, using a four-parameter variational approximation based on a dissipation functional formulation of the dynamics. We concentrate on spatially periodic potentials with the periods of the real and imaginary part being either the same or different. Our results for the time evolution of the collective coordinates of our variational ansatz are in good agreement with direct numerical simulation of the NLSE. We compare our method with a collective coordinate approach of Kominis and give examples where the two methods give qualitatively different answers. In our variational approach, we are able to give analytic results for the small oscillation frequency of the solitary wave oscillating parameters which agree with the numerical solution of the collective coordinate equations. We also verify that instabilities set in when the slope dp(t)/dv(t) becomes negative when plotted parametrically as a function of time, where p(t) is the momentum of the solitary wave and v(t) the velocity.

Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos

The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order dispersion and stimulated Raman scattering effects gives rise to rich dynamics: this extends from Poincaré-Bendixson-type scenarios, in the sense that bounded solutions may converge either to distinct equilibria via orbital connections or to space-time periodic solutions, to the emergence of almost periodic and chaotic behavior. One of our main results is that third-order dispersion has a dominant role in the development of such complex dynamics, since it can be chiefly responsible (even in the absence of other higher-order effects) for the existence of periodic, quasiperiodic, and chaotic spatiotemporal structures. Suitable low-dimensional phase-space diagnostics are devised and used to illustrate the different possibilities and identify their respective parametric intervals over multiple parameters of the model.

Soliton dynamics in optical fibers using the generalized traveling-wave method

The generalized traveling wave method (GTWM) is applied to the nonlinear Schrödinger (NLS) equation with general perturbations in order to obtain the equations of motion for an ansatz with six collective coordinates, namely the soliton position, the amplitude, the inverse of the soliton width, the velocity, the chirp, and the phase. The advantage of the new ansatz is that it yields three pairs of canonically conjugated coordinates and momenta that all are well-behaved. The new ansatz is applied to model the dynamics of a soliton in a dispersion-shifted optical fiber described by the generalized NLS, including dissipation, higher-order dispersion, Raman scattering, and self-steepening perturbations. It is shown that the GTWM is equivalent to the modified method of moments, which considers the time variation of the norm, the first and the second moment of the norm, the momentum, the first moment of the momentum, and the energy for the perturbed NLS equation.

The role of structural parameters in DNA cyclization

BACKGROUND

The intrinsic bendability of DNA plays an important role with relevance for myriad of essential cellular mechanisms. The flexibility of a DNA fragment can be experimentally and computationally examined by its propensity for cyclization, quantified by the Jacobson-Stockmayer J factor. In this study, we use a well-established coarse-grained three-dimensional model of DNA and seven distinct sets of experimentally and computationally derived conformational parameters of the double helix to evaluate the role of structural parameters in calculating DNA cyclization.

RESULTS

We calculate the cyclization rates of 86 DNA sequences with previously measured J factors and lengths between 57 and 325 bp as well as of 20,000 randomly generated DNA sequences with lengths between 350 and 4000 bp. Our comparison with experimental data is complemented with analysis of simulated data.

CONCLUSIONS

Our data demonstrate that all sets of parameters yield very similar results for longer DNA fragments, regardless of the nucleotide sequence, which are in agreement with experimental measurements. However, for DNA fragments shorter than 100 bp, all sets of parameters performed poorly yielding results with several orders of magnitude difference from the experimental measurements. Our data show that DNA cyclization rates calculated using conformational parameters based on nucleosome packaging data are most similar to the experimental measurements. Overall, our study provides a comprehensive large-scale assessment of the role of structural parameters in calculating DNA cyclization rates.

Possible Demonstration of a Polaronic Bose-Einstein(-Mott) Condensate in UO2(+x) by Ultrafast THz Spectroscopy and Microwave Dissipation

Bose-Einstein condensates (BECs) composed of polarons would be an advance because they would combine coherently charge, spin, and a crystal lattice. Following our earlier report of unique structural and spectroscopic properties, we now identify potentially definitive evidence for polaronic BECs in photo- and chemically doped UO_2(+x) on the basis of exceptional coherence in the ultrafast time dependent terahertz absorption and microwave spectroscopy results that show collective behavior including dissipation patterns whose precedents are condensate vortex and defect disorder and condensate excitations. That some of these signatures of coherence in an atom-based system extend to ambient temperature suggests a novel mechanism that could be a synchronized, dynamical, disproportionation excitation, possibly via the solid state analog of a Feshbach resonance that promotes the coherence. Such a mechanism would demonstrate that the use of ultra-low temperatures to establish the BEC energy distribution is a convenience rather than a necessity, with the actual requirement for the particles being in the same state that is not necessarily the ground state attainable by other means. A macroscopic quantum object created by chemical doping that can persist to ambient temperature and resides in a bulk solid would be revolutionary in a number of scientific and technological fields.

Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity

We consider a two-dimensional (2D) generalization of a recently proposed model [Gligorić et al., Phys. Rev. E 88, 032905 (2013)], which gives rise to bright discrete solitons supported by the defocusing nonlinearity whose local strength grows from the center to the periphery. We explore the 2D model starting from the anticontinuum (AC) limit of vanishing coupling. In this limit, we can construct a wide variety of solutions including not only single-site excitations, but also dipole and quadrupole ones. Additionally, two separate families of solutions are explored: the usual "extended" unstaggered bright solitons, in which all sites are excited in the AC limit, with the same sign across the lattice (they represent the most robust states supported by the lattice, their 1D counterparts being those considered as 1D bright solitons in the above-mentioned work), and the vortex cross, which is specific to the 2D setting. For all the existing states, we explore their stability (also analytically, when possible). Typical scenarios of instability development are exhibited through direct simulations.

Allostery through protein-induced DNA bubbles

Allostery through DNA is increasingly recognized as an important modulator of DNA functions. Here, we show that the coalescence of protein-induced DNA bubbles can mediate allosteric interactions that drive protein aggregation. We propose that such allostery may regulate DNA's flexibility and the assembly of the transcription machinery. Mitochondrial transcription factor A (TFAM), a dual-function protein involved in mitochondrial DNA (mtDNA) packaging and transcription initiation, is an ideal candidate to test such a hypothesis owing to its ability to locally unwind the double helix. Numerical simulations demonstrate that the coalescence of TFAM-induced bubbles can explain experimentally observed TFAM oligomerization. The resulting melted DNA segment, approximately 10 base pairs long, around the joints of the oligomers act as flexible hinges, which explains the efficiency of TFAM in compacting DNA. Since mitochondrial polymerase (mitoRNAP) is involved in melting the transcription bubble, TFAM may use the same allosteric interaction to both recruit mitoRNAP and initiate transcription.

Soliton stability criterion for generalized nonlinear Schrödinger equations

A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p'(v)<0 is a sufficient condition for instability, while p'(v)>0 is a necessary condition for stability; here, v is the soliton velocity and p=P/N, where P and N are the soliton momentum and norm, respectively. To date, the curve p(v) was calculated approximately by a collective coordinate theory, and the criterion was confirmed by simulations. The goal of this paper is to calculate p(v) exactly for several classes and cases of the generalized NLSE: a soliton moving in a real potential, in particular a time-dependent ramp potential, and a time-dependent confining quadratic potential, where the nonlinearity in the NLSE also has a time-dependent coefficient. Moreover, we investigate a logarithmic and a cubic NLSE with a time-independent quadratic potential well. In the latter case, there is a bisoliton solution that consists of two solitons with asymmetric shapes, forming a bound state in which the shapes and the separation distance oscillate. Finally, we consider a cubic NLSE with parametric driving. In all cases, the p(v) curve is calculated either analytically or numerically, and the stability criterion is confirmed.

A rare functional noncoding variant at the GWAS-implicated MIR137/MIR2682 locus might confer risk to schizophrenia and bipolar disorder

Schizophrenia (SZ) genome-wide association studies (GWASs) have identified common risk variants in >100 susceptibility loci; however, the contribution of rare variants at these loci remains largely unexplored. One of the strongly associated loci spans MIR137 (miR137) and MIR2682 (miR2682), two microRNA genes important for neuronal function. We sequenced ∼6.9 kb MIR137/MIR2682 and upstream regulatory sequences in 2,610 SZ cases and 2,611 controls of European ancestry. We identified 133 rare variants with minor allele frequency (MAF) <0.5%. The rare variant burden in promoters and enhancers, but not insulators, was associated with SZ (p = 0.021 for MAF < 0.5%, p = 0.003 for MAF < 0.1%). A rare enhancer SNP, 1:g.98515539A>T, presented exclusively in 11 SZ cases (nominal p = 4.8 × 10(-4)). We further identified its risk allele T in 2 of 2,434 additional SZ cases, 11 of 4,339 bipolar (BP) cases, and 3 of 3,572 SZ/BP study controls and 1,688 population controls; yielding combined p values of 0.0007, 0.0013, and 0.0001 for SZ, BP, and SZ/BP, respectively. The risk allele T of 1:g.98515539A>T reduced enhancer activity of its flanking sequence by >50% in human neuroblastoma cells, predicting lower expression of MIR137/MIR2682. Both empirical and computational analyses showed weaker transcription factor (YY1) binding by the risk allele. Chromatin conformation capture (3C) assay further indicated that 1:g.98515539A>T influenced MIR137/MIR2682, but not the nearby DPYD or LOC729987. Our results suggest that rare noncoding risk variants are associated with SZ and BP at MIR137/MIR2682 locus, with risk alleles decreasing MIR137/MIR2682 expression.

Attractive inverse square potential, U(1) gauge, and winding transitions

The inverse square potential arises in a variety of different quantum phenomena, yet notoriously it must be handled with care: it suffers from pathologies rooted in the mathematical foundations of quantum mechanics. We show that its recently studied conformality breaking corresponds to an infinitely smooth winding-unwinding topological transition for the classical statistical mechanics of a one-dimensional system: this describes the tangling or untangling of floppy polymers under a biasing torque. When the ratio between torque and temperature exceeds a critical value the polymer undergoes tangled oscillations, with an extensive winding number. At lower torque or higher temperature the winding number per unit length is zero. Approaching criticality, the correlation length of the order parameter-the extensive winding number-follows a Kosterlitz-Thouless-type law. The model is described by the Wilson line of a (0+1) U(1) gauge theory, and applies to the tangling or untangling of floppy polymers and to the winding or diffusing kinetics in diffusion-convection reactions.

Static and dynamic phases for magnetic vortex matter with attractive and repulsive interactions

Exotic vortex states with long range attraction and short range repulsion have recently been proposed to arise in certain superconducting hybrid structures such as type-I/type-II layered systems as well as multi-band superconductors. In previous work it has been shown that such systems can form clump or phase separated states, but little is known about how they behave in the presence of pinning and under an applied drive. Using large scale simulations we examine the static and dynamic properties of such vortex states interacting with random and periodic pinning. In the absence of pinning this system does not form patterns but instead undergoes complete phase separation. When pinning is present there is a transition from inhomogeneous to homogeneous vortex configurations similar to a wetting phenomenon. Under an applied drive, a dynamical dewetting process can occur from a strongly pinned homogeneous state into pattern forming states, such as moving stripes that are aligned with the direction of drive or moving labyrinth or clump phases. We show that a signature of the exotic vortex interactions observable with transport measurements is a robust double peak feature in the differential resistance curves. Our results should be valuable for determining whether such vortex interactions are occurring in these systems and also for addressing the general problem of systems with competing interactions in the presence of random and periodic pinning.

RKKY interaction and intrinsic frustration in non-Fermi-liquid metals

We study the RKKY interaction in non-Fermi-liquid metals. We find that the RKKY interaction mediated by some non-Fermi-liquid metals can be of much longer range than for a Fermi liquid. The oscillatory nature of the RKKY interaction thus becomes more important in such non-Fermi liquids, and gives rise to enhanced frustration when the spins form a lattice. Frustration suppresses the magnetic ordering temperature of the lattice spin system. Furthermore, we find that the spin system with a longer range RKKY interaction can be described by the Brazovskii model, where the ordering wave vector lies on a higher dimensional manifold. Strong fluctuations in such a model lead to a first-order phase transition and/or glassy phase. This may explain some recent experiments where glassy behavior was observed in stoichiometric heavy fermion material close to a ferromagnetic quantum critical point.

Binding of nucleoid-associated protein fis to DNA is regulated by DNA breathing dynamics

Physicochemical properties of DNA, such as shape, affect protein-DNA recognition. However, the properties of DNA that are most relevant for predicting the binding sites of particular transcription factors (TFs) or classes of TFs have yet to be fully understood. Here, using a model that accurately captures the melting behavior and breathing dynamics (spontaneous local openings of the double helix) of double-stranded DNA, we simulated the dynamics of known binding sites of the TF and nucleoid-associated protein Fis in Escherichia coli. Our study involves simulations of breathing dynamics, analysis of large published in vitro and genomic datasets, and targeted experimental tests of our predictions. Our simulation results and available in vitro binding data indicate a strong correlation between DNA breathing dynamics and Fis binding. Indeed, we can define an average DNA breathing profile that is characteristic of Fis binding sites. This profile is significantly enriched among the identified in vivo E. coli Fis binding sites. To test our understanding of how Fis binding is influenced by DNA breathing dynamics, we designed base-pair substitutions, mismatch, and methylation modifications of DNA regions that are known to interact (or not interact) with Fis. The goal in each case was to make the local DNA breathing dynamics either closer to or farther from the breathing profile characteristic of a strong Fis binding site. For the modified DNA segments, we found that Fis-DNA binding, as assessed by gel-shift assay, changed in accordance with our expectations. We conclude that Fis binding is associated with DNA breathing dynamics, which in turn may be regulated by various nucleotide modifications.

Cellular transcription factors (TFs) are proteins that regulate gene expression, and thereby cellular activity and fate, by binding to specific DNA segments. The physicochemical determinants of protein-DNA binding specificity are not completely understood. Here, we report that the propensity of transient opening and re-closing of the double helix, resulting from thermal fluctuations, aka “DNA breathing” or “DNA bubbles,” can be associated with binding affinity in the case of Fis, a well-studied nucleoid-associated protein in Escherichia coli. We found that a particular breathing profile is characteristic of high-affinity Fis binding sites and that DNA fragments known to bind Fis in vivo are statistically enriched for this profile. Furthermore, we used simulations of DNA breathing dynamics to guide design of gel-shift experiments aimed at testing the idea that local breathing influences Fis binding. As a result, we show that via nucleotide modifications but without modifying nucleotides that directly contact Fis, we were able to transform a low-affinity Fis binding site into a high-affinity site and vice versa. The nucleotide modifications were designed only based on DNA breathing simulations. Our study suggests that strong Fis-DNA binding depends on DNA breathing - a novel physicochemical characteristic that could be used for prediction and rational design of TF binding sites.

Inelastic electron tunneling spectroscopy for topological insulators

Inelastic electron tunneling spectroscopy is a powerful spectroscopy that allows one to investigate the nature of local excitations and energy transfer in the system of interest. We study inelastic electron tunneling spectroscopy for topological insulators and investigate the role of inelastic scattering on the Dirac node states on the surface of topological insulators. Local inelastic scattering is shown to significantly modify the Dirac node spectrum. In the weak coupling limit, peaks and steps are induced in second derivative d2I/dV2. In the strong coupling limit, the local negative-U centers are formed at impurity sites, and the Dirac cone structure is fully destroyed locally. At intermediate coupling, resonance peaks emerge. We map out the evolution of the resonance peaks from weak to strong coupling, which interpolate nicely between the two limits. There is a sudden qualitative change of behavior at intermediate coupling, indicating the possible existence of a local quantum phase transition. We also find that, even for a simple local phonon mode, the inherent coupling of spin and orbital degrees in topological insulators leads to the spin-polarized texture in inelastic Friedel oscillations induced by the local mode.

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.

Discrete breathers in a nonlinear polarizability model of ferroelectrics

We present a family of discrete breathers, which exists in a nonlinear polarizability model of ferroelectric materials. The core-shell model is set up in its nondimensionalized Hamiltonian form and its linear spectrum is examined in a range of temperatures. Subsequently, seeking localized solutions in the gap of the linear spectrum, we establish that numerically exact and potentially stable discrete breathers exist for a wide range of frequencies therein. In addition, we present nonlinear normal mode, extended spatial profile solutions from which the breathers bifurcate, as well as other associated phenomena such as the formation of phantom breathers within the model. The full bifurcation picture of the emergence and disappearance of the breathers is complemented by direct numerical simulations of their dynamical instability, when the latter arises. The effect of breathers on properties such as nonlinear dielectric response is discussed.

DNA breathing dynamics distinguish binding from nonbinding consensus sites for transcription factor YY1 in cells

The genome-wide mapping of the major gene expression regulators, the transcription factors (TFs) and their DNA binding sites, is of great importance for describing cellular behavior and phenotypic diversity. Presently, the methods for prediction of genomic TF binding produce a large number of false positives, most likely due to insufficient description of the physiochemical mechanisms of protein–DNA binding. Growing evidence suggests that, in the cell, the double-stranded DNA (dsDNA) is subject to local transient strands separations (breathing) that contribute to genomic functions. By using site-specific chromatin immunopecipitations, gel shifts, BIOBASE data, and our model that accurately describes the melting behavior and breathing dynamics of dsDNA we report a specific DNA breathing profile found at YY1 binding sites in cells. We find that the genomic flanking sequence variations and SNPs, may exert long-range effects on DNA dynamics and predetermine YY1 binding. The ubiquitous TF YY1 has a fundamental role in essential biological processes by activating, initiating or repressing transcription depending upon the sequence context it binds. We anticipate that consensus binding sequences together with the related DNA dynamics profile may significantly improve the accuracy of genomic TF binding sites and TF binding-related functional SNPs.

Non-thermal effects of terahertz radiation on gene expression in mouse stem cells

In recent years, terahertz radiation sources are increasingly being exploited in military and civil applications. However, only a few studies have so far been conducted to examine the biological effects associated with terahertz radiation. In this study, we evaluated the cellular response of mesenchymal mouse stem cells exposed to THz radiation. We apply low-power radiation from both a pulsed broad-band (centered at 10 THz) source and from a CW laser (2.52 THz) source. Modeling, empirical characterization, and monitoring techniques were applied to minimize the impact of radiation-induced increases in temperature. qRT-PCR was used to evaluate changes in the transcriptional activity of selected hyperthermic genes. We found that temperature increases were minimal, and that the differential expression of the investigated heat shock proteins (HSP105, HSP90, and CPR) was unaffected, while the expression of certain other genes (Adiponectin, GLUT4, and PPARG) showed clear effects of the THz irradiation after prolonged, broad-band exposure.

Thermomechanics of DNA: theory of thermal stability under load

A theory for thermomechanical behavior of homogeneous DNA at thermal equilibrium predicts critical temperatures for denaturation under torque and stretch, phase diagrams for stable B-DNA, supercoiling, optimally stable torque, and the overstretching transition as force-induced DNA melting. Agreement with available single molecule manipulation experiments is excellent.

Refined empirical stability criterion for nonlinear Schrödinger solitons under spatiotemporal forcing

We investigate the dynamics of traveling oscillating solitons of the cubic nonlinear Schrödinger (NLS) equation under an external spatiotemporal forcing of the form f(x,t)=aexp[iK(t)x]. For the case of time-independent forcing, a stability criterion for these solitons, which is based on a collective coordinate theory, was recently conjectured. We show that the proposed criterion has a limited applicability and present a refined criterion which is generally applicable, as confirmed by direct simulations. This includes more general situations where K(t) is harmonic or biharmonic, with or without a damping term in the NLS equation. The refined criterion states that the soliton will be unstable if the "stability curve" p(v), where p(t) and v(t) are the normalized momentum and the velocity of the soliton, has a section with a negative slope. In the case of a constant K and zero damping, we use the collective coordinate solutions to compute a "phase portrait" of the soliton where its dynamics is represented by two-dimensional projections of its trajectories in the four-dimensional space of collective coordinates. We conjecture, and confirm by simulations, that the soliton is unstable if a section of the resulting closed curve on the portrait has a negative sense of rotation.

DNA dynamics is likely to be a factor in the genomic nucleotide repeats expansions related to diseases

Trinucleotide repeats sequences (TRS) represent a common type of genomic DNA motif whose expansion is associated with a large number of human diseases. The driving molecular mechanisms of the TRS ongoing dynamic expansion across generations and within tissues and its influence on genomic DNA functions are not well understood. Here we report results for a novel and notable collective breathing behavior of genomic DNA of tandem TRS, leading to propensity for large local DNA transient openings at physiological temperature. Our Langevin molecular dynamics (LMD) and Markov Chain Monte Carlo (MCMC) simulations demonstrate that the patterns of openings of various TRSs depend specifically on their length. The collective propensity for DNA strand separation of repeated sequences serves as a precursor for outsized intermediate bubble states independently of the G/C-content. We report that repeats have the potential to interfere with the binding of transcription factors to their consensus sequence by altered DNA breathing dynamics in proximity of the binding sites. These observations might influence ongoing attempts to use LMD and MCMC simulations for TRS–related modeling of genomic DNA functionality in elucidating the common denominators of the dynamic TRS expansion mutation with potential therapeutic applications.

Anisotropic sliding dynamics, peak effect, and metastability in stripe systems

A variety of soft and hard condensed matter systems are known to form stripe patterns. Here we use numerical simulations to analyze how such stripe states depin and slide when interacting with a random substrate and with driving in different directions with respect to the orientation of the stripes. Depending on the strength and density of the substrate disorder, we find that there can be pronounced anisotropy in the transport produced by different dynamical flow phases. We also find a disorder-induced "peak effect" similar to that observed for superconducting vortex systems, which is marked by a transition from elastic depinning to a state where the stripe structure fragments or partially disorders at depinning. Under the sudden application of a driving force, we observe pronounced metastability effects similar to those found near the order-disorder transition associated with the peak effect regime for three-dimensional superconducting vortices. The characteristic transient time required for the system to reach a steady state diverges in the region where the flow changes from elastic to disordered. We also find that anisotropy of the flow persists in the presence of thermal disorder when thermally induced particle hopping along the stripes dominates. The thermal effects can wash out the effects of the quenched disorder, leading to a thermally induced stripe state. We map out the dynamical phase diagram for this system, and discuss how our results could be explored in electron liquid crystal systems, type-1.5 superconductors, and pattern-forming colloidal assemblies.

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.

Mammalian stem cells reprogramming in response to terahertz radiation

We report that extended exposure to broad-spectrum terahertz radiation results in specific changes in cellular functions that are closely related to DNA-directed gene transcription. Our gene chip survey of gene expression shows that whereas 89% of the protein coding genes in mouse stem cells do not respond to the applied terahertz radiation, certain genes are activated, while other are repressed. RT-PCR experiments with selected gene probes corresponding to transcripts in the three groups of genes detail the gene specific effect. The response was not only gene specific but also irradiation conditions dependent. Our findings suggest that the applied terahertz irradiation accelerates cell differentiation toward adipose phenotype by activating the transcription factor peroxisome proliferator-activated receptor gamma (PPARG). Finally, our molecular dynamics computer simulations indicate that the local breathing dynamics of the PPARG promoter DNA coincides with the gene specific response to the THz radiation. We propose that THz radiation is a potential tool for cellular reprogramming.

Structural transitions, melting, and intermediate phases for stripe- and clump-forming systems

We numerically examine the properties of a two-dimensional system of particles which have competing long-range repulsive and short-range attractive interactions as a function of density and temperature. For increasing density, there are well-defined transitions between a low-density clump phase, an intermediate stripe phase, an anticlump phase, and a high-density uniform phase. To characterize the transitions between these phases we propose several measures which take into account the different length scales in the system. For increasing temperature, we find an intermediate phase that is liquidlike on the short length scale of interparticle spacing but solidlike on the larger length scale of the clump, stripe, or anticlump pattern. This intermediate phase persists over the widest temperature range in the stripe phase when the local particle lattice within an individual stripe melts well below the temperature at which the entire stripe structure breaks down, and is characterized by intrastripe diffusion of particles without interstripe diffusion. This is followed at higher temperatures by the onset of interstripe diffusion in an anisotropic diffusion phase and then by breakup of the stripe structure. We identify the transitions between these regimes through diffusion, heat capacity, and energy fluctuation measurements and find that within the intrastripe liquid regime, the excess entropy goes into disordering the particle arrangements within the stripe rather than affecting the stripe structure itself. The clump and anticlump phases also show multiple temperature-induced diffusive regimes which are not as pronounced as those of the stripe phase.

Generalized traveling-wave method, variational approach, and modified conserved quantities for the perturbed nonlinear Schrödinger equation

The generalized traveling wave method (GTWM) is developed for the nonlinear Schrödinger equation (NLSE) with general perturbations in order to obtain the equations of motion for an arbitrary number of collective coordinates. Regardless of the particular ansatz that is used, it is shown that this alternative approach is equivalent to the Lagrangian formalism, but has the advantage that only the Hamiltonian of the unperturbed system is required, instead of the Lagrangian for the perturbed system. As an explicit example, we take 4 collective coordinates, namely the position, velocity, amplitude and phase of the soliton, and show that the GTWM yields the same equations of motion as the perturbation theory based on the Inverse Scattering Transform and as the time variation of the norm, first moment of the norm, momentum, and energy for the perturbed NLSE.

Nonlinear Schrödinger equation with spatiotemporal perturbations

We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation (NLSE) with the following perturbations: nonparametric spatiotemporal driving of the form f(x,t)=a exp[iK(t)x], damping, and a linear term which serves to stabilize the driven soliton. Using the time evolution of norm, momentum and energy, or, alternatively, a Lagrangian approach, we develop a collective-coordinate-theory which yields a set of ordinary differential equations (ODEs) for our four collective coordinates. These ODEs are solved analytically and numerically for the case of a constant, spatially periodic force f(x). The soliton position exhibits oscillations around a mean trajectory with constant velocity. This means that the soliton performs, on the average, a unidirectional motion although the spatial average of the force vanishes. The amplitude of the oscillations is much smaller than the period of f(x). In order to find out for which regions the above solutions are stable, we calculate the time evolution of the soliton momentum P(t) and the soliton velocity V(t): This is a parameter representation of a curve P(V) which is visited by the soliton while time evolves. Our conjecture is that the soliton becomes unstable, if this curve has a branch with negative slope. This conjecture is fully confirmed by our simulations for the perturbed NLSE. Moreover, this curve also yields a good estimate for the soliton lifetime: the soliton lives longer, the shorter the branch with negative slope is.

DNA dynamics play a role as a basal transcription factor in the positioning and regulation of gene transcription initiation

We assess the role of DNA breathing dynamics as a determinant of promoter strength and transcription start site (TSS) location. We compare DNA Langevin dynamic profiles of representative gene promoters, calculated with the extended non-linear PBD model of DNA with experimental data on transcription factor binding and transcriptional activity. Our results demonstrate that DNA dynamic activity at the TSS can be suppressed by mutations that do not affect basal transcription factor binding–DNA contacts. We use this effect to establish the separate contributions of transcription factor binding and DNA dynamics to transcriptional activity. Our results argue against a purely ‘transcription factor-centric’ view of transcription initiation, suggesting that both DNA dynamics and transcription factor binding are necessary conditions for transcription initiation.

Phonon affected transport through molecular quantum dots

To describe the interaction of molecular vibrations with electrons at a quantum dot contacted to metallic leads, we extend an analytical approach that we previously developed for the many-polaron problem. Our scheme is based on an incomplete variational Lang-Firsov transformation, combined with a perturbative calculation of the electron-phonon self-energy in the framework of generalized Matsubara functions. This allows us to describe the system at weak-to-strong coupling and intermediate-to-large phonon frequencies. We present results for the quantum dot spectral function and for the kinetic coefficient that characterizes the electron transport through the dot. With these results we critically examine the strengths and limitations of our approach, and discuss the properties of the molecular quantum dot in the context of polaron physics. We place particular emphasis on the importance of corrections to the concept of an anti-adiabatic dot polaron suggested by the complete Lang-Firsov transformation.

Nonlinearity in DNA and its relation to specific functions

In memory of Alwyn Scott, we discuss the connection between the nonlinear dynamics of double-stranded DNA, experimental findings, and specific DNA functions. We begin by discussing how thermally induced localized openings (bubbles) of the DNA double-strand are important for interpreting dynamic force spectroscopy data. Then, we demonstrate a correlation between the sequence-dependent propensity for bubble formation and transcription initiation and other regulatory effects in viral DNA. Finally, we discuss the possibility of a connection between DNA dynamics and the ability of repair proteins to recognize ultraviolet-radiation damage.

Toward a detailed description of the thermally induced dynamics of the core promoter

Establishing the general and promoter-specific mechanistic features of gene transcription initiation requires improved understanding of the sequence-dependent structural/dynamic features of promoter DNA. Experimental data suggest that a spontaneous dsDNA strand separation at the transcriptional start site is likely to be a requirement for transcription initiation in several promoters. Here, we use Langevin molecular dynamic simulations based on the Peyrard-Bishop-Dauxois nonlinear model of DNA (PBD LMD) to analyze the strand separation (bubble) dynamics of 80-bp-long promoter DNA sequences. We derive three dynamic criteria, bubble probability, bubble lifetime, and average strand separation, to characterize bubble formation at the transcriptional start sites of eight mammalian gene promoters. We observe that the most stable dsDNA openings do not necessarily coincide with the most probable openings and the highest average strand displacement, underscoring the advantages of proper molecular dynamic simulations. The dynamic profiles of the tested mammalian promoters differ significantly in overall profile and bubble probability, but the transcriptional start site is often distinguished by large (longer than 10 bp) and long-lived transient openings in the double helix. In support of these results are our experimental transcription data demonstrating that an artificial bubble-containing DNA template is transcribed bidirectionally by human RNA polymerase alone in the absence of any other transcription factors.

Accessing the information encoded in DNA requires that RNA polymerases recognize the core promoter, a sequence that marks the start of a gene. Statistical analysis of known promoter sequences has failed to reveal a simple code for identifying promoters, leading to the suggestion that promoter DNA is distinguished by certain structural/dynamic properties encoded in nonobvious ways by the literal sequence. Because the DNA strands at the promoter need to be separated for transcription to begin, we previously proposed that promoter sequences exhibit a propensity for spontaneous strand separation. Here, we conduct simulations of the ultrafast, small-scale strand separation motions of eight mammalian promoters and show that start sites tend to form larger and more stable openings in the double helix compared to other sequences. Experimentally, we show that an artificial permanent opening in the double helix is sufficient for transcription in the absence of sequence-specific protein–DNA contacts. These findings support a view of DNA as a structurally active participant in gene expression, rather than the commonly envisioned passive digital storage device. Our analysis suggests that functionally relevant structural variation in genomic DNA occurs at the level of fast motions not readily observed by traditional molecular structure analysis.

A nonlinear dynamic model of DNA with a sequence-dependent stacking term

No simple model exists that accurately describes the melting behavior and breathing dynamics of double-stranded DNA as a function of nucleotide sequence. This is especially true for homogenous and periodic DNA sequences, which exhibit large deviations in melting temperature from predictions made by additive thermodynamic contributions. Currently, no method exists for analysis of the DNA breathing dynamics of repeats and of highly G/C- or A/T-rich regions, even though such sequences are widespread in vertebrate genomes. Here, we extend the nonlinear Peyrard-Bishop-Dauxois (PBD) model of DNA to include a sequence-dependent stacking term, resulting in a model that can accurately describe the melting behavior of homogenous and periodic sequences. We collect melting data for several DNA oligos, and apply Monte Carlo simulations to establish force constants for the 10 dinucleotide steps (CG, CA, GC, AT, AG, AA, AC, TA, GG, TC). The experiments and numerical simulations confirm that the GG/CC dinucleotide stacking is remarkably unstable, compared with the stacking in GC/CG and CG/GC dinucleotide steps. The extended PBD model will facilitate thermodynamic and dynamic simulations of important genomic regions such as CpG islands and disease-related repeats.

Pre-melting dynamics of DNA and its relation to specific functions

We discuss connections between the nonlinear dynamics of double-stranded DNA, experimental findings, and specific DNA functions. We begin by discussing how thermally induced localized openings (bubbles) of the DNA double strand are important for interpreting dynamic force spectroscopy data. Then we demonstrate a correlation between a sequence-dependent propensity for pre-melting bubble formation and transcription initiation and other regulatory effects in viral DNA. Finally, we discuss the possibility of a connection between DNA dynamics and the ability of repair proteins to recognize ultraviolet (UV) radiation damage sites.

Chaotic transport in deterministic sine-Gordon soliton ratchets

We investigate homogeneous and inhomogeneous sine-Gordon ratchet systems in which a temporal symmetry and the spatial symmetry, respectively, are broken. We demonstrate that in the inhomogeneous systems with ac driving the soliton dynamics is chaotic in certain parameter regions, although the soliton motion is unidirectional. This is qualitatively explained by a one-collective-coordinate theory which yields an equation of motion for the soliton that is identical to the equation of motion for a single particle ratchet which is known to exhibit chaotic transport in its underdamped regime. For a quantitative comparison with our simulations we use a two-collective-coordinate (2CC) theory. In contrast to this, homogeneous sine-Gordon ratchets with biharmonic driving, which breaks a temporal shift symmetry, do not exhibit chaos. This is explained by a 2CC theory which yields two ODEs: one is linear, the other one describes a parametrically driven oscillator which does not exhibit chaos. The latter ODE can be solved by a perturbation theory which yields a hierarchy of linear equations that can be solved exactly order by order. The results agree very well with the simulations.

Discrete solitons and vortices in hexagonal and honeycomb lattices: existence, stability, and dynamics

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the "hexapole" of alternating phases (0-pi) , as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.

Kondo stripes in an Anderson-Heisenberg model of heavy fermion systems

We study the interplay between the spin-liquid and Kondo physics, as related to the nonmagnetic part of the phase diagram of heavy fermion materials. Within the unrestricted mean-field treatment of the infinite-U 2D Anderson-Heisenberg model, we find that there are two topologically distinct nondegenerate uniform heavy Fermi liquid states that may form as a consequence of the Kondo coupling between spinons and conduction electrons. For certain carrier concentrations, the uniform Fermi liquid becomes unstable with respect to the formation of a new kind of anharmonic "Kondo stripe" state with inhomogeneous Kondo screening strength and the charge density modulation. These features are experimentally measurable and thus may help to establish the relevance of the spin-liquid correlations to heavy fermion materials.