Soliton oscillations in DNA

Evidence for DNA resonance signaling via longitudinal hydrogen bonds

The theory of the morphogenic field suggests that chemical signaling is supplemented by electromagnetic signaling governing the structure and shape of tissues, organs and the body. The theory of DNA resonance suggests that the morphogenic field is created by the genomic DNA which sends and receives electromagnetic signals in a sequence-specific manner. Previously, the authors have proposed the existence of HIDERs, genomic elements that serve as antennas in resonance signaling and demonstrated that they occur nonrandomly and are conserved in evolution. Here, it is proposed that longitudinal hydrogen bonds exist in the double helix, that chains of these bonds form delocalized proton clouds, that the shapes of these clouds are sequence-specific and form the basis of sequence-specificity of resonance between HIDERs. Based on longitudinal hydrogen bonds, a proton DNA resonance code was devised and used to identify HIDERs which are enriched 20 fold in the genome and conserved in evolution. It was suggested that these HIDERs are the key elements responsible for DNA resonance signaling and the formation of the morphogenic field.

Possible traces of resonance signaling in the genome

Although theories regarding the role of sequence-specific DNA resonance in biology have abounded for over 40 years, the published evidence for it is lacking. Here, the authors reasoned that for sustained resonance signaling, the number of oscillating DNA sequences per genome should be exceptionally high and that, therefore, genomic repeats of various sizes are good candidates for serving as resonators. Moreover, it was suggested that for the two DNA sequences to resonate, they do not necessarily have to be identical. Therefore, the existence of sequences differing in the primary sequence but having similar resonating sub-structures was proposed. It was hypothesized that such sequences, named HIDERs, would be enriched in the genomes of multicellular species. Specifically, it was hypothesized that delocalized electron clouds of purine-pyrimidine sequences could serve as the basis of HIDERs. The consequent computational genomic analysis confirmed the enrichment of purine-pyrimidine HIDERs in a few selected genomes of mammals, an insect, and a plant, compared to randomized sequence controls. Similarly, it was suggested that hypothetical delocalized proton clouds of the hydrogen bonds of multiple stacked bases could serve as sequence-dependent hydrogen-bond-based HIDERs. Similarly, the enrichment of such HIDERs was observed. It is suggested that these enrichments are the first evidence in support of sequence-specific resonance signaling in the genome.

Parametric resonance in DNA

We consider a simple mesoscopic model of DNA in which the binding of the RNA polymerase enzyme molecule to the promoter sequence of the DNA is included through a substrate energy term modeling the enzymatic interaction with the DNA strands. We focus on the differential system for solitary waves and derive conditions--in terms of the model parameters--for the occurrence of the parametric resonance phenomenon. We find that what truly matters for parametric resonance is not the ratio between the strength of the stacking and the inter-strand forces but the ratio between the substrate and the inter-strands. On the basis of these results, the standard objection that longitudinal motion is negligible because of the second order seems to fail, suggesting that all the studies involving the longitudinal degree of freedom in DNA should be reconsidered when the interaction of the RNA polymerase with the DNA macromolecule is not neglected.

Dispersion of discontinuous periodic waves

The dynamic evolution of linearly dispersive waves on periodic domains with discontinuous initial profiles is shown to depend remarkedly upon the asymptotics of the dispersion relation at large wavenumbers. Asymptotically linear or sublinear dispersion relations produce slowly changing waves, while those with polynomial growth exhibit dispersive quantization, a.k.a. the Talbot effect, being (approximately) quantized at rational times, but a non-differentiable fractal at irrational times. Numerical experiments suggest that such effects persist into the nonlinear regime, for both integrable and non-integrable systems. Implications for the successful modelling of wave phenomena on bounded domains and numerical challenges are discussed.

Bubble solitons in an inhomogeneous, helical DNA molecular chain with flexible strands

Base pair opening in an inhomogeneous, DNA double helical molecular chain with flexible strands is investigated by studying its internal dynamics. For the study, a generalized model which takes into account the energies involved in stacking and hydrogen bonds along with inhomogeneity, helicity, and phonons coupled to the stacking and hydrogen bonds is proposed. The internal dynamics of the proposed DNA model is governed by a perturbed nonlinear Schrödinger equation. The unperturbed, completely integrable nonlinear Schrödinger equation which admits soliton solutions and forming a bubble corresponds to DNA dynamics with homogeneous and rigid strands. The results of the soliton perturbation analysis show that the inhomogeneity in stacking and hydrogen bonds in localized and periodic forms and the helicity do not alter the amplitude under perturbation. However, the flexibility of the strands diminishes the perturbed amplitude. On the other hand, the velocity of the soliton and bubble are unaltered due to all the above effects. However, the position and phase of the soliton and the bubble vary linearly in time. While the position of the soliton depends on the initial velocity, the phase depends on both the initial velocity and the initial amplitude of the soliton. The above effects introduce small fluctuation in the tail of the soliton, without affecting the robust nature of the soliton and the bubble during propagation. The soliton and the bubble obtained as solutions of the internal dynamics of the DNA molecule represent an opening of the base pairs which is essential for the transcription process.

Formation of random dark envelope solitons from incoherent waves

This Letter reports experimental results on random temporal dark solitons. One excites an incoherent large-amplitude propagating spin-wave packet in a ferromagnetic film strip with a repulsive, instantaneous nonlinearity. One then observes the random formation of dark solitons from this wave packet. The solitons appear randomly in time and in position relative to the entire wave packet. They can be gray or black. In spite of the randomness of the initial wave packets and the random formation processes, the solitons show signatures that are found for conventional coherent dark solitons.

Perturbative study of classical Ablowitz-Ladik type soliton dynamics in relation to energy transport in alpha-helical proteins

Classical Ablowitz-Ladik type soliton dynamics from three closely related classical nonlinear equations is studied using a perturbative method. Model nonintegrable equations are derived by assuming nearest neighbor hopping of an exciton(vibron) in the presence of a full exciton(vibron)-phonon interaction in soft molecular chains in general and spines of alpha-helices in particular. In all cases, both trapped and moving solitons are found implying activation energy barrier for propagating solitons. Analysis further shows that staggered and nearly staggered trapped solitons will have a negative effective mass. In some models the exciton(vibron)-phonon coupling affects the hopping. For these models, when the conservation of probability is taken into account, only propagating solitons with a broad profile are found to be acceptable solutions. Of course, for the soliton to be a physically meaningful entity, total nonlinear coupling strength should exceed a critical value. On the basis of the result, a plausible modification in the mechanism for biological energy transport involving conformational change in alpha-helix is proposed. Future directions of the work are also mentioned.

Microwave absorption spectroscopy of DNA

By utilizing a novel approach to microwave spectrometry, we have measured the absolute absorption spectrum of plasmid DNA (pUC8.c2), in buffered aqueous solution, from 5 to 20 GHz. Our technique does not suffer from the same experimental difficulties that plague other methods. We observe no absorption resonances in this frequency range, but we do see broadband differences, between DNA and pure buffer, that are attributable to changes in the ionic conductivity of the solutions. These results constitute the first verification, by a totally different technique, of the absence of resonances in the microwave absorption spectrum of DNA, and the first data obtained by any technique in the 10-20-GHz band.

Dielectric behavior of aqueous solutions of plasmid DNA at microwave frequencies

The relative permittivity and dielectric loss of aqueous solutions of plasmid (pUC8.c1 and pUC8.c2) DNA have been measured at 20 degrees C over the frequency range 100 MHz-10 GHz. The solutions had a concentration of 0.1% DNA, and were studied both in the relaxed and the supercoiled form. The dielectric measurements were made using a variety of techniques including frequency domain and time domain methods of operation. No evidence of any resonance absorption, nor of any other kind of enhanced absorption, was observed.

Solitons in DNA

DNA is modeled as a homogeneous, cylindrical rod with nonlinear elasticity using the Ostrovskii-Sutin equation (OSE) with periodic boundary conditions. This equation predicts that longitudinal sound waves will be concentrated into packets called solitons. From a study of the damped OSE, we conclude that decay time is almost independent of the solitonic character of the solution. For the damped, driven OSE, on the other hand, we find that spectral features (such as absorption line widths and fine structure) are strongly influenced by the presence of anharmonicity. This effect is enhanced as the length of the DNA is increased.

"Resonances" in the dielectric absorption of DNA?

An attempt was made to confirm previous reports of resonant-like dielectric absorption of plasmid DNA in aqueous solutions at 1-10 GHz. The dielectric properties of the sample were measured using an automatic network analyzer with two different techniques. One technique used an open-ended coaxial probe immersed in the sample; the other employed a coaxial transmission line. No resonances were observed that could be attributed to the sample; however, resonance-type artifacts were prominent in the probe measurements. The coaxial line technique appears to be less susceptible to such artifacts. We note two important sources of error in the calibration of the automatic network analyzer using the probe technique.