Base pair opening and bubble transport in a DNA double helix induced by a protein molecule in a viscous medium

We study the nonlinear dynamics of a protein-DNA molecular system by treating DNA as a set of two coupled linear chains and protein in the form of a single linear chain sliding along the DNA at the physiological temperature in a viscous medium. The nonlinear dynamics of the above molecular system in general is governed by a perturbed nonlinear Schr\"{o}dinger equation. In the non-viscous limit, the equation reduces to the completely integrable nonlinear Schr\"{o}dinger (NLS) equation which admits N-soliton solutions. The soliton excitations of the DNA bases make localized base pair opening and travel along the DNA chain in the form of a bubble. This may represent the bubble generated during the transcription process when an RNA-polymerase binds to a promoter site in the DNA double helical chain. The perturbed NLS equation is solved using a perturbation theory by treating the viscous effect due to surrounding as a weak perturbation and the results show that the viscosity of the solvent in the surrounding damps out the amplitude of the soliton.Comment: 4. Submitted to Phys. Rev.

Yang-Mills condensates in cosmology

We discuss homogeneous and isotropic cosmological models driven by SU(2) gauge fields in the framework of Einstein gravity. There exists a Yang-Mills field configuration, parametrized by a single scalar function, which consists of parallel electric and magnetic fields and has the stress tensor mimicking an homogeneous and isotropic fluid. The unique SU(2) gauge theory with spontaneous symmetry breaking sharing the same property is the Yang-Mills coupled to the complex doublet Higgs, this exists only in the case of the closed universe. This model contains an intrinsic mechanism for inflation due to the Higgs potential. Our second goal is to show that a successful inflation can be achieved also within the pure Yang-Mills theory adding an appropriate theta-term.Comment: Submitted to Proceedings of "Quantum field theory under the influence of external conditions", Benasque, Spain, September 18-24, 2011 2011, Sep 18 -- Sep 2

A Note on Stress-Energy Tensor and Variational Principle for Null Strings

A straightforward application of the variational principle to null strings meets difficulties since string's world-sheets are degenerate. It is known that the variational principle in this case can be formulted with the help of two-vector density on the string world-sheet which plays a role of Lagrange multipliers. It is shown that recently suggested stress-energy tensor of null strings can be derived by variation over the background metric of the action used to describe tensionless limit in the string theory. One of the Lagrange multipliers is related to the energy of the null string.Comment: 4 page

Quadrupole transitions near interface: general theory and application to atom inside a planar cavity

Quadrupole radiation of an atom in an arbitrary environment is investigated within classical as well as quantum electrodynamical approaches. Analytical expressions for decay rates are obtained in terms of Green function of Maxwell equations. The equivalence of both approaches is shown. General expressions are applied to analyze the quadrupole decay rate of an atom placed between two half spaces with arbitrary dielectric constant. It is shown that in the case when the atom is close to the surface, the total decay rate is inversely proportional to the fifth power of distance between an atom and a plane interface.Comment: 18 pages, 7 figure

Benchmarking calculations of excitonic couplings between bacteriochlorophylls

Excitonic couplings between (bacterio)chlorophyll molecules are necessary for simulating energy transport in photosynthetic complexes. Many techniques for calculating the couplings are in use, from the simple (but inaccurate) point-dipole approximation to fully quantum-chemical methods. We compared several approximations to determine their range of applicability, noting that the propagation of experimental uncertainties poses a fundamental limit on the achievable accuracy. In particular, the uncertainty in crystallographic coordinates yields an uncertainty of about 20% in the calculated couplings. Because quantum-chemical corrections are smaller than 20% in most biologically relevant cases, their considerable computational cost is rarely justified. We therefore recommend the electrostatic TrEsp method across the entire range of molecular separations and orientations because its cost is minimal and it generally agrees with quantum-chemical calculations to better than the geometric uncertainty. We also caution against computationally optimizing a crystal structure before calculating couplings, as it can lead to large, uncontrollable errors. Understanding the unavoidable uncertainties can guard against striving for unrealistic precision; at the same time, detailed benchmarks can allow important qualitative questions--which do not depend on the precise values of the simulation parameters--to be addressed with greater confidence about the conclusions

Anomalous tunneling of bound pairs in crystal lattices

A novel method of solving scattering problems for bound pairs on a lattice is developed. Two different break ups of the hamiltonian are employed to calculate the full Green operator and the wave function of the scattered pair. The calculation converges exponentially in the number of basis states used to represent the non-translation invariant part of the Green operator. The method is general and applicable to a variety of scattering and tunneling problems. As the first application, the problem of pair tunneling through a weak link on a one-dimensional lattice is solved. It is found that at momenta close to \pi the pair tunnels much easier than one particle, with the transmission coefficient approaching unity. This anomalously high transmission is a consequence of the existence of a two-body resonant state localized at the weak link.Comment: REVTeX, 5 pages, 4 eps figure