Energy funneling in a bent chain of Morse oscillators with long-range coupling

Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity

The dynamics of DNA in the presence of uniform damping and periodic force is studied. The damped and driven Joyeux-Buyukdagli model is used to investigate the formation of intrinsic localized modes (ILMs). Branches of ILMs are identified as well as their orbital stabilities. A study of the effect of inhomogeneity introduced into the DNA lattice and its ability to control chaotic behavior is conducted. It is seen that a single defect in the chain can induce synchronized spatiotemporal patterns, despite the fact that the entire set of oscillators and the impurity are chaotic when uncoupled. It is also shown that the periodic excitation applied on a specific site can drive the whole lattice into chaotic or regular spatial and temporal patterns.

Energy localization and shape transformations in semiflexible polymer rings

Shape transformations in driven and damped molecular chains are considered. Closed chains of weakly coupled molecular subunits under the action of spatially homogeneous time-periodic external field are studied. The coupling between the internal excitations and the bending degrees of freedom of the chain modifies the local bending rigidity of the chain. In the absence of driving the array takes a circular shape. When the energy pumped into the system exceeds some critical value the chain undergoes a nonequilibrium phase transition: The circular shape of the aggregate becomes unstable and the chain takes the shape of an ellipse or, in general, of a polygon. The excitation energy distribution becomes spatially nonuniform: It localizes in such places where the chain is more flat. The weak interaction of the chain with a flat surface restricts the dynamics to a flat manifold.

A stationary-wave model of enzyme catalysis

An expression for the external force driving a system of two coupled oscillators in the condensed phase was derived in the frame of the Debye theory of solids. The time dependence and amplitude of the force is determined by the size of the cell embedding the coupled oscillators and its Debye temperature (theta(D)). The dynamics of the driven system of oscillators were followed in the two regimes of (a) low theta(D) and cell diameter, as a model of liquid water, and (b) large theta(D) and cell diameter, as a model of the core of a protein. The response in potential energy of the reference oscillator was computed for all possible values of the internal parameters of the system under investigation. For protein cores, the region in the parameter space of high maximum potential energy of the reference oscillator is considerably extended with respect to the corresponding simulation for water.

Discrete instability in the DNA double helix

Modulational instability (MI) is explored in the framework of the base-rotor model of DNA dynamics. We show, in fact, that the helicoidal coupling introduced in the spin model of DNA reduces the system to a modified discrete sine-Gordon (sG) equation. The MI criterion is thus modified and displays interesting features because of the helicoidal coupling. In the simulations, we have found that a train of pulses is generated when the lattice is subjected to MI, in agreement with analytical results obtained in a modified discrete sG equation. Also, the competitive effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. In the same way, it is shown that MI can lead to energy localization which becomes high for some values of the helicoidal coupling constant.

Dynamics of a curved Fermi-Pasta-Ulam chain: effects of geometry, long-range interaction, and nonlinear dispersion

We study the dynamics of the bent Fermi-Pasta-Ulam (FPU) chain, incorporating the complicated effects of geometry, long-range interactions, as well as nonlinear dispersion. Within the rotating wave approximation, we obtain several exact discrete breather (DB) solutions, such as the odd-parity and even-parity discrete breathers, compactlike discrete breathers and moving discrete breathers for various geometries of the chain. In presence of long-range nonlinear dispersive interactions, we show that DBs exist in the discrete curved lattice for next-nearest-neighbor interactions as well. For all neighbors interactions, we treat the problem in the long-wavelength (continuum) and weakly nonlinear limit of the system and obtain exact static breather solutions and large-amplitude, traveling kink-soliton solutions. The curved FPU chain also admits finite amplitude discrete nonlinear sinusoidal wave solutions with short commensurate as well as incommensurate wavelengths. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.

Bubble generation in a twisted and bent DNA-like model

The DNA molecule is modeled by a parabola embedded chain with long-range interactions between twisted base pair dipoles. A mechanism for bubble generation is presented and investigated in two different configurations. Using random normally distributed initial conditions to simulate thermal fluctuations, a relationship between bubble generation, twist and curvature is established. An analytical approach supports the numerical results.