Lattice stretching bistability and dynamic heterogeneity

A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearest-neighbor interaction of a Morse-like potential (required to have a saturation branch) and an harmonic second-neighbor coupling. Under an external stretching applied t o the chain ends, the intersite Morse-like potential results in the appearance of a double-well potential within each chain monomer, whereas the interaction between the second neighbors provide s a homogeneous bistable (degenerate) ground state, at least within a certain part of the chain. As a result, different conformational changes occur in the chain under the external forcing. The transition regions between these conformations are described as topological solitons. With a strong second-neighbor interaction, the solitons describe the transition between the bistable ground states. However, the key point of the model is the appearance of a heterogenous structure, when the second-neighbor coupling is sufficiently weak. In this case, a part of the chain has short bonds with a single-well potential, whereas the complementary part admits strongly stretched bonds with a double-well potential. This case allows us to explain the existence of a plateau in the force-stretching diagram for DNA and alpha-helix protein. Finally, the soliton dynamics are studied in detail.Comment: Submitted to Phys. Rev. E, 13 figure

Pendulum as a model system for driven rotation in molecular nanoscale machines

We suggest a ratchet mechanism of rotatory (or translatory) motion of a Brownian rotator (or a particle) in a spatially symmetric periodic potential. The asymmetry that drives the ratchet motion is due to a special sequence of activation of catalytic sites arranged in space circularly and periodically. A pendulum driven by short impulses at its stable equilibrium point is shown to be a simple mechanical model which can be constructed easily and used for visual observation of the ratchet rotation. A possible application of this mechanism in nanotechnology is briefly discussed

Ratchet-like dynamics of fluxons in annular Josephson junctions driven by bi-harmonic microwave fields

Experimental observation of the unidirectional motion of a topological soliton driven by a bi-harmonic ac force of zero mean is reported. The observation is made by measuring the current-voltage characteristics for a fluxon trapped in an annular Josephson junction that was placed into a microwave field. The measured dependence of the fluxon mean velocity (rectified voltage) at zero dc bias versus the phase shift between the first and second harmonic of the driving force is in qualitative agreement with theoretical expectations.Comment: 6 figure

Controlling a resonant transmission across the δ′\delta'-potential: the inverse problem

Recently, the non-zero transmission of a quantum particle through the one-dimensional singular potential given in the form of the derivative of Dirac's delta function, $\lambda \delta'(x)$, with $\lambda \in \R$, being a potential strength constant, has been discussed by several authors. The transmission occurs at certain discrete values of $\lambda$ forming a resonance set ${\lambda_n}_{n=1}^\infty$. For $\lambda \notin {\lambda_n}_{n=1}^\infty$ this potential has been shown to be a perfectly reflecting wall. However, this resonant transmission takes place only in the case when the regularization of the distribution $\delta'(x)$ is constructed in a specific way. Otherwise, the $\delta'$-potential is fully non-transparent. Moreover, when the transmission is non-zero, the structure of a resonant set depends on a regularizing sequence $\Delta'_\varepsilon(x)$ that tends to $\delta'(x)$ in the sense of distributions as $\varepsilon \to 0$. Therefore, from a practical point of view, it would be interesting to have an inverse solution, i.e. for a given $\bar{\lambda} \in \R$ to construct such a regularizing sequence $\Delta'_\varepsilon(x)$ that the $\delta'$-potential at this value is transparent. If such a procedure is possible, then this value $\bar{\lambda}$ has to belong to a corresponding resonance set. The present paper is devoted to solving this problem and, as a result, the family of regularizing sequences is constructed by tuning adjustable parameters in the equations that provide a resonance transmission across the $\delta'$-potential.Comment: 21 pages, 4 figures. Corrections to the published version added; http://iopscience.iop.org/1751-8121/44/37/37530

Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

Two-phase stretching of molecular chains

While stretching of most polymer chains leads to rather featureless force-extension diagrams, some, notably DNA, exhibit non-trivial behavior with a distinct plateau region. Here we propose a unified theory that connects force-extension characteristics of the polymer chain with the convexity properties of the extension energy profile of its individual monomer subunits. Namely, if the effective monomer deformation energy as a function of its extension has a non-convex (concave up) region, the stretched polymer chain separates into two phases: the weakly and strongly stretched monomers. Simplified planar and 3D polymer models are used to illustrate the basic principles of the proposed model. Specifically, we show rigorously that when the secondary structure of a polymer is mostly due to weak non-covalent interactions, the stretching is two-phase, and the force-stretching diagram has the characteristic plateau. We then use realistic coarse-grained models to confirm the main findings and make direct connection to the microscopic structure of the monomers. We demostrate in detail how the two-phase scenario is realized in the \alpha-helix, and in DNA double helix. The predicted plateau parameters are consistent with single molecules experiments. Detailed analysis of DNA stretching demonstrates that breaking of Watson-Crick bonds is not necessary for the existence of the plateau, although some of the bonds do break as the double-helix extends at room temperature. The main strengths of the proposed theory are its generality and direct microscopic connection.Comment: 16 pges, 22 figure

Origin of resonant tunneling through single-point barriers

The physical interpretation of the appearance of resonant transmission through single-point barriers is discussed on the basis of a double-layer heterostructure in the squeezing limit as both the thickness of the layers and the distance between them tend to zero simultaneously. In this limit, the electron transmission through a barrier-well structure is derived to be non-zero at certain discrete values of the system parameters forming the so-called resonance set, while beyond this set, the structure behaves as a perfectly reflecting wall. The origin of this phenomenon is shown to result from the reflection coefficients at the interfaces in the inter-layer space. The transmission amplitude is computed as a set function defined on the trihedral angle surface in a three-dimensional parameter space.Comment: 2 figure

Single point potentials with total resonant tunneling

Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar tunneling properties are studied in considerable detail. Particularly, in the zero-range limit when the potentials are squeezed to a single point, sharp peaks with total transmission are observed at certain (positive and negative) quantized values of the potential strength constant forming infinite discrete sets. Beyond these sets, the barrier-well structures behave as a perfectly reflecting wall. The transcendental equations with respect to potential strengths, the solutions of which determine transmission (resonance) sets, are derived. In this regard, both the models are exactly solvable. The energy dependence of an incident particle is shown to reveal a resonance behavior, being completely different from that observed in a typical double barrier structure.Comment: 8 figure