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Biomedical subjects

P L Christiansen

Publications and source records attributed to P L Christiansen.

16 recordsLinked to original sources
PubMed2006

Conformational transformations induced by the charge-curvature interaction: Mean-field approach.

A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom of closed molecular aggregates may act as drivers giving impetus to conformational dynamics of biopolymers. It is demonstrated that initially circular aggregates may undergo transformation to polygonal shapes and possible application to aggregates of bacteriochlorophyl a molecules is considered.

Bacteriochlorophyll A↗
PubMed2004

Discrete kink dynamics in hydrogen-bonded chains: the two-component model.

We study discrete topological solitary waves (kinks and antikinks) in two nonlinear diatomic chain models that describe the collective dynamics of proton transfers in one-dimensional hydrogen-bonded networks. The essential ingredients of the models are (i) a realistic (anharmonic) ion-proton interaction in the hydrogen bond, (ii) a harmonic coupling between the protons in adjacent hydrogen bonds, and (iii) a harmonic coupling between the nearest-neighbor heavy ions (an isolated diatomic chain with the lowest acoustic band) or instead a harmonic on-site potential for the heavy ions (a diatomic chain subject to a substrate with two optical bands), both providing a bistability of the hydrogen-bonded proton. Exact two-component (kink and antikink) discrete solutions for these models are found numerically. We compare the soliton solutions and their properties in both the one- (when the heavy ions are fixed) and two-component models. The effect of stability switchings, discovered previously for a class of one-component kink-bearing models, is shown to exist in these two-component models as well. However, the presence of the second component, i.e., the softness of the heavy-ion sublattice, brings principal differences, like a significant difference in the stability switchings behavior for the kinks and the antikinks. Water-filled carbon nanotubes are briefly discussed as possible realistic systems, where topological discrete (anti)kink states might exist.

Journal Article↗
PubMed2004

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.

Journal Article↗
PubMed2003

Discrete breathers in classical ferromagnetic lattices with easy-plane anisotropy.

Discrete breathers (nonlinear localized modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. This paper is devoted to the investigation of a classical d-dimensional ferromagnetic lattice with easy plane anisotropy. Its dynamics is described via the Heisenberg model. Discrete breathers exist in such a model and represent excitations with locally tilted magnetization. They possess energy thresholds and have no analogs in the continuum limit. We are going to review the previous results on such solutions and also to report new results. Among the new results we show the existence of a big variety of these breather solutions, depending on the respective orientation of the tilted spins. Floquet stability analysis has been used to classify the stable solutions depending on their spatial structure, their frequency, and other system parameters, such as exchange interaction and local (single-ion) anisotropy.

Journal Article↗
PubMed2002

Discrete kink dynamics in hydrogen-bonded chains: 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 the 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 traveling-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).

Journal Article↗
PubMed2002

A model for glucose-induced wave propagation in pancreatic islets of Langerhans.

A reaction-diffusion type model is constructed, describing the spatio-temporal dynamics of the basic intracellular variables assumed to be involved in the initiation of the insulin secretion process by beta -cells in the pancreatic islets of Langerhans. The model includes equations for the electric membrane potential of the cells, with respective kinetics for ionic currents, for concentrations of both free and stored intracellular calcium, and for the intra- and extracellular concentrations of glucose. An empirical expression connecting the equation for the intracellular glucose concentration to the electrical equation is introduced. The model reproduces the events observed in experiments in vitro upon external glucose application to the islets of Langerhans, such as usual bursting oscillations of the membrane potential and corresponding oscillations of the intracellular calcium concentration. It also allows simulation of electric wave propagation through the islet, initiated by the spatial gradient of glucose concentration within the islet. The gradient emerges due to glucose diffusing into the islets from the external medium, being high at the edges. The latter results show that glucose diffusion presents a means for wave initiation in the islets, which supports our previous assumption (Aslanidi et al., 2001).

Animals↗
PubMed2001

Interplay of nonlinearity and geometry in a DNA-related, Klein-Gordon model with long-range dipole-dipole interaction.

Most of the studies on mathematical models of DNA are limited to next neighbor interaction. However, the coupling between base pairs is thought to be caused by dipole interaction, and, when the DNA strand is bent, the distances between base pairs become shorter, therefore the interactions with distant base pairs have to be taken into account. In this paper we analyze the existence and stability of breathers, i.e., localized oscillations in a simple model of bent DNA with long-range dipole interaction. Breathers have been suggested as precursors of the denaturation bubble.

Journal Article↗
PubMed2001

Ratchet due to broken friction symmetry.

A ratchet mechanism that occurs due to asymmetric dependence of the friction of a moving system on its velocity or a driving force is reported. For this kind of ratchet, instead of a particle moving in a periodic potential, the dynamics of which have broken space-time symmetry, the system must be provided with some internal structure realizing such a velocity- or force-friction dependence. For demonstration of a ratchet mechanism of this type, an experimental setup (gadget) that converts longitudinal oscillating or fluctuating motion into a unidirectional rotation has been built and experiments with it have been carried out. In this device, an asymmetry of friction dependence on an applied force appears, resulting in rectification of rotary motion. In experiments, our setup is observed to rotate only in one direction, which is in accordance with given theoretical arguments. Despite the setup being three dimensional, the ratchet rotary motion is proved to be described by one dynamical equation. This kind of motion is a result of the interplay of friction and inertia. We also consider a case with viscous friction, which is irrelevant to this gadget, but it can be a possible mechanism of rotary unidirectional motion of some swimming organisms in a liquid.

Journal Article↗
PubMed2001

Collapse arresting in an inhomogeneous two-dimensional nonlinear Schrödinger model.

Collapse of (2+1)-dimensional beams in the inhomogeneous two-dimensional cubic nonlinear Schrödinger equation is analyzed numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams that in a homogeneous medium would collapse may be arrested under certain circumstances.

Journal Article↗
PubMed2001

Nonlinearity and disorder: classification and stability of nonlinear impurity modes.

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of nonlinear impurity modes, one- and two-hump symmetric localized modes and asymmetric localized modes, for both focusing and defocusing nonlinearity and two different (attractive or repulsive) types of impurity. We obtain an analytical stability criterion for the nonlinear localized modes and consider the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site.

Journal Article↗
PubMed2001

Excitation wave propagation as a possible mechanism for signal transmission in pancreatic islets of Langerhans.

In response to glucose application, beta-cells forming pancreatic islets of Langerhans start bursting oscillations of the membrane potential and intracellular calcium concentration, inducing insulin secretion by the cells. Until recently, it has been assumed that the bursting activity of beta-cells in a single islet of Langerhans is synchronized across the whole islet due to coupling between the cells. However, time delays of several seconds in the activity of distant cells are usually observed in the islets of Langerhans, indicating that electrical/calcium wave propagation through the islets can occur. This work presents both experimental and theoretical evidence for wave propagation in the islets of Langerhans. Experiments with Fura-2 fluorescence monitoring of spatiotemporal calcium dynamics in the islets have clearly shown such wave propagation. Furthermore, numerical simulations of the model describing a cluster of electrically coupled beta-cells have supported our view that the experimentally observed calcium waves are due to electric pulses propagating through the cluster. This point of view is also supported by independent experimental results. Based on the model equations, an approximate analytical expression for the wave velocity is introduced, indicating which parameters can alter the velocity. We point to the possible role of the observed waves as signals controlling the insulin secretion inside the islets of Langerhans, in particular, in the regions that cannot be reached by any external stimuli such as high glucose concentration outside the islets.

Animals↗
PubMed1999

Collapse arresting in an inhomogeneous quintic nonlinear Schrödinger model.

Collapse of (1+1)-dimensional beams in the inhomogeneous one-dimensional quintic nonlinear Schrödinger equation is analyzed both numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams in which the homogeneous medium would blow up may be delayed and even arrested.

Journal Article↗
PubMed1999

Three-wave interaction in two-component quadratic nonlinear lattices.

We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that energy conversion and pulse propagation known from three-wave interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained in non-phase-matched lattices by tilting the interacting plane waves with respect to each other.

Journal Article↗
PubMed1999

Engineered nonlinear lattices.

We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term a quasilattice, which interpolates between a lattice system and a continuous system.

Journal Article↗
PubMed1988

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.

DNA↗