PubMed Health⌕ Search
Home/Archive/PubMed

PubMed · 15447560

Spatiotemporal structures in a model with delay and diffusion.

M Bestehorn·E V Grigorieva·S A Kaschenko
View original source ↗Export metadata ↓

Abstract

Pattern formation described by differential-difference equations with diffusion is investigated. It is shown that an arbitrarily small diffusion induces space-time turbulence just at the instability threshold of the homogeneous stationary solution. We prove this property by deriving a complex Ginzburg-Landau equation on the basis of normal form analysis. Well above threshold, such turbulent structures give way to synchronized states ordered by spirals and targets. This secondary instability can be understood with an asymptotic method representing the system as a cellular automaton network.

Explore related subjects

BiophysicsDiffusionModels, StatisticalModels, TheoreticalOscillometryJournal Article

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M Bestehorn, E V Grigorieva, S A Kaschenko. 2004-08-09. Spatiotemporal structures in a model with delay and diffusion.. https://doi.org/10.1103/physreve.70.026202

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2005

Field theoretic study of bilayer membrane fusion: II. Mechanism of a stalk-hole complex.

We use self-consistent field theory to determine structural and energetic properties of intermediates and transition states involved in bilayer membrane fusion. In particular, we extend our original calculations from those of the standard hemifusion mechanism, which was studied in detail in the first article of this series, to consider a possible alternative to it. This mechanism involves non-axial stalk expansion, in contrast to the axially symmetric evolution postulated in the classical mechanism. Elongation of the initial stalk facilitates the nucleation of holes and leads to destabilization of the fusing membranes via the formation of a stalk-hole complex. We study properties of this complex in detail, and show how transient leakage during fusion, previously predicted and recently observed in experiment, should vary with lipid architecture and tension. We also show that the barrier to fusion in the alternative mechanism is lower than that of the standard mechanism by a few k(B)T over most of the relevant region of system parameters, so that this alternative mechanism is a viable alternative to the standard pathway. We emphasize that any mechanism, such as this alternative one, which affects, even modestly, the line tension of a hole in a membrane, affects greatly the ability of that membrane to undergo fusion.

Biophysics↗
PubMed2005

Detection of forces and displacements along the axial direction in an optical trap.

We present measurements of the forces on, and displacements of, an optically trapped bead along the propagation direction of the trapping laser beam (the axial direction). In a typical experimental configuration, the bead is trapped in an aqueous solution using an oil-immersion, high-numerical-aperture objective. This refractive index mismatch complicates axial calibrations due to both a shift of the trap center along the axial direction and spherical aberrations. In this work, a known DNA template was unzipped along the axial direction and its characteristic unzipping force-extension data were used to determine 1), the location of the trap center along the axial direction; 2), the axial displacement of the bead from the trap center; and 3), the axial force exerted on the bead. These axial calibrations were obtained for trap center locations up to approximately 4 microm into the aqueous solution and with axial bead displacements up to approximately 600 nm from the trap center. In particular, the axial trap stiffness decreased substantially when the trap was located further into the aqueous solution. This approach, together with conventional lateral calibrations, results in a more versatile optical trapping instrument that is accurately calibrated in all three dimensions.

Biophysics↗