321 research outputs found
Membrane mediated aggregation of curvature inducing nematogens and membrane tubulation
The shapes of cell membranes are largely regulated by membrane associated,
curvature active, proteins. We use a numerical model of the membrane with
elongated membrane inclusions, recently developed by us, which posses
spontaneous directional curvatures that could be different along and
perpendicular to its long axis. We show that, due to membrane mediated
interactions these curvature inducing membrane nematogens can oligomerize
spontaneously, even at low concentrations, and change the local shape of the
membrane. We demonstrate that for a large group of such inclusions, where the
two spontaneous curvatures have equal sign, the tubular conformation and
sometime the sheet conformation of the membrane are the common equilibrium
shapes. We elucidate the factors necessary for the formation of these {\it
protein lattices}. Furthermore, the elastic properties of the tubes, like their
compressional stiffness and persistence length are calculated. Finally, we
discuss the possible role of nematic disclination in capping and branching of
the tubular membranes.Comment: 15pages, 8 figure
Semi-Empirical Model for Nano-Scale Device Simulations
We present a new semi-empirical model for calculating electron transport in
atomic-scale devices. The model is an extension of the Extended H\"uckel method
with a self-consistent Hartree potential. This potential models the effect of
an external bias and corresponding charge re-arrangements in the device. It is
also possible to include the effect of external gate potentials and continuum
dielectric regions in the device. The model is used to study the electron
transport through an organic molecule between gold surfaces, and it is
demonstrated that the results are in closer agreement with experiments than ab
initio approaches provide. In another example, we study the transition from
tunneling to thermionic emission in a transistor structure based on graphene
nanoribbons.Comment: 8 pages, 8 figures. Submitted to PR
Investigation of the XCAT phantom as a validation tool in cardiac MRI tracking algorithms.
PURPOSE: To describe our magnetic resonance imaging (MRI) simulated implementation of the 4D digital extended cardio torso (XCAT) phantom to validate our previously developed cardiac tracking techniques. Real-time tracking will play an important role in the non-invasive treatment of atrial fibrillation with MRI-guided radiosurgery. In addition, to show how quantifiable measures of tracking accuracy and patient-specific physiology could influence MRI tracking algorithm design. METHODS: Twenty virtual patients were subjected to simulated MRI scans that closely model the proposed real-world scenario to allow verification of the tracking technique's algorithm. The generated phantoms provide ground-truth motions which were compared to the target motions output from our tracking algorithm. The patient-specific tracking error, ep, was the 3D difference (vector length) between the ground-truth and algorithm trajectories. The tracking errors of two combinations of new tracking algorithm functions that were anticipated to improve tracking accuracy were studied. Additionally, the correlation of key physiological parameters with tracking accuracy was investigated. RESULTS: Our original cardiac tracking algorithm resulted in a mean tracking error of 3.7 ± 0.6 mm over all virtual patients. The two combinations of tracking functions demonstrated comparable mean tracking errors however indicating that the optimal tracking algorithm may be patient-specific. CONCLUSIONS: Current and future MRI tracking strategies are likely to benefit from this virtual validation method since no time-resolved 4D ground-truth signal can currently be derived from purely image-based studies
Self-organized stable pacemakers near the onset of birhythmicity
General amplitude equations for reaction-diffusion systems near to the soft
onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation
are derived. Using these equations and applying singular perturbation theory,
we show that stable autonomous pacemakers represent a generic kind of
spatiotemporal patterns in such systems. This is verified by numerical
simulations, which also show the existence of breathing and swinging pacemaker
solutions. The drift of self-organized pacemakers in media with spatial
parameter gradients is analytically and numerically investigated.Comment: 4 pages, 4 figure
Monte Carlo simulations of fluid vesicles with in plane orientational ordering
We present a method for simulating fluid vesicles with in-plane orientational
ordering. The method involves computation of local curvature tensor and
parallel transport of the orientational field on a randomly triangulated
surface. It is shown that the model reproduces the known equilibrium
conformation of fluid membranes and work well for a large range of bending
rigidities. Introduction of nematic ordering leads to stiffening of the
membrane. Nematic ordering can also result in anisotropic rigidity on the
surface leading to formation of membrane tubes.Comment: 11 Pages, 12 Figures, To appear in Phys. Rev.
Role of disclinations in determining the morphology of deformable fluid interfaces
We study the equilibrium shapes of vesicles, with an in-plane nematic order,
using a Monte-Carlo scheme and show that highly curved shapes, like tubes and
discs, with a striking similarity to the structures engendered by certain
curvature sensing peripheral membrane proteins, can be spontaneously generated
by anisotropic directional curvature with nematic disclinations playing and
important role. We show that the coupling between nematic order and local
curvature could lead to like defects moving towards each other and unlike
defects moving away, in turn leading to tube formation. Thermally induced
defect pair production lead to branched tubular structures. It is also shown
that helical arrangement of the membrane tubes, with nematic field spiraling
around it, is a dominant soft mode of the system.Comment: 6 Figures; Soft Matter, Advance Article 201
Global Hopf bifurcation in the ZIP regulatory system
Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been
modeled by a system of ordinary differential equations based on the uptake of
zinc, expression of a transporter protein and the interaction between an
activator and inhibitor. For certain parameter choices the steady state of this
model becomes unstable upon variation in the external zinc concentration.
Numerical results show periodic orbits emerging between two critical values of
the external zinc concentration. Here we show the existence of a global Hopf
bifurcation with a continuous family of stable periodic orbits between two Hopf
bifurcation points. The stability of the orbits in a neighborhood of the
bifurcation points is analyzed by deriving the normal form, while the stability
of the orbits in the global continuation is shown by calculation of the Floquet
multipliers. From a biological point of view, stable periodic orbits lead to
potentially toxic zinc peaks in plant cells. Buffering is believed to be an
efficient way to deal with strong transient variations in zinc supply. We
extend the model by a buffer reaction and analyze the stability of the steady
state in dependence of the properties of this reaction. We find that a large
enough equilibrium constant of the buffering reaction stabilizes the steady
state and prevents the development of oscillations. Hence, our results suggest
that buffering has a key role in the dynamics of zinc homeostasis in plant
cells.Comment: 22 pages, 5 figures, uses svjour3.cl
Expansion algorithm for the density matrix
A purification algorithm for expanding the single-particle density matrix in
terms of the Hamiltonian operator is proposed. The scheme works with a
predefined occupation and requires less than half the number of matrix-matrix
multiplications compared to existing methods at low (90%)
occupancy. The expansion can be used with a fixed chemical potential in which
case it is an asymmetric generalization of and a substantial improvement over
grand canonical McWeeny purification. It is shown that the computational
complexity, measured as number of matrix multiplications, essentially is
independent of system size even for metallic materials with a vanishing band
gap.Comment: 5 pages, 4 figures, to appear in Phys. Rev.
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