2,981 research outputs found
Non-equilibrium phase transitions in biomolecular signal transduction
We study a mechanism for reliable switching in biomolecular
signal-transduction cascades. Steady bistable states are created by system-size
cooperative effects in populations of proteins, in spite of the fact that the
phosphorylation-state transitions of any molecule, by means of which the switch
is implemented, are highly stochastic. The emergence of switching is a
nonequilibrium phase transition in an energetically driven, dissipative system
described by a master equation. We use operator and functional integral methods
from reaction-diffusion theory to solve for the phase structure, noise
spectrum, and escape trajectories and first-passage times of a class of minimal
models of switches, showing how all critical properties for switch behavior can
be computed within a unified framework
Well-posedness of parabolic equations containing hysteresis with diffusive thresholds
We study complex systems arising, in particular, in population dynamics,
developmental biology, and bacterial metabolic processes, in which each
individual element obeys a relatively simple hysteresis law (a non-ideal
relay). Assuming that hysteresis thresholds fluctuate, we consider the arising
reaction-diffusion system. In this case, the spatial variable corresponds to
the hysteresis threshold. We describe the collective behavior of such a system
in terms of the Preisach operator with time-dependent measure which is a part
of the solution for the whole system. We prove the well-posedness of the system
and discuss the long-term behavior of solutions.Comment: 30 pages, 1 figur
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
We review a scalable two- and three-dimensional computer code for
low-temperature plasma simulations in multi-material complex geometries. Our
approach is based on embedded boundary (EB) finite volume discretizations of
the minimal fluid-plasma model on adaptive Cartesian grids, extended to also
account for charging of insulating surfaces. We discuss the spatial and
temporal discretization methods, and show that the resulting overall method is
second order convergent, monotone, and conservative (for smooth solutions).
Weak scalability with parallel efficiencies over 70\% are demonstrated up to
8192 cores and more than one billion cells. We then demonstrate the use of
adaptive mesh refinement in multiple two- and three-dimensional simulation
examples at modest cores counts. The examples include two-dimensional
simulations of surface streamers along insulators with surface roughness; fully
three-dimensional simulations of filaments in experimentally realizable
pin-plane geometries, and three-dimensional simulations of positive plasma
discharges in multi-material complex geometries. The largest computational
example uses up to million mesh cells with billions of unknowns on
computing cores. Our use of computer-aided design (CAD) and constructive solid
geometry (CSG) combined with capabilities for parallel computing offers
possibilities for performing three-dimensional transient plasma-fluid
simulations, also in multi-material complex geometries at moderate pressures
and comparatively large scale.Comment: 40 pages, 21 figure
Switch and template pattern formation in a discrete reaction diffusion system inspired by the Drosophila eye
We examine a spatially discrete reaction diffusion model based on the
interactions that create a periodic pattern in the Drosophila eye imaginal
disc. This model is capable of generating a regular hexagonal pattern of gene
expression behind a moving front, as observed in the fly system. In order to
better understand the novel switch and template mechanism behind this pattern
formation, we present here a detailed study of the model's behavior in one
dimension, using a combination of analytic methods and numerical searches of
parameter space. We find that patterns are created robustly provided that there
is an appropriate separation of timescales and that self-activation is
sufficiently strong, and we derive expressions in this limit for the front
speed and the pattern wavelength. Moving fronts in pattern-forming systems near
an initial linear instability generically select a unique pattern, but our
model operates in a strongly nonlinear regime where the final pattern depends
on the initial conditions as well as on parameter values. Our work highlights
the important role that cellularization and cell-autonomous feedback can play
in biological pattern formation
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