467 research outputs found
Diffusive Boundary Layers in the Free-Surface Excitable Medium Spiral
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a
great variety of excitable systems. In the limit of a large separation in
timescale between fast excitation and slow recovery, one can reduce the spiral
problem to one involving the motion of a free surface separating the excited
and quiescent phases. In this work, we study the free surface problem in the
limit of small diffusivity for the slow field variable. Specifically, we show
that a previously found spiral solution in the diffusionless limit can be
extended to finite diffusivity, without significant alteration. This extension
involves the creation of a variety of boundary layers which cure all the
undesirable singularities of the aforementioned solution. The implications of
our results for the study of spiral stability are briefly discussed.Comment: 6 pages, submitted to PRE Rapid Com
Discrete stochastic modeling of calcium channel dynamics
We propose a simple discrete stochastic model for calcium dynamics in living
cells. Specifically, the calcium concentration distribution is assumed to give
rise to a set of probabilities for the opening/closing of channels which
release calcium thereby changing those probabilities. We study this model in
one dimension, analytically in the mean-field limit of large number of channels
per site N, and numerically for small N. As the number of channels per site is
increased, the transition from a non-propagating region of activity to a
propagating one changes in nature from one described by directed percolation to
that of deterministic depinning in a spatially discrete system. Also, for a
small number of channels a propagating calcium wave can leave behind a novel
fluctuation-driven state, in a parameter range where the limiting deterministic
model exhibits only single pulse propagation.Comment: 4 pages, 5 figures, submitted to PR
Mechanisms underlying sequence-independent beta-sheet formation
We investigate the formation of beta-sheet structures in proteins without
taking into account specific sequence-dependent hydrophobic interactions. To
accomplish this, we introduce a model which explicitly incorporates both
solvation effects and the angular dependence (on the protein backbone) of
hydrogen bond formation. The thermodynamics of this model is studied by
comparing the restricted partition functions obtained by "unfreezing"
successively larger segments of the native beta-sheet structure. Our results
suggest that solvation dynamics together with the aforementioned angular
dependence gives rise to a generic cooperativity in this class of systems; this
result explains why pathological aggregates involving beta-sheet cores can form
from many different proteins. Our work provides the foundation for the
construction of phenomenological models to investigate the competition between
native folding and non-specific aggregation.Comment: 20 pages, 5 figures, Revtex4, simulation mpeg movie available at
http://www-physics.ucsd.edu/~guochin/Images/sheet1.mp
Analytic approach to the evolutionary effects of genetic exchange
We present an approximate analytic study of our previously introduced model
of evolution including the effects of genetic exchange. This model is motivated
by the process of bacterial transformation. We solve for the velocity, the rate
of increase of fitness, as a function of the fixed population size, . We
find the velocity increases with , eventually saturated at an which
depends on the strength of the recombination process. The analytical treatment
is seen to agree well with direct numerical simulations of our model equations
Embryonic Pattern Scaling Achieved by Oppositely Directed Morphogen Gradients
Morphogens are proteins, often produced in a localised region, whose
concentrations spatially demarcate regions of differing gene expression in
developing embryos. The boundaries of expression must be set accurately and in
proportion to the size of the one-dimensional developing field; this cannot be
accomplished by a single gradient. Here, we show how a pair of morphogens
produced at opposite ends of a developing field can solve the pattern-scaling
problem. In the most promising scenario, the morphogens effectively interact
according to the annihilation reaction and the switch occurs
according to the absolute concentration of or . In this case embryonic
markers across the entire developing field scale approximately with system
size; this cannot be achieved with a pair of non-interacting gradients that
combinatorially regulate downstream genes. This scaling occurs in a window of
developing-field sizes centred at a few times the morphogen decay length.Comment: 24 pages; 11 figures; uses iopar
Two State Behavior in a Solvable Model of -hairpin folding
Understanding the mechanism of protein secondary structure formation is an
essential part of protein-folding puzzle. Here we describe a simple model for
the formation of the -hairpin, motivated by the fact that folding of a
-hairpin captures much of the basic physics of protein folding. We argue
that the coupling of ``primary'' backbone stiffness and ``secondary'' contact
formation (similar to the coupling between the ``secondary'' and ``tertiary''
structure in globular proteins), caused for example by side-chain packing
regularities, is responsible for producing an all-or-none 2-state
-hairpin formation. We also develop a recursive relation to compute the
phase diagram and single exponential folding/unfolding rate arising via a
dominant transition state.Comment: Revised versio
Evolution on a smooth landscape
We study in detail a recently proposed simple discrete model for evolution on
smooth landscapes. An asymptotic solution of this model for long times is
constructed. We find that the dynamics of the population are governed by
correlation functions that although being formally down by powers of (the
population size) nonetheless control the evolution process after a very short
transient. The long-time behavior can be found analytically since only one of
these higher-order correlators (the two-point function) is relevant. We compare
and contrast the exact findings derived herein with a previously proposed
phenomenological treatment employing mean field theory supplemented with a
cutoff at small population density. Finally, we relate our results to the
recently studied case of mutation on a totally flat landscape.Comment: Revtex, 15 pages, + 4 embedded PS figure
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