9,957 research outputs found
Scenarios of domain pattern formation in a reaction-diffusion system
We performed an extensive numerical study of a two-dimensional
reaction-diffusion system of the activator-inhibitor type in which domain
patterns can form. We showed that both multidomain and labyrinthine patterns
may form spontaneously as a result of Turing instability. In the stable
homogeneous system with the fast inhibitor one can excite both localized and
extended patterns by applying a localized stimulus. Depending on the parameters
and the excitation level of the system stripes, spots, wriggled stripes, or
labyrinthine patterns form. The labyrinthine patterns may be both connected and
disconnected. In the the stable homogeneous system with the slow inhibitor one
can excite self-replicating spots, breathing patterns, autowaves and
turbulence. The parameter regions in which different types of patterns are
realized are explained on the basis of the asymptotic theory of instabilities
for patterns with sharp interfaces developed by us in Phys. Rev. E. 53, 3101
(1996). The dynamics of the patterns observed in our simulations is very
similar to that of the patterns forming in the ferrocyanide-iodate-sulfite
reaction.Comment: 15 pages (REVTeX), 15 figures (postscript and gif), submitted to
Phys. Rev.
Primordial RNA Replication and Applications in PCR Technology
The emergence of self-replication and information transmission in life's
origin remains unexplained despite extensive research on the topic. A
hypothesis explaining the transition from a simple organic world to a complex
RNA world is offered here based on physical factors in hydrothermal vent
systems. An interdisciplinary approach is taken using techniques from
thermodynamics, fluid dynamics, oceanography, statistical mechanics, and
stochastic processes to examine nucleic acid dynamics and kinetics in a
hydrothermal vent from first principles. Analyses are carried out using both
analytic and computational methods and confirm the plausibility of a reaction
involving the PCR-like assembly of ribonucleotides. The proposal is put into
perspective with established theories on the origin of life and more generally
the onset of order and information transmission in prebiotic systems. A
biomimicry application of this hypothetical process to PCR technology is
suggested and its viability is evaluated in a rigorous logical analysis.
Optimal temperature curves begin to be established using Monte Carlo
simulation, variational calculus, and Fourier analysis. The converse argument
is also made but qualitatively, asserting that the success of such a
modification to PCR would in turn reconfirm the biological theory.Comment: 20 pages, 7 figure
An iterative method for the canard explosion in general planar systems
The canard explosion is the change of amplitude and period of a limit cycle
born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon
is well understood in singular perturbation problems where a small parameter
controls the slow/fast dynamics. However, canard explosions are also observed
in systems where no such parameter is present. Here we show how the iterative
method of Roussel and Fraser, devised to construct regular slow manifolds, can
be used to determine a canard point in a general planar system of nonlinear
ODEs. We demonstrate the method on the van der Pol equation, showing that the
asymptotics of the method is correct, and on a templator model for a
self-replicating system.Comment: Paper presented at the 9th AIMS Conference on Dynamical Systems,
Differential Equations and Applications, Orlando, Florida, USA July 1 - 5,
201
The identification of complex spatiotemporal patterns using Coupled map lattice model
Many complex and interesting spatiotemporal patterns have been observed in a wide range of scienti¯c areas. In this paper, two kinds of spatiotemporal patterns including spot replication and Turing systems are investigated and new identi¯cation methods are proposed to obtain Coupled Map Lattice (CML) models for this class of systems. Initially, a new correlation analysis method is introduced to determine an appropriate temporal and spatial data sampling step procedure for the identification of spatiotemporal systems. A new combined Orthogonal Forward Regression and Bayesian Learning algorithm with Laplace priors is introduced to identify sparse and robust CML models for complex spatiotemporal patterns. The final identified CML models are validated using correlation based model validation tests for spatiotemporal systems. Numerical re-sults illustrate the identification procedure and demonstrate the validity of the identified models
Phase resetting reveals network dynamics underlying a bacterial cell cycle
Genomic and proteomic methods yield networks of biological regulatory
interactions but do not provide direct insight into how those interactions are
organized into functional modules, or how information flows from one module to
another. In this work we introduce an approach that provides this complementary
information and apply it to the bacterium Caulobacter crescentus, a paradigm
for cell-cycle control. Operationally, we use an inducible promoter to express
the essential transcriptional regulatory gene ctrA in a periodic, pulsed
fashion. This chemical perturbation causes the population of cells to divide
synchronously, and we use the resulting advance or delay of the division times
of single cells to construct a phase resetting curve. We find that delay is
strongly favored over advance. This finding is surprising since it does not
follow from the temporal expression profile of CtrA and, in turn, simulations
of existing network models. We propose a phenomenological model that suggests
that the cell-cycle network comprises two distinct functional modules that
oscillate autonomously and couple in a highly asymmetric fashion. These
features collectively provide a new mechanism for tight temporal control of the
cell cycle in C. crescentus. We discuss how the procedure can serve as the
basis for a general approach for probing network dynamics, which we term
chemical perturbation spectroscopy (CPS)
Amplitude bounds for biochemical oscillators
We present a practical method to obtain bounds for the oscillation minima and
maxima of large classes of biochemical oscillator models that generate
oscillations through a negative feedback. These bounds depend on the feedback
nonlinearity and are independent of explicit or effective feedback delays. For
specific systems, we obtain explicit analytical expressions for the bounds and
demonstrate their effectiveness in comparison with numerical simulations.Comment: 6 pages, 4 figure
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