3,413 research outputs found
Dynamical topology and statistical properties of spatiotemporal chaos
For spatiotemporal chaos described by partial differential equations, there
are generally locations where the dynamical variable achieves its local
extremum or where the time partial derivative of the variable vanishes
instantaneously. To a large extent, the location and movement of these
topologically special points determine the qualitative structure of the
disordered states. We analyze numerically statistical properties of the
topologically special points in one-dimensional spatiotemporal chaos. The
probability distribution functions for the number of point, the lifespan, and
the distance covered during their lifetime are obtained from numerical
simulations. Mathematically, we establish a probabilistic model to describe the
dynamics of these topologically special points. In despite of the different
definitions in different spatiotemporal chaos, the dynamics of these special
points can be described in a uniform approach.Comment: 6 pages, 5 figure
Attraction of Spiral Waves by Localized Inhomogeneities with Small-World Connections in Excitable Media
Trapping and un-trapping of spiral tips in a two-dimensional homogeneous
excitable medium with local small-world connections is studied by numerical
simulation. In a homogeneous medium which can be simulated with a lattice of
regular neighborhood connections, the spiral wave is in the meandering regime.
When changing the topology of a small region from regular connections to
small-world connections, the tip of a spiral waves is attracted by the
small-world region, where the average path length declines with the
introduction of long distant connections. The "trapped" phenomenon also occurs
in regular lattices where the diffusion coefficient of the small region is
increased. The above results can be explained by the eikonal equation and the
relation between core radius and diffusion coefficient.Comment: 5 pages, 4 figure
Robustness and modular design of the Drosophila segment polarity network
Biomolecular networks have to perform their functions robustly. A robust
function may have preferences in the topological structures of the underlying
network. We carried out an exhaustive computational analysis on network
topologies in relation to a patterning function in Drosophila embryogenesis. We
found that while the vast majority of topologies can either not perform the
required function or only do so very fragilely, a small fraction of topologies
emerges as particularly robust for the function. The topology adopted by
Drosophila, that of the segment polarity network, is a top ranking one among
all topologies with no direct autoregulation. Furthermore, we found that all
robust topologies are modular--each being a combination of three kinds of
modules. These modules can be traced back to three sub-functions of the
patterning function and their combinations provide a combinatorial variability
for the robust topologies. Our results suggest that the requirement of
functional robustness drastically reduces the choices of viable topology to a
limited set of modular combinations among which nature optimizes its choice
under evolutionary and other biological constraints.Comment: Supplementary Information and Synopsis available at
http://www.ucsf.edu/tanglab
Dynamic Studies of Scaffold-dependent Mating Pathway in Yeast
The mating pathway in \emph{Saccharomyces cerevisiae} is one of the best
understood signal transduction pathways in eukaryotes. It transmits the mating
signal from plasma membrane into the nucleus through the G-protein coupled
receptor and the mitogen-activated protein kinase (MAPK) cascade. According to
the current understandings of the mating pathway, we construct a system of
ordinary differential equations to describe the process. Our model is
consistent with a wide range of experiments, indicating that it captures some
main characteristics of the signal transduction along the pathway.
Investigation with the model reveals that the shuttling of the scaffold protein
and the dephosphorylation of kinases involved in the MAPK cascade cooperate to
regulate the response upon pheromone induction and to help preserving the
fidelity of the mating signaling. We explored factors affecting the
dose-response curves of this pathway and found that both negative feedback and
concentrations of the proteins involved in the MAPK cascade play crucial role.
Contrary to some other MAPK systems where signaling sensitivity is being
amplified successively along the cascade, here the mating signal is transmitted
through the cascade in an almost linear fashion.Comment: 36 pages, 9 figure
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