25 research outputs found
Specification of spatial relationships in directed graphs of cell signaling networks
Graph theory provides a useful and powerful tool for the analysis of cellular signaling networks. Intracellular components such as cytoplasmic signaling proteins, transcription factors and genes are connected by links, representing various types of chemical interactions that result in functional consequences. However, these graphs lack important information regarding the spatial distribution of cellular components. The ability of two cellular components to interact depends not only on their mutual chemical affinity but also on co-localization to the same subcellular region. Localization of components is often used as a regulatory mechanism to achieve specific effects in response to different receptor signals. Here we describe an approach for incorporating spatial distribution into graphs, and for the development of mixed graphs where links are specified by mutual chemical affinity as well as colocalization. We suggest that such mixed graphs will provide more accurate descriptions of functional cellular networks and their regulatory capabilities and aid in the development of large-scale predictive models of cellular behavior
The formation of H_2 and HD with the master equation approach
The formation of H2 and HD molecules on interstellar dust grains is studied
using rate equation and master equation models. Rate equations are used in the
analysis of laboratory experiments which examine the formation of molecular
hydrogen on astrophysically relevant surfaces. However, under interstellar
conditions, rate equations are not suitable for the calculation of reaction
rates on dust-grain surfaces. Due to the low flux and the sub-micron size of
the grains, the populations of H and D atoms on a single grain are likely to be
small. In this case the reaction rates are dominated by fluctuations and should
be calculated using stochastic methods. The rate of molecular hydrogen
formation in interstellar clouds is evaluated using the master equation, taking
into account the distribution of grain sizes.Comment: 10 pages, 2 figures. IAU symposium 231 conference proceeding
An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm
Many physical and biological processes are stochastic in nature.
Computational models and simulations of such processes are a mathematical and
computational challenge. The basic stochastic simulation algorithm was
published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys.
Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make
the algorithm more efficient in terms of running time. All accelerated versions
of the algorithm are aimed at minimizing the running time required to produce a
stochastic trajectory in state space. In these simulations, a necessary
condition for reliable statistics is averaging over a large number of
simulations. In this study I present a new accelerating approach which does not
alter the stochastic algorithm, but reduces the number of required runs. By
analysis of collected data I demonstrate high precision levels with fewer
simulations. Moreover, the suggested approach provides a good estimation of
statistical error, which may serve as a tool for determining the number of
required runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19
pages, including 2 Tables and 4 Figure
The effect of grain size distribution on H formation rate in the interstellar medium
The formation of molecular hydrogen in the interstellar medium takes place on
the surfaces of dust grains. Hydrogen molecules play a role in gas-phase
reactions that produce other molecules, some of which serve as coolants during
gravitational collapse and star formation. Thus, the evaluation of the
roduction rate of hydrogen molecules and its dependence on the physical
conditions in the cloud are of great importance. Interstellar dust grains
exhibit a broad size distribution in which the small grains capture most of the
surface area. Recent studies have shown that the production efficiency strongly
depends on the grain composition and temperature as well as on its size. In
this paper we present a formula which provides the total production rate of
H per unit volume in the cloud, taking into account the grain composition
and temperature as well as the grain size distribution. The formula agrees very
well with the master equation results. It shows that for a physically relevant
range of grain temperatures, the production rate of H is significantly
enhanced due to their broad size distribution.Comment: to appear in MNRA
Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns
We analyze a recent experiment of Sharon \textit{et al.} (2003) on the
coarsening, due to surface tension, of fractal viscous fingering patterns
(FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw
model, a natural model for that experiment, belongs to the same universality
class as model B of phase ordering. Two series of numerical simulations with
model B are performed, with the FVFPs grown in the experiment, and with
Diffusion Limited Aggregates, as the initial conditions. We observed
Lifshitz-Slyozov scaling at intermediate distances and very slow
convergence to this scaling at small distances. Dynamic scale invariance breaks
down at large distances.Comment: 4 pages, 4 eps figures; to appear in Phys. Rev.