113 research outputs found
The sweeping rate in diffusion-mediated reactions on dust grain surfaces
A prominent chemical reaction in interstellar clouds is the formation of
molecular hydrogen by recombination, which essentially takes place on dust
grain surfaces. Analytical approaches to model such a system have hitherto
neglected the spatial aspects of the problem by employing a simplistic version
of the sweeping rate of reactants. We show how these aspects can be accounted
for by a consistent definition of the sweeping rate, and calculate it exactly
for a spherical grain. Two regimes can be identified: Small grains, on which
two reactants almost surely meet, and large grains, where this is very
unlikely. We compare the true sweeping rate to the conventional approximation
and find a characteristic reduction in both regimes, most pronounced for large
grains. These effects can be understood heuristically using known results from
the analysis of two-dimensional random walks. We finally examine the influence
of using the true sweeping rate in the calculation of the efficiency of
hydrogen recombination: For fixed temperature, the efficiency can be reduced
considerably, and relative to that, small grains gain in importance, but the
temperature window in which recombination is efficient is not changed
substantially.Comment: 10 pages, 6 figure
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
Reaction Kinetics in a Tight Spot
The standard analysis of reaction networks based on deterministic rate
equations fails in confined geometries, commonly encountered in fields such as
astrochemistry, thin film growth and cell biology. In these systems the small
reactant population implies anomalous behavior of reaction rates, which can be
accounted for only by following the full distribution of reactant numbers
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