801 research outputs found
Evaluation of the Multiplane Method for Efficient Simulations of Reaction Networks
Reaction networks in the bulk and on surfaces are widespread in physical,
chemical and biological systems. In macroscopic systems, which include large
populations of reactive species, stochastic fluctuations are negligible and the
reaction rates can be evaluated using rate equations. However, many physical
systems are partitioned into microscopic domains, where the number of molecules
in each domain is small and fluctuations are strong. Under these conditions,
the simulation of reaction networks requires stochastic methods such as direct
integration of the master equation. However, direct integration of the master
equation is infeasible for complex networks, because the number of equations
proliferates as the number of reactive species increases. Recently, the
multiplane method, which provides a dramatic reduction in the number of
equations, was introduced [A. Lipshtat and O. Biham, Phys. Rev. Lett. 93,
170601 (2004)]. The reduction is achieved by breaking the network into a set of
maximal fully connected sub-networks (maximal cliques). Lower-dimensional
master equations are constructed for the marginal probability distributions
associated with the cliques, with suitable couplings between them. In this
paper we test the multiplane method and examine its applicability. We show that
the method is accurate in the limit of small domains, where fluctuations are
strong. It thus provides an efficient framework for the stochastic simulation
of complex reaction networks with strong fluctuations, for which rate equations
fail and direct integration of the master equation is infeasible. The method
also applies in the case of large domains, where it converges to the rate
equation results
Efficient Stochastic Simulations of Complex Reaction Networks on Surfaces
Surfaces serve as highly efficient catalysts for a vast variety of chemical
reactions. Typically, such surface reactions involve billions of molecules
which diffuse and react over macroscopic areas. Therefore, stochastic
fluctuations are negligible and the reaction rates can be evaluated using rate
equations, which are based on the mean-field approximation. However, in case
that the surface is partitioned into a large number of disconnected microscopic
domains, the number of reactants in each domain becomes small and it strongly
fluctuates. This is, in fact, the situation in the interstellar medium, where
some crucial reactions take place on the surfaces of microscopic dust grains.
In this case rate equations fail and the simulation of surface reactions
requires stochastic methods such as the master equation. However, in the case
of complex reaction networks, the master equation becomes infeasible because
the number of equations proliferates exponentially. To solve this problem, we
introduce a stochastic method based on moment equations. In this method the
number of equations is dramatically reduced to just one equation for each
reactive species and one equation for each reaction. Moreover, the equations
can be easily constructed using a diagrammatic approach. We demonstrate the
method for a set of astrophysically relevant networks of increasing complexity.
It is expected to be applicable in many other contexts in which problems that
exhibit analogous structure appear, such as surface catalysis in nanoscale
systems, aerosol chemistry in stratospheric clouds and genetic networks in
cells
A Unified Monte Carlo Treatment of Gas-Grain Chemistry for Large Reaction Networks. I. Testing Validity of Rate Equations in Molecular Clouds
In this study we demonstrate for the first time that the unified Monte Carlo
approach can be applied to model gas-grain chemistry in large reaction
networks. Specifically, we build a time-dependent gas-grain chemical model of
the interstellar medium, involving about 6000 gas-phase and 200 grain surface
reactions. This model is used to test the validity of the standard and modified
rate equation methods in models of dense and translucent molecular clouds and
to specify under which conditions the use of the stochastic approach is
desirable.
We found that at temperatures 25--30 K gas-phase abundances of HO,
NH, CO and many other gas-phase and surface species in the stochastic model
differ from those in the deterministic models by more than an order of
magnitude, at least, when tunneling is accounted for and/or diffusion energies
are 3x lower than the binding energies. In this case, surface reactions,
involving light species, proceed faster than accretion of the same species. In
contrast, in the model without tunneling and with high binding energies, when
the typical timescale of a surface recombination is greater than the timescale
of accretion onto the grain, we obtain almost perfect agreement between results
of Monte Carlo and deterministic calculations in the same temperature range. At
lower temperatures ( K) gaseous and, in particular, surface abundances
of most important molecules are not much affected by stochastic processes.Comment: 33 pages, 9 figures, 1 table. Accepted for publication in Ap
Quantifying the connectivity of a network: The network correlation function method
Networks are useful for describing systems of interacting objects, where the
nodes represent the objects and the edges represent the interactions between
them. The applications include chemical and metabolic systems, food webs as
well as social networks. Lately, it was found that many of these networks
display some common topological features, such as high clustering, small
average path length (small world networks) and a power-law degree distribution
(scale free networks). The topological features of a network are commonly
related to the network's functionality. However, the topology alone does not
account for the nature of the interactions in the network and their strength.
Here we introduce a method for evaluating the correlations between pairs of
nodes in the network. These correlations depend both on the topology and on the
functionality of the network. A network with high connectivity displays strong
correlations between its interacting nodes and thus features small-world
functionality. We quantify the correlations between all pairs of nodes in the
network, and express them as matrix elements in the correlation matrix. From
this information one can plot the correlation function for the network and to
extract the correlation length. The connectivity of a network is then defined
as the ratio between this correlation length and the average path length of the
network. Using this method we distinguish between a topological small world and
a functional small world, where the latter is characterized by long range
correlations and high connectivity. Clearly, networks which share the same
topology, may have different connectivities, based on the nature and strength
of their interactions. The method is demonstrated on metabolic networks, but
can be readily generalized to other types of networks.Comment: 10 figure
Stochastic Analysis of Dimerization Systems
The process of dimerization, in which two monomers bind to each other and
form a dimer, is common in nature. This process can be modeled using rate
equations, from which the average copy numbers of the reacting monomers and of
the product dimers can then be obtained. However, the rate equations apply only
when these copy numbers are large. In the limit of small copy numbers the
system becomes dominated by fluctuations, which are not accounted for by the
rate equations. In this limit one must use stochastic methods such as direct
integration of the master equation or Monte Carlo simulations. These methods
are computationally intensive and rarely succumb to analytical solutions. Here
we use the recently introduced moment equations which provide a highly
simplified stochastic treatment of the dimerization process. Using this
approach, we obtain an analytical solution for the copy numbers and reaction
rates both under steady state conditions and in the time-dependent case. We
analyze three different dimerization processes: dimerization without
dissociation, dimerization with dissociation and hetero-dimer formation. To
validate the results we compare them with the results obtained from the master
equation in the stochastic limit and with those obtained from the rate
equations in the deterministic limit. Potential applications of the results in
different physical contexts are discussed.Comment: 10 figure
Survival Advantage of Both Human Hepatocyte Xenografts and Genome-Edited Hepatocytes for Treatment of α-1 Antitrypsin Deficiency.
Hepatocytes represent an important target for gene therapy and editing of single-gene disorders. In α-1 antitrypsin (AAT) deficiency, one missense mutation results in impaired secretion of AAT. In most patients, lung damage occurs due to a lack of AAT-mediated protection of lung elastin from neutrophil elastase. In some patients, accumulation of misfolded PiZ mutant AAT protein triggers hepatocyte injury, leading to inflammation and cirrhosis. We hypothesized that correcting the Z mutant defect in hepatocytes would confer a selective advantage for repopulation of hepatocytes within an intact liver. A human PiZ allele was crossed onto an immune-deficient (NSG) strain to create a recipient strain (NSG-PiZ) for human hepatocyte xenotransplantation. Results indicate that NSG-PiZ recipients support heightened engraftment of normal human primary hepatocytes as compared with NSG recipients. This model can therefore be used to test hepatocyte cell therapies for AATD, but more broadly it serves as a simple, highly reproducible liver xenograft model. Finally, a promoterless adeno-associated virus (AAV) vector, expressing a wild-type AAT and a synthetic miRNA to silence the endogenous allele, was integrated into the albumin locus. This gene-editing approach leads to a selective advantage of edited hepatocytes, by silencing the mutant protein and augmenting normal AAT production, and improvement of the liver pathology. Mol Ther 2017 Nov 1; 25(11):2477-2489
Survival Advantage of Both Human Hepatocyte Xenografts and Genome-Edited Hepatocytes for Treatment of alpha-1 Antitrypsin Deficiency
Hepatocytes represent an important target for gene therapy and editing of single-gene disorders. In alpha-1 antitrypsin (AAT) deficiency, one missense mutation results in impaired secretion of AAT. In most patients, lung damage occurs due to a lack of AAT-mediated protection of lung elastin from neutrophil elastase. In some patients, accumulation of misfolded PiZ mutant AAT protein triggers hepatocyte injury, leading to inflammation and cirrhosis. We hypothesized that correcting the Z mutant defect in hepatocytes would confer a selective advantage for repopulation of hepatocytes within an intact liver. A human PiZ allele was crossed onto an immune-deficient (NSG) strain to create a recipient strain (NSG-PiZ) for human hepatocyte xenotransplantation. Results indicate that NSG-PiZ recipients support heightened engraftment of normal human primary hepatocytes as compared with NSG recipients. This model can therefore be used to test hepatocyte cell therapies for AATD, but more broadly it serves as a simple, highly reproducible liver xenograft model. Finally, a promoterless adeno-associated virus (AAV) vector, expressing a wild-type AAT and a synthetic miRNA to silence the endogenous allele, was integrated into the albumin locus. This gene-editing approach leads to a selective advantage of edited hepatocytes, by silencing the mutant protein and augmenting normal AAT production, and improvement of the liver pathology
Ice Lines, Planetesimal Composition and Solid Surface Density in the Solar Nebula
To date, there is no core accretion simulation that can successfully account
for the formation of Uranus or Neptune within the observed 2-3 Myr lifetimes of
protoplanetary disks. Since solid accretion rate is directly proportional to
the available planetesimal surface density, one way to speed up planet
formation is to take a full accounting of all the planetesimal-forming solids
present in the solar nebula. By combining a viscously evolving protostellar
disk with a kinetic model of ice formation, we calculate the solid surface
density in the solar nebula as a function of heliocentric distance and time. We
find three effects that strongly favor giant planet formation: (1) a decretion
flow that brings mass from the inner solar nebula to the giant planet-forming
region, (2) recent lab results (Collings et al. 2004) showing that the ammonia
and water ice lines should coincide, and (3) the presence of a substantial
amount of methane ice in the trans-Saturnian region. Our results show higher
solid surface densities than assumed in the core accretion models of Pollack et
al. (1996) by a factor of 3 to 4 throughout the trans-Saturnian region. We also
discuss the location of ice lines and their movement through the solar nebula,
and provide new constraints on the possible initial disk configurations from
gravitational stability arguments.Comment: Version 2: reflects lead author's name and affiliation change,
contains minor changes to text from version 1. 12 figures, 7 tables, accepted
for publication in Icaru
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