18,882 research outputs found
Computation of biochemical pathway fluctuations beyond the linear noise approximation using iNA
The linear noise approximation is commonly used to obtain intrinsic noise
statistics for biochemical networks. These estimates are accurate for networks
with large numbers of molecules. However it is well known that many biochemical
networks are characterized by at least one species with a small number of
molecules. We here describe version 0.3 of the software intrinsic Noise
Analyzer (iNA) which allows for accurate computation of noise statistics over
wide ranges of molecule numbers. This is achieved by calculating the next order
corrections to the linear noise approximation's estimates of variance and
covariance of concentration fluctuations. The efficiency of the methods is
significantly improved by automated just-in-time compilation using the LLVM
framework leading to a fluctuation analysis which typically outperforms that
obtained by means of exact stochastic simulations. iNA is hence particularly
well suited for the needs of the computational biology community.Comment: 5 pages, 2 figures, conference proceeding IEEE International
Conference on Bioinformatics and Biomedicine (BIBM) 201
The interplay between discrete noise and nonlinear chemical kinetics in a signal amplification cascade
We used various analytical and numerical techniques to elucidate signal
propagation in a small enzymatic cascade which is subjected to external and
internal noise. The nonlinear character of catalytic reactions, which underlie
protein signal transduction cascades, renders stochastic signaling dynamics in
cytosol biochemical networks distinct from the usual description of stochastic
dynamics in gene regulatory networks. For a simple 2-step enzymatic cascade
which underlies many important protein signaling pathways, we demonstrated that
the commonly used techniques such as the linear noise approximation and the
Langevin equation become inadequate when the number of proteins becomes too
low. Consequently, we developed a new analytical approximation, based on mixing
the generating function and distribution function approaches, to the solution
of the master equation that describes nonlinear chemical signaling kinetics for
this important class of biochemical reactions. Our techniques work in a much
wider range of protein number fluctuations than the methods used previously. We
found that under certain conditions the burst-phase noise may be injected into
the downstream signaling network dynamics, resulting possibly in unusually
large macroscopic fluctuations. In addition to computing first and second
moments, which is the goal of commonly used analytical techniques, our new
approach provides the full time-dependent probability distributions of the
colored non-Gaussian processes in a nonlinear signal transduction cascade.Comment: 16 pages, 9 figure
On Projection-Based Model Reduction of Biochemical Networks-- Part II: The Stochastic Case
In this paper, we consider the problem of model order reduction of stochastic
biochemical networks. In particular, we reduce the order of (the number of
equations in) the Linear Noise Approximation of the Chemical Master Equation,
which is often used to describe biochemical networks. In contrast to other
biochemical network reduction methods, the presented one is projection-based.
Projection-based methods are powerful tools, but the cost of their use is the
loss of physical interpretation of the nodes in the network. In order alleviate
this drawback, we employ structured projectors, which means that some nodes in
the network will keep their physical interpretation. For many models in
engineering, finding structured projectors is not always feasible; however, in
the context of biochemical networks it is much more likely as the networks are
often (almost) monotonic. To summarise, the method can serve as a trade-off
between approximation quality and physical interpretation, which is illustrated
on numerical examples.Comment: Submitted to the 53rd CD
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