10,621 research outputs found
Translated Chemical Reaction Networks
Many biochemical and industrial applications involve complicated networks of
simultaneously occurring chemical reactions. Under the assumption of mass
action kinetics, the dynamics of these chemical reaction networks are governed
by systems of polynomial ordinary differential equations. The steady states of
these mass action systems have been analysed via a variety of techniques,
including elementary flux mode analysis, algebraic techniques (e.g. Groebner
bases), and deficiency theory. In this paper, we present a novel method for
characterizing the steady states of mass action systems. Our method explicitly
links a network's capacity to permit a particular class of steady states,
called toric steady states, to topological properties of a related network
called a translated chemical reaction network. These networks share their
reaction stoichiometries with their source network but are permitted to have
different complex stoichiometries and different network topologies. We apply
the results to examples drawn from the biochemical literature
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
Uniformisation techniques for stochastic simulation of chemical reaction networks
This work considers the method of uniformisation for continuous-time Markov
chains in the context of chemical reaction networks. Previous work in the
literature has shown that uniformisation can be beneficial in the context of
time-inhomogeneous models, such as chemical reaction networks incorporating
extrinsic noise. This paper lays focus on the understanding of uniformisation
from the viewpoint of sample paths of chemical reaction networks. In
particular, an efficient pathwise stochastic simulation algorithm for
time-homogeneous models is presented which is complexity-wise equal to
Gillespie's direct method. This new approach therefore enlarges the class of
problems for which the uniformisation approach forms a computationally
attractive choice. Furthermore, as a new application of the uniformisation
method, we provide a novel variance reduction method for (raw) moment
estimators of chemical reaction networks based upon the combination of
stratification and uniformisation
Asymptotology of Chemical Reaction Networks
The concept of the limiting step is extended to the asymptotology of
multiscale reaction networks. Complete theory for linear networks with well
separated reaction rate constants is developed. We present algorithms for
explicit approximations of eigenvalues and eigenvectors of kinetic matrix.
Accuracy of estimates is proven. Performance of the algorithms is demonstrated
on simple examples. Application of algorithms to nonlinear systems is
discussed.Comment: 23 pages, 8 figures, 84 refs, Corrected Journal Versio
Joining and decomposing reaction networks
In systems and synthetic biology, much research has focused on the behavior
and design of single pathways, while, more recently, experimental efforts have
focused on how cross-talk (coupling two or more pathways) or inhibiting
molecular function (isolating one part of the pathway) affects systems-level
behavior. However, the theory for tackling these larger systems in general has
lagged behind. Here, we analyze how joining networks (e.g., cross-talk) or
decomposing networks (e.g., inhibition or knock-outs) affects three properties
that reaction networks may possess---identifiability (recoverability of
parameter values from data), steady-state invariants (relationships among
species concentrations at steady state, used in model selection), and
multistationarity (capacity for multiple steady states, which correspond to
multiple cell decisions). Specifically, we prove results that clarify, for a
network obtained by joining two smaller networks, how properties of the smaller
networks can be inferred from or can imply similar properties of the original
network. Our proofs use techniques from computational algebraic geometry,
including elimination theory and differential algebra.Comment: 44 pages; extensive revision in response to referee comment
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