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Cellular Automata Approaches to Enzymatic
Reaction Networks
Jorg R. Weimar
Institute of Scientific Computing, Technical University Braunschweig,
D-38092 Braunschweig, Germany
J.Weimar@tu-bs.de , http://www.jweimar.de
Abstract. Cellular automata simulations for enzymatic reaction net-
works differ from other models for reaction-diffusion systems, since en-
zymes and metabolites have very different properties. This paper presents
a model where each lattice site can can contain at most one enzyme
molecule, but many metabolite molecules. The rules are constructed to
conform to the Michaelis-Menten kinetics by modeling the underlying
mechanism of enzymatic conversion. Different possible approaches to rule
construction are presented and analyzed, and simulations are shown for
single reactions and simple enzyme networks.
1 Enzymatic Reaction Networks
Most reactions in biological systems are catalyzed by enzymes. These enzymes
are complex molecules (they are proteins) which are not consumed in the reac-
tion,but simply facilitate the reaction of smaller molecules called metabolites
(such as sugar). In a biological cell,thousands of different enzymes are active.
Each enzymatic reaction takes molecules of one or more metabolite species,the
substrates of this reaction,and converts them into molecules of one or more other
species,the products. The products are again substrates to other reactions,and
thus the reactions form complex networks. Enzymatic reactions can be described
and modeled on different levels of detail:
Static Interaction Networks: A first level is the static interaction network,such
as the pathways collected in the KEGG database [9,10,11], or in the Boehringer-
Mannheim map [13]. Such interaction networks can be constructed from purely
qualitative information without relying on any quantitative information,such as
reaction rates (except possibly for stoichiometric coe 5 cients). Some analyses can
extract additional information from these networks,such as inferring elementary
metabolic flux modes [14,15] (although these rely on the information whether
a given reaction is reversible or not,which in turn is a semi-quantitative infor-
mation on the order of magnitude of the equilibrium constant). Simply on the
basis of such interaction networks,no quantitative time-dependent simulation is
possible.
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