Biology Reference
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where S is the substrate concentration at the given rate of reaction, V the maximum rate of hydrolysis
and K
m
the Michaelis constant. V and K
m
are two constants that characterize the interactions of
the enzyme with its substrate. Enzymes can be controlled by modifying the affinity, efficiency, and
specificity of the enzyme. However, genes and their regulation mechanisms, biosynthesis and their
catalytic, cell communication processes and liveliness of all these components are called elementary
metabolic processes, which define the behavior of the metabolism. All these processes build metabolic
networks, which are interconnected with elementary metabolic processes influencing each other in a well
defined way.
Related works
The simulation of metabolic processes is based on specific models, which can be subdivided into
the classes of abstract, discrete, and analytical models. The abstract models are based on automata and
logical models, which permit the global discussion of fundamental aspects. The goal of analytical models
is the exact quantitative simulation, where the analysis of kinetic features of enzymes is important. The
paper of Waser
et al.
[15] presents a computer simulation of phosphofructokinase. This enzyme is
part of the glycolysis pathway. Waser
et al.
model all kinetic features of the metabolic reaction by
computer simulation. This computer program is based on chemical reaction rules, which are described
by differential equations. Franco and Canelas simulate the purine metabolism by differential equations,
where each reaction is described by the relevant substance and the catalytic enzyme using the Michaelis-
constant of each enzyme [16]. Discrete models are based on state transition diagrams. Simple models of
this class are based on simple production units, which can be combined. Overbeek presented an amino
acid production system, a black-box with an input-set and an output-set describing a specific production
unit [17]. The graphical model of Kohen and Letzkus [18], which allows the discussion of metabolic
regulation processes, is representative for the class of graph theoretical approaches. They expand the
graph theory by specific functions which allow the modeling of dynamic processes. In this case the
approach of Petrinets is a new method. Reddy
et al.
[9] presented the first application of Petrinets in
molecular biology. This formalism is able to model metabolic pathways. The highest abstraction level of
this model class is represented by expert systems [19] and object oriented systems [20]. Expert systems
and object oriented systems are developed by higher programming languages (Lisp, C++) and allow the
modeling of metabolic processes by facts/classes (proteins and enzymes) and rules/classes (chemical
reactions). The grammatical formalization is able to model complex metabolic networks [21].
PETRINETS - BASICS
Petrinets, a graph-oriented formalism, allow the modeling and analysis of systems, which comprise
properties such as concurrency and synchronization. A Petrinet consists of transitions and places, which
are connected by arcs. In the graphical representation, places are drawn as circles, transitions are drawn
as thin bars or as rectangles, and arcs are drawn as arrows. The places and transitions are labeled with
their names. Places may contain tokens, which are drawn as dots. The vector representing the number
of tokens in each place is the state of the Petrinet and is referred to as marking. The marking can be
changed by the firing of the transitions, which is determined by arcs. The arcs can further be divided into
input and output arcs. Generally, arcs may have multiplicities greater than one. In the following only
single arcs are assumed. A transition is said to be enabled, if all places connected with input arcs contain
tokens. An enabled transition may fire by removing a token from each place connected with an input
