A Model of Metabolic Processes using Maple

N. Dimitrova,  S. Markov
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Acad. G. Bonchev str., bldg. 8,   Sofia 1113, Bulgaria
e-mail:  {smarkov, nelid}@bio.bas.bg

Metabolic processes can be effectively described mathematically by systems of
nonlinear differential equations.  The basic model of enzyme kinetics is
proposed by Michaelis and Menten and describes the conversion of a substrate
into a product  in the presence of an enzyme.  Metabolic processes involve
thousands of substrates and enzymes.

In an organism the enzymes (and more generally the proteins) are a product of
biochemical reactions involving other enzymes.  Thus, formally speaking,
enzymes reproduce themselves.  This observation lies at the basis of the
proposed models.  We also assume that in the long term the reproduction of
enzymes depends on the type of the subsrates entering the organism.  Under a
number of assumptions aiming at the simplification of the whole process we
build a mathematical model and present the results of relevant numerical
experiments.  As a computer platform we use the computer algebra system MAPLE.