Modelling of General Biotechnological Processes

A. Ilchmann and A. Ilchmann

Mathematical and Computer Modelling of Dynamical Systems, 1999, vol. 5, issue 2, 152-178

Abstract: A general biotechnological process is modelled by a finite dimensional ordinary differential equation. The stoichiometry is only modelled qualitatively. It is shown that the usual biochemically motivated assumptions are not sufficient to guarantee boundedness of the solution. To overcome this, the concept of non-cyclic biotechnological processes is introduced. Loosely speaking it means that the process does not contain any “reaction loop”. The assumption of non-cyclicity replaces the common assumption of Conservation of Mass. An algorithm is presented so that after finitely many steps it is decided whether a process is non-cyclic or cyclic. Non-cyclicity is also characterised in terms of an echelon matrix derived from the stoichiometric matrix via permutations of columns and rows.

Date: 1999
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DOI: 10.1076/mcmd.5.2.152.6172

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