Malaysian Journal of Mathematical Sciences, August 2012, Vol. 6(S)
Special Issue: International Workshop on Mathematical Analysis (IWOMA)
Application of Computer Algebra Matrix Operation Techniques to the Enzymes Kinetics Systems
Mustafa Bayram and Abdullah Kaplan
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
Metabolic control analysis allows one to quantify the behaviour of a metabolic pathway in steady state in terms of dimensionless coefficients. From the definition of metabolite and flux control coefficients and elasticities we are able to derive symbolic forms of these parameters, in terms of conventional kinetic parameters. At the simplest level we are able to substitute values of these kinetic parameters, to yield values for the metabolic control coefficients. Since we are substituting into symbolic equations we can always guarantee the conservation relationships hold. The basic relationships are the summation and connectivity theorems. The ability to define the control coefficient equations in matrix form not only allows easy solution by numerical inversion, but also opens up the possibility of obtaining the algebraic solutions by symbolic manipulation of the matrix. However, for matrixes longer than rank 4 or 5, this latter possibility, if done by hand, becomes very tedious and is prone to error. The solution to this problem is to develop computer software to automatically carry out this procedure.
Keywords: Conservation relationship, metabolic network, stoichiometry matrix, elasticity coefficient, metabolic and flux control coefficients, MAPLE, Lineer algebra matrix properties
