Applications Of Computer Algebra In Biochemistry

Computer algebra theory is an emerging discipline, which is a combination of computer science and mathematics. Computer algebra theory is concerned with almost all areas of mathematics. Computer algebra theory has been applied to the vast majority of scientific research and engineering, since it is capable to deduce large-scale formula and perform complex calculations, which cannot be done by human. Based on the computer algebra theory, this paper mainly studies the interpolating polynomials model of the reverse engineering in biochemistry and the enzyme kinetics model. The principle research results are shown as follows:1. A novel algebraic method for building the interpolating polynomials is presented, which is based on the theories of Grobner bases, and this method is much more important and efficient for the research on reverse engineering in biochemistry. By using the well-known modular BM-algorithm and Chinese remainder theorem, the method can not only work much more efficient on rational number field, but also avoid the intermediate expressions swell quickly.2. This paper studies the analysis of enzyme kinetics model, based on Wu elimination method in the computer algebra theory and the qualitative theory of dynamical systems. This research includes the analysis of the simplest enzyme kinetics system, the unstable enzyme kinetics system and anther unstable enzyme kinetics system, the analytical solution set of all the enzyme kinetics models are obtained. Some examples will illustrate the validity of the method and the efficiency of algorithms in this paper.