Traveling wave solution and the stability of critical points of an enzyme-inhibitor system under diffusion effects: with special reference to dimer molecule

Enzymes are absolutely essential biological catalysts in human body that catalyze all cellular processes in physiological network. However, there are certain low molecular weight chemical compounds known as inhibitors, that reduce or completely inhibit the enzyme catalytic activity. Mathematical modeling plays a key role in the control and stability of metabolic enzyme inhibition. Enzyme stability is an important issue for protein engineers, because of its great importance and impact on optimal utility of material in biological tissues. In this outlook, we have first determined the existence of traveling wave solution for the enzyme-inhibitor system and then emphasized the stability of critical points that arise in the reactions. The study of traveling wave solution of an enzyme-inhibitor system with reaction diffusion equations involve quite complex mathematical analysis. The results obtained in this model indicate that the traveling wave solution may give a well explained method for improving enzyme kinetic stability. The present study will be helpful in understanding the stability of critical points of an enzyme-inhibitor system to give an idea about the inhibition of less stable enzymes. Moreover, the role of diffusion on the enzyme activity has been exhaustively discussed using mathematical tools related to eigen values and eigen function analysis.