Enzyme And Cellcatalyzed Reactions

Mechanistic mathematization of a biological phenomenon is the first step toward quantifying, solving, and controlling (quantitatively) it. The difficulty faced is not that it cannot be solved, but rather that the result is of such algebraic complexity as to render little conceptual understanding of the process involved. Not to condemn the total empirical approach (which is usually limited in its applicability) to the analysis of data (such as curve fitting), a rigorous mechanistic approach yielding monumental amounts of mathematical expressions fail, usually, just as badly in terms of its usefulness in actual process operation. In such cases, a midway approach seems to be beneficial. The development of simplified kinetics of enzyme-catalyzed reactions provides one of the best examples of the judicious use of approximations to render a complicated system-equation intuitively understandable and practically useful. As discussed in the following, the steady-state and equilibrium assumptions in enzyme kinetics achieve exactly that.

Most biological reactions, those catalyzed by enzymes, follow Michaelis-Menten kinetics (equation 10), which represents mixed-order reactions. Enzyme-catalyzed reactions follow a first-order kinetic at low value of substrate to enzyme concentration ratio, and they become zero order when values of the said ratios are high (in that case, enzyme molecules are saturated with substrates). The reaction rate in this region (zero order) is then independent of substrate concentration. Enzymes play important roles in the growth and maintenance of cells. The design of such enzyme-catalyzed reactions as the functioning unit of the metabolic machinery in biological systems is of primary importance to the economy of the cell. The growth and maintenance of the cell require a highly integrated interplay of anabolism and catabolism. The subtle and precise metabolic controls are achieved through the regulations of the rate of enzyme formation (induction) and of enzyme activities (activation or inhibition).

Cell growth involves concurrent and serial reactions using enzyme as catalysts. The overall specific growth rate of cells, in either microbial, animal, or plant cell culture, has been modeled by using Monod equation (equation 11), where S denotes the limiting substrate concentration.

V, max ksPo

Ku and Ks are saturation constants. When S/E is small, or Ku > S, equation 10 can be reduced to

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