Plant metabolites are exploited for biotechnological, biomaterial and recently nanomedicine applications. The dynamics of plant metabolic networks are predominated by the activities of enzymes. These enzymes regulate metabolic pathway via a concerted interplay of many biochemical reactions essential to sustain life. Differential mathematical modeling of metabolic pathway is often closely associated with changes in metabolite concentrations that are described by enzyme kinetic rate laws, such as the Michaelis-Menten equation. Metabolic pathway with enzyme kinetic model was adopted and Differential Transform Spectrum was formulated, solved with the algorithm Mathematica. This study reveals analytical solutions for the models of the concentration of substrate and product using differential transformation method (DTM) for all values of reaction-diffusion parameters. It is hoped that the simulation results will be useful for improving the productivity of meaningful plant metabolites for medicinal and industrial use.