The changes in the concentrations of plasma amino acids do not always follow the flow-based metabolic pathway network. We have previously shown that there is a control-based network structure among plasma amino acids besides the metabolic pathway map. Based on this network structure, in this study, we performed dynamic analysis using time-course data of the plasma samples of rats fed single essential amino acid deficient diet. Using S-system model (conceptual mathematical model represented by power-law formalism), we inferred the dynamic network structure which reproduces the actual time-courses within the error allowance of 13.17%. By performing sensitivity analysis, three of the most dominant relations in this network were selected; the control paths from leucine to valine, from methionine to threonine, and from leucine to isoleucine. This result is in good agreement with the biological knowledge regarding branched-chain amino acids, and suggests the biological importance of the effect from methionine to threonine.