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This paper extends our early study on a mathematical formulation of the central dogma of molecular biology, and focuses discussions on recent insights obtained by employing advanced systems theoretic analysis. The goal of this paper is to mathematically represent and interpret the genetic information flow at the molecular level, and explore the fundamental principle of molecular biology at the system level. Specifically, group theory was employed to interpret concepts and properties of gene mutation, and predict backbone torsion angle along the peptide chain. Finite state machine theory was extensively applied to interpret key concepts and analyze the processes related to DNA hybridization. Using the proposed model, we have transferred the character-based model in molecular biology to a sophisticated mathematical model for calculation and interpretation.