The antizyme protein, Oaz1, regulates synthesis of the polyamines putrescine, spermidine and spermine by controlling stability of the polyamine biosynthetic enzyme, ornithine decarboxylase. Antizyme mRNA translation depends upon a polyamine-stimulated +1 ribosomal frameshift, forming a complex negative feedback system in which the translational frameshifting event may be viewed in engineering terms as a feedback controller for intracellular polyamine concentrations. In this article, we present the first systems level study of the characteristics of this feedback controller, using an integrated experimental and modeling approach. Quantitative analysis of mutant yeast strains in which polyamine synthesis and interconversion were blocked revealed marked variations in frameshift responses to the different polyamines. Putrescine and spermine, but not spermidine, showed evidence of co-operative stimulation of frameshifting and the existence of multiple ribosome binding sites. Combinatorial polyamine treatments showed polyamines compete for binding to common ribosome sites. Using concepts from enzyme kinetics and control engineering, a mathematical model of the translational controller was developed to describe these complex ribosomal responses to combinatorial polyamine effects. Each one of a range of model predictions was successfully validated against experimental frameshift frequencies measured in S-adenosylmethionine-decarboxylase and antizyme mutants, as well as in the wild-type genetic background.