Polyamines are considered as essential compounds in living cells, since they are involved in cell proliferation, transcription, and translation processes. Furthermore, polyamine homeostasis is necessary to cell survival, and its deregulation is involved in relevant processes, such as cancer and neurodegenerative disorders. Great efforts have been made to elucidate the nature of polyamine homeostasis, giving rise to relevant information concerning the behavior of the different components of polyamine metabolism, and a great amount of information has been generated. However, a complex regulation at transcriptional, translational, and metabolic levels as well as the strong relationship between polyamines and essential cell processes make it difficult to discriminate the role of polyamine regulation itself from the whole cell response when an experimental approach is given in vivo. To overcome this limitation, a bottom-up approach to model mathematically metabolic pathways could allow us to elucidate the systemic behavior from individual kinetic and molecular properties. In this paper, we propose a mathematical model of polyamine metabolism from kinetic constants and both metabolite and enzyme levels extracted from bibliographic sources. This model captures the tendencies observed in transgenic mice for the so-called key enzymes of polyamine metabolism, ornithine decarboxylase, S-adenosylmethionine decarboxylase and spermine spermidine N-acetyl transferase. Furthermore, the model shows a relevant role of S-adenosylmethionine and acetyl-CoA availability in polyamine homeostasis, which are not usually considered in systemic experimental studies.