title: Oscillations in theoretical models of induction.
abstract: A two-variable model for the genetic regulatory mechanism of induction is proposed. In a feedforward step an autocatalytically accumulated substrate induces the transcription of its own degrading enzyme. The differential equations for enzyme and substrate are treated analytically and it is found that in a defined parameter range the system becomes unstable and shows structurally stable limit cycle oscillations. The system behaves like an activator-inhibitor model and instability is likely to arise if the transcription process is slow. In a slightly modified system oscillations inside a cell are generated if an external parameter (extracellular substrate concentration) exceeds a certain threshold and all other parameters are unchanged. Possible biological implications of these results are destabilization of metabolic units by transport processes and feedforward catalysis.
mesh_terms: D001693:Biological Transport, Active; D004790:Enzyme Induction; D004798:Enzymes / Q000096:biosynthesis* / Q000235:genetics; D005246:Feedback; D005786:Gene Expression Regulation; D005809:Genes, Regulator; D007700:Kinetics; D008954:Models, Biological; D008957:Models, Genetic; D014176:Protein Biosynthesis; D014158:Transcription, Genetic
chemical_list: D004798:Enzymes