Oscillations in theoretical models of induction

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.