Uniqueness and global attractivity of glycolytic oscillations suggested by Selkov's model

In this work, we study the qualitative properties of the model proposed by Selkov Eur J Biochem 4: 79-86 (1968) for the description of the glycolytic oscillations. First we show that the Selkov's model can be put in form of a Newton's equation, thus allowing to define a pseudo-energy. Then, we show without imposing additional conditions that the limit cycle, if it exists, it is unique and globally attractive, thus precluding the possibility of multi-rythmicity. Finally, based on energetic and geometric considerations, we investigate the global properties of the unique equilibrium (idest of the arrest of the oscillations). Some biochemical remarks on the relevance of the uniqueness of sustained oscillations end the work.