biochemistry Biochemistry or biological chemistry is the study of chemical processes within and relating to living organisms. A sub-discipline of both chemistry and biology, biochemistry may be divided into three fields: structural biology, enzymology ...

, a glycolytic oscillation is the repetitive fluctuation of in the concentrations of

metabolite In biochemistry, a metabolite is an intermediate or end product of metabolism. The term is usually used for small molecules. Metabolites have various functions, including fuel, structure, signaling, stimulatory and inhibitory effects on enzymes, ...

s, classically observed experimentally in yeast and muscle. The first observations of oscillatory behaviour in glycolysis were made by Duysens and Amesz in 1957. The problem of modelling glycolytic oscillation has been studied in

control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

and

dynamical systems In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...

since the 1960s since the behaviour depends on the rate of

substrate Substrate may refer to: Physical layers *Substrate (biology), the natural environment in which an organism lives, or the surface or medium on which an organism grows or is attached ** Substrate (locomotion), the surface over which an organism lo ...

injection. Early models used two variables, but the most complex behaviour they could demonstrate was period oscillations due to the

Poincaré–Bendixson theorem In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere. Theorem Given a differentiable real dynamical system defined on an o ...

, so later models introduced further variables.

References

{{Biochem-stub Control theory