Intermolecular autophosphorylation refers to the process where a molecule of an enzyme phosphorylates another molecule of the same enzyme and thereby catalyses its own phosphorylation. We developed a generic model of intermolecular autophosphorylation that also includes dephosphorylation by a phosphatase of constant concentration. The model is written as one ordinary differential equation that relies upon mass action and Michaelis-Menten kinetics. A lag in the phosphorylation of enzyme is observable when phosphorylated enzyme is plotted against time for suitable parameter values.

When steady state values of phosphorylated enzyme are plotted against total enzyme concentration, a threshold concentration of enzyme for phosphorylation or dephosphorylation is observable and, for suitable parameter values, a sigmoidal response or a bistable switch in the phosphorylation of enzyme are possible.

The model has the advantage that it is relatively easy to analyse and can be used to describe many different systems. As a case study, we developed a model of Aurora B kinase in prophase and metaphase. Aurora B is an important regulator of several mitotic processes whose cellular localisation changes throughout mitosis. In prophase and metaphase, it phosphorylates H3 histones at Ser10. This Aurora B activity is dependent upon its localisation at centromeres, the constricted region of chromatin that joins sister chromatids. Aurora B binds to centromeres, is autophosphorylated and diffuses in the cytoplasm.

In order to model the activation of Aurora B throughout the cytoplasm, the generic model of autophosphorylation is extended to include a spatial dependence and consists of a system of partial differential equations. The model accurately describes the proposed activation of Aurora B throughout the cytoplasm due to its concentration at centromeres and reproduces the experimentally observed behaviour of the system. This model of Aurora B activation provides a novel description of activation of a protein throughout the cell due to an increase in concentration at a specific subcellular location.