title: Some mathematical models of intermolecular autophosphorylation.
abstract: Intermolecular autophosphorylation refers to the process whereby a molecule of an enzyme phosphorylates another molecule of the same enzyme. The enzyme thereby catalyses its own phosphorylation. In the present paper, we develop two generic models of intermolecular autophosphorylation that also include dephosphorylation by a phosphatase of constant concentration. The first of these, a solely time-dependent model, is written as one ordinary differential equation that relies upon mass-action and Michaelis-Menten kinetics. Beginning with the enzyme in its dephosphorylated state, it predicts a lag before the enzyme becomes significantly phosphorylated, for suitable parameter values. It also predicts that there exists a threshold concentration for the phosphorylation of enzyme and that for suitable parameter values, a continuous or discontinuous switch in the phosphorylation of enzyme are possible. The model developed here has the advantage that it is relatively easy to analyse compared with most existing models for autophosphorylation and can qualitatively describe many different systems. We also extend our time-dependent model of autophosphorylation to include a spatial dependence, as well as localised binding reactions. This spatio-temporal model consists of a system of partial differential equations that describe a soluble autophosphorylating enzyme in a spherical geometry. We use the spatio-temporal model to describe the phosphorylation of an enzyme throughout the cell due to an increase in local concentration by binding. Using physically realistic values for model parameters, our results provide a proof-of-concept of the process of activation by local concentration and suggest that, in the presence of a phosphatase, this activation can be irreversible.
authors: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland; AgroParisTech, CRNH-IdF, UMR914, Nutrition Physiology and Ingestive Behavior, F-75005 Paris, France; INRA, CRNH-IdF, UMR914 Nutrition Physiology and Ingestive Behavior, F-75005 Paris, France. Electronic address: kevin.doherty@agroparistech.fr.
authors: Kevin
authors: K
authors: Doherty
authors: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland. Electronic address: martin.meere@nuigalway.ie.
authors: Martin
authors: M
authors: Meere
authors: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, University Road, Galway, Ireland. Electronic address: petri.piiroinen@nuigalway.ie.
authors: Petri T
authors: PT
authors: Piiroinen
mesh_terms: D055162:Biocatalysis; D007700:Kinetics; D008954:Models, Biological; D010766:Phosphorylation; D011494:Protein Kinases / Q000378:metabolism; D012995:Solubility; D013997:Time Factors
chemical_list: D011494:Protein Kinases
keywords: Cell biology; Differential equations; Dynamical systems; Enzyme kinetics