Some mathematical models of intermolecular autophosphorylation

Area of Science:

• Biochemistry
• Enzymology
• Mathematical Biology

Background:

• Intermolecular autophosphorylation involves an enzyme phosphorylating another molecule of itself.
• Dephosphorylation by a phosphatase is a crucial regulatory mechanism in biological systems.

Purpose of the Study:

• To develop generic mathematical models for intermolecular autophosphorylation with dephosphorylation.
• To analyze the dynamics of enzyme phosphorylation, including lag phases, thresholds, and switching behaviors.
• To investigate the role of localized binding and spatial effects on enzyme activation.

Main Methods:

• Developed a time-dependent ordinary differential equation model using mass-action and Michaelis-Menten kinetics.
• Extended the model to a spatio-temporal system of partial differential equations for a spherical geometry.
• Simulated enzyme phosphorylation dynamics under various parameter values and localized concentration changes.

Main Results:

• The time-dependent model predicts a lag phase before significant enzyme phosphorylation.
• A threshold concentration for enzyme phosphorylation was identified.
• The spatio-temporal model demonstrates activation by local concentration, potentially leading to irreversible changes in the presence of a phosphatase.

Conclusions:

• The developed models offer a simplified yet comprehensive approach to studying autophosphorylation systems.
• Localized concentration increases can trigger enzyme activation, which may become irreversible when phosphatases are present.
• These findings provide a proof-of-concept for activation by local concentration in cellular processes.