A single-cell model of PIP₃ dynamics using chemical dimerization

Most cellular processes are driven by simple biochemical mechanisms such as protein and lipid phosphorylation, but the sum of all these conversions is exceedingly complex. Hence, intuition alone is not enough to discern the underlying mechanisms in the light of experimental data. Toward this end, mathematical models provide a conceptual and numerical framework to formally evaluate the plausibility of biochemical processes. To illustrate the use of these models, here we built a mechanistic computational model of PI3K (phosphatidylinositol 3-kinase) activity, to determine the kinetics of lipid metabolizing enzymes in single cells. The model is trained to data generated upon perturbation with a reversible small-molecule based chemical dimerization system that allows for the very rapid manipulation of the PIP₃ (phosphatidylinositol 3,4,5-trisphosphate) signaling pathway, and monitored with live-cell microscopy. We find that the rapid relaxation system used in this work decreased the uncertainty of estimating kinetic parameters compared to methods based on in vitro assays. We also examined the use of Bayesian parameter inference and how the use of such a probabilistic method gives information on the kinetics of PI3K and PTEN activity.