Mathematical modelling of Akt : Insulin signalling and glucose metabolism

Abstract

Akt is a signalling protein that regulates many processes in the cell, such as cell growth, anti-apoptosis, and glucose metabolism. The abnormal regulation of Akt is implicated in the development of a number of diseases, including cancer, cardiovascular disease, and type two diabetes.

Initially synthesized on the endoplasmic reticulum, Akt moves to the plasma membrane in response to insulin, where it is activated by phosphorylation. Phosphorylated Akt is found in many cellular locations, and the spatial distribution of Akt is thought to be an important determinant of downstream regulation. However, this aspect of Akt signalling has received scant treatment in the mathematical modelling literature to date.

This thesis consists of a number of mathematical models of Akt translocation and phosphorylation. The Akt Switch model is a simple, linear, ordinary differential equation (ODE) model of Akt activation that tracks both the biochemical state and cellular location of Akt. Whilst elucidating some of the apparent anomalies of Akt signalling, it enables the differential regulation of downstream substrates via the two branches of Akt signalling (plasma membrane-bound and cytosolic), without recourse to complex feedback mechanisms.

However, the Akt Switch model has some limitations, including a noticeable discrepancy between the model output and the experimental data in the early stages of simulation. As a result, the Akt Translocation model was developed to further investigate the translocation of Akt in response to insulin in vitro.

The Akt Translocation model is a three-compartment ODE model that reproduces the salient features of Akt translocation. Analysis of the model shows that it behaves as a heavily damped harmonic oscillator with solution curves that either increase monotonically or overshoot.

Optimisation of the model to TIRF microscopy data quantified a time delay of approximately 0.4 min between the application of insulin and the Akt translocation response. In addition, the optimisation revealed that the processes regulating the size of the plasma membrane bound pool vary with the insulin level. For physiological insulin, the rate limiting step is the release of Akt to the plasma membrane. At high insulin levels, however, the down-regulation of Akt movement away from the plasma membrane is also necessary to explain the data.

The models developed in this thesis provide a framework for understanding the dynamics of this vital signalling node.