Periodic insulin stimulation of Akt: Dynamic steady states and robustness.

The periodic secretion of insulin is a salient feature of the blood glucose control system in vivo. Insulin levels in the blood exhibit oscillations on multiple time scales - rapid, ultradian, and circadian - and the improved metabolic regulation resulting from pulsatile insulin release has been well established. Although numerous mathematical models investigating the causal mechanisms of insulin oscillations have appeared in the literature, to date there has been comparatively little attention given to the influence of periodic insulin stimulation on downstream components of the insulin signalling pathway. In this paper, we explore the effect of high frequency periodic insulin stimulation on Akt (also known as PKB), a crucial crosstalk node in the insulin signalling pathway that coordinates metabolic and mitogenic processes in the cell. We analyse a mathematical model of Akt translocation to the plasma membrane under both single step insulin perturbations and periodic insulin stimulation with an emphasis on - but not limited to - the physiological range of parameter values. It was shown that the system rapidly attains a robust dynamic steady state entrained to the periodic insulin stimulation. Moreover, the translocation of Akt to the plasma membrane in the model permits a sufficient level of phosphorylation to trigger downstream metabolic regulators. However, the modelling also indicated that further investigation of this activation process is required to determine whether the response of Akt is a key determinant of the enhanced metabolic control observed under periodic insulin stimulation.

From insulin to Akt: Time delays and dominant processes.

Akt/PKB regulates numerous processes in the mammalian cell, including cell survival and proliferation, and glucose uptake in response to insulin. Abnormalities in Akt signalling are linked to the development of Type 2 diabetes, cardio-vascular disease, and cancer. In the absence of insulin, Akt is predominantly found in the inactive state in the cytosol. Following insulin stimulation, Akt translocates to the plasma membrane, docks, and is phosphorylated to take on the active conformation. In turn, the activated Akt travels to and phosphorylates its many downstream substrates. Although crucial to the activation process, the translocation of Akt from the cytosol to the plasma membrane is currently not well understood. Here we detail the parameter optimisation of a mathematical model of Akt translocation to experimental data. We have quantified the time delay between the application of insulin and the downstream Akt translocation response, indicating the constraints on the timing of the intermediate processes. A delay of approximately 0.4 min prior to the Akt response was determined for the application of 1 nM insulin to cells in the basal state, whereas it was found that a further transition from physiological insulin to higher stimuli did not incur a delay. Furthermore, our investigation indicates that the dominant processes regulating the appearance of Akt at the plasma membrane differ with the insulin level. For physiological insulin, the rate limiting step was the release of Akt to the plasma membrane in response to the insulin signal. In contrast, at high insulin levels, regulation of the recycling of Akt from the plasma membrane to the cytosol was also required.

Crosstalk in transition: the translocation of Akt.

Akt/PKB is an important crosstalk node at the junction between a number of major signalling pathways in the mammalian cell. As a significant nutrient sensor, Akt plays a central role in many cellular processes, including cell growth, cell survival and glucose metabolism. The dysregulation of Akt signalling is implicated in the development of many diseases, from diabetes to cancer. The translocation of Akt from cytosol to plasma membrane is a crucial step in Akt activation. Akt is initially synthesized on the endoplasmic reticulum, but translocates to the plasma membrane (PM) in response to insulin stimulation, where it may be activated. The Akt is then recycled to the cytoplasm. The activated Akt may propagate signals to downstream substrates both at the PM and in the cytosol, hence understanding the translocation dynamics is an important step in dissecting the signalling system. At the present time, however, knowledge concerning the translocation of either activated and unactivated Akt is scant. Here we present a simple, deterministic, three-compartment ordinary differential equation model of Akt translocation in vitro. This model can reproduce the salient features of Akt translocation in a manner consistent with the experimental data. Furthermore, we demonstrate that this system is equivalent to a damped harmonic oscillator, and analyse the steady state and transient behaviour of the model over the entire parameter space.

The Akt switch model: Is location sufficient?

Akt/PKB is a biochemical regulator that functions as an important cross-talk node between several signalling pathways in the mammalian cell. In particular, Akt is a key mediator of glucose transport in response to insulin. The phosphorylation (activation) of only a small percentage of the Akt pool of insulin-sensitive cells results in maximal translocation of glucose transporter 4 (GLUT4) to the plasma membrane (PM). This enables the diffusion of glucose into the cell. The dysregulation of Akt signalling is associated with the development of diabetes, cancer and cardiovascular disease. Akt is synthesised in the cytoplasm in the inactive state. Under the influence of insulin, it moves to the PM, where it is phosphorylated to form pAkt. Although phosphorylation occurs only at the PM, pAkt is found in many cellular locations, including the PM, the cytoplasm, and the nucleus. Indeed, the spatial distribution of pAkt within the cell appears to be an important determinant of downstream regulation. Here we present a simple, linear, four-compartment ordinary differential equation (ODE) model of Akt activation that tracks both the biochemical state and the physical location of Akt. This model embodies the main features of the activation of this important cross-talk node and is consistent with the experimental data. In particular, it allows different downstream signalling motifs without invoking separate feedback pathways. Moreover, the model is computationally tractable, readily analysed, and elucidates some of the apparent anomalies in insulin signalling via Akt.

A receptor state space model of the insulin signalling system in glucose transport.

Insulin is a potent peptide hormone that regulates glucose levels in the blood. Insulin-sensitive cells respond to insulin stimulation with the translocation of glucose transporter 4 (GLUT4) to the plasma membrane (PM), enabling the clearance of glucose from the blood. Defects in this process can give rise to insulin resistance and ultimately diabetes. One widely cited model of insulin signalling leading to glucose transport is that of Sedaghat et al. (2002) Am. J. Physiol. Endocrinol. Metab. 283, E1084-E1101. Consisting of 20 deterministic ordinary differential equations (ODEs), it is the most comprehensive model of insulin signalling to date. However, the model possesses some major limitations, including the non-conservation of key components. In the current work, we detail mathematical and sensitivity analyses of the Sedaghat model. Based on the results of these analyses, we propose a reduced state space model of the insulin receptor subsystem. This reduced model maintains the input-output relation of the original model but is computationally more efficient, analytically tractable and resolves some of the limitations of the Sedaghat model.