Figure 1.
Insulin AKT Signalling Pathway Structure.
AKT is activated by PDK1 and PDK2 downstream of insulin. Activated AKT (pAKT) enables the translocation of glucose transporter-4 (GLUT-4). pAKT activates mTOR by phosphorylating the tuberous sclerosis complex (TSC). mTOR activates S6K which phosphorylates and inhibits IRS1.
Figure 2.
Interaction Between AKT and Ang II Pathways.
Renin Angiotensin System (RAS) interacts with insulin signalling through several mechanisms.
Figure 3.
Insulin AKT Signalling Feedback Loops.
Signs + and − indicate positive and negative feedback loops, respectively. Parameters () on the edges denote the strengths of the edges.
is the nutrient level sensed my mTOR.
Figure 4.
AKT-Angiotensin II Feedback Loops.
A hierarchy of feedback loops defines the interactions between the AKT and Ang II signalling pathways.Interaction parameters are labeled on the directed edges between the interacting nodes.
Table 1.
Feedback Loops.
Figure 5.
Response Curves of the AKT model. Insulin level is redefined as [45].
(A) Steady-state response curves of pAKT vs insulin for different feedback strengths
.
. The curves are calculated by setting equations (10) and (11) equal to zero. (B) Dynamic response curve in red superimposed on the steady-state curve shows the normal insulin cycle between states A and B.
At State A, the cell has low nutrient level and requires glucose uptake. By stimulating insulin, the system switches to State B, where pAKT is activated and glucose is taken into the cell. Withdrawing insulin enables the switch back to low pAKT levels. (C) Bistability is lost under excess negative feedback
Steady-state curves in (A) are identical to those in [45]. Dynamic responses in (B) and (C) are new and they are generated form the dynamic model equations (10) and (11).
Figure 6.
Steady State Response Curves for Different values.
Bistability exists for values of between 0.84 and 2.07. Larger values of
would correspond to the decreased function of PTEN. In this case pAKT stays at a high level once it is activated. This leads to elevated mTOR signalling and tumor growth.
Figure 7.
Steady State Response Curves for Different Levels of Inhibition by ONOO.
The strength of inhibition is represented by the parameter. Increasing
or inhibition reduces the sensitivity to insulin.
Figure 8.
Bifurcation Diagram Showing Bistability Limits for β for Different k3 Values when λ = 0.5.
As k3 increases, bistability is lost unless β increases to compensate the inhibitory action of ONOO by activating pAKT more.
Figure 9.
Steady State Solutions and Trajectories Predicted by ANGII-AKT Model.
S1, S2 and S3 denote the three steady-states when insulin level λ = 0.5. The steady-states are at the intersection of red curves and black curve. Solid blue lines are the trajectories that start from different initial conditions I1, I2, I3 and I4. NO and pAKT both exhibit the desired bistability and switching dynamics behavior.
Figure 10.
State Solution Curves for the Base Scenario Showing Joint Bistability for Various Insulin Levels.
(A) for pAKT and (B) for NO.
Figure 11.
Comparison of Base Case (k7 = 0.1) with the Case k7 = 100.
Red curves are the steady-state curves for the base case (k7 = 0.1). Green curves are the same curves when k7 = 100. Intersections of red and green curves with the black define the steady-states for the two cases. Solid blue curve is the state trajectory for the base case. Dashed blue curve is the state trajectory for the case when k7 = 100. As the effect of Ang II is increased by increasing k7, the system loses bistability. Trajectories converge to the single steady-state S1 at low levels of pAKT and NO.
Figure 12.
Comparison of Base Case (k4 = 0.01) and the Case k4 = 0.015.
Red curves are the steady-state curves for both cases. Black curve is the steady-state curve for the base case (k4 = 0.01). Green curve is the new curve when k4 = 0.015. Intersections of red curves with the black define the steady-states for the two cases. Solid blue curve is the state trajectory for the base case. Dashed blue curve is the state trajectory for the case when k4 = 0.015. NO production by pAKT is enhanced by Increasing the value of parameter increases availability of NO and production of ONOO which impairs insulin signalling. Bistability is lost and the system settles to the single steady-state S1 where both pAKT and NO are low. In normal conditions (
= 0.01), pIRS1-pAKT-pIRS1 and pAKT-NO-pAKT feedback loops work in coordination to maintain both insulin sensitivity and the right amount of NO by switching between S1 and S3 as necessary.
Figure 13.
Points S1, Sh1, Sh2, Sh3 represent the steady-states. At these steady states NO levels increase as the parameter or hyperglycemia effect increases. Black, green, brown and red curves for k9 = 0, 0.005, 0.02 and 0.04, respectively. Intersections of these curves with the low-pAKT steady-state curve (red) define the steady-states for different levels of hyperglycemia. Dynamic simulations starting from initial condition I converge to different steady-states. Solid blue curves are the state trajectories for different k9 values. pAKT stays below the threshold value 0.2 and increasing
or hyperglycemia shifts the steady state to higher NO levels.