Figure 1.
Schematics of oxidative phosphorylation, anaerobic glycolysis, and aerobic glycolysis.
(A) To enable rapid proliferation, cancer cells shift their metabolic machinary toward high levels of glucose uptake and lactate production (aerobic glycolysis, the Warburg Effect”). (B) Differentiated cells favor oxidative phosphorylation and anaerobic glycolysis.
Figure 2.
Proposed role of miR-451 in the regulation of LKB1 signaling in response to fluctuating glucose.
miR-451 levels determine cell migration or proliferation in response to glucose (blue triangle on the left). (A) Low glucose level reduces miR-451 and leads to upregulation of AMPK and enhanced cell motility. (B) Normal glucose level upregulates miR-451, which in turn leads to increased proliferation and decreased cell migration by inhibiting CAB39-LKB1-AMPK pathway. Schematic components of miR-451 and the CAB39/LKB1/AMPK complex is represented by modules ‘M’ (box with red dotted line) and ‘A’ (box with blue dotted line) in our theoretical framework. Blue arrows on the right indicate the switching behavior between a migratory mode in (A) and the proliferative state in (B) in response to fluctuating glucose.
Figure 3.
A simplified model of the network shown in Figure 2.
Two key molecules, miR-451 and AMPK complex, are represented by and
respectively. The dynamics of miR451 includes input from glucose (
), decay (
), and autocatalytic increase. AMPK complex is induced by source (
), and undergoes autocatalytic increase with natural decay (
). In addition, there are mutual inhibition mechanisms between
and
.
Table 1.
Parameters that are used in the internal dynamics model (miR-451/AMPK system).
Figure 4.
The hysteresis loop:
is upregulated when
varies in the upper stable branch, and downregulated when
varies in the lower stable branch.
We define the migration region by and the proliferation region by
, and take
.
Figure 5.
Effect of glucose deprivation on miR-451 expression levels. In [2], miR-451 level was reduced by 21% for different cell lines (U251, LN229) after cells are cultured for 24 hr in normal (+, glucose or reduced glucose (−, glucose 0.3 g/l). Simulation results (red) are in good agreement with experimental results (blue; U251 cell line) from [2]. Y-axis in the figure is the relative miR-451 concentration for high (glucose+; dimensionless value
in simulation) and low (glucose−, glucose−,
in simulation) level of glucose in the medium.
Figure 6.
Two different growth schemes of tumor spheroids (gray filled circle) with same initial size in response to fluctuating and steady glucose (green solid line).
(A) Cycle of growth and invasion in response to fluctuating glucose. Tumor cells (blue filled circle) at the surface of the spheroid begin to migrate away from the core when miR-451 levels are low (blue solid line; high AMPK activity) due to low glucose. These migratory cells become proliferative cells when high glucose is introduced and miR-451 levels are high (red solid line; low AMPK activity). (B) Monotonic growth due to steady supply of glucose; the total supply of glucose is the same as in (A). We hypothesize that tumor spheroids with fluctuating glucose in (A) will grow faster than ones grown in steady glucose supply in (B).
Table 2.
Parameters used in the tumor model.
Table 3.
Reference variables used in the model.
Figure 7.
Typical evolution of spatial profiles of tumor density () and concentrations of ECM (
), MMPs (
), glucose (
), miR-451 (
), and AMPK (
).
In each subfigure x-axis indicates the computational domain, left end () being the center of tumor mass and right end (
) being the farthest field away from the tumor. Glucose was provided on the right hand side of the domain near
and glucose is transported by diffusion. Injection of glucose (
) was given on the right side of domain (
) at time
. Levels of miR-451 and AMPK change in response to fluctuating glucose and determine whether cells would invade or grow. The red dotted line (−.) indicates the threshold
.
Figure 8.
Dynamics of tumor invasion/growth.
(A) Time evolution of total tumor population and total glucose level. Cells adapt growth phase (red arrows) via low AMPK level (high miR-451) when glucose supply is high and invasive phase (black arrows) via high AMPK level (low miR-451) in response to low glucose levels. (B) Time evolution of total concentrations of miR-451 and AMPK. High peaks of miR-451 are consistent with high peaks of glucose in (A) and lead to low levels of AMPK. *Data from Figure 7.
Figure 9.
Time evolution of total tumor population and total glucose level near far away field. In responds to periodic input of high glucose, tumor population shows alternating growth and invasion pattern (solid;black). When same amount of glucose without glucose fluctuation was provided to the system near , tumor population growth is induced from diffused glucose level and followed high miR-451 and low AMPK concentration at cell site. This induces a low chance of cell invsion near the surface and eventually total growth is low compared to the case with fluctuating glucose level.
Figure 10.
Effect of inhibition strength () of miR-451 by AMPK.
(A–B) Time evolution of tumor population and AMPK concentration within the system for different values of . The control case was marked as star (*) for each subfigure.
Figure 11.
Effect of inhibition strength () of AMPK by miR-451.
(A–B) Time evolution of tumor population and AMPK concentration within the system for different values of . The control case was marked as star (*) for each subfigure.
Figure 12.
Time evolution of tumor population and the corresponding miR-451 and AMPK for different values of injection period () and injection supply amount (
).