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Computational Model Sheds Light on Autophagy in Cancer Cells

By Mehrshad Sadria and Anita Layton

According to the World Heath Organization, cancer is the second leading cause of death in the world. Cancer occurs when cell proliferation becomes abnormal and uncontrolled, which necessitates a supply of energy to generate ATP and metabolic intermediates to produce biomass. This alters the energy metabolism in cancer cells, leading to high glucose consumption and glycolysis rates. Indeed, such metabolic reprogramming is a hallmark of cancer. 

Conventional wisdom states that tumor suppressors restrain cell growth and division, whereas tumor promotors foster cell growth and division. However, this division may be overly simplistic in the context of adenosine monophosphate-activated protein kinase (AMPK). AMPK is a master regulator of cellular metabolism and energy homeostasis in both normal and cancer cells. It switches on when cellular energy levels fall, such as when the supply of nutrients or oxygen becomes low due to poor blood supply. Studies on both animals and humans have suggested that AMPK activation generally has health-promoting effects, including improvements in diabetes, cardiovascular health, and mitochondrial diseases; it might even extend life span. However, AMPK’s role in tumorigenesis is controversial: While some studies suggest that AMPK suppresses cancer cell proliferation and tumor formation, others show evidence to the contrary (see Figure 1). 

Upon activation, AMPK kickstarts activities in the cell that restore energy while simultaneously restraining cell growth and division. It does so by inhibiting mTORC1 (mechanistic target of rapamycin complex 1) — a protein kinase that promotes cell growth and is hyperactive in most cancers. AMPK’s inhibition of mTORC1 therefore suggests that it would restrain growth and act as a tumor suppressor; some cell experiments in mice have indeed confirmed this role. Curiously, in other mouse studies where T-cell lymphoma is already established, the deletion of the AMPK gene appears to slow the disease — thus indicating that AMPK is a tumor promoter! These conflicting findings suggest that AMPK normally acts as a tumor suppressor, but it switches to a tumor promoter if a tumor does arise. This outcome may occur because AMPK activates another mTOR complex, mTORC2, that facilitates cell survival. AMPK may hence protect tumor cells from the stresses of their rapid cell growth and division, as well as poor blood supply. Such protection helps these abnormal cells survive.

Figure 1. A cartoon illustration of the potential effects of AMPK in healthy versus cancerous cells. Figure courtesy of Mehrshad Sadria and Anita Layton, who hold the copyright.

A Computational Model of the Metabolic Signaling Network

Given AMPK’s multifaceted, controversial role in cancer and its beneficial capacity in many other diseases, under what conditions is its activation advantageous? And how does the cell’s microenvironment impact these effects? It is difficult to untangle the multitude of biochemical reactions and feedback loops that are involved in the metabolic pathway. As such, we developed a computational model to simulate the effects of pharmacological maneuvers that target key metabolic signaling nodes, with a specific focus on AMPK [1]. Figure 2 depicts a schematic diagram of our model’s signaling pathway. The model represents key proteins in cellular metabolism, including the insulin receptor substrate (IRS) and Akt, which collectively modulate most of insulin’s effects on metabolism; mTORC1, which controls cell growth; mTORC2, which promotes cell survival; DEPTOR and ULK1, which mediate mTORC1’s signal in autophagy initiation; and AMPK and sirtuin 1, the two key energy sensors. We model the signaling pathway dynamics as a system of ordinary differential equations that involves Michaelis-Menten and mass action kinetics. 

Figure 2 shows that two activating arrows and one inhibiting arrow point towards mTORC1. This means that mTORC1’s rate of phosphorylation is given by

\[\begin{aligned} \frac{d[\textrm{mTORC1}^*]}{dt} &= \frac{V_{\textrm{mTORC1, AKT}}[\textrm{AKT}^*][\textrm{mTORC1}]}{K_{\textrm{M, mTORC1, AKT}}+[\textrm{mTORC1}]} \\ &-\frac{(V_{\textrm{mTORC1}}+V_{\textrm{mTORC1, AMPK}}[\textrm{AMPK}^*])[\textrm{mTORC1}^*]}{K_{\textrm{M, mTORC1}}+[\textrm{mTORC1}^*]} \\ &-\frac{V_{\textrm{mTORC1, ULK}}[\textrm{ULK}^*][\textrm{mTORC1}^*]}{K_{\textrm{M, mTORC1, ULK}}+[\textrm{mTORC1}^*]}.\end{aligned}\]

Here, the asterisk indicates a phosphorylated compound. The three terms on the right describe mTORC1’s activation by Akt and inhibition by AMPK and ULK1. Similarly, the rate of phosphorylation of mTORC2 is given by its activation by IRS and AMPK, in addition to its dephosphorylation (not shown in Figure 2):

\[\begin{aligned}\frac{d[\textrm{mTORC2}^*]}{dt} &=\frac{V_{\textrm{mTORC2, IRS}}[\textrm{IRS}^*][\textrm{mTORC2}]}{K_{\textrm{M,mTORC1, AKT}}+[\textrm{mTORC2}]}+  \frac{V_{\textrm{mTORC2, AMPK}}[\textrm{AMPK}^*][\textrm{mTORC2}]}{K_{\textrm{M, mTORC2, AMPK}}+ [\textrm{mTORC2}]} \\ &-\frac{V_{\textrm{mTORC2}}[\textrm{mTORC2}^*]}{K_{\textrm{M, mTORC2}}+[\textrm{mTORC2}^*]}.\end{aligned}\]

Figure 2. Model metabolic signaling network. This schematic diagram depicts the interactions and feedback loops within the mTORC network, as well as their connections to AMPK. Normal, blunt, and dashed arrows respectively denote activation, inhibition, and complex formation. Figure courtesy of [1].

Is AMPK a Cancer Suppressor or Promoter? It Depends on the Cellular Nutrient Level

AMPK activation is generally considered beneficial. However, AMPK’s impact on cellular energy and cycles—as well as the heterogeneity of cancer cell types—inspires the following question: Are there microenvironments under which AMPK activation is harmful to an organism’s overall survival? To investigate this possibility, we simulated cellular microenvironments with different metabolic stress (nutrition) levels. We varied AMPK abundance and analyzed the resulting changes in mTORC1 and mTORC2 to assess the effects on cell population. Figure 3b presents the results as a surface plot. We are particularly interested in the implications for cancer; because mTORC1 and mTORC2 promote cell proliferation and survival respectively, the simultaneous inhibition of both proteins may help limit the proliferation of cancer cells.

For a given AMPK activation level, an increase in nutrient availability generally promotes cell population growth; this result is intuitive and not at all surprising. A more interesting consideration is the way in which AMPK activation may impact tumor cell populations at different nutrient levels. Activation of AMPK facilitates the phosphorylation of mTORC2 but inhibits mTORC1, so what is AMPK activation’s combined effect on cancer cell proliferation and survival? The answer depends on the cell microenvironment, specifically the nutrient level of the cancer environment. 

At low nutrient levels (left group of bars in Figure 3a), increasing AMPK abundance from 20 to 480 increases phosphorylated mTORC2 by almost four-fold but has a relatively negligible effect on mTORC1 activation (despite AMPK’s general inhibitory effect on mTORC1). This outcome occurs because AMPK’s inhibition of mTORC1 is partially offset by mTORC2’s indirect activation of mTORC1. Taken together, enhancing AMPK abundance yields a significant increase in total phosphorylated mTORC1 and mTORC2 — suggesting that AMPK activation may have a detrimental effect by promoting the population of cancer cells (see the left set of bars in Figure 3a and the red diamonds in Figure 3b). 

In contrast, increasing AMPK abundance from 20 to 480 in a microenvironment with sufficiently high nutrient levels significantly reduces the total phosphorylated mTORC1 and mTORC2 (see the right set of bars in Figure 3a and the blue squares in Figure 3b). These results indicate that AMPK inactivation is expected to beneficially limit the cancer cell population when cancer cells experience chronic nutrient deprivation.

Figure 3. The effect of AMPK activation and nutrient levels on cell proliferation and survival, given by the sum of phosphorylated mTORC1 and mTORC2. 3a. The results for low and high nutritional levels and three AMPK values. 3b. The full dependence of phosphorylated mTORC1 and mTORC2 on nutritional levels and AMPK. The data points that correspond to those in 3a are marked by red diamonds (limited nutrients) and blue squares (plentiful nutrients). Figure modified from [1].

Implications for Cancer and Diabetes Treatments

The strange case of Dr. Jekyll and Mr. Hyde that is AMPK’s role in cancer has important health implications. Researchers can leverage AMPK’s tumor suppressor function to protect people who are at high risk of developing cancer. Intriguingly, such a drug already exists: metformin, which is a common treatment for type 2 diabetes. This is a particularly happy coincidence because patients with diabetes are more likely to develop a variety of cancers—like colon, rectal, pancreas, and liver cancer—as compared to non-diabetic patients. Many doctors prescribe metformin to decrease fasting and post-fasting glucose levels, which are the surrogate markers of glycemic control hemoglobin A1c and insulin resistance. Metformin reduces glycogenesis via AMPK signaling and thus increases glucose uptake in diabetic patients’ muscle cells, thereby causing a decrease in blood glucose and insulin levels. Recent analyses and studies indicate that metformin also reduces the proliferation of cancer cells and the possibility of malignancies in a number of different cancers.

However, AMPK can be a double-edged sword for those with cancer. In most cancers, the affected organs (e.g., the spleen) are well perfused and cancer cells have access to sufficient nutrients; under these conditions, AMPK opposes cancer growth and proliferation. But the microenvironments are nutrient poor in some cancers (e.g., bone marrow leukemia), meaning that cancer cells are more dependent on AMPK activity. In these cases, AMPK activation would increase tumor cell viability and thereby potentially decrease a patient’s likelihood of survival. Therefore, an AMPK inhibitor—rather than an activator—might be therapeutically useful in cancers like bone marrow leukemia.

Our work highlights the importance of precision medicine in the context of metformin’s use for cancer and other diseases. No one drug—not even metformin, despite its popularity and general benefits—works for everyone. Practitioners must account for each patient’s age, gender, genetic and epigenetic profiles, comorbidity, and concurrent medications when developing their treatment plans. 


References
[1] Sadria., M., Seo, D., & Layton, A.T. (2022). The mixed blessing of AMPK signaling in cancer treatments. BMC Cancer, 22
, 105.

Merhshad Sadria is a Ph.D. candidate in applied mathematics at the University of Waterloo in Canada. His research interests include mathematical modeling, computational biology, deep learning, and regenerative medicine. Anita Layton is the Canada 150 Research Chair in Mathematical Biology and Medicine and a professor of applied mathematics, computer science, biology, and pharmacy at the University of Waterloo. She leads a diverse and interdisciplinary team of researchers to use computational modeling tools to better understand aspects of health and disease.

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