Overview

Mathematical and computational modeling is a crucial component of synthetic biology, providing a means to gain a deeper understanding of biological processes and reducing the workload in wet laboratories. By employing mathematical models, we can quantitatively analyze and predict the behavior of biological systems, facilitating the design and optimization of synthetic biology projects. These models allow us to identify key parameters and variables that influence system behavior and perform sensitivity analysis to determine critical factors affecting system performance.

With Michaelis-Menten equation and chemical reaction kinetic equation, we established a model of glucose and lipid metabolism balance in adipocyte based on the key role of rate-limiting enzymes in the reaction. Through the sensitivity analysis of different parameters, we found that the efficiency of the electron transport chain has a crucial reuse in affecting the balance of glucose and lipid metabolism, especially in biasing the balance to lipid metabolism. Subsequently, we simulated according to the results, and the results are the same as our expectations.

Figure 1. UCP1 Uncoupling Electron Transportation with ATP Synthesis

Assumption

1.Assume that the rate of glucose input into cells, either through external supply or constant intracellular production, is constant. This assumption allows the establishment of a model under steady-state conditions, facilitating a better exploration of the kinetic characteristics of intracellular glucose and lipid metabolism.

2.Assume that intracellular lipid (fat) and glucose (sugar) are consumed simultaneously as part of the metabolic process within the cells, considering the interrelated nature of intracellular glucose and lipid metabolism and the adaptive regulatory mechanisms of cells to maintain energy demands.

3.Assume that the concentration of glucose is at a level sufficient to support basal metabolic activities, without significant accumulation in the form of stored fat.

4.Assume that the main substrate for gluconeogenesis in adipocytes is glycerol, which is produced through the breakdown of triglycerides during lipolysis and subsequently utilized for gluconeogenic processes.

5.Assume that the rate of gluconeogenesis, the process by which glucose is synthesized from non-carbohydrate substrates, is constant and largely unaffected by small changes in protein intake and gluconeogenic precursors.

Method and solution

Glucose and lipids are essential sources of energy and materials for cells and organisms. The metabolism of glucose and lipids is intricately interconnected and tightly regulated at multiple levels. For instance, glucose can be catabolized, initiating de novo synthesis pathways to produce fatty acids and cholesterol. Excess lipids can be transported through the bloodstream as lipoprotein granules for utilization by tissues or stored as esterified forms in lipid droplets. Moreover, glucose and lipid metabolites can be secreted or transported intracellularly to specific organelles for further conversions. The homeostasis of glucose and lipid metabolism plays a crucial role in maintaining normal physiological function, and disruptions in this balance have been linked to the development of obesity.

Intracellular glucose and lipid metabolism involves a variety of enzymes and intermediates. Simplifying the relevant steps can better simplify the model and understand the metabolic process. By identifying key metabolic pathways, rate-limiting enzymes and key intermediates, intracellular glucose and lipid metabolism can be simplified. At the same time, considering the regulation mechanism of rate-limiting enzymes, such as substrate concentration, enzyme activity regulation and feedback inhibition, can better simulate the regulation process of glucose and lipid metabolism.

As rate-limiting enzymes control the rate and balance of entire metabolic pathways, their activities, regulation mechanisms, and substrate concentrations are critical factors that affect energy production and substrate utilization efficiency. By focusing on these aspects, we can gain a deeper understanding and manipulate the process of glucose metabolism.

Figure 2. Glucose metabolism and lipid metabolism in adipocytes

In our model, we have simplified intracellular glucose metabolism into three steps related to rate-limiting enzymes: glycolysis, the tricarboxylic acid cycle , and oxidative phosphorylation：
1.Glycolysis: Glucose is broken down into two molecules of pyruvate through the glycolytic pathway, generating a small amount of ATP and NADH. This step is crucial for cellular energy production.
2.Tricarboxylic Acid Cycle: Pyruvate enters the tricarboxylic acid cycle and undergoes a series of reactions to generate more ATP, NADH, and FADH2. This cycle is the major pathway for glucose to be completely oxidized into carbon dioxide and provides energy for the cell.
3.Oxidative Phosphorylation: NADH and FADH2 enter the respiratory chain in the mitochondria, where oxidative phosphorylation occurs, leading to the production of more ATP. This step is the key process in converting glucose into energy.

For lipid metabolism, we simplified the steps from triacylglycerol (TAG) to acetyl-CoA, as these steps encompass the most significant transformations and key enzyme-catalyzed reactions in lipid metabolism. TAG represents the main form of energy storage in adipocytes, while acetyl-CoA is a crucial substance for fatty acid oxidation and synthesis.

This simplified model includes the following steps:
1.Lipolysis: TAG is hydrolyzed by lipases into fatty acids and glycerol.
2.Fatty acid beta-oxidation: Fatty acids enter the mitochondria and undergo a series of beta-oxidation reactions, producing acetyl-CoA, NADH, FADH2, etc.
3.Further metabolism of acetyl-CoA: Acetyl-CoA can further participate in the tricarboxylic acid cycle or be used for the synthesis of other biomolecules.

Figure 3.Model of glucose metabolism and fat metabolism in adipocytes

We utilized a system of differential equations, such as the mass action kinetics equations, to mathematically describe the dynamics of biochemical reactions and depict the temporal changes in reaction rates and reactant/product concentrations. Additionally, we employed the Michaelis-Menten equation, a widely used mathematical model in enzyme kinetics, to characterize the enzymatic reaction rates by relating the enzyme-substrate concentrations and providing insights into the enzymatic activity.
The following differential equations are used to simulate the reaction rate of key steps of glycolysis and the content changes of important intermediates:

\begin{matrix} \frac{d [G]}{d t} = V_{G N G} + S - k 1 * [G] \\ \frac{d [G 1]}{d t} = k_{1} * [G] - \frac{(V_{m 1} * [G 1])}{(1 + k_{A T P} * [A T P]) * (k_{m 1} + [G 1])} \\ \frac{d [G 2]}{d t} = - k_{2} * [G 2] + \frac{(V_{m 1} * [G 1])}{(1 + k_{A T P} * [A T P]) * (k_{m 1} + [G 1])} \end{matrix}

The following differential equation is used to simulate the effect of cellular ATP concentration on fat metabolism rate:

\frac{d [T A G]}{d t} = S^{'} - \frac{(V_{m 2} * [T A G])}{(1 + k_{c A M P} * [A T P]) * (k_{m 2} + [T A G])}

The following differential equations are used to simulate the metabolic rate of acetyl-CoA and ATP synthesis in mitochondria:

\begin{matrix} \frac{d [Acetyl - C o A]}{d t} = \frac{(V_{m 2} * [TAG])}{(1 + k_{cAMP} * [ATP]) * (k_{m 2} + [TAG])} + k_{2} * [G 2] - k_{3} * [Acetyl - CoA] \\ \frac{d [ATP]}{d t} = - M + k_{3} * [Acetyl - CoA] \end{matrix}

Obtaining parameter

Our parameters are mainly derived from a comprehensive review of relevant literature including studies by Jahoor and Miji along with the integration of biological knowledge and reasonable estimation based on professional expertise and mathematical methods.

Sensitivity analysis

Sensitivity analysis is a method used to study and analyze the sensitivity of a system or model's state or output changes to variations in system parameters or surrounding conditions, providing valuable insights into the stability and behavior of the model.
In our study, we aimed to determine which parameter has the most direct and significant effect on biasing the balance of intracellular glucose and lipid metabolism towards lipid metabolism.

We conducted a sensitivity analysis using a built-in program that calculated the time dependence and sensitivity of the lipid metabolism rate to each parameter. Through this analysis, we observed that the parameters characterizing the Uncoupling Protein 1 (UCP1), which plays a crucial role in coupling glucose and lipid metabolism, showed the highest sensitivity. This indicates that the balance of intracellular glucose and lipid metabolism biased towards lipid metabolism is most sensitive to changes in UCP1 levels or activity. These findings provide valuable insights into the mechanisms of glucose and lipid metabolism and form the basis for further model refinement and exploration.

Simulation

According to the results of sensitivity analysis, we adjust the parameters of the efficiency of the electron transport chain and simulate it to verify whether our conclusion is reliable.

Conclusion and Discussion

result

We established a simplified computational model of intracellular glucose metabolism and lipid metabolism, based on a mathematical framework, to test the effect of uncoupling rate on intracellular glucose concentration and fatty acid concentration. Additionally, we conducted an analysis of the sensitivity of the electron transport chain to the system.

From the model, we observed that in cells, when uncoupling is enhanced, there is a significant shift in the balance of glucose and fat metabolism, favoring increased fat metabolism. Specifically, the rate of lipid metabolism increases by 483%>compared to glucose metabolism under these conditions. Our findings provide compelling evidence that UCP1 plays a critical role in enhancing lipid metabolism, as demonstrated by Sensitivity analysis.

UCP1 enhances the conductivity of the mitochondrial inner membrane to protons, leading to the dissipation of proton gradients and uncoupling oxidative phosphorylation from ATP synthesis. This process converts the energy derived from substrate oxidation into heat energy, facilitating fat thermogenesis. Implications include potential therapeutic applications in treating obesity and related metabolic disorders. The results of the study provide compelling evidence to support UCP1 as an important therapeutic target for these conditions.

Improvement and outlook

In the establishment of the intracellular glucose and lipid metabolism model, it is important to consider the estimation of various reaction rate constants, enzyme activity, and other parameters. While these estimations are typically based on experimental data and literature reports, they may introduce errors and uncertainties. To facilitate analysis and interpretation of the model, simplifications are often made in the intracellular glucose and lipid metabolism processes. However, these simplifications may not accurately reflect the complexity of real biological systems, thus limiting the scope and accuracy of the model. Additionally, the model may overlook intracellular dynamics and complexity, further impacting its applicability. It is crucial to acknowledge these limitations when using the model, and to combine it with experimental data and other validation methods to enhance reliability and applicability.

In our project, the ultimate goal is to develop weight loss drugs for the treatment of obesity. As a drug delivery tool, the degradation efficiency and mode of PVC in the human body are essential for ensuring the safety of the project.
Therefore, in our future modeling efforts, we will focus on exploring and modeling the degradation cycle and mode of PVC in the human body, as well as determining the optimal concentration of injected drugs. Furthermore, we are committed to continuously improving our metabolic model by incorporating relevant data, aiming to provide more robust evidence for the effectiveness of UCP1.

Reference

01.Jahoor, F., Peters, E. J., & Wolfe, R. R. (1990). The relationship between gluconeogenic substrate supply and glucose production in humans. American Journal of Physiology-Endocrinology and Metabolism, 258(2), E288–E296. https://www.osti.gov/biblio/6995001

02. Jeon, M., Kang, HW. & An, S. A Mathematical Model for Enzyme Clustering in Glucose Metabolism. Sci Rep 8, 2696 (2018). https://doi.org/10.1038/s41598-018-20348-7

03. Laudette M, Sainte-Marie Y, Cousin G, Bergonnier D, Belhabib I, Brun S, Formoso K, Laib L, Tortosa F, Bergoglio C, Marcheix B, Borén J, Lairez O, Fauconnier J, Lucas A, Mialet-Perez J, Moro C, Lezoualc'h F. Cyclic AMP-binding protein Epac1 acts as a metabolic sensor to promote cardiomyocyte lipotoxicity. Cell Death Dis. 2021 Sep 1;12(9):824. https://pubmed.ncbi.nlm.nih.gov/34471096

04. Chen WW, Kang K, Lv J, Yue L, Zhang WQ. Galactose-NlGr11 inhibits AMPK phosphorylation by activating the PI3K-AKT-PKF-ATP signaling cascade via insulin receptor and Gβγ. Insect Sci. 2021 Jun;28(3):735-745. https://pubmed.ncbi.nlm.nih.gov/323480148014.