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Petri nets in modelling glucose regulating processes in the liver

Kamila Barylska, Anna Gogolińska

TL;DR

Diabetes drives dysregulation of blood glucose and understanding hepatic glucose control is essential. The authors propose a Petri net representation of glycolysis and glucose synthesis in the liver, grounded in medical literature, to study regulatory interactions across feeding and fasting. They apply standard PN analyses—reachability graphs, traps, and stubborn reduced reachability graphs—to demonstrate that the model captures insulin-, glucose-, and glucagon-driven control of key enzymes and metabolites, and to identify deadlock states that correspond to phase transitions between glycolysis and glucose production. This PN-based hepatic regulation work serves as a foundational step toward a whole-body model for healthy and diabetic conditions and outlines future directions for model extensions and validation.

Abstract

Diabetes is a chronic condition, considered one of the civilization diseases, that is characterized by sustained high blood sugar levels. There is no doubt that more and more people is going to suffer from diabetes, hence it is crucial to understand better its biological foundations. The essential processes related to the control of glucose levels in the blood are: glycolysis (process of breaking down of glucose) and glucose synthesis, both taking place in the liver. The glycolysis occurs during feeding and it is stimulated by insulin. On the other hand, the glucose synthesis arises during fasting and it is stimulated by glucagon. In the paper we present a Petri net model of glycolysis and glucose synthesis in the liver. The model is created based on medical literature. Standard Petri nets techniques are used to analyse the properties of the model: traps, reachability graphs, tokens dynamics, deadlocks analysis. The results are described in the paper. Our analysis shows that the model captures the interactions between different enzymes and substances, which is consistent with the biological processes occurring during fasting and feeding. The model constitutes the first element of our long-time goal to create the whole body model of the glucose regulation in a healthy human and a person with diabetes.

Petri nets in modelling glucose regulating processes in the liver

TL;DR

Diabetes drives dysregulation of blood glucose and understanding hepatic glucose control is essential. The authors propose a Petri net representation of glycolysis and glucose synthesis in the liver, grounded in medical literature, to study regulatory interactions across feeding and fasting. They apply standard PN analyses—reachability graphs, traps, and stubborn reduced reachability graphs—to demonstrate that the model captures insulin-, glucose-, and glucagon-driven control of key enzymes and metabolites, and to identify deadlock states that correspond to phase transitions between glycolysis and glucose production. This PN-based hepatic regulation work serves as a foundational step toward a whole-body model for healthy and diabetic conditions and outlines future directions for model extensions and validation.

Abstract

Diabetes is a chronic condition, considered one of the civilization diseases, that is characterized by sustained high blood sugar levels. There is no doubt that more and more people is going to suffer from diabetes, hence it is crucial to understand better its biological foundations. The essential processes related to the control of glucose levels in the blood are: glycolysis (process of breaking down of glucose) and glucose synthesis, both taking place in the liver. The glycolysis occurs during feeding and it is stimulated by insulin. On the other hand, the glucose synthesis arises during fasting and it is stimulated by glucagon. In the paper we present a Petri net model of glycolysis and glucose synthesis in the liver. The model is created based on medical literature. Standard Petri nets techniques are used to analyse the properties of the model: traps, reachability graphs, tokens dynamics, deadlocks analysis. The results are described in the paper. Our analysis shows that the model captures the interactions between different enzymes and substances, which is consistent with the biological processes occurring during fasting and feeding. The model constitutes the first element of our long-time goal to create the whole body model of the glucose regulation in a healthy human and a person with diabetes.
Paper Structure (4 sections, 7 figures)

This paper contains 4 sections, 7 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Model
  4. Conclusions and Future Work

Figures (7)

  • Figure 1: A Petri net and its reachability graph.
  • Figure 2: The PN model representing the process of maintaining a glucose homeostasis by the liver. During feeding, when the levels of glucose and insulin are high, and glucagon is not present, the glycolysis occurs. During fasting, when the level of glucagon is high, the synthesis of glucose occurs.
  • Figure 3: The reachability graph obtained for the PN model with the initial marking presented in Figure \ref{['fig2']} with a slight change: place Glucose contains 1 token. Created using snoopy.
  • Figure 4: The reachability graph obtained for the PN model with the initial marking presented in Figure \ref{['fig2']}. The initial marking is located top left and depicted blue, while the final (deadlock) marking is on the right corner of the figure (depicted black). Created using charlie.
  • Figure 5: Changes in markings of places Glucose (red), Pyruvate (blue) and Insulin (green) in the feeding phase. In the initial marking places Glucose and Insulin contained each 100 tokens. At the end of places dynamics simulation place Glucose contains zero tokens, and Pyruvate contains 100 tokens. Created using holmes2holmes1.
  • ...and 2 more figures