Stochastic Simulation of Cellular Metabolism

Time and dose selective glucose metabolism for glucose homeostasis and energy conversion in the liver

Hepatic glucose metabolism serves dual purposes: maintaining glucose homeostasis and converting glucose into energy sources; however, the underlying mechanisms are unclear. We quantitatively measured liver metabolites, gene expression, and phosphorylated insulin signaling molecules in mice orally administered varying doses of glucose, and constructed a transomic network. Rapid phosphorylation of insulin signaling molecules in response to glucose intake was observed, in contrast to the more gradual changes in gene expression. Glycolytic and gluconeogenic metabolites and expression of genes involved in glucose metabolism including glucose-6-phosphate, G6pc, and Pck1, demonstrated high glucose dose sensitivity. Whereas, glucokinase expression and glycogen accumulation showed low glucose dose sensitivity. During the early phase after glucose intake, metabolic flux was geared towards glucose homeostasis regardless of the glucose dose but shifted towards energy conversion during the late phase at higher glucose doses. Our research provides a comprehensive view of time- and dose-dependent selective glucose metabolism.

The Distance Between: An Algorithmic Approach to Comparing Stochastic Models to Time-Series Data

While mean-field models of cellular operations have identified dominant processes at the macroscopic scale, stochastic models may provide further insight into mechanisms at the molecular scale. In order to identify plausible stochastic models, quantitative comparisons between the models and the experimental data are required. The data for these systems have small sample sizes and time-evolving distributions. The aim of this study is to identify appropriate distance metrics for the quantitative comparison of stochastic model outputs and time-evolving stochastic measurements of a system. We identify distance metrics with features suitable for driving parameter inference, model comparison, and model validation, constrained by data from multiple experimental protocols. In this study, stochastic model outputs are compared to synthetic data across three scales: that of the data at the points the system is sampled during the time course of each type of experiment; a combined distance across the time course of each experiment; and a combined distance across all the experiments. Two broad categories of comparators at each point were considered, based on the empirical cumulative distribution function (ECDF) of the data and of the model outputs: discrete based measures such as the Kolmogorov-Smirnov distance, and integrated measures such as the Wasserstein-1 distance between the ECDFs. It was found that the discrete based measures were highly sensitive to parameter changes near the synthetic data parameters, but were largely insensitive otherwise, whereas the integrated distances had smoother transitions as the parameters approached the true values. The integrated measures were also found to be robust to noise added to the synthetic data, replicating experimental error. The characteristics of the identified distances provides the basis for the design of an algorithm suitable for fitting stochastic models to real world stochastic data.

Integrating glycolysis, citric acid cycle, pentose phosphate pathway, and fatty acid beta-oxidation into a single computational model

The metabolic network of a living cell is highly intricate and involves complex interactions between various pathways. In this study, we propose a computational model that integrates glycolysis, the pentose phosphate pathway (PPP), the fatty acids beta-oxidation, and the tricarboxylic acid cycle (TCA cycle) using queueing theory. The model utilizes literature data on metabolite concentrations and enzyme kinetic constants to calculate the probabilities of individual reactions occurring on a microscopic scale, which can be viewed as the reaction rates on a macroscopic scale. However, it should be noted that the model has some limitations, including not accounting for all the reactions in which the metabolites are involved. Therefore, a genetic algorithm (GA) was used to estimate the impact of these external processes. Despite these limitations, our model achieved high accuracy and stability, providing real-time observation of changes in metabolite concentrations. This type of model can help in better understanding the mechanisms of biochemical reactions in cells, which can ultimately contribute to the prevention and treatment of aging, cancer, metabolic diseases, and neurodegenerative disorders.

Conversion of fat to cellular fuel-Fatty acids β-oxidation model

β-oxidation of fatty acids plays a significant role in the energy metabolism of the cell. This paper presents a β-oxidation model of fatty acids based on queueing theory. It uses Michaelis-Menten enzyme kinetics, and literature data on metabolites' concentration and enzymatic constants. A genetic algorithm was used to optimize the parameters for the pathway reactions. The model enables real-time tracking of changes in the concentrations of metabolites with different carbon chain lengths. Another application of the presented model is to predict the changes caused by system disturbance, such as altered enzyme activity or abnormal fatty acid concentration. The model has been validated against experimental data. There are diseases that change the metabolism of fatty acids and the presented model can be used to understand the cause of these changes, analyze metabolites abnormalities, and determine the initial target of treatment.

Kullback-Leibler Divergence of an Open-Queuing Network of a Cell-Signal-Transduction Cascade

Queuing networks (QNs) are essential models in operations research, with applications in cloud computing and healthcare systems. However, few studies have analyzed the cell's biological signal transduction using QN theory. This study entailed the modeling of signal transduction as an open Jackson's QN (JQN) to theoretically determine cell signal transduction, under the assumption that the signal mediator queues in the cytoplasm, and the mediator is exchanged from one signaling molecule to another through interactions between the signaling molecules. Each signaling molecule was regarded as a network node in the JQN. The JQN Kullback-Leibler divergence (KLD) was defined using the ratio of the queuing time (λ) to the exchange time (μ), λ/μ. The mitogen-activated protein kinase (MAPK) signal-cascade model was applied, and the KLD rate per signal-transduction-period was shown to be conserved when the KLD was maximized. Our experimental study on MAPK cascade supported this conclusion. This result is similar to the entropy-rate conservation of chemical kinetics and entropy coding reported in our previous studies. Thus, JQN can be used as a novel framework to analyze signal transduction.

Queueing theory model of mTOR complexes' impact on Akt-mediated adipocytes response to insulin

A queueing theory based model of mTOR complexes impact on Akt-mediated cell response to insulin is presented in this paper. The model includes several aspects including the effect of insulin on the transport of glucose from the blood into the adipocytes with the participation of GLUT4, and the role of the GAPDH enzyme as a regulator of mTORC1 activity. A genetic algorithm was used to optimize the model parameters. It can be observed that mTORC1 activity is related to the amount of GLUT4 involved in glucose transport. The results show the relationship between the amount of GAPDH in the cell and mTORC1 activity. Moreover, obtained results suggest that mTORC1 inhibitors may be an effective agent in the fight against type 2 diabetes. However, these results are based on theoretical knowledge and appropriate experimental tests should be performed before making firm conclusions.

Queueing theory model of pentose phosphate pathway

Due to its role in maintaining the proper functioning of the cell, the pentose phosphate pathway (PPP) is one of the most important metabolic pathways. It is responsible for regulating the concentration of simple sugars and provides precursors for the synthesis of amino acids and nucleotides. In addition, it plays a critical role in maintaining an adequate level of NADPH, which is necessary for the cell to fight oxidative stress. These reasons prompted the authors to develop a computational model, based on queueing theory, capable of simulating changes in PPP metabolites’ concentrations. The model has been validated with empirical data from tumor cells. The obtained results prove the stability and accuracy of the model. By applying queueing theory, this model can be further expanded to include successive metabolic pathways. The use of the model may accelerate research on new drugs, reduce drug costs, and reduce the reliance on laboratory animals necessary for this type of research on which new methods are tested.

Queueing theory model of Krebs cycle

MOTIVATION

Queueing theory can be effective in simulating biochemical reactions taking place in living cells, and the article paves a step toward development of a comprehensive model of cell metabolism. Such a model could help to accelerate and reduce costs for developing and testing investigational drugs reducing number of laboratory animals needed to evaluate drugs.

RESULTS

The article presents a Krebs cycle model based on queueing theory. The model allows for tracking of metabolites concentration changes in real time. To validate the model, a drug-induced inhibition affecting activity of enzymes involved in Krebs cycle was simulated and compared with available experimental data.

AVAILABILITYAND IMPLEMENTATION

The source code is freely available for download at https://github.com/UTP-WTIiE/KrebsCycleUsingQueueingTheory, implemented in C# supported in Linux or MS Windows.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.