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. The difficulty arises from the fact that compounds, which act as substrates and products in the cell’s metabolic reactions, are like a system of interconnected vessels. Any change in the concentration of a compound in a cell indirectly affects other, seemingly unrelated compounds, and thus the reactions in which they participate. Many external as well as internal factors affect the course of reactions taking place in the cell, possibly accelerating, inhibiting, or blocking them. Due to the complexity of metabolism during computational modeling, it is necessary to adopt certain start and end points. Therefore, the best target for modeling seems to be those thoroughly studied metabolic pathways that are described in the scientific literature3. Nevertheless, it is necessary to determine certain simplifications that make such modeling possible. These simplifications may include the flow of metabolites between the cytoplasm and mitochondrion depending on the cell’s momentary demand, or the flow between different metabolic reactions, since the vast majority of metabolites are used in several different metabolic pathways.Cellular metabolism modeling is an important but difficult task4. In addition, suitably adapted models can map what happens in a cell under inhibition induced by a specific molecule or gene knockdown. It has long been known that cancer cells reprogram their metabolism and alter activity in pathways that are major sources of energy5. However, issues related to metabolism and cancer are still in the orbit of researchers’ interest7. In cancer, it has been found that many cancer cells have altered metabolism, often characterized by an increased reliance on glucose and a decreased reliance on oxygen for energy production. This metabolic reprogramming allows cancer cells to proliferate and survive in a hostile environment. Targeting the metabolic pathways of cancer cells is becoming a promising new avenue for cancer therapy. Recent research has shown that metabolism plays a key role in many fields that were previously not considered to be related to metabolism, such as aging8, and neurodegeneration10. In aging and neurodegeneration, it is becoming increasingly clear that metabolic dysfunction plays a key role in the development of these conditions. For example, research has shown that aging is associated with a decline in the function of the mitochondria, the cell’s power plants, which can lead to metabolic dysfunction. Similarly, many neurodegenerative diseases, such as Alzheimer’s disease, are associated with metabolic dysfunction in the brain. Targeting these metabolic pathways may be a promising new approach for treating these conditions. Overall, the emerging role of metabolism in these fields highlights the importance of understanding the complex interactions between metabolism and disease. Therefore, metabolic modeling and analysis can be used in cancer therapy, as it will contribute to testing the effects of specific molecules as early as at the planning stage of experiments. Another of the advantages of using metabolic models is that they reduce the number of laboratory animals used in research. Many times this type of research can lead to long-term damage to the health of these animals or even their death13.Metabolic models can serve scientists in better planning of experiments. They allow predicting the effects of specific conditions on cell metabolism. Thanks to the ongoing development of metabolomics and computational biology, modeling can speed up the processes of diagnosing metabolic diseases and contribute to development of effective treatment methods14, insulin-related disorders and diseases15, glycolysis model16, tricarboxylic acid cycle (TCA cycle) model17, and the pentose phosphate pathway model18. The departure from deterministic models and the incorporation of fluctuations in metabolic simulations represent a significant advancement in our understanding of biological systems. Traditionally, deterministic models have been extensively used to study metabolic processes, assuming precise and predictable behavior. However, it is increasingly recognized that biological systems exhibit inherent stochasticity, where random fluctuations play a fundamental role in shaping cellular behavior. By implementing a flavor of the Kinetic Monte Carlo method19, similar to the Gillespie algorithm20, in our simulations, we have taken a crucial step towards capturing the effects of these fluctuations. Incorporating fluctuations in metabolic simulations is of utmost importance as it allows us to bridge the gap between the deterministic models and the real-world dynamics of biological systems. Fluctuations arise from various sources such as the discreteness of molecular species, spatial heterogeneity, and the inherent randomness of molecular interactions. Ignoring these fluctuations can lead to an incomplete and biased understanding of cellular processes.The modeling method used in this work is based on queueing theory. Queueing theory is mainly used in issues related to engineering and telecommunications. However, there is evidence that it can be successfully used to model stochastic biological processes. Examples of applications of queueing theory to model biological processes include studies of signal transduction cascade in the cell23. They can drive cellular decision-making, affect cellular responses to perturbations, and contribute to the emergence of complex phenomena at the system level.By considering the inherent stochasticity in our model, we gain valuable insights into the behavior of metabolic networks that deterministic models fail to capture. Fluctuations have been shown to influence key aspects of cellular metabolism, including reaction rates, pathway efficiency, and robustness24.Incorporating fluctuations in metabolic simulations also provides a more accurate representation of biological reality. By acknowledging the stochastic nature of cellular processes, we can better understand and reproduce experimental observations. Fluctuations play a role in generating the observed biological variability, and their inclusion in simulations allows us to better match experimental data and validate the model’s predictions. Moreover, by simulating fluctuations, we can explore the effects of different sources of variability, such as noise in gene expression or environmental fluctuations, on metabolic behavior. This information is crucial for understanding how cells respond and adapt to changing conditions and for unraveling the underlying principles governing cellular decision-making19, have made it increasingly feasible to simulate stochastic models at reasonable timescales. The departure from deterministic models and the incorporation of fluctuations in metabolic simulations represent a significant advancement in computational biology. By embracing the inherent stochasticity of biological systems, we gain deeper insights into the dynamics and behavior of metabolic networks, which would otherwise be overlooked by deterministic models16. Incorporating fluctuations allows us to better match experimental observations, understand biological variability, and explore the impact of stochasticity on cellular processes. These advancements pave the way for more accurate and comprehensive models of cellular metabolism and contribute to our overall understanding of complex biological systems.It is important to note that incorporating fluctuations in metabolic simulations is not without challenges. Stochastic simulations can be computationally demanding, requiring specialized algorithms and efficient simulation techniques. However, advancements in computational power and the development of efficient algorithms, such as the Kinetic Monte Carlo method25, PPP is a pathway parallel to glycolysis, in which NADPH and 5-carbon sugars are generated26. Beta-oxidation is a series of reactions that break down long carbon chain fatty acids in order to generate acetyl-CoA and co-enzymes used in the electron transport chain, such as FADH27. TCA cycle is an important metabolic pathway which uses acetyl-CoA produced in catabolic reactions of carbohydrate, fat, and protein metabolism, to generate energy28. TCA cycle is a source of various important biochemical compounds used in many other metabolic reactions in the cell. The presented model enables tracking of changes in the concentrations of individual metabolites of the aforementioned pathways. The innovation of this study is that the model has been based on queueing theory, compared to ODE-based models, which are commonly used for this kind of research. Another innovation is its nature that integrates pathways related to the formation and utilization of acetyl-CoA. In addition, it was showed that artificial intelligence algorithms can be successfully used to tune coefficients of the enzyme equations.The purpose of the present study was to develop an integrated computational model of the cell’s energy metabolism. This model consists of reactions included in important metabolic pathways and cycles, i.e. glycolysis, the pentose-phosphate pathway (PPP), the TCA cycle, and beta-oxidation. These are the pathways that play an important role in energy metabolism of the cell. Glycolysis is a simple metabolic pathway that regulates metabolic functions of various cellsThe TCA metabolites’ concentration values reported in the literature were either single-number measurements or ranges Table . As a reThe last column in the table presents the Z-score of modeled substrates’ concentration values regarding the estimated mean and standard deviation of the corresponding Gaussian distribution. All values of substrates, except for 39. In the initial phase of the simulation, the course of glycolysis, PPP, and TCA cycle reactions were modeled. The product of glycolysis, pyruvate, underwent reactions that converted pyruvate to oxaloacetate or acetyl-CoA, which are metabolites of the TCA cycle. Over the course of the simulation, the glucose concentration decreased. As the glucose concentration decreased, the reactions of the glycolysis pathway were extinguished. This was due to a decrease in the probability of occurrence of glycolysis reactions and, consequently, a decrease in the speed of these reactions. As a consequence of the decrease in glycolysis activity, the probability of occurrence of reactions entering the fatty acid beta-oxidation pathway increased, which, after glucose utilization, became the main source of acetyl-CoA used in the TCA cycle. The use of GA allowed combining the reaction of enzymatic kinetics of several energetically important biochemical pathways. Due to the large differences in numerical values between consecutive reactions, as well as influence of the reactions not included in the model on reaction rates, it was necessary to tune the model. GA proved to be an effective tool in this process.During the experiment, glucose consumption in the cell was simulated. At the start of the model, the glucose concentration was fixed at 5 mM. This is a value in the range of normal blood glucose concentrationIn order to check the validity of the results generated by the computational model, they were compared to concentration values measured under experimental conditions. For this purpose, the metabolites concentration values presented in scientific publications Table  on the TThe results presented in Table The observed discrepancies in the metabolite ranges compared to laboratory data are a significant aspect to address in our research. In order to develop our model, we relied on data obtained from diverse literature sources. It is important to acknowledge that the measurements reported in the literature exhibit considerable variability across different studies and sources. This variability arises from factors such as variations in laboratory setups, measurement techniques, experimental conditions, and potential inter-individual differences. It is crucial to recognize that the data we employed from the literature may not necessarily represent dynamic or steady-state biological measurements. Rather, these measurements often represent snapshots of metabolite concentrations taken under specific experimental conditions that may not precisely align with the steady-state conditions assumed in our model. Consequently, inherent discrepancies can arise between the measured values and the simulated results due to these variations in experimental setups. These factors highlight the need to carefully consider and address the limitations and sources of variability when interpreting and comparing our model outputs with laboratory data.The results of the sensitivity analysis are presented in Table The change in activity of individual pathways, clearly depends on changes in glucose concentration. During the simulation run, the model strives to achieve the concentration values presented in the literature, while taking care to maintain the stability of the obtained results. We realize that the concentration of glucose in the cell under real conditions is maintained at a relatively constant level, such as through glycogenolysis or gluconeogenesis. However, due to the complexity and number of connections between biologically active molecules, the presented model does not take into account the maintenance of glucose at a constant level. By designing the model in this way, a change in the activity of the pathways is highlighted, changing the source of acetyl-CoA used in the TCA cycle. The presented results indicate the stability of the system, which is dependent on the concentration of glucose in the cell. It is also reflected in the sensitivity analysis. For each measured substrate, 90 percent of scores landed in close proximity to 1.0, thus implying the model’s robustness on changes in the starting values.This paper introduces a comprehensive model of interconnected metabolic pathways, utilizing queueing theory, with the added benefit of being able to conduct real-time calculations that are not excessively complex. The experiment can be run on a regular desktop computer, as it does not require significant computing power. By examining glucose as a case study, the study illustrated that following carbohydrate depletion, the cell shifts its metabolic activity towards alternative sources of cellular energy, such as beta-oxidation of fatty acids . These sources provide the necessary acetyl-CoA for energy conversion in the TCA cycle.In our analysis, it is important to acknowledge that while the majority of TCA metabolites exhibited Z-scores within two standard deviations of the estimated mean, Metabolic modeling plays a crucial role in bridging the gap between theoretical understanding and practical implementations in the field of biology. The ultimate aim of metabolic modeling is to provide insights that can guide the development of effective therapeutic approaches for metabolic disorders. By simulating and analyzing the intricate metabolic pathways within cells, we can unravel the underlying mechanisms and identify potential targets for intervention.In this context, the queueing methodology utilized in our study offers distinct advantages over traditional methods such as ODEs and FBA. While ODEs assume continuous and deterministic behavior, the queueing methodology embraces the discrete and stochastic nature of biochemical reactions, providing a more realistic representation of cellular processes. By capturing the inherent variability and fluctuations in metabolic networks, the queueing methodology allows for a deeper understanding of the dynamic behavior and robustness of biological systems.One key advantage of the queueing methodology is its ability to account for queueing delays and waiting times, which are essential factors in cellular processes. These delays reflect the finite capacity of cellular resources and the time required for reactants to interact and traverse various metabolic steps. By considering queueing phenomena, our methodology enables the investigation of how delays impact metabolic fluxes, reaction rates, and overall system behavior. Additionally, the queueing methodology offers unique insights into emergent properties and system-level behaviors that are challenging to capture using other methods. The inherent stochasticity and variability incorporated through the queueing approach allow for the exploration of rare events, transient behaviors, and non-equilibrium phenomena. This capability is particularly relevant in studying metabolic diseases, where small perturbations or rare events can have significant consequences for cellular function and overall health. Furthermore, the queueing methodology facilitates real-time tracking of metabolite concentrations, enabling dynamic simulations that closely mirror the temporal aspects of cellular metabolism. This temporal resolution provides a more comprehensive understanding of metabolic changes and their implications for cellular function.By highlighting these distinctive features of the queueing methodology, we emphasize its potential in generating insights that cannot be obtained through traditional approaches like ODEs and FBA. The utilization of queueing theory enriches the toolbox of metabolic modeling, expanding the possibilities for practical applications in therapeutic development, personalized medicine, and precision interventions for metabolic disorders.40. These conditions have garnered significant attention from researchers due to the rising prevalence of metabolic disorders and their impact on health42. While regulatory pathways typically maintain metabolite concentrations within narrow bounds43, individual metabolite levels can vary among individuals and deviate from established norms. An example of altered metabolism is found in cancer44, where a process known as metabolic reprogramming occurs. Cancer cells exhibit a shift in energy utilization, bypassing the citric acid cycle in mitochondria and relying heavily on glycolysis, followed by lactate fermentation in the cytosol45.Metabolic changes are observed in various diseases, including metabolic disorders such as diabetes and obesity, as well as in the aging process9. Studies have demonstrated reduced activity of the citric acid cycle in the brains of affected individuals46. One potential therapeutic approach for neurodegenerative diseases involves targeting the mitochondria and the citric acid cycle to improve their function. This can be achieved through various strategies, including increasing the levels of citric acid cycle enzymes such as citrate synthase or utilizing drugs that target specific enzymes within the cycle. Conversely, another approach involves reducing citric acid cycle activity by inhibiting enzymes, such as isocitrate dehydrogenase, which can help mitigate the production of reactive oxygen species (ROS) within mitochondria and reduce associated cellular damage47. Although these approaches are experimental, they hold promise for slowing disease progression and potentially ameliorating symptoms of neurodegenerative diseases. It is important to note that further research is needed to fully comprehend the therapeutic benefits of targeting the citric acid cycle in these conditions.In neurodegenerative diseases like Alzheimer’s and Parkinson’s disease, mounting evidence suggests that mitochondrial dysfunction plays a pivotal role in disease development and progression48, or the impact of an unbalanced diet on the development of metabolism-related diseases49. The information they contain is extremely valuable and provides a better understanding of metabolic disorders. The purpose of our work, however, was to focus on the changes in metabolism in relation to glucose concentration at the cellular level. By combining these different types of studies, a more comprehensive understanding of metabolism and related processes such as aging can be achieved. Computational modeling of metabolic pathways also holds the potential to expedite the development of effective therapeutic approaches for alleviating metabolic disorders.To date, most scientific publications have focused on modeling macronutrient balance. These studies were focused on different dietary states, so-called intermediate fasting or semi-starvation18, thus reducing the likelihood of the aforementioned scenario. The presented outcomes demonstrate that the model is useful and appropriate for simulations of alterations in metabolite concentrations with high precision. In the future, we plan to refine the model and continue this research with the objective of creating an application that allows users to input their measured parameters and receive simulation outcomes for the entered values.There are several limitations to the presented model. Although it is a complex model that includes 68 reactions, it does not take into account numerous other reactions in which the metabolites are involved. The impact of these unaccounted reactions was evaluated using GA see "". AnotheOur model is intentionally designed to be generic, incorporating data from various sources, tissues, and organisms due to the limitations in obtaining comprehensive and tissue-specific data from a single organism. However, we recognize the importance of tissue or cell type-specific applications in addressing specific biological questions. The modularity and flexibility of our model allow for the integration of tissue or cell type-specific data in future studies, which can enhance the relevance and applicability of our model to specific biological systems. By leveraging the power of queueing theory in conjunction with more precise and targeted data, we can achieve improved accuracy and gain deeper insights into tissue-specific metabolic dynamics. While our current study focuses on the broader implications of metabolic modeling and the advantages of queueing theory, we appreciate the reviewer’s comment as it highlights an important direction for future research, which can further enhance the biological relevance and applicability of our model.50 such as in MATLAB. Furthermore, ODE models assume well-mixed conditions and neglect the spatial organization and heterogeneity commonly found in biological systems. However, spatial effects can significantly impact the dynamics of biochemical reactions. Alternative simulation methods, such as partial differential equations (PDEs) or spatial stochastic simulations, take into account the spatial aspects and may yield more accurate results for certain biological phenomena. In addition, ODE models heavily rely on precise knowledge of model parameters, including reaction rate constants and initial conditions. Yet, in many biological systems, these parameters are uncertain and can vary across individuals or experimental conditions. The presence of parameter uncertainty introduces variability and can affect the accuracy of ODE simulations. Alternative approaches like Bayesian inference or sensitivity analysis can help address parameter uncertainty and provide more robust predictions. Another consideration is the computational efficiency of ODE simulations. As mentioned earlier, ODEs can accumulate errors and become computationally demanding, especially for large-scale models or long simulation times. This computational burden restricts the exploration of complex biological systems or extensive parameter sweeps. To overcome these limitations, approximate or alternative simulation methods such as network-free methods or reduced-order modeling can offer more computationally efficient alternatives while still capturing essential dynamics. Moreover, certain biological systems exhibit emergent phenomena, which arise from collective interactions at the system level rather than being solely determined by individual molecular components. ODE models, focusing on the behavior of individual components, may fail to accurately capture these emergent properties. Other modeling techniques such as network models, agent-based modeling, or machine learning approaches can better capture these emergent behaviors and complex system-level dynamics. Considering these factors can provide researchers with a more comprehensive understanding of the limitations of ODEs in biological simulations. Exploring alternative modeling approaches that better suit the specific characteristics of the biological system under investigation will contribute to more accurate and insightful simulations.While ordinary differential equations (ODEs) have been widely used in computational modeling of biological processes, there are several factors to consider that suggest they may not be the ideal method for biological simulations. One important limitation is that ODEs are deterministic in nature, failing to accurately capture the inherent stochasticity often observed in biological systems. These systems exhibit discrete and random molecular interactions, which are better represented by stochastic simulation methods such as the Gillespie algorithm or agent-based modeling. In addition, negative results can occur in the course of calculations, requiring the use of non-negative ODE solvers52. By assuming a steady-state condition, where the rates of production and consumption of metabolites within the network are balanced, FBA optimizes an objective function, typically biomass production, while considering mass balance and reaction constraints.Another approach used in the computational biology studies is flux balance analysis (FBA). FBA is a computational method used to study and analyze the metabolic capabilities of biological systems, particularly metabolic networks53. However, FBA does have certain limitations. It assumes a steady-state condition, disregarding the temporal dynamics of metabolic networks. This means it cannot capture transient behavior or time-dependent responses of biochemical reactions, limiting its applicability in certain biological processes.FBA offers several advantages in computational biology studies. Firstly, it demonstrates predictive power by computing the optimal flux distribution that maximizes the production of a specific metabolite or biomass. This enables researchers to make inferences about the metabolic capabilities of an organism under different conditions. Furthermore, FBA is suitable for high-throughput analysis, as it can handle large-scale metabolic networks. It can explore the behavior of thousands of reactions simultaneously, providing a comprehensive understanding of cellular metabolism. This makes it particularly useful for analyzing genome-scale metabolic models and conducting extensive studies. The constraint-based framework utilized by FBA simplifies the representation of complex biochemical networks. By relying on stoichiometric constraints, thermodynamic constraints, and steady-state assumptions, FBA becomes computationally efficient and mathematically tractable. This allows researchers to model and analyze metabolic networks in a practical mannerMoreover, FBA relies on several simplifying assumptions that may not hold true in all biological contexts. For instance, it assumes the absence of regulatory mechanisms and optimality of growth. These assumptions can limit the ability of FBA to capture the full complexity of cellular processes and may lead to deviations from real-world observations. Additionally, the accuracy of FBA predictions heavily relies on the completeness and accuracy of the metabolic network model used. Our knowledge of metabolic networks is still incomplete, and the absence of certain reactions or pathways in the model can affect the accuracy of FBA predictions.In summary, FBA is a powerful computational tool for analyzing metabolic networks. It offers predictive capabilities, high-throughput analysis, and integration with experimental data. However, researchers should consider FBA’s assumptions about steady-state conditions, simplified representations of cellular processes, and its inability to capture temporal dynamics. FBA finds extensive application in metabolic engineering, drug target identification, and understanding disease metabolism in computational biology studies.However, it is important to acknowledge that the methods mentioned above are not without limitations, which prompted us to explore the application of a queueing theory-based approach. Biochemical reactions occur in living organisms in an orderly fashion, and for this reason queueing theory seems well suited for use in such simulation-computing studies. The optimized model has low computational complexity and it is possible to track changes in metabolite concentrations in real time. In addition, using queueing theory, the nature of the simulation is closer to reality, because there is no possibility for negative results to occur, just as in a cell, metabolites cannot reach negative concentrations. Thus, there is no need for artificially forcing non-negative solutions as is the case with ODEs.The scheme of using queueing theory to model metabolite concentrations is shown in Fig. 54.Various metabolic pathways, which are incorporated in the presented model can be mimicked by a composition of interconnected queues based on the Michaelis-Menten equations. The flow of metabolite concentration from one queue to another is sequential, so that a decrease in concentration in one queue will cause an increase in the next queue. Thus, a network of interrelated queues can be equivalent to a set of differential equationsThe utilization of queueing theory as the foundation for our metabolic simulation model aims to capture the stochastic Markovian processes that represent variations in metabolite concentrations. To obtain the average change in concentration, we average the results from multiple simulation runs. At the core of this stochastic model are the Michaelis-Menten kinetic equations, which describe the relationship between substrate-product pairs and reaction velocities.By representing a network of interconnected queues and digitizing the concentrations It is important to note that we adopt a finite time increment, mentclass2pt{minimTo ensure the accuracy of the simulation, it is crucial to carefully select the simulation time step, entclass1pt{minimaHowever, it is not necessary for both the simulation time step, entclass1pt{minimaentclass1pt{minimaIn recognition of the stochastic nature of chemical reactions, wherein reaction rates can vary under different environmental conditions, it is possible to introduce randomness by adding Gaussian (or other) noise to the kinetic constants used for computing values of 16. The reaction probability ranges from 0 to 1, and the reaction speed is considered a macroscopic representation of numerous microscopic reactions, resulting in the conversion of metabolites. The forward and reverse reaction velocities determine whether a metabolite increases or decreases. The probabilities of concentration gain and loss for each metabolite are correlated with the accumulation or increase in concentration of other metabolites. By adopting this approach, we have developed a self-regulating and stochastic model that integrates multiple metabolic pathways. The outcomes of the Michaelis-Menten equations can be interpreted as the arrival frequency and service rate in Poisson processes, with service times modeled using an exponential distribution (the time gaps between two consecutive output events). These suppositions align with traditional queueing theory methods. As a result, the count of arrivals in a specific time period The reaction velocity serves as a macroscopic representation of numerous microscopic reactions, determining the frequency of reaction occurrence and its connection to the probabilities of increasing or decreasing specific substances. By utilizing these probabilities, we achieve a self-regulating and stochastic process that accurately simulates the behavior of biochemical pathways. The Michaelis-Menten kinetic equations calculate the probability of a reaction occurring based on substrate and product quantities, as well as kinetic constants and the duration of the time interval. These equations provide insights into the arrival and service rates in Poisson processes, where the arrival rate represents the probability of substance production, and the service rate represents the probability of substance consumption. The service time, which represents the interval between consecutive output events, is modeled using an exponential distribution. These assumptions align with classical queueing theory approaches, establishing a framework that integrates probabilities of increasing and decreasing substrates. This enables us to simulate biochemical pathways in a stochastic and self-regulating manner. In our model, the probability of a reaction occurring is determined by the Michaelis-Menten kinetic equations, where the concentration of metabolite-substrate and the kinetic constants play crucial roles. Each Michaelis-Menten equation is associated with a specific substrate and influences whether a reaction occurs at a given time point(t)τ Eq. :3\documek arrivals in the interval . In such a case, enzyme kinetics data on the second metabolite of the pair were used17. In the study presented here, such a situation occurred twice, when describing kinetic reactions involving isocitrate and cis-aconitate as well as succinyl-CoA and succinate, which are the metabolites of TCA cycle. To model such a complex metabolic network, it was necessary to establish a specific, rigid framework and scope of model coverage. The influence of cellular processes that are not directly included in the kinetic equations, such as the flow of a metabolite between compartments of a cell, was finetuned using a genetic algorithm (GA)17.It is assumed that all concentration values are sampled from Gaussian distribution specific to the type of examined concentration. The distributions were estimated using maximum log likelihood estimationons Eqs. :6\docume18. This procedure was intended to allow combining the reactions of pathways whose computational values of individual reactions can differ markedly. The GA plays a crucial role in our study by optimizing the parameter values within the ranges reported in the literature. It is important to note that these parameter values can vary significantly between different studies and cell types. In order to achieve system stability and ensure consistency with experimental values, the GA searches for parameter values that allow the model to approximate the observed behavior. By employing the GA, we aim to find parameter values that not only make the system stable but also provide results that are consistent or approximate to experimental values. The algorithm iteratively explores the parameter space, evaluating different combinations of parameter values, and selecting those that best align with the experimental data.The equations were supplemented with coefficients selected using a GA. The choice of the algorithm was made arbitrarily, due to its effectiveness in previous similar studies that have been conductedThe loss function was calculated with the use of ‘chromosomes’ that consist of two parameters: (1) metabolite’s concentration described in the literature and (2) a current optimization stage of the simulations. There are one hundred ’chromosomes’ in the population, each of which is a potential solution for the table of kinetic constants. Evaluation of the ‘chromosome’ involves using its ‘genes’ as the values of constants parametrizing Michaelis-Menten equations. In this process, the simulation time series is generated.The resulting time series is sampled at fixed time stamps in order to compare simulated results with real-life experiments results registered in the literature. The loss function quantifying fitness of the ‘chromosomes’ is the sum of squares of the distances of the sampled points from simulation time series to the literature results Eq. .8\documeX - vector of substrate concentrations described by a literature,The loss function is designed to guide the GA to identify a ‘chromosome’ with a table of kinetic constants that leads to stable concentrations of products and minimizes the distance between initial values and stable points, which generates computational results that are closest to those obtained in laboratory measurements. Evaluating one ’chromosome’ entails running a simulation using its set of genes as the table of kinetic constants. The simulation function returns the values of substrate concentrations at each second. This table is used by the equation to determine the ’chromosome’s’ score. The function calculates the average vector of the last 100 recordings and computes the absolute difference with the initial simulation concentrations. In the final step, the average of the differences is calculated. The ’chromosome’ that minimizes this function is selected as the optimal table of kinetic constant values. The evaluation of each ’chromosome’ is done by simulating the model for the first hour. There are 100 ’chromosomes’ in the population at each step of optimization, and only the 10 sets of constants that minimize the fitness function are selected for reproduction. The reproductive algorithm is a variation of the standard crossover with an additional mechanism to prevent finding a trivial solution to minimize the loss function problem, which is to zero the probability of every reaction. The main disadvantage of the fitness function described above is the existence of a trivial solution for its minimization problem. If the ’chromosome’ contains only zeros, then no reaction would occur, so the settling points of concentrations of products in the model would have the same values as initial concentrations, thus finding a global minimum. To prevent the GA from converging to this solution, the reproduction mechanism requires that each reaction at The resulting simulations of the trained model were subjected to the variance-based sensitivity analysis. It is used to analyze the sensitivity of a model’s output to changes in the input variables. It is based on the idea that the variance of the output of a model can be used to measure the model’s sensitivity to changes in the input variables Eq. :9\documeV(Y) - variance of signal Y,Y generated using input value j.Y represents a set of values of one substrate at the end of each simulation. Each value is a result of a simulation conducted using specific starting values denoted as j. The sensitivity analysis was conducted for each substrate making the cell’s measurable state.In this paper, Supplementary Information.


Although numerous studies support a dose–effect relationship between Endocrine disruptors (EDs) and the progression and malignancy of tumors, the impact of a chronic exposure to non-lethal concentrations of EDs in cancer remains unknown. More specifically, a number of studies have reported the impact of Aldrin on a variety of cancer types, including prostate cancer. In previous studies, we demonstrated the induction of the malignant phenotype in DU145 prostate cancer (PCa) cells after a chronic exposure to Aldrin (an ED). Proteins are pivotal in the regulation and control of a variety of cellular processes. However, the mechanisms responsible for the impact of ED on PCa and the role of proteins in this process are not yet well understood. Here, two complementary computational approaches have been employed to investigate the molecular processes underlying the acquisition of malignancy in prostate cancer. First, the metabolic reprogramming associated with the chronic exposure to Aldrin in DU145 cells was studied by integrating transcriptomics and metabolomics via constraint-based metabolic modeling. Second, gene set enrichment analysis was applied to determine (i) altered regulatory pathways and (ii) the correlation between changes in the transcriptomic profile of Aldrin-exposed cells and tumor progression in various types of cancer. Experimental validation confirmed predictions revealing a disruption in metabolic and regulatory pathways. This alteration results in the modification of protein levels crucial in regulating triacylglyceride/cholesterol, linked to the malignant phenotype observed in Aldrin-exposed cells. Prostate cancer (PCa) is the most common type of cancer and a second leading cause of cancer deaths in the male population. Almost one million new cases are diagnosed globally per year, imposing a high burden on healthcare systems worldwide ,2.Similarly to numerous other types of cancer, prostate cancer has also been linked to particular environmental exposures. It is widely accepted that environmental factors play a significant role in tumor initiation, progression, and phenotype. In this sense, a number of studies describe a dose–effect relationship between endocrine disruptors (EDs) and the onset and progression of prostate cancer (PCa). These compounds can disrupt the endocrine system by mimicking the effect of certain hormones which alters the cancer metabolism, enhancing tumor progression and malignancy ,4. More Thus, to fully understand the metabolic processes involved in a complex and multifaceted disease such as cancer, it is crucial to take a global perspective. This requires an integrated approach that considers the entire metabolic network, as well as the cross-talk with regulatory mechanisms.In this context, genome-scale metabolic models (GEMs) have emerged as a potential solution to decipher the complexity of the molecular mechanisms underlying cancer within the framework of systems biology ,10. ThisWhile GEMs allow for a comprehensive understanding of the metabolic network’s activity in a given condition , they are not suitable to study the dysregulated gene regulatory and signaling pathways that contribute to the abnormal tumoral metabolism, and thus lack the ability to provide a more comprehensive understanding of the molecular mechanisms involved. In this context, gene set enrichment analysis (GSEA)  proves tThis study represents a first approach in the integration of multi-omics data, leveraging two powerful and complementary systems biology methods, GEMs and GSEA, to unveil the molecular mechanisms underlying the gain of malignancy in PCa due to the chronic exposure to non-lethal concentrations of Aldrin, using the well-established DU145 PCa cell line as a cellular model.Here, we have integrated metabolomic, lipidomic, transcriptomic and literature-based data a by applSecond, the entire gene expression dataset of Aldrin-exposed and non-exposed cells was compared with the curated gene signatures associated with different cellular mechanisms d. As resHMGCoA, that are consistent with the previously reported enhanced malignant phenotype associated with the chronic exposure to Aldrin in prostate cancer cells. This method presents a high potential as it allows for the study of the crucial role that proteins play in human diseases through the integration and analysis of various omics data.The multi-level computational analysis unveiled the molecular mechanisms involving both metabolic and gene regulatory processes, including the dysregulation of The proposed approach offers a comprehensive understanding of intricate and multifaceted diseases, as demonstrated by the current study. It has the potential to be extrapolated to other human diseases in both clinical and environmental settings.2 at 37 °C.DU145 prostate cancer cells were obtained from the American Type Culture Collection. The Aldrin, cell culture media, and reagents were obtained from Merk . DU145 cells were cultured in an RPMI 1640 medium supplemented with 10% heat-inactivated fetal bovine serum, 100 μg/mL of streptomycin, and 100 U/mL of penicillin. The cell culture was grown in an incubator humidified with 5% of COThe DU145 PCa cells were exposed to sub-lethal concentrations of Aldrin (not affecting cell growth) for 50 days (Aldrin-exposed), while the control condition was carried out for the same period in Aldrin-free media (non-exposed), as described in Bedia et al.’s 2015 study . After 5Transcriptomics: for the transcriptomic analysis, the Aldrin-exposed and non-exposed DU145 cells were harvested at 85% confluence using a rubber scraper into 2 mL of ice-cold PBS. The cells were centrifuged at 1300 rpm for 3 min at 4 °C and were washed twice with cold PBS. The NucleoSpin RNA kit  was used to extract the total RNA . The AgiMetabolomics: for metabolomics, cells and culture media were used for the analysis. The cell media was collected in 1.5 mL tubes, centrifuged, and the supernatants were lyophilized. The cells for lipidomics and metabolomics were harvested using a rubber scraper into 2 mL of ice-cold PBS. Next, the cells were centrifuged for 3 min at 1300 rpm and 4 °C and were washed twice with cold PBS.13C D-Glucose standard . The mixture was vortexed vigorously, sonicated for 5 min, and centrifuged for 10 min at 15,000 rpm. The supernatant was transferred to another tube and solvent was evaporated under N2 stream. Next, the samples were resuspended in 150 μL of methanol, centrifugated again 10 min at 15,000 rpm, and 100 μL was transferred to glass vials for injection. For quantitative purposes, homemade standard mix solutions of metabolites  at different concentrations ranging from 2.5 to 20 ppm were prepared in methanol.For metabolite extraction, 1 mL of 90% chloroform/methanol mixture 1:9 in water was added to the cell pellet or media dried samples. This mixture was fortified with 500 pmol −1 and the injection volume was 5 μL. The Exactive Orbitrap mass spectrometer  with heated electrospray (HESI) as an ionization source was used. HESI was used separately in positive and negative mode and metabolites were fragmented in HCD collision cell by alternating the MS scans of the precursor ions and all ion fragmentation (AIF) scans. Mass spectra acquisition was conducted in profile mode at a resolution of 50,000 full width half maximum (FWHM) at m/z 200. The following parameters were used: a sheath gas flow rate of 45 arbitrary units (a.u.); an electrospray voltage of 3.0 kV; an auxiliary gas flow rate of 10 a.u.; and a heated capillary temperature of 300 °C. The range of the full scan mass range was set between m/z 80 and m/z 1000. A normalized collision energy (NCE) of 25 eV was used to perform the AIF. Raw data were exported to a cdf format using the Excalibur file converter tool .Chromatographic separations were carried on an the Accela UHPLC system  using a hydrophilic interaction liquid chromatography (HILIC) column  from Tosoh Bioscience  at room temperature. Two solvents were used to perform the elution gradient: acetonitrile (A) and 5 mM of ammonium acetate adjusted to pH 5.5 with acetic acid (B). Solvents A and B were mixed as follows: 0–8 min, linear gradient from 25 to 30% B; 8–10 min, from 30 to 60% B; 10–12 min, 60% B; 12–14 min, back from 60% to 25% B; and from 14 to 20 min, 25% B. The mobile phase flow rate was set to 0.15 mL·minm/z features detected in each chromatographic run. Data were normalized by the number of cells and the amount of internal standard in each sample. Only the lipids and metabolites present in the GEM and that could be detected under the conducted metabolomics/lipidomics analytical procedure were quantified using the appropriate calibration curves. The annotation of metabolites and lipids was performed by exact mass matching in Human Metabolome Database [The cdf files from metabolomics and lipidomics were subjected to the ROI procedure  to extraDatabase  and LipiDatabase  online dDatabase ,29,30. TIn this study, we have used one of the most widely used reconstructions of the human metabolism  as a plaEnabling GEM for lipidomic data integration: the intracellular lipidomic profiles of Aldrin-exposed and non-exposed DU145 cells were measured at two time points within the exponential growth phase (at 0 and 5 h). Since these measurements correspond to the whole-cell extracts/lysates, the contribution of each cellular compartment defined in the model is unknown. Thus, in order to integrate the lipidomic data into our computational analysis, the metabolic model was expanded as follows: (i) first an additional boundary compartment was defined, along with the corresponding boundary metabolites that encompass all the measured lipids present in multiple intracellular compartments ; (ii) subsequently, the transport reactions between intracellular lipids and their corresponding boundary lipids were established. (iii) In addition, a sink reaction was introduced for each boundary lipid and, (iv) finally, a sink reaction was defined for the measured lipids that are restricted to a single intra-cellular compartment. This expanded GEM includes a boundary compartment accounting for all the measured lipids annotated in the metabolic model. Both exchange reactions associated with boundary lipids and sink reactions enabled the integration of the lipidomic data in the model-driven analysis in the form of constraints.Model reduction: in order to reduce the computational time necessary to perform the analysis, the metabolic model (Recon2.2)  was reduBefore the metabolomics network reconstruction can be used to compute its properties, an important step must be taken in which the network reconstruction is mathematically represented. This conversion translates the reconstructed network into a chemically accurate mathematical format, the stoichiometric S matrix that becomes the basis for the genome-scale model. In the S matrix, the reactions are in the columns and the metabolites in the rows. Each metabolite’s entry has its stoichiometric coefficient in the corresponding reaction. The stoichiometric matrix describes the quantitative relations between metabolites through the metabolic reactions and the steady-state assumption imposes flux balance constraints on the network, ensuring that the overall amount of any compound being produced is equal to the overall amount being consumed. The next step in FBA analysis is to define the objective function, usually the biomass production. The biomass production represents the rate at which metabolic compounds are converted into biomass constituents such as nucleic acids, proteins, and lipids. The objective of biomass production is mathematically represented by a global biomass reaction that becomes an extra column of coefficients in the stoichiometric matrix.Once imposed on a network reconstruction, these balances and bounds define a space of allowable flux distributions in a network describing the possible rates at which every metabolite can be produced/consumed in the network. Here, the data integration plays an important part, in which FBA is able to perform simulations under different conditions by altering the constraints of the model.The integration of biological information from different “omics” into a metabolic reconstruction analysis allows to further constraint the space of feasible solutions and provides a metabolic flux profile specific to a particular event, condition, or environment. GEMs encompass all known metabolic reactions that are encoded by an organism’s genome. Therefore, they serve as an ideal platform for integrating a diverse range of omics data, including transcriptomic and metabolic data. In this work, transcriptomic metabolomic and lipidomic data have been integrated in a metabolic network reconstruction analysis as follows.Transcriptomic data integration into GEMs: gene expression profiles can be mapped onto a GEM via gene–protein–reaction associations (GPR). These associations enable each reaction to be connected to single or multiple genes associated with proteins/enzymes linked to a reaction. Gene expression levels can be utilized to infer metabolic reaction activity states via GPRs. This enables the development of a metabolic flux profile that accurately defines the phenotype associated with a specific gene expression profile.H- and lowly RL-expressed reactions.The transcriptomic data were integrated by applying the iMAT algorithm, which incorporates gene expression data into a GEM via GPRs to predict global metabolic flux activity . This apThis information was used to formulate a mixed integer linear problem (MILP) , which iv is the flux vector and S is a stoichiometric matrix. In Equation (3), maximum and minimum allowable flux is defined for each reaction by setting lower and upper flux bounds . For each highly expressed reaction, the Boolean variables +y and −y represent whether the reaction is active  or inactive . For each lowly expressed reaction, a Boolean variable x representing whether a reaction is inactive or active  is defined. A reaction associated with a highly expressed gene reaction is considered to be active if its predicted metabolic flux above or below the positive (ε) or negative (−ε) thresholds, respectively (Equations (4) and (5), respectively). A lowly expressed reaction is considered inactive if it does not carry a flux that is greater than 0 in either direction (Equation (6)). The optimization maximizes the number of reactions that exhibit similar levels of activity as their expression state.In Equation (1), a MILP is represented which maximizes the number of reactions whose activity is consistent with their expression state. The mass balance constraint is enforced in Equation (2), where This approach considers the mRNA levels as clues for the likelihood that the enzyme in question carries a metabolic flux in its associated reaction(s), and then solves a constraint-based modeling optimization problem (in this case a MILP) to find a steady-state metabolic flux distribution by assigning permissible flux ranges to all the reactions in the network consistent with their expression state. As a final result, the iMAT algorithm provides a steady-state flux profile that maximizes the number of reactions associated with highly expressed genes and the number of inactive reactions associated with lowly expressed genes, while the thermodynamic and stoichiometric constraints embedded into the model are satisfied.Metabolomic and lipidomic data integration: endo- and exometabolomics and lipidomic sampling and measurements were conducted after 50 days of exposure and once again after 5 h. Thus, the metabolomic/lipidomic dataset considers two time points with triplicate sample measurements , allowinHere, ub and lb are the upper and lower boundaries, respectively, while c0 is the average concentration of a specie measured in triplicate samples at time zero and c5 the average concentration of the same species measured in triplicate samples after 5 h. Additionally, Sd0 is a standard deviation of triplicate data at time zero, while Sd5 is a standard deviation of triplicate data at 5 h.The metabolomic and lipidomic data were integrated as an exchange reaction of the lower and upper bounds into our metabolic network reconstruction analysis by applying the COBRA toolbox function ‘changeRxnBounds’ ,23.This study utilizes an optimization method to determine the optimal values of system variables that maximize a particular objective function while satisfying certain constraints. In this case, the variables are the computed metabolic fluxes, and the objective function of the iMat algorithm is to maximize the similarity between the activity state of the metabolic network and the gene expression profile. In other words, it aims to maximize the number of active reactions associated with highly expressed genes and the inactive reactions associated with lowly expressed genes. Although a single solution is provided, there are multiple optimal solutions that define alternative combinations of metabolic fluxes. To account for the non-uniqueness of solutions and identify those reactions that are unambiguously active or inactive across all the solutions, a sensitivity analysis was conducted. Furthermore, the algorithm requires a predetermined set of thresholds to specify genes that are highly and lowly expressed. This could potentially offer an arbitrary aspect to the analysis. Here, a robustness analysis was conducted by performing a sensitivity analysis using various thresholds. Only reactions that maintained consistent activity states across the different thresholds are considered. Below a more detailed explanation of the sensitivity and robustness analysis is provided:Sensitivity analysis: in gene expression data integration analysis, an optimal solution can be achieved by maximizing the objective function. However, it should be noted that this optimal solution may not be unique, meaning there could be multiple solutions with the same objective function value. Thus, a further exploration is necessary to determine the most suitable solution for the specific needs of the analysis. This is achieved by applying a sensitivity analysis . The proRobustness analysis: the algorithm used to integrate the gene expression levels into GEMs uses upper and lower thresholds to define highly or lowly expressed genes, while genes with expression values falling within these are considered moderately expressed. It raises the necessity to perform a robustness analysis in order to demonstrate the lack of dependency of a model’s predictions to the thresholds used in the analysis. In order to determine the robustness of the model’s predictions, a sensitivity analysis using the following pairs of thresholds defining the upper and lower boundaries, respectively, was conducted: percentiles 30th and 70th, 33rd and 66th, and 40th and 60th. Thereby, a set of reactions unambiguously predicted to be either active or inactive across the different thresholds was defined.A more detailed explanation of the overall methodology including the sensitivity, robustness, and significance analysis can be found in Marin de Mas et al. (2018) .Transcriptomic expression data for Aldrin-exposed and non-exposed DU145 cells (GSE132063) were analyzed using the list of curated gene signatures (Molecular Signatures Database V5.1). Enrichment in the gene set was considered significant for FDR values ≤ 0.1, NES > 1.5 and a leading edge signal > 50%.Next, the resulting relevant gene sets were evaluated in order to identify the genes contributing to the significance of the gene set.Finally, in order to establish a comprehensive understanding of the underlying mechanisms driving different metabolic activities between conditions, a literature-based analysis was conducted. This analysis sought to connect the relevant genes identified through the GSEA analysis with the metabolic reactions that exhibit different activity states between conditions, as determined by the model-driven analysis. This analysis provided a more holistic perspective on the functional implications of the observed differences.A metabolic gene set with a significant differential expression between Aldrin-exposed and non-exposed DU145 cells was generated by applying the multivariate discriminant PLS-DA method ,36,37. RsiRNA experiments: siRNA sequences  against INSIG2 (L-021039) and non-targeting sequences (D-001810) and the transfection reagent DharmaFECT1 were purchased from Dharmacon Thermo Scientific .Western blot: cells were harvested by trypsinization, centrifuged, and washed twice with PBS 1X. Next, cell lysed was performed using mammalian lysis buffer 1X  together with the cocktail protein inhibitor 1X . The proteins in cell lysates were quantified using the BCA assay (Thermo Scientific), and 50 mg of proteins per sample was resolved by 10% SDS-PAGE. Next, PVDF membranes  were used to transfer the proteins. Membranes were blocked with TBS 1X containing 0.1% Tween 20 and probed with the antibodies to INSIG2 , HMGCR , and β-actin . Membranes were developed using the chemiluminescent signal detection kit ECL Prime Western Blotting detection reagent  and visualized using a LICOR C-DiGit blot scanner. The relative quantification of the relative Western blot band intensity quantification was determined using the software Image Studio Lite version 5.0 ; values were normalized to those of β-actin, and differences between the samples were calculated.Our study aimed to explore the metabolic mechanisms that contribute to the promotion of a malignant phenotype in DU145 prostate cancer cells following a chronic exposure to non-lethal concentrations of Aldrin. The multi-level approach utilized in this study underwent several phases, which are detailed upon further below.First, the experimentally measured metabolomic, lipidomic, and transcriptomic data were pre-processed for integration into a Genome-scale metabolic reconstruction analysis. Next, a PLS-DA analysis revealed the relevant compounds that were able to discriminate between treated and non-treated samples. As a result, 167 metabolites and 82 lipids were selected and mapped into the GEM . The genNext, by applying the iMat algorithm , the metp < 0.01, which further validates the reliability of the computational model’s predictions.In order to validate the reliability of the model’s predictions, the consumption/secretion rates of 55 metabolites not integrated previously in the analysis were compared with the predicted values from the model, and Fisher’s test was used to determine the statistical significance of the results see . This anThe comparative analysis of flux profiles of 7696 reactions in the model revealed the reactions with differential activity states between Aldrin-exposed and non-exposed conditions . Here, tp-value [To assess how the thresholds impact the inference of the metabolic pathway’s activity state, we conducted Fisher’s exact test for each pathway across different threshold values and applied a corrected Bonferroni p-value  to analyThe computational analysis unveiled marked differences in the activity state of DU145 prostate cancer cells in response to the chronic exposure to Aldrin. Aldrin-exposed cells were predicted to have a more active metabolism with a higher number of active reactions. More specifically, transport reactions through the cell membrane or to peroxisome, Golgi apparatus, or endoplasmic reticulum were found to be more active in this group. Other relevant metabolic pathways that were predicted to be active in Aldrin-exposed cells were the metabolism of eicosanoids, glycerophospholipids, folate, N-glycan synthesis, NAD, and some amino acids such as valine, leucine, isoleucine, thiamine, and glutathione. On the other hand, the cholesterol metabolism was predicted to be enhanced in DU145 PCa non-exposed cells a. This fA further analysis comparing the activity state of the metabolic reactions between Aldrin-exposed and non-exposed cells was performed. To identify consistent differences between the conditions, the metabolic reactions were analyzed for their activity states across various thresholds. This allowed for the identification of reactions that showed significant changes in activity levels between conditions and remained consistent across the different threshold values. From this analysis, two main reactions were found to be active in Aldrin-exposed cells and inactive in non-exposed cells. One of the reactions corresponds to the beta-oxidation of Arachidoyl-CoA into Acetyl-CoA . This mePrevious analysis integrates both metabolomic and transcriptomic data. However, since the transcriptomic data are integrated through the gene–protein–reaction associations described in GEMs, only the expression levels of metabolic genes (genes encoding enzymes) can be used. In this sense, GSEA complements the GEM-based analysis by enabling the analysis of the full transcriptomic dataset. More specifically, GSEA was used to identify gene regulatory mechanisms and signaling pathways strongly correlated with the genes deferentially expressed between conditions . To thisIn order to unveil the molecular mechanism underlying the gain of malignancy in DU145 PCa cells associated with the chronic exposure to Aldrin, the results extracted from the GEM-based analysis and from the GSEA method were combined. These two complementary approaches describe two different processes occurring at two different layers within the cell: (i). metabolisms formalized as a genome-scale constraint-based metabolic network model, and (ii). gene regulation analyzed by applying GSEA. In order to study the cross-talk between the metabolism and gene regulation, literature-based data were also integrated in the analysis. This information was used to link the metabolic alterations predicted by the GEM-based analysis with the mechanisms and relevant genes defined in the GSEA method. Based on the analysis, it was discovered that the two genes, PLIN2 and INSIG2, play a significant role in regulating the metabolism. The research predicted an increase in the expression of these genes in cells exposed to Aldrin as opposed to those that were not exposed c. PLIN2 The rise in cholesterol levels was found to be more significant in cells exposed to Aldrin as compared to those that were not exposed when INSIG2 was inhibited. This observation suggests that the inhibition of HMGCoA through INSIG2 is stronger in Aldrin-exposed cells under basal conditions. In addition, the relative HMGCoA increment was higher in Aldrin-exposed cells than in non-exposed cells when INSIG2 was inhibited . This also indicates a stronger inhibition of HMGCoA in Aldrin-exposed cells in basal conditions. Finally, the cell viability decreased less in non-exposed cells when INSIG2 was inhibited, showing that non-exposed SiRNA-INIG2 cells were closer to the basal conditions where the INSIG2 expression is lower than in the Aldrin-exposed group . TherefoMore specifically, PLIN2 and INSIG2 were predicted to be upregulated via hypoxia and the lack of SOX4-induced inhibition. PLIN2 enhances arachidonoyl-CoA degradation by activating beta oxidation, which in turn reduces the inhibitory effects of this compound on INSIG2. The up-regulation of INSIG2 increases HMGCoA protein ubiquitination. This is the limiting reaction in the cholesterol synthesis pathway which is consistent with measured lower cholesterol levels in Aldrin-exposed cells e. The inTo investigate whether the alterations observed in Aldrin-exposed cells at the transcriptomic level are linked to tumor progression and metastasis, we employed the GSEA methodology. First, we utilized the PLS-DA method to identify a set of differentially expressed genes between cells exposed to Aldrin and those that were not. Specifically, we selected genes with a VIP score of 1.5 or greater. Using this approach, we identified a set of 101 genes that exhibited significant changes in expression levels .The gene set associated with the malignant phenotypic changes observed in Aldrin-exposed cells was significantly enriched, concomitant with eight types of human tumors. Thus, the transcriptomic signature of the malignant phenotype found in Aldrin-exposed cells correlates well with the malignant progression of eight other types of human tumors retrieved from the Cancer Genome Atlas (TCGA) database , includiA holistic analysis of molecular alterations triggering complex and multi-factorial diseases such as cancer enables us to increase our understanding of how environmental perturbations affect tumor progression and malignancy acquisition. Exploring the overall processes that occur within a cell is essential when investigating the effects of a prolonged exposure to widespread environmental pollutants such as EDs at non-lethal concentrations.Bedia et al.  reportedDeveloping a comprehensive understanding of the mechanisms involved in the acquisition of malignancy is crucial for the development of more effective therapeutic interventions. It is also important for improving our ability to assess and regulate environmental pollutants, such as specifically Aldrin and other EDs linked to cancer development.Systems biology tools, such as genome-scale metabolic network modeling using constraint-based methods (GEM-based CBM) and gene set enrichment analysis (GSEA), provide a powerful means to integrate multiple layers of the hierarchical mechanistic structure that govern cellular processes. By capturing the complexity and dynamics of biological systems, these tools enable us to analyze them in a comprehensive and holistic manner.Our study sought to delve into the metabolic mechanisms that contribute to the enhanced malignant phenotype resulting from a prolonged exposure to non-lethal concentrations of Aldrin in DU145 PCa cells. To this aim, two complementary approaches combining model-driven and data-driven techniques were applied. This strategy facilitated the investigation of metabolic dysregulations from a mechanistic point of view by means of constraint-based modeling techniques while finding potential gene regulatory or signaling mechanisms by applying GSEA.Finally, a comprehensive literature review was conducted to investigate the cross-talk between metabolic and gene regulatory processes and establish a single mechanism explaining the increased likelihood of developing malignancy in cases of a chronic exposure to Aldrin in PCa. Experimental validations confirmed these findings, while extensive support from the literature further reinforced them.Our multi-level approach has enabled us to identify various alterations in important metabolic pathways. Specifically, changes were detected in eicosanoids, glycerophospholipids, folate, N-glycan synthesis, NAD, as well as key amino acids such as valine, leucine, isoleucine, thiamine, and glutathione metabolism. Thus, tumorigenic activity has been reported in some eicosanoid metabolism intermediates ; it is aFurthermore, we employed PLS-DA analysis to identify the specific set of genes associated with a chronic exposure to Aldrin. We then utilized GSEA to compare this set of genes with the TGCA database. We discovered a strong correlation between the genes modified in DU-145 prostate cancer cells following a chronic exposure to Aldrin and tumor progression and metastasis in up to eight distinct cancer types. This implies that this approach has the potential to be utilized in other cancer types.In this study, we have identified a potential cellular mechanism underlying the gain of malignancy associated with the chronic exposure to Aldrin in PCa cells. This approach allows the study of different levels in the cell hierarchy, such as genomic, proteomic, or metabolomic, as well as the cross-talk between them. Here, the gene dysregulation discovered through gene set enrichment analysis (GSEA) has a significant influence on the levels of HMGCoA protein. This, in turn, directly impacts the metabolism and affects the ratio TAG/Cholesterol as well as the gene regulatory levels. These findings align with the alterations observed in the GEM analysis and are consistent with the results reported by Bedia et al. .Metabolic reactions require enzymatic catalysis to achieve the appropriate rate of activity due to their proximity to thermodynamic equilibrium. Enzymatic levels and activity are tightly regulated through intricate gene regulatory pathways and metabolic processes. This underscores the crucial involvement of proteins in regulating the metabolism and their contribution to diseases characterized by dysregulated metabolic functions.Factors that affect enzyme activity include the reactants, substrate, inhibitors, pH, temperature, and different proteoforms . The rolIn this work, we have studied different levels of the cell hierarchical mechanisms by applying two different and complementary approaches, CBM and GSEA, to analyze gene regulation and metabolism using multiple omics data, including transcriptomic, metabolomic, lipidomic, and literature-based data.Our computational analysis revealed that the dysregulation of the HMGCoA enzyme by the SOX4 gene through INSIG2 in cells exposed to Aldrin altered the ratio of TAG/cholesterol, leading to an enhanced malignant phenotype in these cells. This method provides a holistic perspective that enables a more complete understanding of cellular processes.Furthermore, we also established a correlation between the observed changes in the gene expression profile of Aldrin in DU145 cells after a chronic exposure to Aldrin and the progression of the tumor in different cancer types, providing crucial insights into the underlying mechanisms governing cancer onset and development.In the present work, two main goals have been achieved. First, we developed a comprehensive computational pipeline to investigate the hierarchical molecular mechanisms occurring within a cell’s various layers. This computational approach presents a significant conceptual shift in the way we study the metabolism and gene regulation. Rather than viewing the metabolism as the final product of gene regulation, this study proposes a bi-directional cross-talk between the metabolic, proteomic, and gene regulatory levels, where changes in either of them can affect the others. Second, a unified mechanism underlying the enhanced malignancy in PCa following a chronic exposure to Aldrin has been described.The approach presented here offers a comprehensive tool for studying the molecular mechanisms that drive metabolic reprogramming in response to a chronic exposure to sub-lethal concentrations of pollutants. This not only allows for a more holistic understanding of the underlying processes but deepens our knowledge of the intricate interplay between these systems and opens up new avenues for research and discovery, with potential clinical and environmental applications.


E. coli. The MetPath algorithm provides a useful tool for metabolic network-based statistical analyses of high-throughput data.Pathway analysis is ubiquitous in biological data analysis due to the ability to integrate small simultaneous changes in functionally related components. While pathways are often defined based on either manual curation or network topological properties, an attractive alternative is to generate pathways around specific functions, in which metabolism can be defined as the production and consumption of specific metabolites. In this work, we present an algorithm, termed MetPath, that calculates pathways for condition-specific production and consumption of specific metabolites. We demonstrate that these pathways have several useful properties. Pathways calculated in this manner (1) take into account the condition-specific metabolic role of a gene product, (2) are localized around defined metabolic functions, and (3) quantitatively weigh the importance of expression to a function based on the flux contribution of the gene product. We demonstrate how these pathways elucidate network interactions between genes across different growth conditions and between cell types. Furthermore, the calculated pathways compare favorably to manually curated pathways in predicting the expression correlation between genes. To facilitate the use of these pathways, we have generated a large compendium of pathways under different growth conditions for  High-throughput molecular data such as genome-scale gene expression measurements are ubiquitous; however, this abundance of data comes with the challenge of efficiently extracting biological knowledge from the data. It is largely this challenge that has catalyzed the rise of systems biology . As cellMetabolic pathways have historically been manually defined based on an intuitive understanding of the function of particular sets of enzymes. Classical pathway examples such as glycolysis and the TCA cycle appear in textbooks and pathway databases and have well-accepted structure and content ,8. HowevThe first challenge in designing a pathway-based data analysis is to obtain a functional definition of a pathway, which we propose can be defined as a set of genes working together to achieve a function. In a metabolic network, function can be defined succinctly in terms of the production and degradation of metabolites. Using these definitions, we can define a metabolic pathway as a sequential set of enzymes that is involved in the production or degradation of a metabolite under a defined metabolic flux state. This definition inherently assumes that the flux directions through the network are defined, but in fact, these are not fixed across growth conditions. A set of reactions may be involved in the consumption of a metabolite under one condition and the production of the metabolite under another condition, for example, the relationship between the reactions involving glycolysis and glucose under glycolytic compared to gluconeogenic conditions. Thus, the functional interpretation of changes in enzyme levels depends on the flux directions in the network. Furthermore, the relative importance of enzyme changes depends on the contribution of a pathway to a metabolic function. As an example, the pathways of glycolysis and glycogen synthesis both consume glucose. However, glycolysis operates at a rate greatly exceeding that of glycogen synthesis. Thus, a 10% increase in expression of glycolytic enzymes presumably would have a much greater impact on glucose turnover than a 10% decrease in glycogen synthesis. We can use this type of analysis to examine how gene expression changes in these pathways in order to identify coordinated expression shifts that serve specific metabolic functions in terms of increased or decreased capacity for the production or degradation of specific metabolites.E. coli K12 MG1655. We examined the performance of MetPath using two case studies in E. coli, looking at the tryptophan pathway during aerobic growth on glucose with and without tryptophan supplementation as well as glucose growth under the condition of aerobic–anaerobic shift. Finally, we looked at the ability of MetPath pathways to interpret cell-specific differences in gene expression, specifically examining neurotransmitter pathway expression in human neural cell subtypes based on single-cell transcriptomics data.In this work, we developed a constraint-based modeling method, termed MetPath, to calculate condition-specific production and consumption pathways for the purpose of differential analysis of metabolic expression data. Using metabolic modeling, we calculated metabolic pathways for specific flux conditions by defining weighted, context-specific pathways in terms of metabolic functions, i.e., production/consumption of specific metabolites. We compared this method qualitatively and quantitatively to existing pathway databases, specifically the KEGG database, and found that the MetPath pathways show a higher intergene correlation within the same pathways across different conditions in We define the functions of a metabolic network as the production and degradation of metabolites . Utilizilb and vub are the lower and upper bounds of the reaction fluxes, respectively; c is the linear objective vector, which is typically the biomass reaction but can be changed by the user; and F is a diagonal scaling matrix used as a secondary flux length objective and is set to an arbitrarily small value of 10−6. The flux state is calculated by minimizing the total length of the flux vector subjected to constraints, and represents the principle that a cell will try to achieve its metabolic function using as little enzyme expenditure as possible to minimize precursor costs. The purpose of this flux state estimation is to identify possible reaction directions and relative pathway flux values, given the established literature on aspects such as metabolite synthesis versus de novo uptake and relative energy production between glycolysis and beta-oxidation. These relative weightings and pathway directions add important information when calculating production and degradation pathways, as they lend context to the interpretation of a gene expression change related to the potential for production and degradation of different metabolites in the network.To calculate state-specific production and degradation pathways, we first calculate the estimated metabolic state. We solve the quadratic programming flux balance analysis problem of a metabolic model constrained by the estimated metabolite uptakes as follows: Then, using this estimated flux state, we calculate weighted production and degradation pathways for each metabolite as follows: First, reactions that carry flux in the estimated flux state are extracted as zero-flux reactions do not contribute to pathways under the selected condition. Then, a desired pathway length D is defined. For each metabolite, reactions that are within the distance D by means of a forward traversal (in the case of degradation) or reverse traversal (in the case of production) of the flux-carrying network are identified. For non-cofactor metabolites, cofactors are first removed from the network before traversal to prevent spurious connections. The production or degradation pathway subnetworks are then extracted and mass balanced by adding compensating input and output reactions for unbalanced metabolites. These subnetworks are then broken down into elementary modes using a published algorithm . These eTo construct perturbed production and degradation scores for each metabolite, we first define reaction fold-change scores by averaging the fold change for all genes that are involved in the catalysis of each reaction as follows: The reaction weightings w are assigned according to the reaction fluxes within each pathway and are normalized by the sum of those fluxes. These final production and degradation scores for each metabolite represent the expression change in reactions involved in the production and degradation of the metabolite, respectively, weighted by the degree of contribution of each reaction to the metabolite production/degradation in the estimated flux state.E. coli cultures. With this purpose, we simulated 64 different growing conditions. Starting from what we considered to be the standard growing conditions , we obtained 20 different cultures, each characterized by a supplement of a single amino acid  automatically calculated, (2) intuitively defined, (3) condition specific, and (4) numerically tractable. We believe that this particular set of traits distinguishes the obtained pathways from existing pathway sets and enables the algorithm to be broadly useful across new data sets and organisms.


Clostridium autoethanogenum at different biomass‐specific growth rates show that elevated ethanol production occurs at increasing growth rates. The increased allocation of electrons towards ethanol at higher growth rates strongly suggests that C. autoethanogenum employs a form of overflow metabolism to cope with high dissolved CO concentrations. We argue that this overflow branch enables acetogens to efficiently use CO at highly variable substrate influxes by increasing the conversion rate almost instantaneously when required to remove toxic substrate and promote growth. In this perspective, we will address the case study of C. autoethanogenum grown solely on CO and syngas mixtures to assess how it employs acetate reduction to ethanol as a form of overflow metabolism.Carboxydotrophic metabolism is gaining interest due to its applications in gas fermentation technology, enabling the conversion of carbon monoxide to fuels and commodities. Acetogenic carboxydotrophs play a central role in current gas fermentation processes. In contrast to other energy‐rich microbial substrates, CO is highly toxic, which makes it a challenging substrate to utilize. Instantaneous scavenging of CO upon entering the cell is required to mitigate its toxicity. Experiments conducted with  Microorganisms have a pivotal role in the production of biofuels. Here, we explain how microorganisms that consume (waste) carbon monoxide can be pushed to produce bioethanol. This co0′ = −520 mV) that can be directly transferred to ferredoxin. Reduced ferredoxin can, among other things, be used for the generation of a cation gradient using the Rnf or Ech complex  is typically associated with highly variable substrate influxes and it has been recognized that ethanol production in gas‐fermenting organisms is controlled by redox and thermodynamics rather than gene or protein expression levels  reported for CODH2 of Carboxydothermus hydrogenoformans are used  was assumed to be 1 picogram. The following parameters were used to calculate the CODH activity:In this calculation, kinetic parameters and molecular weight  and dx=Dmembrane. Then:The diffusion flux can be calculated using Fick's law:C. autoethanogenum is an acetogen that employs the Wood–Ljungdahl pathway for carbon fixation. This pathway leads to the production of acetate and ethanol as main products. In light of the objective to convert waste gas into (bio)fuels, substantial efforts have been made to shift the product spectrum of C. autoethanogenum and closely related species towards ethanol production, for example, through medium optimization, changing the gas composition and metabolic engineering  and the independent reduction of acetate to ethanol using CO is the shorter, inefficient strategy (YATP/CO = 0.27 mol/molCO)  Figure , Table 1Independent CO‐limited continuous cultivation studies show that at higher dilution rates and consequently higher growth rates (μ = D), more ethanol is produced Figure . The dilC. autoethanogenum:The catabolic flux is increasingly diverted to an energy‐inefficient pathway at increasing dilution rates Figure No significant changes in transcriptome or proteome of the central carbon metabolism, including acetate conversion to ethanol, are observed at different growth rates, but genes involved in biosynthesis are upregulated.Thus, the key characteristics of overflow metabolism are distinguished in continuous cultures of 2 by summing the biomass‐specific CO and H2 rates to an overall electron uptake rate (qelectron) also resulted in an apparent linear correlation between qelectron and qEtOH  concentrations keep increasing with increasing agitation  low extracellular acetate concentrations. If the theory applies, the microorganisms will sustain lower biomass‐specific CO uptake rates than when acetate is available in abundance.To provide a full picture of overflow metabolism in 2 via the CODH also results in production of reduced ferredoxin. The rate of oxidation of CO therefore directly influences the redox state of the cell, as ferredoxin needs to be re‐oxidized at an equally high rate to maintain cellular homeostasis. The primary mechanism for ferredoxin reoxidation in carboxydotrophic acetogens is through the generation of a cation gradient via the Rnf complex or similar enzymes. This bifurcating enzyme transfers the electrons from reduced ferredoxin to NAD+, generating NADH that again must be re‐oxidized. NADH oxidation through acetate formation requires 12 enzymatic steps ; formal analysis ; investigation ; visualization ; writing – original draft (lead); writing – review and editing . Martijn Diender: Formal analysis ; investigation ; writing – original draft ; writing – review and editing . Diana Z. Sousa: Funding acquisition ; supervision ; writing – review and editing . Robbert Kleerebezem: Funding acquisition ; supervision ; writing – review and editing .The authors declare no conflict of interest. This can be added.This study was funded by Nederlandse Organisatie voor Wetenschappelijk Onderzoek .