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Physiology-based large-scale kinetic model of liver metabolism

The epidemic increase of non-alcoholic fatty liver diseases (NAFLD) requires a deeper understanding of the regulatory circuits controlling the response of liver metabolism to nutritional challenges, medical drugs, and genetic enzyme variants. As in vivo studies of human liver metabolism are encumbered with serious ethical and technical issues, we developed a comprehensive biochemistry-based kinetic model of the central liver metabolism including the regulation of enzyme activities by their reactants, allosteric effectors, and hormone-dependent phosphorylation (HEPATOKIN1). The utility of the model for basic research and applications in medicine and pharmacology is illustrated by simulating diurnal variations of the metabolic state of the liver at various perturbations caused by nutritional challenges (alcohol), drugs (valproate), and inherited enzyme disorders (galactosemia) [1]. The model can be used to functionally interpret proteomics data by scaling maximal enzyme activities. We applied it to highlight individual differences in the metabolic functions of normal hepatocytes and malignant liver cells (adenoma and hepatocellular carcinoma) in patients and animal models [1,2,3] and to investigate zonal differences in the central metabolism of hepatocytes [4].
Publications:
- Berndt N, Bulik S, Wallach I, Wünsch T, König M, Stockmann M, Meierhofer D, Holzhütter HG. HEPATOKIN1 is a biochemistry-based model of liver metabolism for applications in medicine and pharmacology. Nat Commun. 2018 Jun 19;9(1):2386.
- Berndt N*, Egners A*, Mastrobuoni G*, Vvedenskaya O, Fragoulis A, Dugourd A, Bulik S, Pietzke M, Bielow C, van Gassel R, Damink SWO, Erdem M, Saez-Rodriguez J, Holzhütter HG*, Kempa S*, Cramer T*. Kinetic modelling of quantitative proteome data predicts metabolic reprogramming of liver cancer. Br J Cancer. 2020 Jan;122(2):233-244.
- Berndt N, Eckstein J, Heucke N, Wuensch T, Gajowski R, Stockmann M, Meierhofer D, Holzhütter HG. Metabolic heterogeneity of human hepatocellular carcinoma: implications for personalized pharmacological treatment. FEBS J. 2021 Apr;288(7):2332-2346.
- Berndt N*, Kolbe E*, Gajowski R, Eckstein J, Ott F, Meierhofer D, Holzhütter HG*, Matz-Soja M*. Functional consequences of metabolic zonation in murine livers: New insights for an old story. Hepatology. 2021 Feb;73(2):795-810.
Project funding: Systems Biology Programs "Virtual Liver" (grant no. 0315741) and "LiSyM" (grant no. 31L0057), as well as the e:Bio (Module I) project "HepatomaSys" (grant no. 0316172A), all sponsored by the German Federal Ministry of Education and Research (BMBF).
Cooperation partners:
- Hermann-Georg Holzhütter (Charité, Institute of Biochemistry, Computational Systems Biochemistry Group)
- Martin Stockmann (Charité, Department of General, Visceral and Transplantation Surgery, Workgroup for the Liver)
- David Meierhofer (Max Planck Institute of Molecular Genetics, Mass Spectrometry Facility)
- Madlen Matz-Soja (Leipzig University, Institute of Biochemistry, Working Group Matz-Soja)
- Thorsten Cramer (RWTH Aachen University, Department of General, Visceral and Transplantation Surgery, Molecular Tumor Biology)
- Stefan Kempa (Max-Delbrück-Center for Molecular Medicine, Berlin Institute for Medical Systems Biology, Proteomics and Metabolomics Platform)
Multi-scale modeling of liver tissue

The capacity of the liver to convert the metabolic input received from the incoming portal and arterial blood into the metabolic output of the outgoing venous blood has three major determinants: The intra-hepatic blood flow, the transport of metabolites between blood vessels (sinusoids) and hepatocytes, and the metabolic capacity of hepatocytes. These determinants are not constant across the organ: Even in the normal organ, but much more pronounced in the fibrotic and cirrhotic liver, regional variability of the capillary blood pressure, tissue architecture, and the expression level of metabolic enzymes (‘metabolic zonation’) have been reported. Understanding how this variability may affect the regional metabolic capacity of the liver is important for the interpretation of functional liver tests and the planning of pharmacological and surgical interventions. The liver can be treated as an ensemble of a large number (more than a million) of sinusoidal tissue units (STUs), each composed of a single sinusoid surrounded by the space of Disse and a monolayer of hepatocytes. We develop spatio-temporal kinetic models of the STU and calculate the total metabolic output of the liver (arterio-venous glucose difference) by integration across the metabolic output of a sufficiently large number of representative STUs differing in their anatomical structure (thickness and length of the sinusoid, number and size of hepatocytes, etc.). Application of the model to the hepatic glucose metabolism provided the following major results: (i) At portal glucose concentrations between 6 to 8 mM, an intra-sinusoidal glucose cycle may occur, which is constituted by glucose producing periportal hepatocytes and glucose consuming pericentral hepatocytes. (ii) Regional variability of hepatic blood flow is higher than the corresponding regional variability of the metabolic output. (iii) A spatially resolved metabolic functiogram of the liver is constructed showing the metabolic activities in various liver regions in a time-resolved manner. The model suggests that variations of tissue parameters are equally important as variations of enzyme activities for the control of the arterio-venous glucose difference.
Publications:
- Berndt N, Horger MS, Bulik S, Holzhütter HG. A multiscale modelling approach to assess the impact of metabolic zonation and microperfusion on the hepatic carbohydrate metabolism. PLoS Comput Biol. 2018 Feb 15;14(2):e1006005.
- Berndt N, Holzhütter HG. Dynamic Metabolic Zonation of the Hepatic Glucose Metabolism Is Accomplished by Sinusoidal Plasma Gradients of Nutrients and Hormones. Front Physiol. 2018 Dec 12;9:1786.
Project funding: Systems Biology Programs "Virtual Liver" (grant no. 0315741) and "LiSyM" (grant no. 31L0057), as well as the e:Bio (Module I) project "HepatomaSys" (grant no.0316172A), all sponsored by the German Federal Ministry of Education and Research (BMBF)
Cooperation partners:
- Hermann-Georg Holzhütter (Charité, Institute of Biochemistry, Computational Systems Biochemistry Group)
- Marius Horger (University Hospital and Faculty of Medicine Tübingen, Department of Diagnostic and Interventional Radiology)
Multilayer control of cellular metabolism: hierarchical or democratic?

Adaptation of cellular metabolism to varying external conditions is brought about by regulated changes in the activity of enzymes and transporters. Hormone-dependent reversible enzyme phosphorylation and concentration changes of reactants and allosteric effectors are the major types of rapid kinetic enzyme regulation, whereas on longer time scales changes in protein abundance may also become operative. We used a comprehensive mathematical model of the hepatic glucose metabolism of rat hepatocytes to decipher the relative importance of different regulatory modes and their mutual interdependencies in the hepatic control of plasma glucose homeostasis.
Model simulations reveal significant differences in the capability of liver metabolism to counteract variations of plasma glucose in different physiological settings (starvation, ad libitum nutrient supply, diabetes). Changes in enzyme abundances adjust the metabolic output to the anticipated physiological demand but may turn into a regulatory disadvantage if sudden unexpected changes of the external conditions occur. Allosteric and hormonal control of enzyme activities allows the liver to assume a broad range of metabolic states and may even fully reverse flux changes resulting from changes in enzyme abundances alone. Metabolic control analysis reveals that – depending on the (patho)physiological condition – control of the hepatic glucose metabolism is mainly exerted by specific enzymes, which are differently controlled by alterations in enzyme abundance, reversible phosphorylation, and allosteric effects.
In hepatic glucose metabolism, regulation of enzyme activities by changes of reactants, allosteric effects, and reversible phosphorylation is equally important as changes in protein abundance of key regulatory enzymes.
Publication: Bulik S, Holzhütter HG, Berndt N. The relative importance of kinetic mechanisms and variable enzyme abundances for the regulation of hepatic glucose metabolism - insights from mathematical modeling. BMC Biol. 2016 Mar 2;14:15.
Project funding: Systems Biology Programs "Virtual Liver" (grant no. 0315741) and "LiSyM" (grant no. 31L0057), as well as the e:Bio (Module I) project "HepatomaSys" (grant no.0316172A), all sponsored by the German Federal Ministry of Education and Research (BMBF).
Cooperation partner: Hermann-Georg Holzhütter (Charité, Institute of Biochemistry, Computational Systems Biochemistry Group)
Integration of metabolism and signaling

The regulation of key reaction steps in mutually opposing pathways (e.g., glycolysis and gluconeogenesis, lipid synthesis and lipolysis) by hormone-dependent reversible enzyme phosphorylation represents an important regulatory principle to control the direction of the net flux [1]. The signaling part of the HEPATOKIN1 model [2] comprises the insulin- and glucagon-dependent regulation of key regulatory enzymes by reversible phosphorylation. The rate laws for these enzymes take into account that the phosphorylated and de-phosphorylated states of the enzyme possess differing maximal activities and kinetic properties. So far, we have used phenomenological mathematical functions to relate the enzyme’s phosphorylation state to the plasma concentrations of glucose [1,2]. In addition to the short-term regulation of metabolic enzymes, hormonal signaling is an important regulator of gene expression controlling variable protein abundance in physiological and pathological conditions [3].
To take better into account the mutual influence of the insulin, glucagon, and epinephrine signaling pathways under normal and pathophysiological conditions such as diabetes type 2, we plan in a future project to set up kinetic models, which describe the dynamic state of individual constituents (receptors, kinases, phosphatases) by ordinary differential equations. These models will include different cellular compartments (cell membrane, cytosol, mitochondria, and endoplasmic reticulum). This integrated metabolic-signaling model aims to predict the metabolic effects elicited by agonists and antagonists of the insulin, glucagon, and epinephrine receptors.
Publications:
- Bulik S, Holzhütter HG, Berndt N. The relative importance of kinetic mechanisms and variable enzyme abundances for the regulation of hepatic glucose metabolism - insights from mathematical modeling. BMC Biol. 2016 Mar 2;14:15.
- Berndt N, Bulik S, Wallach I, Wünsch T, König M, Stockmann M, Meierhofer D, Holzhütter HG. HEPATOKIN1 is a biochemistry-based model of liver metabolism for applications in medicine and pharmacology. Nat Commun. 2018 Jun 19;9(1):2386.
- Berndt N, Holzhütter HG. Dynamic Metabolic Zonation of the Hepatic Glucose Metabolism Is Accomplished by Sinusoidal Plasma Gradients of Nutrients and Hormones. Front Physiol. 2018 Dec 12;9:1786.
Project funding: Systems Biology Programs "Virtual Liver" (grant no. 0315741) and "LiSyM" (grant no. 31L0057), as well as the e:Bio (Module I) project "HepatomaSys" (grant no.0316172A), all sponsored by the German Federal Ministry of Education and Research (BMBF).
Cooperation partner: Hermann-Georg Holzhütter (Charité, Institute of Biochemistry, Computational Systems Biochemistry Group)
Hepatic lipid droplet metabolism

The liver responds to elevated plasma concentrations of free fatty acids (FFAs) with enhanced uptake and esterification of FFAs to triacylglycerol (TAG). This may result in massive hepatic TAG accumulation called fatty liver (steatosis hepatis), the first stage on the route towards more serious liver diseases, such as cirrhosis, fibrosis or hepatocellular carcinoma. In hepatocytes, the poor water-soluble TAG is packed in lipid droplets (LDs) serving as transient cellular deposit or lipoproteins transporting TAG and cholesterol esters to extra-hepatic tissues. The dynamics of these ‘organelles’ is controlled by a variety of regulatory surface proteins (RSPs). Knockdown or overexpression of RSPs may significantly affect the total number and size distribution of LDs. Intriguingly, a large cell-to-cell heterogeneity with respect to the number and size of LDs has been found in various cell types including hepatocytes. These findings suggest that the extent of cellular lipid accumulation is determined not only by the imbalance between lipid supply and utilization but also by variations in the expression of RSPs and metabolic enzymes. To better understand the relative regulatory impact of individual processes involved in the cellular TAG turnover, we developed a comprehensive kinetic model encompassing the pathways of the fatty acid and TAG metabolism and the main molecular processes governing the dynamics of LDs [1]. We are using the model to investigate LD size distributions in human hepatocytes under physiological and pathological conditions such as steatosis, fibrosis, cirrhosis or hepatocellular carcinoma [2].
Publications:
- Wallstab C, Eleftheriadou D, Schulz T, Damm G, Seehofer D, Borlak J, Holzhütter HG, Berndt N. A unifying mathematical model of lipid droplet metabolism reveals key molecular players in the development of hepatic steatosis. FEBS J. 2017 Oct;284(19):3245-3261.
- Berndt N, Eckstein J, Heucke N, Gajowski R, Stockmann M, Meierhofer D, Holzhütter HG. Characterization of Lipid and Lipid Droplet Metabolism in Human HCC. Cells. 2019 May 27;8(5):512.
Project funding: Graduate school "Computational Systems Biology" (GRK 1722) sponsored by the DFG (German Research Foundation) and the Systems Biology Program "LiSyM" sponsored by the German Federal Ministry of Education and Research (BMBF) (grant no. 31L0057) and the Max Planck Society.
Cooperation partners:
- Hermann-Georg Holzhütter (Charité, Institute of Biochemistry, Computational Systems Biochemistry Group)
- Georg Damm and Daniel Seehofer (University of Leipzig, Department of Hepatobiliary Surgery and Visceral Transplantation, Liver Regeneration Group)
- Jürgen Borlak (Hannover Medical School, Institute for Pharmaco- and Toxicogenomics)
- Martin Stockmann (Charité, Department of General, Visceral and Transplantation Surgery, Workgroup for the Liver)
- David Meierhofer (Max Planck Institute of Molecular Genetics, Mass Spectrometry Facility)
Metabolic alterations in hepatocellular carcinoma

Hepatocellular carcinoma (HCC) represents the fifth most common cancer and the third most common cause of cancer-related deaths in the world. The incidence of HCC in Europe and the United States is constantly rising, turning HCC into a pivotal threat to general health. Robust therapy resistance and very poor prognosis characterize HCC. Most cases of HCC develop on pre-existing chronic liver disease, but between 15% and 50% of HCCs develop in the absence of a known etiology of liver disease, and different lines of evidence identify nonalcoholic fatty liver disease as a possible relevant risk factor for HCC. The transformation of a normal liver cell (hepatocyte) to a tumor cell is accompanied by alterations of cellular metabolism and differs between cancer stages. In Berndt et al. 2018 [1], we showed how metabolic profiles differ between normal hepatocytes and malignant liver cells like adenoma and HCC. While previous metabolic studies of HCC have mainly focused on glucose metabolism (Warburg effect), less attention has been paid to tumor‐specific features of the lipid metabolism. We used protein intensity profiles of eleven human HCCs to parameterize tumor‐specific kinetic models of cellular lipid metabolism including formation, enlargement, and degradation of lipid droplets (LDs). Our analysis shows that LD metabolism in HCC is heterogeneous among individual tumors, however, functional and regulatory features are highly interdependent. Especially those HCCs that are characterized by a very active fatty acid metabolism comprise regulatory peculiarities that render them susceptible to selective targeting without affecting healthy tissue [2].
Metabolic alterations can serve as targets for diagnosis and cancer therapy. Due to the highly complex regulation of cellular metabolism, definite identification of metabolic pathway alterations remains challenging and requires sophisticated experimentation. Metabolic reprogramming is a characteristic feature of cancer cells, but there is no unique metabolic program for all tumors. We used comprehensive kinetic modeling of central carbon metabolism [1] to characterize metabolic reprogramming in murine liver cancer. Our systems biology approach establishes that combining cellular experimentation with computer simulations of physiology-based metabolic models enables a deeper understanding of deregulated energetics in cancer [3] and allows the in silico evaluation of treatment options. Translating this approach, we used protein intensity profiles of ten human HCCs and the adjacent noncancerous tissue to evaluate 18 metabolic functions related to carbohydrate, lipid, and nitrogen metabolism. We showed that while there was a general tendency among the tumors toward downregulated glucose uptake and glucose release, large inter-tumor variability exists. Our approach provides a comprehensive and quantitative characterization of HCC metabolism that may pave the way for a computational a priori assessment of pharmacological therapies targeting metabolic processes of HCC [4].
Publications:
- Berndt N, Bulik S, Wallach I, Wünsch T, König M, Stockmann M, Meierhofer D, Holzhütter HG. HEPATOKIN1 is a biochemistry-based model of liver metabolism for applications in medicine and pharmacology. Nat Commun. 2018 Jun 19;9(1):2386.
- Berndt N, Eckstein J, Heucke N, Gajowski R, Stockmann M, Meierhofer D, Holzhütter HG. Characterization of Lipid and Lipid Droplet Metabolism in Human HCC. Cells. 2019 May 27;8(5):512.
- Berndt N*, Egners A*, Mastrobuoni G*, Vvedenskaya O, Fragoulis A, Dugourd A, Bulik S, Pietzke M, Bielow C, van Gassel R, Damink SWO, Erdem M, Saez-Rodriguez J, Holzhütter HG*, Kempa S*, Cramer T*. Kinetic modelling of quantitative proteome data predicts metabolic reprogramming of liver cancer. Br J Cancer. 2020 Jan;122(2):233-244.
- Berndt N, Eckstein J, Heucke N, Wuensch T, Gajowski R, Stockmann M, Meierhofer D, Holzhütter HG. Metabolic heterogeneity of human hepatocellular carcinoma: implications for personalized pharmacological treatment. FEBS J. 2021 Apr;288(7):2332-2346.
Project funding: Systems Biology Programs "Virtual Liver" (grant no. 0315741) and "LiSyM" (grant no. 31L0057), as well as the e:Bio (Module I) project "HepatomaSys" (grant no.0316172A), all sponsored by the German Federal Ministry of Education and Research (BMBF).
Cooperation partners:
- Hermann-Georg Holzhütter (Charité, Institute of Biochemistry, Computational Systems Biochemistry Group)
- Martin Stockmann (Charité, Department of General, Visceral and Transplantation Surgery, Workgroup for the Liver)
- David Meierhofer (Max Planck Institute of Molecular Genetics, Mass Spectrometry Facility)
- Thorsten Cramer (RWTH Aachen University, Department of General, Visceral and Transplantation Surgery), Molecular Tumor Biology
- Stefan Kempa (Max-Delbrück-Center for Molecular Medicine, Berlin Institute for Medical Systems Biology, Proteomics and Metabolomics Platform)
Liver metabolism of adolescents with non-alcoholic fatty liver disease (NAFLD)

Non-alcoholic fatty liver disease (NAFLD) is the most common chronic liver disease in children and is associated with overweight and insulin resistance (IR). Almost nothing is known about in vivo alterations of liver metabolism in NAFLD, especially in the early stages of non-alcoholic steatohepatitis (NASH). Here, we used a complex mathematical model of liver metabolism to quantify the central hepatic metabolic functions of 71 children with biopsy-proven NAFLD. For each patient, a personalized model variant was generated based on enzyme abundances determined by mass spectroscopy. Our analysis revealed statistically significant alterations in the hepatic carbohydrate, lipid, and ammonia metabolism, which increased with the degree of obesity and severity of NAFLD. Histologic features of NASH and IR displayed opposing associations with changes in carbohydrate and lipid metabolism but synergistically decreased urea synthesis in favor of the increased release of glutamine, a driver of liver fibrosis. Taken together, our study reveals already significant alterations in the NASH liver of pediatric patients, which, however, are differently modulated by the simultaneous presence of IR.
Publication: Berndt N*, Hudert CA*, Eckstein J, Loddenkemper C, Henning S, Bufler P, Meierhofer D, Sack I, Wiegand S, Wallach I, Holzhütter HG. Alterations of Central Liver Metabolism of Pediatric Patients with Non-Alcoholic Fatty Liver Disease. Int J Mol Sci. 2022;23(19):11072.
Project funding: Systems Biology Program "LiSyM" (grant no. 31L0057) sponsored by the German Federal Ministry of Education and Research (BMBF).
Cooperation partners:
- Hermann-Georg Holzhütter (Charité, Institute of Biochemistry, Computational Systems Biochemistry Group)
- David Meierhofer (Max Planck Institute of Molecular Genetics, Mass Spectrometry Facility)
- Ingolf Sack (Charité, Institute for Radiology)
- Susanna Wiegand (Charité, Center for Chronically Sick Children)
- Christian Hudert & Philip Bufler (Charité, Department of Pediatrics, Division of Gastroenterology, Nephrology and Metabolic Medicine)
LiSyM-Cancer – DEEP-HCC – Metabolic phenotyping

Within the DEEP-HCC consortium, our goal is the detection of novel imaging biomarkers and potential targets for early hepatocellular carcinoma (HCC) detection and prevention. Focusing on early human HCC, our molecularly resolved kinetic models enable the metabolic functional interpretation of protein abundances. Based on proteomic data of tissue from different tumor zones and adjacent and non-cancerous tissue, we will generate personalized metabolic models of individual HCCs to 1) identify metabolic alterations in HCC, 2) differentiate metabolic alterations in different tumor zones, 3) provide functional molecular markers for metabolic alterations, and 4) identify potential targets suited as biomarkers or for intervention.
We will also explore the possibility to use transcriptomics for the generation of personalized metabolic models of early HCC. Finally, we will provide metabolic submodules to be used in tissue-scale spatial models of HCC.
Project funding: Systems Medicine Program LiSyM-Cancer – DEEP-HCC (grant no. 031L0258H) sponsored by the German Federal Ministry of Education and Research (BMBF).
Cooperation partners:
- Jochen Hampe (Medical Department 1, University Hospital Dresden)
- Madlen Matz-Soja (Leipzig University, Institute of Biochemistry, Working Group Matz-Soja)
- Jens Pietzsch (Helmholtz-Zentrum Dresden-Rossendorf, Radiopharmaceutical and Chemical Biology)
- Thorsten Cramer (RWTH Aachen University, Department of General, Visceral and Transplantation Surgery, Molecular Tumor Biology)
Earlier publications:
- Berndt N, Bulik S, Wallach I, Wünsch T, König M, Stockmann M, Meierhofer D, Holzhütter HG. HEPATOKIN1 is a biochemistry-based model of liver metabolism for applications in medicine and pharmacology. Nat Commun. 2018 Jun 19;9(1):2386.
- Berndt N, Eckstein J, Heucke N, Gajowski R, Stockmann M, Meierhofer D, Holzhütter HG. Characterization of Lipid and Lipid Droplet Metabolism in Human HCC. Cells. 2019 May 27;8(5):512.
- Berndt N*, Egners A*, Mastrobuoni G*, Vvedenskaya O, Fragoulis A, Dugourd A, Bulik S, Pietzke M, Bielow C, van Gassel R, Damink SWO, Erdem M, Saez-Rodriguez J, Holzhütter HG*, Kempa S*, Cramer T*. Kinetic modelling of quantitative proteome data predicts metabolic reprogramming of liver cancer. Br J Cancer. 2020 Jan;122(2):233-244.
- Berndt N, Eckstein J, Heucke N, Wuensch T, Gajowski R, Stockmann M, Meierhofer D, Holzhütter HG. Metabolic heterogeneity of human hepatocellular carcinoma: implications for personalized pharmacological treatment. FEBS J. 2021 Apr;288(7):2332-2346.