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Modeling of Metabolic Processes in the Liver

Physiology-based large-scale kinetic model of liver metabolism

Reaction scheme of the metabolic sub-model

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:

  1. 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.
  2. 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.
  3. 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.
  4. 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:

Multi-scale modeling of liver tissue

Schematic model representation. (A) Model of carbohydrate metabolism describing glycolysis, gluconeogenesis as well as glycogen synthesis and utilization. (B) Sinusoidal unit describing blood flow, nutrient and hormone distribution within the sinusoids.

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:

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: Marius Horger (University Hospital and Faculty of Medicine Tübingen, Department of Diagnostic and Interventional Radiology)

Multilayer control of cellular metabolism: hierarchical or democratic?

Schematic representation of the model of rat hepatocyte carbohydrate metabolism.

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).

Integration of metabolism and signaling

Exemplary interaction of signaling and metabolic pathways: Insulin and catecholamines activate their respective signaling pathways leading to the activation or inactivation of different regulatory metabolic enzymes through reversible phosphorylation/dephosphorylation, thereby modulating metabolic activity.

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 [1,2]. The signaling part of the HEPATOKIN1 model [3] 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 [2,3]. 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 [4].

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:

  1. König M., Bulik S. and Holzhütter HG. Quantifying the Contribution of the Liver to the Homeostasis of Plasma Glucose: A Detailed Kinetic Model of Hepatic Glucose Metabolism. PLoS Comput Biol. 2012;8(6):e1002577.
  2. 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.
  3. 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.
  4. 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).

Hepatic lipid droplet metabolism

Schematic representation of the processes included into the LD model.

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:

  1. 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.
  2. 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:

Membrane domain formation and lipid secretion into the bile

Liquid ordered (blue, red) and liquid disordered (dark blue, green) membrane domains with raft proteins (white) and non-raft proteins (black) of different sizes (4/3/2 nm radius).
Simulated (shadowed line) and experimental values (dots) of bile salt dependent secretion of cholesterol (left) an phospholipid (right) into the bile for wild type (blue) and Abcb4(+/-) knock out mice.

We developed a mathematical model of lateral diffusion of lipids and proteins in cellular membranes. The movement of lipids and proteins along the membrane surface is modeled as a movement on a triangular lattice, governed by nearest-neighbor interactions. The lipids may switch between two alternative states of ordering energy resulting in different mobilities. Minimizing the ordering energies results in the formation of liquid-ordered or liquid-disordered phase domains. The model also includes proteins of two different species that have a high affinity for either one of the two phases. The lipid and protein mobilities were parameterized using experimental data from different model membranes. The influence of protein size and density on the formation of lipid domains can be studied.  

Model simulations provided support for a budding mechanism of lipid transfer into the bile consisting of the bile-salt-dependent extraction of membrane patches from liquid disordered microdomains of the canalicular membrane. We applied the model to the canalicular membrane of hepatocytes to study how changes in the lipid composition and protein density may influence the size distribution of microdomains and the efficiency of lipid extraction into the bile. Our simulations recapitulate the dependence of lipid secretion from the bile salt secretion measured in mouse models.

Publications:

Project funding: SFB 618 "Theoretical Biology: Robustness, Modularity and Evolutionary Design of Living Systems" (grant no. 5485271) and the Research Training Group (Graduiertenkolleg 1772) "Computational Systems Biology", both sponsored by the DFG (German Research Foundation) as well as the Systems Biology Program "LiSyM" (grant no. 31L0057), sponsored by the German Federal Ministry of Education and Research (BMBF).

Cooperation partner: Frank Lammert (Saarland University Medical Center and Saarland University Faculty of Medicine, Gastroenterology and Endocrinology

Improvement of the liver function breath test

Schematic representation of the procedures of the 2DOB test and the LiMAx test

The principle of dynamic liver function breath tests is founded on the administration of a 13C-labeled drug and subsequent monitoring of 13CO2 in the breath, quantified as time series delta over natural baseline 13CO2 (DOB) liberated from the drug during hepatic CYP-dependent detoxification. One confounding factor limiting the diagnostic value of such tests is that only a fraction of the liberated 13CO2 is immediately exhaled while another fraction is taken up by body compartments from which it returns with delay to the plasma.

We established an improved variant of the LiMAx liver function breath test, which promises a significantly higher specificity and selectivity compared to the conventional test. For the elimination of its limiting factor, we extended the breath test by applying a defined dose of 13C-labeled bicarbonate prior to the administration of the test drug (Methacetin®). Using compartment modeling, it was possible to separately determine the kinetic parameters determining the systemic CO2 distribution and the hepatic drug detoxification from the time-course of exhaled 13CO2. When applied to about 20 healthy volunteers and 20 patients with different types of liver diseases, the novel test yielded significantly better discrimination of healthy and diseased livers compared to the conventional LiMAx test [1].

Publications:

  1. Holzhütter HG, Wuensch T, Gajowski R, Berndt N, Bulik S, Meierhofer D, Stockmann M. A novel variant of the 13C-methacetin liver function breath test that eliminates the confounding effect of individual differences in systemic CO2 kinetics. Arch Toxicol. 2020 Feb;94(2):401-415.

Project funding: Systems Biology Programs "Virtual Liver" (grant no. 0315741) and "LiSyM" (grant no. 31L0057) sponsored by the German Federal Ministry of Education and Research (BMBF).

Cooperation partners:

Metabolic alterations in hepatocellular carcinoma

Using protein intensities obtained by quantitative proteomics of individual HCCs, we created personalized variants of the comprehensive kinetic model of liver metabolism (HEPATOKIN1) to assess the metabolic alterations and resulting treatment options for each tumor.

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:

  1. 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.
  2. 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.
  3. 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.
  4. 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:

Pediatric non-alcoholic fatty liver disease and steatohepatitis

Nogrady B. Childhood obesity: A growing concern. Nature. 2017 Nov 23;551(7681).

One focus of the BMBF sponsored LiSyM project was the comprehensive characterization of histological, biomechanical, and metabolic changes during the progression of pediatric patients with biopsy-proven non-alcoholic steatohepatitis (NASH). Liver ultrasound time-harmonic elastography was further advanced to allow a reliable assessment of the viscosity and stiffness of the liver in very obese patients [1]. This improved the prediction of fibrosis grading from elastography data [2]. The model-based analysis correctly predicted the histologically assessed degree of steatosis and the relationship between insulin resistance (IR) and hepatic glucose metabolism. Importantly, NASH and IR had opposing effects on carbohydrate and lipid metabolism, but synergistically decrease urea synthesis in favor of the increased release of glutamine, a driver for the development of liver fibrosis [in preparation].

Other activities included the consideration of altered CYP activities in tumor tissue in preoperative volume determination [3], identification of SNP variants associated with pediatric non-alcoholic fatty liver disease (NAFLD) [4], and the development of a new score that correlates histologic features of pediatric NASH with elastography data [5].

Publications: 

  1. Hudert CA, Tzschätzsch H, Guo J, Rudolph B, Bläker H, Loddenkemper C, Luck W, Müller HP, Baumgart DC, Hamm B, Braun J, Holzhütter HG, Wiegand S, Sack I. US Time-Harmonic Elastography: Detection of Liver Fibrosis in Adolescents with Extreme Obesity with Nonalcoholic Fatty Liver Disease. Radiology. 2018 Jul;288(1):99-106. 
  2. Hudert CA, Tzschätzsch H, Rudolph B, Bläker H, Loddenkemper C, Müller HP, Henning S, Bufler P, Hamm B, Braun J, Holzhütter HG, Wiegand S, Sack I, Guo J. Tomoelastography for the Evaluation of Pediatric Nonalcoholic Fatty Liver Disease. Invest Radiol. 2019 Apr;54(4):198-203.
  3. Kalveram L, Schunck WH, Rothe M, Rudolph B, Loddenkemper C, Holzhütter HG, Henning S, Bufler P, Schulz M, Meierhofer D, Zhang IW, Weylandt KH, Wiegand S, Hudert CA. Regulation of the cytochrome P450 epoxyeicosanoid pathway is associated with distinct histologic features in pediatric non-alcoholic fatty liver disease. Prostaglandins Leukot Essent Fatty Acids. 2021 Jan;164:102229.
  4. Hudert CA, Selinski S, Rudolph B, Bläker H, Loddenkemper C, Thielhorn R, Berndt N, Golka K, Cadenas C, Reinders J, Henning S, Bufler P, Jansen PLM, Holzhütter HG, Meierhofer D, Hengstler JG, Wiegand S. Genetic determinants of steatosis and fibrosis progression in pediatric non-alcoholic fatty liver disease. Liver Int. 2019 Mar;39(3):540-556.
  5. Hudert CA, Tzschätzsch H, Rudolph B, Loddenkemper C, Holzhütter HG, Kalveram L, Wiegand S, Braun J, Sack I, Guo J. How histopathologic changes in pediatric nonalcoholic fatty liver disease influence in vivo liver stiffness. Acta Biomater. 2021 Jan 17;S1742-7061(21)00046-5. Online ahead of print.

Project funding: Systems Biology Program "LiSyM" (grant no. 31L0057) sponsored by the German Federal Ministry of Education and Research (BMBF).

Cooperation partners:

Modeling of Metabolic and Electrophysiological Processes in Neuronal Cells

Oxygen consumption rates in brain slices

Depth profiles of partial oxygen pressure (pO2) during three different activity states. (A) Representative sample traces of pO2 depth profiles in the absence of spiking (TTX, black trace), spontaneous network activity (SPON, dark gray trace), and cholinergically induced gamma oscillations (GAM, light gray trace). (B) Quantification of lowest pO2 values as determined during the three different activity states. (C) Quantification of oxygen consumption rate in the different activity states.

The brain is an organ with a high metabolic capacity, adapting energy utilization during different activity states of neuronal networks. To quantify energetic demand, we addressed this issue in area CA3 of hippocampal slice cultures under well-defined recording conditions using a 20% O2 gas mixture. We combined recordings of local field potential and interstitial partial oxygen pressure (pO2) during three different activity states, namely fast network oscillations in the gamma frequency band (30 to 100 Hz), spontaneous network activity, and absence of spiking (action potentials). Oxygen consumption rates were determined by pO2 depth profiles with high spatial resolution and a mathematical model that considers convective transport, diffusion, and activity-dependent consumption of oxygen. We show that: (1) Relative oxygen consumption rate during cholinergic gamma oscillations was 2.2-fold and 5.3-fold higher compared with spontaneous activity and absence of spiking, respectively. (2) Gamma oscillations were associated with a similarly large decrease in pO2 as observed previously with a 95% O2 gas mixture. (3) Sufficient oxygenation during fast network oscillations in vivo is ensured by the calculated critical radius of 30 to 40 mm around a capillary. We conclude that the structural and biophysical features of brain tissue permit variations in local oxygen consumption by a factor of about five [1].

Publications:

  1. Huchzermeyer C*, Berndt N*, Holzhütter HG*, Kann O*. Oxygen consumption rates during three different neuronal activity states in the hippocampal CA3 network. J Cereb Blood Flow Metab. 2013 Feb;33(2):263-71.

Project funding: Collaborative Research Center for "Theoretical Biology: Robustness, Modularity and Evolutionary Design of Living Systems" SFB 618 (grant no. 5485271) sponsored by the DFG (German Research Foundation).

Cooperation partners:

How NAD(P)H fluorescence mirrors neuronal energy metabolism

(A) Reactions and transport processes included in the single-cell kinetic model. (B) Schematic representation of the slice model used to simulate spatial oxygen gradients within a brain slice. (C) Schematic representation of the tissue model used to simulate in vivo NADH transients.

Imaging of the cellular fluorescence of the reduced form of nicotinamide adenine dinucleotide (phosphate) (NAD(P)H) is one of the few metabolic readouts that enable noninvasive and time-resolved monitoring of the functional status of mitochondria in neuronal tissues. Stimulation-induced transient changes in NAD(P)H fluorescence intensity frequently display a biphasic characteristic that is influenced by various molecular processes, e.g., intracellular calcium dynamics, tricarboxylic acid cycle activity, the malate–aspartate shuttle, the glycerol-3-phosphate shuttle, oxygen supply or ATP demand. To evaluate the relative impact of these processes, we developed and validated a detailed physiologic mathematical model of the energy metabolism of neuronal cells and used the model to simulate metabolic changes of single cells and tissue slices under different settings of stimulus-induced activity and varying nutritional supply of glucose, pyruvate or lactate [1]. Our computational approach reconciles different and sometimes even controversial experimental findings and improves our mechanistic understanding of the metabolic changes underlying live-cell NAD(P)H fluorescence transients. In a subsequent study, we investigated the energy metabolism underlying cortical information processing [2]. We concluded that gamma oscillations featuring high energetics require a hemodynamic response to match oxygen consumption of respiring mitochondria and that perisomatic inhibition significantly contributes to the brain energy budget. In summary, our data show that energy expenditure is strongly dependent on the neuronal network activity state and may reach critical levels during higher brain functions.

Publications:

  1. Berndt N, Kann O, Holzhütter HG. Physiology-based kinetic modeling of neuronal energy metabolism unravels the molecular basis of temporal NAD(P)H fluorescence profiles. J Cereb Blood Flow Metab. 2015 Sep;35(9):1494-506.
  2. Schneider J*, Berndt N*, Papageorgiou IE, Maurer J, Bulik S, Both M, Draguhn A, Holzhütter HG, Kann O. Local oxygen homeostasis during various neuronal network activity states in the mouse hippocampus. J Cereb Blood Flow Metab. 2019 May;39(5):859-873.

Project funding: The projects were in part funded by the German Systems Biology Program “Virtual Liver” (grant no. 0315741) sponsored by the German Federal Ministry of Education and Research (BMBF) and by the German Research Foundation (DFG) within the Collaborative Research Center (SFB) 1134.

Cooperation partner: Oliver Kann (Medical Faculty of Heidelberg, Institute of Physiology and Pathophysiology)

Metabolic alterations in neurodegenerative diseases

Schematic of the mathematical model of mitochondrial energy metabolism.

Steadily growing experimental evidence suggests that mitochondrial dysfunction plays a key role in the age-dependent impairment of nerve cells underlying several neurodegenerative diseases. Especially, reduced activity of brain α-ketoglutarate dehydrogenase complex (KGDHC), reduced activity of complex I of the respiratory chain (RC), and increased reactive oxygen species (ROS) production occur in several neurodegenerative diseases like Parkinson's disease and Alzheimer's disease. To understand the metabolic regulation underlying these experimental findings we developed and applied a detailed kinetic model of mitochondrial energy metabolism. Model simulations revealed a threshold-like decline of the ATP production rate at about 60% inhibition of KGDHC accompanied by a significant increase of the mitochondrial membrane potential. We also showed that the reduction state of those sites of the respiratory chain proposed to be involved in ROS production decreased with increasing degree of KGDHC inhibition suggesting a ROS-reducing effect of KGDHC inhibition [1].

Next, we applied the model to a situation where both KGDHC and complex I exhibit reduced activities. These calculations reveal synergistic effects concerning the energy metabolism but antagonistic effects concerning ROS formation: the drop in the ATP production capacity is more pronounced than at inhibition of either enzyme complex alone. Interestingly, however, the reduction state of the ROS-generating sites of the impaired complex I becomes significantly lowered if additionally the activity of the KGDHC is reduced [2].

Publications:

  1. Berndt N, Bulik S, Holzhütter HG. Kinetic Modeling of the Mitochondrial Energy Metabolism of Neuronal Cells: The Impact of Reduced α-Ketoglutarate Dehydrogenase Activities on ATP Production and Generation of Reactive Oxygen Species. Int J Cell Biol. 2012;2012:757594.
  2. Berndt N, Holzhütter HG, Bulik S. Implications of enzyme deficiencies on mitochondrial energy metabolism and reactive oxygen species formation of neurons involved in rotenone-induced Parkinson's disease: a model-based analysis. FEBS J. 2013 Oct;280(20):5080-93.

Project funding: The project was in part funded by the German Systems Biology Program “Virtual Liver” (grant no. 0315741) sponsored by the German Federal Ministry of Education and Research (BMBF).

Impact of anesthetics on cerebral energy metabolism during light and deep anesthesia

Illustration of the effects of propofol on neuronal functionality during and after anesthesia.

General anesthesia is a drug-induced, reversible state of unconsciousness, amnesia, analgesia and akinesia. The cortical electroencephalogram displays typical dose-dependent changes during anesthesia with characteristic stages of neuronal activity. Despite undisputable improvements in anesthesiology, major concerns related to the long-term effects of anesthetics on the central nervous system are rising. Specifically, deep anesthesia has been associated with postoperative delirium, long lasting postoperative cognitive dysfunction and increased mortality. The underlying role of anesthetics in these neurological complications remains unclear and needs urgent clarification.
Propofol is the most frequently used intravenous anesthetic for induction and maintenance of anesthesia acting primarily as a GABAA-agonist, but effects on other neuronal receptors and voltage-gated ion channels have been described. Besides its direct effect on neurotransmission, propofol-dependent impairment of mitochondrial function in neurons has been suggested to be responsible for neurotoxicity and postoperative brain dysfunction. To clarify the potential neurotoxic effect in more detail, we investigated the effects of propofol on neuronal energy metabolism of hippocampal slices of the stratum pyramidale of area CA3 at different activity states. We combined oxygen-measurements, electrophysiology and Flavin adenine dinucleotide (FAD)-imaging with computational modeling to uncover molecular targets in mitochondrial energy metabolism that are directly inhibited by propofol. We found that high concentrations of propofol (100 μM) significantly decrease population spikes, paired pulse ratio, the cerebral metabolic rate of oxygen consumption (CMRO2), frequency and power of gamma oscillations and increase FAD-oxidation. Model-based simulation of mitochondrial FAD redox state at inhibition of different respiratory chain (RC) complexes and the pyruvate-dehydrogenase show that the alterations in FAD autofluorescence during propofol administration can be explained with a strong direct inhibition of the complex II (cxII) of the RC. While this inhibition may not affect ATP availability under normal conditions, it may have an impact at high energy demand. Our data support the notion that propofol may lead to neurotoxicity and neuronal dysfunction by directly affecting the energy metabolism in neurons.
In a current study, we are investigating the effect of the gas anesthetics isoflurane in neuronal transmission and metabolism in anesthetized Wistar rats and in brain slices of the same species using the same methods as above.

Publications:

Project funding: This work is in part funded by the DFG grant no. 650953 and 408355133 as well as the German Systems Biology Program "LiSyM" (grant no. 31L0057) sponsored by the German Federal Ministry of Education and Research (BMBF). Agustin Liotta is participant in the BIH Charité Clinician Scientist Program funded by the Charité – Universitätsmedizin Berlin and the Berlin Institute of Health.

Cooperation partners:

Modeling of Metabolic Processes in the Heart

Integrative model of cardiac metabolism

Reaction scheme of the metabolic sub-model

The heart is energetically one of the most expensive organs. One-third of the cellular volume of cardiac myocytes is occupied by mitochondria. Per gram tissue, the heart has the highest oxygen consumption rate and the ATP turnover during one day amounts to 20 times its weight. This requires a robust and high rate of ATP production to maintain cardiac functionality. ATP is spent on electrophysiological processes of ion pumping as well as on mechanical work in its contractile apparatus. Perturbations in ATP-generating processes may therefore directly affect contractile function. The heart can rely on any energy source available like carbohydrates, amino acids, lipids, and ketone bodies. Under normal conditions, oxidation of free fatty acids is the prevailing energy source contributing around 70% to ATP production rate, while the utilization of glucose becomes increasingly important during ischemia, hypoxia, or increased workload. The use of different substrates is tightly regulated under physiological conditions and there is ample crosstalk between the different metabolic pathways.

Kinetic modeling of cardiac metabolism has a long tradition starting in the late 70s, but all of the available models neglect crucial factors determining the energetic status of the heart, such as the influence of alternating substrate supply, hormonal metabolic control, or variable gene expression of key metabolic enzymes necessary for the understanding of metabolic alterations in heart disease. In this work, we developed a kinetic multi-pathway model for cardiomyocytes with hitherto unprecedented scope and level of detail [1]. The model includes the regulation of enzyme activities by allosteric effectors, hormone-dependent reversible phosphorylation, and variable protein abundances. For each enzyme, rate equations have been developed that take into account the enzyme’s kinetic and regulatory features determined by decades of biochemical research. We use the model to analyze proteomic data obtained from patients with valve disease. We show that ATP production capacity is significantly diminished in patients and correlates with mechanic energy demand. However, there are large differences in the energetic state of the myocardium even between patients with similar clinical and imaging-based hypertrophy and functional markers.

Publications:

  1. Berndt N, Eckstein J, Wallach I, Nordmeyer S, Kelm M, Kirchner M, Goubergrits L, Schafstedde M, Hennemuth A, Kraus M, Grune T, Mertins P, Kuehne T, Holzhütter HG. CARDIOKIN1: Computational Assessment of Myocardial Metabolic Capability in Healthy Controls and Patients With Valve Diseases. Circulation. 2021 Dec 14;144(24):1926-1939.

Project funding: This project is funded by the German Research Foundation (DFG) (grant no. 422215721) and by the German Federal Ministry of Education and Research (BMBF) within the framework of the EU initiative ERA PerMed „Personalised Medicine: Multidisciplinary Research towards Implementation" (grant no. 01KU2011A, „HeartMed“).

Cooperation partners:

Cardiac metabolism of patients with heart failure

MVATP(rest) and MVATP(max) for controls and patients with mitral valve insufficiency (MVI) and aortic stenosis (AS). A, Bottom values of the bars refer to MVATP(rest); top values refer to MVATP(max). The bar length indicates the myocardial ATP production reserve (MAPR = MVATP[max] – MVATP[rest]). B-D, Box plots showing mean values, upper and lower quartiles, and total span of MVATP(rest), MVATP(max), and MAPR for controls and patients with MVI and AS. Significant differences between the patient groups are indicated by connecting brackets with asterisks giving the significance level (*P<0.05, **P<0.01, ***P<0.001). A Bonferroni correction was applied to account for multiple testing.

For proper functionality, the heart relies on coordinated utilization of different energy-providing substrates like glucose, fatty acids, glycogen, and lactate. Depending on substrate availability and energy demand, the heart needs to adapt its internal energy delivering pathways to ensure demand-matching energy supply. In pathological situations like aortic stenosis (AS), the efficiency of cardiac muscle activity is disturbed and maladaptation might lead to metabolic alterations contributing to declined cardiac function. Experimental assessment of cardiac energy metabolism is not possible due to ethical and technical restrictions.

In this project, we present a detailed, comprehensive, biochemistry-based kinetic model of the central cardiac metabolism including the regulation of enzymes by kinetic allosteric and hormonal regulation [1]. We show the ability of the model to investigate substrate utilization under different conditions. We use the model to investigate the alterations in cardiac energy metabolism in a cohort of patients with AS and mitral valve insufficiency (MVI).

The figure depicts the specific energetic parameters myocardial ATP consumption at rest (MVATP(rest)), at maximal workload (MVATP(max)), and the myocardial ATP production reserve (MAPR) for individual patients. Compared with controls, the individual variations of these parameters were much larger for the two patient groups (see box plots B-D). For patients with MVI, the mean value of the parameter MVATP(rest) was significantly higher, whereas MVATP(max) was significantly lower when compared with control values. For patients with AS, the mean value of the parameter MVATP(rest) was also significantly higher and MVATP(max) was also significantly lower. For both groups of patients, the parameter MAPR was on average significantly lower compared with the controls. Hence, both groups of patients had on average a reduced ATP production reserve, which was caused by increased MVATP(rest) and decreased MVATP(max).

Publication:

  1. Berndt N, Eckstein J, Wallach I, Nordmeyer S, Kelm M, Kirchner M, Goubergrits L, Schafstedde M, Hennemuth A, Kraus M, Grune T, Mertins P, Kuehne T, Holzhütter HG. CARDIOKIN1: Computational Assessment of Myocardial Metabolic Capability in Healthy Controls and Patients With Valve Diseases. Circulation. 2021 Dec 14;144(24):1926-1939.

Project funding: This project is funded by the German Research Foundation (DFG) (grant no. 422215721) and by the German Federal Ministry of Education and Research (BMBF) within the framework of the EU initiative ERA PerMed „Personalised Medicine: Multidisciplinary Research towards Implementation" (grant no. 01KU2011A, „HeartMed“).

Cooperation partners:

Cardiac metabolism of diabetic patients

Graphical work plan description of the DFG project “Mathematical modeling of the metabolic implications of the diabetic heart”.

Diabetes mellitus is an epidemically growing disease worldwide having an overall prevalence of 9.8% in Germany in 2015, with the vast majority of cases (9.5%) attributable to type2 diabetes mellitus. Heart failure, the most common cardiovascular disease associated with diabetes, is a clinical syndrome in which myocardial pump function is inadequate for maintaining and supporting an individual’s physiological requirements. Heart failure in a patient with diabetes may arise from myocardial damage resulting from an ischemic, thrombotic event. In many cases, however, heart failure cannot be attributed to any cardiovascular disease, such as hypertension or coronary artery disease.

Adaptive processes start often at the cellular level by changes in signaling and metabolic pathways, typically evolving to changes in the structural organization of the tissue as, for example, enhanced formation of extracellular matrix (fibrosis) and finally result in alterations of functional parameters such as the cardiac output. A major problem in the treatment of cardiovascular diseases consists in the poor predictability of the responses that are potentially elicited by medical intervention, whether it is dietary, pharmacologically, or surgically. In the worst case, treatment-induced adaptive changes can even exacerbate the pathological situation. A promising approach to overcome this dilemma consists in the use of mathematical models, which integrate existing knowledge on central molecular and physiological circuits operative at the cellular levels and provide reliable predictions of the heart's functional capacity and performance in response to intervention.

The goal of this project is to systematically investigate the metabolic and functional changes associated with the diabetic heart. To this end, we will develop, test, and verify a computational model of cardiac energy metabolism [1]. The main objective is to understand the short-term and long-term metabolic adaptation of the cardiomyocyte and the functional metabolic changes arising from changes in metabolic enzyme abundance and signaling pathways in dependence of external substrate supply, hormonal stimuli, and internal demand.

Publication:

  1. Berndt N, Eckstein J, Wallach I, Nordmeyer S, Kelm M, Kirchner M, Goubergrits L, Schafstedde M, Hennemuth A, Kraus M, Grune T, Mertins P, Kuehne T, Holzhütter HG. CARDIOKIN1: Computational Assessment of Myocardial Metabolic Capability in Healthy Controls and Patients With Valve Diseases. Circulation. 2021 Dec 14;144(24):1926-1939.

Project funding: This project is funded by the German Research Foundation (DFG) (grant no. 422215721).

Cooperation partner: Tilman Grune (German Institute of Human Nutrition Potsdam-Rehbrücke (DIfE)/Dept. of Molecular Toxicology)