Integrated metabolic spatial-temporal model for the prediction of ammonia detoxification during liver damage and regeneration

Quantifying fat zonation in liver lobules: an integrated multiscale in silico model combining disturbed microperfusion and fat metabolism via a continuum biomechanical bi-scale, tri-phasic approach

Metabolic zonation refers to the spatial separation of metabolic functions along the sinusoidal axes of the liver. This phenomenon forms the foundation for adjusting hepatic metabolism to physiological requirements in health and disease (e.g., metabolic dysfunction-associated steatotic liver disease/MASLD). Zonated metabolic functions are influenced by zonal morphological abnormalities in the liver, such as periportal fibrosis and pericentral steatosis. We aim to analyze the interplay between microperfusion, oxygen gradient, fat metabolism and resulting zonated fat accumulation in a liver lobule. Therefore we developed a continuum biomechanical, tri-phasic, bi-scale, and multicomponent in silico model, which allows to numerically simulate coupled perfusion-function-growth interactions two-dimensionally in liver lobules. The developed homogenized model has the following specifications: (i) thermodynamically consistent, (ii) tri-phase model (tissue, fat, blood), (iii) penta-substances (glycogen, glucose, lactate, FFA, and oxygen), and (iv) bi-scale approach (lobule, cell). Our presented in silico model accounts for the mutual coupling between spatial and time-dependent liver perfusion, metabolic pathways and fat accumulation. The model thus allows the prediction of fat development in the liver lobule, depending on perfusion, oxygen and plasma concentration of free fatty acids (FFA), oxidative processes, the synthesis and the secretion of triglycerides (TGs). The use of a bi-scale approach allows in addition to focus on scale bridging processes. Thus, we will investigate how changes at the cellular scale affect perfusion at the lobular scale and vice versa. This allows to predict the zonation of fat distribution (periportal or pericentral) depending on initial conditions, as well as external and internal boundary value conditions.

A liver digital twin for in silico testing of cellular and inter-cellular mechanisms in regeneration after drug-induced damage

This communication presents a mathematical mechanism-based model of the regenerating liver after drug-induced pericentral lobule damage resolving tissue microarchitecture. The consequence of alternative hypotheses about the interplay of different cell types on regeneration was simulated. Regeneration dynamics has been quantified by the size of the damage-induced dead cell area, the hepatocyte density and the spatial-temporal profile of the different cell types. We use deviations of observed trajectories from the simulated system to identify branching points, at which the systems behavior cannot be explained by the underlying set of hypotheses anymore. Our procedure reflects a successful strategy for generating a fully digital liver twin that, among others, permits to test perturbations from the molecular up to the tissue scale. The model simulations are complementing current knowledge on liver regeneration by identifying gaps in mechanistic relationships and guiding the system toward the most informative (lacking) parameters that can be experimentally addressed.

In silico modeling for the hepatic circulation and transport: From the liver organ to lobules

The function of the liver depends critically on its blood supply. Numerous in silico models have been developed to study various aspects of the hepatic circulation, including not only the macro-hemodynamics at the organ level, but also the microcirculation at the lobular level. In addition, computational models of blood flow and bile flow have been used to study the transport, metabolism, and clearance of drugs in pharmacokinetic studies. These in silico models aim to provide insights into the liver organ function under both healthy and diseased states, and to assist quantitative analysis for surgical planning and postsurgery treatment. The purpose of this review is to provide an update on state-of-the-art in silico models of the hepatic circulation and transport processes. We introduce the numerical methods and the physiological background of these models. We also discuss multiscale frameworks that have been proposed for the liver, and their linkage with the large context of systems biology, systems pharmacology, and the Physiome project. This article is categorized under: Metabolic Diseases > Computational Models Metabolic Diseases > Biomedical Engineering Cardiovascular Diseases > Computational Models.

In vitro to in vivo acetaminophen hepatotoxicity extrapolation using classical schemes, pharmacodynamic models and a multiscale spatial-temporal liver twin

In vitro to in vivo extrapolation represents a critical challenge in toxicology. In this paper we explore extrapolation strategies for acetaminophen (APAP) based on mechanistic models, comparing classical (CL) homogeneous compartment pharmacodynamic (PD) models and a spatial-temporal (ST), multiscale digital twin model resolving liver microarchitecture at cellular resolution. The models integrate consensus detoxification reactions in each individual hepatocyte. We study the consequences of the two model types on the extrapolation and show in which cases these models perform better than the classical extrapolation strategy that is based either on the maximal drug concentration (Cmax) or the area under the pharmacokinetic curve (AUC) of the drug blood concentration. We find that an CL-model based on a well-mixed blood compartment is sufficient to correctly predict the in vivo toxicity from in vitro data. However, the ST-model that integrates more experimental information requires a change of at least one parameter to obtain the same prediction, indicating that spatial compartmentalization may indeed be an important factor.

Digital twin demonstrates significance of biomechanical growth control in liver regeneration after partial hepatectomy

Partial liver removal is an important therapy option for liver cancer. In most patients within a few weeks, the liver is able to fully regenerate. In some patients, however, regeneration fails with often severe consequences. To better understand the control mechanisms of liver regeneration, experiments in mice were performed, guiding the creation of a spatiotemporal 3D model of the regenerating liver. The model represents cells and blood vessels within an entire liver lobe, a macroscopic liver subunit. The model could reproduce the experimental data only if a biomechanical growth control (BGC)-mechanism, inhibiting cell cycle entrance at high compression, was taken into account and predicted that BGC may act as a short-range growth inhibitor minimizing the number of proliferating neighbor cells of a proliferating cell, generating a checkerboard-like proliferation pattern. Model-predicted cell proliferation patterns in pigs and mice were found experimentally. The results underpin the importance of biomechanical aspects in liver growth control.

Chronic heat stress causes liver damage via endoplasmic reticulum stress-induced apoptosis in broilers

Liver is a central metabolic organ, which is sensitive to heat stress. Liver damage affects animals' health and endangers the livestock and poultry industry. This study aimed to investigate the mechanism of chronic heat stress-induced liver damage in broiler chickens. Broilers were divided into 3 treatments: normal control group (NOR, 22°C), heat stress group (HS, 32°C) and pair-feeding group (PF, 22°C) for a 7-d and 14-d trial. The results showed that 7 d heat exposure caused microvesicular steatosis and reduced glutamine synthetase activity in broiler liver (P < 0.05). After 14 d of heat exposure, heat stress caused vacuolar degeneration and apoptosis in the liver; elevated liver relative weight and liver glutaminase activity as well as plasma ammonia level (P < 0.05). Additionally, heat stress enhanced GRP78 protein expression and the mRNA expressions of endoplasmic reticulum (ER) stress responses genes and apoptosis-related genes in broiler liver after 14 d of heat exposure (P < 0.05). In conclusion, chronic heat stress triggered ER stress-induced apoptosis and caused liver damage, which may compromise ammonia detoxification in broiler liver.

From Seeing to Simulating: A Survey of Imaging Techniques and Spatially-Resolved Data for Developing Multiscale Computational Models of Liver Regeneration

Liver regeneration, which leads to the re-establishment of organ mass, follows a specifically organized set of biological processes acting on various time and length scales. Computational models of liver regeneration largely focused on incorporating molecular and signaling detail have been developed by multiple research groups in the recent years. These modeling efforts have supported a synthesis of disparate experimental results at the molecular scale. Incorporation of tissue and organ scale data using noninvasive imaging methods can extend these computational models towards a comprehensive accounting of multiscale dynamics of liver regeneration. For instance, microscopy-based imaging methods provide detailed histological information at the tissue and cellular scales. Noninvasive imaging methods such as ultrasound, computed tomography and magnetic resonance imaging provide morphological and physiological features including volumetric measures over time. In this review, we discuss multiple imaging modalities capable of informing computational models of liver regeneration at the organ-, tissue- and cellular level. Additionally, we discuss available software and algorithms, which aid in the analysis and integration of imaging data into computational models. Such models can be generated or tuned for an individual patient with liver disease. Progress towards integrated multiscale models of liver regeneration can aid in prognostic tool development for treating liver disease.

Automated Detection of Portal Fields and Central Veins in Whole-Slide Images of Liver Tissue

Many physiological processes and pathological phenomena in the liver tissue are spatially heterogeneous. At a local scale, biomarkers can be quantified along the axis of the blood flow, from portal fields (PFs) to central veins (CVs), i.e., in zonated form. This requires detecting PFs and CVs. However, manually annotating these structures in multiple whole-slide images is a tedious task. We describe and evaluate a fully automated method, based on a convolutional neural network, for simultaneously detecting PFs and CVs in a single stained section. Trained on scans of hematoxylin and eosin-stained liver tissue, the detector performed well with an F1 score of 0.81 compared to annotation by a human expert. It does, however, not generalize well to previously unseen scans of steatotic liver tissue with an F1 score of 0.59. Automated PF and CV detection eliminates the bottleneck of manual annotation for subsequent automated analyses, as illustrated by two proof-of-concept applications: We computed lobulus sizes based on the detected PF and CV positions, where results agreed with published lobulus sizes. Moreover, we demonstrate the feasibility of zonated quantification of biomarkers detected in different stainings based on lobuli and zones obtained from the detected PF and CV positions. A negative control (hematoxylin and eosin) showed the expected homogeneity, a positive control (glutamine synthetase) was quantified to be strictly pericentral, and a plausible zonation for a heterogeneous F4/80 staining was obtained. Automated detection of PFs and CVs is one building block for automatically quantifying physiologically relevant heterogeneity of liver tissue biomarkers. Perspectively, a more robust and automated assessment of zonation from whole-slide images will be valuable for parameterizing spatially resolved models of liver metabolism and to provide diagnostic information.

Spatio-Temporal Multiscale Analysis of Western Diet-Fed Mice Reveals a Translationally Relevant Sequence of Events during NAFLD Progression

Mouse models of non-alcoholic fatty liver disease (NAFLD) are required to define therapeutic targets, but detailed time-resolved studies to establish a sequence of events are lacking. Here, we fed male C57Bl/6N mice a Western or standard diet over 48 weeks. Multiscale time-resolved characterization was performed using RNA-seq, histopathology, immunohistochemistry, intravital imaging, and blood chemistry; the results were compared to human disease. Acetaminophen toxicity and ammonia metabolism were additionally analyzed as functional readouts. We identified a sequence of eight key events: formation of lipid droplets; inflammatory foci; lipogranulomas; zonal reorganization; cell death and replacement proliferation; ductular reaction; fibrogenesis; and hepatocellular cancer. Functional changes included resistance to acetaminophen and altered nitrogen metabolism. The transcriptomic landscape was characterized by two large clusters of monotonously increasing or decreasing genes, and a smaller number of 'rest-and-jump genes' that initially remained unaltered but became differentially expressed only at week 12 or later. Approximately 30% of the genes altered in human NAFLD are also altered in the present mouse model and an increasing overlap with genes altered in human HCC occurred at weeks 30-48. In conclusion, the observed sequence of events recapitulates many features of human disease and offers a basis for the identification of therapeutic targets.

Application of Magnetic Resonance Imaging in Liver Biomechanics: A Systematic Review

MRI-based biomechanical studies can provide a deep understanding of the mechanisms governing liver function, its mechanical performance but also liver diseases. In addition, comprehensive modeling of the liver can help improve liver disease treatment. Furthermore, such studies demonstrate the beginning of an engineering-level approach to how the liver disease affects material properties and liver function. Aimed at researchers in the field of MRI-based liver simulation, research articles pertinent to MRI-based liver modeling were identified, reviewed, and summarized systematically. Various MRI applications for liver biomechanics are highlighted, and the limitations of different viscoelastic models used in magnetic resonance elastography are addressed. The clinical application of the simulations and the diseases studied are also discussed. Based on the developed questionnaire, the papers' quality was assessed, and of the 46 reviewed papers, 32 papers were determined to be of high-quality. Due to the lack of the suitable material models for different liver diseases studied by magnetic resonance elastography, researchers may consider the effect of liver diseases on constitutive models. In the future, research groups may incorporate various aspects of machine learning (ML) into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification.

Subcellular spatio-temporal intravital kinetics of aflatoxin B1 and ochratoxin A in liver and kidney

Local accumulation of xenobiotics in human and animal tissues may cause adverse effects. Large differences in their concentrations may exist between individual cell types, often due to the expression of specific uptake and export carriers. Here we established a two-photon microscopy-based technique for spatio-temporal detection of the distribution of mycotoxins in intact kidneys and livers of anesthetized mice with subcellular resolution. The mycotoxins ochratoxin A (OTA, 10 mg/kg b.w.) and aflatoxin B1 (AFB1, 1.5 mg/kg b.w.), which both show blue auto-fluorescence, were analyzed after intravenous bolus injections. Within seconds after administration, OTA was filtered by glomeruli, and enriched in distal tubular epithelial cells (dTEC). A striking feature of AFB1 toxicokinetics was its very rapid uptake from sinusoidal blood into hepatocytes (t1/2 ~ 4 min) and excretion into bile canaliculi. Interestingly, AFB1 was enriched in the nuclei of hepatocytes with zonal differences in clearance. In the cytoplasm of pericentral hepatocytes, the half-life (t1/2~ 63 min) was much longer compared to periportal hepatocytes of the same lobules (t1/2 ~ 9 min). In addition, nuclear AFB1 from periportal hepatocytes cleared faster compared to the pericentral region. These local differences in AFB1 clearance may be due to the pericentral expression of cytochrome P450 enzymes that activate AFB1 to protein- and DNA-binding metabolites. In conclusion, the present study shows that large spatio-temporal concentration differences exist within the same tissues and its analysis may provide valuable additional information to conventional toxicokinetic studies.

Mechanical homeostasis of liver sinusoid is involved in the initiation and termination of liver regeneration

Organogenesis and regeneration are fundamental for developmental progress and are associated with morphogenesis, size control and functional properties for whole-body homeostasis. The liver plays an essential role in maintaining homeostasis of the entire body through various functions, including metabolic functions, detoxification, and production of bile, via the three-dimensional spatial arrangement of hepatic lobules and has high regenerative capacity. The regeneration occurs as hypertrophy, which strictly controls the size and lobule structure. In this study, we established a three-dimensional sinusoidal network analysis method and determined valuable parameters after partial hepatectomy by comparison to the static phase of the liver. We found that mechanical homeostasis, which is crucial for organ morphogenesis and functions in various phenomena, plays essential roles in liver regeneration for both initiation and termination of liver regeneration, which is regulated by cytokine networks. Mechanical homeostasis plays critical roles in the initiation and termination of organogenesis, tissue repair and organ regeneration in coordination with cytokine networks.

Functional Consequences of Metabolic Zonation in Murine Livers: Insights for an Old Story

BACKGROUND AND AIMS

Zone-dependent differences in expression of metabolic enzymes along the portocentral axis of the acinus are a long-known feature of liver metabolism. A prominent example is the preferential localization of the enzyme, glutamine synthetase, in pericentral hepatocytes, where it converts potentially toxic ammonia to the valuable amino acid, glutamine. However, with the exception of a few key regulatory enzymes, a comprehensive and quantitative assessment of zonal differences in the abundance of metabolic enzymes and, much more important, an estimation of the associated functional differences between portal and central hepatocytes is missing thus far.

APPROACH AND RESULTS

We addressed this problem by establishing a method for the separation of periportal and pericentral hepatocytes that yields sufficiently pure fractions of both cell populations. Quantitative shotgun proteomics identified hundreds of differentially expressed enzymes in the two cell populations. We used zone-specific proteomics data for scaling of the maximal activities to generate portal and central instantiations of a comprehensive kinetic model of central hepatic metabolism (Hepatokin1).

CONCLUSIONS

The model simulations revealed significant portal-to-central differences in almost all metabolic pathways involving carbohydrates, fatty acids, amino acids, and detoxification.

CaliPro: A Calibration Protocol That Utilizes Parameter Density Estimation to Explore Parameter Space and Calibrate Complex Biological Models

Introduction

Mathematical and computational modeling have a long history of uncovering mechanisms and making predictions for biological systems. However, to create a model that can provide relevant quantitative predictions, models must first be calibrated by recapitulating existing biological datasets from that system. Current calibration approaches may not be appropriate for complex biological models because: 1) many attempt to recapitulate only a single aspect of the experimental data (such as a median trend) or 2) Bayesian techniques require specification of parameter priors and likelihoods to experimental data that cannot always be confidently assigned. A new calibration protocol is needed to calibrate complex models when current approaches fall short.

Methods

Herein, we develop CaliPro, an iterative, model-agnostic calibration protocol that utilizes parameter density estimation to refine parameter space and calibrate to temporal biological datasets. An important aspect of CaliPro is the user-defined pass set definition, which specifies how the model might successfully recapitulate experimental data. We define the appropriate settings to use CaliPro.

Results

We illustrate the usefulness of CaliPro through four examples including predator-prey, infectious disease transmission, and immune response models. We show that CaliPro works well for both deterministic, continuous model structures as well as stochastic, discrete models and illustrate that CaliPro can work across diverse calibration goals.

Conclusions

We present CaliPro, a new method for calibrating complex biological models to a range of experimental outcomes. In addition to expediting calibration, CaliPro may be useful in already calibrated parameter spaces to target and isolate specific model behavior for further analysis.

Highlight report: New insights in liver physiology: Canalicular bile flux is diffusion dominated

One of the central functions of the liver is excretion of bile into the intestine. Currently, bile excretion is explained by the osmotic model, according to which bile acids are excreted by hepatocytes into the bile canaliculi and since bile acids are osmotically active they draw water into the canalicular lumen. Bile canaliculi are closed at the central side. Therefore, bile was postulated to flow to the open side into the ducts. However, bile flow in canaliculi has never been measured because of the small canalicular diameter which does not allow analysis of flux by conventional methods. Recently, methods have been developed that allow flow analysis in bile canaliculi and ducts. Interestingly, no measurable directed flow was observed in the canaliculi. Instead, small molecules in bile canaliculi reached the larger bile ducts by diffusion. Only there measurable flow sets in. The pathophysiological implications of this novel observation are discussed.

Modeling of Nanotherapy Response as a Function of the Tumor Microenvironment: Focus on Liver Metastasis

The tumor microenvironment (TME) presents a challenging barrier for effective nanotherapy-mediated drug delivery to solid tumors. In particular for tumors less vascularized than the surrounding normal tissue, as in liver metastases, the structure of the organ itself conjures with cancer-specific behavior to impair drug transport and uptake by cancer cells. Cells and elements in the TME of hypovascularized tumors play a key role in the process of delivery and retention of anti-cancer therapeutics by nanocarriers. This brief review describes the drug transport challenges and how they are being addressed with advanced in vitro 3D tissue models as well as with in silico mathematical modeling. This modeling complements network-oriented techniques, which seek to interpret intra-cellular relevant pathways and signal transduction within cells and with their surrounding microenvironment. With a concerted effort integrating experimental observations with computational analyses spanning from the molecular- to the tissue-scale, the goal of effective nanotherapy customized to patient tumor-specific conditions may be finally realized.

SBML Level 3: an extensible format for the exchange and reuse of biological models

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

A mechanobiological mathematical model of liver metabolism

The liver plays a complex role in metabolism and detoxification, and better tools are needed to understand its function and to develop liver-targeted therapies. In this study, we establish a mechanobiological model of liver transport and hepatocyte biology to elucidate the metabolism of urea and albumin, the production/detoxification of ammonia, and consumption of oxygen and nutrients. Since hepatocellular shear stress (SS) can influence the enzymatic activities of liver, the effect of SS on the urea and albumin synthesis are empirically modeled through the mechanotransduction mechanisms. The results demonstrate that the rheology and dynamics of the sinusoid flow can significantly affect liver metabolism. We show that perfusate rheology and blood hematocrit can affect urea and albumin production by changing hepatocyte mechanosensitive metabolism. The model can also simulate enzymatic diseases of the liver such as hyperammonemia I, hyperammonemia II, hyperarginemia, citrollinemia, and argininosuccinicaciduria, which disrupt the urea metabolism and ammonia detoxification. The model is also able to predict how aggregate cultures of hepatocytes differ from single cell cultures. We conclude that in vitro perfusable devices for the study of liver metabolism or personalized medicine should be designed with similar morphology and fluid dynamics as patient liver tissue. This robust model can be adapted to any type of hepatocyte culture to determine how hepatocyte viability, functionality, and metabolism are influenced by liver pathologies and environmental conditions.

Resilience of three-dimensional sinusoidal networks in liver tissue

Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every hepatocyte in liver tissue, by building on recent advances in high-resolution imaging and digital reconstruction of adult mice liver tissue. We find that the topology of the three-dimensional sinusoidal network reflects its two design requirements of a space-filling network that connects all hepatocytes, while using shortest transport routes: sinusoidal networks are sub-graphs of the Delaunay graph of their set of branching points, and also contain the corresponding minimum spanning tree, both to good approximation. To overcome the spatial limitations of experimental samples and generate arbitrarily-sized networks, we developed a network generation algorithm that reproduces the statistical features of 0.3-mm-sized samples of sinusoidal networks, using multi-objective optimization for node degree and edge length distribution. Nematic order in these simulated networks implies anisotropic transport properties, characterized by an empirical linear relation between a nematic order parameter and the anisotropy of the permeability tensor. Under the assumption that all sinusoid tubes have a constant and equal flow resistance, we predict that the distribution of currents in the network is very inhomogeneous, with a small number of edges carrying a substantial part of the flow-a feature known for hierarchical networks, but unexpected for plexus-like networks. We quantify network resilience in terms of a permeability-at-risk, i.e., permeability as function of the fraction of removed edges. We find that sinusoidal networks are resilient to random removal of edges, but vulnerable to the removal of high-current edges. Our findings suggest the existence of a mechanism counteracting flow inhomogeneity to balance metabolic load on the liver.

Liver Bioreactor Design Issues of Fluid Flow and Zonation, Fibrosis, and Mechanics: A Computational Perspective

Tissue engineering, with the goal of repairing or replacing damaged tissue and organs, has continued to make dramatic science-based advances since its origins in the late 1980’s and early 1990’s. Such advances are always multi-disciplinary in nature, from basic biology and chemistry through physics and mathematics to various engineering and computer fields. This review will focus its attention on two topics critical for tissue engineering liver development: (a) fluid flow, zonation, and drug screening, and (b) biomechanics, tissue stiffness, and fibrosis, all within the context of 3D structures. First, a general overview of various bioreactor designs developed to investigate fluid transport and tissue biomechanics is given. This includes a mention of computational fluid dynamic methods used to optimize and validate these designs. Thereafter, the perspective provided by computer simulations of flow, reactive transport, and biomechanics responses at the scale of the liver lobule and liver tissue is outlined, in addition to how bioreactor-measured properties can be utilized in these models. Here, the fundamental issues of tortuosity and upscaling are highlighted, as well as the role of disease and fibrosis in these issues. Some idealized simulations of the effects of fibrosis on lobule drug transport and mechanics responses are provided to further illustrate these concepts. This review concludes with an outline of some practical applications of tissue engineering advances and how efficient computational upscaling techniques, such as dual continuum modeling, might be used to quantify the transition of bioreactor results to the full liver scale.

Holland C, Zaza A, Murad W, Hassan R, A. Ahmed Y, Abbas T, A. Abdelrahim E, Schneider KM, Matz-Soja M, Reinders J, Gebhardt R, Berres ML, Hatting M, Drasdo D, Saez-Rodriguez J, Trautwein C, G. Hengstler J. Influence of Liver Fibrosis on Lobular Zonation

Little is known about how liver fibrosis influences lobular zonation. To address this question, we used three mouse models of liver fibrosis, repeated CCl4 administration for 2, 6 and 12 months to induce pericentral damage, as well as bile duct ligation (21 days) and mdr2-/- mice to study periportal fibrosis. Analyses were performed by RNA-sequencing, immunostaining of zonated proteins and image analysis. RNA-sequencing demonstrated a significant enrichment of pericentral genes among genes downregulated by CCl4; vice versa, periportal genes were enriched among the upregulated genes. Immunostaining showed an almost complete loss of pericentral proteins, such as cytochrome P450 enzymes and glutamine synthetase, while periportal proteins, such as arginase 1 and CPS1 became expressed also in pericentral hepatocytes. This pattern of fibrosis-associated 'periportalization' was consistently observed in all three mouse models and led to complete resistance to hepatotoxic doses of acetaminophen (200 mg/kg). Characterization of the expression response identified the inflammatory pathways TGFβ, NFκB, TNFα, and transcription factors NFKb1, Stat1, Hif1a, Trp53, and Atf1 among those activated, while estrogen-associated pathways, Hnf4a and Hnf1a, were decreased. In conclusion, liver fibrosis leads to strong alterations of lobular zonation, where the pericentral region adopts periportal features. Beside adverse consequences, periportalization supports adaptation to repeated doses of hepatotoxic compounds.

Effects of a high protein diet and liver disease in an in silico model of human ammonia metabolism

BACKGROUND

After proteolysis, the majority of released amino acids from dietary protein are transported to the liver for gluconeogenesis or to peripheral tissues where they are used for protein synthesis and eventually catabolized, producing ammonia as a byproduct. High ammonia levels in the brain are a major contributor to the decreased neural function that occurs in several pathological conditions such as hepatic encephalopathy when liver urea cycle function is compromised. Therefore, it is important to gain a deeper understanding of human ammonia metabolism. The objective of this study was to predict changes in blood ammonia levels resulting from alterations in dietary protein intake, from liver disease, or from partial loss of urea cycle function.

METHODS

A simple mathematical model was created using MATLAB SimBiology and data from published studies. Simulations were performed and results analyzed to determine steady state changes in ammonia levels resulting from varying dietary protein intake and varying liver enzyme activity levels to simulate liver disease. As a toxicity reference, viability was measured in SH-SY5Y neuroblastoma cells following differentiation and ammonium chloride treatment.

RESULTS

Results from control simulations yielded steady state blood ammonia levels within normal physiological limits. Increasing dietary protein intake by 72% resulted in a 59% increase in blood ammonia levels. Simulations of liver cirrhosis increased blood ammonia levels by 41 to 130% depending upon the level of dietary protein intake. Simulations of heterozygous individuals carrying a loss of function allele of the urea cycle carbamoyl phosphate synthetase I (CPS1) gene resulted in more than a tripling of blood ammonia levels (from roughly 18 to 60 μM depending on dietary protein intake). The viability of differentiated SH-SY5Y cells was decreased by 14% by the addition of a slightly higher amount of ammonium chloride (90 μM).

CONCLUSIONS

Data from the model suggest decreasing protein consumption may be one simple strategy to decrease blood ammonia levels and minimize the risk of developing hepatic encephalopathy for many liver disease patients. In addition, the model suggests subjects who are known carriers of disease-causing CPS1 alleles may benefit from monitoring blood ammonia levels and limiting the level of protein intake if ammonia levels are high.

Spatial heterogeneity in the mammalian liver

Hepatocytes operate in highly structured repeating anatomical units termed liver lobules. Blood flow along the lobule radial axis creates gradients of oxygen, nutrients and hormones, which, together with morphogenetic fields, give rise to a highly variable microenvironment. In line with this spatial variability, key liver functions are expressed non-uniformly across the lobules, a phenomenon termed zonation. Technologies based on single-cell transcriptomics have constructed a global spatial map of hepatocyte gene expression in mice revealing that ~50% of hepatocyte genes are expressed in a zonated manner. This broad spatial heterogeneity suggests that hepatocytes in different lobule zones might have not only different gene expression profiles but also distinct epigenetic features, regenerative capacities, susceptibilities to damage and other functional aspects. Here, we present genomic approaches for studying liver zonation, describe the principles of liver zonation and discuss the intrinsic and extrinsic factors that dictate zonation patterns. We also explore the challenges and solutions for obtaining zonation maps of liver non-parenchymal cells. These approaches facilitate global characterization of liver function with high spatial resolution along physiological and pathological timescales.

Modeling of xenobiotic transport and metabolism in virtual hepatic lobule models

Computational models of normal liver function and xenobiotic induced liver damage are increasingly being used to interpret in vitro and in vivo data and as an approach to the de novo prediction of the liver’s response to xenobiotics. The microdosimetry (dose at the level of individual cells) of xenobiotics vary spatially within the liver because of both compound-independent and compound-dependent factors. In this paper, we build model liver lobules to investigate the interplay between vascular structure, blood flow and cellular transport that lead to regional variations in microdosimetry. We then compared simulation results obtained using this complex spatial model with a simpler linear pipe model of a sinusoid and a very simple single box model. We found that variations in diffusive transport, transporter-mediated transport and metabolism, coupled with complex liver sinusoid architecture and blood flow distribution, led to three essential patterns of xenobiotic exposure within the virtual liver lobule: (1) lobular-wise uniform, (2) radially varying and (3) both radially and azimuthally varying. We propose to use these essential patterns of exposure as a reference for selection of model representations when a computational study involves modeling detailed hepatic responses to xenobiotics.

Robustness of a Reconstituted Escherichia coli Protein Translation System Analyzed by Computational Modeling

Robustness against environmental changes is one of the major features of biological systems, but its origin is not well understood. We recently constructed a large-scale computational model of an Escherichia coli-based reconstituted in vitro translation system that enumerates all protein synthesis processes in detail. Our model synthesizes a formyl-Met-Gly-Gly tripeptide (MGG peptide) from 27 initial molecular components through 968 biochemical reactions. Among the 968 kinetic parameters, 483 are nonzero parameters, and the simulator was used to determine how perturbations of 483 individual reactions affect the complex reaction network. We found that even when the kinetic parameter was changed from 100- to 0.01-fold, 94% of the changes hardly affected the two indicators of reaction dynamics in MGG peptide synthesis, which represent the yield of the MGG peptide and the initial lag-time of the peptide synthesis. Moreover, none of the indicators increased proportionally to these changes: e.g., a 100-fold increase in the kinetic parameter increased the yield by only 2.2-fold at most, indicating the insensitivity of the reaction network to perturbation. Robustness and insensitivity are likely to be a common feature of large-scale biological reaction networks.

Zonation of hepatic fat accumulation: insights from mathematical modelling of nutrient gradients and fatty acid uptake

Intrinsic of non-alcoholic fatty liver diseases is an aberrant accumulation of triglycerides (steatosis), which occurs inhomogeneously within lobules. To improve our understanding of the mechanisms involved in this zonation patterning, we developed a mathematical multicompartment model of hepatic fatty acid metabolism accompanied by blood flow simulations. A model analysis determines the influence of the uptake process of fatty acids, the porto-central gradient of plasma fatty acid concentration, and the oxygen supply via blood on the zonation of triglyceride accumulation. From this theoretical perspective, the plasma oxygen gradient, but not the fatty acid gradient, leads the way to a zonated triglyceride accumulation by its decisive role in oxidative processes. In addition, the uptake mechanism of fatty acids seems to be fundamental for a pericentral dominance of steatosis. However, the mechanism of cellular fatty acid uptake from the blood is still under debate. Our theoretical approach supports the transporter-mediated uptake mechanism and reveals that the maximal velocity of fatty acid uptake affects the switching between a periportal and a pericentral triglyceride accumulation. Further research on hepatic fatty acid uptake is needed to push forward our understanding of aberrant triglyceride accumulation in diet-induced steatosis.

Model Prediction and Validation of an Order Mechanism Controlling the Spatiotemporal Phenotype of Early Hepatocellular Carcinoma

Recently, hepatocyte-sinusoid alignment (HSA) has been identified as a mechanism that supports the coordination of hepatocytes during liver regeneration to reestablish a functional micro-architecture (Hoehme et al. in Proc Natl Acad Sci 107(23):10371-10376, 2010). HSA means that hepatocytes preferentially align along the closest micro-vessels. Here, we studied whether this mechanism is still active in early hepatocellular tumors. The same agent-based spatiotemporal model that previously correctly predicted HSA in liver regeneration was further developed to simulate scenarios in early tumor development, when individual initiated hepatocytes gain increased proliferation capacity. The model simulations were performed under conditions of realistic liver micro-architectures obtained from 3D reconstructions of confocal laser scanning micrographs. Interestingly, the established model predicted that initiated hepatocytes at first arrange in elongated patterns. Only when the tumor progresses to cell numbers of approximately 4000, does it adopt spherical structures. This prediction may have relevant consequences, since elongated tumors may reach critical structures faster, such as larger vessels, compared to a spherical tumor of similar cell number. Interestingly, this model prediction was confirmed by analysis of the spatial organization of initiated hepatocytes in a rat liver tumor initiation study using single doses of 250 mg/kg of the genotoxic carcinogen N-nitrosomorpholine (NNM). Indeed, small clusters of GST-P positive cells induced by NNM were elongated, almost columnar, while larger GDT-P positive foci of approximately the size of liver lobuli adopted spherical shapes. From simulations testing numerous possible mechanisms, only HSA could explain the experimentally observed initial deviation from spherical shape. The present study demonstrates that the architecture of small cell clusters of hepatocytes early after initiation is still controlled by physiological mechanisms. However, this coordinating influence is lost when the tumor grows to approximately 4000 cells, leading to further growth in spherical shape. Our findings stress the potential importance of organ micro-architecture in understanding tumor phenotypes.

Creation of Three-Dimensional Liver Tissue Models from Experimental Images for Systems Medicine

In this chapter, we illustrate how three-dimensional liver tissue models can be created from experimental image modalities by utilizing a well-established processing chain of experiments, microscopic imaging, image processing, image analysis and model construction. We describe how key features of liver tissue architecture are quantified and translated into model parameterizations, and show how a systematic iteration of experiments and model simulations often leads to a better understanding of biological phenomena in systems biology and systems medicine.

Computational Modeling in Liver Surgery

The need for extended liver resection is increasing due to the growing incidence of liver tumors in aging societies. Individualized surgical planning is the key for identifying the optimal resection strategy and to minimize the risk of postoperative liver failure and tumor recurrence. Current computational tools provide virtual planning of liver resection by taking into account the spatial relationship between the tumor and the hepatic vascular trees, as well as the size of the future liver remnant. However, size and function of the liver are not necessarily equivalent. Hence, determining the future liver volume might misestimate the future liver function, especially in cases of hepatic comorbidities such as hepatic steatosis. A systems medicine approach could be applied, including biological, medical, and surgical aspects, by integrating all available anatomical and functional information of the individual patient. Such an approach holds promise for better prediction of postoperative liver function and hence improved risk assessment. This review provides an overview of mathematical models related to the liver and its function and explores their potential relevance for computational liver surgery. We first summarize key facts of hepatic anatomy, physiology, and pathology relevant for hepatic surgery, followed by a description of the computational tools currently used in liver surgical planning. Then we present selected state-of-the-art computational liver models potentially useful to support liver surgery. Finally, we discuss the main challenges that will need to be addressed when developing advanced computational planning tools in the context of liver surgery.

Large-scale computational models of liver metabolism: How far from the clinics?

Understanding the dynamics of human liver metabolism is fundamental for effective diagnosis and treatment of liver diseases. This knowledge can be obtained with systems biology/medicine approaches that account for the complexity of hepatic responses and their systemic consequences in other organs. Computational modeling can reveal hidden principles of the system by classification of individual components, analyzing their interactions and simulating the effects that are difficult to investigate experimentally. Herein, we review the state-of-the-art computational models that describe liver dynamics from metabolic, gene regulatory, and signal transduction perspectives. We focus especially on large-scale liver models described either by genome scale metabolic networks or an object-oriented approach. We also discuss the benefits and limitations of each modeling approach and their value for clinical applications in diagnosis, therapy, and prevention of liver diseases as well as precision medicine in hepatology. (Hepatology 2017;66:1323-1334).

Physiologically-based modelling in mice suggests an aggravated loss of clearance capacity after toxic liver damage

Diseases and toxins may lead to death of active liver tissue, resulting in a loss of total clearance capacity at the whole-body level. However, it remains difficult to study, whether the loss of metabolizing tissue is sufficient to explain loss of metabolic capacity of the liver or whether the surviving tissue undergoes an adaptive response to compensate the loss. To understand the cellular impact of toxic liver damage in an in vivo situation, we here used physiologically-based pharmacokinetic modelling to investigate pharmacokinetics of a specifically designed drug cocktail at three different sampling sites of the body in healthy mice and mice treated with carbon tetrachloride (CCl4). Liver zonation was explicitly quantified in the models through immunostaining of cytochrome P450s enzymes. Comparative analyses between the simulated decrease in clearance capacity and the experimentally measured loss in tissue volume indicated that CCl4-induced impairment of metabolic functions goes beyond the mere loss of metabolically active tissue. The here established integrative modelling strategy hence provides mechanistic insights into functional consequences of toxic liver damage in an in vivo situation, which would not have been accessible by conventional methods.

Facing the challenges of multiscale modelling of bacterial and fungal pathogen-host interactions

Recent and rapidly evolving progress on high-throughput measurement techniques and computational performance has led to the emergence of new disciplines, such as systems medicine and translational systems biology. At the core of these disciplines lies the desire to produce multiscale models: mathematical models that integrate multiple scales of biological organization, ranging from molecular, cellular and tissue models to organ, whole-organism and population scale models. Using such models, hypotheses can systematically be tested. In this review, we present state-of-the-art multiscale modelling of bacterial and fungal infections, considering both the pathogen and host as well as their interaction. Multiscale modelling of the interactions of bacteria, especially Mycobacterium tuberculosis, with the human host is quite advanced. In contrast, models for fungal infections are still in their infancy, in particular regarding infections with the most important human pathogenic fungi, Candida albicans and Aspergillus fumigatus. We reflect on the current availability of computational approaches for multiscale modelling of host-pathogen interactions and point out current challenges. Finally, we provide an outlook for future requirements of multiscale modelling.