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.

Introduction to In Silico Modeling to Study ROS Dynamics.

This book chapter is drafted for biologists with experimental experiences in ROS biology but being newcomers in the field of modeling. We start with a general introduction about computational modeling in biology and an overview of software tools suitable for beginners. This chapter encompasses an introduction to computational models with special focus on simulation of ROS dynamics. A step-by-step tutorial follows providing guidance for all relevant model development processes. This course of action gives a comprehensible way to understand the benefits of computational models and to gain the necessary knowledge to build own small equation-based models. Small models can be created without any special programming expertise or in-depth technical and mathematical knowledge. Afterward in the final section, a short overview of pitfalls, challenges, and limitations is provided, combined with suggestions for further reading to improve and expand modeling skills of biologists.

Computational Modeling of Oxidative Stress in Fatty Livers Elucidates the Underlying Mechanism of the Increased Susceptibility to Ischemia/Reperfusion Injury.

QUESTION: Donor liver organs with moderate to high fat content (i.e. steatosis) suffer from an enhanced susceptibility to ischemia/reperfusion injury (IRI) during liver transplantation. Responsible for the cellular injury is an increased level of oxidative stress, however the underlying mechanistic network is still not fully understood. METHOD: We developed a phenomenological mathematical model of key processes of hepatic lipid metabolism linked to pathways of oxidative stress. The model allows the simulation of hypoxia (i.e. ischemia-like conditions) and reoxygenation (i.e. reperfusion-like conditions) for various degrees of steatosis and predicts the level of hepatic lipid peroxidation (LPO) as a marker of cell damage caused by oxidative stress. RESULTS & CONCLUSIONS: Our modeling results show that the underlying feedback loop between the formation of reactive oxygen species (ROS) and LPO leads to bistable systems behavior. Here, the first stable state corresponds to a low basal level of ROS production. The system is directed to this state for healthy, non-steatotic livers. The second stable state corresponds to a high level of oxidative stress with an enhanced formation of ROS and LPO. This state is reached, if steatotic livers with a high fat content undergo a hypoxic phase. Theoretically, our proposed mechanistic network would support the prediction of the maximal tolerable ischemia time for steatotic livers: Exceeding this limit during the transplantation process would lead to severe IRI and a considerable increased risk for liver failure.

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.

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.

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.

How to Predict Molecular Interactions between Species?

Organisms constantly interact with other species through physical contact which leads to changes on the molecular level, for example the transcriptome. These changes can be monitored for all genes, with the help of high-throughput experiments such as RNA-seq or microarrays. The adaptation of the gene expression to environmental changes within cells is mediated through complex gene regulatory networks. Often, our knowledge of these networks is incomplete. Network inference predicts gene regulatory interactions based on transcriptome data. An emerging application of high-throughput transcriptome studies are dual transcriptomics experiments. Here, the transcriptome of two or more interacting species is measured simultaneously. Based on a dual RNA-seq data set of murine dendritic cells infected with the fungal pathogen Candida albicans, the software tool NetGenerator was applied to predict an inter-species gene regulatory network. To promote further investigations of molecular inter-species interactions, we recently discussed dual RNA-seq experiments for host-pathogen interactions and extended the applied tool NetGenerator (Schulze et al., 2015). The updated version of NetGenerator makes use of measurement variances in the algorithmic procedure and accepts gene expression time series data with missing values. Additionally, we tested multiple modeling scenarios regarding the stimuli functions of the gene regulatory network. Here, we summarize the work by Schulze et al. (2015) and put it into a broader context. We review various studies making use of the dual transcriptomics approach to investigate the molecular basis of interacting species. Besides the application to host-pathogen interactions, dual transcriptomics data are also utilized to study mutualistic and commensalistic interactions. Furthermore, we give a short introduction into additional approaches for the prediction of gene regulatory networks and discuss their application to dual transcriptomics data. We conclude that the application of network inference on dual-transcriptomics data is a promising approach to predict molecular inter-species interactions.