Mathematical modelling of oxygen gradients in stem cell-derived liver tissue.

A major bottleneck in the study of human liver physiology is the provision of stable liver tissue in sufficient quantity. As a result, current approaches to modelling human drug efficacy and toxicity rely heavily on immortalized human and animal cell lines. These models are informative but do possess significant drawbacks. To address the issues presented by those models, researchers have turned to pluripotent stem cells (PSCs). PSCs can be generated from defined genetic backgrounds, are scalable, and capable of differentiation to all the cell types found in the human body, representing an attractive source of somatic cells for in vitro and in vivo endeavours. Although unlimited numbers of somatic cell types can be generated in vitro, their maturation still remains problematic. In order to develop high fidelity PSC-derived liver tissue, it is necessary to better understand the cell microenvironment in vitro including key elements of liver physiology. In vivo a major driver of zonated liver function is the oxygen gradient that exists from periportal to pericentral regions. In this paper, we demonstrate how cell culture conditions for PSC-derived liver sphere systems can be optimised to recapitulate physiologically relevant oxygen gradients by using mathematical modelling. The mathematical model incorporates some often-understated features and mechanisms of traditional spheroid systems such as cell-specific oxygen uptake, media volume, spheroid size, and well dimensions that can lead to a spatially heterogeneous distribution of oxygen. This mathematical modelling approach allows for the calibration and identification of culture conditions required to generate physiologically realistic function within the microtissue through recapitulation of the in vivo microenvironment.

Multiscale modelling of drug transport and metabolism in liver spheroids.

In early preclinical drug development, potential candidates are tested in the laboratory using isolated cells. These in vitro experiments traditionally involve cells cultured in a two-dimensional monolayer environment. However, cells cultured in three-dimensional spheroid systems have been shown to more closely resemble the functionality and morphology of cells in vivo. While the increasing usage of hepatic spheroid cultures allows for more relevant experimentation in a more realistic biological environment, the underlying physical processes of drug transport, uptake and metabolism contributing to the spatial distribution of drugs in these spheroids remain poorly understood. The development of a multiscale mathematical modelling framework describing the spatio-temporal dynamics of drugs in multicellular environments enables mechanistic insight into the behaviour of these systems. Here, our analysis of cell membrane permeation and porosity throughout the spheroid reveals the impact of these properties on drug penetration, with maximal disparity between zonal metabolism rates occurring for drugs of intermediate lipophilicity. Our research shows how mathematical models can be used to simulate the activity and transport of drugs in hepatic spheroids and in principle any organoid, with the ultimate aim of better informing experimentalists on how to regulate dosing and culture conditions to more effectively optimize drug delivery.

Mathematical modelling of fluid flow and solute transport to define operating parameters for in vitro perfusion cell culture systems.

In recent years, there has been a move away from the use of static in vitro two-dimensional cell culture models for testing the chemical safety and efficacy of drugs. Such models are increasingly being replaced by more physiologically relevant cell culture systems featuring dynamic flow and/or three-dimensional structures of cells. While it is acknowledged that such systems provide a more realistic environment within which to test drugs, progress is being hindered by a lack of understanding of the physical and chemical environment that the cells are exposed to. Mathematical and computational modelling may be exploited in this regard to unravel the dependency of the cell response on spatio-temporal differences in chemical and mechanical cues, thereby assisting with the understanding and design of these systems. In this paper, we present a mathematical modelling framework that characterizes the fluid flow and solute transport in perfusion bioreactors featuring an inlet and an outlet. To demonstrate the utility of our model, we simulated the fluid dynamics and solute concentration profiles for a variety of different flow rates, inlet solute concentrations and cell types within a specific commercial bioreactor chamber. Our subsequent analysis has elucidated the basic relationship between inlet flow rate and cell surface flow speed, shear stress and solute concentrations, allowing us to derive simple but useful relationships that enable prediction of the behaviour of the system under a variety of experimental conditions, prior to experimentation. We describe how the model may used by experimentalists to define operating parameters for their particular perfusion cell culture systems and highlight some operating conditions that should be avoided. Finally, we critically comment on the limitations of mathematical and computational modelling in this field, and the challenges associated with the adoption of such methods.

Modelling the effects of glucagon during glucose tolerance testing.

BACKGROUND: Glucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship. RESULTS: Both models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (sG) and insulin sensitivity (sI). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (sE) and glucagon sensitivity (δ). CONCLUSIONS: The models are used to investigate how different degrees of pax'tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted.

Preparation of Primary Rat Hepatocyte Spheroids Utilizing the Liquid-Overlay Technique.

Herein, we describe a protocol for the preparation and analysis of primary isolated rat hepatocytes in a 3D cell culture format described as spheroids. The hepatocyte cells spontaneously self-aggregate into spheroids without the need for synthetic extracellular matrices or hydrogels. Primary rat hepatocytes (PRHs) are a readily available source of primary differentiated liver cells and therefore conserve many of the required liver-specific functional markers, and elicit the natural in vivo phenotype when compared with common hepatic cells lines. We describe the liquid-overlay technique which provides an ultra-low attachment surface on which PRHs can be cultured as spheroids. © 2019 The Authors. Basic Protocol 1: Preparation of agarose-coated plates Basic Protocol 2: Primary rat hepatocyte isolation procedure Basic Protocol 3: Primary rat hepatocyte spheroid culture Basic Protocol 4: Immunofluorescent analysis of PRH spheroids.

CD28 Superagonistic Activation of T Cells Induces a Tumor Cell-Like Metabolic Program.

CD28 superagonist (CD28SA), a therapeutic immunomodulatory monoclonal antibody triggered rapid and exaggerated activation of CD4+ effector memory T cells (TEMs) in humans with unwanted serious adverse effects. It is well known that distinct metabolic programs determine the fate and responses of immune cells. In this study, we show that human CD4+ TEMs stimulated with CD28SA adopt a metabolic program similar to those of tumor cells with enhanced glucose utilization, lipid biosynthesis, and proliferation in hypoxic conditions. Identification of metabolic profiles underlying hyperactive T cell activation would provide a platform to test safety of immunostimulatory antibodies.

In vitro Liver Zonation of Primary Rat Hepatocytes.

The ability of the liver to simultaneously carry out multiple functions is dependent on the metabolic heterogeneity of hepatocytes spatially located within a liver lobule spanning from the portal triad to the central vein. This complex zonal architecture of the liver, however, makes accurate in vitro modeling a challenge and often standard culture systems assume a homogenous model which may lead to inaccurate translatability of results. Here, we use a combination of mathematical modeling and experimental data to demonstrate a readily constructible in vitro flow system capable of liver zonation in primary rat hepatocytes. We show the differential expression of zonation markers, enhanced functionality when compared to standard static cultures and zone-specific metabolism and cell damage in the presence of paracetamol, a known zone-specific toxin. This type of advanced system provides a more in-depth and essential understanding of liver physiology and pathophysiology as well as the accurate evaluation of pharmacological interventions at a zone-specific level.

Attenuation of doxorubicin-induced cardiotoxicity in a human in vitro cardiac model by the induction of the NRF-2 pathway.

Dose-dependent cardiotoxicity is the leading adverse reaction seen in cancer patients treated with doxorubicin. Currently, dexrazoxane is the only approved drug that can partially protect against this toxicity in patients, however, its administration is restricted to those patients receiving a high cumulative dose of anthracyclines. Investigations into the mechanisms of cardiotoxicity and efforts to improve cardioprotective strategies have been hindered by the limited availability of a phenotypically relevant in vitro adult human cardiac model system. Here, we adapted a readily reproducible, functional 3D human multi-cell type cardiac system to emulate patient responses seen with doxorubicin and dexrazoxane. We show that administration of two NRF2 gene inducers namely the semi-synthetic triterpenoid Bardoxolone methyl, and the isothiocyanate sulfurophane, result in cardioprotection against doxorubicin toxicity comparable to dexrazoxane as evidenced by an increase in cell viability and a decrease in the production of reactive oxygen species. We further show a synergistic attenuation of cardiotoxicity when the NRF2 inducers and dexrazoxane are used in tandem. Taken together, our data indicate that the 3D spheroid is a suitable model to investigate drug induced cardiotoxicity and we reveal an essential role of the NRF2 pathway in cardioprotection providing a novel pharmacological mechanism and intervention route towards the alleviation of doxorubicin-induced toxicity.

Characterisation of a functional rat hepatocyte spheroid model.

Many in vitro liver cell models, such as 2D systems, that are used to assess the hepatotoxic potential of xenobiotics suffer major limitations arising from a lack of preservation of physiological phenotype and metabolic competence. To circumvent some of these limitations there has been increased focus on producing more representative 3D models. Here we have used a novel approach to construct a size-controllable 3D hepatic spheroid model using freshly isolated primary rat hepatocytes (PRH) utilising the liquid-overlay technique whereby PRH spontaneously self-assemble in to 3D microtissues. This system produces viable spheroids with a compact in vivo-like structure for up to 21 days with sustained albumin production for the duration of the culture period. F-actin was seen throughout the spheroid body and P-glycoprotein (P-gp) and multidrug resistance-associated protein 2 (MRP2) transporters had polarised expression on the canalicular membrane of hepatocytes within the spheroids upon formation (day 3). The MRP2 transporter was able to functionally transport 5 µM 5-chloromethylfluorescein diacetate (CMFDA) substrates into these canalicular structures. These PRH spheroids display in vivo characteristics including direct cell-cell contacts, cellular polarisation, 3D cellular morphology, and formation of functional secondary structures throughout the spheroid. Such a well-characterised system could be readily exploited for pre-clinical and non-clinical repeat-dose investigations and could make a significant contribution to replace, reduce and refine the use of animals for applied research.

Modelling the impact of changes in the extracellular environment on the cytosolic free NAD+/NADH ratio during cell culture.

Cancer cells depend on glucose metabolism via glycolysis as a primary energy source, despite the presence of oxygen and fully functioning mitochondria, in order to promote growth, proliferation and longevity. Glycolysis relies upon NAD+ to accept electrons in the glyceraldehyde-3-phosphate dehydrogenase (GAPDH) reaction, linking the redox state of the cytosolic NAD+ pool to glycolytic rate. The free cytosolic NAD+/NADH ratio is involved in over 700 oxidoreductive enzymatic reactions and as such, the NAD+/NADH ratio is regarded as a metabolic readout of overall cellular redox state. Many experimental techniques that monitor or measure total NAD+ and NADH are unable to distinguish between protein-bound and unbound forms. Yet total NAD+/NADH measurements yield little information, since it is the free forms of NAD+ and NADH that determine the kinetic and thermodynamic influence of redox potential on glycolytic rate. Indirect estimations of free NAD+/NADH are based on the lactate/pyruvate (L/P) ratio at chemical equilibrium, but these measurements are often undermined by high lability. To elucidate the sensitivity of the free NAD+/NADH ratio to changes in extracellular substrate, an in silico model of hepatocarcinoma glycolysis was constructed and validated against in vitro data. Model simulations reveal that over experimentally relevant concentrations, changes in extracellular glucose and lactate concentration during routine cancer cell culture can lead to significant deviations in the NAD+/NADH ratio. Based on the principles of chemical equilibrium, the model provides a platform from which experimentally challenging situations may be examined, suggesting that extracellular substrates play an important role in cellular redox and bioenergetic homeostasis.

A critical review of adverse effects to the kidney: mechanisms, data sources, and in silico tools to assist prediction.

INTRODUCTION: The kidney is a major target for toxicity elicited by pharmaceuticals and environmental pollutants. Standard testing which often does not investigate underlying mechanisms has proven not to be an adequate hazard assessment approach. As such, there is an opportunity for the application of computational approaches that utilize multiscale data based on the Adverse Outcome Pathway (AOP) paradigm, coupled with an understanding of the chemistry underpinning the molecular initiating event (MIE) to provide a deep understanding of how structural fragments of molecules relate to specific mechanisms of nephrotoxicity. Aims covered: The aim of this investigation was to review the current scientific landscape related to computational methods, including mechanistic data, AOPs, publicly available knowledge bases and current in silico models, for the assessment of pharmaceuticals and other chemicals with regard to their potential to elicit nephrotoxicity. A list of over 250 nephrotoxicants enriched with, where possible, mechanistic and AOP-derived understanding was compiled. Expert opinion: Whilst little mechanistic evidence has been translated into AOPs, this review identified a number of data sources of in vitro, in vivo, and human data that may assist in the development of in silico models which in turn may shed light on the interrelationships between nephrotoxicity mechanisms.

A Combined In Vitro/In Silico Approach to Identifying Off-Target Receptor Toxicity.

Many xenobiotics can bind to off-target receptors and cause toxicity via the dysregulation of downstream transcription factors. Identification of subsequent off-target toxicity in these chemicals has often required extensive chemical testing in animal models. An alternative, integrated in vitro/in silico approach for predicting toxic off-target functional responses is presented to refine in vitro receptor identification and reduce the burden on in vivo testing. As part of the methodology, mathematical modeling is used to mechanistically describe processes that regulate transcriptional activity following receptor-ligand binding informed by transcription factor signaling assays. Critical reactions in the signaling cascade are identified to highlight potential perturbation points in the biochemical network that can guide and optimize additional in vitro testing. A physiologically based pharmacokinetic model provides information on the timing and localization of different levels of receptor activation informing whole-body toxic potential resulting from off-target binding.

Systems Toxicology Approach to Identifying Paracetamol Overdose.

Paracetamol (acetaminophen (APAP)) is one of the most commonly used analgesics in the United Kingdom and the United States. However, exceeding the maximum recommended dose can cause serious liver injury and even death. Promising APAP toxicity biomarkers are thought to add value to those used currently and clarification of the functional relationships between these biomarkers and liver injury would aid clinical implementation of an improved APAP toxicity identification framework. The framework currently used to define an APAP overdose is highly dependent upon time since ingestion and initial dose; information that is often highly unpredictable. A pharmacokinetic/pharmacodynamic (PK/PD) APAP model has been built in order to understand the relationships between a panel of biomarkers and APAP dose. Visualization and statistical tools have been used to predict initial APAP dose and time since administration. Additionally, logistic regression analysis has been applied to histology data to provide a prediction of the probability of liver injury.

Impact of cell types and culture methods on the functionality of in vitro liver systems - A review of cell systems for hepatotoxicity assessment.

Xenobiotic safety assessment is an area that impacts a multitude of different industry sectors such as medicinal drugs, agrochemicals, industrial chemicals, cosmetics and environmental contaminants. As such there are a number of well-developed in vitro, in vivo and in silico approaches to evaluate their properties and potential impact on the environment and to humans. Additionally, there is the continual investment in multidisciplinary scientists to explore non-animal surrogate technologies to predict specific toxicological outcomes and to improve our understanding of the biological processes regarding the toxic potential of xenobiotics. Here we provide a concise, critical evaluation of a number of in vitro systems utilised to assess the hepatotoxic potential of xenobiotics.

Expression and enzyme activity of cytochrome P450 enzymes CYP3A4 and CYP3A5 in human skin and tissue-engineered skin equivalents.

CYP3A4 and CYP4A5 share specificity for a wide range of xenobiotics with the CYP3 subfamily collectively involved in the biotransformation of approximately 30% of all drugs. CYP3A4/5 mRNA transcripts have been reported in the skin, yet knowledge of their protein expression and function is lacking. In this study, we observed gene and protein expression of CYP3A4/5 in both human skin and tissue-engineered skin equivalents (TESEs), and enzyme activity was detected using the model substrate benzyl-O-methyl-cyanocoumarin. Mass spectrometric analysis of TESE lysates following testosterone application revealed a time-dependent increase in metabolite production, confirming the functional expression of these enzymes in skin.

Characterization of a functional C3A liver spheroid model.

More predictive in vitro liver models are a critical requirement for preclinical screening of compounds demonstrating hepatotoxic liability. 3D liver spheroids have been shown to have an enhanced functional lifespan compared to 2D monocultures; however a detailed characterisation of spatiotemporal function and structure of spheroids still needs further attention before widespread use in industry. We have developed and characterized the structure and function of a 3D liver spheroid model formed from C3A hepatoma cells. Spheroids were viable and maintained a compact in vivo-like structure with zonation features for up to 32 days. MRP2 and Pgp transporters had polarised expression on the canalicular membrane of cells in the spheroids and were able to functionally transport CMFDA substrate into these canalicular structures. Spheroids expressed CYP2E1 and were able to synthesise and secrete albumin and urea to a higher degree than monolayer C3A cultures. Penetration of doxorubicin throughout the spheroid core was demonstrated. Spheroids showed increased susceptibility to hepatotoxins when compared to 2D cultures, with acetaminophen having an IC50 of 7.2 mM in spheroids compared to 33.8 mM in monolayer culture. To conclude, we developed an alternative method for creating C3A liver spheroids and demonstrated cellular polarisation and zonation, as well as superior liver-specific functionality and more sensitive toxicological response compared to standard 2D liver models, confirming a more in vivo-like liver model.

Failure to upregulate cell surface PD-1 is associated with dysregulated stimulation of T cells by TGN1412-like CD28 superagonist.

The CD28 superagonist (CD28SA) TGN1412 was administered to humans as an agent that can selectively activate and expand regulatory T cells but resulted in uncontrolled T cell activation accompanied by cytokine storm. The molecular mechanisms that underlie this uncontrolled T cell activation are unclear. Physiological activation of T cells leads to upregulation of not only activation molecules but also inhibitory receptors such as PD-1. We hypothesized that the uncontrolled activation of CD28SA-stimulated T cells is due to both the enhanced expression of activation molecules and the lack of or reduced inhibitory signals. In this study, we show that anti-CD3 antibody-stimulated human T cells undergo time-limited controlled DNA synthesis, proliferation and interleukin-2 secretion, accompanied by PD-1 expression. In contrast, CD28SA-activated T cells demonstrate uncontrolled activation parameters including enhanced expression of LFA-1 and CCR5 but fail to express PD-1 on the cell surface. We demonstrate the functional relevance of the lack of PD-1 mediated regulatory mechanism in CD28SA-stimulated T cells. Our findings provide a molecular explanation for the dysregulated activation of CD28SA-stimulated T cells and also highlight the potential for the use of differential expression of PD-1 as a biomarker of safety for T cell immunostimulatory biologics.

Combined mathematical modelling and experimentation to predict polymersome uptake by oral cancer cells.

This study is motivated by understanding and controlling the key physical properties underlying internalisation of nano drug delivery. We consider the internalisation of specific nanometre size delivery vehicles, comprised of self-assembling amphiphilic block copolymers, called polymersomes that have the potential to specifically deliver anticancer therapeutics to tumour cells. The possible benefits of targeted polymersome drug delivery include reduced off-target toxic effects in healthy tissue and increased drug uptake by diseased tissue. Through a combination of in vitro experimentation and mathematical modelling, we develop a validated model of nanoparticle uptake by cells via the clathrin-mediated endocytotic pathway, incorporating receptor binding, clustering and recycling. The model predicts how the characteristics of receptor targeting, and the size and concentration of polymersomes alter uptake by tumour cells. The number of receptors per cell was identified as being the dominant mechanism accounting for the difference between cell types in polymersome uptake rate. FROM THE CLINICAL EDITOR: This article reports on a validated model developed through a combination of in vitro experimentation and mathematical modeling of nanoparticle uptake by cells via the clathrin-mediated endocytotic pathway. The model incorporates receptor binding, clustering, and recycling and predicts how the characteristics of receptor targeting, the size and concentration alter polymersome uptake by cancer cells.

A cellular automaton model examining the effects of oxygen, hydrogen ions and lactate on early tumour growth.

Some tumours are known to exhibit an extracellular pH that is more acidic than the intracellular, creating a 'reversed pH gradient' across the cell membrane and this has been shown to affect their invasive and metastatic potential. Tumour hypoxia also plays an important role in tumour development and has been directly linked to both tumour morphology and aggressiveness. In this paper, we present a hybrid mathematical model of intracellular pH regulation that examines the effect of oxygen and pH on tumour growth and morphology. In particular, we investigate the impact of pH regulatory mechanisms on the cellular pH gradient and tumour morphology. Analysis of the model shows that: low activity of the Na+/H+ exchanger or a high rate of anaerobic glycolysis can give rise to a "fingering" tumour morphology; and a high activity of the lactate/H+ symporter can result in a reversed transmembrane pH gradient across a large portion of the tumour mass. Also, the reversed pH gradient is spatially heterogeneous within the tumour, with a normal pH gradient observed within an intermediate growth layer within the spheroid. We also include a fractal dimension analysis of the simulated tumour contours, in which we compare the fractal dimensions of the simulated tumour surfaces with those found experimentally via photomicrographs.

Theoretical predictions of lactate and hydrogen ion distributions in tumours.

High levels of lactate and H(+)-ions play an important role in the invasive and metastatic cascade of some tumours. We develop a mathematical model of cellular pH regulation focusing on the activity of the Na(+)/H(+) exchanger (NHE) and the lactate/H(+) symporter (MCT) to investigate the spatial correlations of extracellular lactate and H(+)-ions. We highlight a crucial role for blood vessel perfusion rates in determining the spatial correlation between these two cations. We also predict critical roles for blood lactate, the activity of the MCTs and NHEs on the direction of the cellular pH gradient in the tumour. We also incorporate experimentally determined heterogeneous distributions of the NHE and MCT transporters. We show that this can give rise to a higher intracellular pH and a lower intracellular lactate but does not affect the direction of the reversed cellular pH gradient or redistribution of protons away from the glycolytic source. On the other hand, including intercellular gap junction communication in our model can give rise to a reversed cellular pH gradient and can influence the levels of pH.