Modelling HIF-1α dynamics within single cells and neurospheres

HIF-1 (Hypoxia Inducible Factor-1) is an oxygen-regulated transcription factor that mediates the intracellular response to hypoxia in human cells, targeting specific genes that promote cell survival by inducing processes such as angiogenesis and glycolysis. The HIF-1 signalling pathway has been of considerable interest due to its role in mammalian development and in particular several pathologies such as ischemia and cancer. Low cellular oxygen levels are found in cancer due to the rapid proliferation of tumour cells distant to blood vessels (forming a hypoxic core) and the typically irregular vasculature is unable to properly perfuse the tumour. In the Centre for Cell Imaging at the University of Liverpool, time lapsed imaging in an oxygen-controlled environment has captured the transient dynamics of the oxygen regulated subunit of HIF-1, HIF-1α, and revealed heterogeneity between individual cells. The essential characteristics of this data are modelled with a system of differential equations describing the feedback inhibition between HIF-1α and the pathway’s effective oxygen sensors. This novel model was formulated by employing a minimalist approach initially, allowing us to use the rich variety of single-cell data to determine the structure of the feedback loop between two key pathway components. Once the central regulatory motif was identified, the model was expanded to include more complexity, including experimental measurements for model parameter values and additional system components. Oxygen plays an especially important role in the early stages of tumour formation. Measurements of oxygen within cells have been recorded in cultured spheres of neuroblastoma cells at different atmospheric conditions. This data is representative of the early development stages of an avascular tumour and a spatial oxygen-diffusion model was coupled with the single-cell HIF-1α model to describe the dynamics of HIF-1α across a developing tumour. This coupled model is used to study HIF-1α dynamics in the context of various oxygen-dependent cellular functions such as cell-cycle progression and apoptosis by integrating with modifications of published mathematical models

Environmental change and Rift Valley fever in eastern Africa: projecting beyond HEALTHY FUTURES

Outbreaks of Rift Valley fever (RVF), a relatively recently emerged zoonosis endemic to large parts of sub-Saharan Africa that has the potential to spread beyond the continent, have profound health and socio-economic impacts, particularly in communities where resilience is already low. Here output from a new, dynamic disease model [the Liverpool RVF (LRVF) model], driven by downscaled, bias-corrected climate change data from an ensemble of global circulation models from the Inter-Sectoral Impact Model Intercomparison Project run according to two radiative forcing scenarios [representative concentration pathway (RCP)4.5 and RCP8.5], is combined with results of a spatial assessment of social vulnerability to the disease in eastern Africa. The combined approach allowed for analyses of spatial and temporal variations in the risk of RVF to the end of the current century. Results for both scenarios highlight the high-risk of future RVF outbreaks, including in parts of eastern Africa to date unaffected by the disease. The results also highlight the risk of spread from/to countries adjacent to the study area, and possibly farther afield, and the value of considering the geography of future projections of disease risk. Based on the results, there is a clear need to remain vigilant and to invest not only in surveillance and early warning systems, but also in addressing the socio-economic factors that underpin social vulnerability in order to mitigate, effectively, future impacts

A mathematical investigation into the uptake kinetics of nanoparticles in vitro.

Nanoparticles have the potential to increase the efficacy of anticancer drugs whilst reducing off-target side effects. However, there remain uncertainties regarding the cellular uptake kinetics of nanoparticles which could have implications for nanoparticle design and delivery. Polymersomes are nanoparticle candidates for cancer therapy which encapsulate chemotherapy drugs. Here we develop a mathematical model to simulate the uptake of polymersomes via endocytosis, a process by which polymersomes bind to the cell surface before becoming internalised by the cell where they then break down, releasing their contents which could include chemotherapy drugs. We focus on two in vitro configurations relevant to the testing and development of cancer therapies: a well-mixed culture model and a tumour spheroid setup. Our mathematical model of the well-mixed culture model comprises a set of coupled ordinary differential equations for the unbound and bound polymersomes and associated binding dynamics. Using a singular perturbation analysis we identify an optimal number of ligands on the polymersome surface which maximises internalised polymersomes and thus intracellular chemotherapy drug concentration. In our mathematical model of the spheroid, a multiphase system of partial differential equations is developed to describe the spatial and temporal distribution of bound and unbound polymersomes via advection and diffusion, alongside oxygen, tumour growth, cell proliferation and viability. Consistent with experimental observations, the model predicts the evolution of oxygen gradients leading to a necrotic core. We investigate the impact of two different internalisation functions on spheroid growth, a constant and a bond dependent function. It was found that the constant function yields faster uptake and therefore chemotherapy delivery. We also show how various parameters, such as spheroid permeability, lead to travelling wave or steady-state solutions

An innovative in silico model of the oral mucosa reveals the impact of extracellular spaces on chemical permeation through epithelium

In pharmaceutical therapeutic design or toxicology, accurately predicting the permeation of chemicals through human epithelial tissues is crucial, where permeation is significantly influenced by the tissue's cellular architecture. Current mathematical models for multi-layered epithelium such as the oral mucosa only use simplistic 'bricks and mortar' geometries and therefore do not account for the complex cellular architecture of these tissues at the microscale level, such as the extensive plasma membrane convolutions that define the extracellular spaces between cells. Chemicals often permeate tissues via this paracellular route, meaning that permeation is underestimated. To address this, measurements of human buccal mucosal tissue were conducted to ascertain the width and tortuosity of extracellular spaces across the epithelium. Using mechanistic mathematical modelling, we show that the convoluted geometry of extracellular spaces significantly impacts chemical permeation and that this can be approximated, provided that extracellular tortuosity is accounted for. We next developed an advanced physically-relevant in silico model of oral mucosal chemical permeation using partial differential equations, fitted to chemical permeation in vitro assays on tissue-engineered human oral mucosa. Tissue geometries were measured and captured in silico, and permeation examined and predicted for chemicals with different physicochemical properties. The effect of altering the extracellular space to mimic permeation enhancers was also assessed by perturbing the in silico model. This novel in vitro-in silico approach has the potential to expedite pharmaceutical innovation for testing oromucosal chemical permeation, providing a more accurate, physiologically-relevant model which can reduce animal testing with early screening based on chemical properties

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

An innovative in silico model of the oral mucosa reveals the impact of extracellular spaces on chemical permeation through epithelium

In pharmaceutical therapeutic design or toxicology, accurately predicting the permeation of chemicals through human epithelial tissues is crucial, where permeation is significantly influenced by the tissue's cellular architecture. Current mathematical models for multi-layered epithelium such as the oral mucosa only use simplistic 'bricks and mortar' geometries and therefore do not account for the complex cellular architecture of these tissues at the microscale level, such as the extensive plasma membrane convolutions that define the extracellular spaces between cells. Chemicals often permeate tissues via this paracellular route, meaning that permeation is underestimated. To address this, measurements of human buccal mucosal tissue were conducted to ascertain the width and tortuosity of extracellular spaces across the epithelium. Using mechanistic mathematical modelling, we show that the convoluted geometry of extracellular spaces significantly impacts chemical permeation and that this can be approximated, provided that extracellular tortuosity is accounted for. We next developed an advanced physically-relevant in silico model of oral mucosal chemical permeation using partial differential equations, fitted to chemical permeation in vitro assays on tissue-engineered human oral mucosa. Tissue geometries were measured and captured in silico, and permeation examined and predicted for chemicals with different physicochemical properties. The effect of altering the extracellular space to mimic permeation enhancers was also assessed by perturbing the in silico model. This novel in vitro-in silico approach has the potential to expedite pharmaceutical innovation for testing oromucosal chemical permeation, providing a more accurate, physiologically-relevant model which can reduce animal testing with early screening based on chemical properties

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

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

A dynamic, climate-driven model of Rift Valley fever

Outbreaks of Rift Valley fever (RVF) in eastern Africa have previously occurred following specific rainfall dynamics and flooding events that appear to support the emergence of large numbers of mosquito vectors. As such, transmission of the virus is considered to be sensitive to environmental conditions and therefore changes in climate can impact the spatiotemporal dynamics of epizootic vulnerability. Epidemiological information describing the methods and parameters of RVF transmission and its dependence on climatic factors are used to develop a new spatio-temporal mathematical model that simulates these dynamics and can predict the impact of changes in climate. The Liverpool RVF (LRVF) model is a new dynamic, process-based model driven by climate data that provides a predictive output of geographical changes in RVF outbreak susceptibility as a result of the climate and local livestock immunity. This description of the multi-disciplinary process of model development is accessible to mathematicians, epidemiological modellers and climate scientists, uniting dynamic mathematical modelling, empirical parameterisation and state-of-the-art climate information