Mathematical modelling of a liver hollow fibre bioreactor.

A mathematical model has been developed to assist with the development of a hollow fibre bioreactor (HFB) for hepatotoxicity testing of xenobiotics; specifically, to inform the HFB operating set-up, interpret data from HFB outputs and aid in optimizing HFB design to mimic certain hepatic physiological conditions. Additionally, the mathematical model has been used to identify the key HFB and compound parameters that will affect xenobiotic clearance. The analysis of this model has produced novel results that allow the operating set-up to be calculated, and predictions of compound clearance to be generated. The mathematical model predicts the inlet oxygen concentration and volumetric flow rate that gives a physiological oxygen gradient in the HFB to mimic a liver sinusoid. It has also been used to predict the concentration gradients and clearance of a test drug and paradigm hepatotoxin, paracetamol (APAP). The effect of altering the HFB dimensions and fibre properties on APAP clearance under the condition of a physiological oxygen gradient is analysed. These theoretical predictions can be used to design the most appropriate experimental set up and data analysis to quantitatively compare the functionality of cell types that are cultured within the HFB to those in other systems.

A mathematical model of the mevalonate cholesterol biosynthesis pathway.

We formulate, parameterise and analyse a mathematical model of the mevalonate pathway, a key pathway in the synthesis of cholesterol. Of high clinical importance, the pathway incorporates rate limiting enzymatic reactions with multiple negative feedbacks. In this work we investigate the pathway dynamics and demonstrate that rate limiting steps and negative feedbacks within it act in concert to tightly regulate intracellular cholesterol levels. Formulated using the theory of nonlinear ordinary differential equations and parameterised in the context of a hepatocyte, the governing equations are analysed numerically and analytically. Sensitivity and mathematical analysis demonstrate the importance of the two rate limiting enzymes 3-hydroxy-3-methylglutaryl-CoA reductase and squalene synthase in controlling the concentration of substrates within the pathway as well as that of cholesterol. The role of individual feedbacks, both global (between that of cholesterol and sterol regulatory element-binding protein 2; SREBP-2) and local internal (between substrates in the pathway) are investigated. We find that whilst the cholesterol SREBP-2 feedback regulates the overall system dynamics, local feedbacks activate within the pathway to tightly regulate the overall cellular cholesterol concentration. The network stability is analysed by constructing a reduced model of the full pathway and is shown to exhibit one real, stable steady-state. We close by addressing the biological question as to how farnesyl-PP levels are affected by CYP51 inhibition, and demonstrate that the regulatory mechanisms within the network work in unison to ensure they remain bounded.

A hierarchical Bayesian model for extreme pesticide residues.

The number of residue measurements in an individual field trial, carried out to provide data for a pesticide registration for a particular crop, is generally too small to estimate upper tails of the residue distribution for that crop with any certainty. We present a new method, using extreme value theory, which pools information from various field trials, with different crop and pesticide combinations, to provide a common model for the upper tails of residue distributions generally. The method can be used to improve the estimation of high quantiles of a particular residue distribution. It provides a flexible alternative to the direct fitting of a distribution to each individual dataset, and does not require strong distributional assumptions. By using a hierarchical Bayesian model, our method also accounts for parameter uncertainty. The method is applied to a range of supervised trials containing residues on individual items (e.g. on individual apples), and the results illustrate the variation in tail properties amongst all commodities and pesticides. The outputs could be used to select conservative high percentile residue levels as part of a deterministic risk assessment, taking account of the variability between crops and pesticides and also the uncertainty due to relatively small datasets.

Application of a Bayesian deconvolution approach for high-resolution (1)H NMR spectra to assessing the metabolic effects of acute phenobarbital exposure in liver tissue.

High-resolution (1)H NMR spectroscopy is frequently used in the field of metabolomics to assess the metabolites found in biofluids or tissue extracts to define a metabolic profile that describes a given biological process. In this study, we aimed to increase the utility of NMR-based metabolomics by using advanced Bayesian modeling of the time-domain high-resolution 1D NMR free induction decay (FID). The improvement over traditional nonparametric binning is twofold and associated with enhanced resolution of the analysis and automation of the signal processing stage. The automation is achieved by using a Bayesian formalism for all parameters of the model including the number of components. The approach is illustrated with a study of early markers of acute exposure to different doses of a well-characterized nongenotoxic hepatocarcinogen, phenobarbital, in rats. The results demonstrate that Bayesian deconvolution produces a better model for the NMR spectra that allows the identification of subtle changes in metabolic concentrations and a decrease in the expected false discovery rate compared with approaches based on "binning". These properties suggest that Bayesian deconvolution could facilitate the biomarker discovery process and improve information extraction from high-resolution NMR spectra.

Prediction of photoperiodic regulators from quantitative gene circuit models.

Photoperiod sensors allow physiological adaptation to the changing seasons. The prevalent hypothesis is that day length perception is mediated through coupling of an endogenous rhythm with an external light signal. Sufficient molecular data are available to test this quantitatively in plants, though not yet in mammals. In Arabidopsis, the clock-regulated genes CONSTANS (CO) and FLAVIN, KELCH, F-BOX (FKF1) and their light-sensitive proteins are thought to form an external coincidence sensor. Here, we model the integration of light and timing information by CO, its target gene FLOWERING LOCUS T (FT), and the circadian clock. Among other predictions, our models show that FKF1 activates FT. We demonstrate experimentally that this effect is independent of the known activation of CO by FKF1, thus we locate a major, novel controller of photoperiodism. External coincidence is part of a complex photoperiod sensor: modeling makes this complexity explicit and may thus contribute to crop improvement.