Mechanistic modelling of in vitro transporter processes to improve drug-drug interaction predictions

There is currently a need to evaluate the interaction of drugs in the liver and at the liver membrane, to determine whether the potential for a drug-drug interaction in the clinic could adversely affect a patients prognosis. The interactions of drugs or probe substrates with liver membrane transporters are currently poorly understood at a molecular level, and there is strong interest in terms of the pharmacology of the transporters and how we can examine and understand these interactions through mathematical models. Currently the dynamics of interactions through the use of micro-rate constants, where steady-state assumptions are not implied in data analysis are less favoured. Whilst modelling and data analysis conducted using Michaelis-Menten type kinetics (defined as macro-rate constant mechanistic models), under the assumption of rapid equilibration of substrate with the transporter (association with the transporter is almost instantaneous) are more common. The aim of this thesis is to improve the determination of transporter mediated drug-drug interactions (TrDDIs) in in vitro liver specific cellular systems through the use of structurally identifiable mechanistic models describing the dynamics of the interaction between substrates and inhibitors. This was done by the design of experiments to optimise the data collected for substrate and inhibitors for use within the mechanistic models across different cellular systems (human cell lines, rat and human hepatocytes) under different inhibition conditions. Mechanistic models were developed to obtain robust model fits that adequately described the interaction between substrates and inhibitors, whilst gaining an insight in terms of model selectivity, given the data available. The structural identifiability of the mechanistic models was assessed to ensure that the unknown parameters in the model could be estimated from the experimental data. The mode of inhibition was determined through the use of mechanistic models for each experimental chapter and compared with conclusions drawn in the in literature. The potential for a clinical TrDDI was evaluated for the experimental work in cryopreserved human hepatocytes (Chapter 5), through a worst case scenario static xviii drug interaction model at the entrance to the liver using an \R value", and through the use of a semi-quantitative physiologically based pharmacokinetic (PBPK) model. All the micro-rate constant mechanistic models were at least structurally locally identifiable with no parameters unknown. Conversely, the macro-rate constant mechanistic were only structurally locally identifiable if both substrate and inhibitor were measured (see Chapter 5). Otherwise one to two parameters had to be known for the macro-rate constant mechanistic models to be structurally locally identifiable. Concurrent with the structural identifiability analysis results, in each of the experimental chapters, the use of micro-rate constant mechanistic models were always the best fitting model to the experimental data based on goodness of fit statistics compared to the use of Michaelis-Menten macro-rate constant mechanistic models. Both the micro-rate constant and macro-rate constant mechanistic models were in agreement with regards to the mechanism of inhibition in all experimental cases, whilst the steady-state assumptions required for the use of the Michaelis-Menten equation were only valid for the micro-rate constants derived in Chapter 5. This supported the use of scaled micro-rate constant parameters in Chapter 5 to Michaelis-Menten parameters in the semi-quantitative mechanistic PBPK model in Chapter 6, where there was a potential for a clinical TrDDI given the in vitro data, which was at odds with the determined R value. In conclusion, this work strongly supports the use of micro-rate constants in mechanistic modelling of in vitro TrDDIs to formally test steady-state assumptions through more robust, structurally identifiable parameter estimates.