Analysis of the developmental effects of foetal-maternal thyroid hormone metabolism and signalling using mathematical modelling

Iodine deficiency and other causes of hypothyroidism are known to cause neurological deficits in humans and therefore homeostasis of thyroid hormones via metabolism is essential for brain development. The goal of this work is to understand the regulation of thyroid hormone metabolic pathways in the combined foetal-maternal unit and their impact on development. We will do this by extending our recently developed mathematical model of thyroid hormone homeostasis in the brain, created at a recent Maths in Medicine study group (MMSG). The MMSG participants created a novel sub model that consisted of thyroid hormone metabolism and effects in the brain. In this model blood i.e. external T4 enters the glial cell and is turned into T3 in a reaction that is catalysed by a deiodinase D2. This is regulated by the ubiquitination of the T4-D2 complex, which both inhibits and marks the complex for degradation. In turn, T3 downregulates the production of D2. To model this downregulation, we explicitly included the binding of T3 to thyroid hormone receptors (R) on the DNA to form bound DNA (DNAB). Meanwhile the fraction of the total amount of DNA (DNAT) that is free (DNAF) produces mRNA (m), which in turn gives D2. In neurones close by, a second deiodinase D3 catalyses the production of rT3 from T4 and T2 from T3. The model was formulated as a system of ordinary differential equations (ODEs) and as a Petri Net (PN) - the PN is a graphical based model which is useful in identifying critical perturbations within biological reaction networks and the ODEs can give quantitative information e.g. threshold effect concentrations of T4 etc. Simulation and numerical solutions showed that over a wide range of blood T4 concentrations this model could maintain homeostasis of T3-Thyroid Receptor complex levels, however there was a concentration below which this was not maintained. The extension of this sub-model into a more physiological model including the systemic control of T3 and T4 that includes the control of the hypothalamic-pituitary-thyroid axis and liver metabolism of thyroid hormones was identified as an activity for further study. The objective of this PhD studentship is to build an appropriate model that incorporates these three elements.

We propose to utilise this studentship to take forward this initial work to develop a fully quantitative and validated whole body mother/foetus model for thyroid hormone control. The project will be subdivided into the following interconnected tasks:

* Extend the mathematical models developed at the MMSG study group to generate a fully parameterised/validated submodel of thyroid hormone homeostasis in the brain.
* Use the mathematical models to identify potential long term effects on brain homeostasis from circulating hormone perturbations.
* Use techniques from control analysis to tease out the interplay between the (rapid) deiodinase regulated and (relatively slow) protein synthesis processes in coordination of the thyroid hormone response.
* The student will then develop a whole body physiologically based pharmacokinetic (PK) model with compartments for different areas of the body, including compartments for the liver, blood, thyroid, brain and other tissues. This model will link into our previous ODE mechanistic brain model.
* The student will develop an extended linked mother / foetus PB-PK model which can be used to assess the effects of changes in maternal thyroid levels on the hormone levels in the foetus.