| Summary: | Yes-associated protein (YAP) is a transcription regulator with a highly significant role in a wide variety of cancers. When YAP is transported into the cell nucleus, it activates a programme of genes which promote cell proliferation and confer resistance to regulatory signals that normally limit tissue growth. YAP has been shown to promote malignancy and metastasis in tumours and is thus the object of much current biological and medical research. The aim of this thesis is to investigate quantitatively the factors which cause excessive nuclear accumulation of YAP in cancer-associated fibroblasts. To this end, we utilise data from two common experimental techniques, fluorescence recovery after photobleaching (FRAP) and fluorescence loss in photobleaching (FLIP).
We develop the theory of FRAP, deriving several new (to our knowledge) approximation formulas. We establish conditions to ensure the viability of parameter estimation and propose a fitting protocol which can theoretically produce, at the very least, estimates of the ratio of bound to unbound molecules at chemical equilibrium. We implement a numerical cell simulation which we then fit to empirical FRAP data from fibroblast nuclei.
FLIP can be used to estimate the rate of shuttling between the nucleus and cytoplasm. This process depends on the $3$D geometry of the nuclear membrane, yet often only $2$D imaging data are available. We propose a simple ODE model which can account for $3$D effects when only $2$D data are available. We also implement a numerical FLIP model which incorporates active transport across the nuclear membrane and cell motion during the experiment. Using both the ODE and PDE FLIP models, we are able to investigate quantitatively YAP nucleocytoplasmic shuttling, and the ratio of bound to unbound YAP molecules at equilibrium in fibroblast cytoplasm.
Combing FRAP and FLIP results, we quantify the differences in YAP regulation between normal fibroblasts (NFs) and cancer-associated fibroblasts (CAFs). We find that, in order of importance, increased nuclear import, reduced nuclear export, weaker binding reactions in the cytoplasm and stronger binding reactions in the nucleus all contribute to the localisation of YAP to the nucleus in CAFs. Though YAP is the immediate focus of the thesis, the methodology we develop could be applied to a wide variety of other proteins.
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