Statistical analysis of protein patternation on cell membranes during immunological synapse

A statistical analysis of two different experiments is considered. Both of them are related to understanding the mechanism behind the distribution of molecules involved in formation of organized patterns of protein complexes and molecules in the contact interface between the membranes of an immune cell and an antigen presenting cell. Such patterns are called immunological synapses. In the first experiment a T-cell is adhering to the flat surface of a lipid bilayer. There are molecules of two types on the surface of the bilayer. They are fluorescently labelled with different colours so their distribution can be observed using microscope. During the contact molecules of one type are binding while second type molecules stay unbound. This results in segregation of different type molecules and forming a synapse pattern that can be observed and scanned using confocal microscopy. In the case of lipid bilayer the contact interface is flat and the whole contact interface can be scanned as a single image. The second experiment deals with NK-cells forming synapses with target antigen presenting cells. Two-colour fluorescent labelling is used again and a similar protein patternation on the cell-cell contact interface can observed using confocal microscopy. The main difference with the first experiment is in imaging technique as instead of a single image a series of confocal images is made along the same axis which is approximately parallel to the synapse interface. As a result a stack of cross-section fluorescence images of the interacting cells is considered for the quantitative analysis. In both experiments it is possible to observe the segregation of labelled molecules during the formation of the synapse pattern. In terms of fluorescence intensity values this is expressed in strong negative correlation between different colour fluorescence. We introduce a model based on the hypothesis of exclusion by size which explains the mutual segregation of molecules as a result of elastic properties of single molecules and bonds combined with the properties of the cell membrane. Based on this model a computational algorithm for the Bayesian statistical analysis of fluorescence images is developed in order to estimate relevant physical parameters that cannot be measured explicitly.