In this work we analyse aspects of dynamics and organization of biological membranes from a physical prospective [i.e. perspective]. We provide an analysis of the process of self-assembly and spatial organization of membrane proteins. We illustrate the analysis by considering a channel activated by membrane tension called mechanosensitive channels (MS), in E. coli and the twin arginine translocation system (Tat). We analyse the mechanism of formation of oligomeric protein complexes formed by identical subunits. By derivation of a mathematical approach based on Smoluchowski coagulation equation, we study the deficiency of the process of complex formation, taking into account both irreversible aggregation, as well as fragmentation. We find that a small fragmentation rate increases the efficiency of the formation process, however if the fragmentation rate vanishes the irreversible process is very inefficient. Our second aim is to determine how the spatial organization can affect the function of channels, which are regulated by elastic forces. We map these short-range interactions into a discretized system, from which we obtain the spatial distribution of the channels and its effect on the gating dynamics. We find that organized channels activate at lower membrane tensions, but possess a delay in the reaction time. In the last part we determine how the formation of transient pores on the membrane depends on the dynamics of its assembly process. We analyse the pores formed by the Tat complex, which is responsible for protein transport through the membrane. This system functions by polimerization in response to a signal of transport demand from a protein in the cell cytoplasm. The direct correlation of the size of the assembled pore and the size of the protein determines the speed of the translocation process. Using a differential equation approach we obtain that the flux of a given protein depends quadratically on its size.

Maintenance of apico-basal polarity is essential for epithelial integrity and requires particular reinforcement during tissue morphogenesis, when cells are reorganised, undergo shape changes and remodel their junctions. It is well established that epithelial integrity during morphogenetic processes depends on the dynamic exchange of adherens junction components, but our knowledge on the dynamics of other proteins and their dynamics during these processes is still limited. The early Drosophila embryo is an ideal system to study membrane dynamics during morphogenesis. Here, morphogenetic activities differ along the anterior-posterior axis, with the extending germband showing a high degree of epithelial remodelling. We developed a Fluorescence Recovery After Photobleaching (FRAP) assay with a higher temporal resolution, which allowed the distinction between a fast and a slow component of recovery of membrane proteins during the germband extension stage. We show for the first time that the recovery kinetics of a general membrane marker, SpiderGFP, differs in the anterior and posterior parts of the embryo, which correlates well with the different morphogenetic activities of the respective embryonic regions. Interestingly, absence of crumbs, a polarity regulator essential for epithelial integrity in the Drosophila embryo, decreases the fast component of SpiderGFP and of the apical marker Stranded at Second-Venus specifically in the anterior region. We suggest that the defects in kinetics observed in crumbs mutant embryos are the first signs of tissue instability in this region, explaining the earlier breakdown of the head epidermis in comparison to that of the trunk, and that diffusion in the plasma membrane is affected by the absence of Crumbs.