Membrane coupled to the cytoskeleton: Fluctuations and stability

Gumede, Sthembiso Reuben (2019-04)

Thesis (PhD)--Stellenbosch University, 2019.

Thesis

ENGLISH ABSTRACT : In erythrocytes the plasma membrane is coupled to the underlying two dimensional hexagonal network of spectrin filaments through protein node complexes. There are also other protein complexes that link an individual filament to the bilayer at a random point along its length. This network, together with a repulsive glycocalix, is responsible for large shape changes and shape transformation sequence of these erythrocytes. It has been experimentally shown that the stiffening of the erythrocytes after infection by malaria Plasmodium falciparum parasite, for instance, correlates with the structural transformation in the network. We develop a model to treat the detachment of a membrane from such a substrate, which might be a model for structural failure of erythrocytes. We consider a flexible membrane elastically linked at random points to a substrate under an applied pressure differential across the membrane. This quenched randomness requires the use of the replica formalism, which we investigate from both replica symmetric and weakly broken replica symmetry perspectives. We compare these results with the continuum and the annealed adhesion models we first construct. The fluctuation spectrum as function of the pressure, generally, shows that the average square fluctuations increases with the pressure. However, for the discrete inhomogeneous adhesion, when the position of tethers distribution is quenched the square fluctuation exhibit a non monotonic behavior. Our model characterize the role of the pressure and the disorder in the emergent non monotonic fluctuation spectrum for the different treatment of the tether position distribution randomness. The annealed tether position distribution yields a monotonic relation of increase for the square fluctuations with the removal of tethers for nonzero pressure.

AFRIKAANSE OPSOMMING : In rooi bloedselle word die plasmamembraan aan die onderliggende tweedimensionele seskantige spektrin-netwerk gekoppel deur proteïenkomplekse. Daar bestaan ook ander proteïenkomplekse wat die membraandubbellagie op lukrake plekke verbind. Hierdie netwerk, saam met die afstotend wisselwerkende glikokaliks, is verantwoordelik vir die groot fluktuasies in vorm en volgorde in vormveranderinge van hierdie rooi bloedselle. Daar is deur anderes eksperimenteel bewys dat die verstywing van rooi bloedselle na infeksie deur Plasmodium falciparum, byvoorbeeld, met die strukturele veranderinge in die netwerk gekorreleer is. Ons ontwikkel ’n model om die losmaking van die membraan van die substraat te behandel, wat ’n model kan wees vir die strukturele verval van rooi bloedselle. Ons beskou ’n buigsame membraan wat elasties vasgemaak is aan ’n substraat op lukrake posisies, en wat aan ’n drukverskil op die membraan onderwerp word. Hierdie ingevrore wanorde benodig die replika-formalisme, wat ons sowel uit die replika-simmetriese asook uit die swak replika-simmetrie brekende gesigspunte ondersoek. Ons vergelyk hierdie resultate met die modelle vir kontinue en nie-vaste wanorde, wat ons eers konstrueer. Die spektrum van fluktuasies as funksie van druk, oor die algemeen, toon aan dat die gemiddelde-kwadraat fluktuasies met die druk toeneem. Maar, vir diskrete inhomogene adhesie, wanneer die posisies van die knooppunte vas is, vertoon die fluktuasies ’n nie-monotone gedrag. Ons model karakteriseer die rol van die druk en die wanorde in die daaruit ontstaande nie-monotoniese fluktuasiespektrum vir die verskillende behandelings van die knooppunte se wanorde in posisieverdelings. Die nie-vaste wanorde posisieverdeling van knooppunte gee ’n diskontinue, Heaviside-agtige verband vir die toename in kwadratiese fluktuasies met die verwydering van die knooppunte vir nie-nul druk.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/106212
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