Mechanical properties of cells and modelling of structural instabilities in tissues

Azote, Somiealo (2018-12)

Thesis (PhD)--Stellenbosch University, 2018.

Thesis

ENGLISH ABSTRACT : Cells have inherent mechanical properties that can be modelled physically. Statistical physics approaches permit the understanding of deformation dependence by modelling the various elements of the cytoskeleton and combining these with the constraints and physical properties of the cell membrane. When cells combine to form more complex structures, including, for example, epithelial structures, the resulting structure also needs to be understood. We wish to understand the mechanical contribution to the elastic properties and stability of the cell within the tissue when branching actin cytoskeletal network emerge or grow and their structure, spatial organisation and orientational ordering geometrically constrained by the cell membrane. Based on a grand canonical ensemble formalism by Frisch et al. [1] and Müller-Nedebock et al. [2], we model the structure of branching actin networks of living cell cytoskeletal filaments when these are rigidly contained with geometrical confining regions. The formalism allows a thermodynamic equilibrium calculation of density and orientational order density for fillaments and branch points. We find distinct local orientation, order parameter and density profiles for network filament segments, as the degree of branching and the ratio of persistence lengths of the filaments to the confining region size are varied. These results suggest the role of the confinement in the structural properties and organization of branching actin networks inside the confining region. We next investigated the contribution of the elastic properties of the networks to the elastic properties and stability of the cells within tissues by computing the free energies and forces of networks system. We find that tissue cells are stable against compression while cell under shear become unstable beyond a critical angle.

AFRIKAANSE OPSOMMING : Selle het inherente eienskappe wat met die sika gemodelleer kan word. Statistiese ska benaderingspunte laat toe om die vervormingsafhankliheid te verstaan deur die modellering van verskillende elemente van die sitoskelet en om dit met die randkondisies en siese eienskape van die selmembraan te kombineer. Wanneer selle gekombineer word om meer komplekse strukture te vorm, insluitende, byvoorbeeld, epitele strukture, dan moet die resulterende struktuur ook ondersoek word. Ons wil die meganiese bydrae tot die elastiese eienskappe en die stabiliteit van die sel as deel van die weefsel verstaan, wanneer vertakkende aktien netwerke ontstaan en groei, en hulle struktuur, organisasie in die ruimte deur die geometrie van die sel ingeperk word. Gebaseer op n grootkanoniese formalisme van Frisch, et al., en van Müller-Nedebock et al. modelleer ons die struktuur van vertakkende aktien netwerke van dinamiese selle se sitoskelet- lamente wanneer hierdie tot starre geometriese gebiede beperk word. Die formalisme laat n berekening in die termodinamiese ewewig toe van die digtheid and orde in uitrigtings vir die lamente and vertakkingspunte. Ons bepaal duidelike lokale orientasie-, orderparameter- en digtheidspro ele vir netwerk lamente, in afhanklkheid van hoe die graad van vertakking en die verhouding van die lamente se persistensielengte tot die grootte van die ingrensende gebied varieer. Hierdie resultate dui aan wat die rol van die ingrensing op die strukturele eienskappe en organisasie van die vertakkende aktien netwerke is binne die ingrensende gebied. Ons het ook ondersoek wat die bydrae van die elastiese eienskappe van die netwerke tot die elestiese eienskappe en stabiliteit van van die selle binnekant n weefsel is, deurdat die vrye energië en kragte van die netwerkstelsel bepaal is. Ons vind dat weefsel stabiel teen samepersing is, terwyl dit onder skuifkragte bokant n kritieke hoek onstabiel raak.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/104963
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