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Mathematical Modelling of the Plasma Membrane

Many crucial cellular processes take place at the plasma membrane. The latter is a complex, two-dimensional medium exhibiting significant lateral structure. As a result, a number of non-classical processes, including anomalous diffusion, compartimentalisation and fractal kinetics take place at the membrane surface. The evaluation of various hypotheses and theories about the membrane is currently very difficult because no general modelling framework is available. In this thesis, we present a stochastic, spatially explicit Monte Carlo model for the plasma membrane that accounts for illmixedness, mobile lipid microdomains, fixed proteins, cytoskeletal fence structures and other interactions. We interrogate this model to obtain three classes of results, regarding (1) the effect of lipid microdomains on protein dynamics on the membrane (2) the effects of microdomains, cytoskeletal fences and fixed proteins on the nature of the (anomalous) diffusion on the membrane and (3) the effects of obstructed diffusion on reaction kinetics at the membrane. We find that the presence of lipid microdomains can lead to nonclassical phenomena such as increased collision rates and differences between long-range and short-range diffusion coefficients. Our results also suggest that experimental techniques measuring long-range diffusion may not be sufficiently discriminating and hence cannot be used to infer quantitative information about the presence and characteristics of microdomains. With regard to anomalous diffusion in particular, we find that to explain this phenomenon at the levels observed in vivo, a number of interactions are required, including (but not necessarily limited to) obstacle-induced diffusion and segregation, or exclusion from microdomains. The effects of these different interactions upon the nature of the diffusion appear to be approximately additive. Finally, we show that a widely used non-spatial method, the Stochastic Simulation Algorithm, can be modified to take into account anomalous diffusion and that this significantly increases its predictive accuracy. The model presented in this thesis is expected to be of future value in evaluating different models of cell surface processes.

Identiferoai:union.ndltd.org:ADTP/287423
CreatorsValeriu Dan Nicolau
Source SetsAustraliasian Digital Theses Program
Detected LanguageEnglish

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