Date of Award

2021

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Applied Mathematics

First Advisor

Prashant P. Purohit

Abstract

In this thesis, we analytically investigate three problems in the mechanics of lipid membranes and inclusions embedded in them. We study (a) irradiation-induced oxidation of membranes, (b) elastic and entropic interactions of inclusions on membranes due to bending and kinetics of their self-assembly, and (c) membrane thickness mediated interactions of inclusions and kinetics of self-assembly.Oxidative damage to cell lipid membranes is a ubiquitous phenomenon in biology that often leads to cell death. Oxidative damage occurs in two steps: per molecule area increase, followed by vesicle shrinkage due to formation of pores. We employ a model to study the first step which focuses on thermal fluctuations, tension-area relation and the change in per molecule area caused by irradiation. Our model makes predictions of vesicle shapes, adhesion kinetics and forces under various conditions of irradiation. These results may potentially be applied in photodynamic therapy where controlled oxidative damage is harnessed for killing diseased cells. Interactions between inclusions in lipid membranes is an important topic in biophysics as it can lead to self-assembly (of proteins) that influences a host of biological process, including exo- and endo-cytosis. The rate of self-assembly of inclusions is of interest since interventions made at the right time could help to block the assembly of viruses. We develop a model based on theory of stochastic processes that casts self-assembly of two inclusions as a first passage time problem. A partial differential equation (PDE) is derived to compute the mean first passage time of self-assembly. The validity of the PDE is verified by running Langevin dynamic simulations to estimate the mean first passage time. Our methods provide new ways to study self-assembly which could complement existing methods based on molecular dynamics simulations. We separately study the interactions between inclusions caused by bending deformations and thickness deformations and use both the PDE and Langevin equation to compute the mean first passage time for self-assembly of variously shaped inclusions. Hydrodynamic interactions and rotational diffusion are also considered in our models. Finally, we apply our stochastic model mentioned above to compute the mean and second moment of the first passage time of MutSα protein searching for lesions through one-dimensional diffusion on DNA. The results could enhance the understanding of post-replicative mismatch repair (MMR) for fixing errors in DNA.

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