Mathematical modelling in cellular biology through compartmentalisation and conservation laws

Cusseddu, Davide (2019) Mathematical modelling in cellular biology through compartmentalisation and conservation laws. Doctoral thesis (PhD), University of Sussex.

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Abstract

The aim of this thesis focuses on addressing several open questions in cell biology by using different mathematical approaches and numerical analysis methods to study the evolution of distinct protein families in various cellular phenomena, such as cell polarisation and cytoskeleton remodelling. Our approaches are based on conservation laws and compartmentalisation of proteins within appropriate geometrical subdomains representing different cellular structures, such as the cell membrane and cytosol.

The Rho GTPase are proteins responsible of coordinating the cell polarisation response, which is a biological process involving a huge number of different proteins and intricate networks of biochemical reactions. Rho GTPases localise their activity in specific cell regions where they interact with the cell cytoskeleton. Reducing the biological assumptions to a minimal level of complexity, we will present a simple qualitative model for cell polarisation in which proteins cycle between cell membrane and cytosol in an active and inactive form. This is described through a bulk-surface system of two reaction-diffusion equations coupled by the boundary condition. The model supports pattern formation and we will confirm this claim by using both mathematical analysis and simulations. The bulk-surface finite element method is presented and used to solve the model on different geometries.

Secondly, we will present a mathematical model for keratin intermediate filament dynamics in resting cells. This model, characterised by a quantitative approach, is a datadriven extension of a pre-existing model, initially introduced by Portet et al. (PlosONE, 2015). We will discuss the new assumptions and modelling ideas, and compare the solution of our model to the experimental data. Part of the biological impact of our model relies in its ability to estimate the amount of assembled and disassembled keratin material as a function of space and time, consistent with the biological model proposed by Windoffer et al. (Journal of Cell Biology, 2011).

In the last part we will introduce a second mathematical model for keratin spatiotemporal dynamics in non-resting cells. In this case, the model is derived on two- and three-dimensional geometries and accounts for a more detailed description of the processes involved in the keratin cytoskeleton remodelling process. The evolution of three different forms of keratin is modelled by a system composed of one reaction-diffusion equation and two reaction-advection-diffusion equations. Keratin kinetics are also described by the boundary conditions, which are posed both at the cell membrane and at the nuclear envelope. In solving the model, we will use the Streamline Upwind Petrov Galerkin method, as described in the text. In conclusion, in view of a future estimation of biologically relevant parameters, a simulation is presented, showing consistency of our mathematical model with the biological model proposed by Windoffer et al. (Journal of Cell Biology, 2011).

In summary, this thesis presents methods and techniques for data-driven modelling supported by rigorous mathematical analysis and novel numerical methods and simulations. Our approach involving the use of quantitative methods serves as a blue-print for how to study the synergy interplay between mathematics and its applications to experimental sciences.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QH Natural history > QH0301 Biology > QH0323.5 Biometry. Biomathematics. Mathematical models
Q Science > QH Natural history > QH0301 Biology > QH0573 Cytology
Depositing User: Library Cataloguing
Date Deposited: 12 Jul 2019 10:16
Last Modified: 12 Feb 2020 14:38
URI: http://sro.sussex.ac.uk/id/eprint/84883

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