Models of protein organisation

Thesis

The organisation of atoms and small molecules gives the familiar structures of gases, solids, and other states of matter. The organisation of proteins drives the essential processes of life. This thesis explores three different molecular mechanisms that act to organise proteins by constructing minimal models that can predict or explain phenomena of protein organisation. Firstly, we study the effective interactions that can arise between proteins that catalyse reactions, called enzymes. We develop a thermodynamically consistent model describing the dynamics of a multicomponent mixture where one enzyme component catalyses a reaction between other components. We find that the catalytic activity alone can induce phase separation for sufficiently active systems and large enzymes, without any equilibrium interactions between components. We label this catalysis-induced phase separation and show that it generates a feedback mechanism that can act to autoregulate the enzymatic activity, giving this simple mechanism complex design opportunities in the natural world or engineered systems. Secondly, we explore how proteins that induce curvature in membranes can interact via membrane mediated elastic forces. We derive an interaction energy for many, well-separated, small inclusions in a flat membrane with tension and find that in this limit the interaction energy between many inclusions is the sum of the two-body interactions. This interaction fundamentally changes when the curvature-inducing inclusions are not radially symmetric by the emergence of a well defined equilibrium separation. However, in addition to altering the direction of the force, the anisotropy affects the formation of aggregates of many inclusions, as inclusions experience a geometric frustration that can oppose the equilibrium of the pairwise interaction. As such, the equilibrium arrangements of groups of inclusions are rings, lines and polygonal lattices. Thirdly, we extend existing models of aggregating proteins in living systems, by including a finite rate for aggregate removal mechanisms. The accumulation of protein aggregates is associated with many diseases and a bounded clearance rate can explain observed phenomena such as seeding, recovery of mice following monomer reducing therapies, and the disease incidence. This model is the first theoretical framework to capture all of these behaviours and this key behaviour is robust to changes in exact molecular kinetics. This framework can be used to understand the role of current therapies and for the rational design of future therapies.

Authors: Cotton, MW

• DOI: 10.5287/ora-14w5kebqz
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: statistical physics; protein aggregation; protein organisation; neurodegenerative disease; membrane-mediated interactions; theoretical biophysics; minimal models; phase separation
• Subjects: Theoretical biophysics; Applied mathematics