Decay Behaviour, State Transitions and Escape Rates in Simple Models for Complex Systems

Abstract

Describing phenomena through the lens of decay behaviour, state transitions and escape rates can be applied to many topics across a plethora of disciplines in science and everyday life. In this thesis, I will offer two examples of such cases in physics and biology in different ways. This is done via the construction of simple models for the complex systems that are investigated. In the first topic where this is applied, spontaneous frictional relaxation in atomically thin layered materials is studied. The model for this system was developed by my co-authors, and it mathematically describes the frictional behaviour of atomically thin, layered materials - e.g. graphene. The model mimics an atomic force microscope contact-sliding on a surface. Once this model is subject to temperature and sliding is stopped, the system relaxes via thermal activation. This thermal activation is examined in terms of calculable escape rates and validated using the decay behaviour of the system. The second topic is a molecular model for a keystone mechanism in one type of blood cancer, chronic myeloid leukaemia (CML). The mechanism in focus is the phosphorylation of proteins by Abl1 (an enzyme). The most common treatment for CML is with Abl1 inhibitors or allosteric regulators (specifically imatinib, ponatinib, dasatinib, nilotinib and asciminib in this work). After creating a simple model for this Abl1 enzyme system, the transitions in the system are modelled as decay behaviour. The results of this model for mono-therapy with imatinib, ponatinib and dasatinib lead to the suggestion of an improved method of comparing treatment options for patients experiencing resistance to their current therapy. The model was then extended to include combination therapy of either imatinib, ponatinib, or nilotinib with asciminib, an allosteric regulator. In cases of low synergy or antagonism at patient-relevant treatment concentrations, the improved treatment comparison method for mono-therapy is easily applied for combination therapies.