Liquid crystalline states and self-assembly in biological systems

Abstract

Liquid crystalline structures occur in many biological systems, from organic molecules such as cellulose to cells and living organisms such as bacteria. It is an active field of research with interesting current developments and discoveries, such as the role of liquid crystalline singularities in the dynamics and even the apoptosis and removal of cells and the formation of liquid crystals in biofilms of Pseudomonas aeruginosa bacteria; this crystalline state is conjectured to increase the tolerance of the bacteria against antibiotics. The research presented in this thesis aims to analyse biological liquid crystals from a physical and mathematical point of view, using mathematical models and image analysis techniques. The first chapter introduces the necessary theoretical background, giving an overview of previous work in the process. Subsequently, my research and results are discussed, divided into four subtopics. The first is the mathematical modelling of the viscosity and phase behaviour of liquid crystalline bacteriophage suspensions. We find that the applied phage behaviour model can explain the phase behaviour of mixtures of bacteriophages and polymers qualitatively. In contrast, the established model of the viscosity of rigid rods by Doi and Edwards does not capture the observed behaviour of these suspensions, which may partly be due to strong sequestration of bacteriophages into liquid crystalline droplets; however, the most recent experimental results cannot be explained by this and require further research. The second topic is the mathematical modelling of the diffusion and adsorption of antibiotics in droplets of liquid crystalline bacteriophages, aiming to clarify the mechanism behind the increased antibiotic tolerance of P. aeruginosa biofilms. The liquid crystalline droplets are shown to strongly inhibit antibiotic diffusion, albeit not strongly enough to explain antibiotic tolerance at longer timescales; the droplets possibly give transient protection while other tolerance and resistance mechanisms are activated. The third topic is the modelling of how electric charge affects this antibiotic diffusion. We find that this effect is considerable, because the electric field effectively increases the adsorptive capacity and radius of the bacteriophages. Finally, the application of various image analysis techniques to biological liquid crystals is discussed; this includes detection and analysis of topological singularities, topological data analysis, and analysis using vector fields over discrete measure spaces. We show that these methods can efficiently extract information from the data, for instance regarding the liquid crystalline alignment or chaotic dynamical behaviour.

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Identifiers

ORCID for Giampaolo D'Alessandro: orcid.org/0000-0001-9166-9356

ORCID for Sandra Wilks: orcid.org/0000-0002-4134-9415

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