Continuum description of living matter

Thesis

Living systems are one of the most complex forms of matter. Among their many different aspects, one unifying property of any living matter is activity. Active materials continually extract energy from their surroundings to move, grow, and self-replicate.

To perform these functions, active units exert forces on their environment and this raises the question of the extent to which the behaviour of biological systems can be understood by measuring forces and flows and using the generic physical theories of active matter.

At the microscale, several important aspects of the dynamics of living systems can be described by the theories of active nematics. We discuss, in the second chapter of this thesis, that long-range interactions in active suspensions at the microscale have a nematic symmetry, and this makes active nematic models a powerful tool for studying living systems.

In this thesis, we extract essential features from living systems in experiments to build continuum active nematic models that are able to capture the behaviour of the experiments. Using the continuum models, we then perform numerical simulations and linear stability analyses to explore the dynamical steady states of the model, and compare them with the ones in the experiments. We show that the conventional active nematic models need to be modified and evolved, according to the active system under study, to allow us to capture the patterns observed in different experiments.

Our results indicate that fractal-like patterns that form at the interface of bacterial droplets cannot be explained by the conventional active biphasic models. We suggest that the presence of an active layer at the bacterial interface produces the cell orientation and flow patterns in the experiments.

We then construct a continuum description for living tissues and demonstrate that introducing new continuum fields associated with cell area and aspect ratio and decoupling the direction of the active force from the cell elongation, introduces new phases to the system. Analysing experimental data on MDCK cells, we use our model to understand the misalignment in the cell shape and stress orientation in the experiments.

Finally, we extend our study to three dimensions and show that active materials with extensile activity promote formation of twist-type defects and three-dimensional flows.

Authors: Raeisian Nejad, M

• DOI: 10.5287/ora-eyazdm08d
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: living systems; active matter; continuum theory
• Subjects: living systems