Structural aspects of modelling biopolymer networks

Thesis

Many biological systems involve intricate, hierarchical networks formed from cross-linked filaments, including the cytoskeleton of eukaryotic cells and the collagen scaffold of the extracellular matrix. Experiments performed on these biopolymer networks have identified exotic and desirable mechanical behaviours that cannot be easily understood without discussing the underlying microstructures and their properties. As such, the theoretical and computational modelling of filament assemblies has increasingly utilized discrete fibre network (DFN) models to investigate their complex local and global mechanical properties. This thesis investigates some of the many structural aspects of these networks, and how details of the network architecture can influence the mechanics of the system. We discuss how the geometry of a fibrous substrate can influence the long-ranged displacement fields generated by contractile resident biological cells, and the extent to which long-ranged mechanical communication between distant cells is plausible. A variety of architecture choices are discussed and compared. Motivated by improvements in electrospinning technologies and recent experiments, we develop a new fibre network model, where cross-link density is allowed to vary while geometry is controlled. The affine-nonaffine transition in this model is discussed and characterized, and theoretical predictions for the scaling of the network shear modulus are presented. As much of the DFN literature focusses on monotypic fibre networks, the mechanics of polymer assemblies formed from two or more filament types, which often arise in Nature, is poorly understood. We seek to address this by extending monotypic fibre network models to incorporate two distinct fibre types. In the low density regime we present extensive theoretical predictions and supporting numerical results for the network response as numerous parameters are varied. The importance of network architecture is discussed in the context of nonaffine fluctuations and their influence on the mechanical response. Finally, dense, random heterotypic networks are studied, in light of experiments and theoretical models that observe `exceptional stiffening' in such systems. We propose a novel explanation for this phenomenon, and provide evidence for our interpretation over others given in the literature. The implications of the research presented here for higher dimensional systems and for finite strains are discussed. Together, this thesis constitutes an argument for the mechanical importance of the detailed structural properties possessed by biopolymer networks, in a variety of systems and at multiple scales.

Authors: Humphries, D

• DOI: 10.5287/ora-aqvbm1vpd
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford