PhD Studentship: Upscaling morphing in biological structures

Continuum mechanics approaches have been used to model the mechanical behaviour of biological (and active) systems at length scales that are large enough. For example, when analysed at the micron-scale, biological membranes can be treated as continuum objects that deform regulated by effective properties such as curvature mismatch or active forces. Those effective properties depend on how their fundamental constituents, such as lipids and proteins, evolve at the nano-scale. Continuum modelling approaches have been able to improve the understanding of the behaviour of biological materials, showing the critical role of mechanics in processes like growth and remodelling, but they have two major limitations: They rely on phenomenological assumptions, such as the parameters that describe mechanical properties or active behaviour. Biological materials are fundamentally discrete, thus making the continuum approaches fail when moving at length scales that are not large enough, i.e. the micro-to-nano boundary in the case of biological membranes. The project focuses on providing a link between the microscopic (discrete) nature and the macroscopic (continuum) modelling of biological structures with the double-pronged aim to improve the understanding of the two limitations described above: (i) to provide a quantitative relation between the lumped parameters used in the continuum description and the microscopic mechanics from which they originate them; (ii) to reveal what scale is large enough for the continuum approaches cannot be used. The project aims to develop new theories to understand the root causes of the active morphing of two-dimensional biological membrane-like structures. The project involves three aspects: Theoretical continuum modelling. Starting from the well-known description of the mechanics of two-dimensional bodies, we update this passive description by using effective modelling (like negative capillarity or curvature control) to investigate the competition between bulk elasticity and active control on the global morphing of slender objects. Theoretical discrete modelling. Providing potential modelling ways to couple microscopic features, like the distribution of proteins, the evolution of chemicals and the presence of defects, and macroscopic mechanics. Numerical study. Implementation of the models produced into numerical codes. During this project, you will be part of the Institute for Infrastructure and Environment. You will join a vibrant community of PhD students, postdoctoral research associates and academics. For informal enquiries please contact Dr Matteo Taffetani (matteo.taffetani@ed.ac.uk)