In this thesis, a protein is designed incorporating an electron transport protein that self-assembles into amyloid fibrils in order to investigate the possibility of producing self-assembling bio-electronic conductors. These fibrils are found to display the electron transport protein and as a consequence, exchange electrons with their surroundings. The effects of non beta-sheet core regions on the properties of amyloid fibrils have been studied. In particular it is shown that non-core regions have sufficient flexibility to average their local magnetic environments to yield sharp resonances when observed by solution-state NMR. NMR diffusion measurements are essential for reaching this conclusion. The diffusion properties of the non-core regions on the surface of the fibrils reflect that of the underlying fibrils. A theory of how rotational diffusion will contribute to NMR diffusion measurements is derived and is used to estimate the lengths of the fibrils under study. These lengths are in reasonable accord with those observed using imaging techniques. In a range of different amyloid fibril forming systems, many, but not all were observed to have resonances originating from fibrils. It is shown that in fibril systems where NMR resonances from the non-core regions of fibrils are observed, the tendency for dissociation of the constituent monomers from fibrils is greatly reduced. A systematic study shows that the origin of these effects is non-specific interactions between non-core regions of amyloid fibrils highlighting the importance of these in the process of fibril assembly.