Alzheimer's disease (AD) and Parkinson's diseases (PD) are neurodegenerative diseases that affect $\sim$60,million people worldwide. Both diseases are linked to the misfolding of proteins from their native conformational state into $\beta$-sheeted amyloid fibrils. In AD the implicated proteins are amyloid-$\beta$ and tau, and for PD the implicated protein is $\alpha$-synuclein (aSyn). The motivation for this work is to develop and use physical techniques to better understand the role of amyloid proteins in neurodegenerative diseases. Two techniques used in amyloid research are fluorescence microscopy, to map the protein location and aggregation state, and electrophysiology, to examine the effect of the proteins on neurons. To enable these techniques to be combined, a transparent graphene microelectrode array (MEA) was designed, fabricated and characterised. The active electrode site was graphene since it is electrically conductive, optically transparent and biocompatible. The graphene MEA was characterised using Raman spectroscopy to check the graphene quality, and electrochemical impedance spectroscopy (EIS) to probe the electrode-electrolyte interface. The graphene MEAs enabled voltage trace recordings from cultured neurons to be combined with widefield, confocal fluorescence and fluorescence lifetime imaging microscopy (FLIM). Combining fluorescence imaging and electrophysiology will allow amyloid aggregation to be correlated with neuronal firing patterns. Another physical technique used was Fourier transform infrared spectroscopy (FTIR). A script was written to estimate the protein secondary structure content, and used to investigate polymorphism in the monomeric amyloid protein aSyn.