The misfolding of proteins into highly ordered fibrils with similar physical properties is a hallmark of many degenerative diseases. Here, we use the microtubule associated protein tau as a model system to investigate the role of amino acid side chains in the formation of such fibrils. We identify a region (positions 272-289) in the tau protein that, in the fibrillar state, either forms part of a core of parallel, in-register, beta-strands, or remains unfolded. Single point mutations are sufficient to control this conformational switch with disease mutants G272V and Delta K280 (found in familial forms of dementia) inducing a folded state. Through systematic mutagenesis we derive a propensity scale for individual amino acids to form fibrils with parallel, in-register, beta-strands. This scale should not only apply to tau fibrils but generally to all fibrils with same strand arrangement.