The tau fibrillar structures from the brain of an Alzheimer's patient have a core with a C-shaped motif of the third and fourth repeat domains (R3-R4). Our simulations indicated that the C-shaped motif is only stable for R3-R4, while R1-R2 tends to be linear in shape. These two structural motifs appear in the most stable K18 protofilament. Heparin can further stabilize the C-shaped R3-R4 motif, but not other repeats.