Comparing protein sequences is an essential procedure that has many applications in the field of bioinformatics. The recent advances in computational capabilities and algorithm design, simplified the comparison procedure of protein sequences from several databases. Various algorithms have emerged using state of the art approaches to match protein sequences based on structural and functional properties of the amino acids. The matching involves structural alignment, and this alignment may be global; comprising of the whole length of the protein, or local; comprising of the sub-sequences of the proteins. Families of related proteins are found by clustering sequence alignments. The frequency distributions of the amino acids within these different clusters define the sequence profile. The best alignment algorithm uses these profiles. In this thesis, we have studied different profile alignment algorithms where the cost function for comparing two profiles is changed. These are compared to the FFAS3 (Fold and Function Assignment) algorithm.