The complete sequence of the cDNA encoding a 20 kDa calcium-binding protein of Schistosoma mansoni (Sm20) has been determined. The predicted amino acid sequence contains 4 EF hand domains but examination of the predicted secondary structure of Sm20, together with the specific residues in each calcium-binding domain, suggests that only 1 EF hand (domain IV) is functional. Sm20 is most homologous to calmodulin, troponin C and the regulatory light-chain of myosin, particularly those of invertebrates. However, troponin C and the regulatory light-chain of myosin can be distinguished from Sm20 by size and by their differential levels of expression during the life-cycle. Sm20 also appears to be distinct from calmodulin but may be functionally equivalent to the soluble sarcoplasmic calcium-binding proteins of molluscs and crustacea which may act as a reservoir for calcium in muscle. Sm20 is encoded by a small multi-gene family whose members are clustered within a 15 kb region of the genome. A 20 kDa antigen, cross-reactive with Sm20, is expressed in Schistosoma haematobium, Fasciola hepatica and Paragonomus mexicanus.

Based on the theory of difference equations, we derive necessary and sufficient conditions for the existence of eigenvalues and inverses of Toeplitz matrices with five different diagonals. In the course of derivations, we are also able to derive computational formulas for the eigenvalues, eigenvectors and inverses of these matrices. A number of explicit formulas are computed for illustration and verification.