A G-rich nucleic acid sequence binds hemin and yields a biocatalytic complex (DNAzyme) of peroxidase activity, namely, the biocatalyzed generation of chemiluminescence in the presence of H(2)O(2) and luminol. The DNAzyme is used as a label for the amplified detection of DNA, or for the analysis of telomerase activity in cancer cells, using chemiluminescence as an output signal. In one configuration, the analyzed DNA is hybridized with a primer nucleic acid that is associated with a Au surface, and the DNAzyme label is hybridized with the surface-confined analyte DNA. The DNA is analyzed with a detection limit of approximately 1 x 10(-)(9) M. In the second system, telomerase from HeLa cancer cells induces telomerization of a primer associated with a Au surface and the complementary DNAzyme units are hybridized with the telomere to yield the chemiluminescence. The detection limit of the system corresponds to 1000 HeLa cells in the analyzed sample.