Abstract: This invention identifies a biologically active group of peptide sequences from Type I repeat units of the extracellular matrix protein, human thrombospondin-1, identical or homologous to the sequence, KRFKQDGGWSHWSPWSSC (SEQ ID NO.30). The biological activities residing with the full sequences, portions thereof, and variants of the full or partial sequences are disclosed. The invention describes how biological activity may be enhanced by covalently linking these peptides to suitable carriers, preferably a branched, water-soluble polymer of low (or absent) toxicity and immunogenicity, such as polysucrose (Ficoll.TM.). The invention describes (1) a method for preparing such conjugates, (2) the use of the defined peptides or their conjugates in blocking or modifying the action on cellular processes of heparin (e.g.