Terpene synthase that catalyzes the cyclization of farnesyl diphosphate (FPP) into alpha-muurolene, (-)-beta-caryophyllene, and one unidentified sesquiterpene (PubMed:31839833). TPS4 shows only trace monoterpene synthase activity with geranyl diphosphate (GPP) as substrate and produces very small amounts of myrcene (PubMed:31839833). P.polycephalum has a unique biology and these volatile terpenoids could function in internal communication of P.polycephalum, to mark the territory that have been explored, or they may be involved in chemotaxis (Probable). (2E,6E)-farnesyl diphosphate = alpha-muurolene + diphosphate (2E,6E)-farnesyl diphosphate = (-)-(E)-beta-caryophyllene + diphosphate The 2 conserved active-site motifs D(D/E)XX(D/E) and NSE are required for coordinating the divalent metal ions that stabilize the PPi moiety of the substrate. The C-terminal WxxxxxRY motif is frequently found in terpene synthases and is important to guide product formation. Belongs to the terpene synthase family.