Bioengineering is an interdisciplinary field, so it can be difficult to find one database or research tool that covers every subject area. The most interdisciplinary databases below are Web of Science and Scopus. However, many researchers will prefer to search in a Chemistry-specific database like SciFinder-n (or Reaxys), or do more of a medical-related search in PubMed. BIOSIS is an excellent subject database for all of the biology disciplines. If you are needing a more specialized sub-field resources, see the list the left side of the page or ask your BESE librarian for assistance.
Synthetic biology is covered in the interdisciplinary databases listed above. Particularly, Web of Science, PubMed, and BIOSIS.