Biocryst Pharmaceuticals Inc (BCRX): Billionaire David E. Shaw’s Fund Increases Stake

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13G

Under the Securities Exchange Act of 1934

BioCryst Pharmaceuticals, Inc.

(Name of Issuer)

Common stock, par value $0.01

(Title of Class of Securities)

09058V103

(CUSIP Number)

August 11, 2016

(Date of Event Which Requires Filing of
this Statement)

Check the following box to designate the rule pursuant to which
the Schedule is filed:

*The remainder of this cover page shall be filled out for a
reporting person’s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment
containing information which would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page
shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”)
or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however,
see the Notes).

As of August 11, 2016:

David E. Shaw does not own any shares directly. By virtue of
David E. Shaw’s position as President and sole shareholder of D. E. Shaw & Co., Inc., which is the general partner of
D. E. Shaw & Co., L.P., which in turn is the manager and investment adviser of D. E. Shaw Valence Portfolios, L.L.C., the investment
adviser of D. E. Shaw Oculus Portfolios, L.L.C., and the managing member of D. E. Shaw Investment Management, L.L.C., and by virtue
of David E. Shaw’s position as President and sole shareholder of D. E. Shaw & Co. II, Inc., which is the managing member
of D. E. Shaw & Co., L.L.C., which in turn is the manager of D. E. Shaw Oculus Portfolios, L.L.C., David E. Shaw
may be deemed to have the shared power to vote or direct the vote of 3,698,639 shares, and the shared power to dispose or direct
the disposition of 3,740,239 shares, the 3,740,239 shares as described above constituting 5.1% of the outstanding shares and, therefore,
David E. Shaw may be deemed to be the beneficial owner of such shares. David E. Shaw disclaims beneficial ownership of
such 3,740,239 shares.

By signing below, each of D. E. Shaw & Co., L.P.
and David E. Shaw certify that, to the best of such reporting person’s knowledge and belief, the securities referred to above
were not acquired and are not held for the purpose of or with the effect of changing or influencing the control of the issuer of
the securities and were not acquired and are not held in connection with or as a participant in any transaction having such purposes
or effect.

SIGNATURE

After reasonable inquiry and to the best of their knowledge
and belief, the undersigned certify that the information set forth in this statement is true, complete and correct. A Power of
Attorney, dated December 16, 2014, granted by David E. Shaw in favor of Nathan Thomas, is attached hereto.

Dated: August 22, 2016